Main analysis for the PT (using 34 tests). Check the paper.
ACTUALLY USED IN THE PAPER
DATA PREPARATION: RECODING, MISSING, OUTLIER, IMPUTATION
Sys.setenv(LANG = "en") # make R environment in english
require(MASS)
require(lavaan) # get SEM, CFA, MGCFA programs
require(psych) # get fa.parallel() and VSS() functions
require(GPArotation) # get quartimax rotation
require(survey)
require(psy)
require(dplyr)
require(semTools)
require(MVN) # get mvn
require(RVAideMemoire) # get qqnorm
Mc<-function(object, digits=3){ # McDonald's NC Index, from Beaujean
fit<-inspect(object, "fit")
chisq=unlist(fit["chisq"])
df<-unlist(fit["df"])
n<-object@SampleStats@ntotal
ncp<-max(chisq-df,0)
d<-ncp/(n-1)
Mc=exp((d)*-.5)
Mc
}
# RMSEAd functions taken from Savalei et al. (2023) : https://osf.io/ne5ar for RMSEA CI and https://osf.io/cfubt for RMSEAd
# make sure you DO NOT FORGET TO ADJUST the sample size in the N function or it will produce wrong numbers
RMSEA.CI<-function(T,df,N,G){
#functions taken from lavaan (lav_fit_measures.R)
lower.lambda <- function(lambda) {
(pchisq(T, df=df, ncp=lambda) - 0.95)
}
upper.lambda <- function(lambda) {
(pchisq(T, df=df, ncp=lambda) - 0.05)
}
#RMSEA CI
lambda.l <- try(uniroot(f=lower.lambda, lower=0, upper=T)$root,silent=TRUE)
if(inherits(lambda.l, "try-error")) { lambda.l <- NA; RMSEA.CI.l<-NA
} else { if(lambda.l<0){
RMSEA.CI.l=0
} else {
RMSEA.CI.l<-sqrt(lambda.l*G/((N-1)*df))
}
}
N.RMSEA <- max(N, T*4)
lambda.u <- try(uniroot(f=upper.lambda, lower=0,upper=N.RMSEA)$root,silent=TRUE)
if(inherits(lambda.u, "try-error")) { lambda.u <- NA; RMSEA.CI.u<-NA
} else { if(lambda.u<0){
RMSEA.CI.u=0
} else {
RMSEA.CI.u<-sqrt(lambda.u*G/((N-1)*df))
}
}
RMSEA.CI<-c(RMSEA.CI.l,RMSEA.CI.u)
return(RMSEA.CI)
}
#p-values associated with the critical values of the RMSEA for most common cutoffs
pvals<-function(T,df,N,G){
RMSEA0<-c(0,.01,.05,.06,.08,.1)
eps0<-df*RMSEA0^2/G
nonc<-eps0*(N-G)
pvals<-pchisq(T,df=df,ncp=nonc)
names(pvals)<-c("RMSEA>0","RMSEA>.01","RMSEA>.05","RMSEA>.06","RMSEA>.08","RMSEA>.10")
return(pvals)
}
#based on Yuan & Chan (2016)
min.tol<-function(T,df,N,G){
lower.lambda.mintol <- function(lambda) {
(pchisq(T, df=df, ncp=lambda) - 0.05)
}
l.min.tol<-try(uniroot(f=lower.lambda.mintol, lower=0, upper=T)$root)
l.min.tol
RMSEA.mintol<-sqrt(l.min.tol*G/((N-1)*df))
RMSEA.mintol
out<-c(l.min.tol,RMSEA.mintol)
names(out)<-c("ncp(T)","RMSEA.pop")
return(out)
}
# BEGIN HERE IF WORKING WITH MY IMPUTED DATA
d<-read.csv(file = "C:\\Users\\mh198\\OneDrive\\Documents\\Data\\Project Talent\\TALENTimpute.csv")
table(d$age)
##
## 9.04 12.01 12.04 12.05 12.06 12.07 12.08 12.09 12.1 12.11 13 13.01
## 1 1 1 1 2 4 4 15 44 42 58 55
## 13.02 13.03 13.04 13.05 13.06 13.07 13.08 13.09 13.1 13.11 14 14.01
## 84 89 93 86 90 113 135 191 319 391 579 830
## 14.02 14.03 14.04 14.05 14.06 14.07 14.08 14.09 14.1 14.11 15 15.01
## 1422 1840 2226 2471 2666 2716 2592 2552 2463 2483 2726 2687
## 15.02 15.03 15.04 15.05 15.06 15.07 15.08 15.09 15.1 15.11 16 16.01
## 2881 2927 2969 3131 3355 3171 3115 2916 2865 2960 2992 3118
## 16.02 16.03 16.04 16.05 16.06 16.07 16.08 16.09 16.1 16.11 17 17.01
## 3171 3122 3223 3485 3553 3519 3306 3182 3233 3291 3295 3555
## 17.02 17.03 17.04 17.05 17.06 17.07 17.08 17.09 17.1 17.11 17.99 18
## 3520 3563 3576 3377 3192 2988 2771 2510 2450 2324 5 2022
## 18.01 18.02 18.03 18.04 18.05 18.06 18.07 18.08 18.09 18.1 18.11 18.99
## 1776 1047 816 578 478 392 370 327 243 227 219 2
## 19 19.01 19.02 19.03 19.04 19.05 19.06 19.07 19.08 19.09 19.1 19.11
## 164 142 105 96 80 63 58 44 43 34 36 25
## 20 20.01 20.02 20.03 20.04 20.05 20.06 20.07 20.08 20.09 20.1 20.11
## 20 20 24 15 13 10 10 8 9 9 3 4
## 21 21.01 21.03 21.04 21.05 21.06 21.08 21.1 21.11
## 5 6 4 2 3 3 2 1 1
describeBy(d$age)
## Warning in describeBy(d$age): no grouping variable requested
## vars n mean sd median trimmed mad min max range skew
## X1 1 148242 15.83 1.23 16.03 15.82 1.48 9.04 21.11 12.07 0.03
## kurtosis se
## X1 -0.59 0
d$age<- d$age-16
d$age2<- d$age^2
describeBy(d$age, d$sex) # no difference in age
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew
## X1 1 73219 -0.12 1.26 0.04 -0.13 1.48 -3.99 5.11 9.1 0.06
## kurtosis se
## X1 -0.53 0
## ------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew
## X1 1 75023 -0.22 1.2 0.03 -0.22 1.47 -6.96 5.06 12.02 -0.02
## kurtosis se
## X1 -0.69 0
d$Stest5math<- log(d$Stest5math)
d$Stest8aeronautics<- log10(d$Stest8aeronautics)
d$Stest9electronics<- log(d$Stest9electronics)
d$Stest25wordfunctions<- sqrt(d$Stest25wordfunctions)
d$Stest21capitalization<- (d$Stest21capitalization^8) # a bunch of extreme low scores
d$Stest35tablereading<- log(d$Stest35tablereading)
hist(d$Stest5math)
hist(d$Stest8aeronautics)
hist(d$Stest9electronics)
hist(d$Stest21capitalization)
hist(d$Stest25wordfunctions)
hist(d$Stest35tablereading)
describeBy(d)
## Warning in describeBy(d): no grouping variable requested
## vars n mean sd
## Stest1vocab 1 148850 1.316000e+01 3.950000e+00
## Stest2literature 2 148850 1.328000e+01 4.560000e+00
## Stest3music 3 148850 6.850000e+00 2.930000e+00
## Stest4socialstudies 4 148850 1.558000e+01 5.100000e+00
## Stest5math 5 148850 2.080000e+00 6.700000e-01
## Stest6physicalscience 6 148850 9.180000e+00 4.110000e+00
## Stest7biologicalscience 7 148850 6.330000e+00 2.340000e+00
## Stest8aeronautics 8 148850 5.400000e-01 2.700000e-01
## Stest9electronics 9 148850 1.910000e+00 6.000000e-01
## Stest10mechanics 10 148850 1.037000e+01 3.870000e+00
## Stest11art 11 148850 6.690000e+00 2.480000e+00
## Stest12law 12 148850 4.890000e+00 1.780000e+00
## Stest13health 13 148850 6.210000e+00 1.870000e+00
## Stest14bible 14 148850 7.590000e+00 3.300000e+00
## Stest15theater 15 148850 4.550000e+00 1.770000e+00
## Stest16miscellaneous 16 148850 4.970000e+00 1.710000e+00
## Stest17memsentences 17 148850 9.360000e+00 2.980000e+00
## Stest18memwords 18 148850 1.236000e+01 5.460000e+00
## Stest19disguisedwords 19 148850 1.605000e+01 6.840000e+00
## Stest20spelling 20 148850 9.780000e+00 2.980000e+00
## Stest21capitalization 21 148850 7.769234e+11 3.511487e+11
## Stest22punctuation 22 148850 1.861000e+01 4.390000e+00
## Stest23english 23 148850 1.721000e+01 3.130000e+00
## Stest24expression 24 148850 8.950000e+00 2.180000e+00
## Stest25wordfunctions 25 148850 3.250000e+00 8.600000e-01
## Stest26readingcomprehension 26 148850 3.253000e+01 9.980000e+00
## Stest27creativity 27 148850 9.510000e+00 3.900000e+00
## Stest28mechanicalreasoning 28 148850 1.120000e+01 4.220000e+00
## Stest29visualization2D 29 148850 1.348000e+01 5.470000e+00
## Stest30visualization3D 30 148850 9.070000e+00 3.180000e+00
## Stest31abstractreasoning 31 148850 9.500000e+00 2.790000e+00
## Stest32arithreasoning 32 148850 9.130000e+00 3.490000e+00
## Stest33highschoolmath 33 148850 1.157000e+01 4.920000e+00
## Stest34arithcomputation 34 148850 3.962000e+01 9.800000e+00
## Stest35tablereading 35 148850 2.440000e+00 5.100000e-01
## Stest36clericalchecking 36 148850 3.772000e+01 1.380000e+01
## Stest37objectinspection 37 148850 2.353000e+01 6.860000e+00
## wb 38 148850 4.000000e-02 2.000000e-01
## sex 39 148850 5.100000e-01 5.000000e-01
## age 40 148242 -1.700000e-01 1.230000e+00
## BY_ID_RE 41 148850 4.999295e+07 2.886691e+07
## BY_TESTG 42 148850 1.052000e+01 1.100000e+00
## BY_WTA 43 148850 2.140200e+02 7.610000e+01
## age2 44 148242 1.540000e+00 1.840000e+00
## median trimmed mad
## Stest1vocab 1.300000e+01 1.332000e+01 4.450000e+00
## Stest2literature 1.300000e+01 1.324000e+01 4.450000e+00
## Stest3music 7.000000e+00 6.850000e+00 2.970000e+00
## Stest4socialstudies 1.600000e+01 1.584000e+01 5.930000e+00
## Stest5math 2.200000e+00 2.130000e+00 6.600000e-01
## Stest6physicalscience 9.000000e+00 9.120000e+00 4.450000e+00
## Stest7biologicalscience 6.000000e+00 6.370000e+00 2.970000e+00
## Stest8aeronautics 6.000000e-01 5.600000e-01 2.600000e-01
## Stest9electronics 1.950000e+00 1.950000e+00 5.300000e-01
## Stest10mechanics 1.000000e+01 1.036000e+01 4.450000e+00
## Stest11art 7.000000e+00 6.740000e+00 2.970000e+00
## Stest12law 5.000000e+00 4.880000e+00 1.480000e+00
## Stest13health 6.000000e+00 6.340000e+00 1.480000e+00
## Stest14bible 7.000000e+00 7.510000e+00 2.970000e+00
## Stest15theater 5.000000e+00 4.560000e+00 1.480000e+00
## Stest16miscellaneous 5.000000e+00 4.990000e+00 1.480000e+00
## Stest17memsentences 9.000000e+00 9.390000e+00 2.970000e+00
## Stest18memwords 1.200000e+01 1.209000e+01 5.930000e+00
## Stest19disguisedwords 1.600000e+01 1.598000e+01 7.410000e+00
## Stest20spelling 1.000000e+01 9.830000e+00 2.970000e+00
## Stest21capitalization 8.528910e+11 7.854755e+11 3.656397e+11
## Stest22punctuation 1.900000e+01 1.879000e+01 4.450000e+00
## Stest23english 1.700000e+01 1.735000e+01 2.970000e+00
## Stest24expression 9.000000e+00 9.140000e+00 1.480000e+00
## Stest25wordfunctions 3.320000e+00 3.270000e+00 1.010000e+00
## Stest26readingcomprehension 3.400000e+01 3.329000e+01 1.038000e+01
## Stest27creativity 9.000000e+00 9.450000e+00 4.450000e+00
## Stest28mechanicalreasoning 1.100000e+01 1.119000e+01 4.450000e+00
## Stest29visualization2D 1.400000e+01 1.368000e+01 5.930000e+00
## Stest30visualization3D 9.000000e+00 9.090000e+00 2.970000e+00
## Stest31abstractreasoning 1.000000e+01 9.690000e+00 2.970000e+00
## Stest32arithreasoning 9.000000e+00 9.170000e+00 4.450000e+00
## Stest33highschoolmath 1.100000e+01 1.134000e+01 5.930000e+00
## Stest34arithcomputation 4.000000e+01 3.975000e+01 8.900000e+00
## Stest35tablereading 2.480000e+00 2.460000e+00 4.300000e-01
## Stest36clericalchecking 3.500000e+01 3.611000e+01 1.186000e+01
## Stest37objectinspection 2.300000e+01 2.319000e+01 5.930000e+00
## wb 0.000000e+00 0.000000e+00 0.000000e+00
## sex 1.000000e+00 5.100000e-01 0.000000e+00
## age 3.000000e-02 -1.800000e-01 1.480000e+00
## BY_ID_RE 5.005785e+07 4.999712e+07 3.698814e+07
## BY_TESTG 1.100000e+01 1.053000e+01 1.480000e+00
## BY_WTA 2.100000e+02 2.053900e+02 1.483000e+01
## age2 1.000000e+00 1.290000e+00 1.460000e+00
## min max range skew
## Stest1vocab 1.00 2.100000e+01 2.000000e+01 -0.34
## Stest2literature 1.00 2.400000e+01 2.300000e+01 0.07
## Stest3music 1.00 1.300000e+01 1.200000e+01 -0.02
## Stest4socialstudies 1.00 2.400000e+01 2.300000e+01 -0.39
## Stest5math 0.00 3.140000e+00 3.140000e+00 -0.76
## Stest6physicalscience 1.00 1.800000e+01 1.700000e+01 0.10
## Stest7biologicalscience 1.00 1.100000e+01 1.000000e+01 -0.15
## Stest8aeronautics 0.00 1.000000e+00 1.000000e+00 -0.46
## Stest9electronics 0.00 3.000000e+00 3.000000e+00 -0.69
## Stest10mechanics 1.00 1.900000e+01 1.800000e+01 0.01
## Stest11art 1.00 1.200000e+01 1.100000e+01 -0.16
## Stest12law 1.00 9.000000e+00 8.000000e+00 0.05
## Stest13health 1.00 9.000000e+00 8.000000e+00 -0.60
## Stest14bible 1.00 1.500000e+01 1.400000e+01 0.20
## Stest15theater 1.00 8.000000e+00 7.000000e+00 -0.01
## Stest16miscellaneous 1.00 1.000000e+01 9.000000e+00 -0.06
## Stest17memsentences 1.00 1.600000e+01 1.500000e+01 -0.10
## Stest18memwords 1.00 2.400000e+01 2.300000e+01 0.37
## Stest19disguisedwords 1.00 3.000000e+01 2.900000e+01 0.07
## Stest20spelling 1.00 1.600000e+01 1.500000e+01 -0.17
## Stest21capitalization 1.00 1.406409e+12 1.406409e+12 -0.19
## Stest22punctuation 1.00 2.700000e+01 2.600000e+01 -0.36
## Stest23english 1.00 2.500000e+01 2.400000e+01 -0.51
## Stest24expression 1.00 1.200000e+01 1.100000e+01 -0.83
## Stest25wordfunctions 1.00 4.900000e+00 3.900000e+00 -0.12
## Stest26readingcomprehension 1.00 4.800000e+01 4.700000e+01 -0.58
## Stest27creativity 1.00 2.000000e+01 1.900000e+01 0.14
## Stest28mechanicalreasoning 1.00 2.000000e+01 1.900000e+01 0.02
## Stest29visualization2D 1.00 2.400000e+01 2.300000e+01 -0.27
## Stest30visualization3D 1.00 1.600000e+01 1.500000e+01 -0.05
## Stest31abstractreasoning 1.00 1.500000e+01 1.400000e+01 -0.58
## Stest32arithreasoning 1.00 1.600000e+01 1.500000e+01 -0.08
## Stest33highschoolmath 1.00 2.400000e+01 2.300000e+01 0.39
## Stest34arithcomputation 1.00 7.200000e+01 7.100000e+01 -0.14
## Stest35tablereading 0.00 4.280000e+00 4.280000e+00 -0.62
## Stest36clericalchecking 1.00 7.400000e+01 7.300000e+01 0.95
## Stest37objectinspection 1.00 4.000000e+01 3.900000e+01 0.36
## wb 0.00 1.000000e+00 1.000000e+00 4.61
## sex 0.00 1.000000e+00 1.000000e+00 -0.02
## age -6.96 5.110000e+00 1.207000e+01 0.03
## BY_ID_RE 70.00 9.999902e+07 9.999895e+07 0.00
## BY_TESTG 9.00 1.200000e+01 3.000000e+00 -0.04
## BY_WTA 9.00 7.500000e+02 7.410000e+02 2.84
## age2 0.00 4.844000e+01 4.844000e+01 2.70
## kurtosis se
## Stest1vocab -0.45 0.01
## Stest2literature -0.60 0.01
## Stest3music -0.86 0.01
## Stest4socialstudies -0.61 0.01
## Stest5math 0.40 0.00
## Stest6physicalscience -0.84 0.01
## Stest7biologicalscience -0.70 0.01
## Stest8aeronautics -0.55 0.00
## Stest9electronics 0.66 0.00
## Stest10mechanics -0.70 0.01
## Stest11art -0.57 0.01
## Stest12law -0.49 0.00
## Stest13health -0.17 0.00
## Stest14bible -0.74 0.01
## Stest15theater -0.72 0.00
## Stest16miscellaneous -0.34 0.00
## Stest17memsentences -0.48 0.01
## Stest18memwords -0.67 0.01
## Stest19disguisedwords -0.82 0.02
## Stest20spelling -0.47 0.01
## Stest21capitalization -0.58 910157730.80
## Stest22punctuation -0.29 0.01
## Stest23english 0.63 0.01
## Stest24expression 0.45 0.01
## Stest25wordfunctions -0.84 0.00
## Stest26readingcomprehension -0.46 0.03
## Stest27creativity -0.54 0.01
## Stest28mechanicalreasoning -0.82 0.01
## Stest29visualization2D -0.56 0.01
## Stest30visualization3D -0.69 0.01
## Stest31abstractreasoning 0.04 0.01
## Stest32arithreasoning -0.82 0.01
## Stest33highschoolmath -0.54 0.01
## Stest34arithcomputation 0.29 0.03
## Stest35tablereading 3.93 0.00
## Stest36clericalchecking 0.39 0.04
## Stest37objectinspection -0.11 0.02
## wb 19.29 0.00
## sex -2.00 0.00
## age -0.59 0.00
## BY_ID_RE -1.20 74821.40
## BY_TESTG -1.32 0.00
## BY_WTA 12.55 0.20
## age2 16.52 0.00
d <- d %>% mutate(across(starts_with("Stest"), ~scale(.x, center = TRUE, scale = TRUE)))
# since log10 reduces variance so much and power8 increases variance so much, scale() is needed to stabilize variance across variables, or else cfa won't converge or estimate properly
# d <- d %>% mutate(across(starts_with("Stest"), ~scale(.x, center = TRUE, scale = TRUE)))
# d <- d %>% mutate(across(starts_with("Stest"), ~ . * 15 + 100)) ## if you need to convert into IQ scale after scaling
d<- na.omit(d)
dw<- filter(d, wb==0) # white
db<- filter(d, wb==1) # black
MGCFA FOR WHITES
dmale<- subset(dw, sex==0)
dfemale<- subset(dw, sex==1)
datamale<- select(dmale, starts_with("Stest"), -Stest17memsentences, -Stest18memwords, -Stest27creativity)
datafemale<- select(dfemale, starts_with("Stest"), -Stest17memsentences, -Stest18memwords, -Stest27creativity)
datagroup<- select(dw, starts_with("Stest"), -Stest17memsentences, -Stest18memwords, -Stest27creativity)
dgroup<- select(dw, starts_with("Stest"), wb, age, age2, sex, BY_WTA, -Stest17memsentences, -Stest18memwords, -Stest27creativity)
describeBy(dgroup$age)
## Warning in describeBy(dgroup$age): no grouping variable requested
## vars n mean sd median trimmed mad min max range skew
## X1 1 142157 -0.17 1.22 0.03 -0.18 1.47 -6.96 5.1 12.06 0.01
## kurtosis se
## X1 -0.63 0
dgroup_design <- svydesign(ids = ~1, weights = ~BY_WTA, data = dgroup)
weighted_mean <- svymean(~age, dgroup_design)
weighted_variance <- svyvar(~age, dgroup_design)
weighted_sd <- sqrt(weighted_variance)
weighted_mean # prior to mean centering
## mean SE
## age -0.16191 0.0034
weighted_sd # 1.22
## variance SE
## age 1.2208 0.0048
describeBy(datamale)
## Warning in describeBy(datamale): no grouping variable requested
## vars n mean sd median trimmed mad
## Stest1vocab 1 70776 0.19 0.93 0.21 0.23 1.13
## Stest2literature 2 70776 0.04 0.99 -0.06 0.04 0.98
## Stest3music 3 70776 -0.10 1.00 -0.29 -0.12 1.01
## Stest4socialstudies 4 70776 0.23 0.97 0.47 0.30 0.87
## Stest5math 5 70776 0.22 0.94 0.33 0.30 0.90
## Stest6physicalscience 6 70776 0.35 0.97 0.44 0.37 1.08
## Stest7biologicalscience 7 70776 0.23 0.97 0.29 0.28 1.27
## Stest8aeronautics 8 70776 0.48 0.87 0.59 0.57 0.79
## Stest9electronics 9 70776 0.51 0.83 0.65 0.58 0.84
## Stest10mechanics 10 70776 0.63 0.83 0.68 0.67 0.77
## Stest11art 11 70776 -0.04 0.98 0.13 -0.03 1.20
## Stest12law 12 70776 0.21 1.01 0.06 0.21 0.83
## Stest13health 13 70776 -0.08 1.01 -0.11 -0.01 0.79
## Stest14bible 14 70776 0.00 1.01 -0.18 -0.03 0.90
## Stest15theater 15 70776 -0.15 0.97 -0.31 -0.17 0.84
## Stest16miscellaneous 16 70776 0.14 1.04 0.01 0.15 0.87
## Stest19disguisedwords 17 70776 -0.09 0.98 -0.15 -0.12 1.08
## Stest20spelling 18 70776 -0.24 1.00 -0.26 -0.24 1.00
## Stest21capitalization 19 70776 -0.20 0.98 -0.34 -0.18 0.83
## Stest22punctuation 20 70776 -0.20 0.99 -0.14 -0.18 1.01
## Stest23english 21 70776 -0.13 1.02 -0.07 -0.09 0.95
## Stest24expression 22 70776 -0.11 1.04 0.02 -0.01 0.68
## Stest25wordfunctions 23 70776 -0.13 0.97 -0.10 -0.13 1.22
## Stest26readingcomprehension 24 70776 -0.01 1.02 0.15 0.07 1.04
## Stest28mechanicalreasoning 25 70776 0.53 0.89 0.66 0.58 1.05
## Stest29visualization2D 26 70776 0.22 0.97 0.28 0.28 1.08
## Stest30visualization3D 27 70776 0.20 1.02 0.29 0.23 0.93
## Stest31abstractreasoning 28 70776 0.07 0.98 0.18 0.13 1.06
## Stest32arithreasoning 29 70776 0.13 0.99 0.25 0.15 1.27
## Stest33highschoolmath 30 70776 0.14 1.04 0.09 0.10 1.20
## Stest34arithcomputation 31 70776 -0.07 0.99 -0.06 -0.07 0.91
## Stest35tablereading 32 70776 -0.05 1.03 0.08 -0.03 0.84
## Stest36clericalchecking 33 70776 -0.13 1.01 -0.41 -0.27 0.75
## Stest37objectinspection 34 70776 -0.08 1.03 -0.22 -0.14 0.86
## min max range skew kurtosis se
## Stest1vocab -3.08 1.99 5.07 -0.45 -0.19 0
## Stest2literature -2.70 2.35 5.05 0.02 -0.65 0
## Stest3music -1.99 2.10 4.09 0.10 -0.86 0
## Stest4socialstudies -2.86 1.65 4.51 -0.61 -0.33 0
## Stest5math -3.10 1.58 4.68 -0.88 0.70 0
## Stest6physicalscience -1.99 2.15 4.14 -0.15 -0.79 0
## Stest7biologicalscience -2.28 2.00 4.28 -0.35 -0.53 0
## Stest8aeronautics -1.97 1.69 3.66 -0.97 0.63 0
## Stest9electronics -3.22 1.82 5.03 -0.97 1.52 0
## Stest10mechanics -2.42 2.23 4.65 -0.47 0.00 0
## Stest11art -2.29 2.14 4.44 -0.12 -0.53 0
## Stest12law -2.19 2.32 4.51 -0.09 -0.49 0
## Stest13health -2.78 1.49 4.27 -0.53 -0.29 0
## Stest14bible -2.00 2.24 4.24 0.20 -0.76 0
## Stest15theater -2.01 1.95 3.96 0.09 -0.65 0
## Stest16miscellaneous -2.32 2.94 5.26 -0.13 -0.42 0
## Stest19disguisedwords -2.20 2.04 4.24 0.19 -0.75 0
## Stest20spelling -2.95 2.09 5.04 -0.02 -0.47 0
## Stest21capitalization -2.21 1.79 4.01 -0.02 -0.60 0
## Stest22punctuation -4.01 1.91 5.92 -0.21 -0.32 0
## Stest23english -5.18 2.49 7.66 -0.46 0.57 0
## Stest24expression -3.65 1.40 5.06 -0.78 0.29 0
## Stest25wordfunctions -2.61 1.91 4.52 -0.02 -0.75 0
## Stest26readingcomprehension -3.16 1.55 4.71 -0.58 -0.50 0
## Stest28mechanicalreasoning -2.41 2.08 4.50 -0.43 -0.41 0
## Stest29visualization2D -2.28 1.92 4.21 -0.48 -0.29 0
## Stest30visualization3D -2.54 2.18 4.72 -0.24 -0.69 0
## Stest31abstractreasoning -3.05 1.97 5.03 -0.56 0.09 0
## Stest32arithreasoning -2.33 1.97 4.30 -0.16 -0.78 0
## Stest33highschoolmath -2.15 2.52 4.67 0.29 -0.73 0
## Stest34arithcomputation -3.94 3.30 7.24 0.04 0.19 0
## Stest35tablereading -4.82 3.61 8.43 -0.35 3.20 0
## Stest36clericalchecking -2.66 2.63 5.29 1.11 0.68 0
## Stest37objectinspection -3.28 2.40 5.69 0.49 -0.12 0
describeBy(datafemale)
## Warning in describeBy(datafemale): no grouping variable requested
## vars n mean sd median trimmed mad
## Stest1vocab 1 71381 -0.08 0.98 -0.04 -0.06 1.13
## Stest2literature 2 71381 0.04 0.97 -0.06 0.02 0.98
## Stest3music 3 71381 0.18 0.96 0.05 0.20 1.01
## Stest4socialstudies 4 71381 -0.13 0.94 -0.11 -0.10 1.16
## Stest5math 5 71381 -0.14 0.99 0.00 -0.06 1.04
## Stest6physicalscience 6 71381 -0.27 0.91 -0.29 -0.30 1.08
## Stest7biologicalscience 7 71381 -0.17 0.97 -0.14 -0.16 1.27
## Stest8aeronautics 8 71381 -0.41 0.90 -0.22 -0.38 0.96
## Stest9electronics 9 71381 -0.43 0.88 -0.21 -0.36 0.72
## Stest10mechanics 10 71381 -0.53 0.75 -0.61 -0.54 0.77
## Stest11art 11 71381 0.13 0.97 0.13 0.15 1.20
## Stest12law 12 71381 -0.14 0.94 0.06 -0.14 0.83
## Stest13health 13 71381 0.17 0.92 0.42 0.23 0.79
## Stest14bible 14 71381 0.05 0.99 0.12 0.03 1.35
## Stest15theater 15 71381 0.23 0.96 0.25 0.25 0.84
## Stest16miscellaneous 16 71381 -0.06 0.91 0.01 -0.06 0.87
## Stest19disguisedwords 17 71381 0.17 0.97 0.14 0.18 1.08
## Stest20spelling 18 71381 0.29 0.91 0.41 0.32 1.00
## Stest21capitalization 19 71381 0.28 0.92 0.22 0.31 1.04
## Stest22punctuation 20 71381 0.28 0.90 0.32 0.33 1.01
## Stest23english 21 71381 0.20 0.91 0.25 0.23 0.95
## Stest24expression 22 71381 0.17 0.89 0.48 0.25 0.68
## Stest25wordfunctions 23 71381 0.20 0.99 0.25 0.24 1.13
## Stest26readingcomprehension 24 71381 0.12 0.91 0.25 0.18 1.04
## Stest28mechanicalreasoning 25 71381 -0.43 0.82 -0.52 -0.46 0.70
## Stest29visualization2D 26 71381 -0.15 0.96 -0.09 -0.13 1.08
## Stest30visualization3D 27 71381 -0.12 0.93 -0.02 -0.13 0.93
## Stest31abstractreasoning 28 71381 0.03 0.95 0.18 0.09 1.06
## Stest32arithreasoning 29 71381 -0.04 0.97 -0.04 -0.03 1.27
## Stest33highschoolmath 30 71381 -0.06 0.93 -0.12 -0.11 0.90
## Stest34arithcomputation 31 71381 0.16 0.93 0.14 0.18 0.91
## Stest35tablereading 32 71381 0.10 0.87 0.08 0.12 0.65
## Stest36clericalchecking 33 71381 0.11 0.94 -0.05 0.01 0.75
## Stest37objectinspection 34 71381 0.09 0.94 0.07 0.06 0.86
## min max range skew kurtosis se
## Stest1vocab -3.08 1.99 5.07 -0.18 -0.61 0
## Stest2literature -2.70 2.35 5.05 0.14 -0.58 0
## Stest3music -1.99 2.10 4.09 -0.15 -0.74 0
## Stest4socialstudies -2.86 1.65 4.51 -0.23 -0.64 0
## Stest5math -3.10 1.58 4.68 -0.73 0.37 0
## Stest6physicalscience -1.99 2.15 4.14 0.25 -0.69 0
## Stest7biologicalscience -2.28 2.00 4.28 -0.02 -0.66 0
## Stest8aeronautics -1.97 1.69 3.66 -0.34 -0.66 0
## Stest9electronics -3.22 1.82 5.03 -0.90 1.14 0
## Stest10mechanics -2.42 1.97 4.40 0.15 -0.32 0
## Stest11art -2.29 2.14 4.44 -0.20 -0.51 0
## Stest12law -2.19 2.32 4.51 0.12 -0.37 0
## Stest13health -2.78 1.49 4.27 -0.67 0.08 0
## Stest14bible -2.00 2.24 4.24 0.17 -0.74 0
## Stest15theater -2.01 1.95 3.96 -0.14 -0.66 0
## Stest16miscellaneous -2.32 2.94 5.26 -0.05 -0.22 0
## Stest19disguisedwords -2.20 2.04 4.24 -0.06 -0.79 0
## Stest20spelling -2.95 2.09 5.04 -0.26 -0.41 0
## Stest21capitalization -2.21 1.79 4.01 -0.34 -0.29 0
## Stest22punctuation -4.01 1.91 5.92 -0.47 -0.18 0
## Stest23english -5.18 2.49 7.66 -0.42 0.49 0
## Stest24expression -3.65 1.40 5.06 -0.83 0.57 0
## Stest25wordfunctions -2.61 1.91 4.52 -0.31 -0.79 0
## Stest26readingcomprehension -3.16 1.55 4.71 -0.57 -0.38 0
## Stest28mechanicalreasoning -2.41 2.08 4.50 0.27 -0.40 0
## Stest29visualization2D -2.28 1.92 4.21 -0.15 -0.53 0
## Stest30visualization3D -2.54 2.18 4.72 0.05 -0.55 0
## Stest31abstractreasoning -3.05 1.97 5.03 -0.57 0.10 0
## Stest32arithreasoning -2.33 1.97 4.30 -0.05 -0.80 0
## Stest33highschoolmath -2.15 2.52 4.67 0.43 -0.38 0
## Stest34arithcomputation -3.94 3.30 7.24 -0.17 0.44 0
## Stest35tablereading -4.82 3.61 8.43 -0.56 4.58 0
## Stest36clericalchecking -2.66 2.63 5.29 0.93 0.47 0
## Stest37objectinspection -3.28 2.40 5.69 0.29 -0.02 0
scree(datamale)
VSS.scree(datafemale)
scree(datamale)
VSS.scree(datafemale)
malecor<- cor(datamale) # fa.parallel requires cor matrix if n.obs is to be used
femalecor<- cor(datafemale) # fa.parallel requires cor matrix if n.obs is to be used
eigen(malecor) # all eigenvalues different from zero
## eigen() decomposition
## $values
## [1] 14.5550192 2.2392323 1.8979326 1.4945047 0.8785614 0.8264166
## [7] 0.6978903 0.6430074 0.6275319 0.5870678 0.5739058 0.5452188
## [13] 0.5154235 0.5048464 0.4894658 0.4862850 0.4784490 0.4725578
## [19] 0.4542735 0.4495524 0.4325910 0.4069173 0.3986767 0.3925382
## [25] 0.3885711 0.3565615 0.3465269 0.3265274 0.3236934 0.2737165
## [31] 0.2562350 0.2439508 0.2232105 0.2131417
##
## $vectors
## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.22437957 -0.096505612 0.0154964055 0.09266403 -0.0556623547
## [2,] -0.20893467 -0.032930034 0.1468675196 0.15210053 0.0872492715
## [3,] -0.18622633 -0.035299594 0.1139513244 0.16697746 0.1501555252
## [4,] -0.20953512 -0.061838279 0.1137279766 0.09631629 -0.0703913970
## [5,] -0.20822287 0.008109874 -0.0056610552 -0.11363277 -0.2232390653
## [6,] -0.20631121 -0.141140799 -0.0734051326 0.02601409 -0.2243413099
## [7,] -0.17628480 -0.168512781 -0.0672743153 0.11214471 -0.1383936150
## [8,] -0.16418070 -0.192737008 -0.1315654557 0.19621822 -0.0394839595
## [9,] -0.15930285 -0.211977712 -0.2534950319 0.12631284 -0.2934837504
## [10,] -0.14749038 -0.181813836 -0.2573099042 0.13228337 -0.2289622804
## [11,] -0.18404798 -0.042797253 0.0959822381 0.24687110 0.2395995506
## [12,] -0.17846809 -0.065731782 0.0616087528 0.14843042 0.0232086561
## [13,] -0.17450096 -0.042889586 0.0794554183 0.15930236 -0.0598360761
## [14,] -0.16075379 -0.052489160 0.1374862027 0.07257812 0.1560168768
## [15,] -0.17910949 0.004831818 0.1476854221 0.19612222 0.2228700724
## [16,] -0.18006584 -0.031945363 0.0866786637 0.16197902 0.0419167514
## [17,] -0.17304836 0.202556894 0.0893643871 0.08040751 0.1646905284
## [18,] -0.15634545 0.158705054 0.2449805055 -0.12090233 -0.0666702337
## [19,] -0.16290611 0.084190549 0.1222116474 -0.20096025 0.0017904570
## [20,] -0.19485753 0.072803984 0.1017444873 -0.27174647 0.0029051630
## [21,] -0.17346344 0.026113195 0.1014815492 -0.14989400 0.1559846408
## [22,] -0.15563701 0.010091555 0.0744670056 -0.16999707 0.2213500222
## [23,] -0.18415058 0.070944838 0.0741472529 -0.26344622 -0.0006514032
## [24,] -0.22544146 -0.038393070 0.0996689421 -0.01120709 0.0745268090
## [25,] -0.16001589 -0.098930987 -0.4003206630 -0.08655608 0.0633223149
## [26,] -0.10450347 0.158521518 -0.3805692405 -0.07239863 0.3272454738
## [27,] -0.13646390 -0.026047229 -0.3942550770 -0.17600515 0.2394536940
## [28,] -0.16140298 0.034116791 -0.1941615330 -0.25097547 0.2063559933
## [29,] -0.19527351 0.002865444 -0.0417515507 -0.22807710 -0.1454419322
## [,6] [,7] [,8] [,9] [,10]
## [1,] -0.05133290 0.026459231 0.005576295 0.010194640 -0.04002901
## [2,] 0.13403287 0.002907374 -0.006800524 0.065398309 -0.07162780
## [3,] 0.08492749 0.293813485 0.096712483 0.159699818 -0.06283395
## [4,] 0.16055225 -0.129325539 0.001184661 -0.007608135 0.04544334
## [5,] 0.18142866 0.108659378 0.074152811 0.048944584 -0.08087566
## [6,] 0.10245743 0.080353527 -0.112046179 0.123121597 -0.04398505
## [7,] -0.03082050 -0.208170354 -0.303742822 0.078891181 0.18624929
## [8,] -0.01641919 0.041622060 -0.023123664 0.202857002 -0.12956531
## [9,] -0.15670351 0.145755650 -0.003346154 0.067214709 -0.07947331
## [10,] -0.40526806 -0.032304781 0.051680333 -0.190691773 -0.01616787
## [11,] 0.07820927 0.112302807 0.127369217 -0.005735658 0.11822224
## [12,] 0.05456328 -0.201432527 0.242129442 -0.276737134 -0.09156224
## [13,] -0.08707861 -0.136760502 0.002395832 -0.207699963 0.52848900
## [14,] 0.28889886 -0.452432659 -0.448172433 -0.120464996 -0.24130907
## [15,] 0.01185768 0.205084809 0.318835759 -0.063963567 -0.04732192
## [16,] 0.16084123 0.126876505 -0.015239092 -0.059434956 0.14843031
## [17,] -0.26858481 0.304849771 -0.186536036 -0.050334016 -0.16238731
## [18,] -0.26253262 0.277513445 -0.185957427 -0.085659385 0.03448788
## [19,] -0.13383917 -0.036702531 -0.126481555 0.177924566 0.55566058
## [20,] -0.06602200 0.024276736 -0.131669491 0.093364518 0.04107322
## [21,] -0.34012745 -0.088506228 -0.124962626 0.089045492 -0.17725810
## [22,] -0.40222309 -0.392293829 0.352282520 0.069669472 -0.16207536
## [23,] 0.08441998 0.006292666 -0.151178753 0.088386186 -0.13308066
## [24,] -0.02441268 -0.143693288 0.030125354 -0.025099534 -0.02756081
## [25,] -0.09652043 0.016405996 -0.068604028 -0.006577203 -0.05117006
## [26,] 0.06395913 0.101237360 -0.147406729 -0.587800447 0.09269440
## [27,] 0.14679346 0.064365729 -0.011995755 0.058944366 0.01531622
## [28,] 0.16035564 0.036543897 0.166574513 0.238789728 0.13826335
## [29,] 0.08905913 -0.084048611 0.155552034 -0.102438662 -0.10838228
## [,11] [,12] [,13] [,14] [,15]
## [1,] 0.015521053 0.053698304 -0.039111219 -0.043707985 0.006408271
## [2,] 0.028883360 0.092369487 -0.109688692 -0.125894145 -0.037786585
## [3,] 0.017546600 0.106871191 -0.237449733 -0.127126468 -0.196691697
## [4,] 0.020545132 0.132619772 0.010612572 -0.107689652 -0.026111758
## [5,] 0.100903329 0.114060300 -0.097313885 0.034380165 0.005823099
## [6,] 0.122197757 0.152633751 0.017207377 -0.008183648 0.007052308
## [7,] 0.309616042 0.125800183 -0.208836182 -0.172073776 0.133921024
## [8,] -0.118512620 0.308568622 0.500495350 0.022494638 0.318410103
## [9,] -0.078419775 -0.002885183 0.004985772 0.020030213 -0.197500488
## [10,] -0.180168129 -0.207978074 -0.173889681 -0.040879023 -0.237842963
## [11,] 0.025121762 -0.048713252 0.005222999 -0.072160699 -0.068038024
## [12,] -0.374054333 -0.173366643 -0.148521598 -0.010087482 0.471749770
## [13,] 0.386661936 -0.268877031 0.039348825 0.126153781 0.221792001
## [14,] -0.151796574 -0.170861175 0.075041746 -0.042462754 -0.322857988
## [15,] -0.146006737 -0.046277200 -0.092545871 -0.039292748 0.040924222
## [16,] 0.040605185 -0.075837326 0.314689040 0.562248158 -0.315556389
## [17,] 0.078474182 -0.104686598 0.118472679 -0.013010325 0.064627456
## [18,] 0.061452033 -0.191822096 -0.010442868 -0.167737555 -0.127231567
## [19,] -0.565431097 0.200230382 0.103762735 -0.198364113 -0.058778847
## [20,] -0.100734862 0.002488602 -0.031139409 0.095738595 0.025140299
## [21,] -0.028637010 0.086351165 -0.109089562 0.529157173 0.198442053
## [22,] 0.309887506 0.234001945 0.110494985 -0.178367446 -0.220372467
## [23,] 0.001278785 -0.110420767 -0.184139312 0.093499466 0.138172999
## [24,] 0.013738204 -0.003285593 0.046809972 -0.074266236 0.030256939
## [25,] -0.080014232 -0.133308915 0.089417004 0.051314197 0.022853733
## [26,] 0.042796959 0.477757050 -0.036379028 0.003492273 0.003805163
## [27,] -0.011734363 -0.297659924 -0.068729214 -0.143992552 -0.105209657
## [28,] 0.163450808 -0.280098165 0.297398239 -0.144155258 0.120690140
## [29,] -0.016586030 -0.114863720 -0.036653196 0.013848191 0.057662146
## [,16] [,17] [,18] [,19] [,20]
## [1,] -0.052210955 0.02734283 -0.008041954 0.023977610 -0.059677156
## [2,] -0.059766429 0.01268678 -0.135380477 -0.035830796 -0.041009086
## [3,] -0.181296376 -0.09815856 0.012351965 -0.001947168 0.100780017
## [4,] -0.055829088 0.05863947 -0.245608576 -0.052902813 0.025466375
## [5,] -0.033525910 -0.07909648 -0.022090914 0.031892354 0.111639385
## [6,] 0.011781339 -0.04189904 -0.088802343 0.013847024 0.177475798
## [7,] -0.083034364 -0.02983756 -0.150864473 -0.089829604 -0.513282045
## [8,] 0.083152247 0.34189891 0.280162193 -0.147502427 0.011744132
## [9,] 0.020355029 -0.11638657 -0.037619933 0.102563072 0.414388830
## [10,] 0.014104509 0.04468127 0.039756873 0.124657204 -0.232773382
## [11,] -0.090723405 -0.02690522 0.058562621 0.047797934 0.029755413
## [12,] 0.233351174 0.04796199 -0.333403939 -0.124242861 0.107176643
## [13,] -0.091637017 -0.07381562 0.309058993 -0.003795024 0.360058075
## [14,] -0.017960709 0.13612129 0.190826744 0.248020810 0.154690805
## [15,] -0.093064926 -0.06953217 0.277283558 0.084986113 -0.154730579
## [16,] 0.377787860 -0.19388587 -0.263259378 -0.131381551 -0.227467089
## [17,] 0.049223033 -0.02538845 0.139878363 0.149078690 -0.213626925
## [18,] 0.094239807 0.54107977 -0.200509843 -0.295121684 0.136186382
## [19,] 0.024988662 -0.22794743 -0.002497723 0.086356907 0.004650713
## [20,] 0.042756864 -0.02311818 0.091282990 -0.121639378 0.061217527
## [21,] -0.405427214 -0.01480350 -0.267903252 0.209131248 0.111832197
## [22,] 0.321924508 -0.14615957 -0.001419865 -0.063472545 0.120668853
## [23,] 0.116632753 -0.16299820 0.356308443 -0.328755351 -0.083947860
## [24,] -0.026467702 0.05412764 0.038792169 -0.033032609 -0.090954865
## [25,] 0.003944541 -0.02043758 0.131647754 0.032095355 -0.118447516
## [26,] -0.043719466 0.01625372 -0.031761208 -0.045371393 0.071007046
## [27,] -0.025376586 -0.05583968 -0.113785855 -0.316701316 0.128019146
## [28,] -0.091299302 0.17836609 -0.250994778 0.395667298 -0.079913407
## [29,] 0.071122391 -0.08992713 0.109358892 0.099631224 -0.167692459
## [,21] [,22] [,23] [,24] [,25]
## [1,] 0.036959452 0.033215492 -0.01911125 -0.04967327 0.10320813
## [2,] -0.020568559 0.042564897 -0.10349117 -0.04546864 0.11320472
## [3,] 0.154840513 -0.556735037 -0.19463361 0.06466465 0.11643040
## [4,] -0.008553859 0.039477903 -0.06775265 -0.05087779 0.21863344
## [5,] 0.026649342 0.001430017 0.08041511 -0.12684447 0.14384853
## [6,] 0.075873222 0.057486581 0.22134975 -0.03777870 -0.14278410
## [7,] -0.056288992 -0.016409351 0.16944609 0.14297317 -0.23791382
## [8,] -0.183492438 -0.094928398 -0.15948999 0.08297361 0.12132931
## [9,] 0.167806615 0.179772036 0.10175887 0.07279299 -0.30199350
## [10,] 0.009603922 -0.018583104 -0.39379101 0.08458313 0.20226377
## [11,] -0.251495242 0.467114063 -0.31095036 -0.39895451 -0.34615016
## [12,] 0.145435165 -0.204086614 0.05795515 -0.08055652 -0.22363804
## [13,] 0.004028876 -0.154015922 0.01113285 0.01798137 0.14667453
## [14,] 0.029702051 -0.055541169 0.09104979 0.07077301 -0.02307540
## [15,] -0.057982541 0.233833801 0.41385346 0.54106075 0.01479066
## [16,] 0.007609831 -0.042486168 -0.01659561 0.10767726 0.03746103
## [17,] 0.106326207 -0.260971646 0.23735344 -0.46186156 -0.12635199
## [18,] 0.039459641 0.174791328 0.10528997 0.10004888 0.10418461
## [19,] -0.033148584 -0.043313158 0.06327987 -0.05777180 0.03596835
## [20,] 0.077136072 0.068593497 -0.03571360 0.09004768 -0.07790933
## [21,] -0.253051609 0.024267206 -0.06307610 0.09212430 0.02693410
## [22,] -0.020278498 -0.059637008 0.04309568 0.03190313 -0.07295099
## [23,] 0.202015211 0.055801956 -0.40719110 0.15734905 -0.24829074
## [24,] 0.020143142 0.092214470 -0.01352010 -0.09061162 0.09770744
## [25,] 0.020469164 -0.093768072 0.20925490 -0.10081416 -0.05962648
## [26,] 0.207041415 0.105642624 -0.06961880 0.06082146 0.05279934
## [27,] -0.571421230 -0.171121354 0.08636463 0.02208941 0.01758694
## [28,] 0.342066013 0.025482553 -0.18052317 0.18305926 -0.07068133
## [29,] -0.010909827 0.220011695 0.09437245 -0.24368721 0.43613479
## [,26] [,27] [,28] [,29] [,30]
## [1,] -0.089615223 -0.096252412 -0.091441575 -0.013170238 0.0274699982
## [2,] -0.194258400 -0.088884163 -0.191942690 -0.153566568 -0.6800937569
## [3,] 0.354759391 0.230705905 0.054708531 -0.018104651 0.0996377846
## [4,] -0.036508028 -0.271843718 -0.450944352 -0.100858003 0.3157605920
## [5,] -0.511690473 0.202881921 0.225246162 0.111483825 -0.0126665505
## [6,] -0.024950945 -0.104711117 -0.036685975 -0.039649926 0.4878526684
## [7,] 0.157794378 0.111860261 0.186775919 0.111136038 -0.0840245899
## [8,] 0.058764373 0.017735640 0.143488663 0.089222724 -0.0481743427
## [9,] 0.234582975 -0.231902835 0.023762902 -0.007385114 -0.3242850563
## [10,] -0.244343547 -0.011569070 0.069941671 0.168715429 0.1348796839
## [11,] 0.064021533 0.263558434 0.077366259 0.036694974 0.1349366891
## [12,] 0.016113840 0.077732619 0.085888439 0.057580751 0.0096902389
## [13,] -0.026080269 -0.004140729 -0.009808770 -0.018247515 -0.0649321205
## [14,] -0.019211256 0.075969730 0.156471107 0.057453118 0.0267874613
## [15,] -0.085633998 -0.064392763 -0.012167071 0.012021881 0.0881000263
## [16,] 0.022368492 0.026519882 0.054827919 -0.015944443 -0.0194496577
## [17,] -0.101807603 -0.324313146 0.025326710 0.146281241 -0.0073064216
## [18,] 0.067233145 0.173766773 0.143931022 -0.170289046 0.0187632976
## [19,] -0.042964994 -0.036454909 0.166407481 -0.134581268 -0.0051925091
## [20,] 0.075129512 0.218104002 -0.492218570 0.677708439 -0.0716997729
## [21,] 0.045474178 -0.015638222 0.087390650 -0.107120971 0.0269991723
## [22,] -0.036621554 0.067882959 0.064104052 -0.015799850 0.0233336459
## [23,] -0.037534440 -0.235976322 0.067271275 -0.302254573 0.0781997825
## [24,] -0.008715053 -0.179669561 -0.136573106 -0.090301933 -0.0096704209
## [25,] -0.047979370 0.492896199 -0.410045944 -0.471827341 -0.0148272666
## [26,] 0.024819515 -0.038449459 0.071446961 0.043466165 -0.0099663193
## [27,] -0.025844901 -0.250410802 0.052721069 0.124997731 0.0037069167
## [28,] -0.033650903 -0.061447747 0.073931714 0.054303093 -0.0050345486
## [29,] 0.587192116 -0.052770182 0.112535699 0.005956499 -0.0472585571
## [,31] [,32] [,33] [,34]
## [1,] 0.128527288 0.781640327 0.0244576836 -0.488308149
## [2,] -0.420837149 -0.099504622 -0.1663446264 -0.026902891
## [3,] 0.038857315 0.016727424 0.0220066547 0.091586121
## [4,] 0.307684303 -0.415172608 0.1494040153 -0.212885809
## [5,] 0.403897435 -0.047084220 -0.4216713907 0.161190813
## [6,] -0.603854379 0.073925158 -0.1859919677 0.131651304
## [7,] 0.123234223 -0.071474871 0.0264091468 -0.001525380
## [8,] 0.016007178 -0.083431426 -0.0204340268 -0.014654206
## [9,] 0.256030433 -0.071985742 0.1016337095 0.022580926
## [10,] -0.182377937 -0.123313408 0.0315798874 0.048576908
## [11,] 0.019786873 -0.042478848 -0.0009978842 -0.030448132
## [12,] -0.014699042 0.008950579 -0.0262104312 -0.008062011
## [13,] -0.056278917 -0.031312303 0.0047189558 -0.031936544
## [14,] 0.015144409 -0.011153642 -0.0063179233 -0.060679320
## [15,] 0.012236076 -0.088540810 -0.0270643262 -0.020931068
## [16,] 0.012866541 0.041225136 -0.0002323069 0.026261036
## [17,] 0.026043589 -0.155737893 0.0305166443 -0.064477311
## [18,] 0.015251237 -0.018913261 -0.0081784926 -0.015734744
## [19,] -0.022425782 -0.001325026 -0.0174022401 -0.022547157
## [20,] -0.040613640 0.018159051 -0.0364908917 0.018223234
## [21,] -0.002059006 -0.036652076 -0.0124892724 -0.002208053
## [22,] -0.023466418 -0.046624413 -0.0183062614 -0.091049426
## [23,] 0.052374141 -0.054011572 -0.0935058400 -0.069193261
## [24,] 0.136146514 0.318963168 0.2627430407 0.780905199
## [25,] 0.050249584 -0.040659007 -0.0211676517 -0.013255987
## [26,] -0.017236907 0.005284241 -0.0006449649 0.004886516
## [27,] 0.009081829 0.046940997 -0.0243520498 -0.002711623
## [28,] -0.012293110 -0.011035940 -0.0176742960 -0.029035631
## [29,] -0.044003033 -0.056202030 -0.2581814114 -0.052333168
## [ reached getOption("max.print") -- omitted 5 rows ]
eigen(femalecor) # all eigenvalues different from zero
## eigen() decomposition
## $values
## [1] 13.1135935 2.1963969 1.6499386 1.4601555 1.0757764 0.8546357
## [7] 0.7681494 0.7271142 0.6804028 0.6672430 0.6622445 0.6344815
## [13] 0.6090857 0.5936346 0.5674648 0.5601185 0.5413674 0.5178906
## [19] 0.4991517 0.4810005 0.4675437 0.4610825 0.4524227 0.4289206
## [25] 0.4176737 0.4054928 0.3922097 0.3697384 0.3475079 0.3424633
## [31] 0.2882518 0.2799352 0.2654777 0.2214343
##
## $vectors
## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.23409645 -0.096972294 0.022075150 0.08661918 0.007388215
## [2,] -0.21601621 -0.090893674 0.120817702 0.15581636 0.069975068
## [3,] -0.19737768 -0.078379762 0.087719873 0.15660741 0.089473080
## [4,] -0.21864771 -0.113641504 0.070434731 0.08203959 -0.031760790
## [5,] -0.20024486 -0.024604396 -0.038831737 -0.12443476 -0.266497225
## [6,] -0.19574208 -0.144001572 -0.159235185 0.02806806 -0.273086551
## [7,] -0.18052255 -0.139654338 -0.090310941 0.08855964 -0.086553198
## [8,] -0.11506357 -0.141740930 -0.198374695 0.24536430 -0.030736983
## [9,] -0.11470965 -0.127002721 -0.223285904 0.18770530 -0.475935787
## [10,] -0.14282893 -0.102858315 -0.266197520 0.16826655 -0.108228875
## [11,] -0.19106995 -0.074633403 0.080258859 0.23506845 0.196919159
## [12,] -0.16652873 -0.101588341 0.034354853 0.16450090 0.103074610
## [13,] -0.16538921 -0.057139564 0.092939961 0.13878180 0.012105213
## [14,] -0.16024774 -0.110812913 0.053568734 0.03335165 0.065554164
## [15,] -0.18412756 -0.043577683 0.160667337 0.21101161 0.190837974
## [16,] -0.17369027 -0.057480682 0.045200289 0.14577672 0.021762384
## [17,] -0.17662603 0.212246354 0.170172409 0.08125770 0.079515865
## [18,] -0.16103245 0.120241724 0.305074729 -0.10780375 -0.095750014
## [19,] -0.15653037 0.065424450 0.147712433 -0.20494998 -0.009806650
## [20,] -0.20611578 0.052260928 0.108207183 -0.25096586 -0.003797997
## [21,] -0.17428494 0.019212172 0.153140040 -0.13762443 0.106097812
## [22,] -0.15109176 0.008226392 0.122541682 -0.13460321 0.254300826
## [23,] -0.20039323 0.044195000 0.055974221 -0.25726042 -0.053299282
## [24,] -0.23585837 -0.057716786 0.089000263 -0.01834267 0.112704026
## [25,] -0.16041574 0.020871948 -0.401670152 -0.08139037 0.167284387
## [26,] -0.10788881 0.229296435 -0.356020009 -0.06074942 0.220080226
## [27,] -0.14337141 0.072768024 -0.400112710 -0.17438312 0.225320283
## [28,] -0.16967641 0.092365625 -0.179620264 -0.23280282 0.196786881
## [29,] -0.20060344 0.002943048 -0.055895325 -0.22532560 -0.072255627
## [,6] [,7] [,8] [,9] [,10]
## [1,] 0.006363646 0.0103772755 0.031834145 -0.01770268 -0.02138184
## [2,] -0.159996686 -0.0081795315 0.010229134 -0.03000046 -0.06497245
## [3,] -0.087233748 -0.1793129103 0.148992357 -0.03199727 -0.06603045
## [4,] -0.152018654 0.0732864592 0.018730410 -0.03131671 0.02740070
## [5,] -0.241713461 -0.1474727970 0.106167755 -0.09097414 -0.02355704
## [6,] -0.049290058 -0.0229676933 0.050465308 -0.08977661 -0.18015047
## [7,] 0.046848538 0.2898708906 0.023555734 -0.03081532 -0.30542801
## [8,] 0.123212921 -0.5115990408 -0.681285448 0.03976407 0.04985252
## [9,] 0.325510307 -0.0666611248 0.177286544 -0.15806512 -0.06187090
## [10,] 0.374007263 0.2889088183 0.004428747 0.15792092 0.22639759
## [11,] -0.100528314 -0.1367937698 0.167173869 -0.02400606 0.01732920
## [12,] -0.085539842 0.2073686709 -0.157974204 0.08927744 0.53566418
## [13,] 0.179219690 0.2658331890 0.245274704 0.02476329 0.07285764
## [14,] -0.264688919 0.4429468178 -0.419255006 0.16934641 -0.26480446
## [15,] -0.095648558 -0.2237012374 0.166357138 -0.04445131 0.19854598
## [16,] -0.151548113 -0.0971165317 0.185025986 0.17690041 -0.01702595
## [17,] 0.219255238 -0.1754917771 0.065449208 0.22032751 -0.20163643
## [18,] 0.250128798 -0.0984897072 0.031794330 0.29033647 -0.06015694
## [19,] 0.207018382 0.0224872973 -0.122537975 0.11036856 0.04457647
## [20,] 0.087484607 0.0085863045 -0.093268936 0.06595593 -0.06583591
## [21,] 0.265996774 -0.0160660824 -0.093118406 0.01558024 -0.19962355
## [22,] 0.357626127 0.0227216382 -0.053416056 -0.58315187 0.12151856
## [23,] -0.073597501 0.0197570513 -0.095922882 -0.01269685 -0.10326967
## [24,] -0.020264804 0.0779753813 -0.064420531 -0.06027349 -0.00714649
## [25,] 0.062896292 -0.0424340719 0.019513367 0.03960041 -0.07449471
## [26,] 0.020385804 -0.0598570128 0.162549842 0.42063992 0.12864210
## [27,] -0.043501243 0.0366765715 0.057802652 0.04133201 -0.03726652
## [28,] -0.050201186 -0.0985355067 0.069198389 -0.19557865 -0.02551890
## [29,] -0.078974956 0.0605789512 -0.040044439 -0.05960782 0.17962792
## [,11] [,12] [,13] [,14]
## [1,] -0.036801716 -0.019349726 -0.0649090654 0.074983734
## [2,] -0.059368540 0.065123488 -0.0413019742 0.111128772
## [3,] 0.005553021 0.052670073 -0.0754303439 0.091943198
## [4,] 0.026506664 0.059594691 0.0268047075 0.062854750
## [5,] -0.071683202 -0.079674891 -0.0333235756 0.156403744
## [6,] 0.007811696 0.007540717 0.0561333801 0.106428359
## [7,] 0.130870274 -0.268371668 -0.1214000194 0.247212264
## [8,] 0.177500558 -0.258693608 0.0413510618 -0.023260459
## [9,] -0.094746895 0.414316646 0.3375717094 -0.079256039
## [10,] -0.131587692 -0.027390423 -0.4044929413 -0.137788163
## [11,] 0.057277321 0.074645526 0.0096955988 0.008245748
## [12,] -0.169491851 0.245597080 -0.0796468907 0.196410321
## [13,] 0.432436908 -0.505524741 0.1754073622 -0.013625409
## [14,] -0.150207924 0.098401343 0.3207658102 -0.192942052
## [15,] 0.007403361 0.071747206 -0.0563793092 0.084628717
## [16,] 0.043518900 -0.002220365 0.1592502314 -0.711434982
## [17,] -0.184909136 -0.050809463 -0.0694927107 -0.062614222
## [18,] -0.074349350 -0.001764048 -0.1850649960 -0.043956325
## [19,] 0.625342195 0.461936008 0.0889543986 0.129774797
## [20,] 0.038365027 0.054748455 -0.0265397177 -0.011383586
## [21,] -0.222800894 0.052261335 -0.0119768113 0.113332253
## [22,] -0.274011074 -0.156054955 0.3044174369 -0.060471579
## [23,] -0.022738743 -0.039598232 -0.0499491675 -0.010482859
## [24,] -0.002902235 0.001173909 0.0153029944 0.011579987
## [25,] -0.037443635 0.001616470 -0.1642150111 -0.067145314
## [26,] -0.107378265 -0.093666026 0.5424723961 0.322429343
## [27,] 0.016722203 0.097283454 -0.1578427276 -0.112584250
## [28,] 0.177106223 0.066940445 -0.0909397218 -0.215178328
## [29,] -0.064944961 -0.049841612 -0.0781188733 -0.081126618
## [,15] [,16] [,17] [,18]
## [1,] 0.0009057282 -0.070408918 -0.019241507 -0.018806861
## [2,] -0.0056824093 -0.091049721 -0.011846514 0.031151606
## [3,] -0.0580465144 -0.204426722 -0.089406065 0.036700366
## [4,] -0.0191175756 -0.063516073 0.014937657 0.080140146
## [5,] 0.1523022911 0.011807515 -0.010545747 -0.110881207
## [6,] 0.0697327610 0.031432348 0.096799263 -0.008078174
## [7,] 0.1838103379 -0.078381400 0.180750428 0.077178469
## [8,] -0.0311265455 0.046218286 0.012975436 0.043610546
## [9,] -0.2584852076 0.144345998 -0.070880797 0.071514763
## [10,] 0.1633874354 -0.362531894 -0.135918307 -0.018830865
## [11,] -0.0866976319 -0.122589609 -0.107703881 -0.040724618
## [12,] 0.0381461108 0.487021943 0.306673426 0.085738275
## [13,] -0.2364280487 0.346415741 -0.055329443 -0.105625914
## [14,] -0.2236931404 -0.160251709 -0.132751409 0.012823576
## [15,] -0.0948646478 -0.109388328 -0.181877775 -0.091477485
## [16,] 0.4860324270 0.121582314 0.173891506 0.022678815
## [17,] -0.1093520954 0.014895759 0.103615374 -0.118650810
## [18,] -0.2224443506 -0.003763276 0.104419575 0.406396026
## [19,] 0.2173543903 -0.200781583 0.155529739 -0.196035527
## [20,] 0.0168683606 0.059999799 -0.017086860 0.056911953
## [21,] 0.3295346659 0.409280875 -0.537576955 -0.087952807
## [22,] 0.1151032820 -0.220364302 0.301878950 0.011157021
## [23,] -0.0317033337 0.078246310 0.065685948 -0.004331551
## [24,] -0.0993142301 -0.050272772 -0.019495522 -0.023085210
## [25,] 0.0113115995 0.078618616 0.031928249 -0.241849639
## [26,] 0.1199943085 -0.132669941 -0.046370196 0.091045457
## [27,] -0.2347928930 0.041099879 0.062040815 -0.006413390
## [28,] -0.2998328952 0.100549660 -0.014432612 0.116705975
## [29,] -0.0644260441 0.023518116 0.036893061 -0.050487216
## [,19] [,20] [,21] [,22]
## [1,] 0.0239135958 -0.021509536 0.0338281246 -0.0211496584
## [2,] 0.1162533902 0.012215972 -0.0964846356 -0.0700292898
## [3,] 0.0247578154 0.149654440 0.1580063596 -0.0998597995
## [4,] 0.1551240685 0.007161877 -0.1565077087 -0.0649986531
## [5,] -0.1544744758 0.137421923 0.0310737877 -0.3295221429
## [6,] 0.0813321107 0.013380749 0.0437551908 0.0646683817
## [7,] 0.4077681718 -0.166288449 -0.0003324833 0.3278297316
## [8,] 0.0330761162 0.003586186 -0.0688237550 -0.0638420756
## [9,] -0.0002426662 -0.015696952 0.0301465870 0.0537091235
## [10,] -0.2042619338 -0.146128427 -0.0745656423 -0.2873435728
## [11,] -0.0626807969 -0.053260304 -0.1932511484 0.1320310266
## [12,] 0.0482869195 -0.014397556 0.1042588298 0.0428574357
## [13,] -0.2304774543 0.137584651 -0.0158392355 -0.1500102281
## [14,] -0.2141424806 0.056686833 0.0575714568 -0.0004676406
## [15,] -0.1391195918 -0.019780729 0.0384565713 0.1670508127
## [16,] 0.1147690048 0.004278254 -0.0241489933 -0.0249145701
## [17,] -0.1273318619 -0.091036251 0.2420993489 0.1823438517
## [18,] 0.2573826512 0.236925522 0.1047148859 -0.1892440651
## [19,] -0.1052745218 0.045818043 -0.0570099641 0.0405050499
## [20,] -0.0157149722 -0.008283221 0.1111501944 -0.0978185294
## [21,] 0.0153453207 -0.040476807 -0.3242524526 0.0832750175
## [22,] -0.0225352988 0.145366431 -0.0330927571 -0.0282775654
## [23,] -0.0909891110 -0.065413561 0.2030977023 -0.1217141767
## [24,] 0.0331520942 -0.091799944 0.0169219981 0.0189206552
## [25,] -0.1415125647 0.190868735 0.4206339390 0.3733585458
## [26,] 0.1211236432 -0.139993864 0.0519544085 -0.1640937416
## [27,] 0.1558043879 0.520555628 -0.4567961411 0.0200953557
## [28,] 0.1202620462 -0.607709712 -0.0547893355 -0.1328019377
## [29,] -0.0922765193 -0.205614606 -0.0562849811 0.0805226071
## [,23] [,24] [,25] [,26] [,27]
## [1,] 0.044916899 0.01249009 0.0442107623 0.0359679311 -0.044628789
## [2,] 0.011965693 0.03813840 0.0055257064 0.0462676451 0.187655614
## [3,] -0.399232367 -0.58784225 0.0737530372 0.2703533840 -0.045616889
## [4,] 0.002025889 -0.04489744 0.2622939706 0.2009857060 0.098667322
## [5,] -0.152246845 0.23379476 -0.1620653632 -0.1316443499 -0.066030657
## [6,] -0.106418026 0.13542695 0.2227399312 0.0417383384 -0.218781209
## [7,] 0.057554012 -0.05341353 -0.1905828150 -0.2043837221 -0.031317261
## [8,] 0.038390598 -0.02077420 -0.0141363614 -0.0003328901 -0.006914409
## [9,] 0.117406507 -0.08606035 -0.1070335463 -0.0376580240 0.063029343
## [10,] -0.041701550 0.01593744 -0.0753323552 -0.0208481433 0.014420138
## [11,] 0.176163875 0.48894335 -0.2236179581 0.3905289693 0.207415063
## [12,] -0.174401145 0.01654798 -0.1356800777 0.0207029064 -0.060183057
## [13,] -0.048207516 -0.02258881 0.0475304216 0.0177273198 0.013177355
## [14,] -0.144618744 0.07965042 0.0227874006 -0.1666128650 -0.063412807
## [15,] 0.234687076 -0.14747849 0.0250225324 -0.6868222133 -0.047600074
## [16,] 0.031671172 -0.07000455 -0.0014239329 -0.0658159491 0.015657979
## [17,] -0.057216371 0.10981037 -0.2212762533 0.1692169068 -0.562312631
## [18,] 0.033921368 0.25620093 0.2613759446 -0.1794812968 0.144729543
## [19,] -0.071835990 0.04892627 0.0302701605 -0.0288193830 -0.073538268
## [20,] 0.126179510 -0.17030070 -0.1201923042 0.0619111590 0.182244785
## [21,] -0.117232478 -0.04137583 0.0834948705 -0.0138556114 0.033558378
## [22,] -0.079487127 0.04803483 -0.0015937129 -0.0442599361 0.022978305
## [23,] 0.342515795 -0.27709939 -0.4520451018 0.0945839839 0.263676687
## [24,] 0.135960022 0.03841345 0.0347823317 0.0484097090 -0.022719131
## [25,] -0.122721655 0.11555384 0.2587766740 0.0062768809 0.420816755
## [26,] 0.071057045 -0.01981862 0.0309096426 -0.0013937070 0.016525590
## [27,] 0.072604947 -0.10045325 -0.1993777811 -0.0447831179 -0.225298433
## [28,] -0.373561673 0.08118654 -0.0212530532 -0.1395979743 0.016305853
## [29,] 0.466378563 -0.14018655 0.4822054749 0.2057856143 -0.274232300
## [,28] [,29] [,30] [,31] [,32]
## [1,] -0.083332549 0.168652751 0.002416899 -0.0241210488 0.457088164
## [2,] -0.015088887 0.458728746 0.010676059 -0.6579808234 0.069390328
## [3,] 0.236127275 -0.258197509 -0.067829784 -0.0035438632 -0.001225185
## [4,] -0.264984940 0.372283211 0.065325449 0.5167946636 -0.449993398
## [5,] 0.207514975 0.143294305 0.090407786 0.3641176512 0.363049472
## [6,] -0.635003654 -0.374318817 -0.146398884 -0.1413622560 0.112372660
## [7,] 0.298179064 -0.074647512 0.071737790 0.0769038651 -0.074023672
## [8,] 0.041673341 0.014269268 0.007982410 0.0212638354 -0.014712324
## [9,] 0.184889917 0.092997747 0.042785414 -0.0093052175 -0.044546552
## [10,] -0.073340643 -0.035201503 -0.024495995 -0.0291796979 -0.094959604
## [11,] 0.125871583 -0.391146591 0.010978468 0.0675131892 -0.034804397
## [12,] 0.036858898 -0.093590167 -0.007620610 0.0037451461 0.011390163
## [13,] -0.009674586 0.022435822 -0.009575397 -0.0734949980 -0.026363861
## [14,] 0.098118207 -0.118213534 -0.013209905 0.0255526846 -0.014983800
## [15,] -0.153675756 -0.092314609 0.015179682 0.0793193417 -0.065809572
## [16,] 0.032067074 -0.003150942 -0.010840289 -0.0084585631 0.031524697
## [17,] -0.057942721 0.239743411 0.059861224 0.0205192962 -0.163937226
## [18,] 0.123965596 -0.135314426 -0.160181677 0.0227323336 0.003037790
## [19,] 0.071382277 0.041661302 -0.118422574 -0.0226363243 0.002203393
## [20,] -0.205020647 -0.187040764 0.800875518 -0.0563573325 0.031515663
## [21,] 0.036337535 -0.034863529 -0.127628544 0.0296357819 -0.007804884
## [22,] 0.004173596 -0.042265498 -0.018327428 0.0006865578 -0.039910000
## [23,] -0.183074229 -0.021456414 -0.497320530 0.0614833670 -0.050022486
## [24,] -0.036435162 0.179083303 -0.023983097 0.0632114435 0.161032026
## [25,] 0.043489615 0.118408269 -0.005635156 0.0532827777 -0.003272473
## [26,] -0.004033653 -0.010759778 -0.030827019 -0.0168735681 0.003310944
## [27,] -0.043930211 0.014591564 0.009990927 -0.0075267547 0.025170908
## [28,] 0.001450485 0.004167399 -0.030741128 -0.0010584496 0.002332620
## [29,] 0.309522938 -0.086818058 -0.013596341 -0.0299197534 0.123148963
## [,33] [,34]
## [1,] 6.234857e-01 -0.5146767355
## [2,] -3.517708e-01 -0.0050747495
## [3,] 1.012645e-02 0.0723572863
## [4,] -3.883079e-02 -0.1345595211
## [5,] -2.817367e-01 0.0677014543
## [6,] -1.341174e-01 0.0847211403
## [7,] -4.454841e-02 -0.0141569048
## [8,] -2.075820e-02 -0.0025583966
## [9,] 2.725212e-02 0.0157638875
## [10,] -4.016997e-02 0.0522958048
## [11,] -2.707268e-02 -0.0483954072
## [12,] -1.324592e-02 -0.0007092301
## [13,] -3.810779e-02 -0.0146958523
## [14,] -4.308111e-02 -0.0927495541
## [15,] -8.323733e-02 -0.0269546429
## [16,] 3.476572e-02 0.0327925879
## [17,] -8.966784e-02 -0.0419126616
## [18,] -1.006986e-03 0.0019321559
## [19,] -1.669897e-02 -0.0308476554
## [20,] -3.114590e-02 -0.0059418619
## [21,] -1.227158e-02 -0.0059306944
## [22,] -4.814718e-02 -0.0606188035
## [23,] -6.169595e-02 -0.0825600035
## [24,] 3.715591e-01 0.8098863238
## [25,] -4.272828e-02 0.0044132055
## [26,] 5.151198e-05 0.0086065880
## [27,] 5.481724e-03 0.0017609952
## [28,] -2.788166e-02 -0.0693495806
## [29,] -2.258334e-01 -0.0838822572
## [ reached getOption("max.print") -- omitted 5 rows ]
mpa<- fa.parallel(malecor, n.obs=70776, n.iter=1000)
## Parallel analysis suggests that the number of factors = 8 and the number of components = 4
fpa<- fa.parallel(femalecor, n.obs=71381, n.iter=1000)
## Parallel analysis suggests that the number of factors = 8 and the number of components = 5
mqqnorm(datafemale, main = "Multi-normal Q-Q Plot")
## 115035 131054
## 44259 60278
mqqnorm(datamale, main = "Multi-normal Q-Q Plot")
## [1] 56401 63098
mqqnorm(datagroup, main = "Multi-normal Q-Q Plot")
## [1] 56401 51628
#mvn(data = datamale, mvnTest = "mardia")
#mvn(data = datafemale, mvnTest = "mardia")
#mvn(data = datagroup, mvnTest = "mardia")
#mvn(data = datamale, mvnTest = "hz", multivariatePlot = "qq", multivariateOutlierMethod = "quan") # time consuming
#mvn(data = datafemale, mvnTest = "hz", multivariatePlot = "qq", multivariateOutlierMethod = "quan") # time consuming
#mvn(data = datagroup, mvnTest = "hz", multivariatePlot = "qq", multivariateOutlierMethod = "quan") # time consuming
# standardized loadings for Jensen's MCV
FAmale<-fa(r=datamale, nfactors=6, max.iter=100, warnings=TRUE, rotate="none", fm="pa", weight=dmale$BY_WTA)
print(FAmale, digits=2, cutoff=.10)
## Factor Analysis using method = pa
## Call: fa(r = datamale, nfactors = 6, rotate = "none", max.iter = 100,
## warnings = TRUE, fm = "pa", weight = dmale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 PA3 PA4 PA5 PA6 h2
## Stest1vocab 0.85 -0.14 -0.04 0.11 -0.03 0.06 0.77
## Stest2literature 0.79 -0.04 -0.21 0.17 0.03 -0.14 0.72
## Stest3music 0.70 -0.05 -0.14 0.16 0.06 -0.09 0.55
## Stest4socialstudies 0.80 -0.08 -0.16 0.10 -0.09 -0.10 0.69
## Stest5math 0.79 0.02 0.01 -0.14 -0.22 -0.09 0.69
## Stest6physicalscience 0.78 -0.21 0.08 0.02 -0.20 -0.03 0.70
## Stest7biologicalscience 0.66 -0.22 0.05 0.10 -0.07 0.04 0.50
## Stest8aeronautics 0.61 -0.27 0.13 0.18 -0.02 0.00 0.50
## Stest9electronics 0.60 -0.32 0.29 0.13 -0.18 0.16 0.63
## Stest10mechanics 0.56 -0.27 0.29 0.15 -0.06 0.28 0.57
## Stest11art 0.69 -0.06 -0.13 0.26 0.14 -0.11 0.60
## Stest12law 0.67 -0.08 -0.08 0.14 0.01 -0.03 0.48
## Stest13health 0.65 -0.05 -0.09 0.14 -0.01 0.06 0.46
## Stest14bible 0.60 -0.05 -0.17 0.06 0.05 -0.12 0.41
## Stest15theater 0.67 0.01 -0.18 0.19 0.12 -0.05 0.54
## Stest16miscellaneous 0.67 -0.04 -0.11 0.15 -0.01 -0.08 0.49
## Stest19disguisedwords 0.65 0.27 -0.08 0.10 0.15 0.14 0.56
## Stest20spelling 0.59 0.23 -0.26 -0.11 0.02 0.19 0.51
## Stest21capitalization 0.61 0.13 -0.12 -0.17 0.05 0.09 0.44
## Stest22punctuation 0.74 0.13 -0.12 -0.30 0.06 0.09 0.68
## Stest23english 0.65 0.05 -0.11 -0.14 0.15 0.16 0.50
## Stest24expression 0.58 0.02 -0.08 -0.14 0.15 0.13 0.40
## Stest25wordfunctions 0.69 0.12 -0.08 -0.27 0.02 -0.02 0.57
## Stest26readingcomprehension 0.86 -0.04 -0.14 -0.01 0.09 0.01 0.77
## Stest28mechanicalreasoning 0.61 -0.17 0.51 -0.08 0.11 0.05 0.68
## Stest29visualization2D 0.38 0.17 0.42 -0.04 0.15 -0.07 0.38
## Stest30visualization3D 0.51 -0.06 0.48 -0.16 0.16 -0.15 0.57
## Stest31abstractreasoning 0.60 0.04 0.24 -0.23 0.13 -0.12 0.51
## Stest32arithreasoning 0.74 0.01 0.06 -0.24 -0.08 -0.01 0.61
## Stest33highschoolmath 0.77 0.10 0.02 -0.32 -0.23 -0.14 0.78
## Stest34arithcomputation 0.52 0.45 -0.03 -0.10 -0.21 0.02 0.54
## Stest35tablereading 0.32 0.55 0.20 0.20 -0.08 0.02 0.49
## Stest36clericalchecking 0.17 0.62 0.12 0.28 -0.08 0.05 0.52
## Stest37objectinspection 0.19 0.45 0.35 0.28 0.04 -0.06 0.44
## u2 com
## Stest1vocab 0.23 1.1
## Stest2literature 0.28 1.3
## Stest3music 0.45 1.3
## Stest4socialstudies 0.31 1.2
## Stest5math 0.31 1.2
## Stest6physicalscience 0.30 1.3
## Stest7biologicalscience 0.50 1.3
## Stest8aeronautics 0.50 1.7
## Stest9electronics 0.37 2.6
## Stest10mechanics 0.43 2.8
## Stest11art 0.40 1.5
## Stest12law 0.52 1.1
## Stest13health 0.54 1.2
## Stest14bible 0.59 1.3
## Stest15theater 0.46 1.4
## Stest16miscellaneous 0.51 1.2
## Stest19disguisedwords 0.44 1.7
## Stest20spelling 0.49 2.1
## Stest21capitalization 0.56 1.4
## Stest22punctuation 0.32 1.5
## Stest23english 0.50 1.4
## Stest24expression 0.60 1.4
## Stest25wordfunctions 0.43 1.4
## Stest26readingcomprehension 0.23 1.1
## Stest28mechanicalreasoning 0.32 2.3
## Stest29visualization2D 0.62 2.6
## Stest30visualization3D 0.43 2.7
## Stest31abstractreasoning 0.49 1.8
## Stest32arithreasoning 0.39 1.3
## Stest33highschoolmath 0.22 1.6
## Stest34arithcomputation 0.46 2.4
## Stest35tablereading 0.51 2.3
## Stest36clericalchecking 0.48 1.7
## Stest37objectinspection 0.56 3.1
##
## PA1 PA2 PA3 PA4 PA5 PA6
## SS loadings 14.19 1.74 1.44 1.05 0.46 0.39
## Proportion Var 0.42 0.05 0.04 0.03 0.01 0.01
## Cumulative Var 0.42 0.47 0.51 0.54 0.56 0.57
## Proportion Explained 0.74 0.09 0.07 0.05 0.02 0.02
## Cumulative Proportion 0.74 0.83 0.90 0.96 0.98 1.00
##
## Mean item complexity = 1.7
## Test of the hypothesis that 6 factors are sufficient.
##
## df null model = 561 with the objective function = 20.6 0.1 with Chi Square = 1457685
## df of the model are 372 and the objective function was 0.43
## 0.1
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
## 0.1
## The harmonic n.obs is 70776 with the empirical chi square 11417.18 with prob < 0
## 0.1The total n.obs was 70776 with Likelihood Chi Square = 30500.78 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.969
## RMSEA index = 0.034 and the 90 % confidence intervals are 0.034 0.034 0.1
## BIC = 26346.55
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA2 PA3 PA4
## Correlation of (regression) scores with factors 0.99 0.89 0.88 0.85
## Multiple R square of scores with factors 0.97 0.79 0.77 0.73
## Minimum correlation of possible factor scores 0.95 0.58 0.55 0.45
## PA5 PA6
## Correlation of (regression) scores with factors 0.74 0.70
## Multiple R square of scores with factors 0.55 0.48
## Minimum correlation of possible factor scores 0.10 -0.03
FAfemale<-fa(r=datafemale, nfactors=6, max.iter=100, warnings=TRUE, rotate="none", fm="pa", weight=dfemale$BY_WTA)
print(FAfemale, digits=2, cutoff=.10)
## Factor Analysis using method = pa
## Call: fa(r = datafemale, nfactors = 6, rotate = "none", max.iter = 100,
## warnings = TRUE, fm = "pa", weight = dfemale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 PA3 PA4 PA5 PA6 h2
## Stest1vocab 0.85 -0.15 -0.04 0.10 0.00 0.03 0.75
## Stest2literature 0.78 -0.14 -0.17 0.16 -0.02 -0.14 0.70
## Stest3music 0.70 -0.11 -0.12 0.15 -0.04 -0.08 0.55
## Stest4socialstudies 0.79 -0.17 -0.09 0.07 0.06 -0.08 0.67
## Stest5math 0.71 -0.03 0.08 -0.15 0.25 -0.15 0.62
## Stest6physicalscience 0.70 -0.20 0.19 0.04 0.26 0.05 0.64
## Stest7biologicalscience 0.64 -0.18 0.08 0.10 0.08 0.09 0.47
## Stest8aeronautics 0.40 -0.16 0.13 0.21 0.03 0.03 0.25
## Stest9electronics 0.40 -0.15 0.18 0.17 0.29 0.20 0.37
## Stest10mechanics 0.50 -0.13 0.23 0.20 0.06 0.22 0.42
## Stest11art 0.68 -0.11 -0.12 0.24 -0.12 -0.12 0.58
## Stest12law 0.58 -0.13 -0.06 0.14 -0.04 -0.03 0.38
## Stest13health 0.58 -0.07 -0.10 0.10 0.00 0.10 0.37
## Stest14bible 0.56 -0.13 -0.06 0.03 -0.03 -0.06 0.34
## Stest15theater 0.65 -0.07 -0.20 0.19 -0.11 -0.12 0.54
## Stest16miscellaneous 0.61 -0.07 -0.06 0.12 0.01 -0.05 0.40
## Stest19disguisedwords 0.63 0.28 -0.20 0.06 -0.08 0.13 0.54
## Stest20spelling 0.57 0.16 -0.31 -0.16 0.02 0.17 0.50
## Stest21capitalization 0.55 0.09 -0.11 -0.19 -0.04 0.09 0.37
## Stest22punctuation 0.74 0.09 -0.09 -0.29 -0.06 0.10 0.67
## Stest23english 0.61 0.03 -0.13 -0.14 -0.11 0.13 0.44
## Stest24expression 0.53 0.01 -0.09 -0.11 -0.18 0.09 0.34
## Stest25wordfunctions 0.72 0.07 -0.02 -0.27 0.00 -0.01 0.59
## Stest26readingcomprehension 0.85 -0.09 -0.11 -0.03 -0.13 -0.01 0.77
## Stest28mechanicalreasoning 0.57 0.03 0.46 0.03 -0.16 0.04 0.57
## Stest29visualization2D 0.37 0.28 0.34 0.04 -0.14 -0.01 0.35
## Stest30visualization3D 0.51 0.10 0.46 -0.05 -0.21 -0.04 0.53
## Stest31abstractreasoning 0.60 0.12 0.23 -0.16 -0.19 -0.05 0.49
## Stest32arithreasoning 0.72 0.01 0.10 -0.22 0.02 -0.02 0.57
## Stest33highschoolmath 0.72 0.03 0.14 -0.31 0.26 -0.22 0.75
## Stest34arithcomputation 0.50 0.38 -0.08 -0.15 0.22 0.00 0.47
## Stest35tablereading 0.28 0.58 -0.04 0.17 0.08 -0.02 0.46
## Stest36clericalchecking 0.19 0.62 -0.10 0.25 0.15 0.00 0.51
## Stest37objectinspection 0.22 0.53 0.12 0.28 -0.03 -0.06 0.43
## u2 com
## Stest1vocab 0.25 1.1
## Stest2literature 0.30 1.3
## Stest3music 0.45 1.2
## Stest4socialstudies 0.33 1.2
## Stest5math 0.38 1.5
## Stest6physicalscience 0.36 1.7
## Stest7biologicalscience 0.53 1.3
## Stest8aeronautics 0.75 2.2
## Stest9electronics 0.63 3.6
## Stest10mechanics 0.58 2.5
## Stest11art 0.42 1.5
## Stest12law 0.62 1.3
## Stest13health 0.63 1.2
## Stest14bible 0.66 1.2
## Stest15theater 0.46 1.5
## Stest16miscellaneous 0.60 1.1
## Stest19disguisedwords 0.46 1.8
## Stest20spelling 0.50 2.1
## Stest21capitalization 0.63 1.5
## Stest22punctuation 0.33 1.4
## Stest23english 0.56 1.4
## Stest24expression 0.66 1.5
## Stest25wordfunctions 0.41 1.3
## Stest26readingcomprehension 0.23 1.1
## Stest28mechanicalreasoning 0.43 2.1
## Stest29visualization2D 0.65 3.2
## Stest30visualization3D 0.47 2.4
## Stest31abstractreasoning 0.51 1.8
## Stest32arithreasoning 0.43 1.2
## Stest33highschoolmath 0.25 2.0
## Stest34arithcomputation 0.53 2.5
## Stest35tablereading 0.54 1.7
## Stest36clericalchecking 0.49 1.7
## Stest37objectinspection 0.57 2.1
##
## PA1 PA2 PA3 PA4 PA5 PA6
## SS loadings 12.68 1.66 1.14 0.97 0.60 0.35
## Proportion Var 0.37 0.05 0.03 0.03 0.02 0.01
## Cumulative Var 0.37 0.42 0.46 0.48 0.50 0.51
## Proportion Explained 0.73 0.10 0.07 0.06 0.03 0.02
## Cumulative Proportion 0.73 0.82 0.89 0.95 0.98 1.00
##
## Mean item complexity = 1.7
## Test of the hypothesis that 6 factors are sufficient.
##
## df null model = 561 with the objective function = 17.28 0.1 with Chi Square = 1233206
## df of the model are 372 and the objective function was 0.33
## 0.1
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
## 0.1
## The harmonic n.obs is 71381 with the empirical chi square 10937.95 with prob < 0
## 0.1The total n.obs was 71381 with Likelihood Chi Square = 23448.6 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.972
## RMSEA index = 0.029 and the 90 % confidence intervals are 0.029 0.03 0.1
## BIC = 19291.21
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA2 PA3 PA4
## Correlation of (regression) scores with factors 0.98 0.88 0.84 0.83
## Multiple R square of scores with factors 0.97 0.77 0.71 0.69
## Minimum correlation of possible factor scores 0.94 0.53 0.41 0.38
## PA5 PA6
## Correlation of (regression) scores with factors 0.76 0.66
## Multiple R square of scores with factors 0.59 0.44
## Minimum correlation of possible factor scores 0.17 -0.12
FA<-fa(r=datagroup, nfactors=6, max.iter=100, warnings=TRUE, rotate="none", fm="pa", weight=dgroup$BY_WTA)
print(FA, digits=2, cutoff=.10)
## Factor Analysis using method = pa
## Call: fa(r = datagroup, nfactors = 6, rotate = "none", max.iter = 100,
## warnings = TRUE, fm = "pa", weight = dgroup$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 PA3 PA4 PA5 PA6 h2
## Stest1vocab 0.85 -0.13 -0.11 0.11 -0.01 0.04 0.76
## Stest2literature 0.79 0.06 -0.17 0.20 0.02 -0.13 0.71
## Stest3music 0.68 0.15 -0.15 0.16 0.08 -0.09 0.55
## Stest4socialstudies 0.79 -0.12 -0.14 0.12 -0.09 -0.08 0.68
## Stest5math 0.75 -0.13 0.03 -0.14 -0.23 -0.13 0.66
## Stest6physicalscience 0.72 -0.37 -0.03 0.00 -0.16 -0.01 0.69
## Stest7biologicalscience 0.64 -0.26 -0.08 0.07 -0.02 0.04 0.49
## Stest8aeronautics 0.48 -0.48 0.00 0.15 -0.01 0.04 0.49
## Stest9electronics 0.47 -0.56 0.06 0.09 -0.15 0.14 0.59
## Stest10mechanics 0.46 -0.62 0.11 0.10 -0.05 0.22 0.67
## Stest11art 0.68 0.09 -0.14 0.25 0.16 -0.11 0.59
## Stest12law 0.63 -0.14 -0.09 0.15 0.00 -0.01 0.44
## Stest13health 0.60 0.12 -0.11 0.13 0.02 0.06 0.41
## Stest14bible 0.58 0.05 -0.15 0.06 0.03 -0.08 0.37
## Stest15theater 0.64 0.23 -0.15 0.21 0.12 -0.08 0.55
## Stest16miscellaneous 0.65 -0.06 -0.07 0.15 -0.02 -0.05 0.45
## Stest19disguisedwords 0.63 0.32 0.12 0.13 0.05 0.17 0.55
## Stest20spelling 0.54 0.45 -0.06 -0.05 -0.09 0.18 0.55
## Stest21capitalization 0.55 0.33 -0.05 -0.14 0.01 0.08 0.45
## Stest22punctuation 0.70 0.35 -0.05 -0.26 0.01 0.10 0.69
## Stest23english 0.61 0.25 -0.09 -0.11 0.08 0.17 0.49
## Stest24expression 0.54 0.20 -0.08 -0.11 0.13 0.14 0.39
## Stest25wordfunctions 0.68 0.25 -0.02 -0.25 -0.02 -0.02 0.59
## Stest26readingcomprehension 0.85 0.12 -0.15 0.00 0.09 0.02 0.77
## Stest28mechanicalreasoning 0.54 -0.56 0.27 -0.13 0.16 0.07 0.72
## Stest29visualization2D 0.38 -0.17 0.41 -0.09 0.19 -0.03 0.39
## Stest30visualization3D 0.51 -0.26 0.28 -0.24 0.29 -0.10 0.56
## Stest31abstractreasoning 0.60 -0.02 0.17 -0.26 0.20 -0.08 0.50
## Stest32arithreasoning 0.73 -0.04 0.04 -0.24 -0.06 -0.02 0.59
## Stest33highschoolmath 0.75 -0.03 0.08 -0.30 -0.26 -0.19 0.76
## Stest34arithcomputation 0.51 0.33 0.27 -0.08 -0.27 -0.01 0.51
## Stest35tablereading 0.30 0.28 0.52 0.19 -0.08 0.00 0.48
## Stest36clericalchecking 0.17 0.35 0.52 0.29 -0.13 0.03 0.52
## Stest37objectinspection 0.20 0.19 0.55 0.23 0.11 -0.07 0.44
## u2 com
## Stest1vocab 0.24 1.1
## Stest2literature 0.29 1.3
## Stest3music 0.45 1.4
## Stest4socialstudies 0.32 1.2
## Stest5math 0.34 1.4
## Stest6physicalscience 0.31 1.6
## Stest7biologicalscience 0.51 1.4
## Stest8aeronautics 0.51 2.2
## Stest9electronics 0.41 2.3
## Stest10mechanics 0.33 2.3
## Stest11art 0.41 1.6
## Stest12law 0.56 1.3
## Stest13health 0.59 1.3
## Stest14bible 0.63 1.2
## Stest15theater 0.45 1.8
## Stest16miscellaneous 0.55 1.2
## Stest19disguisedwords 0.45 1.9
## Stest20spelling 0.45 2.3
## Stest21capitalization 0.55 1.9
## Stest22punctuation 0.31 1.8
## Stest23english 0.51 1.7
## Stest24expression 0.61 1.7
## Stest25wordfunctions 0.41 1.6
## Stest26readingcomprehension 0.23 1.1
## Stest28mechanicalreasoning 0.28 2.8
## Stest29visualization2D 0.61 2.9
## Stest30visualization3D 0.44 3.5
## Stest31abstractreasoning 0.50 1.8
## Stest32arithreasoning 0.41 1.2
## Stest33highschoolmath 0.24 1.8
## Stest34arithcomputation 0.49 3.0
## Stest35tablereading 0.52 2.6
## Stest36clericalchecking 0.48 2.9
## Stest37objectinspection 0.56 2.1
##
## PA1 PA2 PA3 PA4 PA5 PA6
## SS loadings 12.86 2.79 1.52 0.99 0.57 0.34
## Proportion Var 0.38 0.08 0.04 0.03 0.02 0.01
## Cumulative Var 0.38 0.46 0.51 0.53 0.55 0.56
## Proportion Explained 0.67 0.15 0.08 0.05 0.03 0.02
## Cumulative Proportion 0.67 0.82 0.90 0.95 0.98 1.00
##
## Mean item complexity = 1.9
## Test of the hypothesis that 6 factors are sufficient.
##
## df null model = 561 with the objective function = 19.78 0.1 with Chi Square = 2811987
## df of the model are 372 and the objective function was 0.39
## 0.1
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
## 0.1
## The harmonic n.obs is 142157 with the empirical chi square 21250.84 with prob < 0
## 0.1The total n.obs was 142157 with Likelihood Chi Square = 55015.06 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.971
## RMSEA index = 0.032 and the 90 % confidence intervals are 0.032 0.032 0.1
## BIC = 50601.39
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA2 PA3 PA4
## Correlation of (regression) scores with factors 0.99 0.94 0.87 0.84
## Multiple R square of scores with factors 0.97 0.88 0.76 0.71
## Minimum correlation of possible factor scores 0.94 0.75 0.52 0.43
## PA5 PA6
## Correlation of (regression) scores with factors 0.77 0.69
## Multiple R square of scores with factors 0.59 0.47
## Minimum correlation of possible factor scores 0.18 -0.06
# EFA: The rotate options "promax" and "Promax" differ slightly. Because unlike "Promax", the "promax" performs a Kaiser normalization before rotation, which is recommended according to Kaizer.
male5<-fa(datamale, nfactors=5, rotate="promax", fm="minres", weight=dmale$BY_WTA)
print(male5, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datamale, nfactors = 5, rotate = "promax", fm = "minres",
## weight = dmale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR4 MR3 MR2 MR5 h2 u2 com
## Stest1vocab 0.68 0.14 0.08 -0.02 0.14 0.77 0.23 1.2
## Stest2literature 0.76 0.17 -0.11 0.03 0.02 0.70 0.30 1.1
## Stest3music 0.67 0.11 -0.04 0.02 -0.02 0.54 0.46 1.1
## Stest4socialstudies 0.65 0.22 -0.11 0.00 0.17 0.68 0.32 1.4
## Stest5math 0.19 0.49 0.03 0.03 0.36 0.69 0.31 2.2
## Stest6physicalscience 0.46 0.15 0.11 -0.04 0.37 0.71 0.29 2.3
## Stest7biologicalscience 0.55 -0.01 0.14 -0.05 0.17 0.50 0.50 1.4
## Stest8aeronautics 0.62 -0.18 0.22 -0.03 0.12 0.50 0.50 1.5
## Stest9electronics 0.45 -0.19 0.32 -0.01 0.31 0.58 0.42 3.1
## Stest10mechanics 0.44 -0.19 0.35 0.00 0.16 0.46 0.54 2.6
## Stest11art 0.80 -0.03 0.00 0.05 -0.11 0.58 0.42 1.0
## Stest12law 0.61 0.08 0.01 0.01 0.05 0.48 0.52 1.1
## Stest13health 0.60 0.09 -0.03 0.04 0.06 0.46 0.54 1.1
## Stest14bible 0.51 0.20 -0.06 -0.05 0.00 0.39 0.61 1.4
## Stest15theater 0.70 0.10 -0.06 0.05 -0.11 0.53 0.47 1.1
## Stest16miscellaneous 0.61 0.11 -0.04 0.05 0.06 0.49 0.51 1.1
## Stest19disguisedwords 0.41 0.29 0.03 0.23 -0.15 0.53 0.47 2.8
## Stest20spelling 0.21 0.58 -0.18 0.05 -0.01 0.47 0.53 1.5
## Stest21capitalization 0.13 0.56 0.02 -0.03 0.02 0.44 0.56 1.1
## Stest22punctuation 0.04 0.77 0.09 -0.09 0.04 0.67 0.33 1.1
## Stest23english 0.25 0.48 0.11 -0.09 -0.08 0.47 0.53 1.8
## Stest24expression 0.20 0.43 0.14 -0.10 -0.09 0.39 0.61 1.9
## Stest25wordfunctions 0.03 0.69 0.09 -0.06 0.08 0.57 0.43 1.1
## Stest26readingcomprehension 0.56 0.38 0.06 -0.08 -0.01 0.77 0.23 1.8
## Stest28mechanicalreasoning 0.07 0.03 0.75 -0.02 0.07 0.69 0.31 1.0
## Stest29visualization2D -0.11 0.09 0.55 0.23 -0.05 0.38 0.62 1.5
## Stest30visualization3D -0.10 0.16 0.70 0.00 0.02 0.53 0.47 1.1
## Stest31abstractreasoning -0.07 0.43 0.46 -0.03 0.02 0.49 0.51 2.1
## Stest32arithreasoning 0.04 0.57 0.19 -0.06 0.23 0.61 0.39 1.6
## Stest33highschoolmath -0.06 0.73 0.07 0.00 0.38 0.75 0.25 1.5
## Stest34arithcomputation -0.10 0.57 -0.15 0.38 0.26 0.54 0.46 2.4
## Stest35tablereading 0.01 0.07 0.04 0.66 0.07 0.49 0.51 1.0
## Stest36clericalchecking 0.03 -0.02 -0.11 0.73 0.02 0.51 0.49 1.1
## Stest37objectinspection 0.04 -0.20 0.24 0.64 -0.06 0.44 0.56 1.5
##
## MR1 MR4 MR3 MR2 MR5
## SS loadings 7.69 5.52 2.59 1.71 1.30
## Proportion Var 0.23 0.16 0.08 0.05 0.04
## Cumulative Var 0.23 0.39 0.46 0.51 0.55
## Proportion Explained 0.41 0.29 0.14 0.09 0.07
## Cumulative Proportion 0.41 0.70 0.84 0.93 1.00
##
## With factor correlations of
## MR1 MR4 MR3 MR2 MR5
## MR1 1.00 0.68 0.54 0.19 0.35
## MR4 0.68 1.00 0.42 0.35 0.15
## MR3 0.54 0.42 1.00 0.18 0.40
## MR2 0.19 0.35 0.18 1.00 -0.08
## MR5 0.35 0.15 0.40 -0.08 1.00
##
## Mean item complexity = 1.6
## Test of the hypothesis that 5 factors are sufficient.
##
## df null model = 561 with the objective function = 20.6 0.1 with Chi Square = 1457685
## df of the model are 401 and the objective function was 0.67
## 0.1
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.02
## 0.1
## The harmonic n.obs is 70776 with the empirical chi square 20842.95 with prob < 0
## 0.1The total n.obs was 70776 with Likelihood Chi Square = 47126.09 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.955
## RMSEA index = 0.041 and the 90 % confidence intervals are 0.04 0.041 0.1
## BIC = 42648.01
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR4 MR3 MR2
## Correlation of (regression) scores with factors 0.97 0.95 0.92 0.88
## Multiple R square of scores with factors 0.94 0.91 0.85 0.78
## Minimum correlation of possible factor scores 0.89 0.82 0.69 0.55
## MR5
## Correlation of (regression) scores with factors 0.83
## Multiple R square of scores with factors 0.68
## Minimum correlation of possible factor scores 0.36
male6<-fa(datamale, nfactors=6, rotate="promax", fm="minres", weight=dmale$BY_WTA)
print(male6, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datamale, nfactors = 6, rotate = "promax", fm = "minres",
## weight = dmale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR4 MR6 MR3 MR5 MR2 h2
## Stest1vocab 0.50 0.17 0.30 -0.03 0.05 -0.01 0.77
## Stest2literature 0.90 0.02 -0.12 -0.03 0.06 0.01 0.72
## Stest3music 0.75 0.03 -0.05 0.00 -0.01 0.01 0.55
## Stest4socialstudies 0.69 0.05 0.03 -0.08 0.19 -0.01 0.69
## Stest5math 0.21 0.22 0.09 0.04 0.44 0.03 0.69
## Stest6physicalscience 0.33 0.01 0.35 0.01 0.30 -0.04 0.70
## Stest7biologicalscience 0.38 0.00 0.35 0.01 0.06 -0.05 0.50
## Stest8aeronautics 0.47 -0.16 0.35 0.10 -0.01 -0.03 0.50
## Stest9electronics 0.04 -0.09 0.74 0.03 0.09 0.01 0.63
## Stest10mechanics -0.06 0.06 0.79 0.03 -0.10 0.04 0.57
## Stest11art 0.91 -0.07 -0.08 0.05 -0.12 0.04 0.60
## Stest12law 0.58 0.05 0.09 -0.01 0.02 0.01 0.48
## Stest13health 0.46 0.14 0.20 -0.10 0.00 0.05 0.46
## Stest14bible 0.64 0.07 -0.14 0.02 0.05 -0.06 0.41
## Stest15theater 0.76 0.09 -0.08 -0.02 -0.10 0.05 0.53
## Stest16miscellaneous 0.65 0.01 0.01 -0.02 0.06 0.04 0.49
## Stest19disguisedwords 0.29 0.46 0.04 -0.01 -0.17 0.24 0.56
## Stest20spelling 0.06 0.71 0.01 -0.21 0.02 0.07 0.51
## Stest21capitalization 0.07 0.57 -0.02 0.02 0.07 -0.02 0.44
## Stest22punctuation 0.00 0.74 -0.04 0.09 0.14 -0.08 0.68
## Stest23english 0.10 0.63 0.07 0.05 -0.10 -0.08 0.50
## Stest24expression 0.10 0.54 0.05 0.10 -0.09 -0.09 0.40
## Stest25wordfunctions 0.10 0.54 -0.12 0.14 0.21 -0.06 0.57
## Stest26readingcomprehension 0.54 0.37 0.02 0.05 0.01 -0.08 0.77
## Stest28mechanicalreasoning -0.11 0.06 0.40 0.58 -0.03 -0.01 0.68
## Stest29visualization2D -0.05 0.02 0.01 0.55 -0.02 0.22 0.38
## Stest30visualization3D 0.02 -0.02 0.01 0.73 0.05 -0.02 0.57
## Stest31abstractreasoning 0.07 0.24 -0.11 0.52 0.13 -0.05 0.51
## Stest32arithreasoning 0.02 0.41 0.09 0.16 0.30 -0.05 0.61
## Stest33highschoolmath 0.05 0.36 -0.07 0.13 0.57 -0.01 0.78
## Stest34arithcomputation -0.10 0.42 -0.04 -0.12 0.37 0.38 0.54
## Stest35tablereading -0.02 0.06 0.04 0.03 0.09 0.65 0.49
## Stest36clericalchecking -0.01 0.04 0.00 -0.11 0.03 0.73 0.52
## Stest37objectinspection 0.09 -0.21 -0.01 0.25 -0.06 0.62 0.44
## u2 com
## Stest1vocab 0.23 1.9
## Stest2literature 0.28 1.0
## Stest3music 0.45 1.0
## Stest4socialstudies 0.31 1.2
## Stest5math 0.31 2.1
## Stest6physicalscience 0.30 3.0
## Stest7biologicalscience 0.50 2.1
## Stest8aeronautics 0.50 2.2
## Stest9electronics 0.37 1.1
## Stest10mechanics 0.43 1.1
## Stest11art 0.40 1.1
## Stest12law 0.52 1.1
## Stest13health 0.54 1.7
## Stest14bible 0.59 1.2
## Stest15theater 0.47 1.1
## Stest16miscellaneous 0.51 1.0
## Stest19disguisedwords 0.44 2.6
## Stest20spelling 0.49 1.2
## Stest21capitalization 0.56 1.1
## Stest22punctuation 0.32 1.1
## Stest23english 0.50 1.2
## Stest24expression 0.60 1.3
## Stest25wordfunctions 0.43 1.7
## Stest26readingcomprehension 0.23 1.9
## Stest28mechanicalreasoning 0.32 1.9
## Stest29visualization2D 0.62 1.3
## Stest30visualization3D 0.43 1.0
## Stest31abstractreasoning 0.49 1.7
## Stest32arithreasoning 0.39 2.4
## Stest33highschoolmath 0.22 1.9
## Stest34arithcomputation 0.46 3.3
## Stest35tablereading 0.51 1.1
## Stest36clericalchecking 0.48 1.1
## Stest37objectinspection 0.56 1.7
##
## MR1 MR4 MR6 MR3 MR5 MR2
## SS loadings 6.88 4.58 2.35 2.03 1.74 1.68
## Proportion Var 0.20 0.13 0.07 0.06 0.05 0.05
## Cumulative Var 0.20 0.34 0.41 0.47 0.52 0.57
## Proportion Explained 0.36 0.24 0.12 0.11 0.09 0.09
## Cumulative Proportion 0.36 0.60 0.72 0.82 0.91 1.00
##
## With factor correlations of
## MR1 MR4 MR6 MR3 MR5 MR2
## MR1 1.00 0.75 0.70 0.50 0.55 0.20
## MR4 0.75 1.00 0.49 0.48 0.53 0.29
## MR6 0.70 0.49 1.00 0.59 0.48 0.05
## MR3 0.50 0.48 0.59 1.00 0.46 0.21
## MR5 0.55 0.53 0.48 0.46 1.00 0.10
## MR2 0.20 0.29 0.05 0.21 0.10 1.00
##
## Mean item complexity = 1.6
## Test of the hypothesis that 6 factors are sufficient.
##
## df null model = 561 with the objective function = 20.6 0.1 with Chi Square = 1457685
## df of the model are 372 and the objective function was 0.43
## 0.1
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
## 0.1
## The harmonic n.obs is 70776 with the empirical chi square 11417.1 with prob < 0
## 0.1The total n.obs was 70776 with Likelihood Chi Square = 30500.3 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.969
## RMSEA index = 0.034 and the 90 % confidence intervals are 0.034 0.034 0.1
## BIC = 26346.08
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR4 MR6 MR3
## Correlation of (regression) scores with factors 0.97 0.95 0.93 0.91
## Multiple R square of scores with factors 0.95 0.90 0.87 0.82
## Minimum correlation of possible factor scores 0.89 0.80 0.73 0.65
## MR5 MR2
## Correlation of (regression) scores with factors 0.89 0.88
## Multiple R square of scores with factors 0.79 0.77
## Minimum correlation of possible factor scores 0.58 0.54
male7<-fa(datamale, nfactors=7, rotate="promax", fm="minres", weight=dmale$BY_WTA)
print(male7, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datamale, nfactors = 7, rotate = "promax", fm = "minres",
## weight = dmale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR4 MR6 MR3 MR2 MR5 MR7
## Stest1vocab 0.51 0.18 0.30 -0.03 -0.01 0.04 0.05
## Stest2literature 0.90 0.03 -0.11 -0.03 0.01 0.05 0.03
## Stest3music 0.76 0.04 -0.03 0.04 -0.05 0.08 0.23
## Stest4socialstudies 0.72 0.06 0.00 -0.11 0.05 0.10 -0.17
## Stest5math 0.21 0.29 0.11 0.05 -0.01 0.40 -0.01
## Stest6physicalscience 0.32 0.05 0.37 0.02 -0.07 0.28 -0.01
## Stest7biologicalscience 0.39 0.00 0.34 0.00 -0.01 0.01 -0.10
## Stest8aeronautics 0.47 -0.17 0.35 0.10 -0.04 0.01 0.01
## Stest9electronics 0.03 -0.08 0.77 0.05 -0.03 0.13 0.06
## Stest10mechanics -0.05 0.05 0.77 0.03 0.05 -0.10 0.02
## Stest11art 0.90 -0.08 -0.07 0.06 0.02 -0.07 0.12
## Stest12law 0.60 0.04 0.08 -0.03 0.05 -0.03 -0.07
## Stest13health 0.47 0.14 0.19 -0.11 0.07 -0.04 -0.02
## Stest14bible 0.67 0.07 -0.16 0.00 -0.01 -0.01 -0.11
## Stest15theater 0.76 0.09 -0.07 0.00 0.01 -0.04 0.18
## Stest16miscellaneous 0.65 0.02 0.02 -0.01 0.02 0.07 0.06
## Stest19disguisedwords 0.26 0.52 0.08 0.03 0.17 -0.08 0.40
## Stest20spelling 0.04 0.78 0.03 -0.19 0.03 0.06 0.24
## Stest21capitalization 0.08 0.61 -0.03 0.01 -0.01 0.05 0.04
## Stest22punctuation -0.01 0.80 -0.04 0.09 -0.09 0.12 0.09
## Stest23english 0.11 0.65 0.06 0.05 -0.07 -0.09 0.11
## Stest24expression 0.10 0.57 0.02 0.08 -0.05 -0.13 0.00
## Stest25wordfunctions 0.10 0.61 -0.12 0.14 -0.07 0.18 0.04
## Stest26readingcomprehension 0.56 0.39 -0.01 0.02 -0.02 -0.08 -0.09
## Stest28mechanicalreasoning -0.11 0.06 0.40 0.57 -0.02 -0.02 0.02
## Stest29visualization2D -0.05 0.02 0.01 0.55 0.21 -0.01 0.04
## Stest30visualization3D 0.01 -0.01 0.02 0.73 -0.03 0.06 -0.01
## Stest31abstractreasoning 0.07 0.27 -0.11 0.51 -0.04 0.10 -0.02
## Stest32arithreasoning 0.02 0.46 0.08 0.15 -0.02 0.21 -0.12
## Stest33highschoolmath 0.04 0.45 -0.05 0.14 -0.04 0.50 -0.05
## Stest34arithcomputation -0.10 0.48 -0.04 -0.12 0.38 0.28 -0.04
## Stest35tablereading -0.01 0.06 0.02 0.00 0.70 0.01 -0.06
## Stest36clericalchecking -0.02 0.04 0.01 -0.10 0.69 0.03 0.14
## Stest37objectinspection 0.10 -0.23 -0.02 0.24 0.62 -0.06 0.03
## h2 u2 com
## Stest1vocab 0.77 0.23 2.0
## Stest2literature 0.72 0.28 1.0
## Stest3music 0.58 0.42 1.2
## Stest4socialstudies 0.72 0.28 1.2
## Stest5math 0.70 0.30 2.6
## Stest6physicalscience 0.71 0.29 3.0
## Stest7biologicalscience 0.51 0.49 2.1
## Stest8aeronautics 0.50 0.50 2.3
## Stest9electronics 0.64 0.36 1.1
## Stest10mechanics 0.57 0.43 1.1
## Stest11art 0.60 0.40 1.1
## Stest12law 0.49 0.51 1.1
## Stest13health 0.47 0.53 1.7
## Stest14bible 0.43 0.57 1.2
## Stest15theater 0.54 0.46 1.2
## Stest16miscellaneous 0.49 0.51 1.1
## Stest19disguisedwords 0.61 0.39 2.8
## Stest20spelling 0.53 0.47 1.3
## Stest21capitalization 0.44 0.56 1.1
## Stest22punctuation 0.67 0.33 1.1
## Stest23english 0.50 0.50 1.2
## Stest24expression 0.42 0.58 1.2
## Stest25wordfunctions 0.57 0.43 1.5
## Stest26readingcomprehension 0.80 0.20 1.9
## Stest28mechanicalreasoning 0.68 0.32 1.9
## Stest29visualization2D 0.38 0.62 1.3
## Stest30visualization3D 0.57 0.43 1.0
## Stest31abstractreasoning 0.51 0.49 1.8
## Stest32arithreasoning 0.62 0.38 1.9
## Stest33highschoolmath 0.79 0.21 2.2
## Stest34arithcomputation 0.54 0.46 2.9
## Stest35tablereading 0.52 0.48 1.0
## Stest36clericalchecking 0.51 0.49 1.1
## Stest37objectinspection 0.44 0.56 1.7
##
## MR1 MR4 MR6 MR3 MR2 MR5 MR7
## SS loadings 6.94 5.11 2.39 2.01 1.65 1.28 0.18
## Proportion Var 0.20 0.15 0.07 0.06 0.05 0.04 0.01
## Cumulative Var 0.20 0.35 0.42 0.48 0.53 0.57 0.58
## Proportion Explained 0.35 0.26 0.12 0.10 0.08 0.07 0.01
## Cumulative Proportion 0.35 0.62 0.74 0.84 0.93 0.99 1.00
##
## With factor correlations of
## MR1 MR4 MR6 MR3 MR2 MR5 MR7
## MR1 1.00 0.77 0.71 0.50 0.24 0.44 -0.33
## MR4 0.77 1.00 0.54 0.50 0.31 0.42 -0.40
## MR6 0.71 0.54 1.00 0.59 0.11 0.34 -0.39
## MR3 0.50 0.50 0.59 1.00 0.27 0.33 -0.32
## MR2 0.24 0.31 0.11 0.27 1.00 0.22 0.08
## MR5 0.44 0.42 0.34 0.33 0.22 1.00 -0.16
## MR7 -0.33 -0.40 -0.39 -0.32 0.08 -0.16 1.00
##
## Mean item complexity = 1.6
## Test of the hypothesis that 7 factors are sufficient.
##
## df null model = 561 with the objective function = 20.6 0.1 with Chi Square = 1457685
## df of the model are 344 and the objective function was 0.29
## 0.1
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
## 0.1
## The harmonic n.obs is 70776 with the empirical chi square 7354.69 with prob < 0
## 0.1The total n.obs was 70776 with Likelihood Chi Square = 20666.17 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.977
## RMSEA index = 0.029 and the 90 % confidence intervals are 0.029 0.029 0.1
## BIC = 16824.63
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR4 MR6 MR3
## Correlation of (regression) scores with factors 0.97 0.95 0.93 0.91
## Multiple R square of scores with factors 0.95 0.91 0.87 0.82
## Minimum correlation of possible factor scores 0.90 0.82 0.74 0.64
## MR2 MR5 MR7
## Correlation of (regression) scores with factors 0.88 0.85 0.75
## Multiple R square of scores with factors 0.78 0.72 0.56
## Minimum correlation of possible factor scores 0.55 0.43 0.11
female5<-fa(datafemale, nfactors=5, rotate="promax", fm="minres", weight=dfemale$BY_WTA)
print(female5, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datafemale, nfactors = 5, rotate = "promax", fm = "minres",
## weight = dfemale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR4 MR5 MR3 MR2 h2 u2 com
## Stest1vocab 0.62 0.17 0.18 0.01 -0.02 0.75 0.25 1.3
## Stest2literature 0.75 0.11 0.09 -0.10 0.01 0.67 0.33 1.1
## Stest3music 0.66 0.07 0.07 -0.04 0.02 0.54 0.46 1.1
## Stest4socialstudies 0.57 0.21 0.21 -0.09 -0.04 0.66 0.34 1.6
## Stest5math -0.01 0.52 0.41 -0.01 -0.01 0.60 0.40 1.9
## Stest6physicalscience 0.16 0.19 0.58 0.02 -0.05 0.65 0.35 1.4
## Stest7biologicalscience 0.38 0.07 0.30 0.05 -0.05 0.46 0.54 2.0
## Stest8aeronautics 0.36 -0.19 0.25 0.10 0.00 0.25 0.75 2.6
## Stest9electronics 0.12 -0.06 0.53 -0.03 0.05 0.31 0.69 1.2
## Stest10mechanics 0.29 -0.13 0.32 0.19 0.02 0.35 0.65 3.0
## Stest11art 0.80 -0.08 -0.01 0.01 0.04 0.56 0.44 1.0
## Stest12law 0.56 0.01 0.09 0.00 -0.01 0.38 0.62 1.0
## Stest13health 0.50 0.11 0.09 -0.06 0.03 0.36 0.64 1.2
## Stest14bible 0.43 0.16 0.07 0.00 -0.07 0.34 0.66 1.4
## Stest15theater 0.76 0.02 -0.06 -0.07 0.06 0.52 0.48 1.0
## Stest16miscellaneous 0.49 0.08 0.13 -0.02 0.04 0.40 0.60 1.2
## Stest19disguisedwords 0.43 0.30 -0.14 -0.01 0.29 0.52 0.48 2.9
## Stest20spelling 0.25 0.58 -0.10 -0.20 0.10 0.47 0.53 1.7
## Stest21capitalization 0.15 0.51 -0.08 0.03 -0.01 0.36 0.64 1.2
## Stest22punctuation 0.13 0.71 -0.08 0.10 -0.07 0.66 0.34 1.2
## Stest23english 0.31 0.44 -0.12 0.05 -0.05 0.43 0.57 2.1
## Stest24expression 0.33 0.32 -0.19 0.12 -0.07 0.33 0.67 3.0
## Stest25wordfunctions 0.05 0.67 0.03 0.11 -0.06 0.60 0.40 1.1
## Stest26readingcomprehension 0.60 0.34 -0.05 0.08 -0.08 0.77 0.23 1.7
## Stest28mechanicalreasoning 0.04 -0.01 0.11 0.67 -0.02 0.57 0.43 1.1
## Stest29visualization2D -0.08 0.03 -0.01 0.55 0.21 0.35 0.65 1.3
## Stest30visualization3D -0.07 0.08 0.01 0.72 -0.02 0.53 0.47 1.1
## Stest31abstractreasoning 0.02 0.34 -0.09 0.50 -0.03 0.49 0.51 1.9
## Stest32arithreasoning 0.03 0.54 0.14 0.20 -0.08 0.57 0.43 1.5
## Stest33highschoolmath -0.20 0.69 0.37 0.07 -0.04 0.66 0.34 1.8
## Stest34arithcomputation -0.18 0.61 0.17 -0.10 0.33 0.48 0.52 2.0
## Stest35tablereading 0.00 0.11 0.00 0.04 0.63 0.46 0.54 1.1
## Stest36clericalchecking 0.01 0.03 0.04 -0.09 0.72 0.51 0.49 1.0
## Stest37objectinspection 0.06 -0.16 -0.02 0.25 0.60 0.43 0.57 1.5
##
## MR1 MR4 MR5 MR3 MR2
## SS loadings 6.30 5.02 2.04 2.01 1.61
## Proportion Var 0.19 0.15 0.06 0.06 0.05
## Cumulative Var 0.19 0.33 0.39 0.45 0.50
## Proportion Explained 0.37 0.30 0.12 0.12 0.09
## Cumulative Proportion 0.37 0.67 0.79 0.91 1.00
##
## With factor correlations of
## MR1 MR4 MR5 MR3 MR2
## MR1 1.00 0.70 0.58 0.56 0.16
## MR4 0.70 1.00 0.44 0.52 0.27
## MR5 0.58 0.44 1.00 0.53 0.01
## MR3 0.56 0.52 0.53 1.00 0.21
## MR2 0.16 0.27 0.01 0.21 1.00
##
## Mean item complexity = 1.6
## Test of the hypothesis that 5 factors are sufficient.
##
## df null model = 561 with the objective function = 17.28 0.1 with Chi Square = 1233206
## df of the model are 401 and the objective function was 0.51
## 0.1
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.02
## 0.1
## The harmonic n.obs is 71381 with the empirical chi square 18707.55 with prob < 0
## 0.1The total n.obs was 71381 with Likelihood Chi Square = 36053.6 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.96
## RMSEA index = 0.035 and the 90 % confidence intervals are 0.035 0.036 0.1
## BIC = 31572.11
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR4 MR5 MR3
## Correlation of (regression) scores with factors 0.97 0.95 0.89 0.90
## Multiple R square of scores with factors 0.93 0.91 0.79 0.81
## Minimum correlation of possible factor scores 0.86 0.81 0.58 0.62
## MR2
## Correlation of (regression) scores with factors 0.87
## Multiple R square of scores with factors 0.76
## Minimum correlation of possible factor scores 0.51
female6<-fa(datafemale, nfactors=6, rotate="promax", fm="minres", weight=dfemale$BY_WTA)
print(female6, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datafemale, nfactors = 6, rotate = "promax", fm = "minres",
## weight = dfemale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR4 MR3 MR6 MR2 MR5 h2
## Stest1vocab 0.56 0.18 0.01 0.03 -0.03 0.18 0.75
## Stest2literature 0.89 -0.02 -0.09 0.10 0.03 -0.08 0.70
## Stest3music 0.72 0.03 -0.03 0.04 0.03 -0.02 0.55
## Stest4socialstudies 0.66 0.06 -0.08 0.18 -0.03 0.06 0.67
## Stest5math 0.20 0.03 0.01 0.57 0.01 0.09 0.62
## Stest6physicalscience 0.15 -0.02 0.02 0.30 -0.05 0.48 0.64
## Stest7biologicalscience 0.28 0.10 0.04 0.03 -0.06 0.34 0.47
## Stest8aeronautics 0.32 -0.16 0.10 -0.04 -0.01 0.27 0.25
## Stest9electronics -0.07 -0.02 -0.07 0.06 0.03 0.67 0.37
## Stest10mechanics 0.03 0.06 0.17 -0.15 0.00 0.55 0.42
## Stest11art 0.89 -0.08 0.01 -0.05 0.06 -0.09 0.58
## Stest12law 0.57 0.02 0.00 -0.01 0.00 0.06 0.38
## Stest13health 0.35 0.26 -0.07 -0.09 0.02 0.19 0.37
## Stest14bible 0.48 0.08 0.01 0.08 -0.06 -0.01 0.34
## Stest15theater 0.86 0.01 -0.06 -0.03 0.08 -0.16 0.54
## Stest16miscellaneous 0.54 0.02 -0.02 0.07 0.05 0.05 0.40
## Stest19disguisedwords 0.22 0.53 -0.02 -0.17 0.27 0.02 0.54
## Stest20spelling 0.02 0.76 -0.22 -0.02 0.08 0.04 0.50
## Stest21capitalization 0.02 0.57 0.03 0.04 -0.02 -0.01 0.37
## Stest22punctuation -0.02 0.73 0.11 0.10 -0.08 -0.02 0.67
## Stest23english 0.12 0.61 0.04 -0.07 -0.07 0.00 0.44
## Stest24expression 0.18 0.50 0.12 -0.13 -0.08 -0.07 0.34
## Stest25wordfunctions 0.06 0.49 0.13 0.26 -0.05 -0.07 0.59
## Stest26readingcomprehension 0.57 0.36 0.09 0.01 -0.08 -0.07 0.77
## Stest28mechanicalreasoning -0.01 -0.01 0.68 -0.01 -0.02 0.17 0.57
## Stest29visualization2D -0.09 -0.01 0.56 0.00 0.21 0.01 0.35
## Stest30visualization3D -0.04 -0.02 0.74 0.05 -0.01 -0.01 0.53
## Stest31abstractreasoning 0.06 0.22 0.52 0.11 -0.02 -0.14 0.49
## Stest32arithreasoning 0.06 0.33 0.22 0.28 -0.08 0.03 0.57
## Stest33highschoolmath 0.07 0.05 0.10 0.74 -0.01 -0.03 0.75
## Stest34arithcomputation -0.15 0.37 -0.09 0.34 0.33 0.05 0.47
## Stest35tablereading 0.01 0.07 0.04 0.05 0.63 -0.02 0.46
## Stest36clericalchecking 0.00 0.03 -0.10 0.01 0.72 0.05 0.51
## Stest37objectinspection 0.11 -0.18 0.25 -0.05 0.61 -0.04 0.43
## u2 com
## Stest1vocab 0.25 1.4
## Stest2literature 0.30 1.1
## Stest3music 0.45 1.0
## Stest4socialstudies 0.33 1.2
## Stest5math 0.38 1.3
## Stest6physicalscience 0.36 1.9
## Stest7biologicalscience 0.53 2.2
## Stest8aeronautics 0.75 2.7
## Stest9electronics 0.63 1.1
## Stest10mechanics 0.58 1.4
## Stest11art 0.42 1.1
## Stest12law 0.62 1.0
## Stest13health 0.63 2.7
## Stest14bible 0.66 1.2
## Stest15theater 0.46 1.1
## Stest16miscellaneous 0.60 1.1
## Stest19disguisedwords 0.46 2.1
## Stest20spelling 0.50 1.2
## Stest21capitalization 0.63 1.0
## Stest22punctuation 0.33 1.1
## Stest23english 0.56 1.1
## Stest24expression 0.66 1.6
## Stest25wordfunctions 0.41 1.8
## Stest26readingcomprehension 0.23 1.8
## Stest28mechanicalreasoning 0.43 1.1
## Stest29visualization2D 0.65 1.3
## Stest30visualization3D 0.47 1.0
## Stest31abstractreasoning 0.51 1.7
## Stest32arithreasoning 0.43 3.0
## Stest33highschoolmath 0.25 1.1
## Stest34arithcomputation 0.53 3.5
## Stest35tablereading 0.54 1.0
## Stest36clericalchecking 0.49 1.1
## Stest37objectinspection 0.57 1.6
##
## MR1 MR4 MR3 MR6 MR2 MR5
## SS loadings 6.08 4.05 2.10 1.96 1.62 1.59
## Proportion Var 0.18 0.12 0.06 0.06 0.05 0.05
## Cumulative Var 0.18 0.30 0.36 0.42 0.46 0.51
## Proportion Explained 0.35 0.23 0.12 0.11 0.09 0.09
## Cumulative Proportion 0.35 0.58 0.70 0.82 0.91 1.00
##
## With factor correlations of
## MR1 MR4 MR3 MR6 MR2 MR5
## MR1 1.00 0.75 0.59 0.58 0.14 0.71
## MR4 0.75 1.00 0.55 0.67 0.29 0.48
## MR3 0.59 0.55 1.00 0.52 0.22 0.55
## MR6 0.58 0.67 0.52 1.00 0.14 0.52
## MR2 0.14 0.29 0.22 0.14 1.00 0.06
## MR5 0.71 0.48 0.55 0.52 0.06 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 6 factors are sufficient.
##
## df null model = 561 with the objective function = 17.28 0.1 with Chi Square = 1233206
## df of the model are 372 and the objective function was 0.33
## 0.1
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
## 0.1
## The harmonic n.obs is 71381 with the empirical chi square 10937.72 with prob < 0
## 0.1The total n.obs was 71381 with Likelihood Chi Square = 23442.78 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.972
## RMSEA index = 0.029 and the 90 % confidence intervals are 0.029 0.03 0.1
## BIC = 19285.38
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR4 MR3 MR6
## Correlation of (regression) scores with factors 0.97 0.95 0.91 0.92
## Multiple R square of scores with factors 0.94 0.90 0.82 0.84
## Minimum correlation of possible factor scores 0.88 0.80 0.64 0.68
## MR2 MR5
## Correlation of (regression) scores with factors 0.87 0.89
## Multiple R square of scores with factors 0.76 0.79
## Minimum correlation of possible factor scores 0.51 0.58
female7<-fa(datafemale, nfactors=7, rotate="promax", fm="minres", weight=dfemale$BY_WTA)
print(female7, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datafemale, nfactors = 7, rotate = "promax", fm = "minres",
## weight = dfemale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR4 MR3 MR6 MR5 MR2 MR7
## Stest1vocab 0.53 0.19 0.01 0.03 0.18 -0.03 0.05
## Stest2literature 0.83 -0.02 -0.10 0.07 -0.07 0.05 0.14
## Stest3music 0.70 0.07 0.01 0.09 0.00 -0.04 -0.10
## Stest4socialstudies 0.62 0.03 -0.11 0.10 0.04 0.04 0.25
## Stest5math 0.20 0.06 0.03 0.56 0.12 -0.04 -0.03
## Stest6physicalscience 0.14 -0.01 0.02 0.26 0.49 -0.06 0.06
## Stest7biologicalscience 0.25 0.08 0.00 -0.04 0.34 0.00 0.20
## Stest8aeronautics 0.31 -0.15 0.11 0.00 0.29 -0.04 -0.04
## Stest9electronics -0.07 -0.01 -0.05 0.08 0.68 0.00 -0.07
## Stest10mechanics 0.03 0.05 0.16 -0.15 0.54 0.02 0.04
## Stest11art 0.85 -0.05 0.04 0.00 -0.08 0.01 -0.05
## Stest12law 0.53 0.00 -0.02 -0.05 0.04 0.04 0.16
## Stest13health 0.33 0.25 -0.09 -0.11 0.18 0.04 0.07
## Stest14bible 0.45 0.04 -0.05 -0.02 -0.05 0.04 0.32
## Stest15theater 0.84 0.04 -0.02 0.04 -0.14 0.00 -0.12
## Stest16miscellaneous 0.51 0.04 0.00 0.09 0.06 0.02 -0.01
## Stest19disguisedwords 0.21 0.65 0.04 -0.08 0.07 0.17 -0.35
## Stest20spelling 0.02 0.83 -0.19 0.02 0.06 0.03 -0.19
## Stest21capitalization 0.02 0.58 0.02 0.02 -0.02 -0.01 0.01
## Stest22punctuation -0.02 0.75 0.10 0.07 -0.03 -0.07 0.01
## Stest23english 0.12 0.64 0.05 -0.05 0.01 -0.08 -0.07
## Stest24expression 0.17 0.51 0.12 -0.12 -0.07 -0.08 -0.01
## Stest25wordfunctions 0.05 0.50 0.11 0.21 -0.08 -0.03 0.09
## Stest26readingcomprehension 0.53 0.34 0.05 -0.06 -0.09 -0.01 0.22
## Stest28mechanicalreasoning -0.01 0.01 0.70 0.02 0.18 -0.06 -0.08
## Stest29visualization2D -0.08 0.01 0.57 0.02 0.01 0.18 -0.08
## Stest30visualization3D -0.04 -0.02 0.72 0.04 -0.01 0.00 0.05
## Stest31abstractreasoning 0.06 0.23 0.51 0.10 -0.14 -0.02 0.01
## Stest32arithreasoning 0.05 0.33 0.20 0.21 0.02 -0.03 0.15
## Stest33highschoolmath 0.07 0.09 0.12 0.72 -0.01 -0.06 0.01
## Stest34arithcomputation -0.14 0.39 -0.09 0.29 0.05 0.33 0.00
## Stest35tablereading 0.01 0.03 0.00 -0.02 -0.04 0.69 0.09
## Stest36clericalchecking 0.00 0.04 -0.09 0.01 0.05 0.69 -0.11
## Stest37objectinspection 0.11 -0.20 0.23 -0.07 -0.05 0.63 0.02
## h2 u2 com
## Stest1vocab 0.75 0.25 1.6
## Stest2literature 0.70 0.30 1.1
## Stest3music 0.56 0.44 1.1
## Stest4socialstudies 0.69 0.31 1.5
## Stest5math 0.64 0.36 1.4
## Stest6physicalscience 0.64 0.36 1.8
## Stest7biologicalscience 0.48 0.52 2.7
## Stest8aeronautics 0.25 0.75 2.8
## Stest9electronics 0.38 0.62 1.1
## Stest10mechanics 0.42 0.58 1.4
## Stest11art 0.59 0.41 1.0
## Stest12law 0.39 0.61 1.2
## Stest13health 0.38 0.62 3.1
## Stest14bible 0.38 0.62 1.9
## Stest15theater 0.56 0.44 1.1
## Stest16miscellaneous 0.40 0.60 1.1
## Stest19disguisedwords 0.60 0.40 2.0
## Stest20spelling 0.51 0.49 1.2
## Stest21capitalization 0.37 0.63 1.0
## Stest22punctuation 0.67 0.33 1.1
## Stest23english 0.44 0.56 1.2
## Stest24expression 0.34 0.66 1.5
## Stest25wordfunctions 0.60 0.40 1.6
## Stest26readingcomprehension 0.79 0.21 2.2
## Stest28mechanicalreasoning 0.58 0.42 1.2
## Stest29visualization2D 0.35 0.65 1.3
## Stest30visualization3D 0.53 0.47 1.0
## Stest31abstractreasoning 0.49 0.51 1.7
## Stest32arithreasoning 0.58 0.42 3.1
## Stest33highschoolmath 0.76 0.24 1.1
## Stest34arithcomputation 0.47 0.53 3.3
## Stest35tablereading 0.49 0.51 1.0
## Stest36clericalchecking 0.50 0.50 1.1
## Stest37objectinspection 0.44 0.56 1.6
##
## MR1 MR4 MR3 MR6 MR5 MR2 MR7
## SS loadings 5.72 4.29 2.07 1.71 1.63 1.59 0.68
## Proportion Var 0.17 0.13 0.06 0.05 0.05 0.05 0.02
## Cumulative Var 0.17 0.29 0.36 0.41 0.45 0.50 0.52
## Proportion Explained 0.32 0.24 0.12 0.10 0.09 0.09 0.04
## Cumulative Proportion 0.32 0.57 0.68 0.78 0.87 0.96 1.00
##
## With factor correlations of
## MR1 MR4 MR3 MR6 MR5 MR2 MR7
## MR1 1.00 0.74 0.57 0.51 0.69 0.23 0.46
## MR4 0.74 1.00 0.56 0.65 0.50 0.35 0.56
## MR3 0.57 0.56 1.00 0.47 0.54 0.29 0.47
## MR6 0.51 0.65 0.47 1.00 0.48 0.26 0.51
## MR5 0.69 0.50 0.54 0.48 1.00 0.12 0.50
## MR2 0.23 0.35 0.29 0.26 0.12 1.00 -0.06
## MR7 0.46 0.56 0.47 0.51 0.50 -0.06 1.00
##
## Mean item complexity = 1.6
## Test of the hypothesis that 7 factors are sufficient.
##
## df null model = 561 with the objective function = 17.28 0.1 with Chi Square = 1233206
## df of the model are 344 and the objective function was 0.22
## 0.1
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
## 0.1
## The harmonic n.obs is 71381 with the empirical chi square 6980.78 with prob < 0
## 0.1The total n.obs was 71381 with Likelihood Chi Square = 15646.8 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.98
## RMSEA index = 0.025 and the 90 % confidence intervals are 0.025 0.025 0.1
## BIC = 11802.33
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR4 MR3 MR6
## Correlation of (regression) scores with factors 0.96 0.95 0.91 0.91
## Multiple R square of scores with factors 0.93 0.91 0.82 0.82
## Minimum correlation of possible factor scores 0.86 0.82 0.64 0.64
## MR5 MR2 MR7
## Correlation of (regression) scores with factors 0.89 0.87 0.82
## Multiple R square of scores with factors 0.80 0.77 0.67
## Minimum correlation of possible factor scores 0.59 0.53 0.34
# ROBUSTNESS ANALYSIS: MINIMUM COVARIANCE DETERMINANT FOR MULTIVARIATE OUTLIERS
dk<- select(dgroup, starts_with("Stest"), age)
alpha <- .001
cutoff <- (qchisq(p = 1 - alpha, df = ncol(dk)))
output75 <- cov.mcd(dk, quantile.used = nrow(dk)*.75)
mhmcd75 <- mahalanobis(dk, output75$center, output75$cov)
names_outlier_MCD75 <- which(mhmcd75 > cutoff)
excluded_mcd75 <- names_outlier_MCD75
dgroup<- dgroup[-excluded_mcd75, ]
START MGCFA
datamale<- select(dmale, starts_with("Stest"), age, -Stest17memsentences, -Stest18memwords, -Stest27creativity)
datafemale<- select(dfemale, starts_with("Stest"), age, -Stest17memsentences, -Stest18memwords, -Stest27creativity)
# within-group CFA
chc.model <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning + Stest34arithcomputation
math =~ Stest5math + Stest6physicalscience + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest13health + Stest28mechanicalreasoning
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest37objectinspection
'
chc.highorder.model <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning + Stest34arithcomputation
math =~ Stest5math + Stest6physicalscience + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest13health + Stest28mechanicalreasoning
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest37objectinspection
g =~ english + math + speed + info + science + spatial
'
chc.bifactor.model <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning + Stest34arithcomputation
math =~ Stest5math + Stest6physicalscience + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest13health + Stest28mechanicalreasoning
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest37objectinspection
g =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
'
maleCFA<-cfa(chc.model, data=datamale, meanstructure=TRUE)
fitMeasures(maleCFA, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 72025.247 495.000 0.000 0.951 0.045 0.035
## aic bic
## 5332089.726 5333318.141
Mc(maleCFA)
## [1] 0.6033031
maleCFA2<-cfa(chc.highorder.model, data=datamale, meanstructure=TRUE)
fitMeasures(maleCFA2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 83848.556 504.000 0.000 0.943 0.048 0.040
## aic bic
## 5343895.036 5345040.945
Mc(maleCFA2)
## [1] 0.5549932
maleCFA3<-cfa(chc.bifactor.model, data=datamale, meanstructure=TRUE, orthogonal=TRUE, std.lv=T)
fitMeasures(maleCFA3, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 66088.560 476.000 0.000 0.955 0.044 0.030
## aic bic
## 5326191.040 5327593.633
Mc(maleCFA3)
## [1] 0.6290596
femaleCFA<-cfa(chc.model, data=datafemale, meanstructure=TRUE)
fitMeasures(femaleCFA, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 56237.684 495.000 0.000 0.955 0.040 0.029
## aic bic
## 5339589.792 5340819.347
Mc(femaleCFA)
## [1] 0.6767426
femaleCFA2<-cfa(chc.highorder.model, data=datafemale, meanstructure=TRUE)
fitMeasures(femaleCFA2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 62581.420 504.000 0.000 0.950 0.042 0.033
## aic bic
## 5345915.528 5347062.502
Mc(femaleCFA2)
## [1] 0.6473698
femaleCFA3<-cfa(chc.bifactor.model, data=datafemale, meanstructure=TRUE, orthogonal=TRUE, std.lv=T)
fitMeasures(femaleCFA3, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 48239.113 476.000 0.000 0.961 0.037 0.026
## aic bic
## 5331629.222 5333033.117
Mc(femaleCFA3)
## [1] 0.7156462
# CHC common factor model
chc.factor.model <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning + Stest34arithcomputation
math =~ Stest5math + Stest6physicalscience + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest13health + Stest28mechanicalreasoning
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest37objectinspection
'
chc.factor.reduced.model <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning + Stest34arithcomputation
math =~ Stest5math + Stest6physicalscience + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest13health + Stest28mechanicalreasoning
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest37objectinspection
info ~ 0*1
'
baseline<-cfa(chc.factor.model, data=dgroup, meanstructure=TRUE, sampling.weights="BY_WTA")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 163710.846 495.000 0.000 0.941 0.049
## srmr aic bic
## 0.041 10537307.850 10538626.760
Mc(baseline)
## [1] 0.5560551
configural<-cfa(chc.factor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T)
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 125508.035 990.000 0.000 0.953 0.043
## srmr aic bic
## 0.031 10329434.534 10332072.354
Mc(configural)
## [1] 0.6390714
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 52 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 268
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 125508.035 110054.287
## Degrees of freedom 990 990
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.140
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 70740.086 62029.891
## 1 54767.949 48024.396
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19dsgsdwrd 0.332 0.007 50.268 0.000 0.319
## Stest20spellng 0.655 0.004 182.086 0.000 0.648
## Stest21cptlztn 0.654 0.003 193.116 0.000 0.647
## Stest22puncttn 0.800 0.003 259.562 0.000 0.794
## Stest23english 0.692 0.004 176.439 0.000 0.684
## Stest24exprssn 0.633 0.004 156.631 0.000 0.625
## Stst25wrdfnctn 0.500 0.007 68.589 0.000 0.486
## Stst26rdngcmpr 0.302 0.005 59.930 0.000 0.292
## Stst31bstrctrs 0.335 0.004 80.295 0.000 0.327
## Stst32rthrsnng 0.233 0.007 31.663 0.000 0.218
## Stst34rthcmptt 0.115 0.009 12.918 0.000 0.098
## math =~
## Stest5math 0.786 0.003 280.362 0.000 0.780
## Stst6physclscn 0.413 0.004 99.354 0.000 0.405
## Stst25wrdfnctn 0.259 0.007 35.366 0.000 0.245
## Stst32rthrsnng 0.454 0.008 57.584 0.000 0.438
## Stst33hghschlm 0.910 0.003 312.149 0.000 0.904
## Stst34rthcmptt 0.361 0.009 40.814 0.000 0.344
## speed =~
## Stst19dsgsdwrd 0.260 0.004 70.475 0.000 0.253
## Stst29vslztn2D 0.227 0.004 57.019 0.000 0.219
## Stst34rthcmptt 0.382 0.004 96.856 0.000 0.375
## Stest35tblrdng 0.696 0.005 147.800 0.000 0.687
## Stst36clrclchc 0.695 0.005 152.628 0.000 0.686
## Stst37bjctnspc 0.572 0.005 124.316 0.000 0.563
## info =~
## Stest1vocab 0.612 0.004 166.439 0.000 0.605
## Stest2literatr 0.830 0.003 294.175 0.000 0.824
## Stest3music 0.727 0.003 248.613 0.000 0.721
## Stest4soclstds 0.797 0.003 255.863 0.000 0.791
## Stst7blgclscnc 0.350 0.005 68.112 0.000 0.340
## Stest8aerontcs 0.223 0.005 46.307 0.000 0.213
## Stest11art 0.715 0.003 227.183 0.000 0.708
## Stest12law 0.689 0.003 206.155 0.000 0.682
## Stest13health 0.589 0.005 109.916 0.000 0.578
## Stest14bible 0.639 0.003 192.610 0.000 0.633
## Stest15theater 0.684 0.003 224.656 0.000 0.678
## Stest16mscllns 0.723 0.003 207.130 0.000 0.717
## Stst19dsgsdwrd 0.267 0.006 42.256 0.000 0.255
## Stst26rdngcmpr 0.613 0.005 122.263 0.000 0.603
## science =~
## Stest1vocab 0.254 0.004 68.245 0.000 0.246
## Stst6physclscn 0.477 0.004 113.194 0.000 0.468
## Stst7blgclscnc 0.394 0.005 74.576 0.000 0.383
## Stest8aerontcs 0.431 0.005 88.824 0.000 0.422
## Stest9elctrncs 0.651 0.003 206.230 0.000 0.645
## Stest10mechncs 0.583 0.003 181.660 0.000 0.577
## Stest13health 0.103 0.005 18.925 0.000 0.092
## Stst28mchnclrs 0.296 0.004 66.431 0.000 0.287
## spatial =~
## Stst28mchnclrs 0.488 0.005 108.054 0.000 0.479
## Stst29vslztn2D 0.510 0.004 128.408 0.000 0.502
## Stst30vslztn3D 0.785 0.004 216.750 0.000 0.778
## Stst31bstrctrs 0.449 0.004 101.527 0.000 0.440
## Stst32rthrsnng 0.156 0.004 37.583 0.000 0.148
## Stst37bjctnspc 0.148 0.004 34.197 0.000 0.139
## ci.upper Std.lv Std.all
##
## 0.345 0.332 0.341
## 0.662 0.655 0.660
## 0.660 0.654 0.674
## 0.806 0.800 0.822
## 0.699 0.692 0.694
## 0.641 0.633 0.619
## 0.514 0.500 0.516
## 0.312 0.302 0.302
## 0.343 0.335 0.345
## 0.247 0.233 0.237
## 0.133 0.115 0.118
##
## 0.791 0.786 0.856
## 0.421 0.413 0.430
## 0.274 0.259 0.268
## 0.469 0.454 0.462
## 0.916 0.910 0.878
## 0.379 0.361 0.370
##
## 0.267 0.260 0.267
## 0.235 0.227 0.236
## 0.390 0.382 0.391
## 0.705 0.696 0.739
## 0.704 0.695 0.714
## 0.581 0.572 0.566
##
## 0.619 0.612 0.663
## 0.835 0.830 0.840
## 0.733 0.727 0.730
## 0.803 0.797 0.826
## 0.361 0.350 0.362
## 0.232 0.223 0.256
## 0.721 0.715 0.736
## 0.695 0.689 0.690
## 0.599 0.589 0.591
## 0.646 0.639 0.632
## 0.690 0.684 0.710
## 0.730 0.723 0.697
## 0.280 0.267 0.275
## 0.622 0.613 0.613
##
## 0.261 0.254 0.275
## 0.485 0.477 0.497
## 0.404 0.394 0.407
## 0.441 0.431 0.497
## 0.657 0.651 0.798
## 0.589 0.583 0.711
## 0.114 0.103 0.103
## 0.305 0.296 0.337
##
## 0.497 0.488 0.556
## 0.517 0.510 0.529
## 0.792 0.785 0.776
## 0.458 0.449 0.463
## 0.164 0.156 0.159
## 0.156 0.148 0.146
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.842 0.002 417.066 0.000 0.838
## speed 0.275 0.005 51.237 0.000 0.264
## info 0.822 0.002 420.856 0.000 0.818
## science 0.535 0.004 123.513 0.000 0.527
## spatial 0.501 0.004 111.694 0.000 0.492
## math ~~
## speed 0.256 0.005 49.174 0.000 0.245
## info 0.805 0.002 383.562 0.000 0.801
## science 0.614 0.004 163.711 0.000 0.606
## spatial 0.579 0.004 145.747 0.000 0.571
## speed ~~
## info 0.252 0.005 49.355 0.000 0.242
## science 0.059 0.006 10.397 0.000 0.048
## spatial 0.175 0.006 29.653 0.000 0.163
## info ~~
## science 0.696 0.003 209.027 0.000 0.689
## spatial 0.463 0.004 107.134 0.000 0.454
## science ~~
## spatial 0.617 0.004 145.521 0.000 0.608
## ci.upper Std.lv Std.all
##
## 0.845 0.842 0.842
## 0.285 0.275 0.275
## 0.826 0.822 0.822
## 0.544 0.535 0.535
## 0.510 0.501 0.501
##
## 0.266 0.256 0.256
## 0.809 0.805 0.805
## 0.621 0.614 0.614
## 0.587 0.579 0.579
##
## 0.262 0.252 0.252
## 0.070 0.059 0.059
## 0.186 0.175 0.175
##
## 0.703 0.696 0.696
## 0.471 0.463 0.463
##
## 0.625 0.617 0.617
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd -0.108 0.004 -27.549 0.000 -0.116
## .Stest20spellng -0.242 0.004 -59.771 0.000 -0.249
## .Stest21cptlztn -0.194 0.004 -49.221 0.000 -0.202
## .Stest22puncttn -0.183 0.004 -46.236 0.000 -0.191
## .Stest23english -0.119 0.004 -29.356 0.000 -0.127
## .Stest24exprssn -0.091 0.004 -21.886 0.000 -0.099
## .Stst25wrdfnctn -0.120 0.004 -30.548 0.000 -0.128
## .Stst26rdngcmpr -0.002 0.004 -0.480 0.632 -0.010
## .Stst31bstrctrs 0.074 0.004 18.667 0.000 0.066
## .Stst32rthrsnng 0.142 0.004 35.487 0.000 0.134
## .Stst34rthcmptt -0.062 0.004 -15.612 0.000 -0.070
## .Stest5math 0.219 0.004 58.635 0.000 0.212
## .Stst6physclscn 0.358 0.004 92.152 0.000 0.350
## .Stst33hghschlm 0.138 0.004 32.978 0.000 0.130
## .Stst29vslztn2D 0.224 0.004 57.484 0.000 0.217
## .Stest35tblrdng -0.047 0.004 -12.373 0.000 -0.055
## .Stst36clrclchc -0.165 0.004 -42.339 0.000 -0.173
## .Stst37bjctnspc -0.098 0.004 -24.085 0.000 -0.106
## .Stest1vocab 0.189 0.004 50.214 0.000 0.181
## .Stest2literatr 0.029 0.004 7.337 0.000 0.022
## .Stest3music -0.121 0.004 -29.896 0.000 -0.128
## .Stest4soclstds 0.228 0.004 57.617 0.000 0.220
## .Stst7blgclscnc 0.243 0.004 61.805 0.000 0.235
## .Stest8aerontcs 0.481 0.004 135.791 0.000 0.474
## .Stest11art -0.054 0.004 -13.827 0.000 -0.062
## .Stest12law 0.208 0.004 51.531 0.000 0.200
## .Stest13health -0.081 0.004 -19.852 0.000 -0.089
## .Stest14bible 0.015 0.004 3.604 0.000 0.007
## .Stest15theater -0.167 0.004 -42.900 0.000 -0.175
## .Stest16mscllns 0.134 0.004 31.520 0.000 0.125
## .Stest9elctrncs 0.522 0.003 156.854 0.000 0.516
## .Stest10mechncs 0.644 0.003 193.961 0.000 0.638
## .Stst28mchnclrs 0.551 0.004 154.563 0.000 0.544
## .Stst30vslztn3D 0.206 0.004 50.236 0.000 0.198
## ci.upper Std.lv Std.all
## -0.101 -0.108 -0.111
## -0.234 -0.242 -0.243
## -0.186 -0.194 -0.200
## -0.175 -0.183 -0.188
## -0.111 -0.119 -0.120
## -0.083 -0.091 -0.089
## -0.112 -0.120 -0.124
## 0.006 -0.002 -0.002
## 0.082 0.074 0.076
## 0.149 0.142 0.144
## -0.054 -0.062 -0.063
## 0.227 0.219 0.239
## 0.365 0.358 0.373
## 0.147 0.138 0.134
## 0.232 0.224 0.233
## -0.040 -0.047 -0.050
## -0.158 -0.165 -0.170
## -0.090 -0.098 -0.097
## 0.196 0.189 0.204
## 0.037 0.029 0.030
## -0.113 -0.121 -0.121
## 0.236 0.228 0.236
## 0.251 0.243 0.251
## 0.488 0.481 0.555
## -0.047 -0.054 -0.056
## 0.216 0.208 0.209
## -0.073 -0.081 -0.081
## 0.023 0.015 0.015
## -0.159 -0.167 -0.173
## 0.142 0.134 0.129
## 0.529 0.522 0.640
## 0.651 0.644 0.786
## 0.558 0.551 0.627
## 0.214 0.206 0.204
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.469 0.003 158.913 0.000 0.463
## .Stest20spellng 0.556 0.003 159.370 0.000 0.550
## .Stest21cptlztn 0.513 0.003 161.067 0.000 0.507
## .Stest22puncttn 0.307 0.002 132.273 0.000 0.303
## .Stest23english 0.515 0.003 149.414 0.000 0.509
## .Stest24exprssn 0.645 0.004 152.712 0.000 0.637
## .Stst25wrdfnctn 0.403 0.003 149.360 0.000 0.398
## .Stst26rdngcmpr 0.229 0.002 135.815 0.000 0.226
## .Stst31bstrctrs 0.477 0.003 148.290 0.000 0.471
## .Stst32rthrsnng 0.382 0.002 156.460 0.000 0.377
## .Stst34rthcmptt 0.499 0.003 144.008 0.000 0.492
## .Stest5math 0.225 0.003 88.541 0.000 0.220
## .Stst6physclscn 0.281 0.002 139.253 0.000 0.277
## .Stst33hghschlm 0.246 0.002 105.451 0.000 0.241
## .Stst29vslztn2D 0.575 0.004 135.571 0.000 0.567
## .Stest35tblrdng 0.402 0.005 82.066 0.000 0.392
## .Stst36clrclchc 0.465 0.005 85.910 0.000 0.455
## .Stst37bjctnspc 0.643 0.005 134.454 0.000 0.634
## .Stest1vocab 0.198 0.001 145.536 0.000 0.195
## .Stest2literatr 0.287 0.002 152.313 0.000 0.283
## .Stest3music 0.462 0.003 167.377 0.000 0.457
## .Stest4soclstds 0.296 0.002 151.590 0.000 0.292
## .Stst7blgclscnc 0.465 0.003 159.066 0.000 0.460
## .Stest8aerontcs 0.384 0.003 121.244 0.000 0.378
## .Stest11art 0.432 0.003 168.386 0.000 0.427
## .Stest12law 0.522 0.003 169.603 0.000 0.516
## .Stest13health 0.553 0.003 172.982 0.000 0.547
## .Stest14bible 0.613 0.003 183.713 0.000 0.607
## .Stest15theater 0.461 0.003 170.892 0.000 0.455
## .Stest16mscllns 0.554 0.003 164.981 0.000 0.548
## .Stest9elctrncs 0.241 0.003 89.854 0.000 0.236
## .Stest10mechncs 0.332 0.002 135.325 0.000 0.327
## .Stst28mchnclrs 0.268 0.002 112.935 0.000 0.263
## .Stst30vslztn3D 0.408 0.004 97.594 0.000 0.400
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.475 0.469 0.495
## 0.563 0.556 0.564
## 0.519 0.513 0.546
## 0.312 0.307 0.324
## 0.522 0.515 0.519
## 0.653 0.645 0.617
## 0.409 0.403 0.430
## 0.233 0.229 0.229
## 0.483 0.477 0.507
## 0.387 0.382 0.397
## 0.506 0.499 0.523
## 0.230 0.225 0.267
## 0.285 0.281 0.305
## 0.251 0.246 0.229
## 0.584 0.575 0.621
## 0.411 0.402 0.453
## 0.476 0.465 0.491
## 0.653 0.643 0.630
## 0.200 0.198 0.232
## 0.291 0.287 0.294
## 0.468 0.462 0.467
## 0.300 0.296 0.318
## 0.471 0.465 0.498
## 0.390 0.384 0.510
## 0.437 0.432 0.458
## 0.528 0.522 0.524
## 0.559 0.553 0.556
## 0.620 0.613 0.600
## 0.466 0.461 0.496
## 0.561 0.554 0.514
## 0.246 0.241 0.363
## 0.336 0.332 0.494
## 0.272 0.268 0.347
## 0.416 0.408 0.398
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19dsgsdwrd 0.375 0.007 56.720 0.000 0.362
## Stest20spellng 0.583 0.003 174.999 0.000 0.576
## Stest21cptlztn 0.561 0.004 158.105 0.000 0.554
## Stest22puncttn 0.732 0.003 251.706 0.000 0.726
## Stest23english 0.596 0.004 169.839 0.000 0.589
## Stest24exprssn 0.505 0.004 139.705 0.000 0.498
## Stst25wrdfnctn 0.524 0.005 95.528 0.000 0.513
## Stst26rdngcmpr 0.285 0.005 62.530 0.000 0.276
## Stst31bstrctrs 0.328 0.004 75.691 0.000 0.319
## Stst32rthrsnng 0.330 0.006 57.486 0.000 0.318
## Stst34rthcmptt 0.139 0.006 21.578 0.000 0.126
## math =~
## Stest5math 0.792 0.003 268.027 0.000 0.786
## Stst6physclscn 0.297 0.005 58.802 0.000 0.287
## Stst25wrdfnctn 0.277 0.005 50.721 0.000 0.267
## Stst32rthrsnng 0.329 0.006 54.153 0.000 0.317
## Stst33hghschlm 0.789 0.003 268.332 0.000 0.784
## Stst34rthcmptt 0.307 0.006 49.539 0.000 0.295
## speed =~
## Stst19dsgsdwrd 0.295 0.004 80.940 0.000 0.288
## Stst29vslztn2D 0.205 0.004 49.225 0.000 0.197
## Stst34rthcmptt 0.335 0.004 86.869 0.000 0.328
## Stest35tblrdng 0.571 0.004 135.282 0.000 0.563
## Stst36clrclchc 0.650 0.004 154.605 0.000 0.641
## Stst37bjctnspc 0.518 0.004 123.295 0.000 0.510
## info =~
## Stest1vocab 0.696 0.005 148.551 0.000 0.687
## Stest2literatr 0.792 0.003 282.574 0.000 0.786
## Stest3music 0.700 0.003 245.760 0.000 0.695
## Stest4soclstds 0.763 0.003 276.846 0.000 0.758
## Stst7blgclscnc 0.327 0.006 51.905 0.000 0.315
## Stest8aerontcs 0.100 0.006 15.719 0.000 0.088
## Stest11art 0.700 0.003 222.608 0.000 0.694
## Stest12law 0.578 0.003 175.559 0.000 0.571
## Stest13health 0.482 0.006 77.684 0.000 0.470
## Stest14bible 0.581 0.003 173.718 0.000 0.575
## Stest15theater 0.669 0.003 218.288 0.000 0.663
## Stest16mscllns 0.568 0.003 175.579 0.000 0.562
## Stst19dsgsdwrd 0.198 0.006 31.737 0.000 0.186
## Stst26rdngcmpr 0.535 0.004 121.114 0.000 0.526
## science =~
## Stest1vocab 0.192 0.005 39.330 0.000 0.182
## Stst6physclscn 0.498 0.005 102.051 0.000 0.489
## Stst7blgclscnc 0.393 0.007 59.310 0.000 0.380
## Stest8aerontcs 0.360 0.007 52.625 0.000 0.346
## Stest9elctrncs 0.485 0.004 132.089 0.000 0.478
## Stest10mechncs 0.468 0.003 150.119 0.000 0.462
## Stest13health 0.077 0.006 12.073 0.000 0.065
## Stst28mchnclrs 0.196 0.004 46.718 0.000 0.187
## spatial =~
## Stst28mchnclrs 0.482 0.004 116.220 0.000 0.474
## Stst29vslztn2D 0.483 0.004 124.839 0.000 0.475
## Stst30vslztn3D 0.703 0.003 203.123 0.000 0.696
## Stst31bstrctrs 0.420 0.004 95.335 0.000 0.412
## Stst32rthrsnng 0.159 0.004 36.916 0.000 0.151
## Stst37bjctnspc 0.149 0.004 38.533 0.000 0.142
## ci.upper Std.lv Std.all
##
## 0.388 0.375 0.387
## 0.589 0.583 0.643
## 0.568 0.561 0.612
## 0.738 0.732 0.817
## 0.603 0.596 0.664
## 0.512 0.505 0.570
## 0.535 0.524 0.534
## 0.294 0.285 0.317
## 0.336 0.328 0.347
## 0.341 0.330 0.342
## 0.152 0.139 0.151
##
## 0.798 0.792 0.818
## 0.307 0.297 0.328
## 0.288 0.277 0.283
## 0.341 0.329 0.342
## 0.795 0.789 0.857
## 0.319 0.307 0.334
##
## 0.303 0.295 0.305
## 0.213 0.205 0.215
## 0.343 0.335 0.365
## 0.579 0.571 0.711
## 0.658 0.650 0.706
## 0.526 0.518 0.562
##
## 0.705 0.696 0.716
## 0.797 0.792 0.825
## 0.706 0.700 0.734
## 0.769 0.763 0.818
## 0.340 0.327 0.338
## 0.113 0.100 0.112
## 0.706 0.700 0.726
## 0.584 0.578 0.615
## 0.494 0.482 0.529
## 0.588 0.581 0.590
## 0.675 0.669 0.698
## 0.574 0.568 0.627
## 0.210 0.198 0.204
## 0.544 0.535 0.595
##
## 0.201 0.192 0.197
## 0.508 0.498 0.549
## 0.406 0.393 0.406
## 0.373 0.360 0.401
## 0.492 0.485 0.559
## 0.475 0.468 0.626
## 0.090 0.077 0.085
## 0.204 0.196 0.238
##
## 0.490 0.482 0.587
## 0.490 0.483 0.507
## 0.710 0.703 0.758
## 0.429 0.420 0.445
## 0.167 0.159 0.165
## 0.157 0.149 0.162
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.760 0.003 299.819 0.000 0.755
## speed 0.270 0.006 48.531 0.000 0.259
## info 0.817 0.002 409.067 0.000 0.813
## science 0.544 0.005 113.354 0.000 0.535
## spatial 0.529 0.004 122.916 0.000 0.521
## math ~~
## speed 0.187 0.005 36.359 0.000 0.177
## info 0.746 0.003 297.326 0.000 0.741
## science 0.626 0.005 133.181 0.000 0.617
## spatial 0.574 0.004 141.064 0.000 0.566
## speed ~~
## info 0.204 0.005 39.555 0.000 0.194
## science 0.074 0.006 13.364 0.000 0.063
## spatial 0.191 0.006 33.146 0.000 0.180
## info ~~
## science 0.727 0.004 199.073 0.000 0.720
## spatial 0.512 0.004 123.796 0.000 0.504
## science ~~
## spatial 0.549 0.005 111.521 0.000 0.539
## ci.upper Std.lv Std.all
##
## 0.765 0.760 0.760
## 0.281 0.270 0.270
## 0.821 0.817 0.817
## 0.554 0.544 0.544
## 0.537 0.529 0.529
##
## 0.197 0.187 0.187
## 0.751 0.746 0.746
## 0.635 0.626 0.626
## 0.582 0.574 0.574
##
## 0.215 0.204 0.204
## 0.085 0.074 0.074
## 0.202 0.191 0.191
##
## 0.734 0.727 0.727
## 0.520 0.512 0.512
##
## 0.559 0.549 0.549
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.156 0.004 40.337 0.000 0.149
## .Stest20spellng 0.288 0.004 79.198 0.000 0.281
## .Stest21cptlztn 0.285 0.004 77.178 0.000 0.278
## .Stest22puncttn 0.289 0.004 80.304 0.000 0.282
## .Stest23english 0.200 0.004 55.481 0.000 0.193
## .Stest24exprssn 0.175 0.004 49.287 0.000 0.169
## .Stst25wrdfnctn 0.208 0.004 52.986 0.000 0.200
## .Stst26rdngcmpr 0.118 0.004 32.716 0.000 0.111
## .Stst31bstrctrs 0.037 0.004 9.666 0.000 0.029
## .Stst32rthrsnng -0.030 0.004 -7.900 0.000 -0.038
## .Stst34rthcmptt 0.175 0.004 47.455 0.000 0.168
## .Stest5math -0.133 0.004 -34.579 0.000 -0.141
## .Stst6physclscn -0.264 0.004 -73.191 0.000 -0.272
## .Stst33hghschlm -0.063 0.004 -17.147 0.000 -0.070
## .Stst29vslztn2D -0.144 0.004 -37.867 0.000 -0.151
## .Stest35tblrdng 0.099 0.003 30.730 0.000 0.092
## .Stst36clrclchc 0.087 0.004 23.895 0.000 0.079
## .Stst37bjctnspc 0.084 0.004 22.958 0.000 0.077
## .Stest1vocab -0.083 0.004 -21.517 0.000 -0.091
## .Stest2literatr 0.025 0.004 6.452 0.000 0.017
## .Stest3music 0.163 0.004 42.478 0.000 0.155
## .Stest4soclstds -0.132 0.004 -35.225 0.000 -0.139
## .Stst7blgclscnc -0.156 0.004 -40.430 0.000 -0.164
## .Stest8aerontcs -0.404 0.004 -112.676 0.000 -0.411
## .Stest11art 0.108 0.004 28.115 0.000 0.101
## .Stest12law -0.138 0.004 -36.597 0.000 -0.145
## .Stest13health 0.168 0.004 45.803 0.000 0.161
## .Stest14bible 0.070 0.004 17.656 0.000 0.062
## .Stest15theater 0.207 0.004 54.125 0.000 0.200
## .Stest16mscllns -0.071 0.004 -19.463 0.000 -0.078
## .Stest9elctrncs -0.416 0.003 -119.952 0.000 -0.423
## .Stest10mechncs -0.511 0.003 -170.689 0.000 -0.517
## .Stst28mchnclrs -0.422 0.003 -128.379 0.000 -0.429
## .Stst30vslztn3D -0.109 0.004 -29.486 0.000 -0.116
## ci.upper Std.lv Std.all
## 0.164 0.156 0.161
## 0.295 0.288 0.318
## 0.292 0.285 0.311
## 0.296 0.289 0.323
## 0.207 0.200 0.223
## 0.182 0.175 0.198
## 0.216 0.208 0.212
## 0.125 0.118 0.132
## 0.044 0.037 0.039
## -0.023 -0.030 -0.032
## 0.182 0.175 0.191
## -0.126 -0.133 -0.138
## -0.257 -0.264 -0.291
## -0.056 -0.063 -0.068
## -0.136 -0.144 -0.151
## 0.105 0.099 0.123
## 0.094 0.087 0.094
## 0.091 0.084 0.091
## -0.076 -0.083 -0.086
## 0.032 0.025 0.026
## 0.170 0.163 0.170
## -0.125 -0.132 -0.142
## -0.149 -0.156 -0.162
## -0.397 -0.404 -0.451
## 0.116 0.108 0.112
## -0.130 -0.138 -0.146
## 0.175 0.168 0.184
## 0.077 0.070 0.071
## 0.215 0.207 0.216
## -0.064 -0.071 -0.078
## -0.409 -0.416 -0.479
## -0.505 -0.511 -0.683
## -0.416 -0.422 -0.514
## -0.102 -0.109 -0.118
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.465 0.003 154.991 0.000 0.459
## .Stest20spellng 0.482 0.003 162.757 0.000 0.477
## .Stest21cptlztn 0.526 0.003 164.033 0.000 0.520
## .Stest22puncttn 0.266 0.002 129.984 0.000 0.262
## .Stest23english 0.450 0.003 157.439 0.000 0.445
## .Stest24exprssn 0.530 0.004 148.744 0.000 0.523
## .Stst25wrdfnctn 0.390 0.003 143.634 0.000 0.385
## .Stst26rdngcmpr 0.192 0.001 139.117 0.000 0.189
## .Stst31bstrctrs 0.463 0.003 152.217 0.000 0.457
## .Stst32rthrsnng 0.404 0.002 163.617 0.000 0.399
## .Stst34rthcmptt 0.489 0.004 139.653 0.000 0.482
## .Stest5math 0.311 0.003 98.168 0.000 0.305
## .Stst6physclscn 0.301 0.002 126.764 0.000 0.296
## .Stst33hghschlm 0.226 0.002 101.390 0.000 0.221
## .Stst29vslztn2D 0.595 0.004 152.212 0.000 0.588
## .Stest35tblrdng 0.319 0.004 86.532 0.000 0.311
## .Stst36clrclchc 0.424 0.005 90.764 0.000 0.414
## .Stst37bjctnspc 0.530 0.004 135.189 0.000 0.523
## .Stest1vocab 0.230 0.002 145.077 0.000 0.227
## .Stest2literatr 0.294 0.002 155.536 0.000 0.290
## .Stest3music 0.420 0.003 164.960 0.000 0.415
## .Stest4soclstds 0.288 0.002 154.735 0.000 0.284
## .Stst7blgclscnc 0.488 0.003 161.393 0.000 0.482
## .Stest8aerontcs 0.613 0.004 174.545 0.000 0.606
## .Stest11art 0.439 0.003 167.385 0.000 0.434
## .Stest12law 0.550 0.003 178.000 0.000 0.544
## .Stest13health 0.538 0.003 173.278 0.000 0.532
## .Stest14bible 0.632 0.003 192.111 0.000 0.626
## .Stest15theater 0.472 0.003 170.803 0.000 0.466
## .Stest16mscllns 0.498 0.003 172.130 0.000 0.492
## .Stest9elctrncs 0.518 0.004 122.201 0.000 0.509
## .Stest10mechncs 0.341 0.002 143.565 0.000 0.337
## .Stst28mchnclrs 0.300 0.002 127.275 0.000 0.295
## .Stst30vslztn3D 0.365 0.004 102.591 0.000 0.358
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.471 0.465 0.496
## 0.488 0.482 0.587
## 0.532 0.526 0.626
## 0.270 0.266 0.332
## 0.456 0.450 0.559
## 0.537 0.530 0.675
## 0.396 0.390 0.406
## 0.195 0.192 0.237
## 0.469 0.463 0.519
## 0.409 0.404 0.436
## 0.496 0.489 0.580
## 0.317 0.311 0.331
## 0.306 0.301 0.366
## 0.230 0.226 0.266
## 0.603 0.595 0.655
## 0.326 0.319 0.494
## 0.433 0.424 0.501
## 0.538 0.530 0.624
## 0.233 0.230 0.243
## 0.298 0.294 0.319
## 0.425 0.420 0.461
## 0.292 0.288 0.331
## 0.494 0.488 0.521
## 0.620 0.613 0.762
## 0.444 0.439 0.472
## 0.556 0.550 0.622
## 0.544 0.538 0.648
## 0.639 0.632 0.652
## 0.477 0.472 0.513
## 0.503 0.498 0.607
## 0.526 0.518 0.688
## 0.346 0.341 0.609
## 0.304 0.300 0.445
## 0.372 0.365 0.425
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
modificationIndices(configural, sort=T, maximum.number=30)
## lhs op rhs block group
## 325 math =~ Stest35tablereading 1 1
## 419 spatial =~ Stest20spelling 1 1
## 403 science =~ Stest5math 1 1
## 383 info =~ Stest33highschoolmath 1 1
## 402 science =~ Stest34arithcomputation 1 1
## 794 Stest6physicalscience ~~ Stest10mechanics 1 1
## 430 spatial =~ Stest35tablereading 1 1
## 297 english =~ Stest35tablereading 1 1
## 299 english =~ Stest37objectinspection 1 1
## 1133 spatial =~ Stest20spelling 2 2
## 327 math =~ Stest37objectinspection 1 1
## 406 science =~ Stest35tablereading 1 1
## 381 info =~ Stest5math 1 1
## 385 info =~ Stest35tablereading 1 1
## 1095 info =~ Stest5math 2 2
## 1160 Stest19disguisedwords ~~ Stest20spelling 2 2
## 382 info =~ Stest6physicalscience 1 1
## 466 Stest19disguisedwords ~~ Stest4socialstudies 1 1
## 446 Stest19disguisedwords ~~ Stest20spelling 1 1
## 1508 Stest6physicalscience ~~ Stest10mechanics 2 2
## 733 Stest34arithcomputation ~~ Stest33highschoolmath 1 1
## 426 spatial =~ Stest34arithcomputation 1 1
## 1117 science =~ Stest5math 2 2
## 1679 Stest11art ~~ Stest15theater 2 2
## 334 math =~ Stest11art 1 1
## 1039 math =~ Stest35tablereading 2 2
## 1011 english =~ Stest35tablereading 2 2
## 1058 speed =~ Stest20spelling 2 2
## 1013 english =~ Stest37objectinspection 2 2
## 1014 english =~ Stest1vocab 2 2
## level mi epc sepc.lv sepc.all sepc.nox
## 325 1 3242.241 0.212 0.212 0.226 0.226
## 419 1 3090.910 -0.232 -0.232 -0.233 -0.233
## 403 1 2956.548 0.200 0.200 0.218 0.218
## 383 1 2952.700 -0.323 -0.323 -0.312 -0.312
## 402 1 2866.471 -0.235 -0.235 -0.240 -0.240
## 794 1 2804.370 -0.078 -0.078 -0.256 -0.256
## 430 1 2775.011 0.205 0.205 0.218 0.218
## 297 1 2549.917 0.190 0.190 0.202 0.202
## 299 1 2514.840 -0.227 -0.227 -0.224 -0.224
## 1133 1 2481.272 -0.205 -0.205 -0.226 -0.226
## 327 1 2427.202 -0.238 -0.238 -0.236 -0.236
## 406 1 2402.718 0.172 0.172 0.183 0.183
## 381 1 2340.401 0.253 0.253 0.276 0.276
## 385 1 2282.484 0.169 0.169 0.180 0.180
## 1095 1 2009.767 0.258 0.258 0.266 0.266
## 1160 1 1977.624 0.088 0.088 0.187 0.187
## 382 1 1874.023 0.235 0.235 0.245 0.245
## 466 1 1844.801 -0.068 -0.068 -0.181 -0.181
## 446 1 1828.925 0.091 0.091 0.178 0.178
## 1508 1 1819.824 -0.076 -0.076 -0.238 -0.238
## 733 1 1817.991 0.079 0.079 0.227 0.227
## 426 1 1789.720 -0.183 -0.183 -0.187 -0.187
## 1117 1 1542.659 0.197 0.197 0.203 0.203
## 1679 1 1531.435 0.072 0.072 0.159 0.159
## 334 1 1495.511 -0.207 -0.207 -0.213 -0.213
## 1039 1 1458.487 0.121 0.121 0.151 0.151
## 1011 1 1451.510 0.124 0.124 0.155 0.155
## 1058 1 1426.603 0.129 0.129 0.142 0.142
## 1013 1 1393.192 -0.161 -0.161 -0.175 -0.175
## 1014 1 1352.032 0.174 0.174 0.179 0.179
metric<-cfa(chc.factor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 134003.685 1035.000 0.000 0.950 0.043
## srmr aic bic
## 0.039 10337840.184 10340035.086
Mc(metric)
## [1] 0.6199442
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 80 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 274
## Number of equality constraints 51
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 134003.685 117537.503
## Degrees of freedom 1035 1035
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.140
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 74471.699 65320.722
## 1 59531.987 52216.781
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.370 0.005 74.653 0.000 0.360
## Stst20s (.p2.) 0.648 0.003 218.865 0.000 0.642
## Stst21c (.p3.) 0.637 0.003 219.320 0.000 0.631
## Stst22p (.p4.) 0.802 0.003 285.350 0.000 0.797
## Stst23n (.p5.) 0.674 0.003 210.836 0.000 0.667
## Stst24x (.p6.) 0.593 0.003 184.627 0.000 0.587
## Stst25w (.p7.) 0.534 0.005 114.419 0.000 0.525
## Stst26r (.p8.) 0.309 0.004 84.905 0.000 0.302
## Stst31b (.p9.) 0.347 0.003 108.979 0.000 0.341
## Stst32r (.10.) 0.304 0.005 62.961 0.000 0.294
## Stst34r (.11.) 0.136 0.006 24.630 0.000 0.126
## math =~
## Stst5mt (.12.) 0.808 0.003 321.249 0.000 0.804
## Stst6ph (.13.) 0.382 0.003 115.005 0.000 0.376
## Stst25w (.14.) 0.275 0.005 59.386 0.000 0.266
## Stst32r (.15.) 0.392 0.005 76.190 0.000 0.382
## Stst33h (.16.) 0.877 0.003 312.945 0.000 0.872
## Stst34r (.17.) 0.343 0.005 63.265 0.000 0.332
## speed =~
## Stst19d (.18.) 0.292 0.003 104.626 0.000 0.286
## Sts292D (.19.) 0.229 0.003 74.288 0.000 0.223
## Stst34r (.20.) 0.379 0.003 121.726 0.000 0.373
## Stst35t (.21.) 0.666 0.004 165.322 0.000 0.658
## Stst36c (.22.) 0.709 0.004 186.188 0.000 0.702
## Stst37b (.23.) 0.575 0.004 155.057 0.000 0.568
## info =~
## Stst1vc (.24.) 0.669 0.003 212.506 0.000 0.663
## Stst2lt (.25.) 0.832 0.003 326.951 0.000 0.827
## Stst3ms (.26.) 0.732 0.002 298.825 0.000 0.728
## Stst4sc (.27.) 0.801 0.003 301.761 0.000 0.795
## Stst7bl (.28.) 0.359 0.004 88.903 0.000 0.351
## Stst8rn (.29.) 0.173 0.004 43.982 0.000 0.165
## Stst11r (.30.) 0.725 0.003 275.976 0.000 0.720
## Stst12l (.31.) 0.651 0.003 234.003 0.000 0.646
## Stst13h (.32.) 0.546 0.004 128.941 0.000 0.537
## Stst14b (.33.) 0.627 0.003 231.675 0.000 0.621
## Stst15t (.34.) 0.694 0.003 275.100 0.000 0.689
## Stst16m (.35.) 0.660 0.003 230.478 0.000 0.654
## Stst19d (.36.) 0.238 0.005 51.792 0.000 0.229
## Stst26r (.37.) 0.586 0.004 159.811 0.000 0.579
## science =~
## Stst1vc (.38.) 0.237 0.003 73.979 0.000 0.231
## Stst6ph (.39.) 0.515 0.003 149.716 0.000 0.508
## Stst7bl (.40.) 0.413 0.004 94.294 0.000 0.405
## Stst8rn (.41.) 0.442 0.004 101.405 0.000 0.434
## Stst9lc (.42.) 0.635 0.003 214.586 0.000 0.629
## Stst10m (.43.) 0.578 0.003 200.465 0.000 0.572
## Stst13h (.44.) 0.105 0.004 23.464 0.000 0.096
## Stst28m (.45.) 0.271 0.003 78.010 0.000 0.264
## spatial =~
## Stst28m (.46.) 0.505 0.003 146.303 0.000 0.498
## Sts292D (.47.) 0.515 0.003 163.105 0.000 0.509
## Sts303D (.48.) 0.773 0.003 238.808 0.000 0.766
## Stst31b (.49.) 0.451 0.003 132.128 0.000 0.445
## Stst32r (.50.) 0.167 0.003 53.910 0.000 0.161
## Stst37b (.51.) 0.155 0.003 51.182 0.000 0.149
## ci.upper Std.lv Std.all
##
## 0.380 0.370 0.374
## 0.654 0.648 0.656
## 0.642 0.637 0.663
## 0.808 0.802 0.822
## 0.680 0.674 0.683
## 0.600 0.593 0.592
## 0.543 0.534 0.532
## 0.317 0.309 0.314
## 0.353 0.347 0.354
## 0.313 0.304 0.306
## 0.147 0.136 0.140
##
## 0.813 0.808 0.867
## 0.389 0.382 0.396
## 0.284 0.275 0.274
## 0.402 0.392 0.395
## 0.883 0.877 0.866
## 0.353 0.343 0.351
##
## 0.297 0.292 0.295
## 0.235 0.229 0.237
## 0.385 0.379 0.389
## 0.674 0.666 0.715
## 0.717 0.709 0.727
## 0.583 0.575 0.568
##
## 0.675 0.669 0.696
## 0.837 0.832 0.841
## 0.737 0.732 0.733
## 0.806 0.801 0.827
## 0.367 0.359 0.364
## 0.181 0.173 0.204
## 0.731 0.725 0.741
## 0.657 0.651 0.668
## 0.554 0.546 0.561
## 0.632 0.627 0.624
## 0.699 0.694 0.715
## 0.666 0.660 0.660
## 0.247 0.238 0.241
## 0.593 0.586 0.595
##
## 0.243 0.237 0.247
## 0.522 0.515 0.534
## 0.422 0.413 0.419
## 0.451 0.442 0.522
## 0.640 0.635 0.787
## 0.584 0.578 0.706
## 0.114 0.105 0.108
## 0.278 0.271 0.310
##
## 0.512 0.505 0.577
## 0.522 0.515 0.534
## 0.779 0.773 0.767
## 0.458 0.451 0.462
## 0.173 0.167 0.169
## 0.161 0.155 0.153
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.838 0.002 413.168 0.000 0.834
## speed 0.262 0.005 50.428 0.000 0.251
## info 0.823 0.002 429.565 0.000 0.820
## science 0.542 0.004 130.962 0.000 0.534
## spatial 0.498 0.004 114.418 0.000 0.490
## math ~~
## speed 0.248 0.005 49.478 0.000 0.238
## info 0.804 0.002 398.815 0.000 0.800
## science 0.619 0.004 169.938 0.000 0.612
## spatial 0.577 0.004 149.494 0.000 0.570
## speed ~~
## info 0.245 0.005 49.445 0.000 0.235
## science 0.051 0.005 9.423 0.000 0.041
## spatial 0.164 0.006 29.186 0.000 0.153
## info ~~
## science 0.705 0.003 217.188 0.000 0.698
## spatial 0.464 0.004 109.229 0.000 0.455
## science ~~
## spatial 0.626 0.004 151.391 0.000 0.618
## ci.upper Std.lv Std.all
##
## 0.842 0.838 0.838
## 0.272 0.262 0.262
## 0.827 0.823 0.823
## 0.550 0.542 0.542
## 0.507 0.498 0.498
##
## 0.257 0.248 0.248
## 0.807 0.804 0.804
## 0.626 0.619 0.619
## 0.585 0.577 0.577
##
## 0.254 0.245 0.245
## 0.062 0.051 0.051
## 0.175 0.164 0.164
##
## 0.711 0.705 0.705
## 0.472 0.464 0.464
##
## 0.634 0.626 0.626
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd -0.108 0.004 -27.549 0.000 -0.116
## .Stest20spellng -0.242 0.004 -59.771 0.000 -0.249
## .Stest21cptlztn -0.194 0.004 -49.221 0.000 -0.202
## .Stest22puncttn -0.183 0.004 -46.236 0.000 -0.191
## .Stest23english -0.119 0.004 -29.356 0.000 -0.127
## .Stest24exprssn -0.091 0.004 -21.886 0.000 -0.099
## .Stst25wrdfnctn -0.120 0.004 -30.548 0.000 -0.128
## .Stst26rdngcmpr -0.002 0.004 -0.480 0.632 -0.010
## .Stst31bstrctrs 0.074 0.004 18.667 0.000 0.066
## .Stst32rthrsnng 0.142 0.004 35.487 0.000 0.134
## .Stst34rthcmptt -0.062 0.004 -15.612 0.000 -0.070
## .Stest5math 0.219 0.004 58.635 0.000 0.212
## .Stst6physclscn 0.358 0.004 92.152 0.000 0.350
## .Stst33hghschlm 0.138 0.004 32.978 0.000 0.130
## .Stst29vslztn2D 0.224 0.004 57.484 0.000 0.217
## .Stest35tblrdng -0.047 0.004 -12.373 0.000 -0.055
## .Stst36clrclchc -0.165 0.004 -42.339 0.000 -0.173
## .Stst37bjctnspc -0.098 0.004 -24.085 0.000 -0.106
## .Stest1vocab 0.189 0.004 50.214 0.000 0.181
## .Stest2literatr 0.029 0.004 7.337 0.000 0.022
## .Stest3music -0.121 0.004 -29.896 0.000 -0.128
## .Stest4soclstds 0.228 0.004 57.617 0.000 0.220
## .Stst7blgclscnc 0.243 0.004 61.805 0.000 0.235
## .Stest8aerontcs 0.481 0.004 135.791 0.000 0.474
## .Stest11art -0.054 0.004 -13.827 0.000 -0.062
## .Stest12law 0.208 0.004 51.531 0.000 0.200
## .Stest13health -0.081 0.004 -19.852 0.000 -0.089
## .Stest14bible 0.015 0.004 3.604 0.000 0.007
## .Stest15theater -0.167 0.004 -42.900 0.000 -0.175
## .Stest16mscllns 0.134 0.004 31.520 0.000 0.125
## .Stest9elctrncs 0.522 0.003 156.854 0.000 0.516
## .Stest10mechncs 0.644 0.003 193.961 0.000 0.638
## .Stst28mchnclrs 0.551 0.004 154.563 0.000 0.544
## .Stst30vslztn3D 0.206 0.004 50.236 0.000 0.198
## ci.upper Std.lv Std.all
## -0.101 -0.108 -0.110
## -0.234 -0.242 -0.244
## -0.186 -0.194 -0.202
## -0.175 -0.183 -0.188
## -0.111 -0.119 -0.121
## -0.083 -0.091 -0.091
## -0.112 -0.120 -0.119
## 0.006 -0.002 -0.002
## 0.082 0.074 0.075
## 0.149 0.142 0.143
## -0.054 -0.062 -0.064
## 0.227 0.219 0.235
## 0.365 0.358 0.371
## 0.147 0.138 0.137
## 0.232 0.224 0.232
## -0.040 -0.047 -0.051
## -0.158 -0.165 -0.169
## -0.090 -0.098 -0.097
## 0.196 0.189 0.197
## 0.037 0.029 0.030
## -0.113 -0.121 -0.121
## 0.236 0.228 0.236
## 0.251 0.243 0.247
## 0.488 0.481 0.568
## -0.047 -0.054 -0.056
## 0.216 0.208 0.214
## -0.073 -0.081 -0.083
## 0.023 0.015 0.015
## -0.159 -0.167 -0.172
## 0.142 0.134 0.134
## 0.529 0.522 0.648
## 0.651 0.644 0.787
## 0.558 0.551 0.630
## 0.214 0.206 0.204
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.463 0.003 159.475 0.000 0.458
## .Stest20spellng 0.557 0.003 162.547 0.000 0.551
## .Stest21cptlztn 0.516 0.003 164.439 0.000 0.510
## .Stest22puncttn 0.308 0.002 134.918 0.000 0.303
## .Stest23english 0.519 0.003 150.439 0.000 0.512
## .Stest24exprssn 0.651 0.004 153.478 0.000 0.643
## .Stst25wrdfnctn 0.401 0.003 149.327 0.000 0.396
## .Stst26rdngcmpr 0.231 0.002 136.902 0.000 0.228
## .Stst31bstrctrs 0.477 0.003 150.153 0.000 0.471
## .Stst32rthrsnng 0.383 0.002 158.290 0.000 0.379
## .Stst34rthcmptt 0.501 0.003 147.320 0.000 0.495
## .Stest5math 0.216 0.003 84.835 0.000 0.211
## .Stst6physclscn 0.276 0.002 139.456 0.000 0.273
## .Stst33hghschlm 0.256 0.002 114.312 0.000 0.251
## .Stst29vslztn2D 0.574 0.004 137.879 0.000 0.566
## .Stest35tblrdng 0.423 0.005 90.075 0.000 0.414
## .Stst36clrclchc 0.450 0.005 89.162 0.000 0.440
## .Stst37bjctnspc 0.641 0.005 138.537 0.000 0.632
## .Stest1vocab 0.197 0.001 143.865 0.000 0.194
## .Stest2literatr 0.286 0.002 153.739 0.000 0.283
## .Stest3music 0.461 0.003 168.831 0.000 0.456
## .Stest4soclstds 0.296 0.002 152.758 0.000 0.292
## .Stst7blgclscnc 0.462 0.003 159.131 0.000 0.457
## .Stest8aerontcs 0.385 0.003 120.564 0.000 0.379
## .Stest11art 0.432 0.003 169.166 0.000 0.427
## .Stest12law 0.527 0.003 171.520 0.000 0.521
## .Stest13health 0.557 0.003 174.326 0.000 0.551
## .Stest14bible 0.615 0.003 185.319 0.000 0.609
## .Stest15theater 0.461 0.003 171.774 0.000 0.455
## .Stest16mscllns 0.564 0.003 167.022 0.000 0.557
## .Stest9elctrncs 0.247 0.003 91.113 0.000 0.242
## .Stest10mechncs 0.336 0.002 138.551 0.000 0.331
## .Stst28mchnclrs 0.265 0.002 118.218 0.000 0.261
## .Stst30vslztn3D 0.418 0.004 109.871 0.000 0.411
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.469 0.463 0.474
## 0.564 0.557 0.570
## 0.522 0.516 0.560
## 0.312 0.308 0.324
## 0.526 0.519 0.533
## 0.659 0.651 0.649
## 0.407 0.401 0.398
## 0.234 0.231 0.239
## 0.483 0.477 0.498
## 0.388 0.383 0.390
## 0.508 0.501 0.527
## 0.221 0.216 0.249
## 0.280 0.276 0.297
## 0.260 0.256 0.250
## 0.582 0.574 0.617
## 0.433 0.423 0.488
## 0.460 0.450 0.472
## 0.650 0.641 0.625
## 0.199 0.197 0.213
## 0.290 0.286 0.293
## 0.466 0.461 0.462
## 0.300 0.296 0.316
## 0.468 0.462 0.476
## 0.392 0.385 0.536
## 0.437 0.432 0.451
## 0.533 0.527 0.554
## 0.563 0.557 0.589
## 0.622 0.615 0.610
## 0.466 0.461 0.489
## 0.570 0.564 0.564
## 0.253 0.247 0.380
## 0.341 0.336 0.501
## 0.270 0.265 0.347
## 0.426 0.418 0.412
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.370 0.005 74.653 0.000 0.360
## Stst20s (.p2.) 0.648 0.003 218.865 0.000 0.642
## Stst21c (.p3.) 0.637 0.003 219.320 0.000 0.631
## Stst22p (.p4.) 0.802 0.003 285.350 0.000 0.797
## Stst23n (.p5.) 0.674 0.003 210.836 0.000 0.667
## Stst24x (.p6.) 0.593 0.003 184.627 0.000 0.587
## Stst25w (.p7.) 0.534 0.005 114.419 0.000 0.525
## Stst26r (.p8.) 0.309 0.004 84.905 0.000 0.302
## Stst31b (.p9.) 0.347 0.003 108.979 0.000 0.341
## Stst32r (.10.) 0.304 0.005 62.961 0.000 0.294
## Stst34r (.11.) 0.136 0.006 24.630 0.000 0.126
## math =~
## Stst5mt (.12.) 0.808 0.003 321.249 0.000 0.804
## Stst6ph (.13.) 0.382 0.003 115.005 0.000 0.376
## Stst25w (.14.) 0.275 0.005 59.386 0.000 0.266
## Stst32r (.15.) 0.392 0.005 76.190 0.000 0.382
## Stst33h (.16.) 0.877 0.003 312.945 0.000 0.872
## Stst34r (.17.) 0.343 0.005 63.265 0.000 0.332
## speed =~
## Stst19d (.18.) 0.292 0.003 104.626 0.000 0.286
## Sts292D (.19.) 0.229 0.003 74.288 0.000 0.223
## Stst34r (.20.) 0.379 0.003 121.726 0.000 0.373
## Stst35t (.21.) 0.666 0.004 165.322 0.000 0.658
## Stst36c (.22.) 0.709 0.004 186.188 0.000 0.702
## Stst37b (.23.) 0.575 0.004 155.057 0.000 0.568
## info =~
## Stst1vc (.24.) 0.669 0.003 212.506 0.000 0.663
## Stst2lt (.25.) 0.832 0.003 326.951 0.000 0.827
## Stst3ms (.26.) 0.732 0.002 298.825 0.000 0.728
## Stst4sc (.27.) 0.801 0.003 301.761 0.000 0.795
## Stst7bl (.28.) 0.359 0.004 88.903 0.000 0.351
## Stst8rn (.29.) 0.173 0.004 43.982 0.000 0.165
## Stst11r (.30.) 0.725 0.003 275.976 0.000 0.720
## Stst12l (.31.) 0.651 0.003 234.003 0.000 0.646
## Stst13h (.32.) 0.546 0.004 128.941 0.000 0.537
## Stst14b (.33.) 0.627 0.003 231.675 0.000 0.621
## Stst15t (.34.) 0.694 0.003 275.100 0.000 0.689
## Stst16m (.35.) 0.660 0.003 230.478 0.000 0.654
## Stst19d (.36.) 0.238 0.005 51.792 0.000 0.229
## Stst26r (.37.) 0.586 0.004 159.811 0.000 0.579
## science =~
## Stst1vc (.38.) 0.237 0.003 73.979 0.000 0.231
## Stst6ph (.39.) 0.515 0.003 149.716 0.000 0.508
## Stst7bl (.40.) 0.413 0.004 94.294 0.000 0.405
## Stst8rn (.41.) 0.442 0.004 101.405 0.000 0.434
## Stst9lc (.42.) 0.635 0.003 214.586 0.000 0.629
## Stst10m (.43.) 0.578 0.003 200.465 0.000 0.572
## Stst13h (.44.) 0.105 0.004 23.464 0.000 0.096
## Stst28m (.45.) 0.271 0.003 78.010 0.000 0.264
## spatial =~
## Stst28m (.46.) 0.505 0.003 146.303 0.000 0.498
## Sts292D (.47.) 0.515 0.003 163.105 0.000 0.509
## Sts303D (.48.) 0.773 0.003 238.808 0.000 0.766
## Stst31b (.49.) 0.451 0.003 132.128 0.000 0.445
## Stst32r (.50.) 0.167 0.003 53.910 0.000 0.161
## Stst37b (.51.) 0.155 0.003 51.182 0.000 0.149
## ci.upper Std.lv Std.all
##
## 0.380 0.337 0.354
## 0.654 0.590 0.648
## 0.642 0.579 0.625
## 0.808 0.730 0.817
## 0.680 0.613 0.675
## 0.600 0.540 0.596
## 0.543 0.486 0.514
## 0.317 0.282 0.308
## 0.353 0.316 0.337
## 0.313 0.276 0.291
## 0.147 0.124 0.135
##
## 0.813 0.756 0.797
## 0.389 0.357 0.397
## 0.284 0.257 0.272
## 0.402 0.366 0.385
## 0.883 0.820 0.869
## 0.353 0.320 0.348
##
## 0.297 0.261 0.274
## 0.235 0.205 0.215
## 0.385 0.339 0.369
## 0.674 0.596 0.735
## 0.717 0.634 0.692
## 0.583 0.514 0.559
##
## 0.675 0.635 0.685
## 0.837 0.790 0.824
## 0.737 0.695 0.731
## 0.806 0.760 0.817
## 0.367 0.341 0.360
## 0.181 0.164 0.177
## 0.731 0.688 0.720
## 0.657 0.618 0.641
## 0.554 0.518 0.553
## 0.632 0.595 0.599
## 0.699 0.659 0.692
## 0.666 0.626 0.664
## 0.247 0.226 0.238
## 0.593 0.556 0.608
##
## 0.243 0.196 0.212
## 0.522 0.427 0.474
## 0.422 0.343 0.362
## 0.451 0.367 0.395
## 0.640 0.526 0.594
## 0.584 0.479 0.639
## 0.114 0.087 0.093
## 0.278 0.225 0.272
##
## 0.512 0.467 0.565
## 0.522 0.476 0.500
## 0.779 0.714 0.767
## 0.458 0.417 0.445
## 0.173 0.155 0.163
## 0.161 0.143 0.156
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.651 0.005 126.329 0.000 0.641
## speed 0.230 0.005 48.363 0.000 0.220
## info 0.704 0.006 123.892 0.000 0.693
## science 0.397 0.005 83.190 0.000 0.388
## spatial 0.447 0.005 90.094 0.000 0.437
## math ~~
## speed 0.161 0.004 37.332 0.000 0.152
## info 0.666 0.005 127.630 0.000 0.656
## science 0.472 0.005 95.344 0.000 0.462
## spatial 0.497 0.005 97.964 0.000 0.488
## speed ~~
## info 0.178 0.004 39.673 0.000 0.169
## science 0.060 0.004 14.665 0.000 0.052
## spatial 0.165 0.005 34.685 0.000 0.155
## info ~~
## science 0.561 0.005 108.596 0.000 0.551
## spatial 0.448 0.005 91.414 0.000 0.438
## science ~~
## spatial 0.409 0.005 83.225 0.000 0.399
## ci.upper Std.lv Std.all
##
## 0.661 0.765 0.765
## 0.239 0.282 0.282
## 0.715 0.815 0.815
## 0.407 0.527 0.527
## 0.456 0.531 0.531
##
## 0.169 0.192 0.192
## 0.676 0.750 0.750
## 0.482 0.609 0.609
## 0.507 0.576 0.576
##
## 0.187 0.210 0.210
## 0.068 0.081 0.081
## 0.174 0.199 0.199
##
## 0.571 0.713 0.713
## 0.457 0.511 0.511
##
## 0.419 0.534 0.534
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.156 0.004 40.337 0.000 0.149
## .Stest20spellng 0.288 0.004 79.198 0.000 0.281
## .Stest21cptlztn 0.285 0.004 77.178 0.000 0.278
## .Stest22puncttn 0.289 0.004 80.304 0.000 0.282
## .Stest23english 0.200 0.004 55.481 0.000 0.193
## .Stest24exprssn 0.175 0.004 49.287 0.000 0.169
## .Stst25wrdfnctn 0.208 0.004 52.986 0.000 0.200
## .Stst26rdngcmpr 0.118 0.004 32.716 0.000 0.111
## .Stst31bstrctrs 0.037 0.004 9.666 0.000 0.029
## .Stst32rthrsnng -0.030 0.004 -7.900 0.000 -0.038
## .Stst34rthcmptt 0.175 0.004 47.455 0.000 0.168
## .Stest5math -0.133 0.004 -34.579 0.000 -0.141
## .Stst6physclscn -0.264 0.004 -73.191 0.000 -0.272
## .Stst33hghschlm -0.063 0.004 -17.147 0.000 -0.070
## .Stst29vslztn2D -0.144 0.004 -37.867 0.000 -0.151
## .Stest35tblrdng 0.099 0.003 30.730 0.000 0.092
## .Stst36clrclchc 0.087 0.004 23.895 0.000 0.079
## .Stst37bjctnspc 0.084 0.004 22.958 0.000 0.077
## .Stest1vocab -0.083 0.004 -21.517 0.000 -0.091
## .Stest2literatr 0.025 0.004 6.452 0.000 0.017
## .Stest3music 0.163 0.004 42.478 0.000 0.155
## .Stest4soclstds -0.132 0.004 -35.225 0.000 -0.139
## .Stst7blgclscnc -0.156 0.004 -40.430 0.000 -0.164
## .Stest8aerontcs -0.404 0.004 -112.676 0.000 -0.411
## .Stest11art 0.108 0.004 28.115 0.000 0.101
## .Stest12law -0.138 0.004 -36.597 0.000 -0.145
## .Stest13health 0.168 0.004 45.803 0.000 0.161
## .Stest14bible 0.070 0.004 17.656 0.000 0.062
## .Stest15theater 0.207 0.004 54.125 0.000 0.200
## .Stest16mscllns -0.071 0.004 -19.463 0.000 -0.078
## .Stest9elctrncs -0.416 0.003 -119.952 0.000 -0.423
## .Stest10mechncs -0.511 0.003 -170.689 0.000 -0.517
## .Stst28mchnclrs -0.422 0.003 -128.379 0.000 -0.429
## .Stst30vslztn3D -0.109 0.004 -29.486 0.000 -0.116
## ci.upper Std.lv Std.all
## 0.164 0.156 0.164
## 0.295 0.288 0.316
## 0.292 0.285 0.307
## 0.296 0.289 0.324
## 0.207 0.200 0.220
## 0.182 0.175 0.194
## 0.216 0.208 0.220
## 0.125 0.118 0.129
## 0.044 0.037 0.039
## -0.023 -0.030 -0.032
## 0.182 0.175 0.190
## -0.126 -0.133 -0.141
## -0.257 -0.264 -0.294
## -0.056 -0.063 -0.066
## -0.136 -0.144 -0.151
## 0.105 0.099 0.121
## 0.094 0.087 0.094
## 0.091 0.084 0.091
## -0.076 -0.083 -0.090
## 0.032 0.025 0.026
## 0.170 0.163 0.171
## -0.125 -0.132 -0.142
## -0.149 -0.156 -0.165
## -0.397 -0.404 -0.436
## 0.116 0.108 0.113
## -0.130 -0.138 -0.143
## 0.175 0.168 0.179
## 0.077 0.070 0.070
## 0.215 0.207 0.218
## -0.064 -0.071 -0.075
## -0.409 -0.416 -0.470
## -0.505 -0.511 -0.682
## -0.416 -0.422 -0.512
## -0.102 -0.109 -0.117
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.475 0.003 163.117 0.000 0.469
## .Stest20spellng 0.482 0.003 165.457 0.000 0.476
## .Stest21cptlztn 0.523 0.003 165.146 0.000 0.517
## .Stest22puncttn 0.266 0.002 132.341 0.000 0.262
## .Stest23english 0.448 0.003 157.779 0.000 0.442
## .Stest24exprssn 0.528 0.004 148.243 0.000 0.521
## .Stst25wrdfnctn 0.400 0.003 147.191 0.000 0.394
## .Stst26rdngcmpr 0.191 0.001 139.258 0.000 0.189
## .Stst31bstrctrs 0.464 0.003 154.202 0.000 0.458
## .Stst32rthrsnng 0.405 0.002 165.928 0.000 0.400
## .Stst34rthcmptt 0.487 0.003 141.554 0.000 0.480
## .Stest5math 0.327 0.003 100.245 0.000 0.321
## .Stst6physclscn 0.315 0.002 144.530 0.000 0.310
## .Stst33hghschlm 0.218 0.002 102.798 0.000 0.214
## .Stst29vslztn2D 0.598 0.004 157.584 0.000 0.590
## .Stest35tblrdng 0.302 0.004 84.435 0.000 0.295
## .Stst36clrclchc 0.438 0.004 99.260 0.000 0.430
## .Stst37bjctnspc 0.533 0.004 140.945 0.000 0.525
## .Stest1vocab 0.241 0.002 149.183 0.000 0.237
## .Stest2literatr 0.294 0.002 158.291 0.000 0.291
## .Stest3music 0.421 0.003 166.568 0.000 0.416
## .Stest4soclstds 0.288 0.002 156.766 0.000 0.284
## .Stst7blgclscnc 0.498 0.003 171.291 0.000 0.493
## .Stest8aerontcs 0.612 0.003 180.593 0.000 0.605
## .Stest11art 0.439 0.003 169.687 0.000 0.434
## .Stest12law 0.548 0.003 177.306 0.000 0.542
## .Stest13health 0.537 0.003 172.767 0.000 0.531
## .Stest14bible 0.631 0.003 192.932 0.000 0.624
## .Stest15theater 0.472 0.003 173.326 0.000 0.467
## .Stest16mscllns 0.497 0.003 170.804 0.000 0.491
## .Stest9elctrncs 0.507 0.004 120.160 0.000 0.499
## .Stest10mechncs 0.333 0.002 150.601 0.000 0.328
## .Stst28mchnclrs 0.301 0.002 135.658 0.000 0.296
## .Stst30vslztn3D 0.357 0.003 109.082 0.000 0.351
## english 0.828 0.007 111.892 0.000 0.813
## math 0.874 0.007 128.094 0.000 0.860
## speed 0.800 0.010 81.221 0.000 0.780
## info 0.901 0.007 134.023 0.000 0.888
## science 0.687 0.007 95.945 0.000 0.673
## spatial 0.854 0.008 101.340 0.000 0.837
## ci.upper Std.lv Std.all
## 0.480 0.475 0.524
## 0.487 0.482 0.581
## 0.530 0.523 0.609
## 0.270 0.266 0.333
## 0.453 0.448 0.544
## 0.535 0.528 0.644
## 0.405 0.400 0.447
## 0.194 0.191 0.229
## 0.470 0.464 0.529
## 0.409 0.405 0.447
## 0.494 0.487 0.575
## 0.333 0.327 0.364
## 0.319 0.315 0.388
## 0.222 0.218 0.245
## 0.605 0.598 0.660
## 0.310 0.302 0.460
## 0.447 0.438 0.521
## 0.540 0.533 0.629
## 0.244 0.241 0.280
## 0.298 0.294 0.321
## 0.426 0.421 0.465
## 0.292 0.288 0.333
## 0.504 0.498 0.555
## 0.619 0.612 0.712
## 0.444 0.439 0.481
## 0.554 0.548 0.589
## 0.543 0.537 0.612
## 0.637 0.631 0.641
## 0.478 0.472 0.521
## 0.502 0.497 0.559
## 0.515 0.507 0.647
## 0.337 0.333 0.592
## 0.305 0.301 0.442
## 0.364 0.357 0.412
## 0.842 1.000 1.000
## 0.887 1.000 1.000
## 0.819 1.000 1.000
## 0.914 1.000 1.000
## 0.701 1.000 1.000
## 0.870 1.000 1.000
lavTestScore(metric, release = 1:51) # X2 test for released constraints among all loadings (including cross loadings)
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 8379.367 51 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p147. 118.277 1 0.000
## 2 .p2. == .p148. 13.664 1 0.000
## 3 .p3. == .p149. 79.251 1 0.000
## 4 .p4. == .p150. 3.579 1 0.059
## 5 .p5. == .p151. 86.323 1 0.000
## 6 .p6. == .p152. 326.342 1 0.000
## 7 .p7. == .p153. 906.198 1 0.000
## 8 .p8. == .p154. 181.251 1 0.000
## 9 .p9. == .p155. 53.061 1 0.000
## 10 .p10. == .p156. 154.052 1 0.000
## 11 .p11. == .p157. 0.718 1 0.397
## 12 .p12. == .p158. 464.557 1 0.000
## 13 .p13. == .p159. 4.808 1 0.028
## 14 .p14. == .p160. 879.958 1 0.000
## 15 .p15. == .p161. 43.670 1 0.000
## 16 .p16. == .p162. 1026.269 1 0.000
## 17 .p17. == .p163. 3.887 1 0.049
## 18 .p18. == .p164. 269.670 1 0.000
## 19 .p19. == .p165. 0.018 1 0.892
## 20 .p20. == .p166. 0.348 1 0.555
## 21 .p21. == .p167. 166.858 1 0.000
## 22 .p22. == .p168. 10.502 1 0.001
## 23 .p23. == .p169. 3.128 1 0.077
## 24 .p24. == .p170. 2035.967 1 0.000
## 25 .p25. == .p171. 2.253 1 0.133
## 26 .p26. == .p172. 8.330 1 0.004
## 27 .p27. == .p173. 6.907 1 0.009
## 28 .p28. == .p174. 231.385 1 0.000
## 29 .p29. == .p175. 772.986 1 0.000
## 30 .p30. == .p176. 45.805 1 0.000
## 31 .p31. == .p177. 384.688 1 0.000
## 32 .p32. == .p178. 428.368 1 0.000
## 33 .p33. == .p179. 32.583 1 0.000
## 34 .p34. == .p180. 34.175 1 0.000
## 35 .p35. == .p181. 965.473 1 0.000
## 36 .p36. == .p182. 30.994 1 0.000
## 37 .p37. == .p183. 258.895 1 0.000
## 38 .p38. == .p184. 1026.254 1 0.000
## 39 .p39. == .p185. 187.125 1 0.000
## 40 .p40. == .p186. 273.215 1 0.000
## 41 .p41. == .p187. 520.508 1 0.000
## 42 .p42. == .p188. 286.146 1 0.000
## 43 .p43. == .p189. 1.255 1 0.263
## 44 .p44. == .p190. 294.206 1 0.000
## 45 .p45. == .p191. 80.673 1 0.000
## 46 .p46. == .p192. 6.891 1 0.009
## 47 .p47. == .p193. 4.278 1 0.039
## 48 .p48. == .p194. 32.249 1 0.000
## 49 .p49. == .p195. 34.691 1 0.000
## 50 .p50. == .p196. 38.437 1 0.000
## 51 .p51. == .p197. 1.079 1 0.299
metric2<-cfa(chc.factor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings"), group.partial=c("info=~Stest1vocab"))
fitMeasures(metric2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 131930.766 1034.000 0.000 0.950 0.043
## srmr aic bic
## 0.038 10335769.265 10337974.010
Mc(metric2)
## [1] 0.6245802
scalar<-cfa(chc.factor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 200513.435 1063.000 0.000 0.924 0.052
## srmr aic bic
## 0.045 10404293.934 10406213.243
Mc(scalar)
## [1] 0.4881272
summary(scalar, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 90 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 280
## Number of equality constraints 85
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 200513.435 175786.410
## Degrees of freedom 1063 1063
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.141
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 108735.315 95326.234
## 1 91778.120 80460.175
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.338 0.004 82.714 0.000 0.330
## Stst20s (.p2.) 0.672 0.003 237.406 0.000 0.666
## Stst21c (.p3.) 0.652 0.003 233.199 0.000 0.647
## Stst22p (.p4.) 0.801 0.003 291.052 0.000 0.795
## Stst23n (.p5.) 0.656 0.003 210.932 0.000 0.650
## Stst24x (.p6.) 0.574 0.003 183.344 0.000 0.568
## Stst25w (.p7.) 0.583 0.003 171.897 0.000 0.576
## Stst26r (.p8.) 0.265 0.003 87.944 0.000 0.259
## Stst31b (.p9.) 0.351 0.003 127.243 0.000 0.346
## Stst32r (.10.) 0.215 0.004 59.191 0.000 0.207
## Stst34r (.11.) 0.226 0.004 56.447 0.000 0.219
## math =~
## Stst5mt (.12.) 0.817 0.002 331.377 0.000 0.812
## Stst6ph (.13.) 0.493 0.003 179.170 0.000 0.488
## Stst25w (.14.) 0.227 0.003 66.251 0.000 0.220
## Stst32r (.15.) 0.469 0.005 100.707 0.000 0.460
## Stst33h (.16.) 0.861 0.003 302.847 0.000 0.855
## Stst34r (.17.) 0.252 0.004 62.532 0.000 0.244
## speed =~
## Stst19d (.18.) 0.290 0.003 104.305 0.000 0.284
## Sts292D (.19.) 0.203 0.003 66.002 0.000 0.197
## Stst34r (.20.) 0.379 0.003 121.678 0.000 0.373
## Stst35t (.21.) 0.658 0.004 162.762 0.000 0.650
## Stst36c (.22.) 0.715 0.004 193.517 0.000 0.708
## Stst37b (.23.) 0.589 0.004 163.111 0.000 0.581
## info =~
## Stst1vc (.24.) 0.724 0.003 281.359 0.000 0.719
## Stst2lt (.25.) 0.829 0.003 325.025 0.000 0.824
## Stst3ms (.26.) 0.728 0.003 285.669 0.000 0.723
## Stst4sc (.27.) 0.798 0.003 302.751 0.000 0.792
## Stst7bl (.28.) 0.471 0.003 162.711 0.000 0.465
## Stst8rn (.29.) 0.146 0.003 48.967 0.000 0.140
## Stst11r (.30.) 0.722 0.003 268.997 0.000 0.716
## Stst12l (.31.) 0.651 0.003 234.419 0.000 0.646
## Stst13h (.32.) 0.683 0.004 187.032 0.000 0.676
## Stst14b (.33.) 0.626 0.003 230.642 0.000 0.620
## Stst15t (.34.) 0.687 0.003 257.605 0.000 0.682
## Stst16m (.35.) 0.660 0.003 231.343 0.000 0.654
## Stst19d (.36.) 0.267 0.004 67.776 0.000 0.259
## Stst26r (.37.) 0.625 0.003 199.940 0.000 0.618
## science =~
## Stst1vc (.38.) 0.166 0.002 97.771 0.000 0.163
## Stst6ph (.39.) 0.344 0.003 137.301 0.000 0.339
## Stst7bl (.40.) 0.266 0.002 111.605 0.000 0.262
## Stst8rn (.41.) 0.496 0.003 188.266 0.000 0.491
## Stst9lc (.42.) 0.596 0.003 230.722 0.000 0.591
## Stst10m (.43.) 0.640 0.002 261.258 0.000 0.635
## Stst13h (.44.) -0.093 0.002 -39.403 0.000 -0.098
## Stst28m (.45.) 0.371 0.003 143.867 0.000 0.366
## spatial =~
## Stst28m (.46.) 0.455 0.003 144.370 0.000 0.449
## Sts292D (.47.) 0.544 0.003 183.409 0.000 0.538
## Sts303D (.48.) 0.739 0.004 207.365 0.000 0.732
## Stst31b (.49.) 0.449 0.003 150.228 0.000 0.443
## Stst32r (.50.) 0.177 0.003 56.664 0.000 0.171
## Stst37b (.51.) 0.134 0.003 46.613 0.000 0.129
## ci.upper Std.lv Std.all
##
## 0.346 0.338 0.343
## 0.677 0.672 0.669
## 0.658 0.652 0.673
## 0.806 0.801 0.823
## 0.662 0.656 0.670
## 0.580 0.574 0.577
## 0.589 0.583 0.579
## 0.271 0.265 0.270
## 0.357 0.351 0.360
## 0.222 0.215 0.216
## 0.234 0.226 0.232
##
## 0.822 0.817 0.868
## 0.499 0.493 0.527
## 0.234 0.227 0.225
## 0.478 0.469 0.473
## 0.866 0.861 0.853
## 0.260 0.252 0.258
##
## 0.295 0.290 0.294
## 0.210 0.203 0.209
## 0.385 0.379 0.387
## 0.665 0.658 0.708
## 0.722 0.715 0.731
## 0.596 0.589 0.579
##
## 0.729 0.724 0.756
## 0.834 0.829 0.837
## 0.733 0.728 0.720
## 0.803 0.798 0.809
## 0.476 0.471 0.483
## 0.151 0.146 0.169
## 0.727 0.722 0.735
## 0.657 0.651 0.658
## 0.691 0.683 0.702
## 0.631 0.626 0.622
## 0.692 0.687 0.695
## 0.666 0.660 0.656
## 0.275 0.267 0.271
## 0.631 0.625 0.636
##
## 0.170 0.166 0.173
## 0.349 0.344 0.368
## 0.271 0.266 0.274
## 0.502 0.496 0.574
## 0.601 0.596 0.760
## 0.645 0.640 0.750
## -0.089 -0.093 -0.096
## 0.376 0.371 0.412
##
## 0.461 0.455 0.506
## 0.550 0.544 0.559
## 0.746 0.739 0.744
## 0.455 0.449 0.460
## 0.183 0.177 0.178
## 0.140 0.134 0.132
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.844 0.002 420.959 0.000 0.840
## speed 0.264 0.005 51.071 0.000 0.254
## info 0.822 0.002 432.814 0.000 0.818
## science 0.510 0.004 122.976 0.000 0.502
## spatial 0.489 0.004 110.889 0.000 0.480
## math ~~
## speed 0.246 0.005 49.204 0.000 0.237
## info 0.825 0.002 442.679 0.000 0.821
## science 0.625 0.004 177.025 0.000 0.618
## spatial 0.575 0.004 146.704 0.000 0.567
## speed ~~
## info 0.241 0.005 48.658 0.000 0.231
## science 0.054 0.005 9.829 0.000 0.043
## spatial 0.177 0.006 30.992 0.000 0.166
## info ~~
## science 0.708 0.003 227.496 0.000 0.702
## spatial 0.458 0.004 106.957 0.000 0.449
## science ~~
## spatial 0.604 0.004 142.073 0.000 0.595
## ci.upper Std.lv Std.all
##
## 0.848 0.844 0.844
## 0.274 0.264 0.264
## 0.826 0.822 0.822
## 0.518 0.510 0.510
## 0.497 0.489 0.489
##
## 0.256 0.246 0.246
## 0.828 0.825 0.825
## 0.632 0.625 0.625
## 0.582 0.575 0.575
##
## 0.250 0.241 0.241
## 0.064 0.054 0.054
## 0.189 0.177 0.177
##
## 0.714 0.708 0.708
## 0.466 0.458 0.458
##
## 0.612 0.604 0.604
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.107) -0.123 0.004 -33.826 0.000 -0.130
## .Stst20s (.108) -0.178 0.004 -48.808 0.000 -0.185
## .Stst21c (.109) -0.155 0.004 -42.995 0.000 -0.162
## .Stst22p (.110) -0.193 0.004 -50.947 0.000 -0.201
## .Stst23n (.111) -0.164 0.004 -45.027 0.000 -0.171
## .Stst24x (.112) -0.139 0.004 -37.930 0.000 -0.146
## .Stst25w (.113) -0.101 0.004 -26.923 0.000 -0.108
## .Stst26r (.114) -0.020 0.004 -5.005 0.000 -0.028
## .Stst31b (.115) 0.080 0.004 21.291 0.000 0.073
## .Stst32r (.116) 0.112 0.004 28.942 0.000 0.105
## .Stst34r (.117) -0.034 0.004 -9.061 0.000 -0.042
## .Stst5mt (.118) 0.176 0.004 46.298 0.000 0.168
## .Stst6ph (.119) 0.409 0.004 109.511 0.000 0.402
## .Stst33h (.120) 0.168 0.004 41.317 0.000 0.160
## .Sts292D (.121) 0.170 0.004 46.795 0.000 0.163
## .Stst35t (.122) -0.082 0.003 -23.506 0.000 -0.089
## .Stst36c (.123) -0.151 0.004 -41.219 0.000 -0.158
## .Stst37b (.124) -0.056 0.004 -15.411 0.000 -0.063
## .Stst1vc (.125) 0.199 0.004 53.494 0.000 0.191
## .Stst2lt (.126) 0.033 0.004 8.589 0.000 0.026
## .Stst3ms (.127) 0.034 0.004 9.055 0.000 0.027
## .Stst4sc (.128) 0.051 0.004 12.729 0.000 0.043
## .Stst7bl (.129) 0.272 0.004 71.908 0.000 0.265
## .Stst8rn (.130) 0.467 0.003 135.933 0.000 0.460
## .Stst11r (.131) 0.032 0.004 8.783 0.000 0.025
## .Stst12l (.132) 0.043 0.004 11.833 0.000 0.036
## .Stst13h (.133) -0.030 0.004 -7.542 0.000 -0.038
## .Stst14b (.134) 0.047 0.004 13.146 0.000 0.040
## .Stst15t (.135) 0.023 0.004 6.303 0.000 0.016
## .Stst16m (.136) 0.030 0.004 8.145 0.000 0.023
## .Stst9lc (.137) 0.548 0.003 181.199 0.000 0.542
## .Stst10m (.138) 0.612 0.003 184.358 0.000 0.605
## .Stst28m (.139) 0.517 0.004 145.684 0.000 0.510
## .Sts303D (.140) 0.271 0.004 69.570 0.000 0.264
## ci.upper Std.lv Std.all
## -0.116 -0.123 -0.125
## -0.171 -0.178 -0.178
## -0.148 -0.155 -0.160
## -0.186 -0.193 -0.199
## -0.157 -0.164 -0.168
## -0.131 -0.139 -0.139
## -0.094 -0.101 -0.100
## -0.012 -0.020 -0.020
## 0.087 0.080 0.082
## 0.120 0.112 0.113
## -0.027 -0.034 -0.035
## 0.183 0.176 0.187
## 0.417 0.409 0.437
## 0.176 0.168 0.167
## 0.177 0.170 0.175
## -0.075 -0.082 -0.089
## -0.144 -0.151 -0.154
## -0.049 -0.056 -0.055
## 0.206 0.199 0.207
## 0.041 0.033 0.033
## 0.041 0.034 0.034
## 0.059 0.051 0.052
## 0.280 0.272 0.280
## 0.474 0.467 0.540
## 0.039 0.032 0.032
## 0.051 0.043 0.044
## -0.022 -0.030 -0.031
## 0.054 0.047 0.046
## 0.031 0.023 0.024
## 0.037 0.030 0.030
## 0.554 0.548 0.699
## 0.618 0.612 0.717
## 0.524 0.517 0.575
## 0.279 0.271 0.273
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.466 0.003 161.034 0.000 0.460
## .Stest20spellng 0.556 0.003 160.060 0.000 0.549
## .Stest21cptlztn 0.514 0.003 163.087 0.000 0.508
## .Stest22puncttn 0.305 0.002 135.998 0.000 0.301
## .Stest23english 0.527 0.003 152.108 0.000 0.521
## .Stest24exprssn 0.661 0.004 157.415 0.000 0.653
## .Stst25wrdfnctn 0.400 0.003 148.425 0.000 0.394
## .Stst26rdngcmpr 0.232 0.002 136.870 0.000 0.228
## .Stst31bstrctrs 0.473 0.003 148.216 0.000 0.467
## .Stst32rthrsnng 0.383 0.002 156.744 0.000 0.378
## .Stst34rthcmptt 0.509 0.003 148.802 0.000 0.502
## .Stest5math 0.218 0.003 86.673 0.000 0.213
## .Stst6physclscn 0.302 0.002 147.794 0.000 0.298
## .Stst33hghschlm 0.276 0.002 122.037 0.000 0.272
## .Stst29vslztn2D 0.569 0.004 135.419 0.000 0.561
## .Stest35tblrdng 0.429 0.005 93.010 0.000 0.420
## .Stst36clrclchc 0.446 0.005 86.247 0.000 0.436
## .Stst37bjctnspc 0.640 0.005 137.351 0.000 0.630
## .Stest1vocab 0.196 0.001 143.123 0.000 0.193
## .Stest2literatr 0.294 0.002 155.443 0.000 0.290
## .Stest3music 0.491 0.003 163.267 0.000 0.485
## .Stest4soclstds 0.335 0.002 145.235 0.000 0.330
## .Stst7blgclscnc 0.477 0.003 163.838 0.000 0.472
## .Stest8aerontcs 0.377 0.003 116.649 0.000 0.370
## .Stest11art 0.444 0.003 167.357 0.000 0.439
## .Stest12law 0.556 0.003 167.714 0.000 0.549
## .Stest13health 0.563 0.003 171.166 0.000 0.557
## .Stest14bible 0.619 0.003 186.149 0.000 0.613
## .Stest15theater 0.505 0.003 163.397 0.000 0.499
## .Stest16mscllns 0.576 0.003 165.270 0.000 0.569
## .Stest9elctrncs 0.260 0.003 89.237 0.000 0.254
## .Stest10mechncs 0.318 0.002 131.625 0.000 0.313
## .Stst28mchnclrs 0.261 0.002 115.825 0.000 0.257
## .Stst30vslztn3D 0.439 0.004 109.894 0.000 0.431
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.471 0.466 0.479
## 0.563 0.556 0.552
## 0.520 0.514 0.547
## 0.309 0.305 0.322
## 0.534 0.527 0.551
## 0.669 0.661 0.668
## 0.405 0.400 0.394
## 0.235 0.232 0.240
## 0.479 0.473 0.497
## 0.388 0.383 0.390
## 0.516 0.509 0.533
## 0.223 0.218 0.246
## 0.306 0.302 0.345
## 0.281 0.276 0.272
## 0.577 0.569 0.602
## 0.438 0.429 0.498
## 0.456 0.446 0.466
## 0.649 0.640 0.620
## 0.198 0.196 0.213
## 0.297 0.294 0.300
## 0.497 0.491 0.481
## 0.339 0.335 0.345
## 0.483 0.477 0.504
## 0.383 0.377 0.504
## 0.449 0.444 0.460
## 0.562 0.556 0.567
## 0.570 0.563 0.594
## 0.626 0.619 0.613
## 0.511 0.505 0.517
## 0.583 0.576 0.569
## 0.266 0.260 0.423
## 0.323 0.318 0.437
## 0.265 0.261 0.322
## 0.447 0.439 0.446
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.338 0.004 82.714 0.000 0.330
## Stst20s (.p2.) 0.672 0.003 237.406 0.000 0.666
## Stst21c (.p3.) 0.652 0.003 233.199 0.000 0.647
## Stst22p (.p4.) 0.801 0.003 291.052 0.000 0.795
## Stst23n (.p5.) 0.656 0.003 210.932 0.000 0.650
## Stst24x (.p6.) 0.574 0.003 183.344 0.000 0.568
## Stst25w (.p7.) 0.583 0.003 171.897 0.000 0.576
## Stst26r (.p8.) 0.265 0.003 87.944 0.000 0.259
## Stst31b (.p9.) 0.351 0.003 127.243 0.000 0.346
## Stst32r (.10.) 0.215 0.004 59.191 0.000 0.207
## Stst34r (.11.) 0.226 0.004 56.447 0.000 0.219
## math =~
## Stst5mt (.12.) 0.817 0.002 331.377 0.000 0.812
## Stst6ph (.13.) 0.493 0.003 179.170 0.000 0.488
## Stst25w (.14.) 0.227 0.003 66.251 0.000 0.220
## Stst32r (.15.) 0.469 0.005 100.707 0.000 0.460
## Stst33h (.16.) 0.861 0.003 302.847 0.000 0.855
## Stst34r (.17.) 0.252 0.004 62.532 0.000 0.244
## speed =~
## Stst19d (.18.) 0.290 0.003 104.305 0.000 0.284
## Sts292D (.19.) 0.203 0.003 66.002 0.000 0.197
## Stst34r (.20.) 0.379 0.003 121.678 0.000 0.373
## Stst35t (.21.) 0.658 0.004 162.762 0.000 0.650
## Stst36c (.22.) 0.715 0.004 193.517 0.000 0.708
## Stst37b (.23.) 0.589 0.004 163.111 0.000 0.581
## info =~
## Stst1vc (.24.) 0.724 0.003 281.359 0.000 0.719
## Stst2lt (.25.) 0.829 0.003 325.025 0.000 0.824
## Stst3ms (.26.) 0.728 0.003 285.669 0.000 0.723
## Stst4sc (.27.) 0.798 0.003 302.751 0.000 0.792
## Stst7bl (.28.) 0.471 0.003 162.711 0.000 0.465
## Stst8rn (.29.) 0.146 0.003 48.967 0.000 0.140
## Stst11r (.30.) 0.722 0.003 268.997 0.000 0.716
## Stst12l (.31.) 0.651 0.003 234.419 0.000 0.646
## Stst13h (.32.) 0.683 0.004 187.032 0.000 0.676
## Stst14b (.33.) 0.626 0.003 230.642 0.000 0.620
## Stst15t (.34.) 0.687 0.003 257.605 0.000 0.682
## Stst16m (.35.) 0.660 0.003 231.343 0.000 0.654
## Stst19d (.36.) 0.267 0.004 67.776 0.000 0.259
## Stst26r (.37.) 0.625 0.003 199.940 0.000 0.618
## science =~
## Stst1vc (.38.) 0.166 0.002 97.771 0.000 0.163
## Stst6ph (.39.) 0.344 0.003 137.301 0.000 0.339
## Stst7bl (.40.) 0.266 0.002 111.605 0.000 0.262
## Stst8rn (.41.) 0.496 0.003 188.266 0.000 0.491
## Stst9lc (.42.) 0.596 0.003 230.722 0.000 0.591
## Stst10m (.43.) 0.640 0.002 261.258 0.000 0.635
## Stst13h (.44.) -0.093 0.002 -39.403 0.000 -0.098
## Stst28m (.45.) 0.371 0.003 143.867 0.000 0.366
## spatial =~
## Stst28m (.46.) 0.455 0.003 144.370 0.000 0.449
## Sts292D (.47.) 0.544 0.003 183.409 0.000 0.538
## Sts303D (.48.) 0.739 0.004 207.365 0.000 0.732
## Stst31b (.49.) 0.449 0.003 150.228 0.000 0.443
## Stst32r (.50.) 0.177 0.003 56.664 0.000 0.171
## Stst37b (.51.) 0.134 0.003 46.613 0.000 0.129
## ci.upper Std.lv Std.all
##
## 0.346 0.308 0.324
## 0.677 0.611 0.661
## 0.658 0.594 0.635
## 0.806 0.729 0.817
## 0.662 0.597 0.663
## 0.580 0.522 0.582
## 0.589 0.530 0.559
## 0.271 0.241 0.264
## 0.357 0.320 0.341
## 0.222 0.195 0.204
## 0.234 0.206 0.223
##
## 0.822 0.764 0.799
## 0.499 0.461 0.518
## 0.234 0.212 0.224
## 0.478 0.439 0.459
## 0.866 0.805 0.855
## 0.260 0.236 0.255
##
## 0.295 0.259 0.273
## 0.210 0.182 0.189
## 0.385 0.339 0.367
## 0.665 0.588 0.727
## 0.722 0.639 0.696
## 0.596 0.526 0.570
##
## 0.729 0.686 0.741
## 0.834 0.785 0.820
## 0.733 0.690 0.719
## 0.803 0.756 0.798
## 0.476 0.446 0.471
## 0.151 0.138 0.149
## 0.727 0.684 0.713
## 0.657 0.617 0.629
## 0.691 0.648 0.685
## 0.631 0.593 0.598
## 0.692 0.651 0.671
## 0.666 0.625 0.660
## 0.275 0.253 0.266
## 0.631 0.592 0.648
##
## 0.170 0.133 0.143
## 0.349 0.275 0.308
## 0.271 0.212 0.224
## 0.502 0.396 0.428
## 0.601 0.476 0.548
## 0.645 0.511 0.671
## -0.089 -0.075 -0.079
## 0.376 0.296 0.353
##
## 0.461 0.426 0.508
## 0.550 0.510 0.530
## 0.746 0.692 0.750
## 0.455 0.420 0.448
## 0.183 0.166 0.173
## 0.140 0.126 0.136
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.662 0.005 126.324 0.000 0.652
## speed 0.230 0.005 48.683 0.000 0.220
## info 0.704 0.006 123.660 0.000 0.692
## science 0.358 0.004 81.459 0.000 0.349
## spatial 0.451 0.005 87.799 0.000 0.441
## math ~~
## speed 0.163 0.004 37.614 0.000 0.154
## info 0.687 0.005 129.389 0.000 0.677
## science 0.459 0.005 95.584 0.000 0.450
## spatial 0.504 0.005 96.727 0.000 0.493
## speed ~~
## info 0.176 0.004 39.424 0.000 0.168
## science 0.063 0.004 15.534 0.000 0.055
## spatial 0.176 0.005 35.714 0.000 0.167
## info ~~
## science 0.542 0.005 109.415 0.000 0.532
## spatial 0.450 0.005 89.415 0.000 0.440
## science ~~
## spatial 0.396 0.005 81.112 0.000 0.387
## ci.upper Std.lv Std.all
##
## 0.673 0.779 0.779
## 0.239 0.282 0.282
## 0.715 0.816 0.816
## 0.366 0.493 0.493
## 0.461 0.529 0.529
##
## 0.171 0.195 0.195
## 0.697 0.776 0.776
## 0.469 0.616 0.616
## 0.514 0.575 0.575
##
## 0.185 0.208 0.208
## 0.070 0.088 0.088
## 0.186 0.210 0.210
##
## 0.551 0.716 0.716
## 0.460 0.507 0.507
##
## 0.406 0.530 0.530
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.107) -0.123 0.004 -33.826 0.000 -0.130
## .Stst20s (.108) -0.178 0.004 -48.808 0.000 -0.185
## .Stst21c (.109) -0.155 0.004 -42.995 0.000 -0.162
## .Stst22p (.110) -0.193 0.004 -50.947 0.000 -0.201
## .Stst23n (.111) -0.164 0.004 -45.027 0.000 -0.171
## .Stst24x (.112) -0.139 0.004 -37.930 0.000 -0.146
## .Stst25w (.113) -0.101 0.004 -26.923 0.000 -0.108
## .Stst26r (.114) -0.020 0.004 -5.005 0.000 -0.028
## .Stst31b (.115) 0.080 0.004 21.291 0.000 0.073
## .Stst32r (.116) 0.112 0.004 28.942 0.000 0.105
## .Stst34r (.117) -0.034 0.004 -9.061 0.000 -0.042
## .Stst5mt (.118) 0.176 0.004 46.298 0.000 0.168
## .Stst6ph (.119) 0.409 0.004 109.511 0.000 0.402
## .Stst33h (.120) 0.168 0.004 41.317 0.000 0.160
## .Sts292D (.121) 0.170 0.004 46.795 0.000 0.163
## .Stst35t (.122) -0.082 0.003 -23.506 0.000 -0.089
## .Stst36c (.123) -0.151 0.004 -41.219 0.000 -0.158
## .Stst37b (.124) -0.056 0.004 -15.411 0.000 -0.063
## .Stst1vc (.125) 0.199 0.004 53.494 0.000 0.191
## .Stst2lt (.126) 0.033 0.004 8.589 0.000 0.026
## .Stst3ms (.127) 0.034 0.004 9.055 0.000 0.027
## .Stst4sc (.128) 0.051 0.004 12.729 0.000 0.043
## .Stst7bl (.129) 0.272 0.004 71.908 0.000 0.265
## .Stst8rn (.130) 0.467 0.003 135.933 0.000 0.460
## .Stst11r (.131) 0.032 0.004 8.783 0.000 0.025
## .Stst12l (.132) 0.043 0.004 11.833 0.000 0.036
## .Stst13h (.133) -0.030 0.004 -7.542 0.000 -0.038
## .Stst14b (.134) 0.047 0.004 13.146 0.000 0.040
## .Stst15t (.135) 0.023 0.004 6.303 0.000 0.016
## .Stst16m (.136) 0.030 0.004 8.145 0.000 0.023
## .Stst9lc (.137) 0.548 0.003 181.199 0.000 0.542
## .Stst10m (.138) 0.612 0.003 184.358 0.000 0.605
## .Stst28m (.139) 0.517 0.004 145.684 0.000 0.510
## .Sts303D (.140) 0.271 0.004 69.570 0.000 0.264
## english 0.613 0.006 101.027 0.000 0.601
## math -0.297 0.006 -48.505 0.000 -0.309
## speed 0.313 0.007 45.830 0.000 0.299
## info -0.015 0.006 -2.422 0.015 -0.027
## science -1.704 0.009 -179.444 0.000 -1.722
## spatial -0.590 0.008 -73.089 0.000 -0.606
## ci.upper Std.lv Std.all
## -0.116 -0.123 -0.129
## -0.171 -0.178 -0.193
## -0.148 -0.155 -0.165
## -0.186 -0.193 -0.217
## -0.157 -0.164 -0.183
## -0.131 -0.139 -0.154
## -0.094 -0.101 -0.106
## -0.012 -0.020 -0.022
## 0.087 0.080 0.085
## 0.120 0.112 0.118
## -0.027 -0.034 -0.037
## 0.183 0.176 0.184
## 0.417 0.409 0.459
## 0.176 0.168 0.178
## 0.177 0.170 0.177
## -0.075 -0.082 -0.102
## -0.144 -0.151 -0.164
## -0.049 -0.056 -0.060
## 0.206 0.199 0.214
## 0.041 0.033 0.035
## 0.041 0.034 0.035
## 0.059 0.051 0.054
## 0.280 0.272 0.288
## 0.474 0.467 0.505
## 0.039 0.032 0.033
## 0.051 0.043 0.044
## -0.022 -0.030 -0.032
## 0.054 0.047 0.047
## 0.031 0.023 0.024
## 0.037 0.030 0.031
## 0.554 0.548 0.632
## 0.618 0.612 0.804
## 0.524 0.517 0.617
## 0.279 0.271 0.294
## 0.625 0.674 0.674
## -0.285 -0.318 -0.318
## 0.326 0.350 0.350
## -0.003 -0.016 -0.016
## -1.685 -2.135 -2.135
## -0.574 -0.629 -0.629
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.478 0.003 164.568 0.000 0.472
## .Stest20spellng 0.481 0.003 163.720 0.000 0.475
## .Stest21cptlztn 0.523 0.003 164.009 0.000 0.517
## .Stest22puncttn 0.265 0.002 131.870 0.000 0.261
## .Stest23english 0.453 0.003 157.635 0.000 0.447
## .Stest24exprssn 0.533 0.004 146.664 0.000 0.526
## .Stst25wrdfnctn 0.398 0.003 145.377 0.000 0.393
## .Stst26rdngcmpr 0.192 0.001 139.313 0.000 0.190
## .Stst31bstrctrs 0.461 0.003 154.196 0.000 0.455
## .Stst32rthrsnng 0.405 0.002 163.160 0.000 0.400
## .Stst34rthcmptt 0.493 0.003 142.950 0.000 0.487
## .Stest5math 0.330 0.003 99.291 0.000 0.324
## .Stst6physclscn 0.350 0.002 159.073 0.000 0.346
## .Stst33hghschlm 0.239 0.002 112.182 0.000 0.234
## .Stst29vslztn2D 0.593 0.004 153.653 0.000 0.586
## .Stest35tblrdng 0.307 0.004 84.655 0.000 0.300
## .Stst36clrclchc 0.435 0.004 100.609 0.000 0.426
## .Stst37bjctnspc 0.531 0.004 139.800 0.000 0.524
## .Stest1vocab 0.239 0.002 148.565 0.000 0.236
## .Stest2literatr 0.299 0.002 159.719 0.000 0.296
## .Stest3music 0.445 0.003 164.530 0.000 0.440
## .Stest4soclstds 0.325 0.002 147.321 0.000 0.321
## .Stst7blgclscnc 0.517 0.003 177.356 0.000 0.511
## .Stest8aerontcs 0.601 0.003 181.848 0.000 0.594
## .Stest11art 0.452 0.003 170.134 0.000 0.447
## .Stest12law 0.580 0.003 172.485 0.000 0.574
## .Stest13health 0.538 0.003 169.968 0.000 0.532
## .Stest14bible 0.632 0.003 192.790 0.000 0.626
## .Stest15theater 0.518 0.003 168.171 0.000 0.512
## .Stest16mscllns 0.506 0.003 170.237 0.000 0.500
## .Stest9elctrncs 0.526 0.004 125.108 0.000 0.518
## .Stest10mechncs 0.318 0.002 141.419 0.000 0.313
## .Stst28mchnclrs 0.300 0.002 133.608 0.000 0.296
## .Stst30vslztn3D 0.372 0.003 112.677 0.000 0.366
## english 0.828 0.007 112.528 0.000 0.814
## math 0.874 0.007 128.351 0.000 0.861
## speed 0.799 0.010 81.184 0.000 0.780
## info 0.898 0.007 133.754 0.000 0.885
## science 0.637 0.007 92.124 0.000 0.623
## spatial 0.878 0.009 97.235 0.000 0.860
## ci.upper Std.lv Std.all
## 0.483 0.478 0.529
## 0.487 0.481 0.563
## 0.529 0.523 0.597
## 0.269 0.265 0.333
## 0.459 0.453 0.560
## 0.540 0.533 0.662
## 0.403 0.398 0.442
## 0.195 0.192 0.231
## 0.466 0.461 0.522
## 0.409 0.405 0.443
## 0.500 0.493 0.579
## 0.337 0.330 0.362
## 0.354 0.350 0.441
## 0.243 0.239 0.269
## 0.601 0.593 0.641
## 0.315 0.307 0.471
## 0.443 0.435 0.515
## 0.539 0.531 0.624
## 0.243 0.239 0.279
## 0.303 0.299 0.327
## 0.451 0.445 0.484
## 0.329 0.325 0.363
## 0.523 0.517 0.577
## 0.607 0.601 0.703
## 0.457 0.452 0.491
## 0.587 0.580 0.604
## 0.544 0.538 0.602
## 0.638 0.632 0.643
## 0.524 0.518 0.550
## 0.512 0.506 0.564
## 0.534 0.526 0.699
## 0.322 0.318 0.549
## 0.304 0.300 0.427
## 0.379 0.372 0.437
## 0.843 1.000 1.000
## 0.888 1.000 1.000
## 0.818 1.000 1.000
## 0.911 1.000 1.000
## 0.650 1.000 1.000
## 0.895 1.000 1.000
lavTestScore(scalar, release = 52:85) # S4 and 15 much larger X2, followed by S12, S3, S6, then a bunch of medium size
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 63064.1 34 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p107. == .p253. 108.123 1 0.000
## 2 .p108. == .p254. 1200.540 1 0.000
## 3 .p109. == .p255. 530.669 1 0.000
## 4 .p110. == .p256. 73.221 1 0.000
## 5 .p111. == .p257. 632.588 1 0.000
## 6 .p112. == .p258. 515.274 1 0.000
## 7 .p113. == .p259. 311.823 1 0.000
## 8 .p114. == .p260. 327.603 1 0.000
## 9 .p115. == .p261. 21.352 1 0.000
## 10 .p116. == .p262. 810.704 1 0.000
## 11 .p117. == .p263. 488.794 1 0.000
## 12 .p118. == .p264. 2699.754 1 0.000
## 13 .p119. == .p265. 4451.121 1 0.000
## 14 .p120. == .p266. 818.227 1 0.000
## 15 .p121. == .p267. 1128.424 1 0.000
## 16 .p122. == .p268. 576.105 1 0.000
## 17 .p123. == .p269. 104.597 1 0.000
## 18 .p124. == .p270. 524.186 1 0.000
## 19 .p125. == .p271. 340.125 1 0.000
## 20 .p126. == .p272. 8.169 1 0.004
## 21 .p127. == .p273. 7106.709 1 0.000
## 22 .p128. == .p274. 15369.971 1 0.000
## 23 .p129. == .p275. 1055.029 1 0.000
## 24 .p130. == .p276. 434.130 1 0.000
## 25 .p131. == .p277. 2596.676 1 0.000
## 26 .p132. == .p278. 7407.245 1 0.000
## 27 .p133. == .p279. 2576.573 1 0.000
## 28 .p134. == .p280. 239.913 1 0.000
## 29 .p135. == .p281. 10915.606 1 0.000
## 30 .p136. == .p282. 2610.002 1 0.000
## 31 .p137. == .p283. 1509.141 1 0.000
## 32 .p138. == .p284. 1741.338 1 0.000
## 33 .p139. == .p285. 2339.563 1 0.000
## 34 .p140. == .p286. 3242.897 1 0.000
scalar2<-cfa(chc.factor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts"), group.partial=c("Stest4socialstudies~1", "Stest15theater~1", "Stest12law~1", "Stest3music~1", "Stest6physicalscience~1", "Stest16miscellaneous~1", "Stest30visualization3D~1", "Stest9electronics~1", "Stest5math~1", "Stest13health~1", "Stest7biologicalscience~1"))
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 143069.378 1052.000 0.000 0.946 0.044
## srmr aic bic
## 0.040 10346871.877 10348899.454
Mc(scalar2)
## [1] 0.6000977
summary(scalar2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 99 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 280
## Number of equality constraints 74
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 143069.378 125460.122
## Degrees of freedom 1052 1052
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.140
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 79331.571 69567.287
## 1 63737.807 55892.834
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.329 0.004 77.966 0.000 0.320
## Stst20s (.p2.) 0.671 0.003 236.606 0.000 0.665
## Stst21c (.p3.) 0.652 0.003 232.794 0.000 0.646
## Stst22p (.p4.) 0.801 0.003 290.425 0.000 0.795
## Stst23n (.p5.) 0.656 0.003 210.679 0.000 0.650
## Stst24x (.p6.) 0.574 0.003 183.278 0.000 0.568
## Stst25w (.p7.) 0.574 0.003 164.457 0.000 0.567
## Stst26r (.p8.) 0.248 0.003 79.367 0.000 0.242
## Stst31b (.p9.) 0.380 0.003 136.768 0.000 0.375
## Stst32r (.10.) 0.233 0.004 60.227 0.000 0.226
## Stst34r (.11.) 0.204 0.004 49.688 0.000 0.196
## math =~
## Stst5mt (.12.) 0.809 0.003 321.278 0.000 0.804
## Stst6ph (.13.) 0.391 0.003 121.700 0.000 0.385
## Stst25w (.14.) 0.237 0.004 67.344 0.000 0.230
## Stst32r (.15.) 0.441 0.005 89.658 0.000 0.431
## Stst33h (.16.) 0.874 0.003 313.027 0.000 0.869
## Stst34r (.17.) 0.278 0.004 67.584 0.000 0.270
## speed =~
## Stst19d (.18.) 0.289 0.003 103.819 0.000 0.283
## Sts292D (.19.) 0.226 0.003 74.446 0.000 0.220
## Stst34r (.20.) 0.379 0.003 122.276 0.000 0.373
## Stst35t (.21.) 0.656 0.004 163.168 0.000 0.648
## Stst36c (.22.) 0.712 0.004 193.567 0.000 0.705
## Stst37b (.23.) 0.594 0.004 165.867 0.000 0.587
## info =~
## Stst1vc (.24.) 0.718 0.003 286.629 0.000 0.713
## Stst2lt (.25.) 0.829 0.003 327.940 0.000 0.824
## Stst3ms (.26.) 0.731 0.002 298.782 0.000 0.727
## Stst4sc (.27.) 0.800 0.003 301.743 0.000 0.795
## Stst7bl (.28.) 0.371 0.004 93.921 0.000 0.363
## Stst8rn (.29.) 0.170 0.003 59.163 0.000 0.165
## Stst11r (.30.) 0.725 0.003 273.128 0.000 0.720
## Stst12l (.31.) 0.651 0.003 234.104 0.000 0.646
## Stst13h (.32.) 0.554 0.004 131.274 0.000 0.545
## Stst14b (.33.) 0.626 0.003 232.029 0.000 0.621
## Stst15t (.34.) 0.692 0.003 274.872 0.000 0.687
## Stst16m (.35.) 0.659 0.003 230.547 0.000 0.654
## Stst19d (.36.) 0.273 0.004 67.432 0.000 0.265
## Stst26r (.37.) 0.637 0.003 196.213 0.000 0.631
## science =~
## Stst1vc (.38.) 0.169 0.002 104.229 0.000 0.166
## Stst6ph (.39.) 0.509 0.003 150.993 0.000 0.502
## Stst7bl (.40.) 0.401 0.004 92.662 0.000 0.393
## Stst8rn (.41.) 0.450 0.003 171.439 0.000 0.444
## Stst9lc (.42.) 0.637 0.003 217.137 0.000 0.632
## Stst10m (.43.) 0.583 0.003 215.324 0.000 0.578
## Stst13h (.44.) 0.094 0.004 21.199 0.000 0.085
## Stst28m (.45.) 0.285 0.003 99.740 0.000 0.279
## spatial =~
## Stst28m (.46.) 0.500 0.003 153.515 0.000 0.494
## Sts292D (.47.) 0.521 0.003 174.534 0.000 0.515
## Sts303D (.48.) 0.773 0.003 236.736 0.000 0.767
## Stst31b (.49.) 0.413 0.003 136.309 0.000 0.407
## Stst32r (.50.) 0.193 0.003 65.452 0.000 0.187
## Stst37b (.51.) 0.123 0.003 44.028 0.000 0.117
## ci.upper Std.lv Std.all
##
## 0.337 0.329 0.334
## 0.676 0.671 0.668
## 0.657 0.652 0.673
## 0.806 0.801 0.823
## 0.662 0.656 0.670
## 0.580 0.574 0.577
## 0.580 0.574 0.570
## 0.254 0.248 0.253
## 0.386 0.380 0.389
## 0.241 0.233 0.235
## 0.212 0.204 0.208
##
## 0.814 0.809 0.867
## 0.397 0.391 0.405
## 0.244 0.237 0.235
## 0.451 0.441 0.444
## 0.880 0.874 0.864
## 0.286 0.278 0.284
##
## 0.294 0.289 0.293
## 0.232 0.226 0.233
## 0.385 0.379 0.387
## 0.664 0.656 0.707
## 0.719 0.712 0.728
## 0.601 0.594 0.585
##
## 0.723 0.718 0.750
## 0.834 0.829 0.838
## 0.736 0.731 0.732
## 0.805 0.800 0.827
## 0.378 0.371 0.376
## 0.176 0.170 0.200
## 0.730 0.725 0.738
## 0.656 0.651 0.668
## 0.562 0.554 0.569
## 0.632 0.626 0.624
## 0.697 0.692 0.713
## 0.665 0.659 0.660
## 0.281 0.273 0.278
## 0.643 0.637 0.650
##
## 0.172 0.169 0.177
## 0.516 0.509 0.527
## 0.410 0.401 0.407
## 0.455 0.450 0.529
## 0.643 0.637 0.789
## 0.588 0.583 0.709
## 0.103 0.094 0.097
## 0.290 0.285 0.324
##
## 0.507 0.500 0.569
## 0.527 0.521 0.539
## 0.780 0.773 0.767
## 0.419 0.413 0.423
## 0.199 0.193 0.195
## 0.128 0.123 0.121
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.842 0.002 416.508 0.000 0.838
## speed 0.267 0.005 51.789 0.000 0.257
## info 0.823 0.002 434.172 0.000 0.819
## science 0.526 0.004 127.565 0.000 0.518
## spatial 0.494 0.004 114.241 0.000 0.486
## math ~~
## speed 0.252 0.005 50.632 0.000 0.242
## info 0.810 0.002 412.883 0.000 0.806
## science 0.617 0.004 171.236 0.000 0.610
## spatial 0.571 0.004 148.801 0.000 0.564
## speed ~~
## info 0.244 0.005 49.546 0.000 0.235
## science 0.055 0.005 10.231 0.000 0.045
## spatial 0.171 0.006 30.550 0.000 0.160
## info ~~
## science 0.711 0.003 229.410 0.000 0.705
## spatial 0.467 0.004 112.141 0.000 0.459
## science ~~
## spatial 0.622 0.004 152.716 0.000 0.614
## ci.upper Std.lv Std.all
##
## 0.846 0.842 0.842
## 0.277 0.267 0.267
## 0.827 0.823 0.823
## 0.534 0.526 0.526
## 0.503 0.494 0.494
##
## 0.262 0.252 0.252
## 0.814 0.810 0.810
## 0.624 0.617 0.617
## 0.579 0.571 0.571
##
## 0.254 0.244 0.244
## 0.066 0.055 0.055
## 0.182 0.171 0.171
##
## 0.717 0.711 0.711
## 0.475 0.467 0.467
##
## 0.630 0.622 0.622
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.107) -0.130 0.004 -35.975 0.000 -0.137
## .Stst20s (.108) -0.177 0.004 -48.394 0.000 -0.184
## .Stst21c (.109) -0.154 0.004 -42.684 0.000 -0.161
## .Stst22p (.110) -0.192 0.004 -50.567 0.000 -0.200
## .Stst23n (.111) -0.164 0.004 -44.750 0.000 -0.171
## .Stst24x (.112) -0.138 0.004 -37.702 0.000 -0.145
## .Stst25w (.113) -0.104 0.004 -27.672 0.000 -0.111
## .Stst26r (.114) -0.035 0.004 -8.821 0.000 -0.043
## .Stst31b (.115) 0.104 0.004 28.001 0.000 0.097
## .Stst32r (.116) 0.114 0.004 29.211 0.000 0.106
## .Stst34r (.117) -0.035 0.004 -9.200 0.000 -0.042
## .Stst5mt 0.219 0.004 58.635 0.000 0.212
## .Stst6ph 0.358 0.004 92.152 0.000 0.350
## .Stst33h (.120) 0.141 0.004 33.468 0.000 0.132
## .Sts292D (.121) 0.212 0.004 58.071 0.000 0.205
## .Stst35t (.122) -0.087 0.003 -24.960 0.000 -0.094
## .Stst36c (.123) -0.156 0.004 -42.707 0.000 -0.163
## .Stst37b (.124) -0.051 0.004 -13.897 0.000 -0.058
## .Stst1vc (.125) 0.202 0.004 54.334 0.000 0.195
## .Stst2lt (.126) 0.008 0.004 2.064 0.039 0.000
## .Stst3ms -0.121 0.004 -29.896 0.000 -0.128
## .Stst4sc 0.228 0.004 57.617 0.000 0.220
## .Stst7bl 0.243 0.004 61.806 0.000 0.235
## .Stst8rn (.130) 0.480 0.003 139.826 0.000 0.473
## .Stst11r (.131) 0.010 0.004 2.714 0.007 0.003
## .Stst12l 0.208 0.004 51.531 0.000 0.200
## .Stst13h -0.081 0.004 -19.852 0.000 -0.089
## .Stst14b (.134) 0.028 0.004 7.823 0.000 0.021
## .Stst15t -0.167 0.004 -42.900 0.000 -0.175
## .Stst16m 0.134 0.004 31.520 0.000 0.125
## .Stst9lc 0.522 0.003 156.854 0.000 0.516
## .Stst10m (.138) 0.643 0.003 195.889 0.000 0.636
## .Stst28m (.139) 0.546 0.004 155.391 0.000 0.539
## .Sts303D 0.206 0.004 50.235 0.000 0.198
## ci.upper Std.lv Std.all
## -0.123 -0.130 -0.132
## -0.170 -0.177 -0.176
## -0.147 -0.154 -0.159
## -0.185 -0.192 -0.198
## -0.156 -0.164 -0.167
## -0.131 -0.138 -0.139
## -0.096 -0.104 -0.103
## -0.027 -0.035 -0.036
## 0.112 0.104 0.107
## 0.121 0.114 0.115
## -0.027 -0.035 -0.035
## 0.227 0.219 0.235
## 0.365 0.358 0.370
## 0.149 0.141 0.139
## 0.219 0.212 0.219
## -0.080 -0.087 -0.094
## -0.148 -0.156 -0.159
## -0.044 -0.051 -0.050
## 0.209 0.202 0.211
## 0.015 0.008 0.008
## -0.113 -0.121 -0.121
## 0.236 0.228 0.236
## 0.251 0.243 0.246
## 0.486 0.480 0.564
## 0.017 0.010 0.010
## 0.216 0.208 0.214
## -0.073 -0.081 -0.083
## 0.034 0.028 0.027
## -0.159 -0.167 -0.172
## 0.142 0.134 0.134
## 0.529 0.522 0.647
## 0.649 0.643 0.782
## 0.553 0.546 0.621
## 0.214 0.206 0.204
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.466 0.003 161.462 0.000 0.460
## .Stest20spellng 0.558 0.003 160.051 0.000 0.551
## .Stest21cptlztn 0.514 0.003 163.016 0.000 0.508
## .Stest22puncttn 0.305 0.002 135.832 0.000 0.300
## .Stest23english 0.527 0.003 152.090 0.000 0.520
## .Stest24exprssn 0.661 0.004 157.357 0.000 0.653
## .Stst25wrdfnctn 0.399 0.003 148.567 0.000 0.394
## .Stst26rdngcmpr 0.234 0.002 137.028 0.000 0.230
## .Stst31bstrctrs 0.484 0.003 150.697 0.000 0.477
## .Stst32rthrsnng 0.383 0.002 157.006 0.000 0.378
## .Stst34rthcmptt 0.505 0.003 148.236 0.000 0.498
## .Stest5math 0.216 0.003 85.425 0.000 0.211
## .Stst6physclscn 0.276 0.002 139.657 0.000 0.272
## .Stst33hghschlm 0.260 0.002 116.145 0.000 0.255
## .Stst29vslztn2D 0.572 0.004 137.086 0.000 0.564
## .Stest35tblrdng 0.430 0.005 93.843 0.000 0.421
## .Stst36clrclchc 0.449 0.005 87.211 0.000 0.439
## .Stst37bjctnspc 0.640 0.005 137.044 0.000 0.631
## .Stest1vocab 0.199 0.001 144.310 0.000 0.196
## .Stest2literatr 0.291 0.002 155.620 0.000 0.287
## .Stest3music 0.463 0.003 169.386 0.000 0.458
## .Stest4soclstds 0.297 0.002 153.484 0.000 0.293
## .Stst7blgclscnc 0.463 0.003 159.313 0.000 0.457
## .Stest8aerontcs 0.383 0.003 118.884 0.000 0.377
## .Stest11art 0.439 0.003 168.144 0.000 0.434
## .Stest12law 0.527 0.003 171.793 0.000 0.521
## .Stest13health 0.557 0.003 174.363 0.000 0.551
## .Stest14bible 0.617 0.003 185.876 0.000 0.610
## .Stest15theater 0.463 0.003 172.480 0.000 0.458
## .Stest16mscllns 0.564 0.003 167.354 0.000 0.558
## .Stest9elctrncs 0.246 0.003 91.209 0.000 0.240
## .Stest10mechncs 0.335 0.002 139.570 0.000 0.331
## .Stst28mchnclrs 0.264 0.002 117.246 0.000 0.259
## .Stst30vslztn3D 0.417 0.004 108.864 0.000 0.410
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.472 0.466 0.481
## 0.564 0.558 0.554
## 0.521 0.514 0.548
## 0.309 0.305 0.322
## 0.534 0.527 0.551
## 0.669 0.661 0.668
## 0.404 0.399 0.394
## 0.237 0.234 0.243
## 0.490 0.484 0.507
## 0.388 0.383 0.389
## 0.511 0.505 0.528
## 0.221 0.216 0.248
## 0.280 0.276 0.296
## 0.264 0.260 0.253
## 0.580 0.572 0.612
## 0.439 0.430 0.500
## 0.459 0.449 0.470
## 0.649 0.640 0.619
## 0.202 0.199 0.217
## 0.294 0.291 0.297
## 0.468 0.463 0.464
## 0.301 0.297 0.317
## 0.469 0.463 0.476
## 0.390 0.383 0.530
## 0.444 0.439 0.455
## 0.533 0.527 0.554
## 0.563 0.557 0.588
## 0.623 0.617 0.611
## 0.468 0.463 0.491
## 0.571 0.564 0.565
## 0.251 0.246 0.377
## 0.340 0.335 0.497
## 0.268 0.264 0.342
## 0.425 0.417 0.411
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.329 0.004 77.966 0.000 0.320
## Stst20s (.p2.) 0.671 0.003 236.606 0.000 0.665
## Stst21c (.p3.) 0.652 0.003 232.794 0.000 0.646
## Stst22p (.p4.) 0.801 0.003 290.425 0.000 0.795
## Stst23n (.p5.) 0.656 0.003 210.679 0.000 0.650
## Stst24x (.p6.) 0.574 0.003 183.278 0.000 0.568
## Stst25w (.p7.) 0.574 0.003 164.457 0.000 0.567
## Stst26r (.p8.) 0.248 0.003 79.367 0.000 0.242
## Stst31b (.p9.) 0.380 0.003 136.768 0.000 0.375
## Stst32r (.10.) 0.233 0.004 60.227 0.000 0.226
## Stst34r (.11.) 0.204 0.004 49.688 0.000 0.196
## math =~
## Stst5mt (.12.) 0.809 0.003 321.278 0.000 0.804
## Stst6ph (.13.) 0.391 0.003 121.700 0.000 0.385
## Stst25w (.14.) 0.237 0.004 67.344 0.000 0.230
## Stst32r (.15.) 0.441 0.005 89.658 0.000 0.431
## Stst33h (.16.) 0.874 0.003 313.027 0.000 0.869
## Stst34r (.17.) 0.278 0.004 67.584 0.000 0.270
## speed =~
## Stst19d (.18.) 0.289 0.003 103.819 0.000 0.283
## Sts292D (.19.) 0.226 0.003 74.446 0.000 0.220
## Stst34r (.20.) 0.379 0.003 122.276 0.000 0.373
## Stst35t (.21.) 0.656 0.004 163.168 0.000 0.648
## Stst36c (.22.) 0.712 0.004 193.567 0.000 0.705
## Stst37b (.23.) 0.594 0.004 165.867 0.000 0.587
## info =~
## Stst1vc (.24.) 0.718 0.003 286.629 0.000 0.713
## Stst2lt (.25.) 0.829 0.003 327.940 0.000 0.824
## Stst3ms (.26.) 0.731 0.002 298.782 0.000 0.727
## Stst4sc (.27.) 0.800 0.003 301.743 0.000 0.795
## Stst7bl (.28.) 0.371 0.004 93.921 0.000 0.363
## Stst8rn (.29.) 0.170 0.003 59.163 0.000 0.165
## Stst11r (.30.) 0.725 0.003 273.128 0.000 0.720
## Stst12l (.31.) 0.651 0.003 234.104 0.000 0.646
## Stst13h (.32.) 0.554 0.004 131.274 0.000 0.545
## Stst14b (.33.) 0.626 0.003 232.029 0.000 0.621
## Stst15t (.34.) 0.692 0.003 274.872 0.000 0.687
## Stst16m (.35.) 0.659 0.003 230.547 0.000 0.654
## Stst19d (.36.) 0.273 0.004 67.432 0.000 0.265
## Stst26r (.37.) 0.637 0.003 196.213 0.000 0.631
## science =~
## Stst1vc (.38.) 0.169 0.002 104.229 0.000 0.166
## Stst6ph (.39.) 0.509 0.003 150.993 0.000 0.502
## Stst7bl (.40.) 0.401 0.004 92.662 0.000 0.393
## Stst8rn (.41.) 0.450 0.003 171.439 0.000 0.444
## Stst9lc (.42.) 0.637 0.003 217.137 0.000 0.632
## Stst10m (.43.) 0.583 0.003 215.324 0.000 0.578
## Stst13h (.44.) 0.094 0.004 21.199 0.000 0.085
## Stst28m (.45.) 0.285 0.003 99.740 0.000 0.279
## spatial =~
## Stst28m (.46.) 0.500 0.003 153.515 0.000 0.494
## Sts292D (.47.) 0.521 0.003 174.534 0.000 0.515
## Sts303D (.48.) 0.773 0.003 236.736 0.000 0.767
## Stst31b (.49.) 0.413 0.003 136.309 0.000 0.407
## Stst32r (.50.) 0.193 0.003 65.452 0.000 0.187
## Stst37b (.51.) 0.123 0.003 44.028 0.000 0.117
## ci.upper Std.lv Std.all
##
## 0.337 0.299 0.315
## 0.676 0.611 0.661
## 0.657 0.594 0.635
## 0.806 0.730 0.818
## 0.662 0.598 0.664
## 0.580 0.523 0.583
## 0.580 0.523 0.552
## 0.254 0.226 0.248
## 0.386 0.347 0.370
## 0.241 0.213 0.223
## 0.212 0.186 0.201
##
## 0.814 0.756 0.798
## 0.397 0.365 0.407
## 0.244 0.221 0.234
## 0.451 0.412 0.431
## 0.880 0.817 0.866
## 0.286 0.259 0.281
##
## 0.294 0.258 0.272
## 0.232 0.202 0.212
## 0.385 0.339 0.367
## 0.664 0.587 0.726
## 0.719 0.637 0.694
## 0.601 0.532 0.576
##
## 0.723 0.682 0.735
## 0.834 0.787 0.822
## 0.736 0.694 0.730
## 0.805 0.759 0.816
## 0.378 0.352 0.371
## 0.176 0.162 0.174
## 0.730 0.688 0.717
## 0.656 0.618 0.640
## 0.562 0.525 0.561
## 0.632 0.594 0.599
## 0.697 0.657 0.690
## 0.665 0.626 0.664
## 0.281 0.259 0.273
## 0.643 0.604 0.662
##
## 0.172 0.139 0.150
## 0.516 0.419 0.466
## 0.410 0.330 0.349
## 0.455 0.370 0.400
## 0.643 0.525 0.594
## 0.588 0.480 0.640
## 0.103 0.078 0.083
## 0.290 0.234 0.283
##
## 0.507 0.463 0.560
## 0.527 0.483 0.506
## 0.780 0.716 0.769
## 0.419 0.382 0.408
## 0.199 0.179 0.187
## 0.128 0.114 0.123
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.658 0.005 126.299 0.000 0.647
## speed 0.234 0.005 49.320 0.000 0.225
## info 0.706 0.006 123.787 0.000 0.695
## science 0.380 0.005 82.752 0.000 0.371
## spatial 0.447 0.005 89.508 0.000 0.437
## math ~~
## speed 0.166 0.004 38.414 0.000 0.157
## info 0.672 0.005 128.842 0.000 0.662
## science 0.464 0.005 95.783 0.000 0.454
## spatial 0.494 0.005 97.594 0.000 0.484
## speed ~~
## info 0.180 0.004 40.154 0.000 0.171
## science 0.061 0.004 15.017 0.000 0.053
## spatial 0.171 0.005 35.799 0.000 0.162
## info ~~
## science 0.554 0.005 108.671 0.000 0.544
## spatial 0.450 0.005 91.653 0.000 0.441
## science ~~
## spatial 0.401 0.005 82.061 0.000 0.392
## ci.upper Std.lv Std.all
##
## 0.668 0.772 0.772
## 0.243 0.287 0.287
## 0.717 0.816 0.816
## 0.389 0.506 0.506
## 0.457 0.529 0.529
##
## 0.174 0.198 0.198
## 0.683 0.758 0.758
## 0.473 0.603 0.603
## 0.503 0.570 0.570
##
## 0.189 0.212 0.212
## 0.069 0.083 0.083
## 0.181 0.207 0.207
##
## 0.564 0.709 0.709
## 0.460 0.512 0.512
##
## 0.411 0.527 0.527
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.107) -0.130 0.004 -35.975 0.000 -0.137
## .Stst20s (.108) -0.177 0.004 -48.394 0.000 -0.184
## .Stst21c (.109) -0.154 0.004 -42.684 0.000 -0.161
## .Stst22p (.110) -0.192 0.004 -50.567 0.000 -0.200
## .Stst23n (.111) -0.164 0.004 -44.750 0.000 -0.171
## .Stst24x (.112) -0.138 0.004 -37.702 0.000 -0.145
## .Stst25w (.113) -0.104 0.004 -27.672 0.000 -0.111
## .Stst26r (.114) -0.035 0.004 -8.821 0.000 -0.043
## .Stst31b (.115) 0.104 0.004 28.001 0.000 0.097
## .Stst32r (.116) 0.114 0.004 29.211 0.000 0.106
## .Stst34r (.117) -0.035 0.004 -9.200 0.000 -0.042
## .Stst5mt 0.056 0.005 11.915 0.000 0.047
## .Stst6ph 0.833 0.009 92.926 0.000 0.816
## .Stst33h (.120) 0.141 0.004 33.468 0.000 0.132
## .Sts292D (.121) 0.212 0.004 58.071 0.000 0.205
## .Stst35t (.122) -0.087 0.003 -24.960 0.000 -0.094
## .Stst36c (.123) -0.156 0.004 -42.707 0.000 -0.163
## .Stst37b (.124) -0.051 0.004 -13.897 0.000 -0.058
## .Stst1vc (.125) 0.202 0.004 54.334 0.000 0.195
## .Stst2lt (.126) 0.008 0.004 2.064 0.039 0.000
## .Stst3ms 0.128 0.004 29.787 0.000 0.120
## .Stst4sc -0.169 0.004 -38.891 0.000 -0.178
## .Stst7bl 0.619 0.010 61.045 0.000 0.599
## .Stst8rn (.130) 0.480 0.003 139.826 0.000 0.473
## .Stst11r (.131) 0.010 0.004 2.714 0.007 0.003
## .Stst12l -0.168 0.004 -39.351 0.000 -0.176
## .Stst13h 0.328 0.010 33.414 0.000 0.309
## .Stst14b (.134) 0.028 0.004 7.823 0.000 0.021
## .Stst15t 0.175 0.004 41.466 0.000 0.167
## .Stst16m -0.101 0.004 -24.008 0.000 -0.110
## .Stst9lc 0.844 0.008 111.535 0.000 0.829
## .Stst10m (.138) 0.643 0.003 195.889 0.000 0.636
## .Stst28m (.139) 0.546 0.004 155.391 0.000 0.539
## .Sts303D 0.509 0.007 71.505 0.000 0.495
## english 0.611 0.006 99.975 0.000 0.599
## math -0.235 0.006 -36.952 0.000 -0.247
## speed 0.327 0.007 47.605 0.000 0.314
## info 0.047 0.006 7.699 0.000 0.035
## science -1.976 0.012 -159.854 0.000 -2.001
## spatial -0.799 0.010 -81.747 0.000 -0.818
## ci.upper Std.lv Std.all
## -0.123 -0.130 -0.137
## -0.170 -0.177 -0.192
## -0.147 -0.154 -0.165
## -0.185 -0.192 -0.216
## -0.156 -0.164 -0.182
## -0.131 -0.138 -0.154
## -0.096 -0.104 -0.109
## -0.027 -0.035 -0.039
## 0.112 0.104 0.111
## 0.121 0.114 0.119
## -0.027 -0.035 -0.037
## 0.065 0.056 0.059
## 0.851 0.833 0.927
## 0.149 0.141 0.149
## 0.219 0.212 0.222
## -0.080 -0.087 -0.108
## -0.148 -0.156 -0.169
## -0.044 -0.051 -0.055
## 0.209 0.202 0.218
## 0.015 0.008 0.008
## 0.137 0.128 0.135
## -0.161 -0.169 -0.182
## 0.639 0.619 0.654
## 0.486 0.480 0.518
## 0.017 0.010 0.010
## -0.160 -0.168 -0.174
## 0.347 0.328 0.350
## 0.034 0.028 0.028
## 0.183 0.175 0.184
## -0.093 -0.101 -0.107
## 0.859 0.844 0.955
## 0.649 0.643 0.858
## 0.553 0.546 0.660
## 0.523 0.509 0.546
## 0.623 0.671 0.671
## -0.222 -0.251 -0.251
## 0.340 0.365 0.365
## 0.058 0.049 0.049
## -1.952 -2.401 -2.401
## -0.780 -0.862 -0.862
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.479 0.003 164.760 0.000 0.473
## .Stest20spellng 0.482 0.003 163.651 0.000 0.476
## .Stest21cptlztn 0.523 0.003 163.873 0.000 0.517
## .Stest22puncttn 0.264 0.002 131.584 0.000 0.260
## .Stest23english 0.453 0.003 157.534 0.000 0.447
## .Stest24exprssn 0.533 0.004 146.648 0.000 0.526
## .Stst25wrdfnctn 0.398 0.003 145.456 0.000 0.392
## .Stst26rdngcmpr 0.194 0.001 139.092 0.000 0.191
## .Stst31bstrctrs 0.471 0.003 156.827 0.000 0.465
## .Stst32rthrsnng 0.405 0.002 163.913 0.000 0.400
## .Stst34rthcmptt 0.490 0.003 142.568 0.000 0.483
## .Stest5math 0.327 0.003 100.508 0.000 0.320
## .Stst6physclscn 0.314 0.002 144.414 0.000 0.310
## .Stst33hghschlm 0.222 0.002 104.070 0.000 0.218
## .Stst29vslztn2D 0.596 0.004 157.452 0.000 0.588
## .Stest35tblrdng 0.308 0.004 85.297 0.000 0.301
## .Stst36clrclchc 0.437 0.004 101.915 0.000 0.428
## .Stst37bjctnspc 0.531 0.004 139.506 0.000 0.524
## .Stest1vocab 0.242 0.002 149.725 0.000 0.238
## .Stest2literatr 0.298 0.002 159.083 0.000 0.294
## .Stest3music 0.422 0.003 167.060 0.000 0.417
## .Stest4soclstds 0.289 0.002 157.581 0.000 0.285
## .Stst7blgclscnc 0.499 0.003 171.643 0.000 0.494
## .Stest8aerontcs 0.609 0.003 184.654 0.000 0.603
## .Stest11art 0.446 0.003 170.115 0.000 0.441
## .Stest12law 0.549 0.003 177.546 0.000 0.543
## .Stest13health 0.537 0.003 172.758 0.000 0.531
## .Stest14bible 0.631 0.003 193.022 0.000 0.625
## .Stest15theater 0.474 0.003 173.974 0.000 0.469
## .Stest16mscllns 0.497 0.003 171.023 0.000 0.492
## .Stest9elctrncs 0.505 0.004 119.878 0.000 0.496
## .Stest10mechncs 0.331 0.002 150.818 0.000 0.327
## .Stst28mchnclrs 0.300 0.002 134.874 0.000 0.296
## .Stst30vslztn3D 0.354 0.003 107.890 0.000 0.347
## english 0.831 0.007 112.179 0.000 0.817
## math 0.873 0.007 128.546 0.000 0.860
## speed 0.801 0.010 81.367 0.000 0.781
## info 0.900 0.007 134.619 0.000 0.887
## science 0.678 0.007 95.505 0.000 0.664
## spatial 0.858 0.008 101.251 0.000 0.842
## ci.upper Std.lv Std.all
## 0.484 0.479 0.531
## 0.488 0.482 0.563
## 0.529 0.523 0.597
## 0.268 0.264 0.331
## 0.458 0.453 0.559
## 0.540 0.533 0.661
## 0.403 0.398 0.442
## 0.196 0.194 0.232
## 0.476 0.471 0.537
## 0.410 0.405 0.444
## 0.497 0.490 0.575
## 0.333 0.327 0.364
## 0.319 0.314 0.389
## 0.226 0.222 0.250
## 0.603 0.596 0.655
## 0.315 0.308 0.472
## 0.445 0.437 0.518
## 0.539 0.531 0.624
## 0.245 0.242 0.281
## 0.301 0.298 0.325
## 0.427 0.422 0.467
## 0.293 0.289 0.334
## 0.505 0.499 0.557
## 0.616 0.609 0.711
## 0.451 0.446 0.485
## 0.555 0.549 0.590
## 0.543 0.537 0.612
## 0.638 0.631 0.641
## 0.480 0.474 0.524
## 0.503 0.497 0.560
## 0.513 0.505 0.647
## 0.336 0.331 0.590
## 0.305 0.300 0.439
## 0.360 0.354 0.408
## 0.846 1.000 1.000
## 0.887 1.000 1.000
## 0.820 1.000 1.000
## 0.914 1.000 1.000
## 0.691 1.000 1.000
## 0.875 1.000 1.000
lavTestScore(scalar2, release = 52:74) # S4 and 15 much larger X2, followed by S12, S3, S6, then a bunch of medium size
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 8896.429 23 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p107. == .p253. 221.298 1 0.000
## 2 .p108. == .p254. 1239.243 1 0.000
## 3 .p109. == .p255. 551.475 1 0.000
## 4 .p110. == .p256. 61.629 1 0.000
## 5 .p111. == .p257. 613.846 1 0.000
## 6 .p112. == .p258. 501.509 1 0.000
## 7 .p113. == .p259. 215.525 1 0.000
## 8 .p114. == .p260. 1168.002 1 0.000
## 9 .p115. == .p261. 689.325 1 0.000
## 10 .p116. == .p262. 766.106 1 0.000
## 11 .p117. == .p263. 446.625 1 0.000
## 12 .p120. == .p266. 25.471 1 0.000
## 13 .p121. == .p267. 87.846 1 0.000
## 14 .p122. == .p268. 764.041 1 0.000
## 15 .p123. == .p269. 48.189 1 0.000
## 16 .p124. == .p270. 718.628 1 0.000
## 17 .p125. == .p271. 785.593 1 0.000
## 18 .p126. == .p272. 372.295 1 0.000
## 19 .p130. == .p276. 9.224 1 0.002
## 20 .p131. == .p277. 1644.366 1 0.000
## 21 .p134. == .p280. 40.633 1 0.000
## 22 .p138. == .p284. 13.692 1 0.000
## 23 .p139. == .p285. 82.675 1 0.000
strict<-cfa(chc.factor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("Stest4socialstudies~1", "Stest15theater~1", "Stest12law~1", "Stest3music~1", "Stest6physicalscience~1", "Stest16miscellaneous~1", "Stest30visualization3D~1", "Stest9electronics~1", "Stest5math~1", "Stest13health~1", "Stest7biologicalscience~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 159637.295 1086.000 0.000 0.940 0.046
## srmr aic bic
## 0.041 10363371.794 10365064.723
Mc(strict)
## [1] 0.5654603
chc.cov<-cfa(chc.factor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("Stest4socialstudies~1", "Stest15theater~1", "Stest12law~1", "Stest3music~1", "Stest6physicalscience~1", "Stest16miscellaneous~1", "Stest30visualization3D~1", "Stest9electronics~1", "Stest5math~1", "Stest13health~1", "Stest7biologicalscience~1"))
fitMeasures(chc.cov, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 146152.984 1067.000 0.000 0.945 0.044
## srmr aic bic
## 0.056 10349925.482 10351805.421
Mc(chc.cov)
## [1] 0.5935126
chc.vcov<-cfa(chc.factor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "lv.variances", "lv.covariances"), group.partial=c("Stest4socialstudies~1", "Stest15theater~1", "Stest12law~1", "Stest3music~1", "Stest6physicalscience~1", "Stest16miscellaneous~1", "Stest30visualization3D~1", "Stest9electronics~1", "Stest5math~1", "Stest13health~1", "Stest7biologicalscience~1"))
fitMeasures(chc.vcov, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 147344.583 1073.000 0.000 0.945 0.044
## srmr aic bic
## 0.057 10351105.082 10352925.965
Mc(chc.vcov)
## [1] 0.5909877
summary(chc.vcov, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 70 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 274
## Number of equality constraints 89
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 147344.583 129223.216
## Degrees of freedom 1073 1073
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.140
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 81269.078 71274.094
## 1 66075.505 57949.122
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.313 0.004 78.335 0.000 0.305
## Stst20s (.p2.) 0.641 0.002 278.526 0.000 0.637
## Stst21c (.p3.) 0.624 0.002 269.919 0.000 0.619
## Stst22p (.p4.) 0.765 0.002 369.224 0.000 0.761
## Stst23n (.p5.) 0.627 0.003 241.991 0.000 0.622
## Stst24x (.p6.) 0.548 0.003 206.531 0.000 0.543
## Stst25w (.p7.) 0.549 0.003 166.327 0.000 0.543
## Stst26r (.p8.) 0.236 0.003 81.725 0.000 0.230
## Stst31b (.p9.) 0.363 0.003 142.143 0.000 0.358
## Stst32r (.10.) 0.220 0.004 59.625 0.000 0.213
## Stst34r (.11.) 0.193 0.004 49.866 0.000 0.186
## math =~
## Stst5mt (.12.) 0.782 0.002 378.212 0.000 0.778
## Stst6ph (.13.) 0.376 0.003 123.108 0.000 0.370
## Stst25w (.14.) 0.229 0.003 67.302 0.000 0.223
## Stst32r (.15.) 0.432 0.005 92.474 0.000 0.422
## Stst33h (.16.) 0.846 0.002 401.122 0.000 0.841
## Stst34r (.17.) 0.270 0.004 68.568 0.000 0.262
## speed =~
## Stst19d (.18.) 0.275 0.003 106.253 0.000 0.270
## Sts292D (.19.) 0.214 0.003 75.648 0.000 0.208
## Stst34r (.20.) 0.359 0.003 130.264 0.000 0.353
## Stst35t (.21.) 0.618 0.003 196.339 0.000 0.611
## Stst36c (.22.) 0.676 0.003 225.808 0.000 0.670
## Stst37b (.23.) 0.562 0.003 188.230 0.000 0.556
## info =~
## Stst1vc (.24.) 0.699 0.002 331.445 0.000 0.695
## Stst2lt (.25.) 0.808 0.002 406.256 0.000 0.804
## Stst3ms (.26.) 0.713 0.002 349.256 0.000 0.709
## Stst4sc (.27.) 0.780 0.002 373.692 0.000 0.776
## Stst7bl (.28.) 0.358 0.004 93.961 0.000 0.351
## Stst8rn (.29.) 0.168 0.003 60.754 0.000 0.163
## Stst11r (.30.) 0.707 0.002 316.330 0.000 0.702
## Stst12l (.31.) 0.635 0.002 268.648 0.000 0.630
## Stst13h (.32.) 0.542 0.004 136.990 0.000 0.535
## Stst14b (.33.) 0.611 0.002 259.230 0.000 0.606
## Stst15t (.34.) 0.675 0.002 312.542 0.000 0.671
## Stst16m (.35.) 0.643 0.002 265.940 0.000 0.639
## Stst19d (.36.) 0.267 0.004 68.264 0.000 0.260
## Stst26r (.37.) 0.622 0.003 210.451 0.000 0.616
## science =~
## Stst1vc (.38.) 0.156 0.001 107.061 0.000 0.153
## Stst6ph (.39.) 0.471 0.003 153.313 0.000 0.465
## Stst7bl (.40.) 0.372 0.004 93.304 0.000 0.364
## Stst8rn (.41.) 0.412 0.002 187.106 0.000 0.408
## Stst9lc (.42.) 0.590 0.002 250.112 0.000 0.585
## Stst10m (.43.) 0.534 0.002 256.278 0.000 0.530
## Stst13h (.44.) 0.083 0.004 20.503 0.000 0.075
## Stst28m (.45.) 0.262 0.002 106.177 0.000 0.257
## spatial =~
## Stst28m (.46.) 0.480 0.003 165.126 0.000 0.474
## Sts292D (.47.) 0.503 0.003 194.183 0.000 0.498
## Sts303D (.48.) 0.747 0.003 296.609 0.000 0.742
## Stst31b (.49.) 0.398 0.003 144.017 0.000 0.392
## Stst32r (.50.) 0.184 0.003 64.930 0.000 0.178
## Stst37b (.51.) 0.119 0.003 44.520 0.000 0.113
## ci.upper Std.lv Std.all
##
## 0.321 0.313 0.325
## 0.646 0.641 0.652
## 0.628 0.624 0.656
## 0.770 0.765 0.810
## 0.632 0.627 0.654
## 0.553 0.548 0.559
## 0.556 0.549 0.561
## 0.242 0.236 0.247
## 0.368 0.363 0.378
## 0.227 0.220 0.227
## 0.201 0.193 0.202
##
## 0.786 0.782 0.861
## 0.382 0.376 0.407
## 0.236 0.229 0.234
## 0.441 0.432 0.446
## 0.850 0.846 0.858
## 0.278 0.270 0.283
##
## 0.280 0.275 0.285
## 0.219 0.214 0.224
## 0.364 0.359 0.375
## 0.624 0.618 0.683
## 0.682 0.676 0.709
## 0.568 0.562 0.563
##
## 0.703 0.699 0.751
## 0.812 0.808 0.831
## 0.717 0.713 0.723
## 0.784 0.780 0.820
## 0.366 0.358 0.374
## 0.174 0.168 0.204
## 0.711 0.707 0.730
## 0.639 0.635 0.658
## 0.550 0.542 0.565
## 0.615 0.611 0.614
## 0.679 0.675 0.704
## 0.648 0.643 0.650
## 0.275 0.267 0.278
## 0.628 0.622 0.650
##
## 0.159 0.156 0.168
## 0.477 0.471 0.510
## 0.379 0.372 0.388
## 0.416 0.412 0.499
## 0.595 0.590 0.764
## 0.538 0.534 0.676
## 0.091 0.083 0.086
## 0.267 0.262 0.310
##
## 0.486 0.480 0.568
## 0.508 0.503 0.527
## 0.752 0.747 0.758
## 0.403 0.398 0.414
## 0.189 0.184 0.190
## 0.124 0.119 0.119
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math (.92.) 0.811 0.002 497.165 0.000 0.808
## speed (.93.) 0.276 0.004 72.296 0.000 0.269
## info (.94.) 0.820 0.001 595.786 0.000 0.817
## science (.95.) 0.517 0.003 166.185 0.000 0.511
## spatial (.96.) 0.511 0.003 165.543 0.000 0.505
## math ~~
## speed (.97.) 0.228 0.004 62.293 0.000 0.220
## info (.98.) 0.787 0.002 493.423 0.000 0.784
## science (.99.) 0.610 0.003 214.707 0.000 0.604
## spatial (.100) 0.571 0.003 204.191 0.000 0.566
## speed ~~
## info (.101) 0.229 0.004 63.122 0.000 0.222
## science (.102) 0.066 0.004 16.541 0.000 0.058
## spatial (.103) 0.187 0.004 45.389 0.000 0.179
## info ~~
## science (.104) 0.708 0.002 293.614 0.000 0.703
## spatial (.105) 0.489 0.003 167.025 0.000 0.483
## science ~~
## spatial (.106) 0.581 0.003 183.287 0.000 0.575
## ci.upper Std.lv Std.all
##
## 0.814 0.811 0.811
## 0.284 0.276 0.276
## 0.822 0.820 0.820
## 0.523 0.517 0.517
## 0.517 0.511 0.511
##
## 0.235 0.228 0.228
## 0.790 0.787 0.787
## 0.616 0.610 0.610
## 0.577 0.571 0.571
##
## 0.236 0.229 0.229
## 0.073 0.066 0.066
## 0.195 0.187 0.187
##
## 0.712 0.708 0.708
## 0.494 0.489 0.489
##
## 0.587 0.581 0.581
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.107) -0.130 0.004 -36.030 0.000 -0.137
## .Stst20s (.108) -0.177 0.004 -48.432 0.000 -0.184
## .Stst21c (.109) -0.154 0.004 -42.704 0.000 -0.161
## .Stst22p (.110) -0.192 0.004 -50.604 0.000 -0.200
## .Stst23n (.111) -0.164 0.004 -44.780 0.000 -0.171
## .Stst24x (.112) -0.138 0.004 -37.688 0.000 -0.145
## .Stst25w (.113) -0.104 0.004 -27.679 0.000 -0.111
## .Stst26r (.114) -0.035 0.004 -8.814 0.000 -0.043
## .Stst31b (.115) 0.104 0.004 27.943 0.000 0.097
## .Stst32r (.116) 0.114 0.004 29.307 0.000 0.107
## .Stst34r (.117) -0.034 0.004 -9.060 0.000 -0.041
## .Stst5mt 0.219 0.004 58.635 0.000 0.212
## .Stst6ph 0.358 0.004 92.152 0.000 0.350
## .Stst33h (.120) 0.140 0.004 33.465 0.000 0.132
## .Sts292D (.121) 0.212 0.004 58.011 0.000 0.204
## .Stst35t (.122) -0.087 0.003 -25.055 0.000 -0.094
## .Stst36c (.123) -0.156 0.004 -42.830 0.000 -0.163
## .Stst37b (.124) -0.051 0.004 -13.851 0.000 -0.058
## .Stst1vc (.125) 0.203 0.004 54.567 0.000 0.195
## .Stst2lt (.126) 0.007 0.004 1.953 0.051 -0.000
## .Stst3ms -0.121 0.004 -29.896 0.000 -0.128
## .Stst4sc 0.228 0.004 57.617 0.000 0.220
## .Stst7bl 0.243 0.004 61.805 0.000 0.235
## .Stst8rn (.130) 0.479 0.003 139.257 0.000 0.473
## .Stst11r (.131) 0.009 0.004 2.630 0.009 0.002
## .Stst12l 0.208 0.004 51.531 0.000 0.200
## .Stst13h -0.081 0.004 -19.852 0.000 -0.089
## .Stst14b (.134) 0.027 0.004 7.746 0.000 0.020
## .Stst15t -0.167 0.004 -42.900 0.000 -0.175
## .Stst16m 0.134 0.004 31.520 0.000 0.125
## .Stst9lc 0.522 0.003 156.854 0.000 0.516
## .Stst10m (.138) 0.642 0.003 195.582 0.000 0.636
## .Stst28m (.139) 0.546 0.004 155.217 0.000 0.539
## .Sts303D 0.206 0.004 50.236 0.000 0.198
## ci.upper Std.lv Std.all
## -0.123 -0.130 -0.135
## -0.170 -0.177 -0.180
## -0.147 -0.154 -0.162
## -0.185 -0.192 -0.204
## -0.156 -0.164 -0.170
## -0.131 -0.138 -0.140
## -0.096 -0.104 -0.106
## -0.027 -0.035 -0.037
## 0.111 0.104 0.108
## 0.122 0.114 0.118
## -0.027 -0.034 -0.036
## 0.227 0.219 0.242
## 0.365 0.358 0.387
## 0.149 0.140 0.142
## 0.219 0.212 0.222
## -0.080 -0.087 -0.096
## -0.149 -0.156 -0.164
## -0.044 -0.051 -0.051
## 0.210 0.203 0.218
## 0.015 0.007 0.008
## -0.113 -0.121 -0.122
## 0.236 0.228 0.240
## 0.251 0.243 0.254
## 0.486 0.479 0.581
## 0.017 0.009 0.010
## 0.216 0.208 0.216
## -0.073 -0.081 -0.084
## 0.034 0.027 0.027
## -0.159 -0.167 -0.174
## 0.142 0.134 0.135
## 0.529 0.522 0.677
## 0.649 0.642 0.813
## 0.553 0.546 0.645
## 0.214 0.206 0.209
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.464 0.003 161.557 0.000 0.459
## .Stest20spellng 0.556 0.003 160.637 0.000 0.550
## .Stest21cptlztn 0.515 0.003 163.409 0.000 0.508
## .Stest22puncttn 0.308 0.002 137.364 0.000 0.303
## .Stest23english 0.527 0.003 152.139 0.000 0.520
## .Stest24exprssn 0.661 0.004 157.440 0.000 0.653
## .Stst25wrdfnctn 0.399 0.003 149.332 0.000 0.394
## .Stst26rdngcmpr 0.233 0.002 136.825 0.000 0.229
## .Stst31bstrctrs 0.484 0.003 150.752 0.000 0.478
## .Stst32rthrsnng 0.383 0.002 157.024 0.000 0.378
## .Stst34rthcmptt 0.506 0.003 148.380 0.000 0.499
## .Stest5math 0.213 0.003 84.031 0.000 0.208
## .Stst6physclscn 0.275 0.002 139.289 0.000 0.271
## .Stst33hghschlm 0.257 0.002 117.097 0.000 0.253
## .Stst29vslztn2D 0.572 0.004 137.772 0.000 0.564
## .Stest35tblrdng 0.437 0.005 94.032 0.000 0.428
## .Stst36clrclchc 0.453 0.005 87.861 0.000 0.443
## .Stst37bjctnspc 0.643 0.005 137.991 0.000 0.634
## .Stest1vocab 0.199 0.001 144.585 0.000 0.197
## .Stest2literatr 0.292 0.002 155.927 0.000 0.288
## .Stest3music 0.463 0.003 169.378 0.000 0.458
## .Stest4soclstds 0.297 0.002 153.683 0.000 0.294
## .Stst7blgclscnc 0.463 0.003 159.514 0.000 0.457
## .Stest8aerontcs 0.385 0.003 118.664 0.000 0.379
## .Stest11art 0.439 0.003 168.244 0.000 0.434
## .Stest12law 0.526 0.003 171.759 0.000 0.520
## .Stest13health 0.557 0.003 174.372 0.000 0.551
## .Stest14bible 0.616 0.003 185.899 0.000 0.610
## .Stest15theater 0.464 0.003 172.529 0.000 0.458
## .Stest16mscllns 0.564 0.003 167.470 0.000 0.558
## .Stest9elctrncs 0.248 0.003 90.429 0.000 0.242
## .Stest10mechncs 0.339 0.002 140.736 0.000 0.334
## .Stst28mchnclrs 0.269 0.002 120.294 0.000 0.265
## .Stst30vslztn3D 0.414 0.004 111.391 0.000 0.407
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.470 0.464 0.500
## 0.563 0.556 0.575
## 0.521 0.515 0.569
## 0.312 0.308 0.344
## 0.534 0.527 0.573
## 0.669 0.661 0.688
## 0.405 0.399 0.417
## 0.236 0.233 0.254
## 0.490 0.484 0.525
## 0.388 0.383 0.409
## 0.513 0.506 0.555
## 0.218 0.213 0.258
## 0.279 0.275 0.322
## 0.261 0.257 0.264
## 0.580 0.572 0.628
## 0.446 0.437 0.534
## 0.463 0.453 0.498
## 0.652 0.643 0.644
## 0.202 0.199 0.230
## 0.295 0.292 0.309
## 0.468 0.463 0.477
## 0.301 0.297 0.328
## 0.469 0.463 0.504
## 0.392 0.385 0.566
## 0.444 0.439 0.468
## 0.532 0.526 0.566
## 0.563 0.557 0.604
## 0.623 0.616 0.623
## 0.469 0.464 0.504
## 0.571 0.564 0.577
## 0.253 0.248 0.416
## 0.344 0.339 0.543
## 0.274 0.269 0.377
## 0.421 0.414 0.426
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.313 0.004 78.335 0.000 0.305
## Stst20s (.p2.) 0.641 0.002 278.526 0.000 0.637
## Stst21c (.p3.) 0.624 0.002 269.919 0.000 0.619
## Stst22p (.p4.) 0.765 0.002 369.224 0.000 0.761
## Stst23n (.p5.) 0.627 0.003 241.991 0.000 0.622
## Stst24x (.p6.) 0.548 0.003 206.531 0.000 0.543
## Stst25w (.p7.) 0.549 0.003 166.327 0.000 0.543
## Stst26r (.p8.) 0.236 0.003 81.725 0.000 0.230
## Stst31b (.p9.) 0.363 0.003 142.143 0.000 0.358
## Stst32r (.10.) 0.220 0.004 59.625 0.000 0.213
## Stst34r (.11.) 0.193 0.004 49.866 0.000 0.186
## math =~
## Stst5mt (.12.) 0.782 0.002 378.212 0.000 0.778
## Stst6ph (.13.) 0.376 0.003 123.108 0.000 0.370
## Stst25w (.14.) 0.229 0.003 67.302 0.000 0.223
## Stst32r (.15.) 0.432 0.005 92.474 0.000 0.422
## Stst33h (.16.) 0.846 0.002 401.122 0.000 0.841
## Stst34r (.17.) 0.270 0.004 68.568 0.000 0.262
## speed =~
## Stst19d (.18.) 0.275 0.003 106.253 0.000 0.270
## Sts292D (.19.) 0.214 0.003 75.648 0.000 0.208
## Stst34r (.20.) 0.359 0.003 130.264 0.000 0.353
## Stst35t (.21.) 0.618 0.003 196.339 0.000 0.611
## Stst36c (.22.) 0.676 0.003 225.808 0.000 0.670
## Stst37b (.23.) 0.562 0.003 188.230 0.000 0.556
## info =~
## Stst1vc (.24.) 0.699 0.002 331.445 0.000 0.695
## Stst2lt (.25.) 0.808 0.002 406.256 0.000 0.804
## Stst3ms (.26.) 0.713 0.002 349.256 0.000 0.709
## Stst4sc (.27.) 0.780 0.002 373.692 0.000 0.776
## Stst7bl (.28.) 0.358 0.004 93.961 0.000 0.351
## Stst8rn (.29.) 0.168 0.003 60.754 0.000 0.163
## Stst11r (.30.) 0.707 0.002 316.330 0.000 0.702
## Stst12l (.31.) 0.635 0.002 268.648 0.000 0.630
## Stst13h (.32.) 0.542 0.004 136.990 0.000 0.535
## Stst14b (.33.) 0.611 0.002 259.230 0.000 0.606
## Stst15t (.34.) 0.675 0.002 312.542 0.000 0.671
## Stst16m (.35.) 0.643 0.002 265.940 0.000 0.639
## Stst19d (.36.) 0.267 0.004 68.264 0.000 0.260
## Stst26r (.37.) 0.622 0.003 210.451 0.000 0.616
## science =~
## Stst1vc (.38.) 0.156 0.001 107.061 0.000 0.153
## Stst6ph (.39.) 0.471 0.003 153.313 0.000 0.465
## Stst7bl (.40.) 0.372 0.004 93.304 0.000 0.364
## Stst8rn (.41.) 0.412 0.002 187.106 0.000 0.408
## Stst9lc (.42.) 0.590 0.002 250.112 0.000 0.585
## Stst10m (.43.) 0.534 0.002 256.278 0.000 0.530
## Stst13h (.44.) 0.083 0.004 20.503 0.000 0.075
## Stst28m (.45.) 0.262 0.002 106.177 0.000 0.257
## spatial =~
## Stst28m (.46.) 0.480 0.003 165.126 0.000 0.474
## Sts292D (.47.) 0.503 0.003 194.183 0.000 0.498
## Sts303D (.48.) 0.747 0.003 296.609 0.000 0.742
## Stst31b (.49.) 0.398 0.003 144.017 0.000 0.392
## Stst32r (.50.) 0.184 0.003 64.930 0.000 0.178
## Stst37b (.51.) 0.119 0.003 44.520 0.000 0.113
## ci.upper Std.lv Std.all
##
## 0.321 0.313 0.323
## 0.646 0.641 0.678
## 0.628 0.624 0.653
## 0.770 0.765 0.832
## 0.632 0.627 0.682
## 0.553 0.548 0.600
## 0.556 0.549 0.562
## 0.242 0.236 0.252
## 0.368 0.363 0.381
## 0.227 0.220 0.225
## 0.201 0.193 0.204
##
## 0.786 0.782 0.806
## 0.382 0.376 0.398
## 0.236 0.229 0.235
## 0.441 0.432 0.441
## 0.850 0.846 0.870
## 0.278 0.270 0.285
##
## 0.280 0.275 0.283
## 0.219 0.214 0.221
## 0.364 0.359 0.379
## 0.624 0.618 0.744
## 0.682 0.676 0.718
## 0.568 0.562 0.598
##
## 0.703 0.699 0.733
## 0.812 0.808 0.829
## 0.717 0.713 0.739
## 0.784 0.780 0.823
## 0.366 0.358 0.367
## 0.174 0.168 0.177
## 0.711 0.707 0.727
## 0.639 0.635 0.651
## 0.550 0.542 0.571
## 0.615 0.611 0.609
## 0.679 0.675 0.700
## 0.648 0.643 0.674
## 0.275 0.267 0.276
## 0.628 0.622 0.664
##
## 0.159 0.156 0.164
## 0.477 0.471 0.499
## 0.379 0.372 0.381
## 0.416 0.412 0.433
## 0.595 0.590 0.639
## 0.538 0.534 0.682
## 0.091 0.083 0.087
## 0.267 0.262 0.304
##
## 0.486 0.480 0.557
## 0.508 0.503 0.521
## 0.752 0.747 0.783
## 0.403 0.398 0.417
## 0.189 0.184 0.188
## 0.124 0.119 0.126
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math (.92.) 0.811 0.002 497.165 0.000 0.808
## speed (.93.) 0.276 0.004 72.296 0.000 0.269
## info (.94.) 0.820 0.001 595.786 0.000 0.817
## science (.95.) 0.517 0.003 166.185 0.000 0.511
## spatial (.96.) 0.511 0.003 165.543 0.000 0.505
## math ~~
## speed (.97.) 0.228 0.004 62.293 0.000 0.220
## info (.98.) 0.787 0.002 493.423 0.000 0.784
## science (.99.) 0.610 0.003 214.707 0.000 0.604
## spatial (.100) 0.571 0.003 204.191 0.000 0.566
## speed ~~
## info (.101) 0.229 0.004 63.122 0.000 0.222
## science (.102) 0.066 0.004 16.541 0.000 0.058
## spatial (.103) 0.187 0.004 45.389 0.000 0.179
## info ~~
## science (.104) 0.708 0.002 293.614 0.000 0.703
## spatial (.105) 0.489 0.003 167.025 0.000 0.483
## science ~~
## spatial (.106) 0.581 0.003 183.287 0.000 0.575
## ci.upper Std.lv Std.all
##
## 0.814 0.811 0.811
## 0.284 0.276 0.276
## 0.822 0.820 0.820
## 0.523 0.517 0.517
## 0.517 0.511 0.511
##
## 0.235 0.228 0.228
## 0.790 0.787 0.787
## 0.616 0.610 0.610
## 0.577 0.571 0.571
##
## 0.236 0.229 0.229
## 0.073 0.066 0.066
## 0.195 0.187 0.187
##
## 0.712 0.708 0.708
## 0.494 0.489 0.489
##
## 0.587 0.581 0.581
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.107) -0.130 0.004 -36.030 0.000 -0.137
## .Stst20s (.108) -0.177 0.004 -48.432 0.000 -0.184
## .Stst21c (.109) -0.154 0.004 -42.704 0.000 -0.161
## .Stst22p (.110) -0.192 0.004 -50.604 0.000 -0.200
## .Stst23n (.111) -0.164 0.004 -44.780 0.000 -0.171
## .Stst24x (.112) -0.138 0.004 -37.688 0.000 -0.145
## .Stst25w (.113) -0.104 0.004 -27.679 0.000 -0.111
## .Stst26r (.114) -0.035 0.004 -8.814 0.000 -0.043
## .Stst31b (.115) 0.104 0.004 27.943 0.000 0.097
## .Stst32r (.116) 0.114 0.004 29.307 0.000 0.107
## .Stst34r (.117) -0.034 0.004 -9.060 0.000 -0.041
## .Stst5mt 0.056 0.005 11.877 0.000 0.047
## .Stst6ph 0.843 0.009 93.910 0.000 0.825
## .Stst33h (.120) 0.140 0.004 33.465 0.000 0.132
## .Sts292D (.121) 0.212 0.004 58.011 0.000 0.204
## .Stst35t (.122) -0.087 0.003 -25.055 0.000 -0.094
## .Stst36c (.123) -0.156 0.004 -42.830 0.000 -0.163
## .Stst37b (.124) -0.051 0.004 -13.851 0.000 -0.058
## .Stst1vc (.125) 0.203 0.004 54.567 0.000 0.195
## .Stst2lt (.126) 0.007 0.004 1.953 0.051 -0.000
## .Stst3ms 0.128 0.004 29.635 0.000 0.119
## .Stst4sc -0.170 0.004 -39.039 0.000 -0.178
## .Stst7bl 0.628 0.010 61.808 0.000 0.608
## .Stst8rn (.130) 0.479 0.003 139.257 0.000 0.473
## .Stst11r (.131) 0.009 0.004 2.630 0.009 0.002
## .Stst12l -0.169 0.004 -39.467 0.000 -0.177
## .Stst13h 0.320 0.010 32.691 0.000 0.301
## .Stst14b (.134) 0.027 0.004 7.746 0.000 0.020
## .Stst15t 0.174 0.004 41.317 0.000 0.166
## .Stst16m -0.102 0.004 -24.131 0.000 -0.110
## .Stst9lc 0.857 0.008 113.568 0.000 0.842
## .Stst10m (.138) 0.642 0.003 195.582 0.000 0.636
## .Stst28m (.139) 0.546 0.004 155.217 0.000 0.539
## .Sts303D 0.509 0.007 71.281 0.000 0.495
## english 0.640 0.007 97.744 0.000 0.627
## math -0.242 0.007 -36.550 0.000 -0.255
## speed 0.346 0.007 50.229 0.000 0.333
## info 0.049 0.006 7.823 0.000 0.036
## science -2.157 0.012 -176.962 0.000 -2.181
## spatial -0.827 0.010 -84.686 0.000 -0.846
## ci.upper Std.lv Std.all
## -0.123 -0.130 -0.134
## -0.170 -0.177 -0.187
## -0.147 -0.154 -0.161
## -0.185 -0.192 -0.209
## -0.156 -0.164 -0.178
## -0.131 -0.138 -0.151
## -0.096 -0.104 -0.106
## -0.027 -0.035 -0.038
## 0.111 0.104 0.109
## 0.122 0.114 0.117
## -0.027 -0.034 -0.036
## 0.065 0.056 0.058
## 0.860 0.843 0.893
## 0.149 0.140 0.145
## 0.219 0.212 0.219
## -0.080 -0.087 -0.105
## -0.149 -0.156 -0.166
## -0.044 -0.051 -0.054
## 0.210 0.203 0.212
## 0.015 0.007 0.008
## 0.136 0.128 0.133
## -0.161 -0.170 -0.179
## 0.648 0.628 0.644
## 0.486 0.479 0.504
## 0.017 0.009 0.010
## -0.160 -0.169 -0.173
## 0.339 0.320 0.337
## 0.034 0.027 0.027
## 0.183 0.174 0.181
## -0.094 -0.102 -0.107
## 0.871 0.857 0.928
## 0.649 0.642 0.821
## 0.553 0.546 0.633
## 0.522 0.509 0.533
## 0.652 0.640 0.640
## -0.229 -0.242 -0.242
## 0.360 0.346 0.346
## 0.061 0.049 0.049
## -2.133 -2.157 -2.157
## -0.808 -0.827 -0.827
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.478 0.003 164.990 0.000 0.473
## .Stest20spellng 0.483 0.003 164.097 0.000 0.478
## .Stest21cptlztn 0.523 0.003 163.778 0.000 0.517
## .Stest22puncttn 0.261 0.002 131.896 0.000 0.257
## .Stest23english 0.453 0.003 157.441 0.000 0.447
## .Stest24exprssn 0.534 0.004 146.819 0.000 0.526
## .Stst25wrdfnctn 0.396 0.003 145.258 0.000 0.390
## .Stst26rdngcmpr 0.194 0.001 139.451 0.000 0.192
## .Stst31bstrctrs 0.470 0.003 156.843 0.000 0.465
## .Stst32rthrsnng 0.405 0.002 163.930 0.000 0.400
## .Stst34rthcmptt 0.490 0.003 142.586 0.000 0.483
## .Stest5math 0.329 0.003 101.231 0.000 0.323
## .Stst6physclscn 0.312 0.002 145.182 0.000 0.308
## .Stst33hghschlm 0.229 0.002 110.566 0.000 0.225
## .Stst29vslztn2D 0.594 0.004 157.323 0.000 0.587
## .Stest35tblrdng 0.307 0.004 85.059 0.000 0.300
## .Stst36clrclchc 0.430 0.004 101.193 0.000 0.422
## .Stst37bjctnspc 0.529 0.004 139.340 0.000 0.521
## .Stest1vocab 0.242 0.002 150.215 0.000 0.238
## .Stest2literatr 0.297 0.002 159.242 0.000 0.293
## .Stest3music 0.422 0.003 167.153 0.000 0.417
## .Stest4soclstds 0.289 0.002 157.717 0.000 0.285
## .Stst7blgclscnc 0.497 0.003 170.968 0.000 0.491
## .Stest8aerontcs 0.609 0.003 182.825 0.000 0.603
## .Stest11art 0.446 0.003 170.281 0.000 0.441
## .Stest12law 0.549 0.003 177.588 0.000 0.543
## .Stest13health 0.537 0.003 172.776 0.000 0.531
## .Stest14bible 0.631 0.003 193.084 0.000 0.625
## .Stest15theater 0.474 0.003 174.005 0.000 0.468
## .Stest16mscllns 0.497 0.003 171.059 0.000 0.491
## .Stest9elctrncs 0.505 0.004 120.149 0.000 0.496
## .Stest10mechncs 0.328 0.002 149.454 0.000 0.323
## .Stst28mchnclrs 0.298 0.002 133.015 0.000 0.293
## .Stst30vslztn3D 0.353 0.003 108.010 0.000 0.346
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.484 0.478 0.508
## 0.489 0.483 0.540
## 0.529 0.523 0.573
## 0.265 0.261 0.308
## 0.458 0.453 0.535
## 0.541 0.534 0.640
## 0.401 0.396 0.415
## 0.197 0.194 0.221
## 0.476 0.470 0.518
## 0.409 0.405 0.422
## 0.496 0.490 0.547
## 0.335 0.329 0.350
## 0.317 0.312 0.351
## 0.233 0.229 0.242
## 0.601 0.594 0.636
## 0.314 0.307 0.446
## 0.439 0.430 0.485
## 0.536 0.529 0.598
## 0.245 0.242 0.266
## 0.300 0.297 0.312
## 0.427 0.422 0.454
## 0.293 0.289 0.322
## 0.503 0.497 0.522
## 0.616 0.609 0.673
## 0.451 0.446 0.472
## 0.555 0.549 0.577
## 0.543 0.537 0.595
## 0.638 0.631 0.629
## 0.479 0.474 0.510
## 0.503 0.497 0.546
## 0.513 0.505 0.592
## 0.332 0.328 0.535
## 0.302 0.298 0.401
## 0.359 0.353 0.387
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
chc.reduced<-cfa(chc.factor.reduced.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "lv.variances", "lv.covariances"), group.partial=c("Stest4socialstudies~1", "Stest15theater~1", "Stest12law~1", "Stest3music~1", "Stest6physicalscience~1", "Stest16miscellaneous~1", "Stest30visualization3D~1", "Stest9electronics~1", "Stest5math~1", "Stest13health~1", "Stest7biologicalscience~1"))
fitMeasures(chc.reduced, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 147414.513 1074.000 0.000 0.945 0.044
## srmr aic bic
## 0.057 10351173.012 10352984.052
Mc(chc.reduced)
## [1] 0.5908413
summary(chc.reduced, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 63 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 273
## Number of equality constraints 89
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 147414.513 129284.429
## Degrees of freedom 1074 1074
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.140
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 81311.657 71311.372
## 1 66102.856 57973.057
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.314 0.004 78.812 0.000 0.306
## Stst20s (.p2.) 0.641 0.002 278.429 0.000 0.637
## Stst21c (.p3.) 0.624 0.002 269.846 0.000 0.619
## Stst22p (.p4.) 0.765 0.002 369.184 0.000 0.761
## Stst23n (.p5.) 0.627 0.003 241.980 0.000 0.622
## Stst24x (.p6.) 0.548 0.003 206.552 0.000 0.543
## Stst25w (.p7.) 0.549 0.003 166.363 0.000 0.542
## Stst26r (.p8.) 0.238 0.003 82.893 0.000 0.233
## Stst31b (.p9.) 0.363 0.003 142.154 0.000 0.358
## Stst32r (.10.) 0.220 0.004 59.654 0.000 0.213
## Stst34r (.11.) 0.193 0.004 49.844 0.000 0.186
## math =~
## Stst5mt (.12.) 0.782 0.002 377.667 0.000 0.778
## Stst6ph (.13.) 0.376 0.003 123.158 0.000 0.370
## Stst25w (.14.) 0.230 0.003 67.405 0.000 0.223
## Stst32r (.15.) 0.432 0.005 92.497 0.000 0.422
## Stst33h (.16.) 0.846 0.002 400.893 0.000 0.842
## Stst34r (.17.) 0.270 0.004 68.610 0.000 0.263
## speed =~
## Stst19d (.18.) 0.275 0.003 106.318 0.000 0.270
## Sts292D (.19.) 0.214 0.003 75.664 0.000 0.208
## Stst34r (.20.) 0.359 0.003 130.271 0.000 0.353
## Stst35t (.21.) 0.618 0.003 196.302 0.000 0.611
## Stst36c (.22.) 0.676 0.003 225.828 0.000 0.670
## Stst37b (.23.) 0.562 0.003 188.242 0.000 0.556
## info =~
## Stst1vc (.24.) 0.701 0.002 330.446 0.000 0.696
## Stst2lt (.25.) 0.809 0.002 406.200 0.000 0.805
## Stst3ms (.26.) 0.713 0.002 349.440 0.000 0.709
## Stst4sc (.27.) 0.780 0.002 372.826 0.000 0.776
## Stst7bl (.28.) 0.359 0.004 94.003 0.000 0.351
## Stst8rn (.29.) 0.168 0.003 60.740 0.000 0.163
## Stst11r (.30.) 0.707 0.002 315.759 0.000 0.702
## Stst12l (.31.) 0.635 0.002 268.386 0.000 0.630
## Stst13h (.32.) 0.543 0.004 136.991 0.000 0.535
## Stst14b (.33.) 0.611 0.002 258.985 0.000 0.606
## Stst15t (.34.) 0.675 0.002 312.590 0.000 0.671
## Stst16m (.35.) 0.643 0.002 265.769 0.000 0.639
## Stst19d (.36.) 0.267 0.004 68.337 0.000 0.259
## Stst26r (.37.) 0.620 0.003 210.664 0.000 0.615
## science =~
## Stst1vc (.38.) 0.154 0.001 108.012 0.000 0.151
## Stst6ph (.39.) 0.471 0.003 153.278 0.000 0.465
## Stst7bl (.40.) 0.371 0.004 93.222 0.000 0.364
## Stst8rn (.41.) 0.412 0.002 186.820 0.000 0.407
## Stst9lc (.42.) 0.590 0.002 249.964 0.000 0.585
## Stst10m (.43.) 0.534 0.002 255.833 0.000 0.530
## Stst13h (.44.) 0.083 0.004 20.429 0.000 0.075
## Stst28m (.45.) 0.262 0.002 106.117 0.000 0.257
## spatial =~
## Stst28m (.46.) 0.480 0.003 165.086 0.000 0.474
## Sts292D (.47.) 0.503 0.003 194.163 0.000 0.498
## Sts303D (.48.) 0.747 0.003 296.573 0.000 0.742
## Stst31b (.49.) 0.398 0.003 144.048 0.000 0.392
## Stst32r (.50.) 0.184 0.003 64.947 0.000 0.178
## Stst37b (.51.) 0.119 0.003 44.531 0.000 0.113
## ci.upper Std.lv Std.all
##
## 0.322 0.314 0.326
## 0.646 0.641 0.652
## 0.628 0.624 0.656
## 0.770 0.765 0.810
## 0.632 0.627 0.654
## 0.553 0.548 0.559
## 0.555 0.549 0.561
## 0.244 0.238 0.249
## 0.368 0.363 0.379
## 0.227 0.220 0.227
## 0.201 0.193 0.202
##
## 0.787 0.782 0.861
## 0.382 0.376 0.407
## 0.236 0.230 0.235
## 0.441 0.432 0.446
## 0.850 0.846 0.858
## 0.278 0.270 0.283
##
## 0.280 0.275 0.285
## 0.219 0.214 0.224
## 0.364 0.359 0.375
## 0.624 0.618 0.682
## 0.682 0.676 0.709
## 0.568 0.562 0.563
##
## 0.705 0.701 0.752
## 0.813 0.809 0.832
## 0.717 0.713 0.723
## 0.784 0.780 0.820
## 0.366 0.359 0.374
## 0.174 0.168 0.204
## 0.711 0.707 0.729
## 0.639 0.635 0.659
## 0.551 0.543 0.565
## 0.615 0.611 0.614
## 0.679 0.675 0.704
## 0.648 0.643 0.651
## 0.275 0.267 0.277
## 0.626 0.620 0.648
##
## 0.157 0.154 0.166
## 0.477 0.471 0.510
## 0.379 0.371 0.388
## 0.416 0.412 0.499
## 0.595 0.590 0.764
## 0.538 0.534 0.676
## 0.090 0.083 0.086
## 0.267 0.262 0.310
##
## 0.486 0.480 0.568
## 0.508 0.503 0.527
## 0.752 0.747 0.758
## 0.403 0.398 0.414
## 0.189 0.184 0.190
## 0.124 0.119 0.119
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math (.93.) 0.811 0.002 497.335 0.000 0.808
## speed (.94.) 0.276 0.004 72.266 0.000 0.269
## info (.95.) 0.820 0.001 595.924 0.000 0.817
## science (.96.) 0.517 0.003 166.125 0.000 0.511
## spatial (.97.) 0.511 0.003 165.628 0.000 0.505
## math ~~
## speed (.98.) 0.228 0.004 62.283 0.000 0.220
## info (.99.) 0.787 0.002 493.503 0.000 0.784
## science (.100) 0.610 0.003 214.643 0.000 0.604
## spatial (.101) 0.571 0.003 204.242 0.000 0.566
## speed ~~
## info (.102) 0.229 0.004 63.094 0.000 0.222
## science (.103) 0.066 0.004 16.540 0.000 0.058
## spatial (.104) 0.187 0.004 45.389 0.000 0.179
## info ~~
## science (.105) 0.708 0.002 293.526 0.000 0.703
## spatial (.106) 0.489 0.003 167.078 0.000 0.483
## science ~~
## spatial (.107) 0.581 0.003 183.275 0.000 0.575
## ci.upper Std.lv Std.all
##
## 0.814 0.811 0.811
## 0.284 0.276 0.276
## 0.822 0.820 0.820
## 0.523 0.517 0.517
## 0.517 0.511 0.511
##
## 0.235 0.228 0.228
## 0.790 0.787 0.787
## 0.615 0.610 0.610
## 0.577 0.571 0.571
##
## 0.236 0.229 0.229
## 0.073 0.066 0.066
## 0.195 0.187 0.187
##
## 0.713 0.708 0.708
## 0.494 0.489 0.489
##
## 0.587 0.581 0.581
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## info 0.000 0.000
## .Stst19d (.108) -0.117 0.003 -37.163 0.000 -0.123
## .Stst20s (.109) -0.167 0.003 -50.575 0.000 -0.173
## .Stst21c (.110) -0.144 0.003 -44.126 0.000 -0.150
## .Stst22p (.111) -0.180 0.003 -53.483 0.000 -0.186
## .Stst23n (.112) -0.153 0.003 -46.324 0.000 -0.160
## .Stst24x (.113) -0.129 0.003 -38.228 0.000 -0.135
## .Stst25w (.114) -0.091 0.003 -26.985 0.000 -0.097
## .Stst26r (.115) -0.017 0.003 -5.558 0.000 -0.023
## .Stst31b (.116) 0.114 0.003 32.942 0.000 0.107
## .Stst32r (.117) 0.127 0.004 36.117 0.000 0.120
## .Stst34r (.118) -0.025 0.004 -6.985 0.000 -0.032
## .Stst5mt 0.232 0.003 71.093 0.000 0.226
## .Stst6ph 0.371 0.003 109.475 0.000 0.364
## .Stst33h (.121) 0.154 0.004 41.091 0.000 0.147
## .Sts292D (.122) 0.218 0.004 61.107 0.000 0.211
## .Stst35t (.123) -0.084 0.003 -24.581 0.000 -0.091
## .Stst36c (.124) -0.153 0.004 -42.394 0.000 -0.160
## .Stst37b (.125) -0.047 0.004 -12.908 0.000 -0.054
## .Stst1vc (.126) 0.220 0.003 73.745 0.000 0.214
## .Stst2lt (.127) 0.027 0.003 9.809 0.000 0.022
## .Stst3ms -0.106 0.003 -30.208 0.000 -0.113
## .Stst4sc 0.244 0.003 74.745 0.000 0.238
## .Stst7bl 0.256 0.004 72.542 0.000 0.249
## .Stst8rn (.131) 0.489 0.003 157.279 0.000 0.483
## .Stst11r (.132) 0.027 0.003 9.586 0.000 0.021
## .Stst12l 0.222 0.004 61.832 0.000 0.215
## .Stst13h -0.068 0.004 -18.779 0.000 -0.076
## .Stst14b (.135) 0.042 0.003 14.746 0.000 0.037
## .Stst15t -0.153 0.003 -44.985 0.000 -0.160
## .Stst16m 0.147 0.004 39.189 0.000 0.140
## .Stst9lc 0.531 0.003 171.346 0.000 0.525
## .Stst10m (.139) 0.650 0.003 210.115 0.000 0.644
## .Stst28m (.140) 0.554 0.003 167.018 0.000 0.548
## .Sts303D 0.214 0.004 54.055 0.000 0.206
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -0.111 -0.117 -0.122
## -0.160 -0.167 -0.169
## -0.137 -0.144 -0.151
## -0.173 -0.180 -0.190
## -0.147 -0.153 -0.160
## -0.122 -0.129 -0.131
## -0.084 -0.091 -0.093
## -0.011 -0.017 -0.017
## 0.121 0.114 0.119
## 0.134 0.127 0.131
## -0.018 -0.025 -0.026
## 0.239 0.232 0.256
## 0.378 0.371 0.401
## 0.162 0.154 0.156
## 0.225 0.218 0.228
## -0.078 -0.084 -0.093
## -0.146 -0.153 -0.160
## -0.040 -0.047 -0.047
## 0.226 0.220 0.236
## 0.033 0.027 0.028
## -0.099 -0.106 -0.107
## 0.251 0.244 0.257
## 0.263 0.256 0.267
## 0.495 0.489 0.592
## 0.032 0.027 0.028
## 0.229 0.222 0.230
## -0.061 -0.068 -0.071
## 0.048 0.042 0.042
## -0.146 -0.153 -0.160
## 0.154 0.147 0.149
## 0.537 0.531 0.688
## 0.656 0.650 0.823
## 0.561 0.554 0.656
## 0.221 0.214 0.217
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.464 0.003 161.506 0.000 0.459
## .Stest20spellng 0.556 0.003 160.655 0.000 0.550
## .Stest21cptlztn 0.515 0.003 163.426 0.000 0.508
## .Stest22puncttn 0.308 0.002 137.363 0.000 0.303
## .Stest23english 0.527 0.003 152.142 0.000 0.520
## .Stest24exprssn 0.661 0.004 157.473 0.000 0.653
## .Stst25wrdfnctn 0.400 0.003 149.345 0.000 0.394
## .Stst26rdngcmpr 0.233 0.002 137.140 0.000 0.229
## .Stst31bstrctrs 0.484 0.003 150.755 0.000 0.478
## .Stst32rthrsnng 0.383 0.002 157.026 0.000 0.378
## .Stst34rthcmptt 0.506 0.003 148.380 0.000 0.499
## .Stest5math 0.213 0.003 84.028 0.000 0.208
## .Stst6physclscn 0.275 0.002 139.284 0.000 0.271
## .Stst33hghschlm 0.257 0.002 117.096 0.000 0.253
## .Stst29vslztn2D 0.572 0.004 137.771 0.000 0.564
## .Stest35tblrdng 0.437 0.005 94.024 0.000 0.428
## .Stst36clrclchc 0.453 0.005 87.856 0.000 0.443
## .Stst37bjctnspc 0.643 0.005 137.990 0.000 0.634
## .Stest1vocab 0.199 0.001 144.445 0.000 0.197
## .Stest2literatr 0.292 0.002 155.919 0.000 0.288
## .Stest3music 0.463 0.003 169.379 0.000 0.458
## .Stest4soclstds 0.297 0.002 153.694 0.000 0.294
## .Stst7blgclscnc 0.463 0.003 159.510 0.000 0.457
## .Stest8aerontcs 0.385 0.003 118.660 0.000 0.379
## .Stest11art 0.439 0.003 168.191 0.000 0.434
## .Stest12law 0.526 0.003 171.760 0.000 0.520
## .Stest13health 0.557 0.003 174.368 0.000 0.551
## .Stest14bible 0.617 0.003 185.984 0.000 0.610
## .Stest15theater 0.464 0.003 172.545 0.000 0.458
## .Stest16mscllns 0.564 0.003 167.473 0.000 0.558
## .Stest9elctrncs 0.248 0.003 90.431 0.000 0.242
## .Stest10mechncs 0.339 0.002 140.715 0.000 0.334
## .Stst28mchnclrs 0.269 0.002 120.292 0.000 0.265
## .Stst30vslztn3D 0.414 0.004 111.395 0.000 0.407
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.470 0.464 0.500
## 0.563 0.556 0.575
## 0.521 0.515 0.569
## 0.312 0.308 0.344
## 0.534 0.527 0.573
## 0.669 0.661 0.688
## 0.405 0.400 0.417
## 0.236 0.233 0.254
## 0.490 0.484 0.525
## 0.388 0.383 0.408
## 0.513 0.506 0.555
## 0.218 0.213 0.258
## 0.279 0.275 0.322
## 0.261 0.257 0.264
## 0.580 0.572 0.628
## 0.446 0.437 0.534
## 0.463 0.453 0.498
## 0.652 0.643 0.644
## 0.202 0.199 0.230
## 0.295 0.292 0.308
## 0.468 0.463 0.477
## 0.301 0.297 0.328
## 0.469 0.463 0.504
## 0.392 0.385 0.565
## 0.444 0.439 0.468
## 0.532 0.526 0.566
## 0.563 0.557 0.604
## 0.623 0.617 0.623
## 0.469 0.464 0.504
## 0.571 0.564 0.577
## 0.253 0.248 0.416
## 0.344 0.339 0.543
## 0.274 0.269 0.377
## 0.421 0.414 0.426
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.314 0.004 78.812 0.000 0.306
## Stst20s (.p2.) 0.641 0.002 278.429 0.000 0.637
## Stst21c (.p3.) 0.624 0.002 269.846 0.000 0.619
## Stst22p (.p4.) 0.765 0.002 369.184 0.000 0.761
## Stst23n (.p5.) 0.627 0.003 241.980 0.000 0.622
## Stst24x (.p6.) 0.548 0.003 206.552 0.000 0.543
## Stst25w (.p7.) 0.549 0.003 166.363 0.000 0.542
## Stst26r (.p8.) 0.238 0.003 82.893 0.000 0.233
## Stst31b (.p9.) 0.363 0.003 142.154 0.000 0.358
## Stst32r (.10.) 0.220 0.004 59.654 0.000 0.213
## Stst34r (.11.) 0.193 0.004 49.844 0.000 0.186
## math =~
## Stst5mt (.12.) 0.782 0.002 377.667 0.000 0.778
## Stst6ph (.13.) 0.376 0.003 123.158 0.000 0.370
## Stst25w (.14.) 0.230 0.003 67.405 0.000 0.223
## Stst32r (.15.) 0.432 0.005 92.497 0.000 0.422
## Stst33h (.16.) 0.846 0.002 400.893 0.000 0.842
## Stst34r (.17.) 0.270 0.004 68.610 0.000 0.263
## speed =~
## Stst19d (.18.) 0.275 0.003 106.318 0.000 0.270
## Sts292D (.19.) 0.214 0.003 75.664 0.000 0.208
## Stst34r (.20.) 0.359 0.003 130.271 0.000 0.353
## Stst35t (.21.) 0.618 0.003 196.302 0.000 0.611
## Stst36c (.22.) 0.676 0.003 225.828 0.000 0.670
## Stst37b (.23.) 0.562 0.003 188.242 0.000 0.556
## info =~
## Stst1vc (.24.) 0.701 0.002 330.446 0.000 0.696
## Stst2lt (.25.) 0.809 0.002 406.200 0.000 0.805
## Stst3ms (.26.) 0.713 0.002 349.440 0.000 0.709
## Stst4sc (.27.) 0.780 0.002 372.826 0.000 0.776
## Stst7bl (.28.) 0.359 0.004 94.003 0.000 0.351
## Stst8rn (.29.) 0.168 0.003 60.740 0.000 0.163
## Stst11r (.30.) 0.707 0.002 315.759 0.000 0.702
## Stst12l (.31.) 0.635 0.002 268.386 0.000 0.630
## Stst13h (.32.) 0.543 0.004 136.991 0.000 0.535
## Stst14b (.33.) 0.611 0.002 258.985 0.000 0.606
## Stst15t (.34.) 0.675 0.002 312.590 0.000 0.671
## Stst16m (.35.) 0.643 0.002 265.769 0.000 0.639
## Stst19d (.36.) 0.267 0.004 68.337 0.000 0.259
## Stst26r (.37.) 0.620 0.003 210.664 0.000 0.615
## science =~
## Stst1vc (.38.) 0.154 0.001 108.012 0.000 0.151
## Stst6ph (.39.) 0.471 0.003 153.278 0.000 0.465
## Stst7bl (.40.) 0.371 0.004 93.222 0.000 0.364
## Stst8rn (.41.) 0.412 0.002 186.820 0.000 0.407
## Stst9lc (.42.) 0.590 0.002 249.964 0.000 0.585
## Stst10m (.43.) 0.534 0.002 255.833 0.000 0.530
## Stst13h (.44.) 0.083 0.004 20.429 0.000 0.075
## Stst28m (.45.) 0.262 0.002 106.117 0.000 0.257
## spatial =~
## Stst28m (.46.) 0.480 0.003 165.086 0.000 0.474
## Sts292D (.47.) 0.503 0.003 194.163 0.000 0.498
## Sts303D (.48.) 0.747 0.003 296.573 0.000 0.742
## Stst31b (.49.) 0.398 0.003 144.048 0.000 0.392
## Stst32r (.50.) 0.184 0.003 64.947 0.000 0.178
## Stst37b (.51.) 0.119 0.003 44.531 0.000 0.113
## ci.upper Std.lv Std.all
##
## 0.322 0.314 0.323
## 0.646 0.641 0.678
## 0.628 0.624 0.653
## 0.770 0.765 0.832
## 0.632 0.627 0.682
## 0.553 0.548 0.600
## 0.555 0.549 0.562
## 0.244 0.238 0.254
## 0.368 0.363 0.381
## 0.227 0.220 0.225
## 0.201 0.193 0.204
##
## 0.787 0.782 0.807
## 0.382 0.376 0.398
## 0.236 0.230 0.235
## 0.441 0.432 0.441
## 0.850 0.846 0.870
## 0.278 0.270 0.286
##
## 0.280 0.275 0.283
## 0.219 0.214 0.221
## 0.364 0.359 0.379
## 0.624 0.618 0.744
## 0.682 0.676 0.718
## 0.568 0.562 0.598
##
## 0.705 0.701 0.735
## 0.813 0.809 0.830
## 0.717 0.713 0.739
## 0.784 0.780 0.823
## 0.366 0.359 0.368
## 0.174 0.168 0.177
## 0.711 0.707 0.727
## 0.639 0.635 0.651
## 0.551 0.543 0.572
## 0.615 0.611 0.609
## 0.679 0.675 0.700
## 0.648 0.643 0.674
## 0.275 0.267 0.275
## 0.626 0.620 0.662
##
## 0.157 0.154 0.162
## 0.477 0.471 0.499
## 0.379 0.371 0.381
## 0.416 0.412 0.433
## 0.595 0.590 0.639
## 0.538 0.534 0.682
## 0.090 0.083 0.087
## 0.267 0.262 0.304
##
## 0.486 0.480 0.557
## 0.508 0.503 0.521
## 0.752 0.747 0.783
## 0.403 0.398 0.417
## 0.189 0.184 0.188
## 0.124 0.119 0.126
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math (.93.) 0.811 0.002 497.335 0.000 0.808
## speed (.94.) 0.276 0.004 72.266 0.000 0.269
## info (.95.) 0.820 0.001 595.924 0.000 0.817
## science (.96.) 0.517 0.003 166.125 0.000 0.511
## spatial (.97.) 0.511 0.003 165.628 0.000 0.505
## math ~~
## speed (.98.) 0.228 0.004 62.283 0.000 0.220
## info (.99.) 0.787 0.002 493.503 0.000 0.784
## science (.100) 0.610 0.003 214.643 0.000 0.604
## spatial (.101) 0.571 0.003 204.242 0.000 0.566
## speed ~~
## info (.102) 0.229 0.004 63.094 0.000 0.222
## science (.103) 0.066 0.004 16.540 0.000 0.058
## spatial (.104) 0.187 0.004 45.389 0.000 0.179
## info ~~
## science (.105) 0.708 0.002 293.526 0.000 0.703
## spatial (.106) 0.489 0.003 167.078 0.000 0.483
## science ~~
## spatial (.107) 0.581 0.003 183.275 0.000 0.575
## ci.upper Std.lv Std.all
##
## 0.814 0.811 0.811
## 0.284 0.276 0.276
## 0.822 0.820 0.820
## 0.523 0.517 0.517
## 0.517 0.511 0.511
##
## 0.235 0.228 0.228
## 0.790 0.787 0.787
## 0.615 0.610 0.610
## 0.577 0.571 0.571
##
## 0.236 0.229 0.229
## 0.073 0.066 0.066
## 0.195 0.187 0.187
##
## 0.713 0.708 0.708
## 0.494 0.489 0.489
##
## 0.587 0.581 0.581
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## info 0.000 0.000
## .Stst19d (.108) -0.117 0.003 -37.163 0.000 -0.123
## .Stst20s (.109) -0.167 0.003 -50.575 0.000 -0.173
## .Stst21c (.110) -0.144 0.003 -44.126 0.000 -0.150
## .Stst22p (.111) -0.180 0.003 -53.483 0.000 -0.186
## .Stst23n (.112) -0.153 0.003 -46.324 0.000 -0.160
## .Stst24x (.113) -0.129 0.003 -38.228 0.000 -0.135
## .Stst25w (.114) -0.091 0.003 -26.985 0.000 -0.097
## .Stst26r (.115) -0.017 0.003 -5.558 0.000 -0.023
## .Stst31b (.116) 0.114 0.003 32.942 0.000 0.107
## .Stst32r (.117) 0.127 0.004 36.117 0.000 0.120
## .Stst34r (.118) -0.025 0.004 -6.985 0.000 -0.032
## .Stst5mt 0.069 0.005 15.325 0.000 0.060
## .Stst6ph 0.855 0.009 97.144 0.000 0.838
## .Stst33h (.121) 0.154 0.004 41.091 0.000 0.147
## .Sts292D (.122) 0.218 0.004 61.107 0.000 0.211
## .Stst35t (.123) -0.084 0.003 -24.581 0.000 -0.091
## .Stst36c (.124) -0.153 0.004 -42.394 0.000 -0.160
## .Stst37b (.125) -0.047 0.004 -12.908 0.000 -0.054
## .Stst1vc (.126) 0.220 0.003 73.745 0.000 0.214
## .Stst2lt (.127) 0.027 0.003 9.809 0.000 0.022
## .Stst3ms 0.148 0.003 43.516 0.000 0.141
## .Stst4sc -0.148 0.003 -45.986 0.000 -0.154
## .Stst7bl 0.642 0.010 64.663 0.000 0.623
## .Stst8rn (.131) 0.489 0.003 157.279 0.000 0.483
## .Stst11r (.132) 0.027 0.003 9.586 0.000 0.021
## .Stst12l -0.151 0.003 -43.395 0.000 -0.158
## .Stst13h 0.336 0.009 35.340 0.000 0.317
## .Stst14b (.135) 0.042 0.003 14.746 0.000 0.037
## .Stst15t 0.193 0.003 56.494 0.000 0.187
## .Stst16m -0.084 0.003 -25.030 0.000 -0.090
## .Stst9lc 0.865 0.007 116.717 0.000 0.850
## .Stst10m (.139) 0.650 0.003 210.115 0.000 0.644
## .Stst28m (.140) 0.554 0.003 167.018 0.000 0.548
## .Sts303D 0.516 0.007 72.749 0.000 0.503
## english 0.606 0.005 123.772 0.000 0.597
## math -0.275 0.005 -51.246 0.000 -0.285
## speed 0.337 0.007 49.763 0.000 0.324
## science -2.185 0.011 -192.546 0.000 -2.207
## spatial -0.848 0.009 -89.569 0.000 -0.866
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -0.111 -0.117 -0.121
## -0.160 -0.167 -0.176
## -0.137 -0.144 -0.151
## -0.173 -0.180 -0.195
## -0.147 -0.153 -0.166
## -0.122 -0.129 -0.141
## -0.084 -0.091 -0.093
## -0.011 -0.017 -0.018
## 0.121 0.114 0.120
## 0.134 0.127 0.130
## -0.018 -0.025 -0.026
## 0.078 0.069 0.071
## 0.872 0.855 0.906
## 0.162 0.154 0.159
## 0.225 0.218 0.225
## -0.078 -0.084 -0.102
## -0.146 -0.153 -0.162
## -0.040 -0.047 -0.050
## 0.226 0.220 0.230
## 0.033 0.027 0.028
## 0.154 0.148 0.153
## -0.142 -0.148 -0.156
## 0.662 0.642 0.658
## 0.495 0.489 0.514
## 0.032 0.027 0.027
## -0.144 -0.151 -0.154
## 0.354 0.336 0.353
## 0.048 0.042 0.042
## 0.200 0.193 0.201
## -0.077 -0.084 -0.088
## 0.879 0.865 0.936
## 0.656 0.650 0.830
## 0.561 0.554 0.643
## 0.530 0.516 0.541
## 0.616 0.606 0.606
## -0.264 -0.275 -0.275
## 0.350 0.337 0.337
## -2.163 -2.185 -2.185
## -0.829 -0.848 -0.848
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.478 0.003 164.990 0.000 0.473
## .Stest20spellng 0.483 0.003 164.114 0.000 0.478
## .Stest21cptlztn 0.523 0.003 163.789 0.000 0.517
## .Stest22puncttn 0.261 0.002 131.965 0.000 0.257
## .Stest23english 0.453 0.003 157.453 0.000 0.447
## .Stest24exprssn 0.534 0.004 146.797 0.000 0.526
## .Stst25wrdfnctn 0.396 0.003 145.268 0.000 0.390
## .Stst26rdngcmpr 0.194 0.001 139.338 0.000 0.192
## .Stst31bstrctrs 0.470 0.003 156.833 0.000 0.464
## .Stst32rthrsnng 0.405 0.002 163.928 0.000 0.400
## .Stst34rthcmptt 0.490 0.003 142.587 0.000 0.483
## .Stest5math 0.329 0.003 101.234 0.000 0.323
## .Stst6physclscn 0.312 0.002 145.174 0.000 0.308
## .Stst33hghschlm 0.229 0.002 110.571 0.000 0.225
## .Stst29vslztn2D 0.594 0.004 157.328 0.000 0.587
## .Stest35tblrdng 0.307 0.004 85.076 0.000 0.300
## .Stst36clrclchc 0.430 0.004 101.197 0.000 0.422
## .Stst37bjctnspc 0.529 0.004 139.337 0.000 0.521
## .Stest1vocab 0.242 0.002 150.291 0.000 0.238
## .Stest2literatr 0.296 0.002 159.335 0.000 0.293
## .Stest3music 0.422 0.003 167.151 0.000 0.417
## .Stest4soclstds 0.289 0.002 157.707 0.000 0.285
## .Stst7blgclscnc 0.497 0.003 170.975 0.000 0.491
## .Stest8aerontcs 0.609 0.003 182.832 0.000 0.603
## .Stest11art 0.446 0.003 170.446 0.000 0.441
## .Stest12law 0.549 0.003 177.590 0.000 0.543
## .Stest13health 0.537 0.003 172.779 0.000 0.531
## .Stest14bible 0.631 0.003 193.016 0.000 0.625
## .Stest15theater 0.474 0.003 174.013 0.000 0.468
## .Stest16mscllns 0.497 0.003 171.057 0.000 0.491
## .Stest9elctrncs 0.504 0.004 120.127 0.000 0.496
## .Stest10mechncs 0.328 0.002 149.401 0.000 0.323
## .Stst28mchnclrs 0.298 0.002 133.009 0.000 0.293
## .Stst30vslztn3D 0.353 0.003 108.015 0.000 0.346
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.484 0.478 0.508
## 0.489 0.483 0.540
## 0.529 0.523 0.573
## 0.265 0.261 0.308
## 0.458 0.453 0.535
## 0.541 0.534 0.640
## 0.401 0.396 0.415
## 0.197 0.194 0.221
## 0.476 0.470 0.518
## 0.409 0.405 0.422
## 0.496 0.490 0.547
## 0.335 0.329 0.350
## 0.317 0.312 0.351
## 0.233 0.229 0.242
## 0.601 0.594 0.636
## 0.314 0.307 0.446
## 0.438 0.430 0.485
## 0.536 0.529 0.598
## 0.245 0.242 0.266
## 0.300 0.296 0.312
## 0.427 0.422 0.453
## 0.293 0.289 0.322
## 0.503 0.497 0.522
## 0.616 0.609 0.673
## 0.452 0.446 0.472
## 0.555 0.549 0.577
## 0.543 0.537 0.595
## 0.638 0.631 0.629
## 0.479 0.474 0.510
## 0.503 0.497 0.546
## 0.513 0.504 0.592
## 0.332 0.328 0.535
## 0.302 0.298 0.401
## 0.359 0.353 0.387
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
# PAR.boot<- bootstrapLavaan(chc.reduced, R=500, type="ordinary", FUN="coef") # bootstrap model parameters, unstandardized
# describeBy(PAR.boot) # check sd column for the standard errors, as sd is the variability of the parameter estimates across the bootstrap samples
tests<-lavTestLRT(configural, metric, scalar2, chc.cov, chc.vcov, chc.reduced)
Td=tests[2:6,"Chisq diff"]
Td
## [1] 7498.93641 7839.21349 2781.82870 994.81382 61.27038
dfd=tests[2:6,"Df diff"]
dfd
## [1] 45 17 15 6 1
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04827480 0.08045894 0.05094240 0.04815214 0.02911963
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04735678 0.04919892
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.07896667 0.08196091
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.04935637 0.05254639
RMSEA.CI(T=Td[4],df=dfd[4],N=N,G=2)
## [1] 0.04565425 0.05069811
RMSEA.CI(T=Td[5],df=dfd[5],N=N,G=2)
## [1] 0.02319047 0.03552975
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.001 0.000 0.000 0.000
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 1.000 0.695 0.000
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.837 0.000 0.000 0.000
round(pvals(T=Td[4],df=dfd[4],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.117 0.000 0.000 0.000
round(pvals(T=Td[5],df=dfd[5],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 0 0 0 0
tests<-lavTestLRT(configural, metric, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 7498.936 57246.421
dfd=tests[2:3,"Df diff"]
dfd
## [1] 45 28
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.0482748 0.1695598
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04735678 0.04919892
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.1683946 0.1707268
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.001 0.000 0.000 0.000
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 1 1 1 1
tests<-lavTestLRT(configural, metric, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 7498.936 7839.213 13017.037
dfd=tests[2:4,"Df diff"]
dfd
## [1] 45 17 34
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04827480 0.08045894 0.07329639
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04735678 0.04919892
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.07896667 0.08196091
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.07224019 0.07435771
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.001 0.000 0.000 0.000
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 1.000 0.695 0.000
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 1 1 0 0
# CHC higher order models
chc.hof.model <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning + Stest34arithcomputation
math =~ Stest5math + Stest6physicalscience + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest13health + Stest28mechanicalreasoning
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest37objectinspection
g =~ english + math + speed + info + science + spatial
'
chc.hof.weak.model <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning + Stest34arithcomputation
math =~ Stest5math + Stest6physicalscience + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest13health + Stest28mechanicalreasoning
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest37objectinspection
g =~ english + math + speed + info + science + spatial
math ~ 0*1
'
baseline<-cfa(chc.hof.model, data=dgroup, meanstructure=TRUE, sampling.weights="BY_WTA")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 218348.391 504.000 0.000 0.921 0.056
## srmr aic bic
## 0.058 10591927.396 10593157.722
Mc(baseline)
## [1] 0.4568867
configural<-cfa(chc.hof.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T)
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 143673.203 1008.000 0.000 0.946 0.045
## srmr aic bic
## 0.036 10347563.701 10350024.354
Mc(configural)
## [1] 0.5987014
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 119 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 250
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 143673.203 125856.085
## Degrees of freedom 1008 1008
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.142
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 82561.471 72322.906
## 1 61111.732 53533.179
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19dsgsdwrd 0.153 0.003 48.680 0.000 0.147
## Stest20spellng 0.287 0.003 106.162 0.000 0.282
## Stest21cptlztn 0.289 0.003 111.205 0.000 0.284
## Stest22puncttn 0.355 0.003 119.596 0.000 0.349
## Stest23english 0.308 0.003 111.694 0.000 0.303
## Stest24exprssn 0.282 0.003 106.485 0.000 0.277
## Stst25wrdfnctn 0.221 0.004 61.934 0.000 0.214
## Stst26rdngcmpr 0.143 0.002 63.952 0.000 0.139
## Stst31bstrctrs 0.148 0.002 71.682 0.000 0.144
## Stst32rthrsnng 0.109 0.003 33.976 0.000 0.102
## Stst34rthcmptt 0.054 0.004 13.533 0.000 0.046
## math =~
## Stest5math 0.312 0.003 98.591 0.000 0.306
## Stst6physclscn 0.174 0.002 88.614 0.000 0.170
## Stst25wrdfnctn 0.103 0.003 33.295 0.000 0.097
## Stst32rthrsnng 0.178 0.003 55.797 0.000 0.172
## Stst33hghschlm 0.357 0.004 93.051 0.000 0.349
## Stst34rthcmptt 0.140 0.004 34.048 0.000 0.132
## speed =~
## Stst19dsgsdwrd 0.255 0.004 70.318 0.000 0.248
## Stst29vslztn2D 0.223 0.004 58.055 0.000 0.215
## Stst34rthcmptt 0.366 0.004 97.317 0.000 0.359
## Stest35tblrdng 0.671 0.004 153.350 0.000 0.663
## Stst36clrclchc 0.668 0.005 139.363 0.000 0.659
## Stst37bjctnspc 0.554 0.005 120.014 0.000 0.545
## info =~
## Stest1vocab 0.271 0.002 130.119 0.000 0.267
## Stest2literatr 0.374 0.003 141.347 0.000 0.369
## Stest3music 0.327 0.002 133.729 0.000 0.322
## Stest4soclstds 0.358 0.002 146.438 0.000 0.353
## Stst7blgclscnc 0.167 0.002 70.726 0.000 0.162
## Stest8aerontcs 0.118 0.002 55.215 0.000 0.114
## Stest11art 0.322 0.002 129.724 0.000 0.317
## Stest12law 0.309 0.002 131.202 0.000 0.304
## Stest13health 0.253 0.003 96.723 0.000 0.248
## Stest14bible 0.288 0.002 125.675 0.000 0.284
## Stest15theater 0.308 0.002 128.670 0.000 0.303
## Stest16mscllns 0.325 0.002 130.744 0.000 0.320
## Stst19dsgsdwrd 0.115 0.003 38.571 0.000 0.109
## Stst26rdngcmpr 0.268 0.003 103.700 0.000 0.263
## science =~
## Stest1vocab 0.205 0.002 85.859 0.000 0.201
## Stst6physclscn 0.329 0.003 108.945 0.000 0.323
## Stst7blgclscnc 0.282 0.004 79.022 0.000 0.275
## Stest8aerontcs 0.292 0.003 86.999 0.000 0.285
## Stest9elctrncs 0.485 0.003 163.794 0.000 0.479
## Stest10mechncs 0.432 0.003 156.853 0.000 0.426
## Stest13health 0.105 0.004 28.534 0.000 0.098
## Stst28mchnclrs 0.263 0.003 91.340 0.000 0.257
## spatial =~
## Stst28mchnclrs 0.374 0.003 112.600 0.000 0.367
## Stst29vslztn2D 0.418 0.004 115.269 0.000 0.411
## Stst30vslztn3D 0.653 0.004 185.352 0.000 0.646
## Stst31bstrctrs 0.369 0.004 101.755 0.000 0.362
## Stst32rthrsnng 0.121 0.003 36.781 0.000 0.114
## Stst37bjctnspc 0.122 0.004 33.910 0.000 0.115
## g =~
## english 2.025 0.020 100.738 0.000 1.986
## math 2.325 0.028 83.620 0.000 2.271
## speed 0.283 0.006 47.619 0.000 0.271
## info 1.991 0.017 114.084 0.000 1.956
## science 0.922 0.009 106.718 0.000 0.905
## spatial 0.707 0.007 95.009 0.000 0.693
## ci.upper Std.lv Std.all
##
## 0.159 0.345 0.355
## 0.293 0.649 0.654
## 0.294 0.653 0.673
## 0.360 0.801 0.822
## 0.313 0.695 0.698
## 0.287 0.636 0.622
## 0.228 0.498 0.515
## 0.148 0.324 0.324
## 0.152 0.335 0.344
## 0.115 0.245 0.250
## 0.061 0.121 0.124
##
## 0.319 0.791 0.861
## 0.178 0.440 0.458
## 0.109 0.260 0.269
## 0.185 0.452 0.461
## 0.364 0.903 0.871
## 0.148 0.354 0.363
##
## 0.262 0.265 0.272
## 0.230 0.232 0.241
## 0.374 0.381 0.390
## 0.680 0.698 0.741
## 0.678 0.694 0.713
## 0.563 0.576 0.570
##
## 0.275 0.603 0.657
## 0.379 0.833 0.843
## 0.332 0.728 0.731
## 0.363 0.797 0.826
## 0.172 0.372 0.386
## 0.122 0.263 0.304
## 0.327 0.717 0.739
## 0.314 0.688 0.689
## 0.258 0.563 0.566
## 0.293 0.642 0.635
## 0.313 0.686 0.712
## 0.330 0.724 0.697
## 0.121 0.256 0.264
## 0.273 0.596 0.597
##
## 0.210 0.279 0.304
## 0.335 0.448 0.466
## 0.289 0.383 0.398
## 0.299 0.397 0.459
## 0.490 0.659 0.808
## 0.437 0.587 0.717
## 0.112 0.143 0.144
## 0.268 0.358 0.415
##
## 0.380 0.458 0.532
## 0.425 0.512 0.532
## 0.660 0.799 0.790
## 0.376 0.452 0.465
## 0.127 0.148 0.151
## 0.129 0.150 0.148
##
## 2.065 0.897 0.897
## 2.380 0.919 0.919
## 0.295 0.272 0.272
## 2.025 0.894 0.894
## 0.939 0.678 0.678
## 0.722 0.577 0.577
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd -0.108 0.004 -27.549 0.000 -0.116
## .Stest20spellng -0.242 0.004 -59.771 0.000 -0.249
## .Stest21cptlztn -0.194 0.004 -49.221 0.000 -0.202
## .Stest22puncttn -0.183 0.004 -46.236 0.000 -0.191
## .Stest23english -0.119 0.004 -29.356 0.000 -0.127
## .Stest24exprssn -0.091 0.004 -21.886 0.000 -0.099
## .Stst25wrdfnctn -0.120 0.004 -30.548 0.000 -0.128
## .Stst26rdngcmpr -0.002 0.004 -0.480 0.632 -0.010
## .Stst31bstrctrs 0.074 0.004 18.667 0.000 0.066
## .Stst32rthrsnng 0.142 0.004 35.487 0.000 0.134
## .Stst34rthcmptt -0.062 0.004 -15.612 0.000 -0.070
## .Stest5math 0.219 0.004 58.635 0.000 0.212
## .Stst6physclscn 0.358 0.004 92.152 0.000 0.350
## .Stst33hghschlm 0.138 0.004 32.978 0.000 0.130
## .Stst29vslztn2D 0.224 0.004 57.484 0.000 0.217
## .Stest35tblrdng -0.047 0.004 -12.373 0.000 -0.055
## .Stst36clrclchc -0.165 0.004 -42.339 0.000 -0.173
## .Stst37bjctnspc -0.098 0.004 -24.085 0.000 -0.106
## .Stest1vocab 0.189 0.004 50.214 0.000 0.181
## .Stest2literatr 0.029 0.004 7.337 0.000 0.022
## .Stest3music -0.121 0.004 -29.896 0.000 -0.128
## .Stest4soclstds 0.228 0.004 57.617 0.000 0.220
## .Stst7blgclscnc 0.243 0.004 61.805 0.000 0.235
## .Stest8aerontcs 0.481 0.004 135.791 0.000 0.474
## .Stest11art -0.054 0.004 -13.827 0.000 -0.062
## .Stest12law 0.208 0.004 51.531 0.000 0.200
## .Stest13health -0.081 0.004 -19.852 0.000 -0.089
## .Stest14bible 0.015 0.004 3.604 0.000 0.007
## .Stest15theater -0.167 0.004 -42.900 0.000 -0.175
## .Stest16mscllns 0.134 0.004 31.520 0.000 0.125
## .Stest9elctrncs 0.522 0.003 156.854 0.000 0.516
## .Stest10mechncs 0.644 0.003 193.961 0.000 0.638
## .Stst28mchnclrs 0.551 0.004 154.563 0.000 0.544
## .Stst30vslztn3D 0.206 0.004 50.236 0.000 0.198
## ci.upper Std.lv Std.all
## -0.101 -0.108 -0.111
## -0.234 -0.242 -0.243
## -0.186 -0.194 -0.200
## -0.175 -0.183 -0.188
## -0.111 -0.119 -0.120
## -0.083 -0.091 -0.089
## -0.112 -0.120 -0.124
## 0.006 -0.002 -0.002
## 0.082 0.074 0.076
## 0.149 0.142 0.144
## -0.054 -0.062 -0.063
## 0.227 0.219 0.239
## 0.365 0.358 0.372
## 0.147 0.138 0.134
## 0.232 0.224 0.233
## -0.040 -0.047 -0.050
## -0.158 -0.165 -0.170
## -0.090 -0.098 -0.097
## 0.196 0.189 0.206
## 0.037 0.029 0.030
## -0.113 -0.121 -0.121
## 0.236 0.228 0.236
## 0.251 0.243 0.252
## 0.488 0.481 0.557
## -0.047 -0.054 -0.056
## 0.216 0.208 0.209
## -0.073 -0.081 -0.081
## 0.023 0.015 0.015
## -0.159 -0.167 -0.173
## 0.142 0.134 0.129
## 0.529 0.522 0.640
## 0.651 0.644 0.786
## 0.558 0.551 0.639
## 0.214 0.206 0.204
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.469 0.003 158.958 0.000 0.463
## .Stest20spellng 0.565 0.004 160.711 0.000 0.558
## .Stest21cptlztn 0.514 0.003 160.869 0.000 0.508
## .Stest22puncttn 0.307 0.002 129.440 0.000 0.302
## .Stest23english 0.510 0.003 148.769 0.000 0.503
## .Stest24exprssn 0.640 0.004 152.033 0.000 0.632
## .Stst25wrdfnctn 0.407 0.003 149.568 0.000 0.402
## .Stst26rdngcmpr 0.228 0.002 135.817 0.000 0.225
## .Stst31bstrctrs 0.472 0.003 145.312 0.000 0.466
## .Stst32rthrsnng 0.384 0.002 156.897 0.000 0.379
## .Stst34rthcmptt 0.507 0.003 146.057 0.000 0.500
## .Stest5math 0.218 0.002 87.843 0.000 0.213
## .Stst6physclscn 0.284 0.002 137.402 0.000 0.280
## .Stst33hghschlm 0.259 0.002 109.697 0.000 0.254
## .Stst29vslztn2D 0.573 0.004 133.245 0.000 0.564
## .Stest35tblrdng 0.399 0.005 80.807 0.000 0.390
## .Stst36clrclchc 0.466 0.005 85.694 0.000 0.455
## .Stst37bjctnspc 0.639 0.005 134.839 0.000 0.630
## .Stest1vocab 0.197 0.001 145.613 0.000 0.194
## .Stest2literatr 0.282 0.002 150.268 0.000 0.278
## .Stest3music 0.461 0.003 166.147 0.000 0.455
## .Stest4soclstds 0.296 0.002 150.400 0.000 0.292
## .Stst7blgclscnc 0.468 0.003 159.858 0.000 0.463
## .Stest8aerontcs 0.393 0.003 122.283 0.000 0.387
## .Stest11art 0.428 0.003 167.429 0.000 0.423
## .Stest12law 0.523 0.003 168.926 0.000 0.517
## .Stest13health 0.555 0.003 173.169 0.000 0.549
## .Stest14bible 0.610 0.003 182.553 0.000 0.603
## .Stest15theater 0.459 0.003 169.866 0.000 0.453
## .Stest16mscllns 0.554 0.003 164.341 0.000 0.547
## .Stest9elctrncs 0.231 0.003 85.787 0.000 0.225
## .Stest10mechncs 0.327 0.002 132.185 0.000 0.322
## .Stst28mchnclrs 0.277 0.002 120.309 0.000 0.272
## .Stst30vslztn3D 0.385 0.004 86.516 0.000 0.377
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.475 0.469 0.497
## 0.572 0.565 0.573
## 0.520 0.514 0.547
## 0.311 0.307 0.324
## 0.517 0.510 0.513
## 0.649 0.640 0.613
## 0.413 0.407 0.434
## 0.231 0.228 0.228
## 0.479 0.472 0.500
## 0.388 0.384 0.399
## 0.514 0.507 0.533
## 0.223 0.218 0.259
## 0.288 0.284 0.307
## 0.264 0.259 0.241
## 0.581 0.573 0.618
## 0.409 0.399 0.451
## 0.477 0.466 0.491
## 0.649 0.639 0.627
## 0.199 0.197 0.233
## 0.286 0.282 0.289
## 0.466 0.461 0.465
## 0.300 0.296 0.318
## 0.474 0.468 0.506
## 0.400 0.393 0.527
## 0.433 0.428 0.454
## 0.529 0.523 0.525
## 0.561 0.555 0.561
## 0.616 0.610 0.597
## 0.464 0.459 0.494
## 0.561 0.554 0.514
## 0.236 0.231 0.347
## 0.331 0.327 0.486
## 0.281 0.277 0.373
## 0.394 0.385 0.376
## 1.000 0.196 0.196
## 1.000 0.156 0.156
## 1.000 0.926 0.926
## 1.000 0.202 0.202
## 1.000 0.540 0.540
## 1.000 0.667 0.667
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19dsgsdwrd 0.191 0.003 56.682 0.000 0.184
## Stest20spellng 0.280 0.003 111.830 0.000 0.275
## Stest21cptlztn 0.272 0.002 111.786 0.000 0.267
## Stest22puncttn 0.356 0.003 130.826 0.000 0.350
## Stest23english 0.290 0.002 117.428 0.000 0.285
## Stest24exprssn 0.245 0.002 106.812 0.000 0.240
## Stst25wrdfnctn 0.255 0.003 84.666 0.000 0.249
## Stst26rdngcmpr 0.145 0.002 66.976 0.000 0.141
## Stst31bstrctrs 0.159 0.002 70.374 0.000 0.155
## Stst32rthrsnng 0.162 0.003 57.227 0.000 0.156
## Stst34rthcmptt 0.080 0.003 24.994 0.000 0.074
## math =~
## Stest5math 0.426 0.003 149.524 0.000 0.420
## Stst6physclscn 0.170 0.003 65.363 0.000 0.164
## Stst25wrdfnctn 0.148 0.003 49.807 0.000 0.142
## Stst32rthrsnng 0.176 0.003 57.164 0.000 0.170
## Stst33hghschlm 0.419 0.003 136.988 0.000 0.413
## Stst34rthcmptt 0.152 0.004 42.965 0.000 0.145
## speed =~
## Stst19dsgsdwrd 0.294 0.004 83.161 0.000 0.287
## Stst29vslztn2D 0.209 0.004 52.160 0.000 0.201
## Stst34rthcmptt 0.323 0.004 88.089 0.000 0.316
## Stest35tblrdng 0.551 0.004 136.848 0.000 0.543
## Stst36clrclchc 0.637 0.004 147.748 0.000 0.629
## Stst37bjctnspc 0.507 0.004 121.842 0.000 0.499
## info =~
## Stest1vocab 0.285 0.003 112.024 0.000 0.280
## Stest2literatr 0.337 0.003 113.635 0.000 0.331
## Stest3music 0.297 0.003 112.232 0.000 0.292
## Stest4soclstds 0.324 0.003 119.030 0.000 0.318
## Stst7blgclscnc 0.143 0.003 54.141 0.000 0.138
## Stest8aerontcs 0.064 0.002 25.647 0.000 0.059
## Stest11art 0.298 0.003 107.361 0.000 0.293
## Stest12law 0.245 0.002 102.758 0.000 0.240
## Stest13health 0.187 0.003 72.312 0.000 0.182
## Stest14bible 0.247 0.002 104.349 0.000 0.242
## Stest15theater 0.285 0.003 106.080 0.000 0.280
## Stest16mscllns 0.241 0.002 104.492 0.000 0.237
## Stst19dsgsdwrd 0.077 0.003 28.214 0.000 0.072
## Stst26rdngcmpr 0.223 0.002 92.388 0.000 0.219
## science =~
## Stest1vocab 0.162 0.003 58.809 0.000 0.157
## Stst6physclscn 0.335 0.003 102.911 0.000 0.328
## Stst7blgclscnc 0.276 0.004 69.573 0.000 0.268
## Stest8aerontcs 0.214 0.004 48.441 0.000 0.206
## Stest9elctrncs 0.343 0.004 97.952 0.000 0.336
## Stest10mechncs 0.327 0.003 112.068 0.000 0.321
## Stest13health 0.094 0.004 24.090 0.000 0.086
## Stst28mchnclrs 0.155 0.003 55.368 0.000 0.150
## spatial =~
## Stst28mchnclrs 0.375 0.003 121.082 0.000 0.369
## Stst29vslztn2D 0.385 0.003 111.568 0.000 0.378
## Stst30vslztn3D 0.565 0.003 168.196 0.000 0.558
## Stst31bstrctrs 0.335 0.004 93.782 0.000 0.328
## Stst32rthrsnng 0.127 0.003 38.892 0.000 0.121
## Stst37bjctnspc 0.127 0.003 39.971 0.000 0.120
## g =~
## english 1.805 0.017 108.423 0.000 1.773
## math 1.583 0.014 111.332 0.000 1.555
## speed 0.241 0.006 41.313 0.000 0.229
## info 2.136 0.022 95.427 0.000 2.093
## science 1.033 0.012 86.366 0.000 1.010
## spatial 0.759 0.008 97.207 0.000 0.744
## ci.upper Std.lv Std.all
##
## 0.198 0.394 0.409
## 0.285 0.579 0.638
## 0.277 0.561 0.612
## 0.361 0.734 0.820
## 0.294 0.597 0.666
## 0.249 0.505 0.570
## 0.261 0.525 0.536
## 0.149 0.299 0.332
## 0.164 0.329 0.348
## 0.167 0.334 0.348
## 0.086 0.165 0.180
##
## 0.432 0.797 0.823
## 0.175 0.317 0.350
## 0.154 0.278 0.283
## 0.182 0.330 0.344
## 0.425 0.785 0.852
## 0.159 0.284 0.310
##
## 0.301 0.303 0.314
## 0.217 0.215 0.226
## 0.331 0.333 0.363
## 0.559 0.566 0.706
## 0.646 0.655 0.713
## 0.515 0.521 0.566
##
## 0.290 0.673 0.694
## 0.343 0.795 0.828
## 0.303 0.702 0.735
## 0.329 0.763 0.818
## 0.148 0.337 0.349
## 0.069 0.151 0.168
## 0.304 0.703 0.730
## 0.250 0.578 0.615
## 0.192 0.441 0.485
## 0.251 0.582 0.591
## 0.290 0.673 0.701
## 0.246 0.569 0.628
## 0.083 0.182 0.189
## 0.228 0.527 0.586
##
## 0.168 0.233 0.241
## 0.341 0.481 0.530
## 0.283 0.396 0.411
## 0.223 0.308 0.344
## 0.350 0.493 0.568
## 0.333 0.470 0.628
## 0.101 0.135 0.148
## 0.161 0.224 0.274
##
## 0.382 0.471 0.577
## 0.392 0.483 0.508
## 0.572 0.709 0.765
## 0.342 0.421 0.445
## 0.134 0.160 0.166
## 0.133 0.159 0.173
##
## 1.838 0.875 0.875
## 1.610 0.845 0.845
## 0.252 0.234 0.234
## 2.180 0.906 0.906
## 1.057 0.719 0.719
## 0.775 0.605 0.605
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.156 0.004 40.337 0.000 0.149
## .Stest20spellng 0.288 0.004 79.198 0.000 0.281
## .Stest21cptlztn 0.285 0.004 77.178 0.000 0.278
## .Stest22puncttn 0.289 0.004 80.304 0.000 0.282
## .Stest23english 0.200 0.004 55.481 0.000 0.193
## .Stest24exprssn 0.175 0.004 49.287 0.000 0.169
## .Stst25wrdfnctn 0.208 0.004 52.986 0.000 0.200
## .Stst26rdngcmpr 0.118 0.004 32.716 0.000 0.111
## .Stst31bstrctrs 0.037 0.004 9.666 0.000 0.029
## .Stst32rthrsnng -0.030 0.004 -7.900 0.000 -0.038
## .Stst34rthcmptt 0.175 0.004 47.455 0.000 0.168
## .Stest5math -0.133 0.004 -34.579 0.000 -0.141
## .Stst6physclscn -0.264 0.004 -73.191 0.000 -0.272
## .Stst33hghschlm -0.063 0.004 -17.147 0.000 -0.070
## .Stst29vslztn2D -0.144 0.004 -37.867 0.000 -0.151
## .Stest35tblrdng 0.099 0.003 30.730 0.000 0.092
## .Stst36clrclchc 0.087 0.004 23.895 0.000 0.079
## .Stst37bjctnspc 0.084 0.004 22.958 0.000 0.077
## .Stest1vocab -0.083 0.004 -21.517 0.000 -0.091
## .Stest2literatr 0.025 0.004 6.452 0.000 0.017
## .Stest3music 0.163 0.004 42.478 0.000 0.155
## .Stest4soclstds -0.132 0.004 -35.225 0.000 -0.139
## .Stst7blgclscnc -0.156 0.004 -40.430 0.000 -0.164
## .Stest8aerontcs -0.404 0.004 -112.676 0.000 -0.411
## .Stest11art 0.108 0.004 28.115 0.000 0.101
## .Stest12law -0.138 0.004 -36.597 0.000 -0.145
## .Stest13health 0.168 0.004 45.803 0.000 0.161
## .Stest14bible 0.070 0.004 17.656 0.000 0.062
## .Stest15theater 0.207 0.004 54.125 0.000 0.200
## .Stest16mscllns -0.071 0.004 -19.463 0.000 -0.078
## .Stest9elctrncs -0.416 0.003 -119.952 0.000 -0.423
## .Stest10mechncs -0.511 0.003 -170.689 0.000 -0.517
## .Stst28mchnclrs -0.422 0.003 -128.379 0.000 -0.429
## .Stst30vslztn3D -0.109 0.004 -29.486 0.000 -0.116
## ci.upper Std.lv Std.all
## 0.164 0.156 0.162
## 0.295 0.288 0.318
## 0.292 0.285 0.311
## 0.296 0.289 0.323
## 0.207 0.200 0.223
## 0.182 0.175 0.198
## 0.216 0.208 0.212
## 0.125 0.118 0.132
## 0.044 0.037 0.039
## -0.023 -0.030 -0.032
## 0.182 0.175 0.191
## -0.126 -0.133 -0.138
## -0.257 -0.264 -0.291
## -0.056 -0.063 -0.068
## -0.136 -0.144 -0.151
## 0.105 0.099 0.123
## 0.094 0.087 0.094
## 0.091 0.084 0.091
## -0.076 -0.083 -0.086
## 0.032 0.025 0.026
## 0.170 0.163 0.170
## -0.125 -0.132 -0.142
## -0.149 -0.156 -0.162
## -0.397 -0.404 -0.451
## 0.116 0.108 0.112
## -0.130 -0.138 -0.146
## 0.175 0.168 0.184
## 0.077 0.070 0.071
## 0.215 0.207 0.216
## -0.064 -0.071 -0.078
## -0.409 -0.416 -0.479
## -0.505 -0.511 -0.683
## -0.416 -0.422 -0.517
## -0.102 -0.109 -0.118
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.464 0.003 154.579 0.000 0.459
## .Stest20spellng 0.488 0.003 163.606 0.000 0.482
## .Stest21cptlztn 0.526 0.003 163.526 0.000 0.519
## .Stest22puncttn 0.263 0.002 127.559 0.000 0.259
## .Stest23english 0.449 0.003 156.630 0.000 0.443
## .Stest24exprssn 0.530 0.004 148.428 0.000 0.523
## .Stst25wrdfnctn 0.392 0.003 143.633 0.000 0.387
## .Stst26rdngcmpr 0.191 0.001 139.224 0.000 0.188
## .Stst31bstrctrs 0.462 0.003 151.202 0.000 0.456
## .Stst32rthrsnng 0.404 0.002 163.935 0.000 0.399
## .Stst34rthcmptt 0.493 0.003 141.154 0.000 0.486
## .Stest5math 0.302 0.003 96.155 0.000 0.296
## .Stst6physclscn 0.305 0.002 127.282 0.000 0.301
## .Stst33hghschlm 0.232 0.002 103.111 0.000 0.227
## .Stst29vslztn2D 0.596 0.004 151.272 0.000 0.588
## .Stest35tblrdng 0.324 0.004 86.818 0.000 0.316
## .Stst36clrclchc 0.416 0.005 89.542 0.000 0.407
## .Stst37bjctnspc 0.527 0.004 135.350 0.000 0.519
## .Stest1vocab 0.229 0.002 145.034 0.000 0.226
## .Stest2literatr 0.289 0.002 154.243 0.000 0.286
## .Stest3music 0.418 0.003 163.935 0.000 0.413
## .Stest4soclstds 0.288 0.002 153.214 0.000 0.284
## .Stst7blgclscnc 0.487 0.003 160.605 0.000 0.481
## .Stest8aerontcs 0.625 0.003 180.672 0.000 0.618
## .Stest11art 0.435 0.003 166.509 0.000 0.429
## .Stest12law 0.550 0.003 177.399 0.000 0.544
## .Stest13health 0.539 0.003 173.324 0.000 0.533
## .Stest14bible 0.632 0.003 191.363 0.000 0.626
## .Stest15theater 0.467 0.003 170.086 0.000 0.462
## .Stest16mscllns 0.497 0.003 171.675 0.000 0.491
## .Stest9elctrncs 0.510 0.004 119.826 0.000 0.501
## .Stest10mechncs 0.340 0.002 140.764 0.000 0.335
## .Stst28mchnclrs 0.303 0.002 130.753 0.000 0.299
## .Stst30vslztn3D 0.356 0.004 97.107 0.000 0.349
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.470 0.464 0.499
## 0.493 0.488 0.593
## 0.532 0.526 0.625
## 0.267 0.263 0.328
## 0.454 0.449 0.557
## 0.537 0.530 0.675
## 0.397 0.392 0.408
## 0.194 0.191 0.237
## 0.468 0.462 0.517
## 0.409 0.404 0.437
## 0.500 0.493 0.586
## 0.308 0.302 0.322
## 0.310 0.305 0.371
## 0.236 0.232 0.273
## 0.603 0.596 0.658
## 0.331 0.324 0.502
## 0.425 0.416 0.492
## 0.535 0.527 0.622
## 0.232 0.229 0.243
## 0.293 0.289 0.314
## 0.423 0.418 0.459
## 0.292 0.288 0.331
## 0.493 0.487 0.523
## 0.632 0.625 0.778
## 0.440 0.435 0.468
## 0.556 0.550 0.622
## 0.545 0.539 0.650
## 0.638 0.632 0.651
## 0.473 0.467 0.508
## 0.503 0.497 0.606
## 0.518 0.510 0.677
## 0.344 0.340 0.605
## 0.308 0.303 0.455
## 0.363 0.356 0.414
## 1.000 0.235 0.235
## 1.000 0.285 0.285
## 1.000 0.945 0.945
## 1.000 0.180 0.180
## 1.000 0.484 0.484
## 1.000 0.634 0.634
## 1.000 1.000 1.000
modificationIndices(configural, sort=T, maximum.number=30)
## lhs op rhs block group
## 1045 science ~~ spatial 1 1
## 442 g =~ Stest34arithcomputation 1 1
## 388 science =~ Stest34arithcomputation 1 1
## 369 info =~ Stest33highschoolmath 1 1
## 447 g =~ Stest35tablereading 1 1
## 311 math =~ Stest35tablereading 1 1
## 405 spatial =~ Stest20spelling 1 1
## 1799 english ~~ science 2 2
## 1030 english ~~ science 1 1
## 283 english =~ Stest35tablereading 1 1
## 814 Stest6physicalscience ~~ Stest10mechanics 1 1
## 368 info =~ Stest6physicalscience 1 1
## 403 science =~ Stest30visualization3D 1 1
## 1174 spatial =~ Stest20spelling 2 2
## 285 english =~ Stest37objectinspection 1 1
## 416 spatial =~ Stest35tablereading 1 1
## 371 info =~ Stest35tablereading 1 1
## 1211 g =~ Stest34arithcomputation 2 2
## 753 Stest34arithcomputation ~~ Stest33highschoolmath 1 1
## 313 math =~ Stest37objectinspection 1 1
## 1042 info ~~ science 1 1
## 1235 Stest19disguisedwords ~~ Stest20spelling 2 2
## 449 g =~ Stest37objectinspection 1 1
## 466 Stest19disguisedwords ~~ Stest20spelling 1 1
## 1043 info ~~ spatial 1 1
## 1138 info =~ Stest33highschoolmath 2 2
## 1099 speed =~ Stest20spelling 2 2
## 1052 english =~ Stest35tablereading 2 2
## 486 Stest19disguisedwords ~~ Stest4socialstudies 1 1
## 1583 Stest6physicalscience ~~ Stest10mechanics 2 2
## level mi epc sepc.lv sepc.all sepc.nox
## 1045 1 3758.476 0.361 0.361 0.361 0.361
## 442 1 3527.433 -1.160 -1.160 -1.189 -1.189
## 388 1 3332.258 -0.188 -0.255 -0.262 -0.262
## 369 1 3323.984 -0.160 -0.357 -0.344 -0.344
## 447 1 3215.560 0.214 0.214 0.227 0.227
## 311 1 3108.016 0.081 0.205 0.218 0.218
## 405 1 3083.761 -0.194 -0.237 -0.239 -0.239
## 1799 1 2988.069 -0.507 -0.507 -0.507 -0.507
## 1030 1 2962.802 -0.433 -0.433 -0.433 -0.433
## 283 1 2717.755 0.085 0.192 0.204 0.204
## 814 1 2703.423 -0.080 -0.080 -0.261 -0.261
## 368 1 2606.989 0.116 0.258 0.268 0.268
## 403 1 2592.774 0.171 0.233 0.230 0.230
## 1174 1 2394.911 -0.160 -0.201 -0.221 -0.221
## 285 1 2392.641 -0.098 -0.222 -0.220 -0.220
## 416 1 2372.534 0.146 0.179 0.190 0.190
## 371 1 2338.845 0.077 0.171 0.182 0.182
## 1211 1 2280.601 -0.619 -0.619 -0.675 -0.675
## 753 1 2238.269 0.089 0.089 0.245 0.245
## 313 1 2096.202 -0.082 -0.208 -0.206 -0.206
## 1042 1 2095.445 0.325 0.325 0.325 0.325
## 1235 1 2016.768 0.090 0.090 0.189 0.189
## 449 1 1948.642 -0.214 -0.214 -0.212 -0.212
## 466 1 1913.907 0.094 0.094 0.182 0.182
## 1043 1 1857.966 -0.303 -0.303 -0.303 -0.303
## 1138 1 1809.753 -0.107 -0.251 -0.273 -0.273
## 1099 1 1778.692 0.135 0.138 0.153 0.153
## 1052 1 1762.132 0.064 0.131 0.164 0.164
## 486 1 1748.079 -0.066 -0.066 -0.178 -0.178
## 1583 1 1657.070 -0.075 -0.075 -0.234 -0.234
metric<-cfa(chc.hof.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 152985.153 1058.000 0.000 0.942 0.045
## srmr aic bic
## 0.044 10356775.652 10358744.174
Mc(metric)
## [1] 0.5790907
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 105 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 257
## Number of equality constraints 57
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 152985.153 134123.674
## Degrees of freedom 1058 1058
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.141
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 86603.675 75926.342
## 1 66381.478 58197.332
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.174 0.002 70.588 0.000 0.169
## Stst20s (.p2.) 0.288 0.002 121.545 0.000 0.284
## Stst21c (.p3.) 0.286 0.002 124.494 0.000 0.281
## Stst22p (.p4.) 0.361 0.003 132.314 0.000 0.355
## Stst23n (.p5.) 0.304 0.002 125.137 0.000 0.299
## Stst24x (.p6.) 0.267 0.002 119.688 0.000 0.263
## Stst25w (.p7.) 0.240 0.003 92.574 0.000 0.235
## Stst26r (.p8.) 0.147 0.002 84.346 0.000 0.143
## Stst31b (.p9.) 0.156 0.002 91.929 0.000 0.153
## Stst32r (.10.) 0.139 0.002 62.481 0.000 0.135
## Stst34r (.11.) 0.069 0.003 27.218 0.000 0.064
## math =~
## Stst5mt (.12.) 0.336 0.003 114.443 0.000 0.330
## Stst6ph (.13.) 0.168 0.002 96.458 0.000 0.164
## Stst25w (.14.) 0.114 0.002 53.375 0.000 0.110
## Stst32r (.15.) 0.163 0.002 67.710 0.000 0.158
## Stst33h (.16.) 0.359 0.003 108.657 0.000 0.352
## Stst34r (.17.) 0.134 0.003 49.290 0.000 0.129
## speed =~
## Stst19d (.18.) 0.287 0.003 105.151 0.000 0.282
## Sts292D (.19.) 0.228 0.003 76.556 0.000 0.222
## Stst34r (.20.) 0.364 0.003 121.107 0.000 0.358
## Stst35t (.21.) 0.641 0.004 165.849 0.000 0.633
## Stst36c (.22.) 0.688 0.004 173.788 0.000 0.680
## Stst37b (.23.) 0.559 0.004 150.067 0.000 0.552
## info =~
## Stst1vc (.24.) 0.283 0.002 142.291 0.000 0.279
## Stst2lt (.25.) 0.363 0.003 144.374 0.000 0.358
## Stst3ms (.26.) 0.319 0.002 141.162 0.000 0.314
## Stst4sc (.27.) 0.348 0.002 147.477 0.000 0.343
## Stst7bl (.28.) 0.163 0.002 85.520 0.000 0.159
## Stst8rn (.29.) 0.096 0.002 56.643 0.000 0.092
## Stst11r (.30.) 0.316 0.002 137.655 0.000 0.312
## Stst12l (.31.) 0.283 0.002 135.906 0.000 0.279
## Stst13h (.32.) 0.224 0.002 105.780 0.000 0.220
## Stst14b (.33.) 0.273 0.002 133.922 0.000 0.269
## Stst15t (.34.) 0.302 0.002 137.381 0.000 0.298
## Stst16m (.35.) 0.287 0.002 135.119 0.000 0.283
## Stst19d (.36.) 0.098 0.002 45.782 0.000 0.093
## Stst26r (.37.) 0.249 0.002 118.318 0.000 0.245
## science =~
## Stst1vc (.38.) 0.200 0.002 96.798 0.000 0.196
## Stst6ph (.39.) 0.357 0.002 145.757 0.000 0.352
## Stst7bl (.40.) 0.299 0.003 100.739 0.000 0.293
## Stst8rn (.41.) 0.290 0.003 97.818 0.000 0.284
## Stst9lc (.42.) 0.470 0.003 167.467 0.000 0.464
## Stst10m (.43.) 0.424 0.003 162.410 0.000 0.419
## Stst13h (.44.) 0.111 0.003 37.745 0.000 0.106
## Stst28m (.45.) 0.238 0.002 97.351 0.000 0.233
## spatial =~
## Stst28m (.46.) 0.392 0.003 146.272 0.000 0.387
## Sts292D (.47.) 0.423 0.003 144.977 0.000 0.418
## Sts303D (.48.) 0.643 0.003 201.290 0.000 0.637
## Stst31b (.49.) 0.371 0.003 128.971 0.000 0.365
## Stst32r (.50.) 0.132 0.002 53.415 0.000 0.127
## Stst37b (.51.) 0.132 0.003 51.710 0.000 0.127
## g =~
## english (.52.) 1.977 0.017 113.093 0.000 1.942
## math (.53.) 2.179 0.022 96.912 0.000 2.135
## speed (.54.) 0.260 0.004 61.285 0.000 0.252
## info (.55.) 2.113 0.017 122.908 0.000 2.079
## science (.56.) 0.910 0.008 120.719 0.000 0.895
## spatial (.57.) 0.725 0.006 123.409 0.000 0.714
## ci.upper Std.lv Std.all
##
## 0.178 0.385 0.390
## 0.293 0.639 0.648
## 0.290 0.633 0.661
## 0.366 0.799 0.822
## 0.308 0.673 0.684
## 0.272 0.592 0.593
## 0.245 0.531 0.532
## 0.150 0.325 0.329
## 0.159 0.346 0.352
## 0.144 0.309 0.312
## 0.074 0.154 0.158
##
## 0.342 0.806 0.871
## 0.171 0.402 0.421
## 0.118 0.273 0.274
## 0.168 0.391 0.396
## 0.365 0.861 0.856
## 0.140 0.322 0.332
##
## 0.292 0.297 0.301
## 0.234 0.235 0.243
## 0.370 0.376 0.388
## 0.649 0.662 0.712
## 0.695 0.711 0.728
## 0.566 0.578 0.571
##
## 0.287 0.661 0.688
## 0.368 0.848 0.848
## 0.323 0.745 0.740
## 0.352 0.813 0.831
## 0.166 0.380 0.388
## 0.099 0.223 0.266
## 0.321 0.739 0.749
## 0.287 0.661 0.673
## 0.228 0.523 0.536
## 0.277 0.638 0.632
## 0.307 0.707 0.722
## 0.291 0.671 0.667
## 0.102 0.228 0.231
## 0.254 0.583 0.589
##
## 0.204 0.271 0.282
## 0.362 0.483 0.506
## 0.305 0.404 0.413
## 0.295 0.392 0.466
## 0.475 0.635 0.794
## 0.429 0.574 0.706
## 0.117 0.151 0.154
## 0.242 0.321 0.375
##
## 0.397 0.484 0.565
## 0.429 0.523 0.541
## 0.649 0.794 0.784
## 0.377 0.458 0.466
## 0.136 0.163 0.164
## 0.137 0.163 0.161
##
## 2.011 0.892 0.892
## 2.224 0.909 0.909
## 0.269 0.252 0.252
## 2.146 0.904 0.904
## 0.924 0.673 0.673
## 0.737 0.587 0.587
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd -0.108 0.004 -27.549 0.000 -0.116
## .Stest20spellng -0.242 0.004 -59.771 0.000 -0.249
## .Stest21cptlztn -0.194 0.004 -49.221 0.000 -0.202
## .Stest22puncttn -0.183 0.004 -46.236 0.000 -0.191
## .Stest23english -0.119 0.004 -29.356 0.000 -0.127
## .Stest24exprssn -0.091 0.004 -21.886 0.000 -0.099
## .Stst25wrdfnctn -0.120 0.004 -30.548 0.000 -0.128
## .Stst26rdngcmpr -0.002 0.004 -0.480 0.632 -0.010
## .Stst31bstrctrs 0.074 0.004 18.667 0.000 0.066
## .Stst32rthrsnng 0.142 0.004 35.487 0.000 0.134
## .Stst34rthcmptt -0.062 0.004 -15.612 0.000 -0.070
## .Stest5math 0.219 0.004 58.635 0.000 0.212
## .Stst6physclscn 0.358 0.004 92.152 0.000 0.350
## .Stst33hghschlm 0.138 0.004 32.978 0.000 0.130
## .Stst29vslztn2D 0.224 0.004 57.484 0.000 0.217
## .Stest35tblrdng -0.047 0.004 -12.373 0.000 -0.055
## .Stst36clrclchc -0.165 0.004 -42.339 0.000 -0.173
## .Stst37bjctnspc -0.098 0.004 -24.085 0.000 -0.106
## .Stest1vocab 0.189 0.004 50.214 0.000 0.181
## .Stest2literatr 0.029 0.004 7.337 0.000 0.022
## .Stest3music -0.121 0.004 -29.896 0.000 -0.128
## .Stest4soclstds 0.228 0.004 57.617 0.000 0.220
## .Stst7blgclscnc 0.243 0.004 61.805 0.000 0.235
## .Stest8aerontcs 0.481 0.004 135.791 0.000 0.474
## .Stest11art -0.054 0.004 -13.827 0.000 -0.062
## .Stest12law 0.208 0.004 51.531 0.000 0.200
## .Stest13health -0.081 0.004 -19.852 0.000 -0.089
## .Stest14bible 0.015 0.004 3.604 0.000 0.007
## .Stest15theater -0.167 0.004 -42.900 0.000 -0.175
## .Stest16mscllns 0.134 0.004 31.520 0.000 0.125
## .Stest9elctrncs 0.522 0.003 156.854 0.000 0.516
## .Stest10mechncs 0.644 0.003 193.961 0.000 0.638
## .Stst28mchnclrs 0.551 0.004 154.563 0.000 0.544
## .Stst30vslztn3D 0.206 0.004 50.236 0.000 0.198
## ci.upper Std.lv Std.all
## -0.101 -0.108 -0.110
## -0.234 -0.242 -0.245
## -0.186 -0.194 -0.202
## -0.175 -0.183 -0.188
## -0.111 -0.119 -0.122
## -0.083 -0.091 -0.091
## -0.112 -0.120 -0.120
## 0.006 -0.002 -0.002
## 0.082 0.074 0.075
## 0.149 0.142 0.143
## -0.054 -0.062 -0.064
## 0.227 0.219 0.237
## 0.365 0.358 0.375
## 0.147 0.138 0.138
## 0.232 0.224 0.232
## -0.040 -0.047 -0.051
## -0.158 -0.165 -0.169
## -0.090 -0.098 -0.097
## 0.196 0.189 0.197
## 0.037 0.029 0.029
## -0.113 -0.121 -0.120
## 0.236 0.228 0.233
## 0.251 0.243 0.248
## 0.488 0.481 0.573
## -0.047 -0.054 -0.055
## 0.216 0.208 0.212
## -0.073 -0.081 -0.083
## 0.023 0.015 0.015
## -0.159 -0.167 -0.171
## 0.142 0.134 0.133
## 0.529 0.522 0.653
## 0.651 0.644 0.793
## 0.558 0.551 0.642
## 0.214 0.206 0.203
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.462 0.003 159.353 0.000 0.456
## .Stest20spellng 0.564 0.003 163.659 0.000 0.558
## .Stest21cptlztn 0.517 0.003 164.336 0.000 0.511
## .Stest22puncttn 0.307 0.002 132.705 0.000 0.303
## .Stest23english 0.514 0.003 149.787 0.000 0.507
## .Stest24exprssn 0.647 0.004 152.798 0.000 0.639
## .Stst25wrdfnctn 0.405 0.003 149.817 0.000 0.400
## .Stst26rdngcmpr 0.229 0.002 136.804 0.000 0.226
## .Stst31bstrctrs 0.472 0.003 148.068 0.000 0.466
## .Stst32rthrsnng 0.385 0.002 158.682 0.000 0.381
## .Stst34rthcmptt 0.510 0.003 149.084 0.000 0.503
## .Stest5math 0.207 0.002 83.263 0.000 0.202
## .Stst6physclscn 0.278 0.002 137.371 0.000 0.274
## .Stst33hghschlm 0.270 0.002 118.889 0.000 0.266
## .Stst29vslztn2D 0.570 0.004 136.074 0.000 0.561
## .Stest35tblrdng 0.426 0.005 89.980 0.000 0.417
## .Stst36clrclchc 0.447 0.005 88.551 0.000 0.437
## .Stst37bjctnspc 0.636 0.005 138.697 0.000 0.627
## .Stest1vocab 0.195 0.001 143.985 0.000 0.193
## .Stest2literatr 0.281 0.002 151.694 0.000 0.277
## .Stest3music 0.459 0.003 167.585 0.000 0.454
## .Stest4soclstds 0.296 0.002 151.694 0.000 0.292
## .Stst7blgclscnc 0.465 0.003 159.612 0.000 0.459
## .Stest8aerontcs 0.396 0.003 121.609 0.000 0.390
## .Stest11art 0.428 0.003 168.172 0.000 0.423
## .Stest12law 0.527 0.003 170.932 0.000 0.521
## .Stest13health 0.559 0.003 174.379 0.000 0.553
## .Stest14bible 0.611 0.003 184.203 0.000 0.605
## .Stest15theater 0.458 0.003 170.751 0.000 0.453
## .Stest16mscllns 0.563 0.003 166.548 0.000 0.556
## .Stest9elctrncs 0.237 0.003 87.020 0.000 0.231
## .Stest10mechncs 0.331 0.002 135.397 0.000 0.326
## .Stst28mchnclrs 0.275 0.002 124.222 0.000 0.271
## .Stst30vslztn3D 0.396 0.004 100.238 0.000 0.388
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.468 0.462 0.475
## 0.571 0.564 0.580
## 0.523 0.517 0.563
## 0.312 0.307 0.325
## 0.520 0.514 0.532
## 0.655 0.647 0.649
## 0.411 0.405 0.406
## 0.233 0.229 0.234
## 0.478 0.472 0.488
## 0.390 0.385 0.395
## 0.517 0.510 0.543
## 0.212 0.207 0.242
## 0.282 0.278 0.306
## 0.275 0.270 0.267
## 0.578 0.570 0.609
## 0.435 0.426 0.492
## 0.457 0.447 0.469
## 0.645 0.636 0.621
## 0.198 0.195 0.212
## 0.285 0.281 0.281
## 0.465 0.459 0.453
## 0.300 0.296 0.309
## 0.470 0.465 0.484
## 0.403 0.396 0.561
## 0.433 0.428 0.440
## 0.533 0.527 0.546
## 0.565 0.559 0.588
## 0.618 0.611 0.600
## 0.464 0.458 0.478
## 0.570 0.563 0.556
## 0.242 0.237 0.370
## 0.336 0.331 0.502
## 0.279 0.275 0.374
## 0.404 0.396 0.386
## 1.000 0.204 0.204
## 1.000 0.174 0.174
## 1.000 0.937 0.937
## 1.000 0.183 0.183
## 1.000 0.547 0.547
## 1.000 0.655 0.655
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.174 0.002 70.588 0.000 0.169
## Stst20s (.p2.) 0.288 0.002 121.545 0.000 0.284
## Stst21c (.p3.) 0.286 0.002 124.494 0.000 0.281
## Stst22p (.p4.) 0.361 0.003 132.314 0.000 0.355
## Stst23n (.p5.) 0.304 0.002 125.137 0.000 0.299
## Stst24x (.p6.) 0.267 0.002 119.688 0.000 0.263
## Stst25w (.p7.) 0.240 0.003 92.574 0.000 0.235
## Stst26r (.p8.) 0.147 0.002 84.346 0.000 0.143
## Stst31b (.p9.) 0.156 0.002 91.929 0.000 0.153
## Stst32r (.10.) 0.139 0.002 62.481 0.000 0.135
## Stst34r (.11.) 0.069 0.003 27.218 0.000 0.064
## math =~
## Stst5mt (.12.) 0.336 0.003 114.443 0.000 0.330
## Stst6ph (.13.) 0.168 0.002 96.458 0.000 0.164
## Stst25w (.14.) 0.114 0.002 53.375 0.000 0.110
## Stst32r (.15.) 0.163 0.002 67.710 0.000 0.158
## Stst33h (.16.) 0.359 0.003 108.657 0.000 0.352
## Stst34r (.17.) 0.134 0.003 49.290 0.000 0.129
## speed =~
## Stst19d (.18.) 0.287 0.003 105.151 0.000 0.282
## Sts292D (.19.) 0.228 0.003 76.556 0.000 0.222
## Stst34r (.20.) 0.364 0.003 121.107 0.000 0.358
## Stst35t (.21.) 0.641 0.004 165.849 0.000 0.633
## Stst36c (.22.) 0.688 0.004 173.788 0.000 0.680
## Stst37b (.23.) 0.559 0.004 150.067 0.000 0.552
## info =~
## Stst1vc (.24.) 0.283 0.002 142.291 0.000 0.279
## Stst2lt (.25.) 0.363 0.003 144.374 0.000 0.358
## Stst3ms (.26.) 0.319 0.002 141.162 0.000 0.314
## Stst4sc (.27.) 0.348 0.002 147.477 0.000 0.343
## Stst7bl (.28.) 0.163 0.002 85.520 0.000 0.159
## Stst8rn (.29.) 0.096 0.002 56.643 0.000 0.092
## Stst11r (.30.) 0.316 0.002 137.655 0.000 0.312
## Stst12l (.31.) 0.283 0.002 135.906 0.000 0.279
## Stst13h (.32.) 0.224 0.002 105.780 0.000 0.220
## Stst14b (.33.) 0.273 0.002 133.922 0.000 0.269
## Stst15t (.34.) 0.302 0.002 137.381 0.000 0.298
## Stst16m (.35.) 0.287 0.002 135.119 0.000 0.283
## Stst19d (.36.) 0.098 0.002 45.782 0.000 0.093
## Stst26r (.37.) 0.249 0.002 118.318 0.000 0.245
## science =~
## Stst1vc (.38.) 0.200 0.002 96.798 0.000 0.196
## Stst6ph (.39.) 0.357 0.002 145.757 0.000 0.352
## Stst7bl (.40.) 0.299 0.003 100.739 0.000 0.293
## Stst8rn (.41.) 0.290 0.003 97.818 0.000 0.284
## Stst9lc (.42.) 0.470 0.003 167.467 0.000 0.464
## Stst10m (.43.) 0.424 0.003 162.410 0.000 0.419
## Stst13h (.44.) 0.111 0.003 37.745 0.000 0.106
## Stst28m (.45.) 0.238 0.002 97.351 0.000 0.233
## spatial =~
## Stst28m (.46.) 0.392 0.003 146.272 0.000 0.387
## Sts292D (.47.) 0.423 0.003 144.977 0.000 0.418
## Sts303D (.48.) 0.643 0.003 201.290 0.000 0.637
## Stst31b (.49.) 0.371 0.003 128.971 0.000 0.365
## Stst32r (.50.) 0.132 0.002 53.415 0.000 0.127
## Stst37b (.51.) 0.132 0.003 51.710 0.000 0.127
## g =~
## english (.52.) 1.977 0.017 113.093 0.000 1.942
## math (.53.) 2.179 0.022 96.912 0.000 2.135
## speed (.54.) 0.260 0.004 61.285 0.000 0.252
## info (.55.) 2.113 0.017 122.908 0.000 2.079
## science (.56.) 0.910 0.008 120.719 0.000 0.895
## spatial (.57.) 0.725 0.006 123.409 0.000 0.714
## ci.upper Std.lv Std.all
##
## 0.178 0.354 0.373
## 0.293 0.588 0.644
## 0.290 0.583 0.627
## 0.366 0.736 0.821
## 0.308 0.619 0.680
## 0.272 0.545 0.600
## 0.245 0.489 0.515
## 0.150 0.300 0.331
## 0.159 0.318 0.341
## 0.144 0.284 0.298
## 0.074 0.141 0.153
##
## 0.342 0.772 0.807
## 0.171 0.385 0.421
## 0.118 0.262 0.276
## 0.168 0.375 0.393
## 0.365 0.824 0.866
## 0.140 0.308 0.334
##
## 0.292 0.267 0.281
## 0.234 0.212 0.223
## 0.370 0.338 0.366
## 0.649 0.596 0.733
## 0.695 0.639 0.696
## 0.566 0.520 0.565
##
## 0.287 0.608 0.662
## 0.368 0.780 0.823
## 0.323 0.685 0.727
## 0.352 0.748 0.812
## 0.166 0.350 0.370
## 0.099 0.205 0.221
## 0.321 0.680 0.718
## 0.287 0.608 0.635
## 0.228 0.481 0.517
## 0.277 0.587 0.594
## 0.307 0.650 0.689
## 0.291 0.617 0.659
## 0.102 0.210 0.221
## 0.254 0.536 0.592
##
## 0.204 0.231 0.252
## 0.362 0.412 0.451
## 0.305 0.345 0.365
## 0.295 0.334 0.359
## 0.475 0.542 0.609
## 0.429 0.490 0.649
## 0.117 0.129 0.138
## 0.242 0.274 0.334
##
## 0.397 0.438 0.533
## 0.429 0.473 0.499
## 0.649 0.718 0.775
## 0.377 0.414 0.443
## 0.136 0.147 0.154
## 0.137 0.148 0.161
##
## 2.011 0.880 0.880
## 2.224 0.862 0.862
## 0.269 0.254 0.254
## 2.146 0.893 0.893
## 0.924 0.716 0.716
## 0.737 0.590 0.590
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.156 0.004 40.337 0.000 0.149
## .Stest20spellng 0.288 0.004 79.198 0.000 0.281
## .Stest21cptlztn 0.285 0.004 77.178 0.000 0.278
## .Stest22puncttn 0.289 0.004 80.304 0.000 0.282
## .Stest23english 0.200 0.004 55.481 0.000 0.193
## .Stest24exprssn 0.175 0.004 49.287 0.000 0.169
## .Stst25wrdfnctn 0.208 0.004 52.986 0.000 0.200
## .Stst26rdngcmpr 0.118 0.004 32.716 0.000 0.111
## .Stst31bstrctrs 0.037 0.004 9.666 0.000 0.029
## .Stst32rthrsnng -0.030 0.004 -7.900 0.000 -0.038
## .Stst34rthcmptt 0.175 0.004 47.455 0.000 0.168
## .Stest5math -0.133 0.004 -34.579 0.000 -0.141
## .Stst6physclscn -0.264 0.004 -73.191 0.000 -0.272
## .Stst33hghschlm -0.063 0.004 -17.147 0.000 -0.070
## .Stst29vslztn2D -0.144 0.004 -37.867 0.000 -0.151
## .Stest35tblrdng 0.099 0.003 30.730 0.000 0.092
## .Stst36clrclchc 0.087 0.004 23.895 0.000 0.079
## .Stst37bjctnspc 0.084 0.004 22.958 0.000 0.077
## .Stest1vocab -0.083 0.004 -21.517 0.000 -0.091
## .Stest2literatr 0.025 0.004 6.452 0.000 0.017
## .Stest3music 0.163 0.004 42.478 0.000 0.155
## .Stest4soclstds -0.132 0.004 -35.225 0.000 -0.139
## .Stst7blgclscnc -0.156 0.004 -40.430 0.000 -0.164
## .Stest8aerontcs -0.404 0.004 -112.676 0.000 -0.411
## .Stest11art 0.108 0.004 28.115 0.000 0.101
## .Stest12law -0.138 0.004 -36.597 0.000 -0.145
## .Stest13health 0.168 0.004 45.803 0.000 0.161
## .Stest14bible 0.070 0.004 17.656 0.000 0.062
## .Stest15theater 0.207 0.004 54.125 0.000 0.200
## .Stest16mscllns -0.071 0.004 -19.463 0.000 -0.078
## .Stest9elctrncs -0.416 0.003 -119.952 0.000 -0.423
## .Stest10mechncs -0.511 0.003 -170.689 0.000 -0.517
## .Stst28mchnclrs -0.422 0.003 -128.379 0.000 -0.429
## .Stst30vslztn3D -0.109 0.004 -29.486 0.000 -0.116
## ci.upper Std.lv Std.all
## 0.164 0.156 0.165
## 0.295 0.288 0.316
## 0.292 0.285 0.307
## 0.296 0.289 0.323
## 0.207 0.200 0.219
## 0.182 0.175 0.193
## 0.216 0.208 0.219
## 0.125 0.118 0.131
## 0.044 0.037 0.039
## -0.023 -0.030 -0.032
## 0.182 0.175 0.190
## -0.126 -0.133 -0.140
## -0.257 -0.264 -0.289
## -0.056 -0.063 -0.066
## -0.136 -0.144 -0.152
## 0.105 0.099 0.121
## 0.094 0.087 0.094
## 0.091 0.084 0.092
## -0.076 -0.083 -0.091
## 0.032 0.025 0.026
## 0.170 0.163 0.172
## -0.125 -0.132 -0.143
## -0.149 -0.156 -0.165
## -0.397 -0.404 -0.434
## 0.116 0.108 0.114
## -0.130 -0.138 -0.144
## 0.175 0.168 0.180
## 0.077 0.070 0.070
## 0.215 0.207 0.220
## -0.064 -0.071 -0.075
## -0.409 -0.416 -0.467
## -0.505 -0.511 -0.677
## -0.416 -0.422 -0.514
## -0.102 -0.109 -0.118
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.476 0.003 163.334 0.000 0.470
## .Stest20spellng 0.487 0.003 166.168 0.000 0.482
## .Stest21cptlztn 0.523 0.003 164.713 0.000 0.517
## .Stest22puncttn 0.263 0.002 130.452 0.000 0.259
## .Stest23english 0.446 0.003 157.022 0.000 0.440
## .Stest24exprssn 0.527 0.004 147.964 0.000 0.520
## .Stst25wrdfnctn 0.401 0.003 147.453 0.000 0.395
## .Stst26rdngcmpr 0.191 0.001 139.475 0.000 0.188
## .Stst31bstrctrs 0.464 0.003 153.173 0.000 0.458
## .Stst32rthrsnng 0.404 0.002 166.291 0.000 0.400
## .Stst34rthcmptt 0.490 0.003 142.570 0.000 0.484
## .Stest5math 0.319 0.003 99.435 0.000 0.313
## .Stst6physclscn 0.321 0.002 145.986 0.000 0.317
## .Stst33hghschlm 0.226 0.002 107.574 0.000 0.222
## .Stst29vslztn2D 0.598 0.004 156.940 0.000 0.591
## .Stest35tblrdng 0.305 0.004 84.191 0.000 0.298
## .Stst36clrclchc 0.434 0.004 98.333 0.000 0.425
## .Stst37bjctnspc 0.529 0.004 140.919 0.000 0.522
## .Stest1vocab 0.240 0.002 149.606 0.000 0.237
## .Stest2literatr 0.290 0.002 156.794 0.000 0.286
## .Stest3music 0.419 0.003 165.716 0.000 0.414
## .Stest4soclstds 0.288 0.002 155.632 0.000 0.284
## .Stst7blgclscnc 0.499 0.003 171.614 0.000 0.493
## .Stest8aerontcs 0.624 0.003 183.140 0.000 0.617
## .Stest11art 0.435 0.003 168.837 0.000 0.430
## .Stest12law 0.548 0.003 176.833 0.000 0.542
## .Stest13health 0.538 0.003 172.873 0.000 0.532
## .Stest14bible 0.630 0.003 192.351 0.000 0.624
## .Stest15theater 0.468 0.003 172.511 0.000 0.463
## .Stest16mscllns 0.495 0.003 170.414 0.000 0.490
## .Stest9elctrncs 0.499 0.004 118.189 0.000 0.490
## .Stest10mechncs 0.330 0.002 147.589 0.000 0.326
## .Stst28mchnclrs 0.306 0.002 139.543 0.000 0.302
## .Stst30vslztn3D 0.343 0.003 101.576 0.000 0.336
## .english 0.937 0.018 52.262 0.000 0.902
## .math 1.351 0.028 48.797 0.000 1.297
## .speed 0.807 0.010 77.004 0.000 0.787
## .info 0.940 0.016 58.326 0.000 0.908
## .science 0.649 0.010 67.188 0.000 0.630
## .spatial 0.813 0.010 79.650 0.000 0.793
## g 0.825 0.007 125.936 0.000 0.812
## ci.upper Std.lv Std.all
## 0.481 0.476 0.528
## 0.493 0.487 0.585
## 0.529 0.523 0.606
## 0.266 0.263 0.326
## 0.451 0.446 0.538
## 0.534 0.527 0.640
## 0.406 0.401 0.444
## 0.193 0.191 0.233
## 0.470 0.464 0.531
## 0.409 0.404 0.445
## 0.497 0.490 0.575
## 0.325 0.319 0.349
## 0.326 0.321 0.385
## 0.231 0.226 0.250
## 0.606 0.598 0.667
## 0.312 0.305 0.462
## 0.442 0.434 0.515
## 0.537 0.529 0.627
## 0.243 0.240 0.285
## 0.293 0.290 0.323
## 0.424 0.419 0.472
## 0.292 0.288 0.340
## 0.505 0.499 0.558
## 0.631 0.624 0.721
## 0.440 0.435 0.485
## 0.554 0.548 0.597
## 0.544 0.538 0.622
## 0.637 0.630 0.647
## 0.474 0.468 0.526
## 0.501 0.495 0.565
## 0.507 0.499 0.629
## 0.335 0.330 0.579
## 0.311 0.306 0.454
## 0.349 0.343 0.399
## 0.973 0.225 0.225
## 1.406 0.256 0.256
## 0.828 0.935 0.935
## 0.972 0.203 0.203
## 0.668 0.487 0.487
## 0.832 0.652 0.652
## 0.838 1.000 1.000
lavTestScore(metric, release = 1:57)
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 9143.042 57 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p140. 112.104 1 0.000
## 2 .p2. == .p141. 21.659 1 0.000
## 3 .p3. == .p142. 91.226 1 0.000
## 4 .p4. == .p143. 0.718 1 0.397
## 5 .p5. == .p144. 118.206 1 0.000
## 6 .p6. == .p145. 378.058 1 0.000
## 7 .p7. == .p146. 769.740 1 0.000
## 8 .p8. == .p147. 128.061 1 0.000
## 9 .p9. == .p148. 79.582 1 0.000
## 10 .p10. == .p149. 122.078 1 0.000
## 11 .p11. == .p150. 1.591 1 0.207
## 12 .p12. == .p151. 275.849 1 0.000
## 13 .p13. == .p152. 68.159 1 0.000
## 14 .p14. == .p153. 731.310 1 0.000
## 15 .p15. == .p154. 29.155 1 0.000
## 16 .p16. == .p155. 946.973 1 0.000
## 17 .p17. == .p156. 13.163 1 0.000
## 18 .p18. == .p157. 264.677 1 0.000
## 19 .p19. == .p158. 3.380 1 0.066
## 20 .p20. == .p159. 2.121 1 0.145
## 21 .p21. == .p160. 198.076 1 0.000
## 22 .p22. == .p161. 10.714 1 0.001
## 23 .p23. == .p162. 2.862 1 0.091
## 24 .p24. == .p163. 2165.916 1 0.000
## 25 .p25. == .p164. 19.809 1 0.000
## 26 .p26. == .p165. 24.581 1 0.000
## 27 .p27. == .p166. 29.684 1 0.000
## 28 .p28. == .p167. 180.939 1 0.000
## 29 .p29. == .p168. 843.758 1 0.000
## 30 .p30. == .p169. 82.924 1 0.000
## 31 .p31. == .p170. 316.433 1 0.000
## 32 .p32. == .p171. 360.445 1 0.000
## 33 .p33. == .p172. 23.835 1 0.000
## 34 .p34. == .p173. 66.767 1 0.000
## 35 .p35. == .p174. 851.286 1 0.000
## 36 .p36. == .p175. 26.884 1 0.000
## 37 .p37. == .p176. 183.051 1 0.000
## 38 .p38. == .p177. 1175.303 1 0.000
## 39 .p39. == .p178. 64.317 1 0.000
## 40 .p40. == .p179. 265.419 1 0.000
## 41 .p41. == .p180. 626.697 1 0.000
## 42 .p42. == .p181. 342.416 1 0.000
## 43 .p43. == .p182. 14.968 1 0.000
## 44 .p44. == .p183. 173.892 1 0.000
## 45 .p45. == .p184. 164.853 1 0.000
## 46 .p46. == .p185. 0.066 1 0.797
## 47 .p47. == .p186. 5.622 1 0.018
## 48 .p48. == .p187. 13.679 1 0.000
## 49 .p49. == .p188. 34.148 1 0.000
## 50 .p50. == .p189. 53.042 1 0.000
## 51 .p51. == .p190. 6.505 1 0.011
## 52 .p52. == .p191. 23.085 1 0.000
## 53 .p53. == .p192. 113.625 1 0.000
## 54 .p54. == .p193. 6.191 1 0.013
## 55 .p55. == .p194. 306.574 1 0.000
## 56 .p56. == .p195. 103.419 1 0.000
## 57 .p57. == .p196. 43.092 1 0.000
scalar<-cfa(chc.hof.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov)
## does not appear to be positive definite! The smallest eigenvalue
## (= 1.969300e-16) is close to zero. This may be a symptom that the
## model is not identified.
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 221270.586 1085.000 0.000 0.917 0.054
## srmr aic bic
## 0.050 10425007.085 10426709.856
Mc(scalar)
## [1] 0.4530566
summary(scalar, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 123 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 264
## Number of equality constraints 91
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 221270.586 193725.390
## Degrees of freedom 1085 1085
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.142
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 121704.728 106554.135
## 1 99565.858 87171.255
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.163 0.002 75.884 0.000 0.159
## Stst20s (.p2.) 0.310 0.002 133.707 0.000 0.305
## Stst21c (.p3.) 0.303 0.002 136.608 0.000 0.299
## Stst22p (.p4.) 0.373 0.003 144.410 0.000 0.368
## Stst23n (.p5.) 0.306 0.002 134.699 0.000 0.302
## Stst24x (.p6.) 0.267 0.002 127.287 0.000 0.263
## Stst25w (.p7.) 0.271 0.002 120.648 0.000 0.267
## Stst26r (.p8.) 0.126 0.002 81.814 0.000 0.123
## Stst31b (.p9.) 0.162 0.002 104.621 0.000 0.159
## Stst32r (.10.) 0.104 0.002 59.172 0.000 0.100
## Stst34r (.11.) 0.109 0.002 54.821 0.000 0.105
## math =~
## Stst5mt (.12.) 0.314 0.003 100.216 0.000 0.308
## Stst6ph (.13.) 0.194 0.002 99.677 0.000 0.191
## Stst25w (.14.) 0.087 0.002 53.823 0.000 0.084
## Stst32r (.15.) 0.177 0.002 78.454 0.000 0.173
## Stst33h (.16.) 0.326 0.003 96.332 0.000 0.320
## Stst34r (.17.) 0.093 0.002 47.487 0.000 0.089
## speed =~
## Stst19d (.18.) 0.283 0.003 104.390 0.000 0.278
## Sts292D (.19.) 0.206 0.003 70.022 0.000 0.200
## Stst34r (.20.) 0.366 0.003 122.251 0.000 0.360
## Stst35t (.21.) 0.633 0.004 163.895 0.000 0.625
## Stst36c (.22.) 0.693 0.004 180.759 0.000 0.686
## Stst37b (.23.) 0.572 0.004 158.115 0.000 0.565
## info =~
## Stst1vc (.24.) 0.298 0.002 140.641 0.000 0.294
## Stst2lt (.25.) 0.346 0.003 137.140 0.000 0.341
## Stst3ms (.26.) 0.303 0.002 133.710 0.000 0.299
## Stst4sc (.27.) 0.331 0.002 140.120 0.000 0.327
## Stst7bl (.28.) 0.197 0.002 113.488 0.000 0.194
## Stst8rn (.29.) 0.073 0.001 54.259 0.000 0.070
## Stst11r (.30.) 0.301 0.002 131.046 0.000 0.297
## Stst12l (.31.) 0.270 0.002 129.984 0.000 0.266
## Stst13h (.32.) 0.275 0.002 127.358 0.000 0.271
## Stst14b (.33.) 0.261 0.002 127.939 0.000 0.257
## Stst15t (.34.) 0.287 0.002 129.817 0.000 0.282
## Stst16m (.35.) 0.275 0.002 129.478 0.000 0.271
## Stst19d (.36.) 0.106 0.002 57.746 0.000 0.103
## Stst26r (.37.) 0.259 0.002 124.073 0.000 0.255
## science =~
## Stst1vc (.38.) 0.136 0.001 100.964 0.000 0.134
## Stst6ph (.39.) 0.246 0.002 126.455 0.000 0.242
## Stst7bl (.40.) 0.202 0.002 106.740 0.000 0.199
## Stst8rn (.41.) 0.356 0.002 175.680 0.000 0.352
## Stst9lc (.42.) 0.447 0.002 193.660 0.000 0.442
## Stst10m (.43.) 0.478 0.002 203.891 0.000 0.474
## Stst13h (.44.) -0.051 0.002 -30.837 0.000 -0.054
## Stst28m (.45.) 0.290 0.002 145.088 0.000 0.286
## spatial =~
## Stst28m (.46.) 0.376 0.003 138.119 0.000 0.371
## Sts292D (.47.) 0.450 0.003 159.530 0.000 0.445
## Sts303D (.48.) 0.616 0.003 194.658 0.000 0.610
## Stst31b (.49.) 0.374 0.003 145.351 0.000 0.369
## Stst32r (.50.) 0.149 0.002 61.167 0.000 0.144
## Stst37b (.51.) 0.117 0.002 48.298 0.000 0.113
## g =~
## english (.52.) 1.896 0.016 121.297 0.000 1.865
## math (.53.) 2.391 0.027 87.799 0.000 2.338
## speed (.54.) 0.259 0.004 61.456 0.000 0.251
## info (.55.) 2.227 0.019 118.328 0.000 2.190
## science (.56.) 0.867 0.007 125.800 0.000 0.854
## spatial (.57.) 0.719 0.006 123.117 0.000 0.707
## ci.upper Std.lv Std.all
##
## 0.168 0.350 0.356
## 0.314 0.664 0.663
## 0.307 0.650 0.671
## 0.378 0.800 0.824
## 0.311 0.656 0.673
## 0.272 0.573 0.577
## 0.275 0.581 0.579
## 0.129 0.270 0.273
## 0.165 0.347 0.353
## 0.107 0.223 0.225
## 0.113 0.234 0.240
##
## 0.320 0.814 0.872
## 0.198 0.504 0.543
## 0.090 0.225 0.225
## 0.182 0.459 0.464
## 0.333 0.845 0.843
## 0.097 0.242 0.248
##
## 0.289 0.293 0.297
## 0.212 0.213 0.218
## 0.372 0.378 0.389
## 0.641 0.654 0.705
## 0.701 0.716 0.732
## 0.579 0.591 0.582
##
## 0.302 0.727 0.760
## 0.351 0.844 0.844
## 0.308 0.741 0.727
## 0.336 0.809 0.813
## 0.200 0.481 0.497
## 0.076 0.178 0.207
## 0.306 0.736 0.743
## 0.274 0.660 0.662
## 0.279 0.671 0.681
## 0.265 0.637 0.631
## 0.291 0.700 0.703
## 0.279 0.670 0.662
## 0.110 0.260 0.264
## 0.263 0.632 0.639
##
## 0.139 0.181 0.189
## 0.250 0.326 0.351
## 0.206 0.268 0.277
## 0.360 0.472 0.548
## 0.451 0.591 0.762
## 0.483 0.633 0.752
## -0.048 -0.068 -0.069
## 0.294 0.383 0.439
##
## 0.381 0.463 0.531
## 0.456 0.555 0.568
## 0.622 0.758 0.757
## 0.379 0.461 0.469
## 0.153 0.183 0.185
## 0.122 0.145 0.142
##
## 1.927 0.885 0.885
## 2.445 0.923 0.923
## 0.267 0.251 0.251
## 2.264 0.912 0.912
## 0.881 0.655 0.655
## 0.730 0.584 0.584
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.99.) -0.127 0.004 -35.176 0.000 -0.134
## .Stst20s (.100) -0.175 0.004 -48.004 0.000 -0.182
## .Stst21c (.101) -0.153 0.004 -42.546 0.000 -0.160
## .Stst22p (.102) -0.192 0.004 -50.573 0.000 -0.199
## .Stst23n (.103) -0.163 0.004 -44.764 0.000 -0.170
## .Stst24x (.104) -0.137 0.004 -37.654 0.000 -0.145
## .Stst25w (.105) -0.098 0.004 -26.328 0.000 -0.106
## .Stst26r (.106) -0.024 0.004 -6.050 0.000 -0.032
## .Stst31b (.107) 0.078 0.004 20.902 0.000 0.071
## .Stst32r (.108) 0.110 0.004 28.450 0.000 0.103
## .Stst34r (.109) -0.035 0.004 -9.418 0.000 -0.043
## .Stst5mt (.110) 0.179 0.004 47.308 0.000 0.172
## .Stst6ph (.111) 0.402 0.004 107.094 0.000 0.395
## .Stst33h (.112) 0.171 0.004 42.279 0.000 0.163
## .Sts292D (.113) 0.164 0.004 45.269 0.000 0.156
## .Stst35t (.114) -0.080 0.003 -23.047 0.000 -0.087
## .Stst36c (.115) -0.150 0.004 -40.913 0.000 -0.157
## .Stst37b (.116) -0.054 0.004 -14.990 0.000 -0.061
## .Stst1vc (.117) 0.208 0.004 56.429 0.000 0.201
## .Stst2lt (.118) 0.029 0.004 7.627 0.000 0.022
## .Stst3ms (.119) 0.031 0.004 8.130 0.000 0.023
## .Stst4sc (.120) 0.047 0.004 11.844 0.000 0.040
## .Stst7bl (.121) 0.274 0.004 72.700 0.000 0.267
## .Stst8rn (.122) 0.454 0.003 130.533 0.000 0.447
## .Stst11r (.123) 0.029 0.004 7.904 0.000 0.022
## .Stst12l (.124) 0.040 0.004 11.016 0.000 0.033
## .Stst13h (.125) -0.011 0.004 -2.882 0.004 -0.019
## .Stst14b (.126) 0.044 0.004 12.337 0.000 0.037
## .Stst15t (.127) 0.021 0.004 5.559 0.000 0.013
## .Stst16m (.128) 0.027 0.004 7.263 0.000 0.019
## .Stst9lc (.129) 0.549 0.003 181.790 0.000 0.543
## .Stst10m (.130) 0.612 0.003 184.633 0.000 0.606
## .Stst28m (.131) 0.526 0.004 148.668 0.000 0.519
## .Sts303D (.132) 0.265 0.004 68.434 0.000 0.257
## ci.upper Std.lv Std.all
## -0.120 -0.127 -0.129
## -0.168 -0.175 -0.174
## -0.146 -0.153 -0.158
## -0.184 -0.192 -0.198
## -0.156 -0.163 -0.167
## -0.130 -0.137 -0.138
## -0.091 -0.098 -0.098
## -0.016 -0.024 -0.025
## 0.086 0.078 0.080
## 0.118 0.110 0.111
## -0.028 -0.035 -0.036
## 0.187 0.179 0.192
## 0.409 0.402 0.433
## 0.179 0.171 0.171
## 0.171 0.164 0.167
## -0.073 -0.080 -0.087
## -0.143 -0.150 -0.153
## -0.047 -0.054 -0.053
## 0.215 0.208 0.218
## 0.037 0.029 0.029
## 0.038 0.031 0.030
## 0.055 0.047 0.048
## 0.282 0.274 0.283
## 0.460 0.454 0.527
## 0.036 0.029 0.029
## 0.048 0.040 0.040
## -0.004 -0.011 -0.011
## 0.051 0.044 0.043
## 0.028 0.021 0.021
## 0.034 0.027 0.026
## 0.555 0.549 0.708
## 0.619 0.612 0.728
## 0.533 0.526 0.602
## 0.272 0.265 0.264
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.465 0.003 161.380 0.000 0.459
## .Stest20spellng 0.564 0.004 160.723 0.000 0.557
## .Stest21cptlztn 0.514 0.003 162.621 0.000 0.508
## .Stest22puncttn 0.302 0.002 133.467 0.000 0.297
## .Stest23english 0.521 0.003 151.428 0.000 0.514
## .Stest24exprssn 0.657 0.004 156.764 0.000 0.649
## .Stst25wrdfnctn 0.403 0.003 148.430 0.000 0.398
## .Stst26rdngcmpr 0.231 0.002 136.857 0.000 0.227
## .Stst31bstrctrs 0.468 0.003 146.209 0.000 0.462
## .Stst32rthrsnng 0.386 0.002 157.298 0.000 0.381
## .Stst34rthcmptt 0.516 0.003 150.061 0.000 0.510
## .Stest5math 0.210 0.002 85.060 0.000 0.205
## .Stst6physclscn 0.302 0.002 146.040 0.000 0.297
## .Stst33hghschlm 0.290 0.002 126.120 0.000 0.285
## .Stst29vslztn2D 0.566 0.004 133.112 0.000 0.558
## .Stest35tblrdng 0.432 0.005 93.077 0.000 0.423
## .Stst36clrclchc 0.443 0.005 85.862 0.000 0.433
## .Stst37bjctnspc 0.636 0.005 137.684 0.000 0.627
## .Stest1vocab 0.197 0.001 143.876 0.000 0.194
## .Stest2literatr 0.288 0.002 153.555 0.000 0.284
## .Stest3music 0.488 0.003 162.512 0.000 0.482
## .Stest4soclstds 0.335 0.002 144.011 0.000 0.331
## .Stst7blgclscnc 0.479 0.003 164.209 0.000 0.474
## .Stest8aerontcs 0.386 0.003 117.110 0.000 0.380
## .Stest11art 0.440 0.003 166.626 0.000 0.435
## .Stest12law 0.558 0.003 167.155 0.000 0.551
## .Stest13health 0.571 0.003 170.354 0.000 0.564
## .Stest14bible 0.615 0.003 185.200 0.000 0.608
## .Stest15theater 0.502 0.003 162.808 0.000 0.496
## .Stest16mscllns 0.576 0.003 164.675 0.000 0.569
## .Stest9elctrncs 0.252 0.003 84.704 0.000 0.246
## .Stest10mechncs 0.307 0.002 125.091 0.000 0.302
## .Stst28mchnclrs 0.265 0.002 119.952 0.000 0.260
## .Stst30vslztn3D 0.428 0.004 105.785 0.000 0.420
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.470 0.465 0.480
## 0.570 0.564 0.561
## 0.520 0.514 0.549
## 0.306 0.302 0.320
## 0.528 0.521 0.548
## 0.665 0.657 0.666
## 0.409 0.403 0.401
## 0.234 0.231 0.236
## 0.474 0.468 0.485
## 0.390 0.386 0.394
## 0.523 0.516 0.546
## 0.215 0.210 0.240
## 0.306 0.302 0.350
## 0.294 0.290 0.289
## 0.574 0.566 0.594
## 0.441 0.432 0.502
## 0.453 0.443 0.464
## 0.645 0.636 0.617
## 0.200 0.197 0.215
## 0.292 0.288 0.288
## 0.494 0.488 0.471
## 0.340 0.335 0.339
## 0.485 0.479 0.512
## 0.393 0.386 0.521
## 0.445 0.440 0.448
## 0.564 0.558 0.562
## 0.577 0.571 0.588
## 0.621 0.615 0.602
## 0.508 0.502 0.506
## 0.583 0.576 0.562
## 0.258 0.252 0.419
## 0.312 0.307 0.434
## 0.269 0.265 0.347
## 0.436 0.428 0.427
## 1.000 0.218 0.218
## 1.000 0.149 0.149
## 1.000 0.937 0.937
## 1.000 0.168 0.168
## 1.000 0.571 0.571
## 1.000 0.659 0.659
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.163 0.002 75.884 0.000 0.159
## Stst20s (.p2.) 0.310 0.002 133.707 0.000 0.305
## Stst21c (.p3.) 0.303 0.002 136.608 0.000 0.299
## Stst22p (.p4.) 0.373 0.003 144.410 0.000 0.368
## Stst23n (.p5.) 0.306 0.002 134.699 0.000 0.302
## Stst24x (.p6.) 0.267 0.002 127.287 0.000 0.263
## Stst25w (.p7.) 0.271 0.002 120.648 0.000 0.267
## Stst26r (.p8.) 0.126 0.002 81.814 0.000 0.123
## Stst31b (.p9.) 0.162 0.002 104.621 0.000 0.159
## Stst32r (.10.) 0.104 0.002 59.172 0.000 0.100
## Stst34r (.11.) 0.109 0.002 54.821 0.000 0.105
## math =~
## Stst5mt (.12.) 0.314 0.003 100.216 0.000 0.308
## Stst6ph (.13.) 0.194 0.002 99.677 0.000 0.191
## Stst25w (.14.) 0.087 0.002 53.823 0.000 0.084
## Stst32r (.15.) 0.177 0.002 78.454 0.000 0.173
## Stst33h (.16.) 0.326 0.003 96.332 0.000 0.320
## Stst34r (.17.) 0.093 0.002 47.487 0.000 0.089
## speed =~
## Stst19d (.18.) 0.283 0.003 104.390 0.000 0.278
## Sts292D (.19.) 0.206 0.003 70.022 0.000 0.200
## Stst34r (.20.) 0.366 0.003 122.251 0.000 0.360
## Stst35t (.21.) 0.633 0.004 163.895 0.000 0.625
## Stst36c (.22.) 0.693 0.004 180.759 0.000 0.686
## Stst37b (.23.) 0.572 0.004 158.115 0.000 0.565
## info =~
## Stst1vc (.24.) 0.298 0.002 140.641 0.000 0.294
## Stst2lt (.25.) 0.346 0.003 137.140 0.000 0.341
## Stst3ms (.26.) 0.303 0.002 133.710 0.000 0.299
## Stst4sc (.27.) 0.331 0.002 140.120 0.000 0.327
## Stst7bl (.28.) 0.197 0.002 113.488 0.000 0.194
## Stst8rn (.29.) 0.073 0.001 54.259 0.000 0.070
## Stst11r (.30.) 0.301 0.002 131.046 0.000 0.297
## Stst12l (.31.) 0.270 0.002 129.984 0.000 0.266
## Stst13h (.32.) 0.275 0.002 127.358 0.000 0.271
## Stst14b (.33.) 0.261 0.002 127.939 0.000 0.257
## Stst15t (.34.) 0.287 0.002 129.817 0.000 0.282
## Stst16m (.35.) 0.275 0.002 129.478 0.000 0.271
## Stst19d (.36.) 0.106 0.002 57.746 0.000 0.103
## Stst26r (.37.) 0.259 0.002 124.073 0.000 0.255
## science =~
## Stst1vc (.38.) 0.136 0.001 100.964 0.000 0.134
## Stst6ph (.39.) 0.246 0.002 126.455 0.000 0.242
## Stst7bl (.40.) 0.202 0.002 106.740 0.000 0.199
## Stst8rn (.41.) 0.356 0.002 175.680 0.000 0.352
## Stst9lc (.42.) 0.447 0.002 193.660 0.000 0.442
## Stst10m (.43.) 0.478 0.002 203.891 0.000 0.474
## Stst13h (.44.) -0.051 0.002 -30.837 0.000 -0.054
## Stst28m (.45.) 0.290 0.002 145.088 0.000 0.286
## spatial =~
## Stst28m (.46.) 0.376 0.003 138.119 0.000 0.371
## Sts292D (.47.) 0.450 0.003 159.530 0.000 0.445
## Sts303D (.48.) 0.616 0.003 194.658 0.000 0.610
## Stst31b (.49.) 0.374 0.003 145.351 0.000 0.369
## Stst32r (.50.) 0.149 0.002 61.167 0.000 0.144
## Stst37b (.51.) 0.117 0.002 48.298 0.000 0.113
## g =~
## english (.52.) 1.896 0.016 121.297 0.000 1.865
## math (.53.) 2.391 0.027 87.799 0.000 2.338
## speed (.54.) 0.259 0.004 61.456 0.000 0.251
## info (.55.) 2.227 0.019 118.328 0.000 2.190
## science (.56.) 0.867 0.007 125.800 0.000 0.854
## spatial (.57.) 0.719 0.006 123.117 0.000 0.707
## ci.upper Std.lv Std.all
##
## 0.168 0.322 0.340
## 0.314 0.611 0.659
## 0.307 0.598 0.638
## 0.378 0.736 0.823
## 0.311 0.604 0.669
## 0.272 0.528 0.586
## 0.275 0.534 0.561
## 0.129 0.248 0.274
## 0.165 0.319 0.341
## 0.107 0.205 0.214
## 0.113 0.215 0.233
##
## 0.320 0.778 0.808
## 0.198 0.482 0.531
## 0.090 0.215 0.226
## 0.182 0.439 0.459
## 0.333 0.808 0.852
## 0.097 0.231 0.250
##
## 0.289 0.263 0.278
## 0.212 0.191 0.200
## 0.372 0.340 0.368
## 0.641 0.588 0.726
## 0.701 0.644 0.701
## 0.579 0.531 0.577
##
## 0.302 0.668 0.729
## 0.351 0.776 0.819
## 0.308 0.681 0.715
## 0.336 0.743 0.793
## 0.200 0.442 0.468
## 0.076 0.164 0.175
## 0.306 0.676 0.711
## 0.274 0.606 0.622
## 0.279 0.616 0.656
## 0.265 0.586 0.593
## 0.291 0.643 0.668
## 0.279 0.616 0.655
## 0.110 0.239 0.252
## 0.263 0.581 0.642
##
## 0.139 0.151 0.165
## 0.250 0.273 0.301
## 0.206 0.224 0.238
## 0.360 0.395 0.421
## 0.451 0.495 0.567
## 0.483 0.530 0.690
## -0.048 -0.057 -0.060
## 0.294 0.321 0.386
##
## 0.381 0.421 0.506
## 0.456 0.504 0.527
## 0.622 0.689 0.752
## 0.379 0.419 0.448
## 0.153 0.166 0.174
## 0.122 0.131 0.143
##
## 1.927 0.874 0.874
## 2.445 0.878 0.878
## 0.267 0.253 0.253
## 2.264 0.903 0.903
## 0.881 0.711 0.711
## 0.730 0.584 0.584
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.99.) -0.127 0.004 -35.176 0.000 -0.134
## .Stst20s (.100) -0.175 0.004 -48.004 0.000 -0.182
## .Stst21c (.101) -0.153 0.004 -42.546 0.000 -0.160
## .Stst22p (.102) -0.192 0.004 -50.573 0.000 -0.199
## .Stst23n (.103) -0.163 0.004 -44.764 0.000 -0.170
## .Stst24x (.104) -0.137 0.004 -37.654 0.000 -0.145
## .Stst25w (.105) -0.098 0.004 -26.328 0.000 -0.106
## .Stst26r (.106) -0.024 0.004 -6.050 0.000 -0.032
## .Stst31b (.107) 0.078 0.004 20.902 0.000 0.071
## .Stst32r (.108) 0.110 0.004 28.450 0.000 0.103
## .Stst34r (.109) -0.035 0.004 -9.418 0.000 -0.043
## .Stst5mt (.110) 0.179 0.004 47.308 0.000 0.172
## .Stst6ph (.111) 0.402 0.004 107.094 0.000 0.395
## .Stst33h (.112) 0.171 0.004 42.279 0.000 0.163
## .Sts292D (.113) 0.164 0.004 45.269 0.000 0.156
## .Stst35t (.114) -0.080 0.003 -23.047 0.000 -0.087
## .Stst36c (.115) -0.150 0.004 -40.913 0.000 -0.157
## .Stst37b (.116) -0.054 0.004 -14.990 0.000 -0.061
## .Stst1vc (.117) 0.208 0.004 56.429 0.000 0.201
## .Stst2lt (.118) 0.029 0.004 7.627 0.000 0.022
## .Stst3ms (.119) 0.031 0.004 8.130 0.000 0.023
## .Stst4sc (.120) 0.047 0.004 11.844 0.000 0.040
## .Stst7bl (.121) 0.274 0.004 72.700 0.000 0.267
## .Stst8rn (.122) 0.454 0.003 130.533 0.000 0.447
## .Stst11r (.123) 0.029 0.004 7.904 0.000 0.022
## .Stst12l (.124) 0.040 0.004 11.016 0.000 0.033
## .Stst13h (.125) -0.011 0.004 -2.882 0.004 -0.019
## .Stst14b (.126) 0.044 0.004 12.337 0.000 0.037
## .Stst15t (.127) 0.021 0.004 5.559 0.000 0.013
## .Stst16m (.128) 0.027 0.004 7.263 0.000 0.019
## .Stst9lc (.129) 0.549 0.003 181.790 0.000 0.543
## .Stst10m (.130) 0.612 0.003 184.633 0.000 0.606
## .Stst28m (.131) 0.526 0.004 148.668 0.000 0.519
## .Sts303D (.132) 0.265 0.004 68.434 0.000 0.257
## .english 1.673 0.011 150.473 0.000 1.651
## .math -0.341 0.008 -42.872 0.000 -0.357
## .speed 0.369 0.007 52.261 0.000 0.355
## .info 0.414 0.008 54.509 0.000 0.399
## .science -2.115 0.012 -174.526 0.000 -2.139
## .spatial -0.550 0.008 -66.931 0.000 -0.566
## g -0.192 0.006 -32.848 0.000 -0.203
## ci.upper Std.lv Std.all
## -0.120 -0.127 -0.134
## -0.168 -0.175 -0.188
## -0.146 -0.153 -0.163
## -0.184 -0.192 -0.214
## -0.156 -0.163 -0.181
## -0.130 -0.137 -0.153
## -0.091 -0.098 -0.103
## -0.016 -0.024 -0.027
## 0.086 0.078 0.084
## 0.118 0.110 0.115
## -0.028 -0.035 -0.038
## 0.187 0.179 0.186
## 0.409 0.402 0.443
## 0.179 0.171 0.180
## 0.171 0.164 0.171
## -0.073 -0.080 -0.099
## -0.143 -0.150 -0.163
## -0.047 -0.054 -0.059
## 0.215 0.208 0.227
## 0.037 0.029 0.031
## 0.038 0.031 0.032
## 0.055 0.047 0.051
## 0.282 0.274 0.291
## 0.460 0.454 0.484
## 0.036 0.029 0.030
## 0.048 0.040 0.041
## -0.004 -0.011 -0.012
## 0.051 0.044 0.044
## 0.028 0.021 0.021
## 0.034 0.027 0.028
## 0.555 0.549 0.629
## 0.619 0.612 0.796
## 0.533 0.526 0.631
## 0.272 0.265 0.289
## 1.695 0.848 0.848
## -0.326 -0.138 -0.138
## 0.383 0.398 0.398
## 0.428 0.184 0.184
## -2.091 -1.908 -1.908
## -0.534 -0.491 -0.491
## -0.181 -0.211 -0.211
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.479 0.003 165.045 0.000 0.473
## .Stest20spellng 0.487 0.003 164.180 0.000 0.481
## .Stest21cptlztn 0.522 0.003 163.293 0.000 0.516
## .Stest22puncttn 0.259 0.002 129.150 0.000 0.255
## .Stest23english 0.450 0.003 156.580 0.000 0.444
## .Stest24exprssn 0.532 0.004 146.233 0.000 0.525
## .Stst25wrdfnctn 0.400 0.003 145.409 0.000 0.394
## .Stst26rdngcmpr 0.192 0.001 139.484 0.000 0.189
## .Stst31bstrctrs 0.460 0.003 153.615 0.000 0.454
## .Stst32rthrsnng 0.405 0.002 163.865 0.000 0.400
## .Stst34rthcmptt 0.496 0.003 143.540 0.000 0.489
## .Stest5math 0.323 0.003 98.706 0.000 0.317
## .Stst6physclscn 0.352 0.002 159.704 0.000 0.347
## .Stst33hghschlm 0.245 0.002 116.035 0.000 0.241
## .Stst29vslztn2D 0.595 0.004 152.691 0.000 0.587
## .Stest35tblrdng 0.310 0.004 84.376 0.000 0.303
## .Stst36clrclchc 0.430 0.004 99.774 0.000 0.422
## .Stst37bjctnspc 0.528 0.004 139.880 0.000 0.521
## .Stest1vocab 0.241 0.002 149.694 0.000 0.238
## .Stest2literatr 0.295 0.002 158.319 0.000 0.292
## .Stest3music 0.443 0.003 163.994 0.000 0.438
## .Stest4soclstds 0.326 0.002 146.064 0.000 0.322
## .Stst7blgclscnc 0.518 0.003 177.908 0.000 0.512
## .Stest8aerontcs 0.613 0.003 179.497 0.000 0.606
## .Stest11art 0.447 0.003 169.397 0.000 0.442
## .Stest12law 0.581 0.003 172.069 0.000 0.575
## .Stest13health 0.544 0.003 170.023 0.000 0.537
## .Stest14bible 0.631 0.003 192.372 0.000 0.625
## .Stest15theater 0.513 0.003 167.644 0.000 0.507
## .Stest16mscllns 0.505 0.003 169.862 0.000 0.499
## .Stest9elctrncs 0.516 0.004 123.504 0.000 0.508
## .Stest10mechncs 0.310 0.002 136.039 0.000 0.306
## .Stst28mchnclrs 0.301 0.002 135.759 0.000 0.296
## .Stst30vslztn3D 0.366 0.003 109.152 0.000 0.359
## .english 0.921 0.017 55.183 0.000 0.888
## .math 1.407 0.031 44.755 0.000 1.346
## .speed 0.807 0.010 77.091 0.000 0.787
## .info 0.933 0.017 55.878 0.000 0.900
## .science 0.608 0.009 65.818 0.000 0.589
## .spatial 0.827 0.011 77.868 0.000 0.806
## g 0.826 0.007 126.169 0.000 0.814
## ci.upper Std.lv Std.all
## 0.485 0.479 0.534
## 0.493 0.487 0.566
## 0.528 0.522 0.594
## 0.263 0.259 0.323
## 0.456 0.450 0.552
## 0.539 0.532 0.657
## 0.405 0.400 0.440
## 0.195 0.192 0.235
## 0.466 0.460 0.527
## 0.410 0.405 0.443
## 0.502 0.496 0.580
## 0.329 0.323 0.348
## 0.356 0.352 0.428
## 0.250 0.245 0.273
## 0.603 0.595 0.651
## 0.317 0.310 0.473
## 0.438 0.430 0.509
## 0.536 0.528 0.623
## 0.244 0.241 0.287
## 0.299 0.295 0.329
## 0.448 0.443 0.489
## 0.330 0.326 0.371
## 0.524 0.518 0.581
## 0.619 0.613 0.697
## 0.452 0.447 0.495
## 0.588 0.581 0.613
## 0.550 0.544 0.617
## 0.637 0.631 0.648
## 0.519 0.513 0.554
## 0.511 0.505 0.571
## 0.525 0.516 0.678
## 0.314 0.310 0.524
## 0.305 0.301 0.434
## 0.372 0.366 0.435
## 0.954 0.237 0.237
## 1.469 0.230 0.230
## 0.828 0.936 0.936
## 0.966 0.185 0.185
## 0.626 0.494 0.494
## 0.848 0.659 0.659
## 0.839 1.000 1.000
lavTestScore(scalar, release = 58:91, standardized=T, epc=T) # It requires 2 intercepts just to get +.001 in CFI. So I also look at the highest sepc.all for fully standardized epc.
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 64616.1 34 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p99. == .p238. 176.407 1 0.000
## 2 .p100. == .p239. 1311.959 1 0.000
## 3 .p101. == .p240. 575.099 1 0.000
## 4 .p102. == .p241. 54.716 1 0.000
## 5 .p103. == .p242. 615.221 1 0.000
## 6 .p104. == .p243. 494.404 1 0.000
## 7 .p105. == .p244. 374.994 1 0.000
## 8 .p106. == .p245. 482.127 1 0.000
## 9 .p107. == .p246. 11.894 1 0.001
## 10 .p108. == .p247. 916.651 1 0.000
## 11 .p109. == .p248. 414.119 1 0.000
## 12 .p110. == .p249. 2449.874 1 0.000
## 13 .p111. == .p250. 3296.587 1 0.000
## 14 .p112. == .p251. 898.377 1 0.000
## 15 .p113. == .p252. 1388.027 1 0.000
## 16 .p114. == .p253. 501.376 1 0.000
## 17 .p115. == .p254. 122.150 1 0.000
## 18 .p116. == .p255. 557.477 1 0.000
## 19 .p117. == .p256. 1112.195 1 0.000
## 20 .p118. == .p257. 0.000 1 0.983
## 21 .p119. == .p258. 6818.048 1 0.000
## 22 .p120. == .p259. 15860.065 1 0.000
## 23 .p121. == .p260. 995.942 1 0.000
## 24 .p122. == .p261. 1284.369 1 0.000
## 25 .p123. == .p262. 2425.616 1 0.000
## 26 .p124. == .p263. 7627.271 1 0.000
## 27 .p125. == .p264. 3922.817 1 0.000
## 28 .p126. == .p265. 200.391 1 0.000
## 29 .p127. == .p266. 10637.285 1 0.000
## 30 .p128. == .p267. 2767.522 1 0.000
## 31 .p129. == .p268. 1725.561 1 0.000
## 32 .p130. == .p269. 1776.497 1 0.000
## 33 .p131. == .p270. 1166.061 1 0.000
## 34 .p132. == .p271. 2673.408 1 0.000
##
## $epc
##
## expected parameter changes (epc) and expected parameter values (epv):
##
## lhs op rhs block
## 1 english =~ Stest19disguisedwords 1
## 2 english =~ Stest20spelling 1
## 3 english =~ Stest21capitalization 1
## 4 english =~ Stest22punctuation 1
## 5 english =~ Stest23english 1
## 6 english =~ Stest24expression 1
## 7 english =~ Stest25wordfunctions 1
## 8 english =~ Stest26readingcomprehension 1
## 9 english =~ Stest31abstractreasoning 1
## 10 english =~ Stest32arithreasoning 1
## 11 english =~ Stest34arithcomputation 1
## 12 math =~ Stest5math 1
## 13 math =~ Stest6physicalscience 1
## 14 math =~ Stest25wordfunctions 1
## 15 math =~ Stest32arithreasoning 1
## 16 math =~ Stest33highschoolmath 1
## 17 math =~ Stest34arithcomputation 1
## 18 speed =~ Stest19disguisedwords 1
## 19 speed =~ Stest29visualization2D 1
## 20 speed =~ Stest34arithcomputation 1
## 21 speed =~ Stest35tablereading 1
## 22 speed =~ Stest36clericalchecking 1
## 23 speed =~ Stest37objectinspection 1
## 24 info =~ Stest1vocab 1
## 25 info =~ Stest2literature 1
## 26 info =~ Stest3music 1
## 27 info =~ Stest4socialstudies 1
## 28 info =~ Stest7biologicalscience 1
## 29 info =~ Stest8aeronautics 1
## 30 info =~ Stest11art 1
## 31 info =~ Stest12law 1
## 32 info =~ Stest13health 1
## 33 info =~ Stest14bible 1
## 34 info =~ Stest15theater 1
## 35 info =~ Stest16miscellaneous 1
## 36 info =~ Stest19disguisedwords 1
## 37 info =~ Stest26readingcomprehension 1
## 38 science =~ Stest1vocab 1
## 39 science =~ Stest6physicalscience 1
## 40 science =~ Stest7biologicalscience 1
## 41 science =~ Stest8aeronautics 1
## 42 science =~ Stest9electronics 1
## 43 science =~ Stest10mechanics 1
## 44 science =~ Stest13health 1
## 45 science =~ Stest28mechanicalreasoning 1
## 46 spatial =~ Stest28mechanicalreasoning 1
## 47 spatial =~ Stest29visualization2D 1
## 48 spatial =~ Stest30visualization3D 1
## 49 spatial =~ Stest31abstractreasoning 1
## 50 spatial =~ Stest32arithreasoning 1
## 51 spatial =~ Stest37objectinspection 1
## 52 g =~ english 1
## 53 g =~ math 1
## 54 g =~ speed 1
## 55 g =~ info 1
## 56 g =~ science 1
## 57 g =~ spatial 1
## 58 Stest19disguisedwords ~~ Stest19disguisedwords 1
## 59 Stest20spelling ~~ Stest20spelling 1
## 60 Stest21capitalization ~~ Stest21capitalization 1
## 61 Stest22punctuation ~~ Stest22punctuation 1
## 62 Stest23english ~~ Stest23english 1
## 63 Stest24expression ~~ Stest24expression 1
## 64 Stest25wordfunctions ~~ Stest25wordfunctions 1
## 65 Stest26readingcomprehension ~~ Stest26readingcomprehension 1
## 66 Stest31abstractreasoning ~~ Stest31abstractreasoning 1
## 67 Stest32arithreasoning ~~ Stest32arithreasoning 1
## 68 Stest34arithcomputation ~~ Stest34arithcomputation 1
## 69 Stest5math ~~ Stest5math 1
## 70 Stest6physicalscience ~~ Stest6physicalscience 1
## 71 Stest33highschoolmath ~~ Stest33highschoolmath 1
## group free label plabel est epc epv sepc.lv sepc.all
## 1 1 1 .p1. .p1. 0.163 0.015 0.178 0.031 0.032
## 2 1 2 .p2. .p2. 0.310 -0.013 0.297 -0.028 -0.028
## 3 1 3 .p3. .p3. 0.303 -0.009 0.294 -0.020 -0.021
## 4 1 4 .p4. .p4. 0.373 -0.001 0.372 -0.003 -0.003
## 5 1 5 .p5. .p5. 0.306 0.005 0.311 0.010 0.010
## 6 1 6 .p6. .p6. 0.267 0.005 0.273 0.011 0.011
## 7 1 7 .p7. .p7. 0.271 -0.023 0.248 -0.050 -0.050
## 8 1 8 .p8. .p8. 0.126 0.019 0.145 0.041 0.041
## 9 1 9 .p9. .p9. 0.162 -0.004 0.158 -0.009 -0.009
## 10 1 10 .p10. .p10. 0.104 0.039 0.143 0.084 0.085
## 11 1 11 .p11. .p11. 0.109 -0.027 0.083 -0.057 -0.058
## 12 1 12 .p12. .p12. 0.314 0.008 0.322 0.020 0.021
## 13 1 13 .p13. .p13. 0.194 -0.023 0.171 -0.060 -0.065
## 14 1 14 .p14. .p14. 0.087 0.019 0.106 0.050 0.050
## 15 1 15 .p15. .p15. 0.177 -0.020 0.157 -0.051 -0.052
## 16 1 16 .p16. .p16. 0.326 0.014 0.340 0.037 0.037
## 17 1 17 .p17. .p17. 0.093 0.024 0.118 0.063 0.065
## 18 1 18 .p18. .p18. 0.283 0.004 0.287 0.004 0.004
## 19 1 19 .p19. .p19. 0.206 0.020 0.226 0.021 0.021
## 20 1 20 .p20. .p20. 0.366 -0.006 0.360 -0.006 -0.006
## 21 1 21 .p21. .p21. 0.633 0.010 0.643 0.010 0.011
## 22 1 22 .p22. .p22. 0.693 -0.004 0.689 -0.004 -0.005
## 23 1 23 .p23. .p23. 0.572 -0.013 0.559 -0.014 -0.014
## 24 1 24 .p24. .p24. 0.298 -0.008 0.290 -0.021 -0.021
## 25 1 25 .p25. .p25. 0.346 0.015 0.361 0.038 0.038
## 26 1 26 .p26. .p26. 0.303 0.014 0.317 0.033 0.033
## 27 1 27 .p27. .p27. 0.331 0.014 0.346 0.035 0.035
## 28 1 28 .p28. .p28. 0.197 -0.019 0.178 -0.047 -0.048
## 29 1 29 .p29. .p29. 0.073 0.020 0.093 0.048 0.056
## 30 1 30 .p30. .p30. 0.301 0.013 0.315 0.033 0.033
## 31 1 31 .p31. .p31. 0.270 0.012 0.282 0.028 0.029
## 32 1 32 .p32. .p32. 0.275 -0.039 0.236 -0.095 -0.097
## 33 1 33 .p33. .p33. 0.261 0.012 0.273 0.028 0.028
## 34 1 34 .p34. .p34. 0.287 0.013 0.300 0.031 0.032
## 35 1 35 .p35. .p35. 0.275 0.012 0.287 0.029 0.029
## 36 1 36 .p36. .p36. 0.106 -0.007 0.099 -0.018 -0.018
## 37 1 37 .p37. .p37. 0.259 -0.004 0.255 -0.009 -0.009
## 38 1 38 .p38. .p38. 0.136 0.060 0.196 0.080 0.083
## 39 1 39 .p39. .p39. 0.246 0.097 0.343 0.128 0.138
## 40 1 40 .p40. .p40. 0.202 0.077 0.279 0.102 0.106
## 41 1 41 .p41. .p41. 0.356 -0.056 0.300 -0.074 -0.087
## 42 1 42 .p42. .p42. 0.447 0.035 0.481 0.046 0.059
## 43 1 43 .p43. .p43. 0.478 -0.040 0.438 -0.053 -0.063
## 44 1 44 .p44. .p44. -0.051 0.150 0.098 0.198 0.201
## 45 1 45 .p45. .p45. 0.290 -0.036 0.254 -0.047 -0.054
## 46 1 46 .p46. .p46. 0.376 0.004 0.380 0.005 0.005
## 47 1 47 .p47. .p47. 0.450 -0.030 0.420 -0.037 -0.038
## 48 1 48 .p48. .p48. 0.616 0.017 0.633 0.021 0.021
## 49 1 49 .p49. .p49. 0.374 0.000 0.374 0.000 0.000
## 50 1 50 .p50. .p50. 0.149 -0.021 0.127 -0.026 -0.026
## 51 1 51 .p51. .p51. 0.117 0.015 0.132 0.018 0.018
## 52 1 52 .p52. .p52. 1.896 0.017 1.913 0.008 0.008
## 53 1 53 .p53. .p53. 2.391 -0.093 2.298 -0.036 -0.036
## 54 1 54 .p54. .p54. 0.259 -0.003 0.256 -0.003 -0.003
## 55 1 55 .p55. .p55. 2.227 -0.114 2.113 -0.047 -0.047
## 56 1 56 .p56. .p56. 0.867 0.007 0.874 0.005 0.005
## 57 1 57 .p57. .p57. 0.719 0.017 0.736 0.014 0.014
## 58 1 58 .p58. 0.465 -0.002 0.462 -0.465 -0.480
## 59 1 59 .p59. 0.564 0.004 0.567 0.564 0.561
## 60 1 60 .p60. 0.514 0.002 0.517 0.514 0.549
## 61 1 61 .p61. 0.302 0.000 0.301 -0.302 -0.320
## 62 1 62 .p62. 0.521 -0.002 0.519 -0.521 -0.548
## 63 1 63 .p63. 0.657 -0.002 0.655 -0.657 -0.666
## 64 1 64 .p64. 0.403 0.004 0.408 0.403 0.401
## 65 1 65 .p65. 0.231 -0.001 0.229 -0.231 -0.236
## 66 1 66 .p66. 0.468 0.001 0.469 0.468 0.485
## 67 1 67 .p67. 0.386 0.003 0.389 0.386 0.394
## 68 1 68 .p68. 0.516 0.001 0.518 0.516 0.546
## 69 1 69 .p69. 0.210 -0.002 0.207 -0.210 -0.240
## 70 1 70 .p70. 0.302 -0.008 0.293 -0.302 -0.350
## 71 1 71 .p71. 0.290 -0.006 0.284 -0.290 -0.289
## sepc.nox
## 1 0.032
## 2 -0.028
## 3 -0.021
## 4 -0.003
## 5 0.010
## 6 0.011
## 7 -0.050
## 8 0.041
## 9 -0.009
## 10 0.085
## 11 -0.058
## 12 0.021
## 13 -0.065
## 14 0.050
## 15 -0.052
## 16 0.037
## 17 0.065
## 18 0.004
## 19 0.021
## 20 -0.006
## 21 0.011
## 22 -0.005
## 23 -0.014
## 24 -0.021
## 25 0.038
## 26 0.033
## 27 0.035
## 28 -0.048
## 29 0.056
## 30 0.033
## 31 0.029
## 32 -0.097
## 33 0.028
## 34 0.032
## 35 0.029
## 36 -0.018
## 37 -0.009
## 38 0.083
## 39 0.138
## 40 0.106
## 41 -0.087
## 42 0.059
## 43 -0.063
## 44 0.201
## 45 -0.054
## 46 0.005
## 47 -0.038
## 48 0.021
## 49 0.000
## 50 -0.026
## 51 0.018
## 52 0.008
## 53 -0.036
## 54 -0.003
## 55 -0.047
## 56 0.005
## 57 0.014
## 58 -0.480
## 59 0.561
## 60 0.549
## 61 -0.320
## 62 -0.548
## 63 -0.666
## 64 0.401
## 65 -0.236
## 66 0.485
## 67 0.394
## 68 0.546
## 69 -0.240
## 70 -0.350
## 71 -0.289
## [ reached 'max' / getOption("max.print") -- omitted 207 rows ]
scalar2<-cfa(chc.hof.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts"), group.partial=c("Stest4socialstudies~1", "Stest15theater~1", "Stest12law~1", "Stest3music~1", "Stest16miscellaneous~1", "Stest13health~1", "Stest6physicalscience~1", "Stest9electronics~1", "Stest30visualization3D~1", "Stest7biologicalscience~1", "Stest1vocab~1"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov)
## does not appear to be positive definite! The smallest eigenvalue
## (= 4.826786e-17) is close to zero. This may be a symptom that the
## model is not identified.
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 163575.281 1074.000 0.000 0.938 0.047
## srmr aic bic
## 0.045 10367333.780 10369144.820
Mc(scalar2)
## [1] 0.5574857
summary(scalar2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 133 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 264
## Number of equality constraints 80
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 163575.281 143251.127
## Degrees of freedom 1074 1074
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.142
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 92295.620 80827.932
## 1 71279.661 62423.195
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.157 0.002 73.387 0.000 0.153
## Stst20s (.p2.) 0.302 0.002 129.099 0.000 0.297
## Stst21c (.p3.) 0.296 0.002 131.775 0.000 0.291
## Stst22p (.p4.) 0.364 0.003 138.657 0.000 0.359
## Stst23n (.p5.) 0.298 0.002 129.946 0.000 0.294
## Stst24x (.p6.) 0.261 0.002 123.419 0.000 0.257
## Stst25w (.p7.) 0.266 0.002 118.701 0.000 0.262
## Stst26r (.p8.) 0.122 0.002 79.575 0.000 0.119
## Stst31b (.p9.) 0.168 0.002 106.223 0.000 0.165
## Stst32r (.10.) 0.113 0.002 64.881 0.000 0.110
## Stst34r (.11.) 0.105 0.002 54.320 0.000 0.101
## math =~
## Stst5mt (.12.) 0.329 0.003 107.304 0.000 0.323
## Stst6ph (.13.) 0.163 0.002 92.607 0.000 0.159
## Stst25w (.14.) 0.089 0.002 55.087 0.000 0.086
## Stst32r (.15.) 0.175 0.002 77.769 0.000 0.170
## Stst33h (.16.) 0.342 0.003 102.228 0.000 0.336
## Stst34r (.17.) 0.100 0.002 50.046 0.000 0.096
## speed =~
## Stst19d (.18.) 0.282 0.003 103.964 0.000 0.276
## Sts292D (.19.) 0.219 0.003 74.765 0.000 0.213
## Stst34r (.20.) 0.366 0.003 122.489 0.000 0.360
## Stst35t (.21.) 0.631 0.004 163.870 0.000 0.623
## Stst36c (.22.) 0.690 0.004 180.524 0.000 0.683
## Stst37b (.23.) 0.575 0.004 159.683 0.000 0.568
## info =~
## Stst1vc (.24.) 0.282 0.002 142.261 0.000 0.278
## Stst2lt (.25.) 0.361 0.002 144.384 0.000 0.356
## Stst3ms (.26.) 0.317 0.002 141.265 0.000 0.313
## Stst4sc (.27.) 0.346 0.002 147.521 0.000 0.342
## Stst7bl (.28.) 0.162 0.002 85.216 0.000 0.158
## Stst8rn (.29.) 0.085 0.001 61.926 0.000 0.082
## Stst11r (.30.) 0.315 0.002 137.746 0.000 0.310
## Stst12l (.31.) 0.282 0.002 135.884 0.000 0.278
## Stst13h (.32.) 0.223 0.002 105.631 0.000 0.219
## Stst14b (.33.) 0.272 0.002 133.952 0.000 0.268
## Stst15t (.34.) 0.301 0.002 137.486 0.000 0.297
## Stst16m (.35.) 0.286 0.002 135.202 0.000 0.282
## Stst19d (.36.) 0.113 0.002 59.089 0.000 0.109
## Stst26r (.37.) 0.269 0.002 131.596 0.000 0.265
## science =~
## Stst1vc (.38.) 0.199 0.002 96.352 0.000 0.195
## Stst6ph (.39.) 0.354 0.002 144.800 0.000 0.349
## Stst7bl (.40.) 0.298 0.003 100.459 0.000 0.293
## Stst8rn (.41.) 0.314 0.002 149.929 0.000 0.310
## Stst9lc (.42.) 0.469 0.003 167.451 0.000 0.463
## Stst10m (.43.) 0.420 0.002 168.513 0.000 0.415
## Stst13h (.44.) 0.110 0.003 37.335 0.000 0.104
## Stst28m (.45.) 0.229 0.002 111.973 0.000 0.225
## spatial =~
## Stst28m (.46.) 0.395 0.003 149.355 0.000 0.390
## Sts292D (.47.) 0.436 0.003 157.974 0.000 0.430
## Sts303D (.48.) 0.642 0.003 203.918 0.000 0.636
## Stst31b (.49.) 0.349 0.003 132.767 0.000 0.344
## Stst32r (.50.) 0.150 0.002 64.270 0.000 0.145
## Stst37b (.51.) 0.109 0.002 46.201 0.000 0.104
## g =~
## english (.52.) 1.955 0.017 117.283 0.000 1.922
## math (.53.) 2.267 0.025 92.445 0.000 2.219
## speed (.54.) 0.263 0.004 62.283 0.000 0.255
## info (.55.) 2.123 0.017 123.248 0.000 2.089
## science (.56.) 0.912 0.008 120.306 0.000 0.897
## spatial (.57.) 0.725 0.006 126.486 0.000 0.714
## ci.upper Std.lv Std.all
##
## 0.161 0.344 0.350
## 0.306 0.662 0.661
## 0.300 0.649 0.671
## 0.369 0.799 0.824
## 0.303 0.655 0.672
## 0.265 0.573 0.577
## 0.271 0.585 0.584
## 0.125 0.268 0.272
## 0.171 0.369 0.375
## 0.117 0.249 0.251
## 0.108 0.229 0.236
##
## 0.335 0.814 0.873
## 0.166 0.404 0.424
## 0.093 0.221 0.221
## 0.179 0.433 0.438
## 0.349 0.848 0.847
## 0.104 0.247 0.254
##
## 0.287 0.291 0.296
## 0.225 0.226 0.233
## 0.372 0.378 0.389
## 0.638 0.652 0.704
## 0.698 0.714 0.731
## 0.582 0.595 0.586
##
## 0.286 0.661 0.689
## 0.366 0.846 0.847
## 0.321 0.744 0.739
## 0.351 0.812 0.831
## 0.165 0.379 0.387
## 0.087 0.199 0.235
## 0.319 0.739 0.746
## 0.286 0.661 0.673
## 0.227 0.524 0.537
## 0.276 0.638 0.632
## 0.305 0.706 0.722
## 0.290 0.670 0.666
## 0.116 0.264 0.269
## 0.273 0.631 0.639
##
## 0.203 0.269 0.280
## 0.359 0.479 0.503
## 0.304 0.404 0.412
## 0.318 0.425 0.502
## 0.474 0.634 0.793
## 0.425 0.568 0.701
## 0.116 0.149 0.153
## 0.233 0.310 0.363
##
## 0.401 0.488 0.572
## 0.441 0.538 0.554
## 0.648 0.793 0.783
## 0.354 0.431 0.439
## 0.154 0.185 0.187
## 0.114 0.135 0.132
##
## 1.987 0.890 0.890
## 2.315 0.915 0.915
## 0.271 0.255 0.255
## 2.157 0.905 0.905
## 0.926 0.674 0.674
## 0.737 0.587 0.587
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.99.) -0.131 0.004 -36.417 0.000 -0.138
## .Stst20s (.100) -0.175 0.004 -47.984 0.000 -0.182
## .Stst21c (.101) -0.154 0.004 -42.580 0.000 -0.161
## .Stst22p (.102) -0.192 0.004 -50.600 0.000 -0.200
## .Stst23n (.103) -0.164 0.004 -44.787 0.000 -0.171
## .Stst24x (.104) -0.138 0.004 -37.707 0.000 -0.145
## .Stst25w (.105) -0.098 0.004 -26.297 0.000 -0.106
## .Stst26r (.106) -0.034 0.004 -8.615 0.000 -0.042
## .Stst31b (.107) 0.096 0.004 25.811 0.000 0.089
## .Stst32r (.108) 0.118 0.004 30.345 0.000 0.110
## .Stst34r (.109) -0.033 0.004 -8.795 0.000 -0.041
## .Stst5mt (.110) 0.187 0.004 49.358 0.000 0.179
## .Stst6ph 0.358 0.004 92.150 0.000 0.350
## .Stst33h (.112) 0.182 0.004 44.678 0.000 0.174
## .Sts292D (.113) 0.196 0.004 53.529 0.000 0.189
## .Stst35t (.114) -0.085 0.003 -24.395 0.000 -0.092
## .Stst36c (.115) -0.154 0.004 -42.322 0.000 -0.161
## .Stst37b (.116) -0.051 0.004 -13.910 0.000 -0.058
## .Stst1vc 0.189 0.004 50.212 0.000 0.181
## .Stst2lt (.118) 0.017 0.004 4.428 0.000 0.010
## .Stst3ms -0.121 0.004 -29.898 0.000 -0.128
## .Stst4sc 0.228 0.004 57.615 0.000 0.220
## .Stst7bl 0.243 0.004 61.803 0.000 0.235
## .Stst8rn (.122) 0.473 0.003 136.912 0.000 0.466
## .Stst11r (.123) 0.018 0.004 4.924 0.000 0.011
## .Stst12l 0.208 0.004 51.529 0.000 0.200
## .Stst13h -0.081 0.004 -19.854 0.000 -0.089
## .Stst14b (.126) 0.034 0.004 9.724 0.000 0.027
## .Stst15t -0.167 0.004 -42.902 0.000 -0.175
## .Stst16m 0.134 0.004 31.518 0.000 0.125
## .Stst9lc 0.522 0.003 156.852 0.000 0.516
## .Stst10m (.130) 0.647 0.003 199.130 0.000 0.641
## .Stst28m (.131) 0.555 0.003 158.873 0.000 0.548
## .Sts303D 0.206 0.004 50.235 0.000 0.198
## ci.upper Std.lv Std.all
## -0.124 -0.131 -0.134
## -0.168 -0.175 -0.175
## -0.147 -0.154 -0.159
## -0.185 -0.192 -0.198
## -0.157 -0.164 -0.168
## -0.131 -0.138 -0.139
## -0.091 -0.098 -0.098
## -0.027 -0.034 -0.035
## 0.104 0.096 0.098
## 0.125 0.118 0.119
## -0.026 -0.033 -0.034
## 0.194 0.187 0.200
## 0.365 0.358 0.375
## 0.190 0.182 0.182
## 0.203 0.196 0.202
## -0.078 -0.085 -0.092
## -0.147 -0.154 -0.158
## -0.044 -0.051 -0.050
## 0.196 0.189 0.197
## 0.025 0.017 0.017
## -0.113 -0.121 -0.120
## 0.236 0.228 0.233
## 0.251 0.243 0.248
## 0.480 0.473 0.559
## 0.025 0.018 0.018
## 0.216 0.208 0.212
## -0.073 -0.081 -0.083
## 0.041 0.034 0.034
## -0.159 -0.167 -0.171
## 0.142 0.134 0.133
## 0.529 0.522 0.653
## 0.653 0.647 0.799
## 0.562 0.555 0.650
## 0.214 0.206 0.203
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.465 0.003 161.691 0.000 0.460
## .Stest20spellng 0.565 0.004 161.026 0.000 0.558
## .Stest21cptlztn 0.515 0.003 162.855 0.000 0.509
## .Stest22puncttn 0.302 0.002 133.968 0.000 0.298
## .Stest23english 0.522 0.003 151.633 0.000 0.515
## .Stest24exprssn 0.657 0.004 156.887 0.000 0.649
## .Stst25wrdfnctn 0.402 0.003 148.331 0.000 0.397
## .Stst26rdngcmpr 0.232 0.002 136.913 0.000 0.229
## .Stst31bstrctrs 0.477 0.003 149.080 0.000 0.471
## .Stst32rthrsnng 0.385 0.002 157.588 0.000 0.380
## .Stst34rthcmptt 0.514 0.003 149.768 0.000 0.507
## .Stest5math 0.206 0.003 82.312 0.000 0.201
## .Stst6physclscn 0.277 0.002 137.703 0.000 0.273
## .Stst33hghschlm 0.282 0.002 120.817 0.000 0.277
## .Stst29vslztn2D 0.567 0.004 135.099 0.000 0.559
## .Stest35tblrdng 0.432 0.005 93.750 0.000 0.423
## .Stst36clrclchc 0.445 0.005 86.490 0.000 0.435
## .Stst37bjctnspc 0.636 0.005 137.436 0.000 0.627
## .Stest1vocab 0.195 0.001 144.112 0.000 0.193
## .Stest2literatr 0.282 0.002 152.206 0.000 0.279
## .Stest3music 0.460 0.003 167.745 0.000 0.455
## .Stest4soclstds 0.296 0.002 151.987 0.000 0.292
## .Stst7blgclscnc 0.465 0.003 159.658 0.000 0.459
## .Stest8aerontcs 0.393 0.003 119.587 0.000 0.386
## .Stest11art 0.435 0.003 166.502 0.000 0.430
## .Stest12law 0.527 0.003 171.047 0.000 0.521
## .Stest13health 0.559 0.003 174.441 0.000 0.553
## .Stest14bible 0.612 0.003 184.503 0.000 0.605
## .Stest15theater 0.459 0.003 170.917 0.000 0.454
## .Stest16mscllns 0.564 0.003 166.661 0.000 0.557
## .Stest9elctrncs 0.237 0.003 87.259 0.000 0.232
## .Stest10mechncs 0.333 0.002 137.109 0.000 0.329
## .Stst28mchnclrs 0.275 0.002 124.333 0.000 0.271
## .Stst30vslztn3D 0.397 0.004 100.846 0.000 0.389
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.471 0.465 0.482
## 0.572 0.565 0.563
## 0.521 0.515 0.550
## 0.307 0.302 0.322
## 0.529 0.522 0.549
## 0.665 0.657 0.667
## 0.408 0.402 0.400
## 0.236 0.232 0.238
## 0.484 0.477 0.495
## 0.390 0.385 0.394
## 0.521 0.514 0.543
## 0.211 0.206 0.237
## 0.281 0.277 0.305
## 0.287 0.282 0.282
## 0.576 0.567 0.601
## 0.441 0.432 0.504
## 0.455 0.445 0.466
## 0.645 0.636 0.616
## 0.198 0.195 0.212
## 0.286 0.282 0.283
## 0.466 0.460 0.454
## 0.300 0.296 0.310
## 0.471 0.465 0.485
## 0.399 0.393 0.548
## 0.441 0.435 0.444
## 0.533 0.527 0.547
## 0.565 0.559 0.588
## 0.618 0.612 0.600
## 0.464 0.459 0.479
## 0.570 0.564 0.556
## 0.243 0.237 0.371
## 0.338 0.333 0.508
## 0.279 0.275 0.377
## 0.405 0.397 0.387
## 1.000 0.207 0.207
## 1.000 0.163 0.163
## 1.000 0.935 0.935
## 1.000 0.182 0.182
## 1.000 0.546 0.546
## 1.000 0.655 0.655
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.157 0.002 73.387 0.000 0.153
## Stst20s (.p2.) 0.302 0.002 129.099 0.000 0.297
## Stst21c (.p3.) 0.296 0.002 131.775 0.000 0.291
## Stst22p (.p4.) 0.364 0.003 138.657 0.000 0.359
## Stst23n (.p5.) 0.298 0.002 129.946 0.000 0.294
## Stst24x (.p6.) 0.261 0.002 123.419 0.000 0.257
## Stst25w (.p7.) 0.266 0.002 118.701 0.000 0.262
## Stst26r (.p8.) 0.122 0.002 79.575 0.000 0.119
## Stst31b (.p9.) 0.168 0.002 106.223 0.000 0.165
## Stst32r (.10.) 0.113 0.002 64.881 0.000 0.110
## Stst34r (.11.) 0.105 0.002 54.320 0.000 0.101
## math =~
## Stst5mt (.12.) 0.329 0.003 107.304 0.000 0.323
## Stst6ph (.13.) 0.163 0.002 92.607 0.000 0.159
## Stst25w (.14.) 0.089 0.002 55.087 0.000 0.086
## Stst32r (.15.) 0.175 0.002 77.769 0.000 0.170
## Stst33h (.16.) 0.342 0.003 102.228 0.000 0.336
## Stst34r (.17.) 0.100 0.002 50.046 0.000 0.096
## speed =~
## Stst19d (.18.) 0.282 0.003 103.964 0.000 0.276
## Sts292D (.19.) 0.219 0.003 74.765 0.000 0.213
## Stst34r (.20.) 0.366 0.003 122.489 0.000 0.360
## Stst35t (.21.) 0.631 0.004 163.870 0.000 0.623
## Stst36c (.22.) 0.690 0.004 180.524 0.000 0.683
## Stst37b (.23.) 0.575 0.004 159.683 0.000 0.568
## info =~
## Stst1vc (.24.) 0.282 0.002 142.261 0.000 0.278
## Stst2lt (.25.) 0.361 0.002 144.384 0.000 0.356
## Stst3ms (.26.) 0.317 0.002 141.265 0.000 0.313
## Stst4sc (.27.) 0.346 0.002 147.521 0.000 0.342
## Stst7bl (.28.) 0.162 0.002 85.216 0.000 0.158
## Stst8rn (.29.) 0.085 0.001 61.926 0.000 0.082
## Stst11r (.30.) 0.315 0.002 137.746 0.000 0.310
## Stst12l (.31.) 0.282 0.002 135.884 0.000 0.278
## Stst13h (.32.) 0.223 0.002 105.631 0.000 0.219
## Stst14b (.33.) 0.272 0.002 133.952 0.000 0.268
## Stst15t (.34.) 0.301 0.002 137.486 0.000 0.297
## Stst16m (.35.) 0.286 0.002 135.202 0.000 0.282
## Stst19d (.36.) 0.113 0.002 59.089 0.000 0.109
## Stst26r (.37.) 0.269 0.002 131.596 0.000 0.265
## science =~
## Stst1vc (.38.) 0.199 0.002 96.352 0.000 0.195
## Stst6ph (.39.) 0.354 0.002 144.800 0.000 0.349
## Stst7bl (.40.) 0.298 0.003 100.459 0.000 0.293
## Stst8rn (.41.) 0.314 0.002 149.929 0.000 0.310
## Stst9lc (.42.) 0.469 0.003 167.451 0.000 0.463
## Stst10m (.43.) 0.420 0.002 168.513 0.000 0.415
## Stst13h (.44.) 0.110 0.003 37.335 0.000 0.104
## Stst28m (.45.) 0.229 0.002 111.973 0.000 0.225
## spatial =~
## Stst28m (.46.) 0.395 0.003 149.355 0.000 0.390
## Sts292D (.47.) 0.436 0.003 157.974 0.000 0.430
## Sts303D (.48.) 0.642 0.003 203.918 0.000 0.636
## Stst31b (.49.) 0.349 0.003 132.767 0.000 0.344
## Stst32r (.50.) 0.150 0.002 64.270 0.000 0.145
## Stst37b (.51.) 0.109 0.002 46.201 0.000 0.104
## g =~
## english (.52.) 1.955 0.017 117.283 0.000 1.922
## math (.53.) 2.267 0.025 92.445 0.000 2.219
## speed (.54.) 0.263 0.004 62.283 0.000 0.255
## info (.55.) 2.123 0.017 123.248 0.000 2.089
## science (.56.) 0.912 0.008 120.306 0.000 0.897
## spatial (.57.) 0.725 0.006 126.486 0.000 0.714
## ci.upper Std.lv Std.all
##
## 0.161 0.317 0.335
## 0.306 0.610 0.658
## 0.300 0.598 0.637
## 0.369 0.736 0.822
## 0.303 0.604 0.669
## 0.265 0.528 0.586
## 0.271 0.539 0.565
## 0.125 0.247 0.274
## 0.171 0.340 0.363
## 0.117 0.229 0.240
## 0.108 0.211 0.229
##
## 0.335 0.781 0.810
## 0.166 0.387 0.423
## 0.093 0.212 0.223
## 0.179 0.415 0.434
## 0.349 0.813 0.859
## 0.104 0.237 0.257
##
## 0.287 0.262 0.277
## 0.225 0.204 0.214
## 0.372 0.340 0.368
## 0.638 0.587 0.725
## 0.698 0.642 0.699
## 0.582 0.535 0.581
##
## 0.286 0.608 0.663
## 0.366 0.779 0.822
## 0.321 0.685 0.726
## 0.351 0.748 0.812
## 0.165 0.349 0.369
## 0.087 0.183 0.196
## 0.319 0.680 0.715
## 0.286 0.608 0.635
## 0.227 0.482 0.518
## 0.276 0.587 0.595
## 0.305 0.650 0.688
## 0.290 0.617 0.659
## 0.116 0.243 0.257
## 0.273 0.581 0.642
##
## 0.203 0.230 0.251
## 0.359 0.410 0.449
## 0.304 0.346 0.365
## 0.318 0.364 0.390
## 0.474 0.543 0.610
## 0.425 0.486 0.645
## 0.116 0.127 0.137
## 0.233 0.266 0.324
##
## 0.401 0.442 0.539
## 0.441 0.487 0.512
## 0.648 0.718 0.775
## 0.354 0.390 0.417
## 0.154 0.168 0.175
## 0.114 0.122 0.132
##
## 1.987 0.879 0.879
## 2.315 0.868 0.868
## 0.271 0.257 0.257
## 2.157 0.894 0.894
## 0.926 0.716 0.716
## 0.737 0.591 0.591
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.99.) -0.131 0.004 -36.417 0.000 -0.138
## .Stst20s (.100) -0.175 0.004 -47.984 0.000 -0.182
## .Stst21c (.101) -0.154 0.004 -42.580 0.000 -0.161
## .Stst22p (.102) -0.192 0.004 -50.600 0.000 -0.200
## .Stst23n (.103) -0.164 0.004 -44.787 0.000 -0.171
## .Stst24x (.104) -0.138 0.004 -37.707 0.000 -0.145
## .Stst25w (.105) -0.098 0.004 -26.297 0.000 -0.106
## .Stst26r (.106) -0.034 0.004 -8.615 0.000 -0.042
## .Stst31b (.107) 0.096 0.004 25.811 0.000 0.089
## .Stst32r (.108) 0.118 0.004 30.345 0.000 0.110
## .Stst34r (.109) -0.033 0.004 -8.795 0.000 -0.041
## .Stst5mt (.110) 0.187 0.004 49.358 0.000 0.179
## .Stst6ph 0.849 0.009 94.365 0.000 0.831
## .Stst33h (.112) 0.182 0.004 44.678 0.000 0.174
## .Sts292D (.113) 0.196 0.004 53.529 0.000 0.189
## .Stst35t (.114) -0.085 0.003 -24.395 0.000 -0.092
## .Stst36c (.115) -0.154 0.004 -42.322 0.000 -0.161
## .Stst37b (.116) -0.051 0.004 -13.910 0.000 -0.058
## .Stst1vc 0.451 0.007 62.666 0.000 0.437
## .Stst2lt (.118) 0.017 0.004 4.428 0.000 0.010
## .Stst3ms 0.145 0.004 33.313 0.000 0.136
## .Stst4sc -0.151 0.004 -34.600 0.000 -0.160
## .Stst7bl 0.660 0.010 66.575 0.000 0.640
## .Stst8rn (.122) 0.473 0.003 136.912 0.000 0.466
## .Stst11r (.123) 0.018 0.004 4.924 0.000 0.011
## .Stst12l -0.153 0.004 -35.836 0.000 -0.162
## .Stst13h 0.460 0.009 49.709 0.000 0.441
## .Stst14b (.126) 0.034 0.004 9.724 0.000 0.027
## .Stst15t 0.190 0.004 44.786 0.000 0.182
## .Stst16m -0.087 0.004 -20.454 0.000 -0.095
## .Stst9lc 0.880 0.008 113.165 0.000 0.865
## .Stst10m (.130) 0.647 0.003 199.130 0.000 0.641
## .Stst28m (.131) 0.555 0.003 158.873 0.000 0.548
## .Sts303D 0.457 0.007 66.159 0.000 0.443
## .english 1.810 0.012 151.037 0.000 1.787
## .math -0.282 0.009 -33.065 0.000 -0.299
## .speed 0.396 0.007 55.330 0.000 0.382
## .info 0.561 0.009 63.995 0.000 0.544
## .science -2.548 0.017 -149.662 0.000 -2.581
## .spatial -0.708 0.010 -68.509 0.000 -0.729
## g -0.238 0.006 -39.923 0.000 -0.249
## ci.upper Std.lv Std.all
## -0.124 -0.131 -0.139
## -0.168 -0.175 -0.189
## -0.147 -0.154 -0.164
## -0.185 -0.192 -0.215
## -0.157 -0.164 -0.181
## -0.131 -0.138 -0.153
## -0.091 -0.098 -0.103
## -0.027 -0.034 -0.038
## 0.104 0.096 0.103
## 0.125 0.118 0.123
## -0.026 -0.033 -0.036
## 0.194 0.187 0.194
## 0.866 0.849 0.928
## 0.190 0.182 0.192
## 0.203 0.196 0.206
## -0.078 -0.085 -0.105
## -0.147 -0.154 -0.168
## -0.044 -0.051 -0.055
## 0.465 0.451 0.491
## 0.025 0.017 0.018
## 0.153 0.145 0.154
## -0.143 -0.151 -0.165
## 0.679 0.660 0.697
## 0.480 0.473 0.507
## 0.025 0.018 0.019
## -0.145 -0.153 -0.160
## 0.478 0.460 0.494
## 0.041 0.034 0.035
## 0.199 0.190 0.202
## -0.078 -0.087 -0.093
## 0.895 0.880 0.988
## 0.653 0.647 0.858
## 0.562 0.555 0.678
## 0.470 0.457 0.493
## 1.834 0.895 0.895
## -0.265 -0.119 -0.119
## 0.410 0.426 0.426
## 0.578 0.260 0.260
## -2.515 -2.200 -2.200
## -0.688 -0.634 -0.634
## -0.226 -0.261 -0.261
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.480 0.003 165.308 0.000 0.474
## .Stest20spellng 0.488 0.003 164.433 0.000 0.482
## .Stest21cptlztn 0.523 0.003 163.419 0.000 0.516
## .Stest22puncttn 0.259 0.002 129.611 0.000 0.255
## .Stest23english 0.451 0.003 156.785 0.000 0.445
## .Stest24exprssn 0.532 0.004 146.330 0.000 0.525
## .Stst25wrdfnctn 0.398 0.003 145.249 0.000 0.393
## .Stst26rdngcmpr 0.193 0.001 139.162 0.000 0.190
## .Stst31bstrctrs 0.468 0.003 155.965 0.000 0.463
## .Stst32rthrsnng 0.405 0.002 164.587 0.000 0.400
## .Stst34rthcmptt 0.494 0.003 143.378 0.000 0.487
## .Stest5math 0.319 0.003 98.100 0.000 0.312
## .Stst6physclscn 0.320 0.002 146.114 0.000 0.316
## .Stst33hghschlm 0.235 0.002 111.176 0.000 0.231
## .Stst29vslztn2D 0.596 0.004 156.285 0.000 0.589
## .Stest35tblrdng 0.310 0.004 84.840 0.000 0.303
## .Stst36clrclchc 0.431 0.004 100.791 0.000 0.423
## .Stst37bjctnspc 0.528 0.004 139.685 0.000 0.521
## .Stest1vocab 0.240 0.002 149.810 0.000 0.237
## .Stest2literatr 0.291 0.002 157.194 0.000 0.288
## .Stest3music 0.420 0.003 166.031 0.000 0.415
## .Stest4soclstds 0.289 0.002 156.048 0.000 0.285
## .Stst7blgclscnc 0.499 0.003 171.630 0.000 0.493
## .Stest8aerontcs 0.620 0.003 184.039 0.000 0.614
## .Stest11art 0.442 0.003 168.861 0.000 0.437
## .Stest12law 0.548 0.003 176.978 0.000 0.542
## .Stest13health 0.538 0.003 172.894 0.000 0.532
## .Stest14bible 0.630 0.003 192.154 0.000 0.624
## .Stest15theater 0.469 0.003 172.789 0.000 0.464
## .Stest16mscllns 0.496 0.003 170.525 0.000 0.490
## .Stest9elctrncs 0.498 0.004 118.218 0.000 0.490
## .Stest10mechncs 0.332 0.002 149.311 0.000 0.327
## .Stst28mchnclrs 0.306 0.002 139.320 0.000 0.302
## .Stst30vslztn3D 0.343 0.003 102.220 0.000 0.336
## .english 0.931 0.017 53.217 0.000 0.897
## .math 1.394 0.030 46.776 0.000 1.336
## .speed 0.808 0.010 77.081 0.000 0.788
## .info 0.933 0.016 58.320 0.000 0.901
## .science 0.653 0.010 67.388 0.000 0.634
## .spatial 0.813 0.010 79.685 0.000 0.793
## g 0.828 0.007 125.941 0.000 0.815
## ci.upper Std.lv Std.all
## 0.486 0.480 0.536
## 0.494 0.488 0.567
## 0.529 0.523 0.594
## 0.263 0.259 0.324
## 0.456 0.451 0.553
## 0.539 0.532 0.657
## 0.404 0.398 0.438
## 0.195 0.193 0.236
## 0.474 0.468 0.537
## 0.409 0.405 0.443
## 0.500 0.494 0.577
## 0.325 0.319 0.343
## 0.324 0.320 0.383
## 0.239 0.235 0.262
## 0.604 0.596 0.659
## 0.318 0.310 0.474
## 0.440 0.431 0.511
## 0.536 0.528 0.622
## 0.243 0.240 0.284
## 0.295 0.291 0.324
## 0.425 0.420 0.473
## 0.292 0.289 0.341
## 0.505 0.499 0.558
## 0.627 0.620 0.712
## 0.447 0.442 0.489
## 0.554 0.548 0.597
## 0.544 0.538 0.621
## 0.637 0.630 0.646
## 0.475 0.469 0.526
## 0.502 0.496 0.566
## 0.506 0.498 0.628
## 0.336 0.332 0.584
## 0.310 0.306 0.456
## 0.349 0.343 0.400
## 0.965 0.227 0.227
## 1.452 0.247 0.247
## 0.829 0.934 0.934
## 0.964 0.200 0.200
## 0.672 0.487 0.487
## 0.833 0.651 0.651
## 0.841 1.000 1.000
lavTestScore(scalar2, release = 58:80, standardized=T, epc=T)
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 10423.35 23 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p99. == .p238. 254.842 1 0
## 2 .p100. == .p239. 1300.388 1 0
## 3 .p101. == .p240. 563.288 1 0
## 4 .p102. == .p241. 62.985 1 0
## 5 .p103. == .p242. 626.133 1 0
## 6 .p104. == .p243. 504.437 1 0
## 7 .p105. == .p244. 381.725 1 0
## 8 .p106. == .p245. 1119.683 1 0
## 9 .p107. == .p246. 378.925 1 0
## 10 .p108. == .p247. 588.440 1 0
## 11 .p109. == .p248. 501.362 1 0
## 12 .p110. == .p249. 1739.747 1 0
## 13 .p112. == .p251. 1757.138 1 0
## 14 .p113. == .p252. 444.725 1 0
## 15 .p114. == .p253. 667.077 1 0
## 16 .p115. == .p254. 62.140 1 0
## 17 .p116. == .p255. 697.230 1 0
## 18 .p118. == .p257. 135.288 1 0
## 19 .p122. == .p261. 160.595 1 0
## 20 .p123. == .p262. 2133.915 1 0
## 21 .p126. == .p265. 98.192 1 0
## 22 .p130. == .p269. 22.279 1 0
## 23 .p131. == .p270. 53.488 1 0
##
## $epc
##
## expected parameter changes (epc) and expected parameter values (epv):
##
## lhs op rhs block
## 1 english =~ Stest19disguisedwords 1
## 2 english =~ Stest20spelling 1
## 3 english =~ Stest21capitalization 1
## 4 english =~ Stest22punctuation 1
## 5 english =~ Stest23english 1
## 6 english =~ Stest24expression 1
## 7 english =~ Stest25wordfunctions 1
## 8 english =~ Stest26readingcomprehension 1
## 9 english =~ Stest31abstractreasoning 1
## 10 english =~ Stest32arithreasoning 1
## 11 english =~ Stest34arithcomputation 1
## 12 math =~ Stest5math 1
## 13 math =~ Stest6physicalscience 1
## 14 math =~ Stest25wordfunctions 1
## 15 math =~ Stest32arithreasoning 1
## 16 math =~ Stest33highschoolmath 1
## 17 math =~ Stest34arithcomputation 1
## 18 speed =~ Stest19disguisedwords 1
## 19 speed =~ Stest29visualization2D 1
## 20 speed =~ Stest34arithcomputation 1
## 21 speed =~ Stest35tablereading 1
## 22 speed =~ Stest36clericalchecking 1
## 23 speed =~ Stest37objectinspection 1
## 24 info =~ Stest1vocab 1
## 25 info =~ Stest2literature 1
## 26 info =~ Stest3music 1
## 27 info =~ Stest4socialstudies 1
## 28 info =~ Stest7biologicalscience 1
## 29 info =~ Stest8aeronautics 1
## 30 info =~ Stest11art 1
## 31 info =~ Stest12law 1
## 32 info =~ Stest13health 1
## 33 info =~ Stest14bible 1
## 34 info =~ Stest15theater 1
## 35 info =~ Stest16miscellaneous 1
## 36 info =~ Stest19disguisedwords 1
## 37 info =~ Stest26readingcomprehension 1
## 38 science =~ Stest1vocab 1
## 39 science =~ Stest6physicalscience 1
## 40 science =~ Stest7biologicalscience 1
## 41 science =~ Stest8aeronautics 1
## 42 science =~ Stest9electronics 1
## 43 science =~ Stest10mechanics 1
## 44 science =~ Stest13health 1
## 45 science =~ Stest28mechanicalreasoning 1
## 46 spatial =~ Stest28mechanicalreasoning 1
## 47 spatial =~ Stest29visualization2D 1
## 48 spatial =~ Stest30visualization3D 1
## 49 spatial =~ Stest31abstractreasoning 1
## 50 spatial =~ Stest32arithreasoning 1
## 51 spatial =~ Stest37objectinspection 1
## 52 g =~ english 1
## 53 g =~ math 1
## 54 g =~ speed 1
## 55 g =~ info 1
## 56 g =~ science 1
## 57 g =~ spatial 1
## 58 Stest19disguisedwords ~~ Stest19disguisedwords 1
## 59 Stest20spelling ~~ Stest20spelling 1
## 60 Stest21capitalization ~~ Stest21capitalization 1
## 61 Stest22punctuation ~~ Stest22punctuation 1
## 62 Stest23english ~~ Stest23english 1
## 63 Stest24expression ~~ Stest24expression 1
## 64 Stest25wordfunctions ~~ Stest25wordfunctions 1
## 65 Stest26readingcomprehension ~~ Stest26readingcomprehension 1
## 66 Stest31abstractreasoning ~~ Stest31abstractreasoning 1
## 67 Stest32arithreasoning ~~ Stest32arithreasoning 1
## 68 Stest34arithcomputation ~~ Stest34arithcomputation 1
## 69 Stest5math ~~ Stest5math 1
## 70 Stest6physicalscience ~~ Stest6physicalscience 1
## 71 Stest33highschoolmath ~~ Stest33highschoolmath 1
## group free label plabel est epc epv sepc.lv sepc.all sepc.nox
## 1 1 1 .p1. .p1. 0.157 0.018 0.174 0.039 0.039 0.039
## 2 1 2 .p2. .p2. 0.302 -0.009 0.293 -0.019 -0.019 -0.019
## 3 1 3 .p3. .p3. 0.296 -0.005 0.291 -0.011 -0.011 -0.011
## 4 1 4 .p4. .p4. 0.364 0.004 0.368 0.009 0.009 0.009
## 5 1 5 .p5. .p5. 0.298 0.009 0.307 0.020 0.020 0.020
## 6 1 6 .p6. .p6. 0.261 0.009 0.270 0.019 0.020 0.020
## 7 1 7 .p7. .p7. 0.266 -0.022 0.244 -0.048 -0.048 -0.048
## 8 1 8 .p8. .p8. 0.122 0.023 0.145 0.050 0.051 0.051
## 9 1 9 .p9. .p9. 0.168 -0.010 0.158 -0.023 -0.023 -0.023
## 10 1 10 .p10. .p10. 0.113 0.029 0.142 0.063 0.063 0.063
## 11 1 11 .p11. .p11. 0.105 -0.029 0.076 -0.063 -0.065 -0.065
## 12 1 12 .p12. .p12. 0.329 -0.003 0.325 -0.008 -0.009 -0.009
## 13 1 13 .p13. .p13. 0.163 0.001 0.164 0.003 0.003 0.003
## 14 1 14 .p14. .p14. 0.089 0.020 0.109 0.049 0.049 0.049
## 15 1 15 .p15. .p15. 0.175 -0.018 0.157 -0.043 -0.044 -0.044
## 16 1 16 .p16. .p16. 0.342 0.004 0.346 0.009 0.009 0.009
## 17 1 17 .p17. .p17. 0.100 0.026 0.126 0.065 0.067 0.067
## 18 1 18 .p18. .p18. 0.282 0.005 0.287 0.005 0.005 0.005
## 19 1 19 .p19. .p19. 0.219 0.009 0.228 0.010 0.010 0.010
## 20 1 20 .p20. .p20. 0.366 -0.006 0.359 -0.007 -0.007 -0.007
## 21 1 21 .p21. .p21. 0.631 0.012 0.643 0.012 0.013 0.013
## 22 1 22 .p22. .p22. 0.690 -0.002 0.688 -0.002 -0.002 -0.002
## 23 1 23 .p23. .p23. 0.575 -0.017 0.559 -0.017 -0.017 -0.017
## 24 1 24 .p24. .p24. 0.282 0.002 0.284 0.006 0.006 0.006
## 25 1 25 .p25. .p25. 0.361 0.002 0.363 0.006 0.006 0.006
## 26 1 26 .p26. .p26. 0.317 0.002 0.319 0.005 0.005 0.005
## 27 1 27 .p27. .p27. 0.346 0.002 0.348 0.005 0.005 0.005
## 28 1 28 .p28. .p28. 0.162 0.002 0.164 0.005 0.005 0.005
## 29 1 29 .p29. .p29. 0.085 0.010 0.095 0.024 0.028 0.028
## 30 1 30 .p30. .p30. 0.315 0.002 0.316 0.004 0.004 0.004
## 31 1 31 .p31. .p31. 0.282 0.002 0.283 0.004 0.004 0.004
## 32 1 32 .p32. .p32. 0.223 0.002 0.225 0.004 0.004 0.004
## 33 1 33 .p33. .p33. 0.272 0.002 0.274 0.004 0.004 0.004
## 34 1 34 .p34. .p34. 0.301 0.002 0.303 0.004 0.005 0.005
## 35 1 35 .p35. .p35. 0.286 0.002 0.287 0.004 0.004 0.004
## 36 1 36 .p36. .p36. 0.113 -0.012 0.100 -0.029 -0.029 -0.029
## 37 1 37 .p37. .p37. 0.269 -0.016 0.253 -0.037 -0.037 -0.037
## 38 1 38 .p38. .p38. 0.199 0.000 0.200 0.001 0.001 0.001
## 39 1 39 .p39. .p39. 0.354 0.000 0.355 0.001 0.001 0.001
## 40 1 40 .p40. .p40. 0.298 0.000 0.299 0.001 0.001 0.001
## 41 1 41 .p41. .p41. 0.314 -0.022 0.292 -0.030 -0.035 -0.035
## 42 1 42 .p42. .p42. 0.469 0.003 0.472 0.004 0.005 0.005
## 43 1 43 .p43. .p43. 0.420 0.005 0.425 0.007 0.009 0.009
## 44 1 44 .p44. .p44. 0.110 0.000 0.110 0.000 0.001 0.001
## 45 1 45 .p45. .p45. 0.229 0.006 0.236 0.009 0.010 0.010
## 46 1 46 .p46. .p46. 0.395 -0.001 0.394 -0.002 -0.002 -0.002
## 47 1 47 .p47. .p47. 0.436 -0.013 0.422 -0.016 -0.017 -0.017
## 48 1 48 .p48. .p48. 0.642 -0.001 0.641 -0.002 -0.002 -0.002
## 49 1 49 .p49. .p49. 0.349 0.023 0.372 0.028 0.029 0.029
## 50 1 50 .p50. .p50. 0.150 -0.020 0.130 -0.025 -0.025 -0.025
## 51 1 51 .p51. .p51. 0.109 0.023 0.132 0.029 0.028 0.028
## 52 1 52 .p52. .p52. 1.955 -0.015 1.939 -0.007 -0.007 -0.007
## 53 1 53 .p53. .p53. 2.267 0.000 2.267 0.000 0.000 0.000
## 54 1 54 .p54. .p54. 0.263 -0.006 0.257 -0.006 -0.006 -0.006
## 55 1 55 .p55. .p55. 2.123 -0.015 2.108 -0.006 -0.006 -0.006
## 56 1 56 .p56. .p56. 0.912 -0.008 0.903 -0.006 -0.006 -0.006
## 57 1 57 .p57. .p57. 0.725 0.004 0.730 0.003 0.003 0.003
## 58 1 58 .p58. 0.465 -0.002 0.463 -0.465 -0.482 -0.482
## 59 1 59 .p59. 0.565 0.003 0.568 0.565 0.563 0.563
## 60 1 60 .p60. 0.515 0.002 0.517 0.515 0.550 0.550
## 61 1 61 .p61. 0.302 -0.001 0.301 -0.302 -0.322 -0.322
## 62 1 62 .p62. 0.522 -0.002 0.520 -0.522 -0.549 -0.549
## 63 1 63 .p63. 0.657 -0.002 0.655 -0.657 -0.667 -0.667
## 64 1 64 .p64. 0.402 0.005 0.407 0.402 0.400 0.400
## 65 1 65 .p65. 0.232 0.000 0.232 0.232 0.238 0.238
## 66 1 66 .p66. 0.477 -0.004 0.473 -0.477 -0.495 -0.495
## 67 1 67 .p67. 0.385 0.003 0.388 0.385 0.394 0.394
## 68 1 68 .p68. 0.514 0.001 0.515 0.514 0.543 0.543
## 69 1 69 .p69. 0.206 0.003 0.209 0.206 0.237 0.237
## 70 1 70 .p70. 0.277 0.000 0.277 -0.277 -0.305 -0.305
## 71 1 71 .p71. 0.282 -0.003 0.279 -0.282 -0.282 -0.282
## [ reached 'max' / getOption("max.print") -- omitted 207 rows ]
strict<-cfa(chc.hof.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("Stest4socialstudies~1", "Stest15theater~1", "Stest12law~1", "Stest3music~1", "Stest16miscellaneous~1", "Stest13health~1", "Stest6physicalscience~1", "Stest9electronics~1", "Stest30visualization3D~1", "Stest7biologicalscience~1", "Stest1vocab~1"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov)
## does not appear to be positive definite! The smallest eigenvalue
## (= 1.109101e-16) is close to zero. This may be a symptom that the
## model is not identified.
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 180233.322 1108.000 0.000 0.932 0.048
## srmr aic bic
## 0.046 10383923.821 10385400.213
Mc(strict)
## [1] 0.5251377
chc.hof<-cfa(chc.hof.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("Stest4socialstudies~1", "Stest15theater~1", "Stest12law~1", "Stest3music~1", "Stest16miscellaneous~1", "Stest13health~1", "Stest6physicalscience~1", "Stest9electronics~1", "Stest30visualization3D~1", "Stest7biologicalscience~1", "Stest1vocab~1"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov)
## does not appear to be positive definite! The smallest eigenvalue
## (= 2.875966e-17) is close to zero. This may be a symptom that the
## model is not identified.
fitMeasures(chc.hof, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 166142.221 1081.000 0.000 0.937 0.047
## srmr aic bic
## 0.060 10369886.719 10371628.861
Mc(chc.hof)
## [1] 0.5523776
summary(chc.hof, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 97 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 257
## Number of equality constraints 80
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 166142.221 145503.634
## Degrees of freedom 1081 1081
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.142
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 93537.440 81917.994
## 1 72604.780 63585.640
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.154 0.002 76.948 0.000 0.150
## Stst20s (.p2.) 0.297 0.002 166.854 0.000 0.293
## Stst21c (.p3.) 0.291 0.002 170.941 0.000 0.287
## Stst22p (.p4.) 0.358 0.002 187.767 0.000 0.354
## Stst23n (.p5.) 0.294 0.002 168.922 0.000 0.290
## Stst24x (.p6.) 0.256 0.002 156.104 0.000 0.253
## Stst25w (.p7.) 0.262 0.002 141.174 0.000 0.258
## Stst26r (.p8.) 0.120 0.001 86.019 0.000 0.117
## Stst31b (.p9.) 0.165 0.001 121.151 0.000 0.162
## Stst32r (.10.) 0.111 0.002 67.142 0.000 0.107
## Stst34r (.11.) 0.102 0.002 55.654 0.000 0.098
## math =~
## Stst5mt (.12.) 0.359 0.002 159.963 0.000 0.355
## Stst6ph (.13.) 0.177 0.002 116.575 0.000 0.174
## Stst25w (.14.) 0.098 0.002 60.522 0.000 0.095
## Stst32r (.15.) 0.192 0.002 99.048 0.000 0.188
## Stst33h (.16.) 0.375 0.002 152.058 0.000 0.370
## Stst34r (.17.) 0.110 0.002 55.945 0.000 0.106
## speed =~
## Stst19d (.18.) 0.269 0.003 107.311 0.000 0.264
## Sts292D (.19.) 0.208 0.003 76.657 0.000 0.203
## Stst34r (.20.) 0.348 0.003 132.351 0.000 0.342
## Stst35t (.21.) 0.596 0.003 200.583 0.000 0.590
## Stst36c (.22.) 0.657 0.003 210.891 0.000 0.651
## Stst37b (.23.) 0.545 0.003 183.040 0.000 0.540
## info =~
## Stst1vc (.24.) 0.277 0.002 170.103 0.000 0.273
## Stst2lt (.25.) 0.353 0.002 179.694 0.000 0.349
## Stst3ms (.26.) 0.310 0.002 174.221 0.000 0.307
## Stst4sc (.27.) 0.339 0.002 187.598 0.000 0.335
## Stst7bl (.28.) 0.158 0.002 90.773 0.000 0.155
## Stst8rn (.29.) 0.083 0.001 64.524 0.000 0.081
## Stst11r (.30.) 0.308 0.002 167.975 0.000 0.305
## Stst12l (.31.) 0.276 0.002 164.667 0.000 0.272
## Stst13h (.32.) 0.219 0.002 119.735 0.000 0.215
## Stst14b (.33.) 0.266 0.002 162.256 0.000 0.263
## Stst15t (.34.) 0.295 0.002 166.011 0.000 0.291
## Stst16m (.35.) 0.280 0.002 165.199 0.000 0.276
## Stst19d (.36.) 0.110 0.002 61.465 0.000 0.107
## Stst26r (.37.) 0.263 0.002 159.573 0.000 0.260
## science =~
## Stst1vc (.38.) 0.181 0.002 100.735 0.000 0.177
## Stst6ph (.39.) 0.328 0.002 150.636 0.000 0.323
## Stst7bl (.40.) 0.273 0.003 103.859 0.000 0.268
## Stst8rn (.41.) 0.287 0.002 167.077 0.000 0.284
## Stst9lc (.42.) 0.431 0.002 188.279 0.000 0.427
## Stst10m (.43.) 0.382 0.002 200.158 0.000 0.379
## Stst13h (.44.) 0.100 0.003 37.439 0.000 0.094
## Stst28m (.45.) 0.207 0.002 123.041 0.000 0.204
## spatial =~
## Stst28m (.46.) 0.379 0.002 168.690 0.000 0.374
## Sts292D (.47.) 0.414 0.002 177.778 0.000 0.410
## Sts303D (.48.) 0.609 0.002 256.778 0.000 0.605
## Stst31b (.49.) 0.331 0.002 143.282 0.000 0.327
## Stst32r (.50.) 0.142 0.002 64.934 0.000 0.138
## Stst37b (.51.) 0.104 0.002 46.826 0.000 0.099
## g =~
## english (.52.) 1.898 0.012 154.239 0.000 1.873
## math (.53.) 1.976 0.015 131.979 0.000 1.946
## speed (.54.) 0.264 0.004 63.610 0.000 0.256
## info (.55.) 2.073 0.014 148.822 0.000 2.046
## science (.56.) 0.957 0.007 136.441 0.000 0.944
## spatial (.57.) 0.729 0.005 139.646 0.000 0.719
## ci.upper Std.lv Std.all
##
## 0.158 0.330 0.344
## 0.300 0.636 0.646
## 0.294 0.624 0.656
## 0.362 0.768 0.812
## 0.297 0.630 0.657
## 0.260 0.550 0.562
## 0.266 0.562 0.574
## 0.123 0.258 0.269
## 0.168 0.354 0.368
## 0.114 0.238 0.246
## 0.106 0.219 0.229
##
## 0.364 0.795 0.870
## 0.180 0.391 0.423
## 0.101 0.217 0.222
## 0.196 0.426 0.440
## 0.380 0.830 0.844
## 0.114 0.244 0.256
##
## 0.274 0.279 0.290
## 0.213 0.215 0.225
## 0.353 0.360 0.377
## 0.602 0.616 0.681
## 0.663 0.679 0.712
## 0.551 0.564 0.565
##
## 0.280 0.637 0.686
## 0.357 0.813 0.837
## 0.314 0.714 0.725
## 0.342 0.780 0.820
## 0.162 0.364 0.381
## 0.086 0.191 0.232
## 0.312 0.709 0.732
## 0.279 0.635 0.658
## 0.223 0.504 0.526
## 0.269 0.613 0.617
## 0.298 0.678 0.708
## 0.283 0.644 0.651
## 0.114 0.254 0.264
## 0.267 0.606 0.634
##
## 0.185 0.251 0.270
## 0.332 0.453 0.490
## 0.279 0.379 0.396
## 0.290 0.397 0.481
## 0.436 0.597 0.772
## 0.386 0.529 0.674
## 0.105 0.138 0.144
## 0.211 0.287 0.346
##
## 0.383 0.469 0.564
## 0.419 0.513 0.537
## 0.614 0.754 0.764
## 0.336 0.410 0.427
## 0.146 0.176 0.182
## 0.108 0.128 0.129
##
## 1.922 0.885 0.885
## 2.005 0.892 0.892
## 0.272 0.255 0.255
## 2.101 0.901 0.901
## 0.971 0.691 0.691
## 0.740 0.589 0.589
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.99.) -0.132 0.004 -36.539 0.000 -0.139
## .Stst20s (.100) -0.175 0.004 -47.972 0.000 -0.182
## .Stst21c (.101) -0.154 0.004 -42.596 0.000 -0.161
## .Stst22p (.102) -0.193 0.004 -50.633 0.000 -0.200
## .Stst23n (.103) -0.164 0.004 -44.822 0.000 -0.171
## .Stst24x (.104) -0.138 0.004 -37.719 0.000 -0.145
## .Stst25w (.105) -0.098 0.004 -26.263 0.000 -0.106
## .Stst26r (.106) -0.034 0.004 -8.600 0.000 -0.042
## .Stst31b (.107) 0.097 0.004 25.895 0.000 0.089
## .Stst32r (.108) 0.118 0.004 30.493 0.000 0.111
## .Stst34r (.109) -0.033 0.004 -8.608 0.000 -0.040
## .Stst5mt (.110) 0.187 0.004 49.401 0.000 0.179
## .Stst6ph 0.358 0.004 92.151 0.000 0.350
## .Stst33h (.112) 0.181 0.004 44.495 0.000 0.173
## .Sts292D (.113) 0.197 0.004 53.602 0.000 0.189
## .Stst35t (.114) -0.085 0.003 -24.473 0.000 -0.092
## .Stst36c (.115) -0.155 0.004 -42.443 0.000 -0.162
## .Stst37b (.116) -0.051 0.004 -13.866 0.000 -0.058
## .Stst1vc 0.189 0.004 50.213 0.000 0.181
## .Stst2lt (.118) 0.017 0.004 4.410 0.000 0.009
## .Stst3ms -0.121 0.004 -29.897 0.000 -0.128
## .Stst4sc 0.228 0.004 57.616 0.000 0.220
## .Stst7bl 0.243 0.004 61.805 0.000 0.235
## .Stst8rn (.122) 0.474 0.003 136.986 0.000 0.467
## .Stst11r (.123) 0.018 0.004 4.909 0.000 0.011
## .Stst12l 0.208 0.004 51.530 0.000 0.200
## .Stst13h -0.081 0.004 -19.853 0.000 -0.089
## .Stst14b (.126) 0.034 0.004 9.720 0.000 0.027
## .Stst15t -0.167 0.004 -42.901 0.000 -0.175
## .Stst16m 0.134 0.004 31.519 0.000 0.125
## .Stst9lc 0.522 0.003 156.854 0.000 0.516
## .Stst10m (.130) 0.647 0.003 198.861 0.000 0.640
## .Stst28m (.131) 0.555 0.003 158.664 0.000 0.548
## .Sts303D 0.206 0.004 50.235 0.000 0.198
## ci.upper Std.lv Std.all
## -0.125 -0.132 -0.137
## -0.168 -0.175 -0.177
## -0.147 -0.154 -0.162
## -0.185 -0.193 -0.204
## -0.157 -0.164 -0.171
## -0.131 -0.138 -0.141
## -0.091 -0.098 -0.100
## -0.027 -0.034 -0.036
## 0.104 0.097 0.100
## 0.126 0.118 0.122
## -0.025 -0.033 -0.034
## 0.194 0.187 0.204
## 0.365 0.358 0.387
## 0.189 0.181 0.184
## 0.204 0.197 0.206
## -0.078 -0.085 -0.094
## -0.148 -0.155 -0.162
## -0.044 -0.051 -0.051
## 0.196 0.189 0.203
## 0.025 0.017 0.017
## -0.113 -0.121 -0.122
## 0.236 0.228 0.240
## 0.251 0.243 0.254
## 0.481 0.474 0.573
## 0.025 0.018 0.018
## 0.216 0.208 0.216
## -0.073 -0.081 -0.084
## 0.041 0.034 0.035
## -0.159 -0.167 -0.174
## 0.142 0.134 0.135
## 0.529 0.522 0.675
## 0.653 0.647 0.823
## 0.562 0.555 0.668
## 0.214 0.206 0.209
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.465 0.003 161.823 0.000 0.459
## .Stest20spellng 0.566 0.004 161.428 0.000 0.559
## .Stest21cptlztn 0.515 0.003 163.229 0.000 0.509
## .Stest22puncttn 0.305 0.002 134.956 0.000 0.300
## .Stest23english 0.522 0.003 151.637 0.000 0.515
## .Stest24exprssn 0.657 0.004 156.894 0.000 0.649
## .Stst25wrdfnctn 0.403 0.003 148.717 0.000 0.398
## .Stst26rdngcmpr 0.232 0.002 136.857 0.000 0.229
## .Stst31bstrctrs 0.479 0.003 149.337 0.000 0.473
## .Stst32rthrsnng 0.385 0.002 157.560 0.000 0.380
## .Stst34rthcmptt 0.515 0.003 149.704 0.000 0.508
## .Stest5math 0.204 0.003 80.635 0.000 0.199
## .Stst6physclscn 0.277 0.002 137.952 0.000 0.273
## .Stst33hghschlm 0.278 0.002 120.928 0.000 0.273
## .Stst29vslztn2D 0.569 0.004 135.926 0.000 0.561
## .Stest35tblrdng 0.438 0.005 93.800 0.000 0.429
## .Stst36clrclchc 0.450 0.005 87.166 0.000 0.439
## .Stst37bjctnspc 0.639 0.005 138.193 0.000 0.630
## .Stest1vocab 0.195 0.001 144.210 0.000 0.193
## .Stest2literatr 0.283 0.002 152.742 0.000 0.280
## .Stest3music 0.460 0.003 168.018 0.000 0.455
## .Stest4soclstds 0.296 0.002 152.212 0.000 0.292
## .Stst7blgclscnc 0.465 0.003 159.895 0.000 0.460
## .Stest8aerontcs 0.394 0.003 119.542 0.000 0.388
## .Stest11art 0.435 0.003 166.764 0.000 0.430
## .Stest12law 0.527 0.003 171.132 0.000 0.521
## .Stest13health 0.559 0.003 174.471 0.000 0.553
## .Stest14bible 0.612 0.003 184.746 0.000 0.606
## .Stest15theater 0.459 0.003 171.150 0.000 0.454
## .Stest16mscllns 0.564 0.003 166.786 0.000 0.557
## .Stest9elctrncs 0.242 0.003 87.317 0.000 0.237
## .Stest10mechncs 0.337 0.002 138.970 0.000 0.333
## .Stst28mchnclrs 0.278 0.002 125.680 0.000 0.274
## .Stst30vslztn3D 0.405 0.004 105.600 0.000 0.397
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.470 0.465 0.503
## 0.573 0.566 0.583
## 0.521 0.515 0.570
## 0.309 0.305 0.341
## 0.528 0.522 0.568
## 0.665 0.657 0.685
## 0.408 0.403 0.420
## 0.235 0.232 0.254
## 0.486 0.479 0.518
## 0.389 0.385 0.411
## 0.522 0.515 0.565
## 0.209 0.204 0.244
## 0.281 0.277 0.324
## 0.282 0.278 0.287
## 0.578 0.569 0.624
## 0.447 0.438 0.536
## 0.460 0.450 0.494
## 0.648 0.639 0.642
## 0.198 0.195 0.227
## 0.287 0.283 0.300
## 0.466 0.460 0.474
## 0.300 0.296 0.327
## 0.471 0.465 0.510
## 0.401 0.394 0.577
## 0.440 0.435 0.464
## 0.533 0.527 0.567
## 0.565 0.559 0.608
## 0.619 0.612 0.620
## 0.464 0.459 0.499
## 0.570 0.564 0.577
## 0.248 0.242 0.405
## 0.342 0.337 0.546
## 0.283 0.278 0.403
## 0.412 0.405 0.416
## 1.000 0.217 0.217
## 1.000 0.204 0.204
## 1.000 0.935 0.935
## 1.000 0.189 0.189
## 1.000 0.522 0.522
## 1.000 0.653 0.653
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.154 0.002 76.948 0.000 0.150
## Stst20s (.p2.) 0.297 0.002 166.854 0.000 0.293
## Stst21c (.p3.) 0.291 0.002 170.941 0.000 0.287
## Stst22p (.p4.) 0.358 0.002 187.767 0.000 0.354
## Stst23n (.p5.) 0.294 0.002 168.922 0.000 0.290
## Stst24x (.p6.) 0.256 0.002 156.104 0.000 0.253
## Stst25w (.p7.) 0.262 0.002 141.174 0.000 0.258
## Stst26r (.p8.) 0.120 0.001 86.019 0.000 0.117
## Stst31b (.p9.) 0.165 0.001 121.151 0.000 0.162
## Stst32r (.10.) 0.111 0.002 67.142 0.000 0.107
## Stst34r (.11.) 0.102 0.002 55.654 0.000 0.098
## math =~
## Stst5mt (.12.) 0.359 0.002 159.963 0.000 0.355
## Stst6ph (.13.) 0.177 0.002 116.575 0.000 0.174
## Stst25w (.14.) 0.098 0.002 60.522 0.000 0.095
## Stst32r (.15.) 0.192 0.002 99.048 0.000 0.188
## Stst33h (.16.) 0.375 0.002 152.058 0.000 0.370
## Stst34r (.17.) 0.110 0.002 55.945 0.000 0.106
## speed =~
## Stst19d (.18.) 0.269 0.003 107.311 0.000 0.264
## Sts292D (.19.) 0.208 0.003 76.657 0.000 0.203
## Stst34r (.20.) 0.348 0.003 132.351 0.000 0.342
## Stst35t (.21.) 0.596 0.003 200.583 0.000 0.590
## Stst36c (.22.) 0.657 0.003 210.891 0.000 0.651
## Stst37b (.23.) 0.545 0.003 183.040 0.000 0.540
## info =~
## Stst1vc (.24.) 0.277 0.002 170.103 0.000 0.273
## Stst2lt (.25.) 0.353 0.002 179.694 0.000 0.349
## Stst3ms (.26.) 0.310 0.002 174.221 0.000 0.307
## Stst4sc (.27.) 0.339 0.002 187.598 0.000 0.335
## Stst7bl (.28.) 0.158 0.002 90.773 0.000 0.155
## Stst8rn (.29.) 0.083 0.001 64.524 0.000 0.081
## Stst11r (.30.) 0.308 0.002 167.975 0.000 0.305
## Stst12l (.31.) 0.276 0.002 164.667 0.000 0.272
## Stst13h (.32.) 0.219 0.002 119.735 0.000 0.215
## Stst14b (.33.) 0.266 0.002 162.256 0.000 0.263
## Stst15t (.34.) 0.295 0.002 166.011 0.000 0.291
## Stst16m (.35.) 0.280 0.002 165.199 0.000 0.276
## Stst19d (.36.) 0.110 0.002 61.465 0.000 0.107
## Stst26r (.37.) 0.263 0.002 159.573 0.000 0.260
## science =~
## Stst1vc (.38.) 0.181 0.002 100.735 0.000 0.177
## Stst6ph (.39.) 0.328 0.002 150.636 0.000 0.323
## Stst7bl (.40.) 0.273 0.003 103.859 0.000 0.268
## Stst8rn (.41.) 0.287 0.002 167.077 0.000 0.284
## Stst9lc (.42.) 0.431 0.002 188.279 0.000 0.427
## Stst10m (.43.) 0.382 0.002 200.158 0.000 0.379
## Stst13h (.44.) 0.100 0.003 37.439 0.000 0.094
## Stst28m (.45.) 0.207 0.002 123.041 0.000 0.204
## spatial =~
## Stst28m (.46.) 0.379 0.002 168.690 0.000 0.374
## Sts292D (.47.) 0.414 0.002 177.778 0.000 0.410
## Sts303D (.48.) 0.609 0.002 256.778 0.000 0.605
## Stst31b (.49.) 0.331 0.002 143.282 0.000 0.327
## Stst32r (.50.) 0.142 0.002 64.934 0.000 0.138
## Stst37b (.51.) 0.104 0.002 46.826 0.000 0.099
## g =~
## english (.52.) 1.898 0.012 154.239 0.000 1.873
## math (.53.) 1.976 0.015 131.979 0.000 1.946
## speed (.54.) 0.264 0.004 63.610 0.000 0.256
## info (.55.) 2.073 0.014 148.822 0.000 2.046
## science (.56.) 0.957 0.007 136.441 0.000 0.944
## spatial (.57.) 0.729 0.005 139.646 0.000 0.719
## ci.upper Std.lv Std.all
##
## 0.158 0.330 0.341
## 0.300 0.636 0.674
## 0.294 0.624 0.653
## 0.362 0.768 0.834
## 0.297 0.630 0.684
## 0.260 0.550 0.602
## 0.266 0.562 0.575
## 0.123 0.258 0.275
## 0.168 0.354 0.371
## 0.114 0.238 0.243
## 0.106 0.219 0.232
##
## 0.364 0.795 0.814
## 0.180 0.391 0.414
## 0.101 0.217 0.223
## 0.196 0.426 0.436
## 0.380 0.830 0.861
## 0.114 0.244 0.259
##
## 0.274 0.279 0.288
## 0.213 0.215 0.222
## 0.353 0.360 0.381
## 0.602 0.616 0.742
## 0.663 0.679 0.721
## 0.551 0.564 0.601
##
## 0.280 0.637 0.669
## 0.357 0.813 0.833
## 0.314 0.714 0.741
## 0.342 0.780 0.824
## 0.162 0.364 0.375
## 0.086 0.191 0.201
## 0.312 0.709 0.730
## 0.279 0.635 0.651
## 0.223 0.504 0.532
## 0.269 0.613 0.611
## 0.298 0.678 0.704
## 0.283 0.644 0.674
## 0.114 0.254 0.262
## 0.267 0.606 0.648
##
## 0.185 0.251 0.263
## 0.332 0.453 0.480
## 0.279 0.379 0.390
## 0.290 0.397 0.417
## 0.436 0.597 0.649
## 0.386 0.529 0.678
## 0.105 0.138 0.146
## 0.211 0.287 0.340
##
## 0.383 0.469 0.554
## 0.419 0.513 0.530
## 0.614 0.754 0.792
## 0.336 0.410 0.429
## 0.146 0.176 0.180
## 0.108 0.128 0.137
##
## 1.922 0.885 0.885
## 2.005 0.892 0.892
## 0.272 0.255 0.255
## 2.101 0.901 0.901
## 0.971 0.691 0.691
## 0.740 0.589 0.589
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.99.) -0.132 0.004 -36.539 0.000 -0.139
## .Stst20s (.100) -0.175 0.004 -47.972 0.000 -0.182
## .Stst21c (.101) -0.154 0.004 -42.596 0.000 -0.161
## .Stst22p (.102) -0.193 0.004 -50.633 0.000 -0.200
## .Stst23n (.103) -0.164 0.004 -44.822 0.000 -0.171
## .Stst24x (.104) -0.138 0.004 -37.719 0.000 -0.145
## .Stst25w (.105) -0.098 0.004 -26.263 0.000 -0.106
## .Stst26r (.106) -0.034 0.004 -8.600 0.000 -0.042
## .Stst31b (.107) 0.097 0.004 25.895 0.000 0.089
## .Stst32r (.108) 0.118 0.004 30.493 0.000 0.111
## .Stst34r (.109) -0.033 0.004 -8.608 0.000 -0.040
## .Stst5mt (.110) 0.187 0.004 49.401 0.000 0.179
## .Stst6ph 0.862 0.009 95.555 0.000 0.844
## .Stst33h (.112) 0.181 0.004 44.495 0.000 0.173
## .Sts292D (.113) 0.197 0.004 53.602 0.000 0.189
## .Stst35t (.114) -0.085 0.003 -24.473 0.000 -0.092
## .Stst36c (.115) -0.155 0.004 -42.443 0.000 -0.162
## .Stst37b (.116) -0.051 0.004 -13.866 0.000 -0.058
## .Stst1vc 0.450 0.007 62.181 0.000 0.436
## .Stst2lt (.118) 0.017 0.004 4.410 0.000 0.009
## .Stst3ms 0.145 0.004 33.297 0.000 0.136
## .Stst4sc -0.152 0.004 -34.616 0.000 -0.160
## .Stst7bl 0.664 0.010 66.716 0.000 0.645
## .Stst8rn (.122) 0.474 0.003 136.986 0.000 0.467
## .Stst11r (.123) 0.018 0.004 4.909 0.000 0.011
## .Stst12l -0.154 0.004 -35.849 0.000 -0.162
## .Stst13h 0.457 0.009 49.579 0.000 0.439
## .Stst14b (.126) 0.034 0.004 9.720 0.000 0.027
## .Stst15t 0.190 0.004 44.760 0.000 0.182
## .Stst16m -0.087 0.004 -20.471 0.000 -0.095
## .Stst9lc 0.893 0.008 114.504 0.000 0.878
## .Stst10m (.130) 0.647 0.003 198.861 0.000 0.640
## .Stst28m (.131) 0.555 0.003 158.664 0.000 0.548
## .Sts303D 0.457 0.007 66.438 0.000 0.443
## .english 1.887 0.010 184.873 0.000 1.867
## .math -0.209 0.008 -26.823 0.000 -0.224
## .speed 0.425 0.007 60.602 0.000 0.411
## .info 0.624 0.008 74.830 0.000 0.608
## .science -2.774 0.016 -173.182 0.000 -2.805
## .spatial -0.729 0.011 -69.029 0.000 -0.750
## g -0.273 0.006 -44.720 0.000 -0.285
## ci.upper Std.lv Std.all
## -0.125 -0.132 -0.136
## -0.168 -0.175 -0.185
## -0.147 -0.154 -0.161
## -0.185 -0.193 -0.209
## -0.157 -0.164 -0.178
## -0.131 -0.138 -0.151
## -0.091 -0.098 -0.101
## -0.027 -0.034 -0.037
## 0.104 0.097 0.101
## 0.126 0.118 0.121
## -0.025 -0.033 -0.034
## 0.194 0.187 0.191
## 0.880 0.862 0.913
## 0.189 0.181 0.188
## 0.204 0.197 0.203
## -0.078 -0.085 -0.102
## -0.148 -0.155 -0.164
## -0.044 -0.051 -0.054
## 0.464 0.450 0.473
## 0.025 0.017 0.017
## 0.153 0.145 0.150
## -0.143 -0.152 -0.160
## 0.684 0.664 0.684
## 0.481 0.474 0.497
## 0.025 0.018 0.018
## -0.145 -0.154 -0.157
## 0.476 0.457 0.483
## 0.041 0.034 0.034
## 0.199 0.190 0.197
## -0.078 -0.087 -0.091
## 0.908 0.893 0.971
## 0.653 0.647 0.829
## 0.562 0.555 0.656
## 0.470 0.457 0.480
## 1.907 0.880 0.880
## -0.194 -0.094 -0.094
## 0.439 0.411 0.411
## 0.640 0.271 0.271
## -2.742 -2.004 -2.004
## -0.709 -0.589 -0.589
## -0.261 -0.273 -0.273
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.479 0.003 165.053 0.000 0.473
## .Stest20spellng 0.487 0.003 164.427 0.000 0.482
## .Stest21cptlztn 0.522 0.003 163.371 0.000 0.516
## .Stest22puncttn 0.258 0.002 129.654 0.000 0.254
## .Stest23english 0.451 0.003 156.688 0.000 0.445
## .Stest24exprssn 0.533 0.004 146.384 0.000 0.526
## .Stst25wrdfnctn 0.398 0.003 145.065 0.000 0.392
## .Stst26rdngcmpr 0.193 0.001 139.179 0.000 0.190
## .Stst31bstrctrs 0.467 0.003 155.689 0.000 0.461
## .Stst32rthrsnng 0.404 0.002 164.565 0.000 0.399
## .Stst34rthcmptt 0.493 0.003 143.205 0.000 0.486
## .Stest5math 0.322 0.003 98.325 0.000 0.316
## .Stst6physclscn 0.314 0.002 144.552 0.000 0.310
## .Stst33hghschlm 0.241 0.002 115.479 0.000 0.237
## .Stst29vslztn2D 0.594 0.004 155.595 0.000 0.587
## .Stest35tblrdng 0.310 0.004 84.782 0.000 0.303
## .Stst36clrclchc 0.425 0.004 100.218 0.000 0.417
## .Stst37bjctnspc 0.526 0.004 139.343 0.000 0.519
## .Stest1vocab 0.239 0.002 149.834 0.000 0.236
## .Stest2literatr 0.291 0.002 157.203 0.000 0.287
## .Stest3music 0.420 0.003 166.020 0.000 0.415
## .Stest4soclstds 0.288 0.002 155.894 0.000 0.285
## .Stst7blgclscnc 0.496 0.003 170.880 0.000 0.491
## .Stest8aerontcs 0.619 0.003 182.611 0.000 0.612
## .Stest11art 0.442 0.003 168.946 0.000 0.437
## .Stest12law 0.549 0.003 176.901 0.000 0.543
## .Stest13health 0.538 0.003 172.925 0.000 0.532
## .Stest14bible 0.630 0.003 192.019 0.000 0.624
## .Stest15theater 0.469 0.003 172.834 0.000 0.463
## .Stest16mscllns 0.496 0.003 170.453 0.000 0.490
## .Stest9elctrncs 0.490 0.004 117.075 0.000 0.481
## .Stest10mechncs 0.329 0.002 146.585 0.000 0.324
## .Stst28mchnclrs 0.303 0.002 137.508 0.000 0.299
## .Stst30vslztn3D 0.338 0.003 100.880 0.000 0.331
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.484 0.479 0.511
## 0.493 0.487 0.546
## 0.528 0.522 0.573
## 0.262 0.258 0.304
## 0.456 0.451 0.532
## 0.540 0.533 0.638
## 0.403 0.398 0.417
## 0.196 0.193 0.220
## 0.473 0.467 0.512
## 0.409 0.404 0.423
## 0.500 0.493 0.554
## 0.328 0.322 0.337
## 0.319 0.314 0.352
## 0.245 0.241 0.259
## 0.602 0.594 0.634
## 0.317 0.310 0.449
## 0.434 0.425 0.480
## 0.533 0.526 0.596
## 0.242 0.239 0.264
## 0.294 0.291 0.306
## 0.425 0.420 0.451
## 0.292 0.288 0.322
## 0.502 0.496 0.526
## 0.626 0.619 0.682
## 0.447 0.442 0.468
## 0.555 0.549 0.577
## 0.544 0.538 0.599
## 0.637 0.630 0.627
## 0.474 0.469 0.505
## 0.502 0.496 0.545
## 0.498 0.490 0.579
## 0.333 0.329 0.540
## 0.308 0.303 0.424
## 0.344 0.338 0.373
## 1.000 0.217 0.217
## 1.000 0.204 0.204
## 1.000 0.935 0.935
## 1.000 0.189 0.189
## 1.000 0.522 0.522
## 1.000 0.653 0.653
## 1.000 1.000 1.000
chc.weak<-cfa(chc.hof.weak.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("Stest4socialstudies~1", "Stest15theater~1", "Stest12law~1", "Stest3music~1", "Stest16miscellaneous~1", "Stest13health~1", "Stest6physicalscience~1", "Stest9electronics~1", "Stest30visualization3D~1", "Stest7biologicalscience~1", "Stest1vocab~1"))
fitMeasures(chc.weak, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 166142.220 1082.000 0.000 0.937 0.047
## srmr aic bic
## 0.060 10369884.719 10371617.019
Mc(chc.weak)
## [1] 0.5523796
summary(chc.weak, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 102 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 256
## Number of equality constraints 80
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 166142.220 145638.230
## Degrees of freedom 1082 1082
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.141
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 93537.261 81993.614
## 1 72604.960 63644.616
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.154 0.002 76.944 0.000 0.150
## Stst20s (.p2.) 0.297 0.002 166.836 0.000 0.293
## Stst21c (.p3.) 0.291 0.002 170.922 0.000 0.287
## Stst22p (.p4.) 0.358 0.002 187.742 0.000 0.354
## Stst23n (.p5.) 0.293 0.002 168.905 0.000 0.290
## Stst24x (.p6.) 0.256 0.002 156.090 0.000 0.253
## Stst25w (.p7.) 0.262 0.002 141.165 0.000 0.258
## Stst26r (.p8.) 0.120 0.001 86.016 0.000 0.117
## Stst31b (.p9.) 0.165 0.001 121.146 0.000 0.162
## Stst32r (.10.) 0.111 0.002 67.141 0.000 0.107
## Stst34r (.11.) 0.102 0.002 55.652 0.000 0.098
## math =~
## Stst5mt (.12.) 0.359 0.002 159.969 0.000 0.355
## Stst6ph (.13.) 0.177 0.002 116.579 0.000 0.174
## Stst25w (.14.) 0.098 0.002 60.521 0.000 0.095
## Stst32r (.15.) 0.192 0.002 99.048 0.000 0.188
## Stst33h (.16.) 0.375 0.002 152.063 0.000 0.370
## Stst34r (.17.) 0.110 0.002 55.946 0.000 0.106
## speed =~
## Stst19d (.18.) 0.269 0.003 107.311 0.000 0.264
## Sts292D (.19.) 0.208 0.003 76.657 0.000 0.203
## Stst34r (.20.) 0.348 0.003 132.350 0.000 0.342
## Stst35t (.21.) 0.596 0.003 200.582 0.000 0.590
## Stst36c (.22.) 0.657 0.003 210.891 0.000 0.651
## Stst37b (.23.) 0.545 0.003 183.040 0.000 0.540
## info =~
## Stst1vc (.24.) 0.277 0.002 170.106 0.000 0.273
## Stst2lt (.25.) 0.353 0.002 179.698 0.000 0.349
## Stst3ms (.26.) 0.310 0.002 174.225 0.000 0.307
## Stst4sc (.27.) 0.339 0.002 187.601 0.000 0.335
## Stst7bl (.28.) 0.158 0.002 90.776 0.000 0.155
## Stst8rn (.29.) 0.083 0.001 64.523 0.000 0.081
## Stst11r (.30.) 0.308 0.002 167.978 0.000 0.305
## Stst12l (.31.) 0.276 0.002 164.669 0.000 0.272
## Stst13h (.32.) 0.219 0.002 119.737 0.000 0.215
## Stst14b (.33.) 0.266 0.002 162.259 0.000 0.263
## Stst15t (.34.) 0.295 0.002 166.014 0.000 0.291
## Stst16m (.35.) 0.280 0.002 165.201 0.000 0.276
## Stst19d (.36.) 0.110 0.002 61.465 0.000 0.107
## Stst26r (.37.) 0.263 0.002 159.575 0.000 0.260
## science =~
## Stst1vc (.38.) 0.181 0.002 100.735 0.000 0.177
## Stst6ph (.39.) 0.328 0.002 150.637 0.000 0.323
## Stst7bl (.40.) 0.273 0.003 103.861 0.000 0.268
## Stst8rn (.41.) 0.287 0.002 167.087 0.000 0.284
## Stst9lc (.42.) 0.431 0.002 188.288 0.000 0.427
## Stst10m (.43.) 0.382 0.002 200.174 0.000 0.379
## Stst13h (.44.) 0.100 0.003 37.439 0.000 0.094
## Stst28m (.45.) 0.207 0.002 123.046 0.000 0.204
## spatial =~
## Stst28m (.46.) 0.379 0.002 168.690 0.000 0.374
## Sts292D (.47.) 0.414 0.002 177.778 0.000 0.410
## Sts303D (.48.) 0.609 0.002 256.777 0.000 0.605
## Stst31b (.49.) 0.331 0.002 143.280 0.000 0.327
## Stst32r (.50.) 0.142 0.002 64.933 0.000 0.138
## Stst37b (.51.) 0.104 0.002 46.826 0.000 0.099
## g =~
## english (.52.) 1.898 0.012 154.221 0.000 1.874
## math (.53.) 1.976 0.015 131.983 0.000 1.946
## speed (.54.) 0.264 0.004 63.610 0.000 0.256
## info (.55.) 2.073 0.014 148.825 0.000 2.046
## science (.56.) 0.957 0.007 136.446 0.000 0.943
## spatial (.57.) 0.729 0.005 139.646 0.000 0.719
## ci.upper Std.lv Std.all
##
## 0.158 0.330 0.344
## 0.300 0.636 0.646
## 0.294 0.624 0.656
## 0.362 0.768 0.812
## 0.297 0.630 0.657
## 0.260 0.550 0.562
## 0.266 0.562 0.574
## 0.123 0.258 0.269
## 0.168 0.354 0.368
## 0.114 0.238 0.246
## 0.106 0.219 0.229
##
## 0.364 0.795 0.870
## 0.180 0.391 0.423
## 0.101 0.217 0.222
## 0.196 0.426 0.440
## 0.380 0.830 0.844
## 0.114 0.244 0.256
##
## 0.274 0.279 0.290
## 0.213 0.215 0.225
## 0.353 0.360 0.377
## 0.602 0.616 0.681
## 0.663 0.679 0.712
## 0.551 0.564 0.565
##
## 0.280 0.637 0.686
## 0.357 0.813 0.837
## 0.314 0.714 0.725
## 0.342 0.780 0.820
## 0.162 0.364 0.381
## 0.086 0.191 0.232
## 0.312 0.709 0.732
## 0.279 0.635 0.658
## 0.223 0.504 0.526
## 0.269 0.613 0.617
## 0.298 0.678 0.708
## 0.283 0.644 0.651
## 0.114 0.254 0.264
## 0.267 0.606 0.634
##
## 0.185 0.251 0.270
## 0.332 0.453 0.490
## 0.279 0.379 0.396
## 0.290 0.397 0.481
## 0.436 0.597 0.772
## 0.386 0.529 0.674
## 0.105 0.138 0.144
## 0.211 0.287 0.346
##
## 0.383 0.469 0.564
## 0.419 0.513 0.537
## 0.614 0.754 0.764
## 0.336 0.410 0.427
## 0.146 0.176 0.182
## 0.108 0.128 0.129
##
## 1.922 0.885 0.885
## 2.005 0.892 0.892
## 0.272 0.255 0.255
## 2.101 0.901 0.901
## 0.971 0.691 0.691
## 0.740 0.589 0.589
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .math 0.000 0.000
## .Stst19d (.100) -0.132 0.004 -36.538 0.000 -0.139
## .Stst20s (.101) -0.175 0.004 -47.970 0.000 -0.182
## .Stst21c (.102) -0.154 0.004 -42.595 0.000 -0.161
## .Stst22p (.103) -0.193 0.004 -50.631 0.000 -0.200
## .Stst23n (.104) -0.164 0.004 -44.821 0.000 -0.171
## .Stst24x (.105) -0.138 0.004 -37.717 0.000 -0.145
## .Stst25w (.106) -0.098 0.004 -26.261 0.000 -0.106
## .Stst26r (.107) -0.034 0.004 -8.599 0.000 -0.042
## .Stst31b (.108) 0.097 0.004 25.897 0.000 0.089
## .Stst32r (.109) 0.118 0.004 30.496 0.000 0.111
## .Stst34r (.110) -0.032 0.004 -8.606 0.000 -0.040
## .Stst5mt (.111) 0.187 0.004 49.404 0.000 0.179
## .Stst6ph 0.358 0.004 92.152 0.000 0.350
## .Stst33h (.113) 0.181 0.004 44.497 0.000 0.173
## .Sts292D (.114) 0.197 0.004 53.604 0.000 0.189
## .Stst35t (.115) -0.085 0.003 -24.473 0.000 -0.092
## .Stst36c (.116) -0.155 0.004 -42.443 0.000 -0.162
## .Stst37b (.117) -0.051 0.004 -13.866 0.000 -0.058
## .Stst1vc 0.189 0.004 50.215 0.000 0.181
## .Stst2lt (.119) 0.017 0.004 4.411 0.000 0.009
## .Stst3ms -0.121 0.004 -29.896 0.000 -0.128
## .Stst4sc 0.228 0.004 57.617 0.000 0.220
## .Stst7bl 0.243 0.004 61.806 0.000 0.235
## .Stst8rn (.123) 0.474 0.003 136.987 0.000 0.467
## .Stst11r (.124) 0.018 0.004 4.911 0.000 0.011
## .Stst12l 0.208 0.004 51.531 0.000 0.200
## .Stst13h -0.081 0.004 -19.852 0.000 -0.089
## .Stst14b (.127) 0.034 0.004 9.721 0.000 0.027
## .Stst15t -0.167 0.004 -42.900 0.000 -0.175
## .Stst16m 0.134 0.004 31.520 0.000 0.125
## .Stst9lc 0.522 0.003 156.854 0.000 0.516
## .Stst10m (.131) 0.647 0.003 198.860 0.000 0.640
## .Stst28m (.132) 0.555 0.003 158.666 0.000 0.548
## .Sts303D 0.206 0.004 50.237 0.000 0.198
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -0.125 -0.132 -0.137
## -0.168 -0.175 -0.177
## -0.147 -0.154 -0.162
## -0.185 -0.193 -0.204
## -0.157 -0.164 -0.171
## -0.131 -0.138 -0.141
## -0.091 -0.098 -0.100
## -0.027 -0.034 -0.036
## 0.104 0.097 0.100
## 0.126 0.118 0.122
## -0.025 -0.032 -0.034
## 0.194 0.187 0.204
## 0.365 0.358 0.387
## 0.189 0.181 0.184
## 0.204 0.197 0.206
## -0.078 -0.085 -0.094
## -0.148 -0.155 -0.162
## -0.044 -0.051 -0.051
## 0.196 0.189 0.203
## 0.025 0.017 0.017
## -0.113 -0.121 -0.122
## 0.236 0.228 0.240
## 0.251 0.243 0.254
## 0.481 0.474 0.573
## 0.025 0.018 0.018
## 0.216 0.208 0.216
## -0.073 -0.081 -0.084
## 0.041 0.034 0.035
## -0.159 -0.167 -0.174
## 0.142 0.134 0.135
## 0.529 0.522 0.675
## 0.653 0.647 0.823
## 0.562 0.555 0.668
## 0.214 0.206 0.209
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.465 0.003 161.823 0.000 0.459
## .Stest20spellng 0.566 0.004 161.428 0.000 0.559
## .Stest21cptlztn 0.515 0.003 163.230 0.000 0.509
## .Stest22puncttn 0.305 0.002 134.957 0.000 0.300
## .Stest23english 0.522 0.003 151.637 0.000 0.515
## .Stest24exprssn 0.657 0.004 156.894 0.000 0.649
## .Stst25wrdfnctn 0.403 0.003 148.717 0.000 0.398
## .Stst26rdngcmpr 0.232 0.002 136.857 0.000 0.229
## .Stst31bstrctrs 0.479 0.003 149.338 0.000 0.473
## .Stst32rthrsnng 0.385 0.002 157.560 0.000 0.380
## .Stst34rthcmptt 0.515 0.003 149.704 0.000 0.508
## .Stest5math 0.204 0.003 80.635 0.000 0.199
## .Stst6physclscn 0.277 0.002 137.953 0.000 0.273
## .Stst33hghschlm 0.278 0.002 120.927 0.000 0.273
## .Stst29vslztn2D 0.569 0.004 135.926 0.000 0.561
## .Stest35tblrdng 0.438 0.005 93.801 0.000 0.429
## .Stst36clrclchc 0.450 0.005 87.166 0.000 0.439
## .Stst37bjctnspc 0.639 0.005 138.193 0.000 0.630
## .Stest1vocab 0.195 0.001 144.210 0.000 0.193
## .Stest2literatr 0.283 0.002 152.743 0.000 0.280
## .Stest3music 0.460 0.003 168.018 0.000 0.455
## .Stest4soclstds 0.296 0.002 152.212 0.000 0.292
## .Stst7blgclscnc 0.465 0.003 159.895 0.000 0.460
## .Stest8aerontcs 0.394 0.003 119.541 0.000 0.388
## .Stest11art 0.435 0.003 166.764 0.000 0.430
## .Stest12law 0.527 0.003 171.132 0.000 0.521
## .Stest13health 0.559 0.003 174.471 0.000 0.553
## .Stest14bible 0.612 0.003 184.746 0.000 0.606
## .Stest15theater 0.459 0.003 171.150 0.000 0.454
## .Stest16mscllns 0.564 0.003 166.786 0.000 0.557
## .Stest9elctrncs 0.242 0.003 87.316 0.000 0.237
## .Stest10mechncs 0.337 0.002 138.969 0.000 0.333
## .Stst28mchnclrs 0.278 0.002 125.680 0.000 0.274
## .Stst30vslztn3D 0.405 0.004 105.599 0.000 0.397
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.470 0.465 0.503
## 0.573 0.566 0.583
## 0.521 0.515 0.570
## 0.309 0.305 0.341
## 0.528 0.522 0.568
## 0.665 0.657 0.685
## 0.408 0.403 0.420
## 0.235 0.232 0.254
## 0.486 0.479 0.518
## 0.389 0.385 0.411
## 0.522 0.515 0.565
## 0.209 0.204 0.244
## 0.281 0.277 0.324
## 0.282 0.278 0.287
## 0.578 0.569 0.624
## 0.447 0.438 0.536
## 0.460 0.450 0.494
## 0.648 0.639 0.642
## 0.198 0.195 0.227
## 0.287 0.283 0.300
## 0.466 0.460 0.474
## 0.300 0.296 0.327
## 0.471 0.465 0.510
## 0.401 0.394 0.577
## 0.440 0.435 0.464
## 0.533 0.527 0.567
## 0.565 0.559 0.608
## 0.619 0.612 0.620
## 0.464 0.459 0.499
## 0.570 0.564 0.577
## 0.248 0.242 0.405
## 0.342 0.337 0.546
## 0.283 0.278 0.403
## 0.412 0.405 0.416
## 1.000 0.217 0.217
## 1.000 0.204 0.204
## 1.000 0.935 0.935
## 1.000 0.189 0.189
## 1.000 0.522 0.522
## 1.000 0.653 0.653
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.154 0.002 76.944 0.000 0.150
## Stst20s (.p2.) 0.297 0.002 166.836 0.000 0.293
## Stst21c (.p3.) 0.291 0.002 170.922 0.000 0.287
## Stst22p (.p4.) 0.358 0.002 187.742 0.000 0.354
## Stst23n (.p5.) 0.293 0.002 168.905 0.000 0.290
## Stst24x (.p6.) 0.256 0.002 156.090 0.000 0.253
## Stst25w (.p7.) 0.262 0.002 141.165 0.000 0.258
## Stst26r (.p8.) 0.120 0.001 86.016 0.000 0.117
## Stst31b (.p9.) 0.165 0.001 121.146 0.000 0.162
## Stst32r (.10.) 0.111 0.002 67.141 0.000 0.107
## Stst34r (.11.) 0.102 0.002 55.652 0.000 0.098
## math =~
## Stst5mt (.12.) 0.359 0.002 159.969 0.000 0.355
## Stst6ph (.13.) 0.177 0.002 116.579 0.000 0.174
## Stst25w (.14.) 0.098 0.002 60.521 0.000 0.095
## Stst32r (.15.) 0.192 0.002 99.048 0.000 0.188
## Stst33h (.16.) 0.375 0.002 152.063 0.000 0.370
## Stst34r (.17.) 0.110 0.002 55.946 0.000 0.106
## speed =~
## Stst19d (.18.) 0.269 0.003 107.311 0.000 0.264
## Sts292D (.19.) 0.208 0.003 76.657 0.000 0.203
## Stst34r (.20.) 0.348 0.003 132.350 0.000 0.342
## Stst35t (.21.) 0.596 0.003 200.582 0.000 0.590
## Stst36c (.22.) 0.657 0.003 210.891 0.000 0.651
## Stst37b (.23.) 0.545 0.003 183.040 0.000 0.540
## info =~
## Stst1vc (.24.) 0.277 0.002 170.106 0.000 0.273
## Stst2lt (.25.) 0.353 0.002 179.698 0.000 0.349
## Stst3ms (.26.) 0.310 0.002 174.225 0.000 0.307
## Stst4sc (.27.) 0.339 0.002 187.601 0.000 0.335
## Stst7bl (.28.) 0.158 0.002 90.776 0.000 0.155
## Stst8rn (.29.) 0.083 0.001 64.523 0.000 0.081
## Stst11r (.30.) 0.308 0.002 167.978 0.000 0.305
## Stst12l (.31.) 0.276 0.002 164.669 0.000 0.272
## Stst13h (.32.) 0.219 0.002 119.737 0.000 0.215
## Stst14b (.33.) 0.266 0.002 162.259 0.000 0.263
## Stst15t (.34.) 0.295 0.002 166.014 0.000 0.291
## Stst16m (.35.) 0.280 0.002 165.201 0.000 0.276
## Stst19d (.36.) 0.110 0.002 61.465 0.000 0.107
## Stst26r (.37.) 0.263 0.002 159.575 0.000 0.260
## science =~
## Stst1vc (.38.) 0.181 0.002 100.735 0.000 0.177
## Stst6ph (.39.) 0.328 0.002 150.637 0.000 0.323
## Stst7bl (.40.) 0.273 0.003 103.861 0.000 0.268
## Stst8rn (.41.) 0.287 0.002 167.087 0.000 0.284
## Stst9lc (.42.) 0.431 0.002 188.288 0.000 0.427
## Stst10m (.43.) 0.382 0.002 200.174 0.000 0.379
## Stst13h (.44.) 0.100 0.003 37.439 0.000 0.094
## Stst28m (.45.) 0.207 0.002 123.046 0.000 0.204
## spatial =~
## Stst28m (.46.) 0.379 0.002 168.690 0.000 0.374
## Sts292D (.47.) 0.414 0.002 177.778 0.000 0.410
## Sts303D (.48.) 0.609 0.002 256.777 0.000 0.605
## Stst31b (.49.) 0.331 0.002 143.280 0.000 0.327
## Stst32r (.50.) 0.142 0.002 64.933 0.000 0.138
## Stst37b (.51.) 0.104 0.002 46.826 0.000 0.099
## g =~
## english (.52.) 1.898 0.012 154.221 0.000 1.874
## math (.53.) 1.976 0.015 131.983 0.000 1.946
## speed (.54.) 0.264 0.004 63.610 0.000 0.256
## info (.55.) 2.073 0.014 148.825 0.000 2.046
## science (.56.) 0.957 0.007 136.446 0.000 0.943
## spatial (.57.) 0.729 0.005 139.646 0.000 0.719
## ci.upper Std.lv Std.all
##
## 0.158 0.330 0.341
## 0.300 0.636 0.674
## 0.294 0.624 0.653
## 0.362 0.768 0.834
## 0.297 0.630 0.684
## 0.260 0.550 0.602
## 0.266 0.562 0.575
## 0.123 0.258 0.275
## 0.168 0.354 0.371
## 0.114 0.238 0.243
## 0.106 0.219 0.232
##
## 0.364 0.795 0.814
## 0.180 0.391 0.414
## 0.101 0.217 0.223
## 0.196 0.426 0.436
## 0.380 0.830 0.861
## 0.114 0.244 0.259
##
## 0.274 0.279 0.288
## 0.213 0.215 0.222
## 0.353 0.360 0.381
## 0.602 0.616 0.742
## 0.663 0.679 0.721
## 0.551 0.564 0.601
##
## 0.280 0.637 0.669
## 0.357 0.813 0.833
## 0.314 0.714 0.741
## 0.342 0.780 0.824
## 0.162 0.364 0.375
## 0.086 0.191 0.201
## 0.312 0.709 0.730
## 0.279 0.635 0.651
## 0.223 0.504 0.532
## 0.269 0.613 0.611
## 0.298 0.678 0.704
## 0.283 0.644 0.674
## 0.114 0.254 0.262
## 0.267 0.606 0.648
##
## 0.185 0.251 0.263
## 0.332 0.453 0.480
## 0.279 0.379 0.390
## 0.290 0.397 0.417
## 0.436 0.597 0.649
## 0.386 0.529 0.678
## 0.105 0.138 0.146
## 0.211 0.287 0.340
##
## 0.383 0.469 0.554
## 0.419 0.513 0.530
## 0.614 0.754 0.792
## 0.336 0.410 0.429
## 0.146 0.176 0.180
## 0.108 0.128 0.137
##
## 1.922 0.885 0.885
## 2.005 0.892 0.892
## 0.272 0.255 0.255
## 2.101 0.901 0.901
## 0.971 0.691 0.691
## 0.740 0.589 0.589
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .math 0.000 0.000
## .Stst19d (.100) -0.132 0.004 -36.538 0.000 -0.139
## .Stst20s (.101) -0.175 0.004 -47.970 0.000 -0.182
## .Stst21c (.102) -0.154 0.004 -42.595 0.000 -0.161
## .Stst22p (.103) -0.193 0.004 -50.631 0.000 -0.200
## .Stst23n (.104) -0.164 0.004 -44.821 0.000 -0.171
## .Stst24x (.105) -0.138 0.004 -37.717 0.000 -0.145
## .Stst25w (.106) -0.098 0.004 -26.261 0.000 -0.106
## .Stst26r (.107) -0.034 0.004 -8.599 0.000 -0.042
## .Stst31b (.108) 0.097 0.004 25.897 0.000 0.089
## .Stst32r (.109) 0.118 0.004 30.496 0.000 0.111
## .Stst34r (.110) -0.032 0.004 -8.606 0.000 -0.040
## .Stst5mt (.111) 0.187 0.004 49.404 0.000 0.179
## .Stst6ph 0.862 0.009 95.558 0.000 0.844
## .Stst33h (.113) 0.181 0.004 44.497 0.000 0.173
## .Sts292D (.114) 0.197 0.004 53.604 0.000 0.189
## .Stst35t (.115) -0.085 0.003 -24.473 0.000 -0.092
## .Stst36c (.116) -0.155 0.004 -42.443 0.000 -0.162
## .Stst37b (.117) -0.051 0.004 -13.866 0.000 -0.058
## .Stst1vc 0.450 0.007 62.182 0.000 0.436
## .Stst2lt (.119) 0.017 0.004 4.411 0.000 0.009
## .Stst3ms 0.145 0.004 33.298 0.000 0.136
## .Stst4sc -0.152 0.004 -34.615 0.000 -0.160
## .Stst7bl 0.664 0.010 66.717 0.000 0.645
## .Stst8rn (.123) 0.474 0.003 136.987 0.000 0.467
## .Stst11r (.124) 0.018 0.004 4.911 0.000 0.011
## .Stst12l -0.154 0.004 -35.848 0.000 -0.162
## .Stst13h 0.457 0.009 49.580 0.000 0.439
## .Stst14b (.127) 0.034 0.004 9.721 0.000 0.027
## .Stst15t 0.190 0.004 44.761 0.000 0.182
## .Stst16m -0.087 0.004 -20.470 0.000 -0.095
## .Stst9lc 0.893 0.008 114.505 0.000 0.878
## .Stst10m (.131) 0.647 0.003 198.860 0.000 0.640
## .Stst28m (.132) 0.555 0.003 158.666 0.000 0.548
## .Sts303D 0.457 0.007 66.440 0.000 0.443
## .english 2.087 0.015 137.087 0.000 2.058
## .speed 0.453 0.007 62.941 0.000 0.439
## .info 0.843 0.014 61.125 0.000 0.816
## .science -2.672 0.017 -155.136 0.000 -2.706
## .spatial -0.652 0.011 -59.478 0.000 -0.674
## g -0.379 0.007 -52.645 0.000 -0.393
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -0.125 -0.132 -0.136
## -0.168 -0.175 -0.185
## -0.147 -0.154 -0.161
## -0.185 -0.193 -0.209
## -0.157 -0.164 -0.178
## -0.131 -0.138 -0.151
## -0.091 -0.098 -0.101
## -0.027 -0.034 -0.037
## 0.104 0.097 0.101
## 0.126 0.118 0.121
## -0.025 -0.032 -0.034
## 0.194 0.187 0.191
## 0.880 0.862 0.913
## 0.189 0.181 0.188
## 0.204 0.197 0.203
## -0.078 -0.085 -0.102
## -0.148 -0.155 -0.164
## -0.044 -0.051 -0.054
## 0.464 0.450 0.473
## 0.025 0.017 0.017
## 0.153 0.145 0.150
## -0.143 -0.152 -0.160
## 0.684 0.664 0.684
## 0.481 0.474 0.497
## 0.025 0.018 0.018
## -0.145 -0.154 -0.157
## 0.475 0.457 0.483
## 0.041 0.034 0.034
## 0.199 0.190 0.197
## -0.078 -0.087 -0.091
## 0.908 0.893 0.971
## 0.653 0.647 0.829
## 0.562 0.555 0.656
## 0.470 0.457 0.480
## 2.117 0.973 0.973
## 0.467 0.438 0.438
## 0.870 0.366 0.366
## -2.638 -1.930 -1.930
## -0.631 -0.527 -0.527
## -0.365 -0.379 -0.379
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.479 0.003 165.053 0.000 0.473
## .Stest20spellng 0.487 0.003 164.428 0.000 0.482
## .Stest21cptlztn 0.522 0.003 163.372 0.000 0.516
## .Stest22puncttn 0.258 0.002 129.655 0.000 0.254
## .Stest23english 0.451 0.003 156.688 0.000 0.445
## .Stest24exprssn 0.533 0.004 146.384 0.000 0.526
## .Stst25wrdfnctn 0.398 0.003 145.065 0.000 0.392
## .Stst26rdngcmpr 0.193 0.001 139.179 0.000 0.190
## .Stst31bstrctrs 0.467 0.003 155.689 0.000 0.461
## .Stst32rthrsnng 0.404 0.002 164.565 0.000 0.399
## .Stst34rthcmptt 0.493 0.003 143.205 0.000 0.486
## .Stest5math 0.322 0.003 98.325 0.000 0.316
## .Stst6physclscn 0.314 0.002 144.552 0.000 0.310
## .Stst33hghschlm 0.241 0.002 115.479 0.000 0.237
## .Stst29vslztn2D 0.594 0.004 155.595 0.000 0.587
## .Stest35tblrdng 0.310 0.004 84.782 0.000 0.303
## .Stst36clrclchc 0.425 0.004 100.218 0.000 0.417
## .Stst37bjctnspc 0.526 0.004 139.343 0.000 0.519
## .Stest1vocab 0.239 0.002 149.834 0.000 0.236
## .Stest2literatr 0.291 0.002 157.202 0.000 0.287
## .Stest3music 0.420 0.003 166.020 0.000 0.415
## .Stest4soclstds 0.288 0.002 155.895 0.000 0.285
## .Stst7blgclscnc 0.496 0.003 170.880 0.000 0.491
## .Stest8aerontcs 0.619 0.003 182.610 0.000 0.612
## .Stest11art 0.442 0.003 168.946 0.000 0.437
## .Stest12law 0.549 0.003 176.901 0.000 0.543
## .Stest13health 0.538 0.003 172.925 0.000 0.532
## .Stest14bible 0.630 0.003 192.019 0.000 0.624
## .Stest15theater 0.469 0.003 172.834 0.000 0.463
## .Stest16mscllns 0.496 0.003 170.453 0.000 0.490
## .Stest9elctrncs 0.490 0.004 117.074 0.000 0.481
## .Stest10mechncs 0.329 0.002 146.584 0.000 0.324
## .Stst28mchnclrs 0.303 0.002 137.508 0.000 0.299
## .Stst30vslztn3D 0.338 0.003 100.879 0.000 0.331
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.484 0.479 0.511
## 0.493 0.487 0.546
## 0.528 0.522 0.573
## 0.262 0.258 0.304
## 0.456 0.451 0.532
## 0.540 0.533 0.638
## 0.403 0.398 0.417
## 0.196 0.193 0.220
## 0.473 0.467 0.512
## 0.409 0.404 0.423
## 0.500 0.493 0.554
## 0.328 0.322 0.337
## 0.319 0.314 0.352
## 0.245 0.241 0.259
## 0.602 0.594 0.634
## 0.317 0.310 0.449
## 0.434 0.425 0.480
## 0.533 0.526 0.596
## 0.242 0.239 0.264
## 0.294 0.291 0.306
## 0.425 0.420 0.451
## 0.292 0.288 0.322
## 0.502 0.496 0.526
## 0.626 0.619 0.682
## 0.447 0.442 0.468
## 0.555 0.549 0.577
## 0.544 0.538 0.599
## 0.637 0.630 0.627
## 0.474 0.469 0.505
## 0.502 0.496 0.545
## 0.498 0.490 0.579
## 0.333 0.329 0.540
## 0.308 0.303 0.424
## 0.344 0.338 0.373
## 1.000 0.217 0.217
## 1.000 0.204 0.204
## 1.000 0.935 0.935
## 1.000 0.189 0.189
## 1.000 0.522 0.522
## 1.000 0.653 0.653
## 1.000 1.000 1.000
standardizedSolution(chc.weak) # get the correct SEs for standardized solution
## lhs op rhs group
## 1 english =~ Stest19disguisedwords 1
## 2 english =~ Stest20spelling 1
## 3 english =~ Stest21capitalization 1
## 4 english =~ Stest22punctuation 1
## 5 english =~ Stest23english 1
## 6 english =~ Stest24expression 1
## 7 english =~ Stest25wordfunctions 1
## 8 english =~ Stest26readingcomprehension 1
## 9 english =~ Stest31abstractreasoning 1
## 10 english =~ Stest32arithreasoning 1
## 11 english =~ Stest34arithcomputation 1
## 12 math =~ Stest5math 1
## 13 math =~ Stest6physicalscience 1
## 14 math =~ Stest25wordfunctions 1
## 15 math =~ Stest32arithreasoning 1
## 16 math =~ Stest33highschoolmath 1
## 17 math =~ Stest34arithcomputation 1
## 18 speed =~ Stest19disguisedwords 1
## 19 speed =~ Stest29visualization2D 1
## 20 speed =~ Stest34arithcomputation 1
## 21 speed =~ Stest35tablereading 1
## 22 speed =~ Stest36clericalchecking 1
## 23 speed =~ Stest37objectinspection 1
## 24 info =~ Stest1vocab 1
## 25 info =~ Stest2literature 1
## 26 info =~ Stest3music 1
## 27 info =~ Stest4socialstudies 1
## 28 info =~ Stest7biologicalscience 1
## 29 info =~ Stest8aeronautics 1
## 30 info =~ Stest11art 1
## 31 info =~ Stest12law 1
## 32 info =~ Stest13health 1
## 33 info =~ Stest14bible 1
## 34 info =~ Stest15theater 1
## 35 info =~ Stest16miscellaneous 1
## 36 info =~ Stest19disguisedwords 1
## 37 info =~ Stest26readingcomprehension 1
## 38 science =~ Stest1vocab 1
## 39 science =~ Stest6physicalscience 1
## 40 science =~ Stest7biologicalscience 1
## 41 science =~ Stest8aeronautics 1
## 42 science =~ Stest9electronics 1
## 43 science =~ Stest10mechanics 1
## 44 science =~ Stest13health 1
## 45 science =~ Stest28mechanicalreasoning 1
## 46 spatial =~ Stest28mechanicalreasoning 1
## 47 spatial =~ Stest29visualization2D 1
## 48 spatial =~ Stest30visualization3D 1
## 49 spatial =~ Stest31abstractreasoning 1
## 50 spatial =~ Stest32arithreasoning 1
## 51 spatial =~ Stest37objectinspection 1
## 52 g =~ english 1
## 53 g =~ math 1
## 54 g =~ speed 1
## 55 g =~ info 1
## 56 g =~ science 1
## 57 g =~ spatial 1
## 58 math ~1 1
## 59 Stest19disguisedwords ~~ Stest19disguisedwords 1
## 60 Stest20spelling ~~ Stest20spelling 1
## 61 Stest21capitalization ~~ Stest21capitalization 1
## 62 Stest22punctuation ~~ Stest22punctuation 1
## 63 Stest23english ~~ Stest23english 1
## 64 Stest24expression ~~ Stest24expression 1
## 65 Stest25wordfunctions ~~ Stest25wordfunctions 1
## 66 Stest26readingcomprehension ~~ Stest26readingcomprehension 1
## 67 Stest31abstractreasoning ~~ Stest31abstractreasoning 1
## 68 Stest32arithreasoning ~~ Stest32arithreasoning 1
## 69 Stest34arithcomputation ~~ Stest34arithcomputation 1
## 70 Stest5math ~~ Stest5math 1
## 71 Stest6physicalscience ~~ Stest6physicalscience 1
## 72 Stest33highschoolmath ~~ Stest33highschoolmath 1
## 73 Stest29visualization2D ~~ Stest29visualization2D 1
## 74 Stest35tablereading ~~ Stest35tablereading 1
## 75 Stest36clericalchecking ~~ Stest36clericalchecking 1
## 76 Stest37objectinspection ~~ Stest37objectinspection 1
## 77 Stest1vocab ~~ Stest1vocab 1
## 78 Stest2literature ~~ Stest2literature 1
## 79 Stest3music ~~ Stest3music 1
## 80 Stest4socialstudies ~~ Stest4socialstudies 1
## 81 Stest7biologicalscience ~~ Stest7biologicalscience 1
## 82 Stest8aeronautics ~~ Stest8aeronautics 1
## 83 Stest11art ~~ Stest11art 1
## 84 Stest12law ~~ Stest12law 1
## 85 Stest13health ~~ Stest13health 1
## 86 Stest14bible ~~ Stest14bible 1
## 87 Stest15theater ~~ Stest15theater 1
## 88 Stest16miscellaneous ~~ Stest16miscellaneous 1
## 89 Stest9electronics ~~ Stest9electronics 1
## 90 Stest10mechanics ~~ Stest10mechanics 1
## label est.std se z pvalue ci.lower ci.upper
## 1 .p1. 0.344 0.004 87.556 0 0.336 0.352
## 2 .p2. 0.646 0.002 329.357 0 0.642 0.650
## 3 .p3. 0.656 0.002 324.118 0 0.652 0.660
## 4 .p4. 0.812 0.001 594.886 0 0.809 0.815
## 5 .p5. 0.657 0.002 325.414 0 0.653 0.661
## 6 .p6. 0.562 0.002 249.088 0 0.557 0.566
## 7 .p7. 0.574 0.003 191.431 0 0.568 0.580
## 8 .p8. 0.269 0.003 94.989 0 0.264 0.275
## 9 .p9. 0.368 0.002 149.720 0 0.364 0.373
## 10 .p10. 0.246 0.003 73.547 0 0.239 0.252
## 11 .p11. 0.229 0.004 60.533 0 0.222 0.236
## 12 .p12. 0.870 0.001 670.698 0 0.867 0.872
## 13 .p13. 0.423 0.003 129.642 0 0.417 0.430
## 14 .p14. 0.222 0.003 68.880 0 0.216 0.228
## 15 .p15. 0.440 0.004 106.503 0 0.432 0.448
## 16 .p16. 0.844 0.001 612.252 0 0.842 0.847
## 17 .p17. 0.256 0.004 67.505 0 0.248 0.263
## 18 .p18. 0.290 0.003 109.893 0 0.285 0.295
## 19 .p19. 0.225 0.003 77.064 0 0.220 0.231
## 20 .p20. 0.377 0.003 138.231 0 0.371 0.382
## 21 .p21. 0.681 0.003 232.511 0 0.676 0.687
## 22 .p22. 0.712 0.003 241.061 0 0.706 0.717
## 23 .p23. 0.565 0.003 204.620 0 0.560 0.571
## 24 .p24. 0.686 0.002 288.925 0 0.681 0.690
## 25 .p25. 0.837 0.001 758.174 0 0.834 0.839
## 26 .p26. 0.725 0.002 462.982 0 0.722 0.728
## 27 .p27. 0.820 0.001 685.147 0 0.818 0.822
## 28 .p28. 0.381 0.004 104.106 0 0.374 0.388
## 29 .p29. 0.232 0.003 76.668 0 0.226 0.238
## 30 .p30. 0.732 0.002 460.449 0 0.729 0.735
## 31 .p31. 0.658 0.002 340.748 0 0.654 0.662
## 32 .p32. 0.526 0.003 151.028 0 0.519 0.533
## 33 .p33. 0.617 0.002 312.009 0 0.613 0.621
## 34 .p34. 0.708 0.002 428.918 0 0.704 0.711
## 35 .p35. 0.651 0.002 330.294 0 0.647 0.655
## 36 .p36. 0.264 0.004 68.273 0 0.256 0.271
## 37 .p37. 0.634 0.003 232.044 0 0.628 0.639
## 38 .p38. 0.270 0.003 98.702 0 0.265 0.275
## 39 .p39. 0.490 0.003 150.464 0 0.484 0.497
## 40 .p40. 0.396 0.004 102.945 0 0.389 0.404
## 41 .p41. 0.481 0.003 170.486 0 0.475 0.486
## 42 .p42. 0.772 0.002 344.771 0 0.767 0.776
## 43 .p43. 0.674 0.002 304.109 0 0.669 0.678
## 44 .p44. 0.144 0.004 37.380 0 0.136 0.151
## 45 .p45. 0.346 0.003 131.820 0 0.340 0.351
## 46 .p46. 0.564 0.003 200.152 0 0.559 0.570
## 47 .p47. 0.537 0.003 209.181 0 0.532 0.542
## 48 .p48. 0.764 0.002 341.383 0 0.760 0.769
## 49 .p49. 0.427 0.003 156.884 0 0.421 0.432
## 50 .p50. 0.182 0.003 64.851 0 0.176 0.187
## 51 .p51. 0.129 0.003 48.738 0 0.123 0.134
## 52 .p52. 0.885 0.001 709.597 0 0.882 0.887
## 53 .p53. 0.892 0.001 647.210 0 0.890 0.895
## 54 .p54. 0.255 0.004 68.049 0 0.248 0.263
## 55 .p55. 0.901 0.001 788.677 0 0.898 0.903
## 56 .p56. 0.691 0.003 261.468 0 0.686 0.697
## 57 .p57. 0.589 0.003 213.940 0 0.584 0.595
## 58 0.000 0.000 NA NA 0.000 0.000
## 59 0.503 0.002 207.355 0 0.498 0.508
## 60 0.583 0.003 230.131 0 0.578 0.588
## 61 0.570 0.003 214.605 0 0.565 0.575
## 62 0.341 0.002 153.742 0 0.336 0.345
## 63 0.568 0.003 214.120 0 0.563 0.573
## 64 0.685 0.003 270.370 0 0.680 0.690
## 65 0.420 0.002 194.523 0 0.416 0.424
## 66 0.254 0.002 145.256 0 0.250 0.257
## 67 0.518 0.003 194.922 0 0.513 0.524
## 68 0.411 0.002 185.078 0 0.407 0.416
## 69 0.565 0.003 205.744 0 0.560 0.570
## 70 0.244 0.002 108.118 0 0.239 0.248
## 71 0.324 0.002 148.172 0 0.320 0.328
## 72 0.287 0.002 123.307 0 0.283 0.292
## 73 0.624 0.003 209.165 0 0.618 0.630
## 74 0.536 0.004 134.128 0 0.528 0.544
## 75 0.494 0.004 117.448 0 0.485 0.502
## 76 0.642 0.003 205.124 0 0.636 0.648
## 77 0.227 0.001 153.215 0 0.224 0.230
## 78 0.300 0.002 162.562 0 0.297 0.304
## 79 0.474 0.002 208.783 0 0.470 0.479
## 80 0.327 0.002 166.753 0 0.324 0.331
## 81 0.510 0.002 206.471 0 0.505 0.515
## 82 0.577 0.003 201.292 0 0.571 0.582
## 83 0.464 0.002 199.119 0 0.459 0.468
## 84 0.567 0.003 222.897 0 0.562 0.572
## 85 0.608 0.003 233.247 0 0.603 0.614
## 86 0.620 0.002 254.207 0 0.615 0.624
## 87 0.499 0.002 213.932 0 0.495 0.504
## 88 0.577 0.003 224.854 0 0.572 0.582
## 89 0.405 0.003 117.195 0 0.398 0.411
## 90 0.546 0.003 183.133 0 0.541 0.552
## [ reached 'max' / getOption("max.print") -- omitted 188 rows ]
# PAR.boot<- bootstrapLavaan(chc.weak, R=500, type="ordinary", FUN="coef") # bootstrap model parameters, unstandardized
# describeBy(PAR.boot) # check sd column for the standard errors, as sd is the variability of the parameter estimates across the bootstrap samples
tests<-lavTestLRT(configural, metric, scalar2, chc.hof, chc.weak)
## Warning: lavaan->lavTestLRT():
## Some restricted models fit better than less restricted models;
## either these models are not nested, or the less restricted model
## failed to reach a global optimum.Smallest difference =
## -4.58825961686671e-05.
Td=tests[2:5,"Chisq diff"]
Td
## [1] 8301.791253 8648.161605 2258.807556 -1.083289
dfd=tests[2:5,"Df diff"]
dfd
## [1] 50 16 7 1
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
## Warning in sqrt((ld) * G/(N - G)): NaNs produced
RMSEAD
## [1] 0.04818624 0.08712318 0.06727451 NaN
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04731516 0.04906278
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.08558483 0.08867099
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.06495571 0.06962262
RMSEA.CI(T=Td[4],df=dfd[4],N=N,G=2)
## [1] NA NA
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 0 0 0 0
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 1 1 1 0
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 1 1 0 0
round(pvals(T=Td[4],df=dfd[4],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 0 0 0 0 0 0
tests<-lavTestLRT(configural, metric, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 8301.791 56749.023
dfd=tests[2:3,"Df diff"]
dfd
## [1] 50 27
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04818624 0.17192059
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04731516 0.04906278
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.170734 0.173109
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 0 0 0 0
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 1 1 1 1
tests<-lavTestLRT(configural, metric, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 8301.791 8648.162 13115.754
dfd=tests[2:4,"Df diff"]
dfd
## [1] 50 16 34
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04818624 0.08712318 0.07357452
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04731516 0.04906278
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.08558483 0.08867099
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.07251832 0.07463582
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 0 0 0 0
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 1 1 1 0
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 1 1 0 0
hof.age <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning + Stest34arithcomputation
math =~ Stest5math + Stest6physicalscience + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest13health + Stest28mechanicalreasoning
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest37objectinspection
g =~ english + math + speed + info + science + spatial
math ~ 0*1
g ~ age
'
hof.age2 <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning + Stest34arithcomputation
math =~ Stest5math + Stest6physicalscience + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest13health + Stest28mechanicalreasoning
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest37objectinspection
g =~ english + math + speed + info + science + spatial
math ~ 0*1
g ~ age + age2
'
sem.age<-sem(hof.age, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("Stest4socialstudies~1", "Stest15theater~1", "Stest12law~1", "Stest3music~1", "Stest16miscellaneous~1", "Stest13health~1", "Stest6physicalscience~1", "Stest9electronics~1", "Stest30visualization3D~1", "Stest7biologicalscience~1", "Stest1vocab~1"))
fitMeasures(sem.age, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 190142.156 1148.000 0.000 0.929 0.049
## srmr ecvi aic bic
## 0.059 1.370 10367701.113 10369453.098
Mc(sem.age)
## [1] 0.5068294
summary(sem.age, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 98 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 258
## Number of equality constraints 80
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 190142.156 166656.472
## Degrees of freedom 1148 1148
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.141
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 104379.861 91487.231
## 1 85762.294 75169.240
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.154 0.002 76.691 0.000 0.150
## Stst20s (.p2.) 0.296 0.002 166.725 0.000 0.293
## Stst21c (.p3.) 0.290 0.002 170.577 0.000 0.287
## Stst22p (.p4.) 0.357 0.002 187.331 0.000 0.354
## Stst23n (.p5.) 0.293 0.002 168.728 0.000 0.290
## Stst24x (.p6.) 0.256 0.002 156.137 0.000 0.253
## Stst25w (.p7.) 0.261 0.002 140.928 0.000 0.258
## Stst26r (.p8.) 0.120 0.001 85.815 0.000 0.117
## Stst31b (.p9.) 0.165 0.001 120.917 0.000 0.162
## Stst32r (.10.) 0.111 0.002 67.408 0.000 0.108
## Stst34r (.11.) 0.101 0.002 55.614 0.000 0.098
## math =~
## Stst5mt (.12.) 0.364 0.002 162.638 0.000 0.359
## Stst6ph (.13.) 0.178 0.002 116.590 0.000 0.175
## Stst25w (.14.) 0.100 0.002 60.934 0.000 0.097
## Stst32r (.15.) 0.194 0.002 99.608 0.000 0.191
## Stst33h (.16.) 0.379 0.002 154.633 0.000 0.375
## Stst34r (.17.) 0.112 0.002 56.584 0.000 0.108
## speed =~
## Stst19d (.18.) 0.269 0.003 107.123 0.000 0.264
## Sts292D (.19.) 0.208 0.003 76.622 0.000 0.203
## Stst34r (.20.) 0.347 0.003 132.259 0.000 0.342
## Stst35t (.21.) 0.596 0.003 200.653 0.000 0.590
## Stst36c (.22.) 0.656 0.003 210.625 0.000 0.650
## Stst37b (.23.) 0.545 0.003 182.965 0.000 0.539
## info =~
## Stst1vc (.24.) 0.274 0.002 168.317 0.000 0.271
## Stst2lt (.25.) 0.350 0.002 177.591 0.000 0.346
## Stst3ms (.26.) 0.308 0.002 171.568 0.000 0.304
## Stst4sc (.27.) 0.336 0.002 184.570 0.000 0.333
## Stst7bl (.28.) 0.157 0.002 90.364 0.000 0.153
## Stst8rn (.29.) 0.082 0.001 63.977 0.000 0.080
## Stst11r (.30.) 0.306 0.002 165.451 0.000 0.302
## Stst12l (.31.) 0.274 0.002 163.086 0.000 0.270
## Stst13h (.32.) 0.217 0.002 118.986 0.000 0.214
## Stst14b (.33.) 0.264 0.002 160.186 0.000 0.261
## Stst15t (.34.) 0.292 0.002 163.880 0.000 0.289
## Stst16m (.35.) 0.277 0.002 162.688 0.000 0.274
## Stst19d (.36.) 0.109 0.002 60.902 0.000 0.105
## Stst26r (.37.) 0.261 0.002 158.092 0.000 0.258
## science =~
## Stst1vc (.38.) 0.181 0.002 100.530 0.000 0.177
## Stst6ph (.39.) 0.328 0.002 150.962 0.000 0.323
## Stst7bl (.40.) 0.273 0.003 103.814 0.000 0.268
## Stst8rn (.41.) 0.287 0.002 167.202 0.000 0.284
## Stst9lc (.42.) 0.431 0.002 188.225 0.000 0.426
## Stst10m (.43.) 0.382 0.002 200.887 0.000 0.378
## Stst13h (.44.) 0.099 0.003 37.380 0.000 0.094
## Stst28m (.45.) 0.207 0.002 123.122 0.000 0.204
## spatial =~
## Stst28m (.46.) 0.379 0.002 168.547 0.000 0.374
## Sts292D (.47.) 0.414 0.002 177.611 0.000 0.410
## Sts303D (.48.) 0.610 0.002 257.092 0.000 0.605
## Stst31b (.49.) 0.331 0.002 143.163 0.000 0.327
## Stst32r (.50.) 0.142 0.002 65.190 0.000 0.138
## Stst37b (.51.) 0.104 0.002 46.797 0.000 0.099
## g =~
## english (.52.) 1.884 0.012 154.017 0.000 1.860
## math (.53.) 1.930 0.015 132.353 0.000 1.901
## speed (.54.) 0.264 0.004 64.118 0.000 0.256
## info (.55.) 2.076 0.014 147.746 0.000 2.049
## science (.56.) 0.951 0.007 137.193 0.000 0.938
## spatial (.57.) 0.722 0.005 139.301 0.000 0.712
## ci.upper Std.lv Std.all
##
## 0.158 0.331 0.344
## 0.300 0.637 0.646
## 0.294 0.624 0.656
## 0.361 0.767 0.812
## 0.297 0.630 0.657
## 0.260 0.551 0.562
## 0.265 0.561 0.573
## 0.123 0.257 0.269
## 0.168 0.354 0.368
## 0.114 0.238 0.246
## 0.105 0.218 0.228
##
## 0.368 0.796 0.870
## 0.181 0.391 0.422
## 0.103 0.218 0.223
## 0.198 0.425 0.440
## 0.384 0.830 0.845
## 0.116 0.245 0.257
##
## 0.274 0.278 0.290
## 0.213 0.215 0.225
## 0.352 0.359 0.376
## 0.602 0.616 0.682
## 0.662 0.679 0.712
## 0.551 0.564 0.565
##
## 0.277 0.637 0.685
## 0.354 0.813 0.837
## 0.311 0.714 0.725
## 0.340 0.780 0.820
## 0.160 0.364 0.380
## 0.085 0.191 0.231
## 0.309 0.709 0.732
## 0.277 0.635 0.659
## 0.221 0.504 0.526
## 0.267 0.613 0.617
## 0.296 0.679 0.708
## 0.281 0.643 0.651
## 0.112 0.253 0.263
## 0.264 0.606 0.634
##
## 0.184 0.251 0.270
## 0.332 0.454 0.491
## 0.278 0.379 0.396
## 0.290 0.398 0.481
## 0.435 0.597 0.771
## 0.386 0.530 0.674
## 0.105 0.138 0.144
## 0.211 0.287 0.346
##
## 0.383 0.469 0.564
## 0.419 0.513 0.537
## 0.614 0.754 0.765
## 0.336 0.410 0.426
## 0.147 0.176 0.182
## 0.108 0.128 0.128
##
## 1.908 0.885 0.885
## 1.958 0.890 0.890
## 0.272 0.257 0.257
## 2.104 0.902 0.902
## 0.965 0.693 0.693
## 0.732 0.589 0.589
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.109 0.004 29.451 0.000 0.102
## ci.upper Std.lv Std.all
##
## 0.117 0.108 0.134
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .math 0.000 0.000
## .Stst19d (.102) -0.124 0.004 -34.200 0.000 -0.131
## .Stst20s (.103) -0.168 0.004 -46.001 0.000 -0.175
## .Stst21c (.104) -0.146 0.004 -40.551 0.000 -0.154
## .Stst22p (.105) -0.184 0.004 -48.026 0.000 -0.191
## .Stst23n (.106) -0.157 0.004 -42.836 0.000 -0.164
## .Stst24x (.107) -0.132 0.004 -36.184 0.000 -0.139
## .Stst25w (.108) -0.089 0.004 -23.605 0.000 -0.096
## .Stst26r (.109) -0.024 0.004 -6.034 0.000 -0.032
## .Stst31b (.110) 0.104 0.004 27.767 0.000 0.097
## .Stst32r (.111) 0.127 0.004 32.680 0.000 0.120
## .Stst34r (.112) -0.026 0.004 -6.763 0.000 -0.033
## .Stst5mt (.113) 0.196 0.004 51.499 0.000 0.189
## .Stst6ph 0.367 0.004 93.130 0.000 0.359
## .Stst33h (.115) 0.191 0.004 46.402 0.000 0.183
## .Sts292D (.116) 0.201 0.004 54.826 0.000 0.194
## .Stst35t (.117) -0.083 0.003 -24.008 0.000 -0.090
## .Stst36c (.118) -0.153 0.004 -41.925 0.000 -0.160
## .Stst37b (.119) -0.048 0.004 -13.111 0.000 -0.055
## .Stst1vc 0.199 0.004 52.733 0.000 0.191
## .Stst2lt (.121) 0.027 0.004 6.904 0.000 0.019
## .Stst3ms -0.112 0.004 -27.615 0.000 -0.120
## .Stst4sc 0.237 0.004 59.768 0.000 0.230
## .Stst7bl 0.251 0.004 63.899 0.000 0.243
## .Stst8rn (.125) 0.480 0.003 138.442 0.000 0.473
## .Stst11r (.126) 0.026 0.004 7.209 0.000 0.019
## .Stst12l 0.216 0.004 53.685 0.000 0.208
## .Stst13h -0.074 0.004 -18.131 0.000 -0.082
## .Stst14b (.129) 0.042 0.004 11.731 0.000 0.035
## .Stst15t -0.159 0.004 -40.721 0.000 -0.167
## .Stst16m 0.141 0.004 33.162 0.000 0.133
## .Stst9lc 0.528 0.003 158.962 0.000 0.521
## .Stst10m (.133) 0.652 0.003 202.387 0.000 0.645
## .Stst28m (.134) 0.561 0.003 160.704 0.000 0.554
## .Sts303D 0.212 0.004 51.734 0.000 0.204
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -0.117 -0.124 -0.129
## -0.160 -0.168 -0.170
## -0.139 -0.146 -0.154
## -0.176 -0.184 -0.194
## -0.149 -0.157 -0.163
## -0.125 -0.132 -0.134
## -0.082 -0.089 -0.091
## -0.016 -0.024 -0.025
## 0.111 0.104 0.108
## 0.135 0.127 0.132
## -0.018 -0.026 -0.027
## 0.204 0.196 0.214
## 0.374 0.367 0.396
## 0.199 0.191 0.194
## 0.208 0.201 0.211
## -0.076 -0.083 -0.092
## -0.145 -0.153 -0.160
## -0.041 -0.048 -0.048
## 0.206 0.199 0.214
## 0.034 0.027 0.027
## -0.104 -0.112 -0.114
## 0.245 0.237 0.250
## 0.258 0.251 0.262
## 0.487 0.480 0.580
## 0.033 0.026 0.027
## 0.224 0.216 0.224
## -0.066 -0.074 -0.077
## 0.049 0.042 0.042
## -0.151 -0.159 -0.166
## 0.149 0.141 0.143
## 0.534 0.528 0.682
## 0.658 0.652 0.829
## 0.568 0.561 0.675
## 0.220 0.212 0.215
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.465 0.003 161.850 0.000 0.459
## .Stest20spellng 0.566 0.004 161.414 0.000 0.559
## .Stest21cptlztn 0.515 0.003 163.252 0.000 0.509
## .Stest22puncttn 0.305 0.002 135.052 0.000 0.301
## .Stest23english 0.521 0.003 151.580 0.000 0.515
## .Stest24exprssn 0.656 0.004 156.864 0.000 0.648
## .Stst25wrdfnctn 0.403 0.003 148.817 0.000 0.398
## .Stst26rdngcmpr 0.232 0.002 136.853 0.000 0.229
## .Stst31bstrctrs 0.480 0.003 149.348 0.000 0.473
## .Stst32rthrsnng 0.385 0.002 157.527 0.000 0.380
## .Stst34rthcmptt 0.515 0.003 149.684 0.000 0.508
## .Stest5math 0.204 0.003 80.215 0.000 0.199
## .Stst6physclscn 0.278 0.002 137.990 0.000 0.274
## .Stst33hghschlm 0.277 0.002 120.465 0.000 0.273
## .Stst29vslztn2D 0.570 0.004 135.942 0.000 0.561
## .Stest35tblrdng 0.438 0.005 93.770 0.000 0.429
## .Stst36clrclchc 0.450 0.005 87.188 0.000 0.440
## .Stst37bjctnspc 0.639 0.005 138.199 0.000 0.630
## .Stest1vocab 0.195 0.001 144.238 0.000 0.193
## .Stest2literatr 0.283 0.002 152.664 0.000 0.279
## .Stest3music 0.461 0.003 168.072 0.000 0.455
## .Stest4soclstds 0.296 0.002 152.276 0.000 0.293
## .Stst7blgclscnc 0.465 0.003 159.887 0.000 0.460
## .Stest8aerontcs 0.394 0.003 119.540 0.000 0.388
## .Stest11art 0.436 0.003 166.820 0.000 0.430
## .Stest12law 0.527 0.003 171.108 0.000 0.521
## .Stest13health 0.559 0.003 174.493 0.000 0.553
## .Stest14bible 0.612 0.003 184.760 0.000 0.606
## .Stest15theater 0.459 0.003 171.179 0.000 0.454
## .Stest16mscllns 0.564 0.003 166.838 0.000 0.558
## .Stest9elctrncs 0.243 0.003 87.415 0.000 0.237
## .Stest10mechncs 0.337 0.002 138.930 0.000 0.332
## .Stst28mchnclrs 0.278 0.002 125.672 0.000 0.274
## .Stst30vslztn3D 0.404 0.004 105.434 0.000 0.397
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.471 0.465 0.503
## 0.573 0.566 0.582
## 0.522 0.515 0.570
## 0.310 0.305 0.341
## 0.528 0.521 0.568
## 0.665 0.656 0.684
## 0.409 0.403 0.420
## 0.235 0.232 0.253
## 0.486 0.480 0.519
## 0.389 0.385 0.411
## 0.521 0.515 0.564
## 0.208 0.204 0.243
## 0.282 0.278 0.325
## 0.282 0.277 0.287
## 0.578 0.570 0.624
## 0.447 0.438 0.535
## 0.460 0.450 0.494
## 0.648 0.639 0.642
## 0.198 0.195 0.226
## 0.287 0.283 0.300
## 0.466 0.461 0.474
## 0.300 0.296 0.327
## 0.471 0.465 0.509
## 0.401 0.394 0.577
## 0.441 0.436 0.464
## 0.533 0.527 0.566
## 0.565 0.559 0.608
## 0.619 0.612 0.620
## 0.464 0.459 0.499
## 0.571 0.564 0.577
## 0.248 0.243 0.405
## 0.342 0.337 0.546
## 0.283 0.278 0.403
## 0.412 0.404 0.415
## 1.000 0.217 0.217
## 1.000 0.209 0.209
## 1.000 0.934 0.934
## 1.000 0.186 0.186
## 1.000 0.520 0.520
## 1.000 0.653 0.653
## 1.000 0.982 0.982
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.154 0.002 76.691 0.000 0.150
## Stst20s (.p2.) 0.296 0.002 166.725 0.000 0.293
## Stst21c (.p3.) 0.290 0.002 170.577 0.000 0.287
## Stst22p (.p4.) 0.357 0.002 187.331 0.000 0.354
## Stst23n (.p5.) 0.293 0.002 168.728 0.000 0.290
## Stst24x (.p6.) 0.256 0.002 156.137 0.000 0.253
## Stst25w (.p7.) 0.261 0.002 140.928 0.000 0.258
## Stst26r (.p8.) 0.120 0.001 85.815 0.000 0.117
## Stst31b (.p9.) 0.165 0.001 120.917 0.000 0.162
## Stst32r (.10.) 0.111 0.002 67.408 0.000 0.108
## Stst34r (.11.) 0.101 0.002 55.614 0.000 0.098
## math =~
## Stst5mt (.12.) 0.364 0.002 162.638 0.000 0.359
## Stst6ph (.13.) 0.178 0.002 116.590 0.000 0.175
## Stst25w (.14.) 0.100 0.002 60.934 0.000 0.097
## Stst32r (.15.) 0.194 0.002 99.608 0.000 0.191
## Stst33h (.16.) 0.379 0.002 154.633 0.000 0.375
## Stst34r (.17.) 0.112 0.002 56.584 0.000 0.108
## speed =~
## Stst19d (.18.) 0.269 0.003 107.123 0.000 0.264
## Sts292D (.19.) 0.208 0.003 76.622 0.000 0.203
## Stst34r (.20.) 0.347 0.003 132.259 0.000 0.342
## Stst35t (.21.) 0.596 0.003 200.653 0.000 0.590
## Stst36c (.22.) 0.656 0.003 210.625 0.000 0.650
## Stst37b (.23.) 0.545 0.003 182.965 0.000 0.539
## info =~
## Stst1vc (.24.) 0.274 0.002 168.317 0.000 0.271
## Stst2lt (.25.) 0.350 0.002 177.591 0.000 0.346
## Stst3ms (.26.) 0.308 0.002 171.568 0.000 0.304
## Stst4sc (.27.) 0.336 0.002 184.570 0.000 0.333
## Stst7bl (.28.) 0.157 0.002 90.364 0.000 0.153
## Stst8rn (.29.) 0.082 0.001 63.977 0.000 0.080
## Stst11r (.30.) 0.306 0.002 165.451 0.000 0.302
## Stst12l (.31.) 0.274 0.002 163.086 0.000 0.270
## Stst13h (.32.) 0.217 0.002 118.986 0.000 0.214
## Stst14b (.33.) 0.264 0.002 160.186 0.000 0.261
## Stst15t (.34.) 0.292 0.002 163.880 0.000 0.289
## Stst16m (.35.) 0.277 0.002 162.688 0.000 0.274
## Stst19d (.36.) 0.109 0.002 60.902 0.000 0.105
## Stst26r (.37.) 0.261 0.002 158.092 0.000 0.258
## science =~
## Stst1vc (.38.) 0.181 0.002 100.530 0.000 0.177
## Stst6ph (.39.) 0.328 0.002 150.962 0.000 0.323
## Stst7bl (.40.) 0.273 0.003 103.814 0.000 0.268
## Stst8rn (.41.) 0.287 0.002 167.202 0.000 0.284
## Stst9lc (.42.) 0.431 0.002 188.225 0.000 0.426
## Stst10m (.43.) 0.382 0.002 200.887 0.000 0.378
## Stst13h (.44.) 0.099 0.003 37.380 0.000 0.094
## Stst28m (.45.) 0.207 0.002 123.122 0.000 0.204
## spatial =~
## Stst28m (.46.) 0.379 0.002 168.547 0.000 0.374
## Sts292D (.47.) 0.414 0.002 177.611 0.000 0.410
## Sts303D (.48.) 0.610 0.002 257.092 0.000 0.605
## Stst31b (.49.) 0.331 0.002 143.163 0.000 0.327
## Stst32r (.50.) 0.142 0.002 65.190 0.000 0.138
## Stst37b (.51.) 0.104 0.002 46.797 0.000 0.099
## g =~
## english (.52.) 1.884 0.012 154.017 0.000 1.860
## math (.53.) 1.930 0.015 132.353 0.000 1.901
## speed (.54.) 0.264 0.004 64.118 0.000 0.256
## info (.55.) 2.076 0.014 147.746 0.000 2.049
## science (.56.) 0.951 0.007 137.193 0.000 0.938
## spatial (.57.) 0.722 0.005 139.301 0.000 0.712
## ci.upper Std.lv Std.all
##
## 0.158 0.331 0.342
## 0.300 0.637 0.674
## 0.294 0.624 0.653
## 0.361 0.767 0.834
## 0.297 0.630 0.684
## 0.260 0.550 0.602
## 0.265 0.561 0.575
## 0.123 0.257 0.275
## 0.168 0.354 0.371
## 0.114 0.238 0.244
## 0.105 0.218 0.231
##
## 0.368 0.795 0.814
## 0.181 0.390 0.413
## 0.103 0.218 0.223
## 0.198 0.425 0.435
## 0.384 0.830 0.861
## 0.116 0.245 0.260
##
## 0.274 0.278 0.287
## 0.213 0.215 0.222
## 0.352 0.359 0.381
## 0.602 0.616 0.742
## 0.662 0.679 0.721
## 0.551 0.564 0.600
##
## 0.277 0.636 0.669
## 0.354 0.813 0.834
## 0.311 0.714 0.740
## 0.340 0.780 0.824
## 0.160 0.363 0.374
## 0.085 0.191 0.200
## 0.309 0.709 0.729
## 0.277 0.635 0.651
## 0.221 0.504 0.532
## 0.267 0.613 0.611
## 0.296 0.678 0.704
## 0.281 0.643 0.674
## 0.112 0.253 0.261
## 0.264 0.606 0.648
##
## 0.184 0.250 0.263
## 0.332 0.454 0.481
## 0.278 0.379 0.390
## 0.290 0.398 0.417
## 0.435 0.597 0.649
## 0.386 0.530 0.679
## 0.105 0.138 0.146
## 0.211 0.287 0.340
##
## 0.383 0.469 0.554
## 0.419 0.513 0.530
## 0.614 0.754 0.792
## 0.336 0.410 0.429
## 0.147 0.176 0.180
## 0.108 0.128 0.136
##
## 1.908 0.885 0.885
## 1.958 0.889 0.889
## 0.272 0.257 0.257
## 2.104 0.902 0.902
## 0.965 0.692 0.692
## 0.732 0.589 0.589
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.110 0.004 31.374 0.000 0.103
## ci.upper Std.lv Std.all
##
## 0.117 0.109 0.130
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .math 0.000 0.000
## .Stst19d (.102) -0.124 0.004 -34.200 0.000 -0.131
## .Stst20s (.103) -0.168 0.004 -46.001 0.000 -0.175
## .Stst21c (.104) -0.146 0.004 -40.551 0.000 -0.154
## .Stst22p (.105) -0.184 0.004 -48.026 0.000 -0.191
## .Stst23n (.106) -0.157 0.004 -42.836 0.000 -0.164
## .Stst24x (.107) -0.132 0.004 -36.184 0.000 -0.139
## .Stst25w (.108) -0.089 0.004 -23.605 0.000 -0.096
## .Stst26r (.109) -0.024 0.004 -6.034 0.000 -0.032
## .Stst31b (.110) 0.104 0.004 27.767 0.000 0.097
## .Stst32r (.111) 0.127 0.004 32.680 0.000 0.120
## .Stst34r (.112) -0.026 0.004 -6.763 0.000 -0.033
## .Stst5mt (.113) 0.196 0.004 51.499 0.000 0.189
## .Stst6ph 0.871 0.009 97.012 0.000 0.854
## .Stst33h (.115) 0.191 0.004 46.402 0.000 0.183
## .Sts292D (.116) 0.201 0.004 54.826 0.000 0.194
## .Stst35t (.117) -0.083 0.003 -24.008 0.000 -0.090
## .Stst36c (.118) -0.153 0.004 -41.925 0.000 -0.160
## .Stst37b (.119) -0.048 0.004 -13.111 0.000 -0.055
## .Stst1vc 0.459 0.007 63.494 0.000 0.445
## .Stst2lt (.121) 0.027 0.004 6.904 0.000 0.019
## .Stst3ms 0.153 0.004 35.194 0.000 0.145
## .Stst4sc -0.142 0.004 -32.466 0.000 -0.151
## .Stst7bl 0.672 0.010 67.492 0.000 0.653
## .Stst8rn (.125) 0.480 0.003 138.442 0.000 0.473
## .Stst11r (.126) 0.026 0.004 7.209 0.000 0.019
## .Stst12l -0.146 0.004 -34.035 0.000 -0.154
## .Stst13h 0.464 0.009 50.296 0.000 0.446
## .Stst14b (.129) 0.042 0.004 11.731 0.000 0.035
## .Stst15t 0.198 0.004 46.581 0.000 0.190
## .Stst16m -0.079 0.004 -18.650 0.000 -0.087
## .Stst9lc 0.897 0.008 115.369 0.000 0.882
## .Stst10m (.133) 0.652 0.003 202.387 0.000 0.645
## .Stst28m (.134) 0.561 0.003 160.704 0.000 0.554
## .Sts303D 0.463 0.007 67.120 0.000 0.450
## .english 2.092 0.015 137.006 0.000 2.062
## .speed 0.454 0.007 63.063 0.000 0.440
## .info 0.854 0.014 61.076 0.000 0.826
## .science -2.672 0.017 -155.283 0.000 -2.705
## .spatial -0.652 0.011 -59.484 0.000 -0.674
## .g -0.373 0.007 -50.252 0.000 -0.388
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -0.117 -0.124 -0.128
## -0.160 -0.168 -0.177
## -0.139 -0.146 -0.153
## -0.176 -0.184 -0.200
## -0.149 -0.157 -0.170
## -0.125 -0.132 -0.144
## -0.082 -0.089 -0.091
## -0.016 -0.024 -0.026
## 0.111 0.104 0.109
## 0.135 0.127 0.130
## -0.018 -0.026 -0.027
## 0.204 0.196 0.201
## 0.889 0.871 0.923
## 0.199 0.191 0.198
## 0.208 0.201 0.208
## -0.076 -0.083 -0.100
## -0.145 -0.153 -0.162
## -0.041 -0.048 -0.051
## 0.473 0.459 0.483
## 0.034 0.027 0.027
## 0.162 0.153 0.159
## -0.134 -0.142 -0.150
## 0.692 0.672 0.692
## 0.487 0.480 0.503
## 0.033 0.026 0.027
## -0.138 -0.146 -0.150
## 0.482 0.464 0.490
## 0.049 0.042 0.041
## 0.207 0.198 0.206
## -0.071 -0.079 -0.083
## 0.912 0.897 0.975
## 0.658 0.652 0.835
## 0.568 0.561 0.663
## 0.477 0.463 0.487
## 2.122 0.975 0.975
## 0.468 0.439 0.439
## 0.881 0.368 0.368
## -2.638 -1.928 -1.928
## -0.631 -0.527 -0.527
## -0.358 -0.370 -0.370
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.479 0.003 165.071 0.000 0.473
## .Stest20spellng 0.487 0.003 164.356 0.000 0.481
## .Stest21cptlztn 0.522 0.003 163.370 0.000 0.516
## .Stest22puncttn 0.258 0.002 129.754 0.000 0.254
## .Stest23english 0.451 0.003 156.658 0.000 0.445
## .Stest24exprssn 0.532 0.004 146.355 0.000 0.525
## .Stst25wrdfnctn 0.398 0.003 145.173 0.000 0.392
## .Stst26rdngcmpr 0.193 0.001 139.242 0.000 0.190
## .Stst31bstrctrs 0.467 0.003 155.711 0.000 0.461
## .Stst32rthrsnng 0.404 0.002 164.558 0.000 0.399
## .Stst34rthcmptt 0.493 0.003 143.188 0.000 0.486
## .Stest5math 0.322 0.003 98.169 0.000 0.315
## .Stst6physclscn 0.315 0.002 144.616 0.000 0.311
## .Stst33hghschlm 0.241 0.002 115.189 0.000 0.236
## .Stst29vslztn2D 0.594 0.004 155.615 0.000 0.587
## .Stest35tblrdng 0.310 0.004 84.760 0.000 0.303
## .Stst36clrclchc 0.426 0.004 100.240 0.000 0.417
## .Stst37bjctnspc 0.526 0.004 139.348 0.000 0.519
## .Stest1vocab 0.239 0.002 149.837 0.000 0.236
## .Stest2literatr 0.290 0.002 157.093 0.000 0.287
## .Stest3music 0.420 0.003 166.071 0.000 0.415
## .Stest4soclstds 0.289 0.002 155.970 0.000 0.285
## .Stst7blgclscnc 0.496 0.003 170.860 0.000 0.491
## .Stest8aerontcs 0.619 0.003 182.622 0.000 0.612
## .Stest11art 0.443 0.003 168.996 0.000 0.438
## .Stest12law 0.548 0.003 176.891 0.000 0.542
## .Stest13health 0.538 0.003 172.933 0.000 0.532
## .Stest14bible 0.630 0.003 192.038 0.000 0.624
## .Stest15theater 0.469 0.003 172.856 0.000 0.463
## .Stest16mscllns 0.496 0.003 170.481 0.000 0.491
## .Stest9elctrncs 0.490 0.004 117.138 0.000 0.482
## .Stest10mechncs 0.328 0.002 146.541 0.000 0.324
## .Stst28mchnclrs 0.303 0.002 137.532 0.000 0.299
## .Stst30vslztn3D 0.338 0.003 100.695 0.000 0.331
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.485 0.479 0.511
## 0.493 0.487 0.546
## 0.528 0.522 0.573
## 0.262 0.258 0.305
## 0.456 0.451 0.532
## 0.539 0.532 0.637
## 0.403 0.398 0.417
## 0.196 0.193 0.220
## 0.473 0.467 0.512
## 0.409 0.404 0.424
## 0.500 0.493 0.554
## 0.328 0.322 0.337
## 0.319 0.315 0.353
## 0.245 0.241 0.259
## 0.602 0.594 0.634
## 0.317 0.310 0.449
## 0.434 0.426 0.480
## 0.533 0.526 0.596
## 0.242 0.239 0.264
## 0.294 0.290 0.305
## 0.425 0.420 0.452
## 0.292 0.289 0.322
## 0.502 0.496 0.526
## 0.626 0.619 0.682
## 0.448 0.443 0.468
## 0.555 0.548 0.576
## 0.544 0.538 0.599
## 0.637 0.630 0.627
## 0.474 0.469 0.505
## 0.502 0.496 0.545
## 0.498 0.490 0.579
## 0.333 0.328 0.539
## 0.308 0.303 0.424
## 0.344 0.338 0.372
## 1.000 0.217 0.217
## 1.000 0.209 0.209
## 1.000 0.934 0.934
## 1.000 0.186 0.186
## 1.000 0.521 0.521
## 1.000 0.654 0.654
## 1.000 0.983 0.983
sem.age2<-sem(hof.age2, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("Stest4socialstudies~1", "Stest15theater~1", "Stest12law~1", "Stest3music~1", "Stest16miscellaneous~1", "Stest13health~1", "Stest6physicalscience~1", "Stest9electronics~1", "Stest30visualization3D~1", "Stest7biologicalscience~1", "Stest1vocab~1"))
fitMeasures(sem.age2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 192743.847 1214.000 0.000 0.928 0.048
## srmr ecvi aic bic
## 0.058 1.389 10366801.715 10368573.385
Mc(sem.age2)
## [1] 0.5022292
summary(sem.age2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 107 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 260
## Number of equality constraints 80
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 192743.847 169107.665
## Degrees of freedom 1214 1214
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.140
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 105552.574 92608.660
## 1 87191.273 76499.006
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.154 0.002 76.696 0.000 0.150
## Stst20s (.p2.) 0.296 0.002 166.765 0.000 0.293
## Stst21c (.p3.) 0.290 0.002 170.645 0.000 0.287
## Stst22p (.p4.) 0.357 0.002 187.380 0.000 0.353
## Stst23n (.p5.) 0.293 0.002 168.762 0.000 0.290
## Stst24x (.p6.) 0.256 0.002 156.183 0.000 0.253
## Stst25w (.p7.) 0.261 0.002 140.963 0.000 0.258
## Stst26r (.p8.) 0.120 0.001 85.817 0.000 0.117
## Stst31b (.p9.) 0.165 0.001 120.912 0.000 0.162
## Stst32r (.10.) 0.111 0.002 67.396 0.000 0.108
## Stst34r (.11.) 0.101 0.002 55.615 0.000 0.098
## math =~
## Stst5mt (.12.) 0.363 0.002 162.759 0.000 0.359
## Stst6ph (.13.) 0.178 0.002 116.472 0.000 0.175
## Stst25w (.14.) 0.100 0.002 60.946 0.000 0.096
## Stst32r (.15.) 0.194 0.002 99.579 0.000 0.190
## Stst33h (.16.) 0.379 0.002 154.754 0.000 0.374
## Stst34r (.17.) 0.112 0.002 56.564 0.000 0.108
## speed =~
## Stst19d (.18.) 0.269 0.003 107.071 0.000 0.264
## Sts292D (.19.) 0.208 0.003 76.598 0.000 0.203
## Stst34r (.20.) 0.347 0.003 132.207 0.000 0.342
## Stst35t (.21.) 0.596 0.003 200.669 0.000 0.590
## Stst36c (.22.) 0.656 0.003 210.560 0.000 0.650
## Stst37b (.23.) 0.545 0.003 182.932 0.000 0.539
## info =~
## Stst1vc (.24.) 0.274 0.002 168.697 0.000 0.271
## Stst2lt (.25.) 0.351 0.002 178.039 0.000 0.347
## Stst3ms (.26.) 0.308 0.002 171.905 0.000 0.304
## Stst4sc (.27.) 0.336 0.002 184.974 0.000 0.333
## Stst7bl (.28.) 0.157 0.002 90.556 0.000 0.153
## Stst8rn (.29.) 0.082 0.001 64.014 0.000 0.080
## Stst11r (.30.) 0.306 0.002 165.767 0.000 0.302
## Stst12l (.31.) 0.274 0.002 163.381 0.000 0.270
## Stst13h (.32.) 0.217 0.002 119.193 0.000 0.214
## Stst14b (.33.) 0.264 0.002 160.485 0.000 0.261
## Stst15t (.34.) 0.293 0.002 164.214 0.000 0.289
## Stst16m (.35.) 0.277 0.002 162.993 0.000 0.274
## Stst19d (.36.) 0.109 0.002 60.937 0.000 0.106
## Stst26r (.37.) 0.261 0.002 158.303 0.000 0.258
## science =~
## Stst1vc (.38.) 0.181 0.002 100.593 0.000 0.177
## Stst6ph (.39.) 0.328 0.002 150.942 0.000 0.324
## Stst7bl (.40.) 0.273 0.003 103.890 0.000 0.268
## Stst8rn (.41.) 0.287 0.002 167.234 0.000 0.284
## Stst9lc (.42.) 0.431 0.002 188.208 0.000 0.426
## Stst10m (.43.) 0.382 0.002 201.003 0.000 0.378
## Stst13h (.44.) 0.100 0.003 37.406 0.000 0.094
## Stst28m (.45.) 0.207 0.002 123.158 0.000 0.204
## spatial =~
## Stst28m (.46.) 0.379 0.002 168.575 0.000 0.374
## Sts292D (.47.) 0.414 0.002 177.615 0.000 0.410
## Sts303D (.48.) 0.610 0.002 257.045 0.000 0.605
## Stst31b (.49.) 0.331 0.002 143.154 0.000 0.327
## Stst32r (.50.) 0.142 0.002 65.184 0.000 0.138
## Stst37b (.51.) 0.104 0.002 46.778 0.000 0.099
## g =~
## english (.52.) 1.878 0.012 154.069 0.000 1.854
## math (.53.) 1.924 0.015 132.521 0.000 1.896
## speed (.54.) 0.264 0.004 64.295 0.000 0.255
## info (.55.) 2.067 0.014 147.965 0.000 2.039
## science (.56.) 0.947 0.007 137.097 0.000 0.934
## spatial (.57.) 0.719 0.005 139.318 0.000 0.709
## ci.upper Std.lv Std.all
##
## 0.158 0.331 0.344
## 0.300 0.638 0.647
## 0.294 0.625 0.656
## 0.361 0.768 0.812
## 0.297 0.631 0.658
## 0.260 0.551 0.563
## 0.265 0.562 0.574
## 0.123 0.258 0.269
## 0.168 0.355 0.369
## 0.114 0.238 0.246
## 0.105 0.218 0.228
##
## 0.368 0.797 0.870
## 0.181 0.391 0.422
## 0.103 0.218 0.223
## 0.198 0.426 0.440
## 0.384 0.831 0.845
## 0.116 0.245 0.257
##
## 0.274 0.278 0.289
## 0.213 0.215 0.225
## 0.352 0.359 0.376
## 0.601 0.617 0.682
## 0.662 0.679 0.712
## 0.551 0.564 0.565
##
## 0.278 0.637 0.686
## 0.354 0.814 0.837
## 0.312 0.715 0.725
## 0.340 0.781 0.820
## 0.160 0.364 0.381
## 0.085 0.191 0.231
## 0.309 0.710 0.732
## 0.277 0.636 0.659
## 0.221 0.505 0.526
## 0.267 0.614 0.617
## 0.296 0.679 0.708
## 0.281 0.644 0.651
## 0.113 0.253 0.263
## 0.265 0.607 0.634
##
## 0.184 0.251 0.270
## 0.332 0.455 0.491
## 0.279 0.379 0.397
## 0.290 0.398 0.481
## 0.435 0.597 0.771
## 0.386 0.530 0.674
## 0.105 0.138 0.144
## 0.211 0.287 0.346
##
## 0.383 0.469 0.564
## 0.419 0.513 0.537
## 0.614 0.755 0.765
## 0.336 0.410 0.426
## 0.147 0.176 0.182
## 0.108 0.128 0.128
##
## 1.901 0.885 0.885
## 1.953 0.890 0.890
## 0.272 0.258 0.258
## 2.094 0.903 0.903
## 0.961 0.693 0.693
## 0.730 0.589 0.589
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.099 0.004 27.105 0.000 0.092
## age2 -0.056 0.003 -21.912 0.000 -0.061
## ci.upper Std.lv Std.all
##
## 0.107 0.098 0.121
## -0.051 -0.055 -0.099
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .math 0.000 0.000
## .Stst19d (.105) -0.074 0.004 -17.253 0.000 -0.083
## .Stst20s (.106) -0.120 0.004 -28.498 0.000 -0.128
## .Stst21c (.107) -0.100 0.004 -24.082 0.000 -0.108
## .Stst22p (.108) -0.126 0.005 -27.373 0.000 -0.135
## .Stst23n (.109) -0.110 0.004 -26.074 0.000 -0.118
## .Stst24x (.110) -0.091 0.004 -22.457 0.000 -0.099
## .Stst25w (.111) -0.031 0.005 -6.647 0.000 -0.040
## .Stst26r (.112) 0.041 0.005 8.258 0.000 0.031
## .Stst31b (.113) 0.151 0.004 35.431 0.000 0.142
## .Stst32r (.114) 0.186 0.005 39.347 0.000 0.176
## .Stst34r (.115) 0.017 0.004 3.956 0.000 0.009
## .Stst5mt (.116) 0.256 0.005 54.553 0.000 0.247
## .Stst6ph 0.422 0.005 90.477 0.000 0.413
## .Stst33h (.118) 0.253 0.005 50.017 0.000 0.243
## .Sts292D (.119) 0.231 0.004 58.990 0.000 0.224
## .Stst35t (.120) -0.070 0.003 -19.998 0.000 -0.076
## .Stst36c (.121) -0.138 0.004 -37.277 0.000 -0.145
## .Stst37b (.122) -0.029 0.004 -7.789 0.000 -0.037
## .Stst1vc 0.262 0.005 55.496 0.000 0.252
## .Stst2lt (.124) 0.088 0.005 18.414 0.000 0.079
## .Stst3ms -0.058 0.005 -12.167 0.000 -0.067
## .Stst4sc 0.297 0.005 62.240 0.000 0.287
## .Stst7bl 0.300 0.004 66.816 0.000 0.292
## .Stst8rn (.128) 0.517 0.004 135.290 0.000 0.510
## .Stst11r (.129) 0.080 0.004 18.369 0.000 0.072
## .Stst12l 0.264 0.005 57.126 0.000 0.255
## .Stst13h -0.027 0.005 -6.031 0.000 -0.036
## .Stst14b (.132) 0.088 0.004 21.237 0.000 0.080
## .Stst15t -0.107 0.005 -23.469 0.000 -0.116
## .Stst16m 0.190 0.005 39.680 0.000 0.181
## .Stst9lc 0.563 0.004 154.296 0.000 0.555
## .Stst10m (.136) 0.682 0.004 193.710 0.000 0.675
## .Stst28m (.137) 0.601 0.004 153.149 0.000 0.593
## .Sts303D 0.249 0.004 55.813 0.000 0.240
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -0.066 -0.074 -0.077
## -0.112 -0.120 -0.122
## -0.092 -0.100 -0.105
## -0.117 -0.126 -0.134
## -0.101 -0.110 -0.114
## -0.083 -0.091 -0.093
## -0.022 -0.031 -0.031
## 0.051 0.041 0.043
## 0.159 0.151 0.157
## 0.195 0.186 0.192
## 0.025 0.017 0.018
## 0.265 0.256 0.279
## 0.431 0.422 0.456
## 0.263 0.253 0.257
## 0.239 0.231 0.242
## -0.063 -0.070 -0.077
## -0.131 -0.138 -0.144
## -0.022 -0.029 -0.029
## 0.271 0.262 0.281
## 0.098 0.088 0.091
## -0.048 -0.058 -0.059
## 0.306 0.297 0.312
## 0.309 0.300 0.314
## 0.525 0.517 0.626
## 0.089 0.080 0.083
## 0.273 0.264 0.274
## -0.018 -0.027 -0.029
## 0.096 0.088 0.089
## -0.098 -0.107 -0.112
## 0.199 0.190 0.192
## 0.570 0.563 0.727
## 0.689 0.682 0.868
## 0.609 0.601 0.723
## 0.258 0.249 0.253
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.465 0.003 161.854 0.000 0.459
## .Stest20spellng 0.566 0.004 161.400 0.000 0.559
## .Stest21cptlztn 0.515 0.003 163.254 0.000 0.509
## .Stest22puncttn 0.305 0.002 135.062 0.000 0.301
## .Stest23english 0.521 0.003 151.575 0.000 0.515
## .Stest24exprssn 0.656 0.004 156.860 0.000 0.648
## .Stst25wrdfnctn 0.403 0.003 148.814 0.000 0.398
## .Stst26rdngcmpr 0.232 0.002 136.861 0.000 0.229
## .Stst31bstrctrs 0.480 0.003 149.345 0.000 0.473
## .Stst32rthrsnng 0.385 0.002 157.535 0.000 0.380
## .Stst34rthcmptt 0.515 0.003 149.691 0.000 0.508
## .Stest5math 0.203 0.003 80.121 0.000 0.198
## .Stst6physclscn 0.278 0.002 138.005 0.000 0.274
## .Stst33hghschlm 0.277 0.002 120.448 0.000 0.273
## .Stst29vslztn2D 0.570 0.004 135.948 0.000 0.561
## .Stest35tblrdng 0.438 0.005 93.758 0.000 0.429
## .Stst36clrclchc 0.450 0.005 87.194 0.000 0.440
## .Stst37bjctnspc 0.639 0.005 138.203 0.000 0.630
## .Stest1vocab 0.195 0.001 144.223 0.000 0.193
## .Stest2literatr 0.283 0.002 152.654 0.000 0.279
## .Stest3music 0.461 0.003 168.069 0.000 0.455
## .Stest4soclstds 0.297 0.002 152.286 0.000 0.293
## .Stst7blgclscnc 0.465 0.003 159.866 0.000 0.459
## .Stest8aerontcs 0.394 0.003 119.540 0.000 0.388
## .Stest11art 0.436 0.003 166.828 0.000 0.431
## .Stest12law 0.527 0.003 171.107 0.000 0.521
## .Stest13health 0.559 0.003 174.486 0.000 0.553
## .Stest14bible 0.612 0.003 184.758 0.000 0.606
## .Stest15theater 0.459 0.003 171.180 0.000 0.454
## .Stest16mscllns 0.564 0.003 166.837 0.000 0.558
## .Stest9elctrncs 0.243 0.003 87.420 0.000 0.237
## .Stest10mechncs 0.337 0.002 138.919 0.000 0.332
## .Stst28mchnclrs 0.278 0.002 125.655 0.000 0.274
## .Stst30vslztn3D 0.404 0.004 105.444 0.000 0.397
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.471 0.465 0.503
## 0.573 0.566 0.582
## 0.522 0.515 0.569
## 0.310 0.305 0.341
## 0.528 0.521 0.567
## 0.665 0.656 0.684
## 0.408 0.403 0.420
## 0.235 0.232 0.253
## 0.486 0.480 0.518
## 0.389 0.385 0.411
## 0.521 0.515 0.564
## 0.208 0.203 0.243
## 0.282 0.278 0.324
## 0.282 0.277 0.286
## 0.578 0.570 0.624
## 0.447 0.438 0.535
## 0.460 0.450 0.494
## 0.648 0.639 0.642
## 0.198 0.195 0.226
## 0.287 0.283 0.299
## 0.466 0.461 0.474
## 0.300 0.297 0.327
## 0.471 0.465 0.509
## 0.401 0.394 0.576
## 0.441 0.436 0.464
## 0.533 0.527 0.566
## 0.565 0.559 0.608
## 0.619 0.612 0.619
## 0.464 0.459 0.499
## 0.571 0.564 0.576
## 0.248 0.243 0.405
## 0.342 0.337 0.545
## 0.283 0.278 0.403
## 0.412 0.404 0.415
## 1.000 0.216 0.216
## 1.000 0.208 0.208
## 1.000 0.933 0.933
## 1.000 0.185 0.185
## 1.000 0.520 0.520
## 1.000 0.653 0.653
## 1.000 0.972 0.972
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.154 0.002 76.696 0.000 0.150
## Stst20s (.p2.) 0.296 0.002 166.765 0.000 0.293
## Stst21c (.p3.) 0.290 0.002 170.645 0.000 0.287
## Stst22p (.p4.) 0.357 0.002 187.380 0.000 0.353
## Stst23n (.p5.) 0.293 0.002 168.762 0.000 0.290
## Stst24x (.p6.) 0.256 0.002 156.183 0.000 0.253
## Stst25w (.p7.) 0.261 0.002 140.963 0.000 0.258
## Stst26r (.p8.) 0.120 0.001 85.817 0.000 0.117
## Stst31b (.p9.) 0.165 0.001 120.912 0.000 0.162
## Stst32r (.10.) 0.111 0.002 67.396 0.000 0.108
## Stst34r (.11.) 0.101 0.002 55.615 0.000 0.098
## math =~
## Stst5mt (.12.) 0.363 0.002 162.759 0.000 0.359
## Stst6ph (.13.) 0.178 0.002 116.472 0.000 0.175
## Stst25w (.14.) 0.100 0.002 60.946 0.000 0.096
## Stst32r (.15.) 0.194 0.002 99.579 0.000 0.190
## Stst33h (.16.) 0.379 0.002 154.754 0.000 0.374
## Stst34r (.17.) 0.112 0.002 56.564 0.000 0.108
## speed =~
## Stst19d (.18.) 0.269 0.003 107.071 0.000 0.264
## Sts292D (.19.) 0.208 0.003 76.598 0.000 0.203
## Stst34r (.20.) 0.347 0.003 132.207 0.000 0.342
## Stst35t (.21.) 0.596 0.003 200.669 0.000 0.590
## Stst36c (.22.) 0.656 0.003 210.560 0.000 0.650
## Stst37b (.23.) 0.545 0.003 182.932 0.000 0.539
## info =~
## Stst1vc (.24.) 0.274 0.002 168.697 0.000 0.271
## Stst2lt (.25.) 0.351 0.002 178.039 0.000 0.347
## Stst3ms (.26.) 0.308 0.002 171.905 0.000 0.304
## Stst4sc (.27.) 0.336 0.002 184.974 0.000 0.333
## Stst7bl (.28.) 0.157 0.002 90.556 0.000 0.153
## Stst8rn (.29.) 0.082 0.001 64.014 0.000 0.080
## Stst11r (.30.) 0.306 0.002 165.767 0.000 0.302
## Stst12l (.31.) 0.274 0.002 163.381 0.000 0.270
## Stst13h (.32.) 0.217 0.002 119.193 0.000 0.214
## Stst14b (.33.) 0.264 0.002 160.485 0.000 0.261
## Stst15t (.34.) 0.293 0.002 164.214 0.000 0.289
## Stst16m (.35.) 0.277 0.002 162.993 0.000 0.274
## Stst19d (.36.) 0.109 0.002 60.937 0.000 0.106
## Stst26r (.37.) 0.261 0.002 158.303 0.000 0.258
## science =~
## Stst1vc (.38.) 0.181 0.002 100.593 0.000 0.177
## Stst6ph (.39.) 0.328 0.002 150.942 0.000 0.324
## Stst7bl (.40.) 0.273 0.003 103.890 0.000 0.268
## Stst8rn (.41.) 0.287 0.002 167.234 0.000 0.284
## Stst9lc (.42.) 0.431 0.002 188.208 0.000 0.426
## Stst10m (.43.) 0.382 0.002 201.003 0.000 0.378
## Stst13h (.44.) 0.100 0.003 37.406 0.000 0.094
## Stst28m (.45.) 0.207 0.002 123.158 0.000 0.204
## spatial =~
## Stst28m (.46.) 0.379 0.002 168.575 0.000 0.374
## Sts292D (.47.) 0.414 0.002 177.615 0.000 0.410
## Sts303D (.48.) 0.610 0.002 257.045 0.000 0.605
## Stst31b (.49.) 0.331 0.002 143.154 0.000 0.327
## Stst32r (.50.) 0.142 0.002 65.184 0.000 0.138
## Stst37b (.51.) 0.104 0.002 46.778 0.000 0.099
## g =~
## english (.52.) 1.878 0.012 154.069 0.000 1.854
## math (.53.) 1.924 0.015 132.521 0.000 1.896
## speed (.54.) 0.264 0.004 64.295 0.000 0.255
## info (.55.) 2.067 0.014 147.965 0.000 2.039
## science (.56.) 0.947 0.007 137.097 0.000 0.934
## spatial (.57.) 0.719 0.005 139.318 0.000 0.709
## ci.upper Std.lv Std.all
##
## 0.158 0.330 0.341
## 0.300 0.636 0.674
## 0.294 0.623 0.653
## 0.361 0.766 0.833
## 0.297 0.629 0.684
## 0.260 0.550 0.602
## 0.265 0.561 0.575
## 0.123 0.257 0.275
## 0.168 0.354 0.371
## 0.114 0.238 0.244
## 0.105 0.218 0.231
##
## 0.368 0.795 0.814
## 0.181 0.390 0.413
## 0.103 0.218 0.223
## 0.198 0.425 0.435
## 0.384 0.829 0.861
## 0.116 0.245 0.260
##
## 0.274 0.278 0.287
## 0.213 0.215 0.222
## 0.352 0.359 0.381
## 0.601 0.616 0.742
## 0.662 0.679 0.721
## 0.551 0.564 0.600
##
## 0.278 0.636 0.668
## 0.354 0.812 0.833
## 0.312 0.713 0.740
## 0.340 0.779 0.823
## 0.160 0.363 0.374
## 0.085 0.190 0.200
## 0.309 0.708 0.729
## 0.277 0.634 0.650
## 0.221 0.503 0.532
## 0.267 0.612 0.610
## 0.296 0.678 0.703
## 0.281 0.642 0.674
## 0.113 0.253 0.261
## 0.265 0.606 0.648
##
## 0.184 0.250 0.263
## 0.332 0.454 0.481
## 0.279 0.379 0.390
## 0.290 0.397 0.417
## 0.435 0.596 0.648
## 0.386 0.529 0.678
## 0.105 0.138 0.146
## 0.211 0.287 0.340
##
## 0.383 0.468 0.554
## 0.419 0.512 0.529
## 0.614 0.754 0.792
## 0.336 0.410 0.429
## 0.147 0.176 0.180
## 0.108 0.128 0.136
##
## 1.901 0.885 0.885
## 1.953 0.889 0.889
## 0.272 0.257 0.257
## 2.094 0.902 0.902
## 0.961 0.692 0.692
## 0.730 0.588 0.588
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.091 0.004 23.971 0.000 0.083
## age2 -0.044 0.003 -16.057 0.000 -0.049
## ci.upper Std.lv Std.all
##
## 0.098 0.090 0.106
## -0.038 -0.043 -0.071
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .math 0.000 0.000
## .Stst19d (.105) -0.074 0.004 -17.253 0.000 -0.083
## .Stst20s (.106) -0.120 0.004 -28.498 0.000 -0.128
## .Stst21c (.107) -0.100 0.004 -24.082 0.000 -0.108
## .Stst22p (.108) -0.126 0.005 -27.373 0.000 -0.135
## .Stst23n (.109) -0.110 0.004 -26.074 0.000 -0.118
## .Stst24x (.110) -0.091 0.004 -22.457 0.000 -0.099
## .Stst25w (.111) -0.031 0.005 -6.647 0.000 -0.040
## .Stst26r (.112) 0.041 0.005 8.258 0.000 0.031
## .Stst31b (.113) 0.151 0.004 35.431 0.000 0.142
## .Stst32r (.114) 0.186 0.005 39.347 0.000 0.176
## .Stst34r (.115) 0.017 0.004 3.956 0.000 0.009
## .Stst5mt (.116) 0.256 0.005 54.553 0.000 0.247
## .Stst6ph 0.927 0.009 99.343 0.000 0.909
## .Stst33h (.118) 0.253 0.005 50.017 0.000 0.243
## .Sts292D (.119) 0.231 0.004 58.990 0.000 0.224
## .Stst35t (.120) -0.070 0.003 -19.998 0.000 -0.076
## .Stst36c (.121) -0.138 0.004 -37.277 0.000 -0.145
## .Stst37b (.122) -0.029 0.004 -7.789 0.000 -0.037
## .Stst1vc 0.522 0.008 67.253 0.000 0.507
## .Stst2lt (.124) 0.088 0.005 18.414 0.000 0.079
## .Stst3ms 0.207 0.005 41.383 0.000 0.198
## .Stst4sc -0.083 0.005 -16.187 0.000 -0.093
## .Stst7bl 0.722 0.010 70.593 0.000 0.702
## .Stst8rn (.128) 0.517 0.004 135.290 0.000 0.510
## .Stst11r (.129) 0.080 0.004 18.369 0.000 0.072
## .Stst12l -0.098 0.005 -20.265 0.000 -0.107
## .Stst13h 0.511 0.009 53.948 0.000 0.492
## .Stst14b (.132) 0.088 0.004 21.237 0.000 0.080
## .Stst15t 0.250 0.005 51.333 0.000 0.240
## .Stst16m -0.030 0.005 -6.314 0.000 -0.040
## .Stst9lc 0.931 0.008 116.909 0.000 0.916
## .Stst10m (.136) 0.682 0.004 193.710 0.000 0.675
## .Stst28m (.137) 0.601 0.004 153.149 0.000 0.593
## .Sts303D 0.501 0.007 70.151 0.000 0.487
## .english 2.093 0.015 137.015 0.000 2.063
## .speed 0.454 0.007 63.090 0.000 0.440
## .info 0.853 0.014 61.096 0.000 0.825
## .science -2.671 0.017 -155.326 0.000 -2.705
## .spatial -0.652 0.011 -59.482 0.000 -0.674
## .g -0.400 0.009 -43.412 0.000 -0.418
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -0.066 -0.074 -0.077
## -0.112 -0.120 -0.127
## -0.092 -0.100 -0.105
## -0.117 -0.126 -0.137
## -0.101 -0.110 -0.119
## -0.083 -0.091 -0.099
## -0.022 -0.031 -0.032
## 0.051 0.041 0.044
## 0.159 0.151 0.158
## 0.195 0.186 0.190
## 0.025 0.017 0.018
## 0.265 0.256 0.262
## 0.945 0.927 0.982
## 0.263 0.253 0.263
## 0.239 0.231 0.239
## -0.063 -0.070 -0.084
## -0.131 -0.138 -0.146
## -0.022 -0.029 -0.031
## 0.537 0.522 0.549
## 0.098 0.088 0.091
## 0.217 0.207 0.215
## -0.073 -0.083 -0.088
## 0.742 0.722 0.743
## 0.525 0.517 0.543
## 0.089 0.080 0.082
## -0.088 -0.098 -0.100
## 0.529 0.511 0.539
## 0.096 0.088 0.088
## 0.259 0.250 0.259
## -0.021 -0.030 -0.032
## 0.947 0.931 1.013
## 0.689 0.682 0.875
## 0.609 0.601 0.711
## 0.515 0.501 0.526
## 2.123 0.975 0.975
## 0.469 0.439 0.439
## 0.880 0.368 0.368
## -2.637 -1.929 -1.929
## -0.631 -0.528 -0.528
## -0.382 -0.396 -0.396
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.479 0.003 165.087 0.000 0.473
## .Stest20spellng 0.487 0.003 164.357 0.000 0.481
## .Stest21cptlztn 0.522 0.003 163.367 0.000 0.516
## .Stest22puncttn 0.258 0.002 129.746 0.000 0.254
## .Stest23english 0.451 0.003 156.671 0.000 0.445
## .Stest24exprssn 0.532 0.004 146.352 0.000 0.525
## .Stst25wrdfnctn 0.398 0.003 145.148 0.000 0.392
## .Stst26rdngcmpr 0.193 0.001 139.241 0.000 0.190
## .Stst31bstrctrs 0.467 0.003 155.715 0.000 0.461
## .Stst32rthrsnng 0.404 0.002 164.590 0.000 0.399
## .Stst34rthcmptt 0.493 0.003 143.196 0.000 0.486
## .Stest5math 0.322 0.003 98.127 0.000 0.315
## .Stst6physclscn 0.315 0.002 144.645 0.000 0.311
## .Stst33hghschlm 0.241 0.002 115.220 0.000 0.236
## .Stst29vslztn2D 0.594 0.004 155.618 0.000 0.587
## .Stest35tblrdng 0.310 0.004 84.752 0.000 0.302
## .Stst36clrclchc 0.426 0.004 100.245 0.000 0.417
## .Stst37bjctnspc 0.526 0.004 139.352 0.000 0.519
## .Stest1vocab 0.239 0.002 149.815 0.000 0.236
## .Stest2literatr 0.290 0.002 157.083 0.000 0.287
## .Stest3music 0.420 0.003 166.071 0.000 0.415
## .Stest4soclstds 0.289 0.002 155.976 0.000 0.285
## .Stst7blgclscnc 0.496 0.003 170.826 0.000 0.490
## .Stest8aerontcs 0.619 0.003 182.622 0.000 0.612
## .Stest11art 0.443 0.003 168.997 0.000 0.438
## .Stest12law 0.548 0.003 176.887 0.000 0.542
## .Stest13health 0.538 0.003 172.930 0.000 0.532
## .Stest14bible 0.630 0.003 192.037 0.000 0.624
## .Stest15theater 0.469 0.003 172.858 0.000 0.463
## .Stest16mscllns 0.496 0.003 170.479 0.000 0.491
## .Stest9elctrncs 0.490 0.004 117.137 0.000 0.482
## .Stest10mechncs 0.328 0.002 146.530 0.000 0.324
## .Stst28mchnclrs 0.303 0.002 137.527 0.000 0.299
## .Stst30vslztn3D 0.338 0.003 100.705 0.000 0.331
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.485 0.479 0.511
## 0.493 0.487 0.546
## 0.528 0.522 0.574
## 0.262 0.258 0.305
## 0.456 0.451 0.533
## 0.539 0.532 0.638
## 0.403 0.398 0.418
## 0.196 0.193 0.221
## 0.473 0.467 0.513
## 0.409 0.404 0.424
## 0.500 0.493 0.555
## 0.328 0.322 0.338
## 0.320 0.315 0.354
## 0.245 0.241 0.259
## 0.602 0.594 0.635
## 0.317 0.310 0.449
## 0.434 0.426 0.480
## 0.533 0.526 0.596
## 0.242 0.239 0.264
## 0.294 0.290 0.306
## 0.425 0.420 0.452
## 0.292 0.289 0.322
## 0.502 0.496 0.526
## 0.626 0.619 0.682
## 0.448 0.443 0.469
## 0.555 0.548 0.577
## 0.544 0.538 0.600
## 0.637 0.630 0.627
## 0.474 0.469 0.505
## 0.502 0.496 0.546
## 0.498 0.490 0.579
## 0.333 0.328 0.540
## 0.308 0.303 0.425
## 0.344 0.338 0.373
## 1.000 0.217 0.217
## 1.000 0.209 0.209
## 1.000 0.934 0.934
## 1.000 0.186 0.186
## 1.000 0.522 0.522
## 1.000 0.654 0.654
## 1.000 0.979 0.979
# CHC Bifactor models
chc.bifactor.model <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning + Stest34arithcomputation
math =~ Stest5math + Stest6physicalscience + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest13health + Stest28mechanicalreasoning
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest37objectinspection
g=~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
'
chc.bifactor.lv.model <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning + Stest34arithcomputation
math =~ Stest5math + Stest6physicalscience + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest13health + Stest28mechanicalreasoning
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest37objectinspection
g=~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
english~~1*english
math~~1*math
info~~1*info
'
chc.bifactor.weak.model <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning + Stest34arithcomputation
math =~ Stest5math + Stest6physicalscience + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest13health + Stest28mechanicalreasoning
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest37objectinspection
g=~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
spatial ~ 0*1
'
baseline<-cfa(chc.bifactor.model, data=dgroup, meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T)
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 172236.342 476.000 0.000 0.938 0.051
## srmr aic bic
## 0.053 10545871.347 10547377.266
Mc(baseline)
## [1] 0.5392306
configural<-cfa(chc.bifactor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T)
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 112400.761 952.000 0.000 0.958 0.041
## srmr aic bic
## 0.028 10316403.260 10319415.099
Mc(configural)
## [1] 0.6698209
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 44 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 306
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 112400.761 99050.086
## Degrees of freedom 952 952
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.135
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 65238.027 57489.221
## 1 47162.734 41560.865
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19dsgsdwrd 0.294 0.005 62.214 0.000 0.285
## Stest20spellng 0.400 0.005 78.996 0.000 0.390
## Stest21cptlztn 0.303 0.005 64.146 0.000 0.293
## Stest22puncttn 0.365 0.004 81.601 0.000 0.357
## Stest23english 0.285 0.005 58.324 0.000 0.275
## Stest24exprssn 0.236 0.006 40.324 0.000 0.225
## Stst25wrdfnctn 0.264 0.004 60.670 0.000 0.256
## Stst26rdngcmpr 0.126 0.004 31.962 0.000 0.119
## Stst31bstrctrs 0.101 0.005 21.991 0.000 0.092
## Stst32rthrsnng 0.094 0.004 21.314 0.000 0.085
## Stst34rthcmptt 0.179 0.005 38.120 0.000 0.170
## math =~
## Stest5math 0.217 0.004 52.066 0.000 0.209
## Stst6physclscn 0.066 0.004 17.080 0.000 0.058
## Stst25wrdfnctn 0.161 0.004 42.722 0.000 0.153
## Stst32rthrsnng 0.186 0.004 47.796 0.000 0.179
## Stst33hghschlm 0.542 0.006 86.630 0.000 0.530
## Stst34rthcmptt 0.280 0.005 54.851 0.000 0.270
## speed =~
## Stst19dsgsdwrd 0.254 0.004 72.347 0.000 0.247
## Stst29vslztn2D 0.229 0.004 59.031 0.000 0.222
## Stst34rthcmptt 0.370 0.004 100.532 0.000 0.363
## Stest35tblrdng 0.639 0.005 137.481 0.000 0.630
## Stst36clrclchc 0.688 0.005 151.712 0.000 0.679
## Stst37bjctnspc 0.595 0.004 135.172 0.000 0.586
## info =~
## Stest1vocab 0.207 0.004 57.893 0.000 0.200
## Stest2literatr 0.367 0.005 78.625 0.000 0.358
## Stest3music 0.358 0.004 85.389 0.000 0.349
## Stest4soclstds 0.224 0.006 37.553 0.000 0.213
## Stst7blgclscnc 0.120 0.006 21.519 0.000 0.109
## Stest8aerontcs 0.180 0.004 45.486 0.000 0.172
## Stest11art 0.452 0.004 114.356 0.000 0.444
## Stest12law 0.260 0.005 49.956 0.000 0.250
## Stest13health 0.236 0.005 44.845 0.000 0.226
## Stest14bible 0.233 0.006 37.007 0.000 0.221
## Stest15theater 0.407 0.004 96.260 0.000 0.399
## Stest16mscllns 0.296 0.005 64.306 0.000 0.287
## Stst19dsgsdwrd 0.236 0.005 50.656 0.000 0.227
## Stst26rdngcmpr 0.220 0.005 44.193 0.000 0.210
## science =~
## Stest1vocab 0.172 0.003 65.418 0.000 0.167
## Stst6physclscn 0.277 0.004 76.059 0.000 0.270
## Stst7blgclscnc 0.259 0.004 64.000 0.000 0.251
## Stest8aerontcs 0.312 0.004 86.047 0.000 0.305
## Stest9elctrncs 0.470 0.004 128.766 0.000 0.463
## Stest10mechncs 0.421 0.004 114.743 0.000 0.414
## Stest13health 0.094 0.004 23.019 0.000 0.086
## Stst28mchnclrs 0.295 0.003 89.137 0.000 0.288
## spatial =~
## Stst28mchnclrs 0.411 0.004 117.378 0.000 0.404
## Stst29vslztn2D 0.462 0.004 109.268 0.000 0.454
## Stst30vslztn3D 0.590 0.004 133.083 0.000 0.582
## Stst31bstrctrs 0.363 0.004 91.331 0.000 0.355
## Stst32rthrsnng 0.113 0.003 32.834 0.000 0.106
## Stst37bjctnspc 0.229 0.004 53.052 0.000 0.220
## g =~
## Stest1vocab 0.760 0.003 231.498 0.000 0.753
## Stest2literatr 0.747 0.003 214.600 0.000 0.740
## Stest3music 0.644 0.003 191.834 0.000 0.638
## Stest4soclstds 0.762 0.004 203.550 0.000 0.755
## Stest5math 0.739 0.003 236.722 0.000 0.733
## Stst6physclscn 0.745 0.003 248.441 0.000 0.739
## Stst7blgclscnc 0.615 0.004 162.106 0.000 0.608
## Stest8aerontcs 0.487 0.004 135.337 0.000 0.480
## Stest9elctrncs 0.459 0.003 134.856 0.000 0.452
## Stest10mechncs 0.410 0.004 116.385 0.000 0.403
## Stest11art 0.599 0.004 161.342 0.000 0.592
## Stest12law 0.634 0.004 165.673 0.000 0.627
## Stest13health 0.608 0.004 146.468 0.000 0.600
## Stest14bible 0.592 0.004 150.875 0.000 0.584
## Stest15theater 0.581 0.003 167.853 0.000 0.574
## Stest16mscllns 0.661 0.004 171.327 0.000 0.653
## Stst19dsgsdwrd 0.551 0.004 151.703 0.000 0.544
## Stest20spellng 0.547 0.004 141.716 0.000 0.540
## Stest21cptlztn 0.577 0.004 159.323 0.000 0.570
## Stest22puncttn 0.708 0.003 204.802 0.000 0.701
## Stest23english 0.628 0.004 154.952 0.000 0.620
## Stest24exprssn 0.582 0.004 137.331 0.000 0.573
## Stst25wrdfnctn 0.659 0.003 205.778 0.000 0.653
## Stst26rdngcmpr 0.838 0.003 241.425 0.000 0.831
## Stst28mchnclrs 0.484 0.003 138.838 0.000 0.477
## Stst29vslztn2D 0.324 0.004 79.928 0.000 0.316
## Stst30vslztn3D 0.491 0.004 120.537 0.000 0.483
## Stst31bstrctrs 0.571 0.004 141.706 0.000 0.563
## Stst32rthrsnng 0.720 0.003 223.441 0.000 0.714
## Stst33hghschlm 0.801 0.003 231.392 0.000 0.794
## Stst34rthcmptt 0.474 0.004 115.549 0.000 0.466
## Stest35tblrdng 0.275 0.004 65.022 0.000 0.267
## Stst36clrclchc 0.141 0.004 33.859 0.000 0.133
## Stst37bjctnspc 0.139 0.004 32.423 0.000 0.131
## ci.upper Std.lv Std.all
##
## 0.303 0.294 0.305
## 0.410 0.400 0.403
## 0.312 0.303 0.312
## 0.374 0.365 0.375
## 0.295 0.285 0.286
## 0.248 0.236 0.231
## 0.273 0.264 0.274
## 0.134 0.126 0.126
## 0.110 0.101 0.104
## 0.102 0.094 0.096
## 0.189 0.179 0.186
##
## 0.226 0.217 0.237
## 0.073 0.066 0.069
## 0.168 0.161 0.166
## 0.194 0.186 0.191
## 0.554 0.542 0.523
## 0.290 0.280 0.290
##
## 0.261 0.254 0.263
## 0.237 0.229 0.238
## 0.378 0.370 0.383
## 0.648 0.639 0.679
## 0.697 0.688 0.706
## 0.603 0.595 0.588
##
## 0.214 0.207 0.224
## 0.377 0.367 0.372
## 0.366 0.358 0.359
## 0.236 0.224 0.233
## 0.131 0.120 0.124
## 0.188 0.180 0.208
## 0.459 0.452 0.465
## 0.271 0.260 0.261
## 0.247 0.236 0.237
## 0.246 0.233 0.231
## 0.415 0.407 0.422
## 0.305 0.296 0.285
## 0.245 0.236 0.245
## 0.230 0.220 0.221
##
## 0.178 0.172 0.187
## 0.285 0.277 0.289
## 0.267 0.259 0.269
## 0.319 0.312 0.361
## 0.477 0.470 0.577
## 0.428 0.421 0.514
## 0.102 0.094 0.094
## 0.301 0.295 0.342
##
## 0.418 0.411 0.477
## 0.470 0.462 0.480
## 0.599 0.590 0.583
## 0.370 0.363 0.373
## 0.120 0.113 0.115
## 0.237 0.229 0.227
##
## 0.766 0.760 0.825
## 0.753 0.747 0.756
## 0.651 0.644 0.648
## 0.769 0.762 0.790
## 0.745 0.739 0.805
## 0.751 0.745 0.775
## 0.623 0.615 0.638
## 0.494 0.487 0.563
## 0.466 0.459 0.563
## 0.417 0.410 0.501
## 0.606 0.599 0.617
## 0.642 0.634 0.635
## 0.617 0.608 0.611
## 0.599 0.592 0.585
## 0.588 0.581 0.603
## 0.668 0.661 0.636
## 0.559 0.551 0.572
## 0.555 0.547 0.551
## 0.584 0.577 0.595
## 0.714 0.708 0.727
## 0.636 0.628 0.630
## 0.590 0.582 0.569
## 0.666 0.659 0.683
## 0.844 0.838 0.839
## 0.491 0.484 0.562
## 0.332 0.324 0.337
## 0.499 0.491 0.485
## 0.579 0.571 0.588
## 0.726 0.720 0.736
## 0.808 0.801 0.773
## 0.482 0.474 0.490
## 0.284 0.275 0.293
## 0.149 0.141 0.145
## 0.148 0.139 0.138
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd -0.108 0.004 -27.549 0.000 -0.116
## .Stest20spellng -0.242 0.004 -59.771 0.000 -0.249
## .Stest21cptlztn -0.194 0.004 -49.221 0.000 -0.202
## .Stest22puncttn -0.183 0.004 -46.236 0.000 -0.191
## .Stest23english -0.119 0.004 -29.356 0.000 -0.127
## .Stest24exprssn -0.091 0.004 -21.886 0.000 -0.099
## .Stst25wrdfnctn -0.120 0.004 -30.548 0.000 -0.128
## .Stst26rdngcmpr -0.002 0.004 -0.480 0.632 -0.010
## .Stst31bstrctrs 0.074 0.004 18.667 0.000 0.066
## .Stst32rthrsnng 0.142 0.004 35.487 0.000 0.134
## .Stst34rthcmptt -0.062 0.004 -15.612 0.000 -0.070
## .Stest5math 0.219 0.004 58.635 0.000 0.212
## .Stst6physclscn 0.358 0.004 92.152 0.000 0.350
## .Stst33hghschlm 0.138 0.004 32.978 0.000 0.130
## .Stst29vslztn2D 0.224 0.004 57.484 0.000 0.217
## .Stest35tblrdng -0.047 0.004 -12.373 0.000 -0.055
## .Stst36clrclchc -0.165 0.004 -42.339 0.000 -0.173
## .Stst37bjctnspc -0.098 0.004 -24.085 0.000 -0.106
## .Stest1vocab 0.189 0.004 50.214 0.000 0.181
## .Stest2literatr 0.029 0.004 7.337 0.000 0.022
## .Stest3music -0.121 0.004 -29.896 0.000 -0.128
## .Stest4soclstds 0.228 0.004 57.617 0.000 0.220
## .Stst7blgclscnc 0.243 0.004 61.805 0.000 0.235
## .Stest8aerontcs 0.481 0.004 135.791 0.000 0.474
## .Stest11art -0.054 0.004 -13.827 0.000 -0.062
## .Stest12law 0.208 0.004 51.531 0.000 0.200
## .Stest13health -0.081 0.004 -19.852 0.000 -0.089
## .Stest14bible 0.015 0.004 3.604 0.000 0.007
## .Stest15theater -0.167 0.004 -42.900 0.000 -0.175
## .Stest16mscllns 0.134 0.004 31.520 0.000 0.125
## .Stest9elctrncs 0.522 0.003 156.854 0.000 0.516
## .Stest10mechncs 0.644 0.003 193.961 0.000 0.638
## .Stst28mchnclrs 0.551 0.004 154.563 0.000 0.544
## .Stst30vslztn3D 0.206 0.004 50.236 0.000 0.198
## ci.upper Std.lv Std.all
## -0.101 -0.108 -0.112
## -0.234 -0.242 -0.243
## -0.186 -0.194 -0.200
## -0.175 -0.183 -0.188
## -0.111 -0.119 -0.120
## -0.083 -0.091 -0.089
## -0.112 -0.120 -0.124
## 0.006 -0.002 -0.002
## 0.082 0.074 0.076
## 0.149 0.142 0.145
## -0.054 -0.062 -0.064
## 0.227 0.219 0.239
## 0.365 0.358 0.373
## 0.147 0.138 0.134
## 0.232 0.224 0.233
## -0.040 -0.047 -0.050
## -0.158 -0.165 -0.170
## -0.090 -0.098 -0.097
## 0.196 0.189 0.205
## 0.037 0.029 0.030
## -0.113 -0.121 -0.121
## 0.236 0.228 0.236
## 0.251 0.243 0.252
## 0.488 0.481 0.557
## -0.047 -0.054 -0.056
## 0.216 0.208 0.209
## -0.073 -0.081 -0.081
## 0.023 0.015 0.015
## -0.159 -0.167 -0.173
## 0.142 0.134 0.129
## 0.529 0.522 0.640
## 0.651 0.644 0.786
## 0.558 0.551 0.640
## 0.214 0.206 0.204
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.420 0.004 118.255 0.000 0.413
## .Stest20spellng 0.526 0.004 130.425 0.000 0.518
## .Stest21cptlztn 0.516 0.003 155.994 0.000 0.509
## .Stest22puncttn 0.314 0.003 120.885 0.000 0.309
## .Stest23english 0.518 0.003 148.429 0.000 0.511
## .Stest24exprssn 0.651 0.004 153.019 0.000 0.643
## .Stst25wrdfnctn 0.401 0.003 141.997 0.000 0.395
## .Stst26rdngcmpr 0.231 0.002 137.480 0.000 0.228
## .Stst31bstrctrs 0.475 0.003 145.085 0.000 0.469
## .Stst32rthrsnng 0.382 0.002 158.375 0.000 0.377
## .Stst34rthcmptt 0.462 0.004 119.209 0.000 0.454
## .Stest5math 0.250 0.003 96.602 0.000 0.245
## .Stst6physclscn 0.287 0.002 142.497 0.000 0.283
## .Stst33hghschlm 0.139 0.005 25.680 0.000 0.128
## .Stst29vslztn2D 0.556 0.005 123.293 0.000 0.547
## .Stest35tblrdng 0.402 0.005 89.215 0.000 0.393
## .Stst36clrclchc 0.456 0.005 86.267 0.000 0.445
## .Stst37bjctnspc 0.595 0.005 125.866 0.000 0.586
## .Stest1vocab 0.199 0.001 148.871 0.000 0.197
## .Stest2literatr 0.283 0.002 144.157 0.000 0.279
## .Stest3music 0.447 0.003 154.842 0.000 0.441
## .Stest4soclstds 0.300 0.002 154.962 0.000 0.297
## .Stst7blgclscnc 0.471 0.003 160.328 0.000 0.465
## .Stest8aerontcs 0.380 0.003 117.455 0.000 0.374
## .Stest11art 0.379 0.003 135.864 0.000 0.374
## .Stest12law 0.526 0.003 170.005 0.000 0.520
## .Stest13health 0.557 0.003 173.109 0.000 0.551
## .Stest14bible 0.617 0.003 183.237 0.000 0.611
## .Stest15theater 0.426 0.003 138.574 0.000 0.420
## .Stest16mscllns 0.554 0.003 164.618 0.000 0.547
## .Stest9elctrncs 0.233 0.003 81.153 0.000 0.228
## .Stest10mechncs 0.326 0.003 122.739 0.000 0.321
## .Stst28mchnclrs 0.251 0.003 98.370 0.000 0.246
## .Stst30vslztn3D 0.435 0.004 98.893 0.000 0.426
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.427 0.420 0.451
## 0.534 0.526 0.534
## 0.522 0.516 0.548
## 0.319 0.314 0.331
## 0.525 0.518 0.521
## 0.660 0.651 0.623
## 0.406 0.401 0.430
## 0.235 0.231 0.232
## 0.481 0.475 0.504
## 0.386 0.382 0.399
## 0.469 0.462 0.494
## 0.255 0.250 0.296
## 0.291 0.287 0.311
## 0.149 0.139 0.129
## 0.565 0.556 0.599
## 0.411 0.402 0.453
## 0.466 0.456 0.480
## 0.605 0.595 0.583
## 0.202 0.199 0.235
## 0.287 0.283 0.290
## 0.453 0.447 0.451
## 0.304 0.300 0.323
## 0.477 0.471 0.506
## 0.387 0.380 0.509
## 0.385 0.379 0.403
## 0.532 0.526 0.528
## 0.563 0.557 0.562
## 0.624 0.617 0.604
## 0.432 0.426 0.459
## 0.560 0.554 0.514
## 0.239 0.233 0.351
## 0.331 0.326 0.486
## 0.256 0.251 0.339
## 0.443 0.435 0.424
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19dsgsdwrd 0.326 0.005 69.330 0.000 0.317
## Stest20spellng 0.384 0.005 83.576 0.000 0.375
## Stest21cptlztn 0.289 0.005 63.273 0.000 0.280
## Stest22puncttn 0.346 0.004 82.640 0.000 0.337
## Stest23english 0.259 0.004 61.462 0.000 0.251
## Stest24exprssn 0.203 0.005 42.617 0.000 0.194
## Stst25wrdfnctn 0.271 0.005 59.359 0.000 0.262
## Stst26rdngcmpr 0.121 0.003 36.371 0.000 0.114
## Stst31bstrctrs 0.154 0.005 32.916 0.000 0.145
## Stst32rthrsnng 0.135 0.005 29.878 0.000 0.126
## Stst34rthcmptt 0.214 0.004 48.224 0.000 0.205
## math =~
## Stest5math 0.342 0.004 79.672 0.000 0.334
## Stst6physclscn 0.139 0.004 39.168 0.000 0.132
## Stst25wrdfnctn 0.159 0.004 41.007 0.000 0.151
## Stst32rthrsnng 0.168 0.004 45.218 0.000 0.161
## Stst33hghschlm 0.532 0.005 114.297 0.000 0.523
## Stst34rthcmptt 0.254 0.004 62.913 0.000 0.247
## speed =~
## Stst19dsgsdwrd 0.287 0.003 82.420 0.000 0.280
## Stst29vslztn2D 0.215 0.004 53.291 0.000 0.208
## Stst34rthcmptt 0.322 0.004 88.823 0.000 0.315
## Stest35tblrdng 0.533 0.004 127.193 0.000 0.525
## Stst36clrclchc 0.648 0.004 153.212 0.000 0.639
## Stst37bjctnspc 0.528 0.004 130.204 0.000 0.520
## info =~
## Stest1vocab 0.212 0.004 48.474 0.000 0.203
## Stest2literatr 0.322 0.006 55.641 0.000 0.310
## Stest3music 0.322 0.004 73.997 0.000 0.314
## Stest4soclstds 0.181 0.006 30.738 0.000 0.169
## Stst7blgclscnc 0.058 0.006 9.576 0.000 0.046
## Stest8aerontcs 0.170 0.005 35.956 0.000 0.161
## Stest11art 0.433 0.005 95.281 0.000 0.425
## Stest12law 0.214 0.006 37.800 0.000 0.203
## Stest13health 0.164 0.005 31.712 0.000 0.153
## Stest14bible 0.104 0.007 14.511 0.000 0.090
## Stest15theater 0.437 0.004 100.183 0.000 0.428
## Stest16mscllns 0.213 0.005 46.912 0.000 0.204
## Stst19dsgsdwrd 0.226 0.005 48.257 0.000 0.217
## Stst26rdngcmpr 0.170 0.005 36.897 0.000 0.161
## science =~
## Stest1vocab 0.124 0.003 39.714 0.000 0.118
## Stst6physclscn 0.328 0.004 81.521 0.000 0.321
## Stst7blgclscnc 0.237 0.005 50.758 0.000 0.228
## Stest8aerontcs 0.269 0.005 56.491 0.000 0.260
## Stest9elctrncs 0.417 0.005 84.379 0.000 0.407
## Stest10mechncs 0.283 0.004 67.696 0.000 0.274
## Stest13health 0.079 0.004 17.731 0.000 0.070
## Stst28mchnclrs 0.165 0.004 44.664 0.000 0.158
## spatial =~
## Stst28mchnclrs 0.400 0.003 117.118 0.000 0.393
## Stst29vslztn2D 0.429 0.004 100.683 0.000 0.420
## Stst30vslztn3D 0.524 0.004 126.382 0.000 0.516
## Stst31bstrctrs 0.346 0.004 87.660 0.000 0.338
## Stst32rthrsnng 0.118 0.003 33.769 0.000 0.111
## Stst37bjctnspc 0.203 0.004 50.123 0.000 0.195
## g =~
## Stest1vocab 0.807 0.003 260.771 0.000 0.801
## Stest2literatr 0.724 0.004 202.115 0.000 0.717
## Stest3music 0.631 0.003 185.427 0.000 0.624
## Stest4soclstds 0.740 0.003 227.982 0.000 0.733
## Stest5math 0.687 0.003 205.566 0.000 0.681
## Stst6physclscn 0.626 0.003 207.176 0.000 0.620
## Stst7blgclscnc 0.622 0.004 174.785 0.000 0.615
## Stest8aerontcs 0.320 0.004 84.934 0.000 0.313
## Stest9elctrncs 0.325 0.004 87.958 0.000 0.317
## Stest10mechncs 0.358 0.003 119.992 0.000 0.352
## Stest11art 0.599 0.004 155.687 0.000 0.591
## Stest12law 0.535 0.004 142.591 0.000 0.527
## Stest13health 0.506 0.004 129.540 0.000 0.498
## Stest14bible 0.574 0.004 151.998 0.000 0.567
## Stest15theater 0.565 0.004 154.934 0.000 0.558
## Stest16mscllns 0.527 0.004 150.396 0.000 0.520
## Stst19dsgsdwrd 0.516 0.004 135.798 0.000 0.508
## Stest20spellng 0.471 0.004 134.131 0.000 0.464
## Stest21cptlztn 0.481 0.004 129.415 0.000 0.474
## Stest22puncttn 0.641 0.003 198.327 0.000 0.635
## Stest23english 0.532 0.004 150.219 0.000 0.525
## Stest24exprssn 0.454 0.004 126.793 0.000 0.447
## Stst25wrdfnctn 0.682 0.003 210.262 0.000 0.676
## Stst26rdngcmpr 0.756 0.003 259.006 0.000 0.751
## Stst28mchnclrs 0.432 0.003 136.991 0.000 0.426
## Stst29vslztn2D 0.305 0.004 77.708 0.000 0.297
## Stst30vslztn3D 0.445 0.004 121.085 0.000 0.438
## Stst31bstrctrs 0.535 0.004 137.455 0.000 0.528
## Stst32rthrsnng 0.676 0.003 208.296 0.000 0.670
## Stst33hghschlm 0.640 0.003 188.932 0.000 0.633
## Stst34rthcmptt 0.397 0.004 99.638 0.000 0.389
## Stest35tblrdng 0.186 0.004 48.955 0.000 0.178
## Stst36clrclchc 0.121 0.004 31.110 0.000 0.114
## Stst37bjctnspc 0.147 0.004 37.736 0.000 0.140
## ci.upper Std.lv Std.all
##
## 0.335 0.326 0.340
## 0.393 0.384 0.423
## 0.298 0.289 0.315
## 0.354 0.346 0.386
## 0.268 0.259 0.289
## 0.212 0.203 0.229
## 0.280 0.271 0.277
## 0.127 0.121 0.135
## 0.163 0.154 0.163
## 0.144 0.135 0.141
## 0.223 0.214 0.236
##
## 0.351 0.342 0.353
## 0.146 0.139 0.153
## 0.167 0.159 0.162
## 0.176 0.168 0.176
## 0.541 0.532 0.577
## 0.262 0.254 0.280
##
## 0.293 0.287 0.299
## 0.223 0.215 0.227
## 0.329 0.322 0.354
## 0.541 0.533 0.664
## 0.656 0.648 0.704
## 0.536 0.528 0.575
##
## 0.221 0.212 0.218
## 0.333 0.322 0.335
## 0.331 0.322 0.338
## 0.192 0.181 0.193
## 0.070 0.058 0.060
## 0.179 0.170 0.190
## 0.442 0.433 0.450
## 0.225 0.214 0.227
## 0.174 0.164 0.180
## 0.118 0.104 0.106
## 0.445 0.437 0.456
## 0.221 0.213 0.235
## 0.236 0.226 0.237
## 0.179 0.170 0.189
##
## 0.130 0.124 0.127
## 0.336 0.328 0.362
## 0.246 0.237 0.245
## 0.278 0.269 0.301
## 0.427 0.417 0.481
## 0.291 0.283 0.377
## 0.087 0.079 0.086
## 0.172 0.165 0.202
##
## 0.407 0.400 0.489
## 0.437 0.429 0.451
## 0.532 0.524 0.565
## 0.354 0.346 0.366
## 0.125 0.118 0.123
## 0.211 0.203 0.220
##
## 0.813 0.807 0.831
## 0.731 0.724 0.754
## 0.637 0.631 0.661
## 0.746 0.740 0.793
## 0.694 0.687 0.709
## 0.632 0.626 0.690
## 0.629 0.622 0.643
## 0.328 0.320 0.358
## 0.332 0.325 0.374
## 0.364 0.358 0.478
## 0.606 0.599 0.621
## 0.542 0.535 0.569
## 0.514 0.506 0.555
## 0.581 0.574 0.583
## 0.573 0.565 0.590
## 0.534 0.527 0.582
## 0.523 0.516 0.539
## 0.478 0.471 0.520
## 0.489 0.481 0.525
## 0.648 0.641 0.716
## 0.539 0.532 0.593
## 0.461 0.454 0.513
## 0.688 0.682 0.697
## 0.762 0.756 0.841
## 0.438 0.432 0.529
## 0.312 0.305 0.321
## 0.452 0.445 0.480
## 0.543 0.535 0.567
## 0.683 0.676 0.705
## 0.646 0.640 0.694
## 0.405 0.397 0.437
## 0.193 0.186 0.232
## 0.129 0.121 0.132
## 0.155 0.147 0.160
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.156 0.004 40.337 0.000 0.149
## .Stest20spellng 0.288 0.004 79.198 0.000 0.281
## .Stest21cptlztn 0.285 0.004 77.178 0.000 0.278
## .Stest22puncttn 0.289 0.004 80.304 0.000 0.282
## .Stest23english 0.200 0.004 55.481 0.000 0.193
## .Stest24exprssn 0.175 0.004 49.287 0.000 0.169
## .Stst25wrdfnctn 0.208 0.004 52.986 0.000 0.200
## .Stst26rdngcmpr 0.118 0.004 32.716 0.000 0.111
## .Stst31bstrctrs 0.037 0.004 9.666 0.000 0.029
## .Stst32rthrsnng -0.030 0.004 -7.900 0.000 -0.038
## .Stst34rthcmptt 0.175 0.004 47.455 0.000 0.168
## .Stest5math -0.133 0.004 -34.579 0.000 -0.141
## .Stst6physclscn -0.264 0.004 -73.191 0.000 -0.272
## .Stst33hghschlm -0.063 0.004 -17.147 0.000 -0.070
## .Stst29vslztn2D -0.144 0.004 -37.867 0.000 -0.151
## .Stest35tblrdng 0.099 0.003 30.730 0.000 0.092
## .Stst36clrclchc 0.087 0.004 23.895 0.000 0.079
## .Stst37bjctnspc 0.084 0.004 22.958 0.000 0.077
## .Stest1vocab -0.083 0.004 -21.517 0.000 -0.091
## .Stest2literatr 0.025 0.004 6.452 0.000 0.017
## .Stest3music 0.163 0.004 42.478 0.000 0.155
## .Stest4soclstds -0.132 0.004 -35.225 0.000 -0.139
## .Stst7blgclscnc -0.156 0.004 -40.430 0.000 -0.164
## .Stest8aerontcs -0.404 0.004 -112.676 0.000 -0.411
## .Stest11art 0.108 0.004 28.115 0.000 0.101
## .Stest12law -0.138 0.004 -36.597 0.000 -0.145
## .Stest13health 0.168 0.004 45.803 0.000 0.161
## .Stest14bible 0.070 0.004 17.656 0.000 0.062
## .Stest15theater 0.207 0.004 54.125 0.000 0.200
## .Stest16mscllns -0.071 0.004 -19.463 0.000 -0.078
## .Stest9elctrncs -0.416 0.003 -119.952 0.000 -0.423
## .Stest10mechncs -0.511 0.003 -170.689 0.000 -0.517
## .Stst28mchnclrs -0.422 0.003 -128.379 0.000 -0.429
## .Stst30vslztn3D -0.109 0.004 -29.486 0.000 -0.116
## ci.upper Std.lv Std.all
## 0.164 0.156 0.163
## 0.295 0.288 0.318
## 0.292 0.285 0.311
## 0.296 0.289 0.323
## 0.207 0.200 0.223
## 0.182 0.175 0.198
## 0.216 0.208 0.213
## 0.125 0.118 0.132
## 0.044 0.037 0.039
## -0.023 -0.030 -0.032
## 0.182 0.175 0.193
## -0.126 -0.133 -0.138
## -0.257 -0.264 -0.292
## -0.056 -0.063 -0.068
## -0.136 -0.144 -0.151
## 0.105 0.099 0.123
## 0.094 0.087 0.094
## 0.091 0.084 0.091
## -0.076 -0.083 -0.086
## 0.032 0.025 0.026
## 0.170 0.163 0.170
## -0.125 -0.132 -0.142
## -0.149 -0.156 -0.162
## -0.397 -0.404 -0.452
## 0.116 0.108 0.112
## -0.130 -0.138 -0.146
## 0.175 0.168 0.184
## 0.077 0.070 0.071
## 0.215 0.207 0.216
## -0.064 -0.071 -0.078
## -0.409 -0.416 -0.479
## -0.505 -0.511 -0.683
## -0.416 -0.422 -0.517
## -0.102 -0.109 -0.118
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.410 0.004 113.810 0.000 0.403
## .Stest20spellng 0.453 0.003 131.298 0.000 0.446
## .Stest21cptlztn 0.525 0.003 159.501 0.000 0.519
## .Stest22puncttn 0.272 0.002 124.681 0.000 0.267
## .Stest23english 0.455 0.003 157.574 0.000 0.450
## .Stest24exprssn 0.538 0.004 149.355 0.000 0.530
## .Stst25wrdfnctn 0.393 0.003 139.413 0.000 0.388
## .Stst26rdngcmpr 0.193 0.001 139.926 0.000 0.190
## .Stst31bstrctrs 0.462 0.003 145.790 0.000 0.456
## .Stst32rthrsnng 0.402 0.002 165.974 0.000 0.398
## .Stst34rthcmptt 0.454 0.004 126.436 0.000 0.447
## .Stest5math 0.349 0.003 106.177 0.000 0.342
## .Stst6physclscn 0.304 0.003 118.930 0.000 0.299
## .Stst33hghschlm 0.156 0.004 37.849 0.000 0.148
## .Stst29vslztn2D 0.581 0.004 139.676 0.000 0.573
## .Stest35tblrdng 0.326 0.004 89.867 0.000 0.319
## .Stst36clrclchc 0.411 0.005 89.230 0.000 0.402
## .Stst37bjctnspc 0.503 0.004 128.180 0.000 0.496
## .Stest1vocab 0.232 0.002 149.126 0.000 0.229
## .Stest2literatr 0.293 0.002 150.380 0.000 0.289
## .Stest3music 0.409 0.003 157.356 0.000 0.403
## .Stest4soclstds 0.291 0.002 155.039 0.000 0.287
## .Stst7blgclscnc 0.490 0.003 161.137 0.000 0.484
## .Stest8aerontcs 0.597 0.004 161.115 0.000 0.589
## .Stest11art 0.383 0.003 132.495 0.000 0.377
## .Stest12law 0.552 0.003 177.351 0.000 0.546
## .Stest13health 0.541 0.003 173.779 0.000 0.535
## .Stest14bible 0.630 0.003 189.599 0.000 0.623
## .Stest15theater 0.409 0.003 123.913 0.000 0.403
## .Stest16mscllns 0.497 0.003 172.061 0.000 0.491
## .Stest9elctrncs 0.473 0.005 103.285 0.000 0.464
## .Stest10mechncs 0.353 0.002 141.454 0.000 0.348
## .Stst28mchnclrs 0.294 0.003 115.872 0.000 0.289
## .Stst30vslztn3D 0.387 0.004 104.908 0.000 0.380
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.418 0.410 0.448
## 0.460 0.453 0.551
## 0.532 0.525 0.625
## 0.276 0.272 0.338
## 0.461 0.455 0.565
## 0.545 0.538 0.685
## 0.399 0.393 0.411
## 0.195 0.193 0.238
## 0.468 0.462 0.518
## 0.407 0.402 0.437
## 0.461 0.454 0.550
## 0.355 0.349 0.372
## 0.309 0.304 0.369
## 0.164 0.156 0.184
## 0.589 0.581 0.643
## 0.333 0.326 0.505
## 0.420 0.411 0.486
## 0.511 0.503 0.595
## 0.235 0.232 0.246
## 0.297 0.293 0.318
## 0.414 0.409 0.449
## 0.294 0.291 0.334
## 0.496 0.490 0.523
## 0.604 0.597 0.745
## 0.388 0.383 0.412
## 0.558 0.552 0.625
## 0.547 0.541 0.652
## 0.636 0.630 0.649
## 0.416 0.409 0.445
## 0.503 0.497 0.606
## 0.482 0.473 0.629
## 0.358 0.353 0.629
## 0.299 0.294 0.440
## 0.395 0.387 0.451
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
modificationIndices(configural, sort=T, maximum.number=30)
## lhs op rhs block
## 130 english ~~ science 1
## 145 science ~~ spatial 1
## 878 Stest6physicalscience ~~ Stest10mechanics 1
## 503 spatial =~ Stest20spelling 1
## 403 math =~ Stest22punctuation 1
## 127 english ~~ math 1
## 318 english ~~ science 2
## 379 english =~ Stest33highschoolmath 1
## 1217 spatial =~ Stest20spelling 2
## 501 science =~ Stest30visualization3D 1
## 1142 speed =~ Stest20spelling 2
## 456 info =~ Stest20spelling 1
## 134 math ~~ info 1
## 1170 info =~ Stest20spelling 2
## 513 spatial =~ Stest33highschoolmath 1
## 428 speed =~ Stest20spelling 1
## 324 math ~~ spatial 2
## 136 math ~~ spatial 1
## 1117 math =~ Stest22punctuation 2
## 877 Stest6physicalscience ~~ Stest9electronics 1
## 635 Stest22punctuation ~~ Stest33highschoolmath 1
## 1592 Stest6physicalscience ~~ Stest10mechanics 2
## 1243 spatial =~ Stest10mechanics 2
## 686 Stest24expression ~~ Stest26readingcomprehension 1
## 550 Stest19disguisedwords ~~ Stest4socialstudies 1
## 1227 spatial =~ Stest33highschoolmath 2
## 519 spatial =~ Stest4socialstudies 1
## 143 info ~~ spatial 1
## 1093 english =~ Stest33highschoolmath 2
## 752 Stest26readingcomprehension ~~ Stest3music 1
## group level mi epc sepc.lv sepc.all sepc.nox
## 130 1 1 3259.064 -0.408 -0.408 -0.408 -0.408
## 145 1 1 3121.255 0.357 0.357 0.357 0.357
## 878 1 1 2674.356 -0.078 -0.078 -0.257 -0.257
## 503 1 1 2602.582 -0.186 -0.186 -0.187 -0.187
## 403 1 1 2505.277 0.162 0.162 0.166 0.166
## 127 1 1 2480.956 0.421 0.421 0.421 0.421
## 318 2 1 2456.828 -0.398 -0.398 -0.398 -0.398
## 379 1 1 2403.755 0.181 0.181 0.174 0.174
## 1217 2 1 2001.475 -0.155 -0.155 -0.171 -0.171
## 501 1 1 1851.498 0.165 0.165 0.163 0.163
## 1142 2 1 1690.938 0.131 0.131 0.145 0.145
## 456 1 1 1616.633 0.166 0.166 0.167 0.167
## 134 1 1 1608.463 -0.335 -0.335 -0.335 -0.335
## 1170 2 1 1547.274 0.158 0.158 0.175 0.175
## 513 1 1 1502.276 0.111 0.111 0.107 0.107
## 428 1 1 1498.940 0.132 0.132 0.133 0.133
## 324 2 1 1455.669 0.240 0.240 0.240 0.240
## 136 1 1 1416.351 0.236 0.236 0.236 0.236
## 1117 2 1 1375.081 0.109 0.109 0.122 0.122
## 877 1 1 1346.962 0.056 0.056 0.216 0.216
## 635 1 1 1322.865 0.053 0.053 0.253 0.253
## 1592 2 1 1287.445 -0.067 -0.067 -0.206 -0.206
## 1243 2 1 1270.102 0.108 0.108 0.145 0.145
## 686 1 1 1232.611 0.057 0.057 0.148 0.148
## 550 1 1 1226.514 -0.055 -0.055 -0.154 -0.154
## 1227 2 1 1219.003 0.099 0.099 0.108 0.108
## 519 1 1 1203.857 -0.095 -0.095 -0.098 -0.098
## 143 1 1 1193.439 -0.230 -0.230 -0.230 -0.230
## 1093 2 1 1189.616 0.116 0.116 0.126 0.126
## 752 1 1 1161.866 -0.047 -0.047 -0.147 -0.147
metric<-cfa(chc.bifactor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 123462.539 1030.000 0.000 0.954 0.041
## srmr aic bic
## 0.038 10327309.037 10329553.153
Mc(metric)
## [1] 0.6438818
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 72 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 313
## Number of equality constraints 85
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 123462.539 108564.963
## Degrees of freedom 1030 1030
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.137
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 70044.177 61592.315
## 1 53418.361 46972.648
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.314 0.003 90.709 0.000 0.308
## Stst20s (.p2.) 0.394 0.004 104.473 0.000 0.386
## Stst21c (.p3.) 0.295 0.004 82.100 0.000 0.288
## Stst22p (.p4.) 0.356 0.004 100.341 0.000 0.349
## Stst23n (.p5.) 0.272 0.003 78.416 0.000 0.265
## Stst24x (.p6.) 0.219 0.004 56.269 0.000 0.211
## Stst25w (.p7.) 0.267 0.003 80.243 0.000 0.261
## Stst26r (.p8.) 0.124 0.003 48.087 0.000 0.119
## Stst31b (.p9.) 0.129 0.003 38.837 0.000 0.123
## Stst32r (.10.) 0.115 0.003 36.404 0.000 0.109
## Stst34r (.11.) 0.199 0.003 60.177 0.000 0.192
## math =~
## Stst5mt (.12.) 0.274 0.003 90.126 0.000 0.268
## Stst6ph (.13.) 0.103 0.003 39.463 0.000 0.098
## Stst25w (.14.) 0.154 0.003 54.355 0.000 0.148
## Stst32r (.15.) 0.176 0.003 60.231 0.000 0.170
## Stst33h (.16.) 0.534 0.005 112.807 0.000 0.525
## Stst34r (.17.) 0.267 0.003 77.137 0.000 0.260
## speed =~
## Stst19d (.18.) 0.282 0.003 106.066 0.000 0.277
## Sts292D (.19.) 0.234 0.003 77.930 0.000 0.228
## Stst34r (.20.) 0.365 0.003 123.480 0.000 0.359
## Stst35t (.21.) 0.616 0.004 156.119 0.000 0.608
## Stst36c (.22.) 0.702 0.004 182.711 0.000 0.694
## Stst37b (.23.) 0.591 0.004 160.535 0.000 0.583
## info =~
## Stst1vc (.24.) 0.213 0.003 74.950 0.000 0.208
## Stst2lt (.25.) 0.350 0.004 86.230 0.000 0.342
## Stst3ms (.26.) 0.347 0.003 104.646 0.000 0.340
## Stst4sc (.27.) 0.203 0.004 46.024 0.000 0.195
## Stst7bl (.28.) 0.092 0.004 21.759 0.000 0.084
## Stst8rn (.29.) 0.171 0.003 54.253 0.000 0.165
## Stst11r (.30.) 0.448 0.003 128.964 0.000 0.441
## Stst12l (.31.) 0.238 0.004 58.507 0.000 0.230
## Stst13h (.32.) 0.199 0.004 50.774 0.000 0.191
## Stst14b (.33.) 0.173 0.005 34.141 0.000 0.163
## Stst15t (.34.) 0.425 0.003 129.136 0.000 0.419
## Stst16m (.35.) 0.251 0.004 69.057 0.000 0.244
## Stst19d (.36.) 0.236 0.003 67.712 0.000 0.229
## Stst26r (.37.) 0.196 0.004 55.487 0.000 0.189
## science =~
## Stst1vc (.38.) 0.164 0.002 71.498 0.000 0.159
## Stst6ph (.39.) 0.316 0.003 108.979 0.000 0.311
## Stst7bl (.40.) 0.267 0.003 78.160 0.000 0.260
## Stst8rn (.41.) 0.322 0.003 101.420 0.000 0.315
## Stst9lc (.42.) 0.483 0.003 147.152 0.000 0.476
## Stst10m (.43.) 0.401 0.003 117.395 0.000 0.395
## Stst13h (.44.) 0.096 0.003 29.089 0.000 0.090
## Stst28m (.45.) 0.267 0.003 88.864 0.000 0.261
## spatial =~
## Stst28m (.46.) 0.425 0.003 150.532 0.000 0.420
## Sts292D (.47.) 0.466 0.003 136.160 0.000 0.459
## Sts303D (.48.) 0.585 0.004 156.797 0.000 0.577
## Stst31b (.49.) 0.372 0.003 119.300 0.000 0.366
## Stst32r (.50.) 0.123 0.003 47.388 0.000 0.118
## Stst37b (.51.) 0.226 0.003 70.928 0.000 0.220
## g =~
## Stst1vc (.52.) 0.807 0.003 291.819 0.000 0.801
## Stst2lt (.53.) 0.766 0.003 258.553 0.000 0.760
## Stst3ms (.54.) 0.664 0.003 243.093 0.000 0.658
## Stst4sc (.55.) 0.784 0.003 258.403 0.000 0.778
## Stst5mt (.56.) 0.739 0.003 266.199 0.000 0.734
## Stst6ph (.57.) 0.716 0.003 266.619 0.000 0.711
## Stst7bl (.58.) 0.642 0.003 215.831 0.000 0.636
## Stst8rn (.59.) 0.437 0.003 148.177 0.000 0.431
## Stst9lc (.60.) 0.420 0.003 150.525 0.000 0.415
## Stst10m (.61.) 0.398 0.003 153.733 0.000 0.393
## Stst11r (.62.) 0.623 0.003 206.643 0.000 0.617
## Stst12l (.63.) 0.612 0.003 196.075 0.000 0.606
## Stst13h (.64.) 0.582 0.003 177.513 0.000 0.576
## Stst14b (.65.) 0.608 0.003 197.088 0.000 0.602
## Stst15t (.66.) 0.596 0.003 211.546 0.000 0.591
## Stst16m (.67.) 0.619 0.003 199.678 0.000 0.613
## Stst19d (.68.) 0.555 0.003 189.478 0.000 0.549
## Stst20s (.69.) 0.531 0.003 180.006 0.000 0.525
## Stst21c (.70.) 0.554 0.003 186.561 0.000 0.548
## Stst22p (.71.) 0.704 0.003 243.973 0.000 0.698
## Stst23n (.72.) 0.605 0.003 193.415 0.000 0.599
## Stst24x (.73.) 0.538 0.003 168.526 0.000 0.532
## Stst25w (.74.) 0.699 0.003 264.381 0.000 0.694
## Stst26r (.75.) 0.831 0.003 282.207 0.000 0.825
## Stst28m (.76.) 0.476 0.003 177.043 0.000 0.471
## Sts292D (.77.) 0.328 0.003 108.461 0.000 0.322
## Sts303D (.78.) 0.488 0.003 160.934 0.000 0.482
## Stst31b (.79.) 0.577 0.003 182.978 0.000 0.570
## Stst32r (.80.) 0.727 0.003 260.954 0.000 0.722
## Stst33h (.81.) 0.751 0.003 248.622 0.000 0.745
## Stst34r (.82.) 0.455 0.003 144.957 0.000 0.448
## Stst35t (.83.) 0.238 0.003 78.000 0.000 0.232
## Stst36c (.84.) 0.136 0.003 45.593 0.000 0.131
## Stst37b (.85.) 0.150 0.003 49.210 0.000 0.144
## ci.upper Std.lv Std.all
##
## 0.321 0.314 0.323
## 0.401 0.394 0.401
## 0.302 0.295 0.309
## 0.363 0.356 0.367
## 0.279 0.272 0.277
## 0.226 0.219 0.219
## 0.274 0.267 0.269
## 0.129 0.124 0.125
## 0.136 0.129 0.132
## 0.122 0.115 0.117
## 0.205 0.199 0.208
##
## 0.280 0.274 0.295
## 0.108 0.103 0.108
## 0.159 0.154 0.155
## 0.182 0.176 0.179
## 0.544 0.534 0.530
## 0.274 0.267 0.280
##
## 0.287 0.282 0.289
## 0.240 0.234 0.242
## 0.371 0.365 0.382
## 0.623 0.616 0.666
## 0.710 0.702 0.719
## 0.598 0.591 0.584
##
## 0.219 0.213 0.222
## 0.358 0.350 0.351
## 0.353 0.347 0.346
## 0.212 0.203 0.208
## 0.101 0.092 0.094
## 0.177 0.171 0.203
## 0.455 0.448 0.456
## 0.246 0.238 0.243
## 0.206 0.199 0.204
## 0.182 0.173 0.171
## 0.432 0.425 0.436
## 0.258 0.251 0.250
## 0.243 0.236 0.242
## 0.203 0.196 0.199
##
## 0.168 0.164 0.170
## 0.322 0.316 0.333
## 0.273 0.267 0.272
## 0.328 0.322 0.383
## 0.489 0.483 0.604
## 0.408 0.401 0.496
## 0.103 0.096 0.099
## 0.273 0.267 0.312
##
## 0.431 0.425 0.497
## 0.473 0.466 0.482
## 0.592 0.585 0.579
## 0.378 0.372 0.380
## 0.128 0.123 0.125
## 0.232 0.226 0.224
##
## 0.812 0.807 0.840
## 0.772 0.766 0.769
## 0.669 0.664 0.662
## 0.790 0.784 0.802
## 0.745 0.739 0.795
## 0.721 0.716 0.753
## 0.648 0.642 0.655
## 0.443 0.437 0.521
## 0.426 0.420 0.526
## 0.403 0.398 0.492
## 0.629 0.623 0.634
## 0.618 0.612 0.624
## 0.589 0.582 0.598
## 0.614 0.608 0.603
## 0.602 0.596 0.611
## 0.626 0.619 0.616
## 0.560 0.555 0.569
## 0.537 0.531 0.541
## 0.560 0.554 0.580
## 0.710 0.704 0.726
## 0.611 0.605 0.617
## 0.544 0.538 0.540
## 0.704 0.699 0.704
## 0.836 0.831 0.841
## 0.481 0.476 0.556
## 0.334 0.328 0.339
## 0.493 0.488 0.483
## 0.583 0.577 0.588
## 0.733 0.727 0.739
## 0.757 0.751 0.745
## 0.461 0.455 0.476
## 0.243 0.238 0.257
## 0.142 0.136 0.140
## 0.156 0.150 0.148
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd -0.108 0.004 -27.549 0.000 -0.116
## .Stest20spellng -0.242 0.004 -59.771 0.000 -0.249
## .Stest21cptlztn -0.194 0.004 -49.221 0.000 -0.202
## .Stest22puncttn -0.183 0.004 -46.236 0.000 -0.191
## .Stest23english -0.119 0.004 -29.356 0.000 -0.127
## .Stest24exprssn -0.091 0.004 -21.886 0.000 -0.099
## .Stst25wrdfnctn -0.120 0.004 -30.548 0.000 -0.128
## .Stst26rdngcmpr -0.002 0.004 -0.480 0.632 -0.010
## .Stst31bstrctrs 0.074 0.004 18.667 0.000 0.066
## .Stst32rthrsnng 0.142 0.004 35.487 0.000 0.134
## .Stst34rthcmptt -0.062 0.004 -15.612 0.000 -0.070
## .Stest5math 0.219 0.004 58.635 0.000 0.212
## .Stst6physclscn 0.358 0.004 92.152 0.000 0.350
## .Stst33hghschlm 0.138 0.004 32.978 0.000 0.130
## .Stst29vslztn2D 0.224 0.004 57.484 0.000 0.217
## .Stest35tblrdng -0.047 0.004 -12.373 0.000 -0.055
## .Stst36clrclchc -0.165 0.004 -42.339 0.000 -0.173
## .Stst37bjctnspc -0.098 0.004 -24.085 0.000 -0.106
## .Stest1vocab 0.189 0.004 50.214 0.000 0.181
## .Stest2literatr 0.029 0.004 7.337 0.000 0.022
## .Stest3music -0.121 0.004 -29.896 0.000 -0.128
## .Stest4soclstds 0.228 0.004 57.617 0.000 0.220
## .Stst7blgclscnc 0.243 0.004 61.805 0.000 0.235
## .Stest8aerontcs 0.481 0.004 135.791 0.000 0.474
## .Stest11art -0.054 0.004 -13.827 0.000 -0.062
## .Stest12law 0.208 0.004 51.531 0.000 0.200
## .Stest13health -0.081 0.004 -19.852 0.000 -0.089
## .Stest14bible 0.015 0.004 3.604 0.000 0.007
## .Stest15theater -0.167 0.004 -42.900 0.000 -0.175
## .Stest16mscllns 0.134 0.004 31.520 0.000 0.125
## .Stest9elctrncs 0.522 0.003 156.854 0.000 0.516
## .Stest10mechncs 0.644 0.003 193.961 0.000 0.638
## .Stst28mchnclrs 0.551 0.004 154.563 0.000 0.544
## .Stst30vslztn3D 0.206 0.004 50.236 0.000 0.198
## ci.upper Std.lv Std.all
## -0.101 -0.108 -0.111
## -0.234 -0.242 -0.246
## -0.186 -0.194 -0.203
## -0.175 -0.183 -0.189
## -0.111 -0.119 -0.122
## -0.083 -0.091 -0.092
## -0.112 -0.120 -0.121
## 0.006 -0.002 -0.002
## 0.082 0.074 0.075
## 0.149 0.142 0.144
## -0.054 -0.062 -0.065
## 0.227 0.219 0.236
## 0.365 0.358 0.376
## 0.147 0.138 0.137
## 0.232 0.224 0.232
## -0.040 -0.047 -0.051
## -0.158 -0.165 -0.169
## -0.090 -0.098 -0.097
## 0.196 0.189 0.197
## 0.037 0.029 0.030
## -0.113 -0.121 -0.120
## 0.236 0.228 0.234
## 0.251 0.243 0.248
## 0.488 0.481 0.574
## -0.047 -0.054 -0.055
## 0.216 0.208 0.213
## -0.073 -0.081 -0.083
## 0.023 0.015 0.015
## -0.159 -0.167 -0.171
## 0.142 0.134 0.133
## 0.529 0.522 0.654
## 0.651 0.644 0.796
## 0.558 0.551 0.644
## 0.214 0.206 0.204
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.408 0.003 126.477 0.000 0.402
## .Stest20spellng 0.528 0.004 143.734 0.000 0.520
## .Stest21cptlztn 0.519 0.003 162.535 0.000 0.512
## .Stest22puncttn 0.318 0.002 131.279 0.000 0.313
## .Stest23english 0.522 0.003 151.329 0.000 0.515
## .Stest24exprssn 0.656 0.004 154.289 0.000 0.648
## .Stst25wrdfnctn 0.401 0.003 145.900 0.000 0.396
## .Stst26rdngcmpr 0.231 0.002 137.320 0.000 0.228
## .Stst31bstrctrs 0.474 0.003 147.289 0.000 0.468
## .Stst32rthrsnng 0.381 0.002 159.872 0.000 0.376
## .Stst34rthcmptt 0.463 0.003 133.209 0.000 0.456
## .Stest5math 0.244 0.003 93.869 0.000 0.239
## .Stst6physclscn 0.281 0.002 143.117 0.000 0.278
## .Stst33hghschlm 0.167 0.004 43.014 0.000 0.159
## .Stst29vslztn2D 0.554 0.004 128.354 0.000 0.546
## .Stest35tblrdng 0.420 0.004 94.668 0.000 0.411
## .Stst36clrclchc 0.441 0.005 88.539 0.000 0.432
## .Stst37bjctnspc 0.599 0.005 131.693 0.000 0.590
## .Stest1vocab 0.199 0.001 147.183 0.000 0.196
## .Stest2literatr 0.284 0.002 149.233 0.000 0.280
## .Stest3music 0.445 0.003 161.019 0.000 0.440
## .Stest4soclstds 0.299 0.002 154.252 0.000 0.296
## .Stst7blgclscnc 0.468 0.003 160.096 0.000 0.463
## .Stest8aerontcs 0.380 0.003 117.197 0.000 0.374
## .Stest11art 0.377 0.003 143.086 0.000 0.371
## .Stest12law 0.529 0.003 172.083 0.000 0.523
## .Stest13health 0.561 0.003 174.883 0.000 0.555
## .Stest14bible 0.619 0.003 186.187 0.000 0.613
## .Stest15theater 0.416 0.003 143.608 0.000 0.410
## .Stest16mscllns 0.563 0.003 167.423 0.000 0.557
## .Stest9elctrncs 0.229 0.003 80.754 0.000 0.223
## .Stest10mechncs 0.336 0.003 131.219 0.000 0.331
## .Stst28mchnclrs 0.253 0.002 106.612 0.000 0.249
## .Stst30vslztn3D 0.441 0.004 112.027 0.000 0.433
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.415 0.408 0.430
## 0.535 0.528 0.547
## 0.525 0.519 0.568
## 0.323 0.318 0.338
## 0.528 0.522 0.543
## 0.665 0.656 0.660
## 0.407 0.401 0.408
## 0.234 0.231 0.237
## 0.480 0.474 0.493
## 0.386 0.381 0.393
## 0.469 0.463 0.506
## 0.249 0.244 0.282
## 0.285 0.281 0.311
## 0.174 0.167 0.164
## 0.563 0.554 0.594
## 0.429 0.420 0.491
## 0.451 0.441 0.463
## 0.608 0.599 0.587
## 0.201 0.199 0.215
## 0.288 0.284 0.286
## 0.450 0.445 0.442
## 0.303 0.299 0.313
## 0.474 0.468 0.488
## 0.387 0.380 0.540
## 0.382 0.377 0.390
## 0.535 0.529 0.551
## 0.568 0.561 0.591
## 0.626 0.619 0.608
## 0.421 0.416 0.436
## 0.570 0.563 0.558
## 0.234 0.229 0.358
## 0.341 0.336 0.512
## 0.258 0.253 0.346
## 0.449 0.441 0.432
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.314 0.003 90.709 0.000 0.308
## Stst20s (.p2.) 0.394 0.004 104.473 0.000 0.386
## Stst21c (.p3.) 0.295 0.004 82.100 0.000 0.288
## Stst22p (.p4.) 0.356 0.004 100.341 0.000 0.349
## Stst23n (.p5.) 0.272 0.003 78.416 0.000 0.265
## Stst24x (.p6.) 0.219 0.004 56.269 0.000 0.211
## Stst25w (.p7.) 0.267 0.003 80.243 0.000 0.261
## Stst26r (.p8.) 0.124 0.003 48.087 0.000 0.119
## Stst31b (.p9.) 0.129 0.003 38.837 0.000 0.123
## Stst32r (.10.) 0.115 0.003 36.404 0.000 0.109
## Stst34r (.11.) 0.199 0.003 60.177 0.000 0.192
## math =~
## Stst5mt (.12.) 0.274 0.003 90.126 0.000 0.268
## Stst6ph (.13.) 0.103 0.003 39.463 0.000 0.098
## Stst25w (.14.) 0.154 0.003 54.355 0.000 0.148
## Stst32r (.15.) 0.176 0.003 60.231 0.000 0.170
## Stst33h (.16.) 0.534 0.005 112.807 0.000 0.525
## Stst34r (.17.) 0.267 0.003 77.137 0.000 0.260
## speed =~
## Stst19d (.18.) 0.282 0.003 106.066 0.000 0.277
## Sts292D (.19.) 0.234 0.003 77.930 0.000 0.228
## Stst34r (.20.) 0.365 0.003 123.480 0.000 0.359
## Stst35t (.21.) 0.616 0.004 156.119 0.000 0.608
## Stst36c (.22.) 0.702 0.004 182.711 0.000 0.694
## Stst37b (.23.) 0.591 0.004 160.535 0.000 0.583
## info =~
## Stst1vc (.24.) 0.213 0.003 74.950 0.000 0.208
## Stst2lt (.25.) 0.350 0.004 86.230 0.000 0.342
## Stst3ms (.26.) 0.347 0.003 104.646 0.000 0.340
## Stst4sc (.27.) 0.203 0.004 46.024 0.000 0.195
## Stst7bl (.28.) 0.092 0.004 21.759 0.000 0.084
## Stst8rn (.29.) 0.171 0.003 54.253 0.000 0.165
## Stst11r (.30.) 0.448 0.003 128.964 0.000 0.441
## Stst12l (.31.) 0.238 0.004 58.507 0.000 0.230
## Stst13h (.32.) 0.199 0.004 50.774 0.000 0.191
## Stst14b (.33.) 0.173 0.005 34.141 0.000 0.163
## Stst15t (.34.) 0.425 0.003 129.136 0.000 0.419
## Stst16m (.35.) 0.251 0.004 69.057 0.000 0.244
## Stst19d (.36.) 0.236 0.003 67.712 0.000 0.229
## Stst26r (.37.) 0.196 0.004 55.487 0.000 0.189
## science =~
## Stst1vc (.38.) 0.164 0.002 71.498 0.000 0.159
## Stst6ph (.39.) 0.316 0.003 108.979 0.000 0.311
## Stst7bl (.40.) 0.267 0.003 78.160 0.000 0.260
## Stst8rn (.41.) 0.322 0.003 101.420 0.000 0.315
## Stst9lc (.42.) 0.483 0.003 147.152 0.000 0.476
## Stst10m (.43.) 0.401 0.003 117.395 0.000 0.395
## Stst13h (.44.) 0.096 0.003 29.089 0.000 0.090
## Stst28m (.45.) 0.267 0.003 88.864 0.000 0.261
## spatial =~
## Stst28m (.46.) 0.425 0.003 150.532 0.000 0.420
## Sts292D (.47.) 0.466 0.003 136.160 0.000 0.459
## Sts303D (.48.) 0.585 0.004 156.797 0.000 0.577
## Stst31b (.49.) 0.372 0.003 119.300 0.000 0.366
## Stst32r (.50.) 0.123 0.003 47.388 0.000 0.118
## Stst37b (.51.) 0.226 0.003 70.928 0.000 0.220
## g =~
## Stst1vc (.52.) 0.807 0.003 291.819 0.000 0.801
## Stst2lt (.53.) 0.766 0.003 258.553 0.000 0.760
## Stst3ms (.54.) 0.664 0.003 243.093 0.000 0.658
## Stst4sc (.55.) 0.784 0.003 258.403 0.000 0.778
## Stst5mt (.56.) 0.739 0.003 266.199 0.000 0.734
## Stst6ph (.57.) 0.716 0.003 266.619 0.000 0.711
## Stst7bl (.58.) 0.642 0.003 215.831 0.000 0.636
## Stst8rn (.59.) 0.437 0.003 148.177 0.000 0.431
## Stst9lc (.60.) 0.420 0.003 150.525 0.000 0.415
## Stst10m (.61.) 0.398 0.003 153.733 0.000 0.393
## Stst11r (.62.) 0.623 0.003 206.643 0.000 0.617
## Stst12l (.63.) 0.612 0.003 196.075 0.000 0.606
## Stst13h (.64.) 0.582 0.003 177.513 0.000 0.576
## Stst14b (.65.) 0.608 0.003 197.088 0.000 0.602
## Stst15t (.66.) 0.596 0.003 211.546 0.000 0.591
## Stst16m (.67.) 0.619 0.003 199.678 0.000 0.613
## Stst19d (.68.) 0.555 0.003 189.478 0.000 0.549
## Stst20s (.69.) 0.531 0.003 180.006 0.000 0.525
## Stst21c (.70.) 0.554 0.003 186.561 0.000 0.548
## Stst22p (.71.) 0.704 0.003 243.973 0.000 0.698
## Stst23n (.72.) 0.605 0.003 193.415 0.000 0.599
## Stst24x (.73.) 0.538 0.003 168.526 0.000 0.532
## Stst25w (.74.) 0.699 0.003 264.381 0.000 0.694
## Stst26r (.75.) 0.831 0.003 282.207 0.000 0.825
## Stst28m (.76.) 0.476 0.003 177.043 0.000 0.471
## Sts292D (.77.) 0.328 0.003 108.461 0.000 0.322
## Sts303D (.78.) 0.488 0.003 160.934 0.000 0.482
## Stst31b (.79.) 0.577 0.003 182.978 0.000 0.570
## Stst32r (.80.) 0.727 0.003 260.954 0.000 0.722
## Stst33h (.81.) 0.751 0.003 248.622 0.000 0.745
## Stst34r (.82.) 0.455 0.003 144.957 0.000 0.448
## Stst35t (.83.) 0.238 0.003 78.000 0.000 0.232
## Stst36c (.84.) 0.136 0.003 45.593 0.000 0.131
## Stst37b (.85.) 0.150 0.003 49.210 0.000 0.144
## ci.upper Std.lv Std.all
##
## 0.321 0.312 0.330
## 0.401 0.391 0.427
## 0.302 0.293 0.315
## 0.363 0.354 0.393
## 0.279 0.270 0.296
## 0.226 0.217 0.239
## 0.274 0.265 0.279
## 0.129 0.123 0.135
## 0.136 0.128 0.137
## 0.122 0.115 0.120
## 0.205 0.197 0.215
##
## 0.280 0.276 0.291
## 0.108 0.104 0.113
## 0.159 0.155 0.162
## 0.182 0.177 0.186
## 0.544 0.537 0.566
## 0.274 0.269 0.292
##
## 0.287 0.254 0.268
## 0.240 0.211 0.222
## 0.371 0.329 0.357
## 0.623 0.554 0.678
## 0.710 0.632 0.689
## 0.598 0.532 0.578
##
## 0.219 0.210 0.228
## 0.358 0.345 0.362
## 0.353 0.341 0.361
## 0.212 0.200 0.217
## 0.101 0.091 0.096
## 0.177 0.168 0.181
## 0.455 0.441 0.463
## 0.246 0.234 0.244
## 0.206 0.196 0.210
## 0.182 0.170 0.172
## 0.432 0.419 0.442
## 0.258 0.247 0.264
## 0.243 0.233 0.246
## 0.203 0.193 0.213
##
## 0.168 0.132 0.143
## 0.322 0.255 0.279
## 0.273 0.215 0.227
## 0.328 0.259 0.280
## 0.489 0.389 0.438
## 0.408 0.324 0.428
## 0.103 0.078 0.083
## 0.273 0.215 0.262
##
## 0.431 0.387 0.471
## 0.473 0.424 0.447
## 0.592 0.532 0.572
## 0.378 0.339 0.362
## 0.128 0.112 0.117
## 0.232 0.206 0.224
##
## 0.812 0.740 0.802
## 0.772 0.702 0.739
## 0.669 0.609 0.643
## 0.790 0.719 0.781
## 0.745 0.678 0.715
## 0.721 0.656 0.718
## 0.648 0.588 0.620
## 0.443 0.401 0.432
## 0.426 0.385 0.433
## 0.403 0.365 0.482
## 0.629 0.571 0.600
## 0.618 0.561 0.585
## 0.589 0.534 0.573
## 0.614 0.558 0.565
## 0.602 0.547 0.577
## 0.626 0.568 0.606
## 0.560 0.508 0.537
## 0.537 0.487 0.531
## 0.560 0.508 0.546
## 0.710 0.645 0.717
## 0.611 0.554 0.607
## 0.544 0.493 0.542
## 0.704 0.641 0.673
## 0.836 0.762 0.838
## 0.481 0.436 0.531
## 0.334 0.301 0.317
## 0.493 0.447 0.481
## 0.583 0.529 0.565
## 0.733 0.667 0.701
## 0.757 0.689 0.726
## 0.461 0.417 0.453
## 0.243 0.218 0.267
## 0.142 0.125 0.136
## 0.156 0.137 0.149
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.156 0.004 40.337 0.000 0.149
## .Stest20spellng 0.288 0.004 79.198 0.000 0.281
## .Stest21cptlztn 0.285 0.004 77.178 0.000 0.278
## .Stest22puncttn 0.289 0.004 80.304 0.000 0.282
## .Stest23english 0.200 0.004 55.481 0.000 0.193
## .Stest24exprssn 0.175 0.004 49.287 0.000 0.169
## .Stst25wrdfnctn 0.208 0.004 52.986 0.000 0.200
## .Stst26rdngcmpr 0.118 0.004 32.716 0.000 0.111
## .Stst31bstrctrs 0.037 0.004 9.666 0.000 0.029
## .Stst32rthrsnng -0.030 0.004 -7.900 0.000 -0.038
## .Stst34rthcmptt 0.175 0.004 47.455 0.000 0.168
## .Stest5math -0.133 0.004 -34.579 0.000 -0.141
## .Stst6physclscn -0.264 0.004 -73.191 0.000 -0.272
## .Stst33hghschlm -0.063 0.004 -17.147 0.000 -0.070
## .Stst29vslztn2D -0.144 0.004 -37.867 0.000 -0.151
## .Stest35tblrdng 0.099 0.003 30.730 0.000 0.092
## .Stst36clrclchc 0.087 0.004 23.895 0.000 0.079
## .Stst37bjctnspc 0.084 0.004 22.958 0.000 0.077
## .Stest1vocab -0.083 0.004 -21.517 0.000 -0.091
## .Stest2literatr 0.025 0.004 6.452 0.000 0.017
## .Stest3music 0.163 0.004 42.478 0.000 0.155
## .Stest4soclstds -0.132 0.004 -35.225 0.000 -0.139
## .Stst7blgclscnc -0.156 0.004 -40.430 0.000 -0.164
## .Stest8aerontcs -0.404 0.004 -112.676 0.000 -0.411
## .Stest11art 0.108 0.004 28.115 0.000 0.101
## .Stest12law -0.138 0.004 -36.597 0.000 -0.145
## .Stest13health 0.168 0.004 45.803 0.000 0.161
## .Stest14bible 0.070 0.004 17.656 0.000 0.062
## .Stest15theater 0.207 0.004 54.125 0.000 0.200
## .Stest16mscllns -0.071 0.004 -19.463 0.000 -0.078
## .Stest9elctrncs -0.416 0.003 -119.952 0.000 -0.423
## .Stest10mechncs -0.511 0.003 -170.689 0.000 -0.517
## .Stst28mchnclrs -0.422 0.003 -128.379 0.000 -0.429
## .Stst30vslztn3D -0.109 0.004 -29.486 0.000 -0.116
## ci.upper Std.lv Std.all
## 0.164 0.156 0.165
## 0.295 0.288 0.314
## 0.292 0.285 0.306
## 0.296 0.289 0.322
## 0.207 0.200 0.219
## 0.182 0.175 0.193
## 0.216 0.208 0.219
## 0.125 0.118 0.130
## 0.044 0.037 0.039
## -0.023 -0.030 -0.032
## 0.182 0.175 0.190
## -0.126 -0.133 -0.141
## -0.257 -0.264 -0.289
## -0.056 -0.063 -0.066
## -0.136 -0.144 -0.152
## 0.105 0.099 0.121
## 0.094 0.087 0.094
## 0.091 0.084 0.091
## -0.076 -0.083 -0.090
## 0.032 0.025 0.026
## 0.170 0.163 0.172
## -0.125 -0.132 -0.143
## -0.149 -0.156 -0.165
## -0.397 -0.404 -0.435
## 0.116 0.108 0.114
## -0.130 -0.138 -0.143
## 0.175 0.168 0.180
## 0.077 0.070 0.070
## 0.215 0.207 0.219
## -0.064 -0.071 -0.075
## -0.409 -0.416 -0.468
## -0.505 -0.511 -0.675
## -0.416 -0.422 -0.514
## -0.102 -0.109 -0.117
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.421 0.003 130.370 0.000 0.415
## .Stest20spellng 0.451 0.003 140.972 0.000 0.445
## .Stest21cptlztn 0.523 0.003 162.617 0.000 0.517
## .Stest22puncttn 0.268 0.002 128.866 0.000 0.264
## .Stest23english 0.453 0.003 158.388 0.000 0.448
## .Stest24exprssn 0.537 0.004 149.344 0.000 0.530
## .Stst25wrdfnctn 0.401 0.003 144.664 0.000 0.395
## .Stst26rdngcmpr 0.194 0.001 141.298 0.000 0.191
## .Stst31bstrctrs 0.464 0.003 151.682 0.000 0.458
## .Stst32rthrsnng 0.404 0.002 168.121 0.000 0.400
## .Stst34rthcmptt 0.452 0.004 128.769 0.000 0.445
## .Stest5math 0.363 0.003 111.399 0.000 0.357
## .Stst6physclscn 0.329 0.002 150.503 0.000 0.325
## .Stst33hghschlm 0.137 0.004 37.493 0.000 0.129
## .Stst29vslztn2D 0.584 0.004 149.028 0.000 0.576
## .Stest35tblrdng 0.313 0.004 88.670 0.000 0.306
## .Stst36clrclchc 0.426 0.004 98.134 0.000 0.417
## .Stst37bjctnspc 0.501 0.004 134.177 0.000 0.494
## .Stest1vocab 0.242 0.002 153.149 0.000 0.239
## .Stest2literatr 0.292 0.002 154.254 0.000 0.288
## .Stest3music 0.409 0.003 160.299 0.000 0.404
## .Stest4soclstds 0.291 0.002 159.542 0.000 0.287
## .Stst7blgclscnc 0.500 0.003 172.205 0.000 0.494
## .Stest8aerontcs 0.605 0.003 175.738 0.000 0.598
## .Stest11art 0.385 0.003 143.590 0.000 0.380
## .Stest12law 0.551 0.003 177.301 0.000 0.545
## .Stest13health 0.540 0.003 173.280 0.000 0.534
## .Stest14bible 0.633 0.003 194.046 0.000 0.627
## .Stest15theater 0.422 0.003 143.446 0.000 0.417
## .Stest16mscllns 0.495 0.003 171.000 0.000 0.490
## .Stest9elctrncs 0.490 0.004 112.687 0.000 0.482
## .Stest10mechncs 0.335 0.002 146.074 0.000 0.330
## .Stst28mchnclrs 0.289 0.002 125.542 0.000 0.285
## .Stst30vslztn3D 0.380 0.003 114.678 0.000 0.374
## english 0.987 0.015 63.990 0.000 0.957
## math 1.010 0.016 61.293 0.000 0.978
## speed 0.810 0.010 78.935 0.000 0.790
## info 0.970 0.015 63.785 0.000 0.940
## science 0.651 0.010 63.476 0.000 0.630
## spatial 0.827 0.010 79.390 0.000 0.806
## g 0.840 0.007 125.288 0.000 0.827
## ci.upper Std.lv Std.all
## 0.427 0.421 0.470
## 0.457 0.451 0.536
## 0.530 0.523 0.603
## 0.272 0.268 0.331
## 0.459 0.453 0.544
## 0.544 0.537 0.649
## 0.406 0.401 0.443
## 0.197 0.194 0.235
## 0.470 0.464 0.531
## 0.409 0.404 0.446
## 0.459 0.452 0.535
## 0.370 0.363 0.404
## 0.334 0.329 0.394
## 0.144 0.137 0.152
## 0.591 0.584 0.650
## 0.320 0.313 0.469
## 0.434 0.426 0.506
## 0.508 0.501 0.593
## 0.245 0.242 0.284
## 0.296 0.292 0.323
## 0.414 0.409 0.456
## 0.295 0.291 0.343
## 0.506 0.500 0.555
## 0.612 0.605 0.703
## 0.391 0.385 0.425
## 0.558 0.551 0.599
## 0.546 0.540 0.621
## 0.640 0.633 0.651
## 0.428 0.422 0.471
## 0.501 0.495 0.564
## 0.499 0.490 0.620
## 0.339 0.335 0.584
## 0.294 0.289 0.428
## 0.387 0.380 0.441
## 1.018 1.000 1.000
## 1.042 1.000 1.000
## 0.830 1.000 1.000
## 0.999 1.000 1.000
## 0.671 1.000 1.000
## 0.847 1.000 1.000
## 0.854 1.000 1.000
lavTestScore(metric, release = 1:85)
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 10526.45 85 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p189. 106.776 1 0.000
## 2 .p2. == .p190. 10.359 1 0.001
## 3 .p3. == .p191. 15.156 1 0.000
## 4 .p4. == .p192. 49.318 1 0.000
## 5 .p5. == .p193. 22.738 1 0.000
## 6 .p6. == .p194. 50.296 1 0.000
## 7 .p7. == .p195. 20.793 1 0.000
## 8 .p8. == .p196. 0.253 1 0.615
## 9 .p9. == .p197. 54.479 1 0.000
## 10 .p10. == .p198. 58.958 1 0.000
## 11 .p11. == .p199. 34.821 1 0.000
## 12 .p12. == .p200. 536.231 1 0.000
## 13 .p13. == .p201. 19.473 1 0.000
## 14 .p14. == .p202. 2.814 1 0.093
## 15 .p15. == .p203. 99.902 1 0.000
## 16 .p16. == .p204. 113.657 1 0.000
## 17 .p17. == .p205. 104.075 1 0.000
## 18 .p18. == .p206. 220.336 1 0.000
## 19 .p19. == .p207. 1.152 1 0.283
## 20 .p20. == .p208. 3.485 1 0.062
## 21 .p21. == .p209. 109.541 1 0.000
## 22 .p22. == .p210. 17.879 1 0.000
## 23 .p23. == .p211. 1.533 1 0.216
## 24 .p24. == .p212. 436.668 1 0.000
## 25 .p25. == .p213. 3.014 1 0.083
## 26 .p26. == .p214. 13.654 1 0.000
## 27 .p27. == .p215. 13.648 1 0.000
## 28 .p28. == .p216. 0.051 1 0.822
## 29 .p29. == .p217. 41.814 1 0.000
## 30 .p30. == .p218. 7.131 1 0.008
## 31 .p31. == .p219. 24.481 1 0.000
## 32 .p32. == .p220. 86.761 1 0.000
## 33 .p33. == .p221. 146.814 1 0.000
## 34 .p34. == .p222. 82.799 1 0.000
## 35 .p35. == .p223. 246.879 1 0.000
## 36 .p36. == .p224. 13.195 1 0.000
## 37 .p37. == .p225. 10.198 1 0.001
## 38 .p38. == .p226. 9.482 1 0.002
## 39 .p39. == .p227. 368.331 1 0.000
## 40 .p40. == .p228. 44.534 1 0.000
## 41 .p41. == .p229. 3.688 1 0.055
## 42 .p42. == .p230. 0.344 1 0.557
## 43 .p43. == .p231. 75.332 1 0.000
## 44 .p44. == .p232. 0.047 1 0.828
## 45 .p45. == .p233. 304.715 1 0.000
## 46 .p46. == .p234. 14.361 1 0.000
## 47 .p47. == .p235. 0.701 1 0.403
## 48 .p48. == .p236. 34.142 1 0.000
## 49 .p49. == .p237. 2.783 1 0.095
## 50 .p50. == .p238. 0.564 1 0.453
## 51 .p51. == .p239. 0.185 1 0.667
## 52 .p52. == .p240. 2052.198 1 0.000
## 53 .p53. == .p241. 17.932 1 0.000
## 54 .p54. == .p242. 29.373 1 0.000
## 55 .p55. == .p243. 74.724 1 0.000
## 56 .p56. == .p244. 283.708 1 0.000
## 57 .p57. == .p245. 30.696 1 0.000
## 58 .p58. == .p246. 266.228 1 0.000
## 59 .p59. == .p247. 986.533 1 0.000
## 60 .p60. == .p248. 399.319 1 0.000
## 61 .p61. == .p249. 0.027 1 0.870
## 62 .p62. == .p250. 48.721 1 0.000
## 63 .p63. == .p251. 307.339 1 0.000
## 64 .p64. == .p252. 310.261 1 0.000
## 65 .p65. == .p253. 0.017 1 0.897
## 66 .p66. == .p254. 17.066 1 0.000
## 67 .p67. == .p255. 695.477 1 0.000
## 68 .p68. == .p256. 16.556 1 0.000
## 69 .p69. == .p257. 56.114 1 0.000
## 70 .p70. == .p258. 122.194 1 0.000
## 71 .p71. == .p259. 1.049 1 0.306
## 72 .p72. == .p260. 137.787 1 0.000
## 73 .p73. == .p261. 400.627 1 0.000
## 74 .p74. == .p262. 889.269 1 0.000
## 75 .p75. == .p263. 177.980 1 0.000
## 76 .p76. == .p264. 1.506 1 0.220
## 77 .p77. == .p265. 6.129 1 0.013
## 78 .p78. == .p266. 10.809 1 0.001
## 79 .p79. == .p267. 33.392 1 0.000
## 80 .p80. == .p268. 123.690 1 0.000
## 81 .p81. == .p269. 967.359 1 0.000
## 82 .p82. == .p270. 0.040 1 0.842
## 83 .p83. == .p271. 321.200 1 0.000
## 84 .p84. == .p272. 8.101 1 0.004
## 85 .p85. == .p273. 58.168 1 0.000
metric2<-cfa(chc.bifactor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings"), group.partial=c("g=~Stest1vocab"))
fitMeasures(metric2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 121374.744 1029.000 0.000 0.954 0.041
## srmr aic bic
## 0.036 10325223.243 10327477.201
Mc(metric2)
## [1] 0.6487314
scalar<-cfa(chc.bifactor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("g=~Stest1vocab"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 151497.690 1056.000 0.000 0.943 0.045
## srmr aic bic
## 0.040 10355292.189 10357280.396
Mc(scalar)
## [1] 0.5821921
summary(scalar, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 109 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 320
## Number of equality constraints 118
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 151497.690 133429.305
## Degrees of freedom 1056 1056
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.135
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 84416.080 74348.189
## 1 67081.610 59081.116
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.179 0.002 75.192 0.000 0.174
## Stst20s (.p2.) 0.388 0.003 145.454 0.000 0.382
## Stst21c (.p3.) 0.360 0.002 149.074 0.000 0.355
## Stst22p (.p4.) 0.410 0.003 162.099 0.000 0.405
## Stst23n (.p5.) 0.309 0.002 134.284 0.000 0.304
## Stst24x (.p6.) 0.265 0.002 115.207 0.000 0.260
## Stst25w (.p7.) 0.306 0.002 135.421 0.000 0.302
## Stst26r (.p8.) 0.147 0.002 84.889 0.000 0.144
## Stst31b (.p9.) 0.174 0.002 91.052 0.000 0.171
## Stst32r (.10.) 0.114 0.002 65.376 0.000 0.111
## Stst34r (.11.) 0.138 0.002 60.800 0.000 0.133
## math =~
## Stst5mt (.12.) 0.295 0.003 101.595 0.000 0.289
## Stst6ph (.13.) 0.120 0.003 36.808 0.000 0.114
## Stst25w (.14.) 0.179 0.003 65.957 0.000 0.173
## Stst32r (.15.) 0.195 0.003 68.300 0.000 0.189
## Stst33h (.16.) 0.572 0.004 138.020 0.000 0.564
## Stst34r (.17.) 0.265 0.003 83.748 0.000 0.259
## speed =~
## Stst19d (.18.) 0.284 0.003 104.170 0.000 0.279
## Sts292D (.19.) 0.207 0.003 68.915 0.000 0.201
## Stst34r (.20.) 0.365 0.003 122.670 0.000 0.359
## Stst35t (.21.) 0.617 0.004 161.786 0.000 0.610
## Stst36c (.22.) 0.710 0.004 190.658 0.000 0.702
## Stst37b (.23.) 0.596 0.004 166.956 0.000 0.589
## info =~
## Stst1vc (.24.) 0.218 0.002 92.342 0.000 0.213
## Stst2lt (.25.) 0.265 0.005 57.025 0.000 0.256
## Stst3ms (.26.) 0.342 0.006 62.123 0.000 0.331
## Stst4sc (.27.) 0.101 0.003 36.108 0.000 0.096
## Stst7bl (.28.) 0.135 0.004 33.583 0.000 0.127
## Stst8rn (.29.) 0.065 0.005 12.146 0.000 0.055
## Stst11r (.30.) 0.325 0.006 51.152 0.000 0.313
## Stst12l (.31.) 0.084 0.003 26.704 0.000 0.078
## Stst13h (.32.) 0.262 0.004 67.636 0.000 0.255
## Stst14b (.33.) 0.189 0.003 60.317 0.000 0.183
## Stst15t (.34.) 0.388 0.007 54.234 0.000 0.374
## Stst16m (.35.) 0.134 0.003 40.417 0.000 0.128
## Stst19d (.36.) 0.108 0.004 26.691 0.000 0.100
## Stst26r (.37.) 0.163 0.003 57.977 0.000 0.157
## science =~
## Stst1vc (.38.) 0.112 0.004 30.072 0.000 0.105
## Stst6ph (.39.) 0.180 0.003 67.873 0.000 0.174
## Stst7bl (.40.) 0.185 0.006 30.285 0.000 0.173
## Stst8rn (.41.) 0.358 0.004 102.151 0.000 0.351
## Stst9lc (.42.) 0.401 0.003 121.046 0.000 0.394
## Stst10m (.43.) 0.474 0.003 140.989 0.000 0.467
## Stst13h (.44.) 0.002 0.007 0.246 0.806 -0.012
## Stst28m (.45.) 0.313 0.003 123.890 0.000 0.308
## spatial =~
## Stst28m (.46.) 0.422 0.003 150.745 0.000 0.417
## Sts292D (.47.) 0.478 0.003 137.015 0.000 0.471
## Sts303D (.48.) 0.573 0.004 150.831 0.000 0.566
## Stst31b (.49.) 0.384 0.003 124.176 0.000 0.378
## Stst32r (.50.) 0.130 0.003 50.438 0.000 0.125
## Stst37b (.51.) 0.222 0.003 69.504 0.000 0.216
## g =~
## Stst1vc 0.774 0.003 256.558 0.000 0.769
## Stst2lt (.53.) 0.800 0.003 274.302 0.000 0.794
## Stst3ms (.54.) 0.678 0.003 217.785 0.000 0.672
## Stst4sc (.55.) 0.818 0.003 306.310 0.000 0.813
## Stst5mt (.56.) 0.739 0.003 278.100 0.000 0.733
## Stst6ph (.57.) 0.716 0.003 227.061 0.000 0.710
## Stst7bl (.58.) 0.640 0.003 206.637 0.000 0.634
## Stst8rn (.59.) 0.481 0.003 165.428 0.000 0.476
## Stst9lc (.60.) 0.433 0.003 148.933 0.000 0.428
## Stst10m (.61.) 0.419 0.003 164.620 0.000 0.414
## Stst11r (.62.) 0.675 0.003 209.149 0.000 0.668
## Stst12l (.63.) 0.665 0.003 237.940 0.000 0.659
## Stst13h (.64.) 0.576 0.003 179.336 0.000 0.570
## Stst14b (.65.) 0.604 0.003 210.426 0.000 0.598
## Stst15t (.66.) 0.623 0.003 178.991 0.000 0.616
## Stst16m (.67.) 0.663 0.003 228.074 0.000 0.657
## Stst19d (.68.) 0.607 0.003 212.437 0.000 0.602
## Stst20s (.69.) 0.532 0.003 181.780 0.000 0.526
## Stst21c (.70.) 0.537 0.003 186.113 0.000 0.531
## Stst22p (.71.) 0.687 0.003 246.588 0.000 0.682
## Stst23n (.72.) 0.598 0.003 196.881 0.000 0.592
## Stst24x (.73.) 0.529 0.003 173.524 0.000 0.523
## Stst25w (.74.) 0.680 0.003 270.619 0.000 0.676
## Stst26r (.75.) 0.841 0.003 308.907 0.000 0.835
## Stst28m (.76.) 0.483 0.003 181.609 0.000 0.478
## Sts292D (.77.) 0.353 0.003 117.306 0.000 0.347
## Sts303D (.78.) 0.466 0.003 149.361 0.000 0.459
## Stst31b (.79.) 0.562 0.003 186.570 0.000 0.556
## Stst32r (.80.) 0.723 0.003 272.095 0.000 0.718
## Stst33h (.81.) 0.736 0.003 252.621 0.000 0.730
## Stst34r (.82.) 0.461 0.003 150.279 0.000 0.455
## Stst35t (.83.) 0.229 0.003 77.298 0.000 0.223
## Stst36c (.84.) 0.134 0.003 44.722 0.000 0.128
## Stst37b (.85.) 0.141 0.003 47.081 0.000 0.135
## ci.upper Std.lv Std.all
##
## 0.184 0.179 0.183
## 0.393 0.388 0.392
## 0.365 0.360 0.374
## 0.415 0.410 0.421
## 0.313 0.309 0.313
## 0.269 0.265 0.264
## 0.311 0.306 0.309
## 0.151 0.147 0.148
## 0.178 0.174 0.178
## 0.118 0.114 0.116
## 0.142 0.138 0.144
##
## 0.300 0.295 0.315
## 0.126 0.120 0.129
## 0.184 0.179 0.180
## 0.200 0.195 0.197
## 0.580 0.572 0.564
## 0.271 0.265 0.278
##
## 0.289 0.284 0.291
## 0.212 0.207 0.211
## 0.371 0.365 0.383
## 0.625 0.617 0.666
## 0.717 0.710 0.726
## 0.603 0.596 0.588
##
## 0.223 0.218 0.235
## 0.275 0.265 0.265
## 0.353 0.342 0.340
## 0.107 0.101 0.102
## 0.143 0.135 0.139
## 0.076 0.065 0.075
## 0.338 0.325 0.331
## 0.090 0.084 0.085
## 0.270 0.262 0.267
## 0.195 0.189 0.187
## 0.402 0.388 0.397
## 0.141 0.134 0.132
## 0.116 0.108 0.111
## 0.168 0.163 0.164
##
## 0.120 0.112 0.121
## 0.185 0.180 0.193
## 0.197 0.185 0.191
## 0.365 0.358 0.414
## 0.407 0.401 0.512
## 0.480 0.474 0.568
## 0.015 0.002 0.002
## 0.318 0.313 0.362
##
## 0.428 0.422 0.489
## 0.484 0.478 0.488
## 0.581 0.573 0.572
## 0.390 0.384 0.391
## 0.135 0.130 0.132
## 0.229 0.222 0.220
##
## 0.780 0.774 0.835
## 0.805 0.800 0.799
## 0.684 0.678 0.674
## 0.824 0.818 0.829
## 0.744 0.739 0.789
## 0.722 0.716 0.769
## 0.646 0.640 0.659
## 0.487 0.481 0.557
## 0.439 0.433 0.554
## 0.424 0.419 0.502
## 0.681 0.675 0.686
## 0.670 0.665 0.670
## 0.582 0.576 0.587
## 0.609 0.604 0.597
## 0.630 0.623 0.638
## 0.669 0.663 0.655
## 0.613 0.607 0.622
## 0.537 0.532 0.538
## 0.543 0.537 0.558
## 0.692 0.687 0.704
## 0.604 0.598 0.607
## 0.535 0.529 0.528
## 0.685 0.680 0.686
## 0.846 0.841 0.847
## 0.488 0.483 0.559
## 0.359 0.353 0.361
## 0.472 0.466 0.465
## 0.568 0.562 0.572
## 0.728 0.723 0.732
## 0.742 0.736 0.726
## 0.467 0.461 0.483
## 0.235 0.229 0.247
## 0.140 0.134 0.137
## 0.147 0.141 0.139
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.148) -0.158 0.004 -39.172 0.000 -0.165
## .Stst20s (.149) -0.241 0.004 -61.450 0.000 -0.249
## .Stst21c (.150) -0.188 0.004 -48.783 0.000 -0.195
## .Stst22p (.151) -0.190 0.004 -48.184 0.000 -0.197
## .Stst23n (.152) -0.117 0.004 -29.517 0.000 -0.125
## .Stst24x (.153) -0.087 0.004 -21.640 0.000 -0.095
## .Stst25w (.154) -0.127 0.004 -32.835 0.000 -0.134
## .Stst26r (.155) -0.011 0.004 -2.655 0.008 -0.019
## .Stst31b (.156) 0.073 0.004 19.030 0.000 0.066
## .Stst32r (.157) 0.120 0.004 30.336 0.000 0.112
## .Stst34r (.158) -0.094 0.004 -24.446 0.000 -0.101
## .Stst5mt (.159) 0.203 0.004 54.179 0.000 0.196
## .Stst6ph (.160) 0.394 0.004 100.161 0.000 0.386
## .Stst33h (.161) 0.134 0.004 31.779 0.000 0.126
## .Sts292D (.162) 0.153 0.004 41.923 0.000 0.146
## .Stst35t (.163) -0.037 0.003 -10.862 0.000 -0.044
## .Stst36c (.164) -0.153 0.004 -41.412 0.000 -0.160
## .Stst37b (.165) -0.068 0.004 -18.214 0.000 -0.076
## .Stst1vc (.166) 0.202 0.004 53.773 0.000 0.194
## .Stst2lt (.167) 0.006 0.004 1.431 0.152 -0.002
## .Stst3ms (.168) -0.113 0.004 -26.872 0.000 -0.121
## .Stst4sc (.169) 0.196 0.004 46.390 0.000 0.187
## .Stst7bl (.170) 0.268 0.004 67.962 0.000 0.260
## .Stst8rn (.171) 0.448 0.004 126.261 0.000 0.441
## .Stst11r (.172) -0.092 0.004 -23.846 0.000 -0.099
## .Stst12l (.173) 0.155 0.005 33.855 0.000 0.146
## .Stst13h (.174) -0.040 0.004 -9.446 0.000 -0.048
## .Stst14b (.175) 0.037 0.004 8.713 0.000 0.029
## .Stst15t (.176) -0.177 0.004 -45.274 0.000 -0.185
## .Stst16m (.177) 0.098 0.004 22.188 0.000 0.089
## .Stst9lc (.178) 0.534 0.003 171.328 0.000 0.528
## .Stst10m (.179) 0.617 0.003 180.136 0.000 0.611
## .Stst28m (.180) 0.535 0.004 148.553 0.000 0.527
## .Sts303D (.181) 0.252 0.004 64.320 0.000 0.245
## ci.upper Std.lv Std.all
## -0.150 -0.158 -0.161
## -0.234 -0.241 -0.244
## -0.180 -0.188 -0.195
## -0.182 -0.190 -0.194
## -0.109 -0.117 -0.119
## -0.080 -0.087 -0.087
## -0.119 -0.127 -0.127
## -0.003 -0.011 -0.011
## 0.081 0.073 0.075
## 0.127 0.120 0.121
## -0.086 -0.094 -0.098
## 0.211 0.203 0.217
## 0.401 0.394 0.423
## 0.142 0.134 0.132
## 0.160 0.153 0.156
## -0.031 -0.037 -0.040
## -0.146 -0.153 -0.156
## -0.061 -0.068 -0.067
## 0.209 0.202 0.218
## 0.014 0.006 0.006
## -0.105 -0.113 -0.112
## 0.204 0.196 0.198
## 0.275 0.268 0.276
## 0.455 0.448 0.518
## -0.084 -0.092 -0.093
## 0.164 0.155 0.156
## -0.032 -0.040 -0.041
## 0.045 0.037 0.036
## -0.169 -0.177 -0.181
## 0.106 0.098 0.096
## 0.540 0.534 0.683
## 0.624 0.617 0.739
## 0.542 0.535 0.618
## 0.260 0.252 0.252
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.460 0.003 161.408 0.000 0.454
## .Stest20spellng 0.544 0.003 157.768 0.000 0.537
## .Stest21cptlztn 0.507 0.003 160.078 0.000 0.501
## .Stest22puncttn 0.311 0.002 133.013 0.000 0.307
## .Stest23english 0.519 0.003 152.589 0.000 0.513
## .Stest24exprssn 0.652 0.004 155.700 0.000 0.644
## .Stst25wrdfnctn 0.396 0.003 148.815 0.000 0.391
## .Stst26rdngcmpr 0.231 0.002 137.738 0.000 0.228
## .Stst31bstrctrs 0.471 0.003 145.234 0.000 0.464
## .Stst32rthrsnng 0.384 0.002 160.249 0.000 0.379
## .Stst34rthcmptt 0.475 0.003 141.910 0.000 0.468
## .Stest5math 0.245 0.003 96.719 0.000 0.240
## .Stst6physclscn 0.307 0.002 151.821 0.000 0.303
## .Stst33hghschlm 0.160 0.004 42.516 0.000 0.152
## .Stst29vslztn2D 0.561 0.004 128.070 0.000 0.552
## .Stest35tblrdng 0.426 0.004 96.458 0.000 0.417
## .Stst36clrclchc 0.435 0.005 85.945 0.000 0.425
## .Stst37bjctnspc 0.602 0.005 131.311 0.000 0.593
## .Stest1vocab 0.200 0.001 142.215 0.000 0.198
## .Stest2literatr 0.293 0.002 156.408 0.000 0.289
## .Stest3music 0.437 0.003 154.340 0.000 0.432
## .Stest4soclstds 0.295 0.002 149.543 0.000 0.291
## .Stst7blgclscnc 0.482 0.003 160.769 0.000 0.476
## .Stest8aerontcs 0.383 0.003 111.566 0.000 0.377
## .Stest11art 0.405 0.003 143.098 0.000 0.400
## .Stest12law 0.534 0.003 169.479 0.000 0.528
## .Stest13health 0.562 0.003 161.690 0.000 0.555
## .Stest14bible 0.621 0.003 184.717 0.000 0.615
## .Stest15theater 0.415 0.003 124.827 0.000 0.408
## .Stest16mscllns 0.567 0.003 167.976 0.000 0.560
## .Stest9elctrncs 0.264 0.003 87.977 0.000 0.258
## .Stest10mechncs 0.297 0.003 113.610 0.000 0.292
## .Stst28mchnclrs 0.238 0.002 103.414 0.000 0.233
## .Stst30vslztn3D 0.459 0.004 113.966 0.000 0.451
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.466 0.460 0.483
## 0.551 0.544 0.557
## 0.514 0.507 0.548
## 0.316 0.311 0.327
## 0.526 0.519 0.534
## 0.661 0.652 0.651
## 0.401 0.396 0.402
## 0.234 0.231 0.234
## 0.477 0.471 0.488
## 0.389 0.384 0.394
## 0.481 0.475 0.522
## 0.250 0.245 0.279
## 0.311 0.307 0.354
## 0.167 0.160 0.155
## 0.569 0.561 0.586
## 0.434 0.426 0.495
## 0.445 0.435 0.455
## 0.611 0.602 0.586
## 0.203 0.200 0.233
## 0.296 0.293 0.292
## 0.443 0.437 0.431
## 0.299 0.295 0.303
## 0.488 0.482 0.510
## 0.390 0.383 0.513
## 0.411 0.405 0.419
## 0.541 0.534 0.543
## 0.568 0.562 0.584
## 0.628 0.621 0.608
## 0.421 0.415 0.435
## 0.574 0.567 0.553
## 0.270 0.264 0.431
## 0.302 0.297 0.426
## 0.243 0.238 0.318
## 0.467 0.459 0.457
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.179 0.002 75.192 0.000 0.174
## Stst20s (.p2.) 0.388 0.003 145.454 0.000 0.382
## Stst21c (.p3.) 0.360 0.002 149.074 0.000 0.355
## Stst22p (.p4.) 0.410 0.003 162.099 0.000 0.405
## Stst23n (.p5.) 0.309 0.002 134.284 0.000 0.304
## Stst24x (.p6.) 0.265 0.002 115.207 0.000 0.260
## Stst25w (.p7.) 0.306 0.002 135.421 0.000 0.302
## Stst26r (.p8.) 0.147 0.002 84.889 0.000 0.144
## Stst31b (.p9.) 0.174 0.002 91.052 0.000 0.171
## Stst32r (.10.) 0.114 0.002 65.376 0.000 0.111
## Stst34r (.11.) 0.138 0.002 60.800 0.000 0.133
## math =~
## Stst5mt (.12.) 0.295 0.003 101.595 0.000 0.289
## Stst6ph (.13.) 0.120 0.003 36.808 0.000 0.114
## Stst25w (.14.) 0.179 0.003 65.957 0.000 0.173
## Stst32r (.15.) 0.195 0.003 68.300 0.000 0.189
## Stst33h (.16.) 0.572 0.004 138.020 0.000 0.564
## Stst34r (.17.) 0.265 0.003 83.748 0.000 0.259
## speed =~
## Stst19d (.18.) 0.284 0.003 104.170 0.000 0.279
## Sts292D (.19.) 0.207 0.003 68.915 0.000 0.201
## Stst34r (.20.) 0.365 0.003 122.670 0.000 0.359
## Stst35t (.21.) 0.617 0.004 161.786 0.000 0.610
## Stst36c (.22.) 0.710 0.004 190.658 0.000 0.702
## Stst37b (.23.) 0.596 0.004 166.956 0.000 0.589
## info =~
## Stst1vc (.24.) 0.218 0.002 92.342 0.000 0.213
## Stst2lt (.25.) 0.265 0.005 57.025 0.000 0.256
## Stst3ms (.26.) 0.342 0.006 62.123 0.000 0.331
## Stst4sc (.27.) 0.101 0.003 36.108 0.000 0.096
## Stst7bl (.28.) 0.135 0.004 33.583 0.000 0.127
## Stst8rn (.29.) 0.065 0.005 12.146 0.000 0.055
## Stst11r (.30.) 0.325 0.006 51.152 0.000 0.313
## Stst12l (.31.) 0.084 0.003 26.704 0.000 0.078
## Stst13h (.32.) 0.262 0.004 67.636 0.000 0.255
## Stst14b (.33.) 0.189 0.003 60.317 0.000 0.183
## Stst15t (.34.) 0.388 0.007 54.234 0.000 0.374
## Stst16m (.35.) 0.134 0.003 40.417 0.000 0.128
## Stst19d (.36.) 0.108 0.004 26.691 0.000 0.100
## Stst26r (.37.) 0.163 0.003 57.977 0.000 0.157
## science =~
## Stst1vc (.38.) 0.112 0.004 30.072 0.000 0.105
## Stst6ph (.39.) 0.180 0.003 67.873 0.000 0.174
## Stst7bl (.40.) 0.185 0.006 30.285 0.000 0.173
## Stst8rn (.41.) 0.358 0.004 102.151 0.000 0.351
## Stst9lc (.42.) 0.401 0.003 121.046 0.000 0.394
## Stst10m (.43.) 0.474 0.003 140.989 0.000 0.467
## Stst13h (.44.) 0.002 0.007 0.246 0.806 -0.012
## Stst28m (.45.) 0.313 0.003 123.890 0.000 0.308
## spatial =~
## Stst28m (.46.) 0.422 0.003 150.745 0.000 0.417
## Sts292D (.47.) 0.478 0.003 137.015 0.000 0.471
## Sts303D (.48.) 0.573 0.004 150.831 0.000 0.566
## Stst31b (.49.) 0.384 0.003 124.176 0.000 0.378
## Stst32r (.50.) 0.130 0.003 50.438 0.000 0.125
## Stst37b (.51.) 0.222 0.003 69.504 0.000 0.216
## g =~
## Stst1vc 0.880 0.004 250.133 0.000 0.873
## Stst2lt (.53.) 0.800 0.003 274.302 0.000 0.794
## Stst3ms (.54.) 0.678 0.003 217.785 0.000 0.672
## Stst4sc (.55.) 0.818 0.003 306.310 0.000 0.813
## Stst5mt (.56.) 0.739 0.003 278.100 0.000 0.733
## Stst6ph (.57.) 0.716 0.003 227.061 0.000 0.710
## Stst7bl (.58.) 0.640 0.003 206.637 0.000 0.634
## Stst8rn (.59.) 0.481 0.003 165.428 0.000 0.476
## Stst9lc (.60.) 0.433 0.003 148.933 0.000 0.428
## Stst10m (.61.) 0.419 0.003 164.620 0.000 0.414
## Stst11r (.62.) 0.675 0.003 209.149 0.000 0.668
## Stst12l (.63.) 0.665 0.003 237.940 0.000 0.659
## Stst13h (.64.) 0.576 0.003 179.336 0.000 0.570
## Stst14b (.65.) 0.604 0.003 210.426 0.000 0.598
## Stst15t (.66.) 0.623 0.003 178.991 0.000 0.616
## Stst16m (.67.) 0.663 0.003 228.074 0.000 0.657
## Stst19d (.68.) 0.607 0.003 212.437 0.000 0.602
## Stst20s (.69.) 0.532 0.003 181.780 0.000 0.526
## Stst21c (.70.) 0.537 0.003 186.113 0.000 0.531
## Stst22p (.71.) 0.687 0.003 246.588 0.000 0.682
## Stst23n (.72.) 0.598 0.003 196.881 0.000 0.592
## Stst24x (.73.) 0.529 0.003 173.524 0.000 0.523
## Stst25w (.74.) 0.680 0.003 270.619 0.000 0.676
## Stst26r (.75.) 0.841 0.003 308.907 0.000 0.835
## Stst28m (.76.) 0.483 0.003 181.609 0.000 0.478
## Sts292D (.77.) 0.353 0.003 117.306 0.000 0.347
## Sts303D (.78.) 0.466 0.003 149.361 0.000 0.459
## Stst31b (.79.) 0.562 0.003 186.570 0.000 0.556
## Stst32r (.80.) 0.723 0.003 272.095 0.000 0.718
## Stst33h (.81.) 0.736 0.003 252.621 0.000 0.730
## Stst34r (.82.) 0.461 0.003 150.279 0.000 0.455
## Stst35t (.83.) 0.229 0.003 77.298 0.000 0.223
## Stst36c (.84.) 0.134 0.003 44.722 0.000 0.128
## Stst37b (.85.) 0.141 0.003 47.081 0.000 0.135
## ci.upper Std.lv Std.all
##
## 0.184 0.171 0.182
## 0.393 0.371 0.406
## 0.365 0.344 0.370
## 0.415 0.392 0.439
## 0.313 0.295 0.324
## 0.269 0.253 0.279
## 0.311 0.293 0.310
## 0.151 0.141 0.156
## 0.178 0.167 0.179
## 0.118 0.109 0.115
## 0.142 0.132 0.144
##
## 0.300 0.291 0.308
## 0.126 0.119 0.131
## 0.184 0.176 0.187
## 0.200 0.192 0.203
## 0.580 0.564 0.599
## 0.271 0.262 0.287
##
## 0.289 0.256 0.272
## 0.212 0.186 0.194
## 0.371 0.329 0.360
## 0.625 0.556 0.681
## 0.717 0.639 0.695
## 0.603 0.536 0.583
##
## 0.223 0.222 0.232
## 0.275 0.271 0.286
## 0.353 0.349 0.368
## 0.107 0.103 0.112
## 0.143 0.137 0.145
## 0.076 0.066 0.071
## 0.338 0.331 0.351
## 0.090 0.085 0.089
## 0.270 0.267 0.285
## 0.195 0.193 0.196
## 0.402 0.396 0.419
## 0.141 0.137 0.146
## 0.116 0.110 0.117
## 0.168 0.166 0.184
##
## 0.120 0.086 0.090
## 0.185 0.137 0.152
## 0.197 0.142 0.150
## 0.365 0.274 0.292
## 0.407 0.307 0.349
## 0.480 0.363 0.476
## 0.015 0.001 0.001
## 0.318 0.239 0.291
##
## 0.428 0.387 0.471
## 0.484 0.438 0.457
## 0.581 0.526 0.572
## 0.390 0.352 0.378
## 0.135 0.119 0.126
## 0.229 0.204 0.222
##
## 0.886 0.792 0.827
## 0.805 0.720 0.762
## 0.684 0.611 0.646
## 0.824 0.737 0.803
## 0.744 0.665 0.705
## 0.722 0.645 0.715
## 0.646 0.577 0.610
## 0.487 0.434 0.463
## 0.439 0.390 0.443
## 0.424 0.377 0.496
## 0.681 0.608 0.643
## 0.670 0.599 0.623
## 0.582 0.519 0.553
## 0.609 0.544 0.552
## 0.630 0.561 0.594
## 0.669 0.597 0.639
## 0.613 0.547 0.582
## 0.537 0.479 0.524
## 0.543 0.484 0.520
## 0.692 0.619 0.692
## 0.604 0.539 0.592
## 0.535 0.476 0.525
## 0.685 0.613 0.649
## 0.846 0.757 0.839
## 0.488 0.435 0.529
## 0.359 0.318 0.332
## 0.472 0.419 0.456
## 0.568 0.506 0.543
## 0.728 0.652 0.689
## 0.742 0.663 0.704
## 0.467 0.415 0.455
## 0.235 0.207 0.253
## 0.140 0.121 0.131
## 0.147 0.127 0.138
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.148) -0.158 0.004 -39.172 0.000 -0.165
## .Stst20s (.149) -0.241 0.004 -61.450 0.000 -0.249
## .Stst21c (.150) -0.188 0.004 -48.783 0.000 -0.195
## .Stst22p (.151) -0.190 0.004 -48.184 0.000 -0.197
## .Stst23n (.152) -0.117 0.004 -29.517 0.000 -0.125
## .Stst24x (.153) -0.087 0.004 -21.640 0.000 -0.095
## .Stst25w (.154) -0.127 0.004 -32.835 0.000 -0.134
## .Stst26r (.155) -0.011 0.004 -2.655 0.008 -0.019
## .Stst31b (.156) 0.073 0.004 19.030 0.000 0.066
## .Stst32r (.157) 0.120 0.004 30.336 0.000 0.112
## .Stst34r (.158) -0.094 0.004 -24.446 0.000 -0.101
## .Stst5mt (.159) 0.203 0.004 54.179 0.000 0.196
## .Stst6ph (.160) 0.394 0.004 100.161 0.000 0.386
## .Stst33h (.161) 0.134 0.004 31.779 0.000 0.126
## .Sts292D (.162) 0.153 0.004 41.923 0.000 0.146
## .Stst35t (.163) -0.037 0.003 -10.862 0.000 -0.044
## .Stst36c (.164) -0.153 0.004 -41.412 0.000 -0.160
## .Stst37b (.165) -0.068 0.004 -18.214 0.000 -0.076
## .Stst1vc (.166) 0.202 0.004 53.773 0.000 0.194
## .Stst2lt (.167) 0.006 0.004 1.431 0.152 -0.002
## .Stst3ms (.168) -0.113 0.004 -26.872 0.000 -0.121
## .Stst4sc (.169) 0.196 0.004 46.390 0.000 0.187
## .Stst7bl (.170) 0.268 0.004 67.962 0.000 0.260
## .Stst8rn (.171) 0.448 0.004 126.261 0.000 0.441
## .Stst11r (.172) -0.092 0.004 -23.846 0.000 -0.099
## .Stst12l (.173) 0.155 0.005 33.855 0.000 0.146
## .Stst13h (.174) -0.040 0.004 -9.446 0.000 -0.048
## .Stst14b (.175) 0.037 0.004 8.713 0.000 0.029
## .Stst15t (.176) -0.177 0.004 -45.274 0.000 -0.185
## .Stst16m (.177) 0.098 0.004 22.188 0.000 0.089
## .Stst9lc (.178) 0.534 0.003 171.328 0.000 0.528
## .Stst10m (.179) 0.617 0.003 180.136 0.000 0.611
## .Stst28m (.180) 0.535 0.004 148.553 0.000 0.527
## .Sts303D (.181) 0.252 0.004 64.320 0.000 0.245
## english 2.201 0.024 90.065 0.000 2.153
## math 0.447 0.018 25.553 0.000 0.413
## speed 0.435 0.008 53.471 0.000 0.419
## info 1.991 0.057 34.914 0.000 1.879
## science -1.786 0.021 -83.461 0.000 -1.828
## spatial -0.205 0.011 -18.772 0.000 -0.227
## g -0.619 0.012 -50.422 0.000 -0.643
## ci.upper Std.lv Std.all
## -0.150 -0.158 -0.168
## -0.234 -0.241 -0.264
## -0.180 -0.188 -0.201
## -0.182 -0.190 -0.212
## -0.109 -0.117 -0.129
## -0.080 -0.087 -0.096
## -0.119 -0.127 -0.134
## -0.003 -0.011 -0.012
## 0.081 0.073 0.079
## 0.127 0.120 0.126
## -0.086 -0.094 -0.103
## 0.211 0.203 0.215
## 0.401 0.394 0.437
## 0.142 0.134 0.142
## 0.160 0.153 0.160
## -0.031 -0.037 -0.046
## -0.146 -0.153 -0.166
## -0.061 -0.068 -0.074
## 0.209 0.202 0.211
## 0.014 0.006 0.006
## -0.105 -0.113 -0.119
## 0.204 0.196 0.213
## 0.275 0.268 0.283
## 0.455 0.448 0.478
## -0.084 -0.092 -0.097
## 0.164 0.155 0.161
## -0.032 -0.040 -0.043
## 0.045 0.037 0.037
## -0.169 -0.177 -0.187
## 0.106 0.098 0.104
## 0.540 0.534 0.607
## 0.624 0.617 0.811
## 0.542 0.535 0.650
## 0.260 0.252 0.275
## 2.249 2.301 2.301
## 0.482 0.453 0.453
## 0.451 0.483 0.483
## 2.103 1.953 1.953
## -1.744 -2.334 -2.334
## -0.184 -0.224 -0.224
## -0.595 -0.687 -0.687
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.476 0.003 164.324 0.000 0.470
## .Stest20spellng 0.469 0.003 157.648 0.000 0.463
## .Stest21cptlztn 0.515 0.003 160.802 0.000 0.508
## .Stest22puncttn 0.263 0.002 127.744 0.000 0.259
## .Stest23english 0.452 0.003 158.216 0.000 0.446
## .Stest24exprssn 0.533 0.004 147.598 0.000 0.526
## .Stst25wrdfnctn 0.399 0.003 142.855 0.000 0.393
## .Stst26rdngcmpr 0.194 0.001 141.111 0.000 0.192
## .Stst31bstrctrs 0.460 0.003 148.941 0.000 0.454
## .Stst32rthrsnng 0.408 0.002 168.657 0.000 0.403
## .Stst34rthcmptt 0.467 0.003 136.856 0.000 0.461
## .Stest5math 0.365 0.003 110.918 0.000 0.358
## .Stst6physclscn 0.364 0.002 169.029 0.000 0.360
## .Stst33hghschlm 0.129 0.004 36.680 0.000 0.122
## .Stst29vslztn2D 0.589 0.004 145.718 0.000 0.581
## .Stest35tblrdng 0.315 0.004 89.151 0.000 0.308
## .Stst36clrclchc 0.421 0.004 99.218 0.000 0.413
## .Stst37bjctnspc 0.502 0.004 133.970 0.000 0.494
## .Stest1vocab 0.234 0.002 146.676 0.000 0.231
## .Stest2literatr 0.300 0.002 159.476 0.000 0.297
## .Stest3music 0.400 0.003 153.437 0.000 0.395
## .Stest4soclstds 0.290 0.002 157.062 0.000 0.286
## .Stst7blgclscnc 0.521 0.003 176.789 0.000 0.515
## .Stest8aerontcs 0.610 0.004 166.676 0.000 0.603
## .Stest11art 0.414 0.003 145.494 0.000 0.408
## .Stest12law 0.559 0.003 175.811 0.000 0.553
## .Stest13health 0.539 0.003 162.531 0.000 0.532
## .Stest14bible 0.639 0.003 193.349 0.000 0.632
## .Stest15theater 0.421 0.003 125.223 0.000 0.414
## .Stest16mscllns 0.499 0.003 171.724 0.000 0.494
## .Stest9elctrncs 0.529 0.004 125.829 0.000 0.520
## .Stest10mechncs 0.306 0.002 129.568 0.000 0.301
## .Stst28mchnclrs 0.280 0.002 123.002 0.000 0.275
## .Stst30vslztn3D 0.393 0.003 116.627 0.000 0.386
## english 0.915 0.014 66.986 0.000 0.888
## math 0.975 0.014 68.022 0.000 0.947
## speed 0.811 0.010 79.391 0.000 0.791
## info 1.039 0.021 49.771 0.000 0.998
## science 0.586 0.009 61.699 0.000 0.567
## spatial 0.841 0.011 79.902 0.000 0.820
## g 0.811 0.006 127.709 0.000 0.799
## ci.upper Std.lv Std.all
## 0.482 0.476 0.540
## 0.475 0.469 0.561
## 0.521 0.515 0.594
## 0.267 0.263 0.329
## 0.457 0.452 0.545
## 0.540 0.533 0.647
## 0.404 0.399 0.447
## 0.197 0.194 0.238
## 0.466 0.460 0.530
## 0.412 0.408 0.455
## 0.474 0.467 0.560
## 0.371 0.365 0.409
## 0.368 0.364 0.448
## 0.136 0.129 0.145
## 0.597 0.589 0.643
## 0.322 0.315 0.473
## 0.430 0.421 0.499
## 0.509 0.502 0.592
## 0.237 0.234 0.255
## 0.304 0.300 0.337
## 0.405 0.400 0.447
## 0.293 0.290 0.343
## 0.527 0.521 0.584
## 0.617 0.610 0.695
## 0.419 0.414 0.463
## 0.566 0.559 0.604
## 0.545 0.539 0.612
## 0.645 0.639 0.657
## 0.428 0.421 0.472
## 0.505 0.499 0.571
## 0.537 0.529 0.682
## 0.311 0.306 0.528
## 0.284 0.280 0.414
## 0.400 0.393 0.465
## 0.942 1.000 1.000
## 1.003 1.000 1.000
## 0.831 1.000 1.000
## 1.080 1.000 1.000
## 0.604 1.000 1.000
## 0.861 1.000 1.000
## 0.824 1.000 1.000
lavTestScore(scalar, release = 85:118) # X2 test for released constraints among the 34 intercepts
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 28717.52 34 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p148. == .p336. 5008.240 1 0.000
## 2 .p149. == .p337. 42.769 1 0.000
## 3 .p150. == .p338. 195.352 1 0.000
## 4 .p151. == .p339. 5.289 1 0.021
## 5 .p152. == .p340. 88.921 1 0.000
## 6 .p153. == .p341. 74.596 1 0.000
## 7 .p154. == .p342. 2.864 1 0.091
## 8 .p155. == .p343. 2.442 1 0.118
## 9 .p156. == .p344. 44.367 1 0.000
## 10 .p157. == .p345. 294.962 1 0.000
## 11 .p158. == .p346. 994.030 1 0.000
## 12 .p159. == .p347. 88.508 1 0.000
## 13 .p160. == .p348. 3376.511 1 0.000
## 14 .p161. == .p349. 145.295 1 0.000
## 15 .p162. == .p350. 1851.560 1 0.000
## 16 .p163. == .p351. 84.441 1 0.000
## 17 .p164. == .p352. 123.870 1 0.000
## 18 .p165. == .p353. 336.016 1 0.000
## 19 .p166. == .p354. 2144.423 1 0.000
## 20 .p167. == .p355. 461.004 1 0.000
## 21 .p168. == .p356. 380.862 1 0.000
## 22 .p169. == .p357. 1355.431 1 0.000
## 23 .p170. == .p358. 1549.017 1 0.000
## 24 .p171. == .p359. 1994.683 1 0.000
## 25 .p172. == .p360. 1513.251 1 0.000
## 26 .p173. == .p361. 2325.644 1 0.000
## 27 .p174. == .p362. 2898.166 1 0.000
## 28 .p175. == .p363. 723.903 1 0.000
## 29 .p176. == .p364. 18.371 1 0.000
## 30 .p177. == .p365. 726.523 1 0.000
## 31 .p178. == .p366. 907.767 1 0.000
## 32 .p179. == .p367. 1525.416 1 0.000
## 33 .p180. == .p368. 388.514 1 0.000
## 34 .p181. == .p369. 1879.833 1 0.000
scalar2<-cfa(chc.bifactor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("g=~Stest1vocab", "Stest19disguisedwords~1", "Stest6physicalscience~1", "Stest13health~1", "Stest9electronics~1", "Stest30visualization3D~1", "Stest1vocab~1", "Stest11art~1", "Stest7biologicalscience~1"))
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 128423.974 1048.000 0.000 0.952 0.042
## srmr aic bic
## 0.038 10332234.473 10334301.421
Mc(scalar2)
## [1] 0.6325376
summary(scalar2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 128 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 320
## Number of equality constraints 110
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 128423.974 112723.935
## Degrees of freedom 1048 1048
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.139
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 72760.152 63865.105
## 1 55663.822 48858.830
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.309 0.003 98.090 0.000 0.303
## Stst20s (.p2.) 0.351 0.003 134.866 0.000 0.346
## Stst21c (.p3.) 0.325 0.002 136.326 0.000 0.320
## Stst22p (.p4.) 0.374 0.003 146.577 0.000 0.369
## Stst23n (.p5.) 0.292 0.002 132.452 0.000 0.287
## Stst24x (.p6.) 0.250 0.002 118.305 0.000 0.246
## Stst25w (.p7.) 0.276 0.002 123.089 0.000 0.272
## Stst26r (.p8.) 0.147 0.002 91.270 0.000 0.144
## Stst31b (.p9.) 0.179 0.002 97.531 0.000 0.176
## Stst32r (.10.) 0.121 0.002 74.227 0.000 0.117
## Stst34r (.11.) 0.106 0.002 52.041 0.000 0.102
## math =~
## Stst5mt (.12.) 0.301 0.002 121.485 0.000 0.296
## Stst6ph (.13.) 0.113 0.002 47.842 0.000 0.108
## Stst25w (.14.) 0.165 0.003 62.403 0.000 0.160
## Stst32r (.15.) 0.182 0.003 66.536 0.000 0.176
## Stst33h (.16.) 0.540 0.005 113.542 0.000 0.531
## Stst34r (.17.) 0.241 0.003 75.737 0.000 0.235
## speed =~
## Stst19d (.18.) 0.289 0.003 110.068 0.000 0.284
## Sts292D (.19.) 0.217 0.003 73.333 0.000 0.212
## Stst34r (.20.) 0.363 0.003 121.690 0.000 0.357
## Stst35t (.21.) 0.619 0.004 162.581 0.000 0.611
## Stst36c (.22.) 0.702 0.004 188.657 0.000 0.695
## Stst37b (.23.) 0.594 0.004 166.506 0.000 0.587
## info =~
## Stst1vc (.24.) 0.190 0.003 72.982 0.000 0.185
## Stst2lt (.25.) 0.314 0.003 104.474 0.000 0.308
## Stst3ms (.26.) 0.373 0.003 132.686 0.000 0.367
## Stst4sc (.27.) 0.163 0.003 52.609 0.000 0.157
## Stst7bl (.28.) 0.073 0.004 19.852 0.000 0.066
## Stst8rn (.29.) 0.122 0.003 41.452 0.000 0.117
## Stst11r (.30.) 0.433 0.004 121.315 0.000 0.426
## Stst12l (.31.) 0.135 0.003 48.537 0.000 0.130
## Stst13h (.32.) 0.176 0.004 47.035 0.000 0.168
## Stst14b (.33.) 0.228 0.003 81.048 0.000 0.223
## Stst15t (.34.) 0.407 0.003 135.896 0.000 0.401
## Stst16m (.35.) 0.185 0.003 69.868 0.000 0.180
## Stst19d (.36.) 0.246 0.003 71.961 0.000 0.239
## Stst26r (.37.) 0.190 0.002 78.417 0.000 0.186
## science =~
## Stst1vc (.38.) 0.165 0.002 71.228 0.000 0.161
## Stst6ph (.39.) 0.317 0.003 111.860 0.000 0.311
## Stst7bl (.40.) 0.262 0.003 76.213 0.000 0.256
## Stst8rn (.41.) 0.351 0.003 123.376 0.000 0.345
## Stst9lc (.42.) 0.483 0.003 146.694 0.000 0.476
## Stst10m (.43.) 0.388 0.003 118.928 0.000 0.382
## Stst13h (.44.) 0.091 0.003 27.415 0.000 0.085
## Stst28m (.45.) 0.236 0.003 88.015 0.000 0.231
## spatial =~
## Stst28m (.46.) 0.430 0.003 152.854 0.000 0.424
## Sts292D (.47.) 0.474 0.003 138.263 0.000 0.467
## Sts303D (.48.) 0.594 0.004 161.969 0.000 0.587
## Stst31b (.49.) 0.377 0.003 123.842 0.000 0.371
## Stst32r (.50.) 0.127 0.003 49.822 0.000 0.122
## Stst37b (.51.) 0.225 0.003 70.364 0.000 0.218
## g =~
## Stst1vc 0.766 0.003 251.220 0.000 0.760
## Stst2lt (.53.) 0.789 0.003 288.292 0.000 0.783
## Stst3ms (.54.) 0.666 0.003 245.797 0.000 0.661
## Stst4sc (.55.) 0.805 0.003 292.407 0.000 0.799
## Stst5mt (.56.) 0.729 0.003 281.805 0.000 0.724
## Stst6ph (.57.) 0.721 0.003 273.696 0.000 0.716
## Stst7bl (.58.) 0.653 0.003 226.296 0.000 0.647
## Stst8rn (.59.) 0.457 0.003 159.769 0.000 0.452
## Stst9lc (.60.) 0.423 0.003 152.086 0.000 0.417
## Stst10m (.61.) 0.405 0.003 156.406 0.000 0.400
## Stst11r (.62.) 0.641 0.003 217.494 0.000 0.636
## Stst12l (.63.) 0.656 0.003 233.244 0.000 0.650
## Stst13h (.64.) 0.598 0.003 186.383 0.000 0.592
## Stst14b (.65.) 0.593 0.003 210.338 0.000 0.587
## Stst15t (.66.) 0.615 0.003 221.733 0.000 0.610
## Stst16m (.67.) 0.652 0.003 225.278 0.000 0.646
## Stst19d (.68.) 0.561 0.003 193.515 0.000 0.555
## Stst20s (.69.) 0.544 0.003 188.152 0.000 0.539
## Stst21c (.70.) 0.549 0.003 190.636 0.000 0.544
## Stst22p (.71.) 0.702 0.003 250.771 0.000 0.696
## Stst23n (.72.) 0.605 0.003 198.803 0.000 0.599
## Stst24x (.73.) 0.535 0.003 175.363 0.000 0.529
## Stst25w (.74.) 0.696 0.003 275.407 0.000 0.691
## Stst26r (.75.) 0.838 0.003 309.652 0.000 0.833
## Stst28m (.76.) 0.471 0.003 177.652 0.000 0.466
## Sts292D (.77.) 0.348 0.003 116.817 0.000 0.342
## Sts303D (.78.) 0.485 0.003 161.663 0.000 0.479
## Stst31b (.79.) 0.564 0.003 187.894 0.000 0.558
## Stst32r (.80.) 0.729 0.003 279.907 0.000 0.724
## Stst33h (.81.) 0.750 0.003 254.857 0.000 0.744
## Stst34r (.82.) 0.482 0.003 157.042 0.000 0.476
## Stst35t (.83.) 0.235 0.003 79.524 0.000 0.229
## Stst36c (.84.) 0.140 0.003 47.503 0.000 0.134
## Stst37b (.85.) 0.143 0.003 48.425 0.000 0.137
## ci.upper Std.lv Std.all
##
## 0.315 0.309 0.316
## 0.356 0.351 0.356
## 0.329 0.325 0.338
## 0.379 0.374 0.384
## 0.296 0.292 0.296
## 0.254 0.250 0.250
## 0.281 0.276 0.278
## 0.150 0.147 0.147
## 0.183 0.179 0.182
## 0.124 0.121 0.122
## 0.110 0.106 0.111
##
## 0.306 0.301 0.324
## 0.117 0.113 0.118
## 0.171 0.165 0.166
## 0.187 0.182 0.184
## 0.549 0.540 0.533
## 0.248 0.241 0.252
##
## 0.294 0.289 0.295
## 0.223 0.217 0.223
## 0.368 0.363 0.379
## 0.626 0.619 0.668
## 0.710 0.702 0.720
## 0.601 0.594 0.587
##
## 0.195 0.190 0.206
## 0.320 0.314 0.313
## 0.378 0.373 0.369
## 0.169 0.163 0.166
## 0.080 0.073 0.074
## 0.128 0.122 0.144
## 0.440 0.433 0.439
## 0.141 0.135 0.137
## 0.183 0.176 0.180
## 0.234 0.228 0.226
## 0.413 0.407 0.415
## 0.190 0.185 0.183
## 0.253 0.246 0.251
## 0.195 0.190 0.191
##
## 0.170 0.165 0.179
## 0.323 0.317 0.332
## 0.269 0.262 0.267
## 0.357 0.351 0.412
## 0.489 0.483 0.603
## 0.394 0.388 0.479
## 0.098 0.091 0.093
## 0.241 0.236 0.277
##
## 0.435 0.430 0.505
## 0.481 0.474 0.486
## 0.601 0.594 0.587
## 0.383 0.377 0.384
## 0.132 0.127 0.128
## 0.231 0.225 0.222
##
## 0.772 0.766 0.831
## 0.794 0.789 0.786
## 0.671 0.666 0.660
## 0.810 0.805 0.818
## 0.734 0.729 0.784
## 0.726 0.721 0.755
## 0.658 0.653 0.663
## 0.463 0.457 0.537
## 0.428 0.423 0.529
## 0.410 0.405 0.501
## 0.647 0.641 0.650
## 0.661 0.656 0.662
## 0.604 0.598 0.611
## 0.598 0.593 0.586
## 0.621 0.615 0.628
## 0.658 0.652 0.644
## 0.566 0.561 0.573
## 0.550 0.544 0.553
## 0.555 0.549 0.572
## 0.707 0.702 0.720
## 0.611 0.605 0.615
## 0.541 0.535 0.535
## 0.701 0.696 0.700
## 0.843 0.838 0.842
## 0.477 0.471 0.554
## 0.354 0.348 0.357
## 0.491 0.485 0.479
## 0.570 0.564 0.574
## 0.734 0.729 0.738
## 0.756 0.750 0.740
## 0.488 0.482 0.503
## 0.240 0.235 0.253
## 0.146 0.140 0.143
## 0.148 0.143 0.141
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d -0.108 0.004 -27.549 0.000 -0.116
## .Stst20s (.149) -0.250 0.004 -63.145 0.000 -0.258
## .Stst21c (.150) -0.187 0.004 -48.288 0.000 -0.194
## .Stst22p (.151) -0.184 0.004 -46.659 0.000 -0.191
## .Stst23n (.152) -0.117 0.004 -29.337 0.000 -0.125
## .Stst24x (.153) -0.085 0.004 -20.946 0.000 -0.093
## .Stst25w (.154) -0.123 0.004 -31.767 0.000 -0.131
## .Stst26r (.155) 0.002 0.004 0.573 0.567 -0.006
## .Stst31b (.156) 0.083 0.004 21.558 0.000 0.076
## .Stst32r (.157) 0.139 0.004 35.263 0.000 0.132
## .Stst34r (.158) -0.088 0.004 -22.768 0.000 -0.096
## .Stst5mt (.159) 0.236 0.004 65.155 0.000 0.228
## .Stst6ph 0.358 0.004 92.152 0.000 0.350
## .Stst33h (.161) 0.137 0.004 32.764 0.000 0.129
## .Sts292D (.162) 0.187 0.004 50.136 0.000 0.180
## .Stst35t (.163) -0.034 0.003 -9.841 0.000 -0.041
## .Stst36c (.164) -0.167 0.004 -45.708 0.000 -0.174
## .Stst37b (.165) -0.080 0.004 -21.132 0.000 -0.087
## .Stst1vc 0.189 0.004 50.214 0.000 0.181
## .Stst2lt (.167) 0.023 0.004 5.846 0.000 0.015
## .Stst3ms (.168) -0.105 0.004 -26.046 0.000 -0.113
## .Stst4sc (.169) 0.225 0.004 57.487 0.000 0.218
## .Stst7bl 0.243 0.004 61.805 0.000 0.235
## .Stst8rn (.171) 0.468 0.004 132.941 0.000 0.461
## .Stst11r -0.054 0.004 -13.826 0.000 -0.062
## .Stst12l (.173) 0.178 0.004 44.284 0.000 0.170
## .Stst13h -0.081 0.004 -19.852 0.000 -0.089
## .Stst14b (.175) 0.048 0.004 11.632 0.000 0.040
## .Stst15t (.176) -0.169 0.004 -43.852 0.000 -0.176
## .Stst16m (.177) 0.113 0.004 27.183 0.000 0.105
## .Stst9lc 0.522 0.003 156.854 0.000 0.516
## .Stst10m (.179) 0.647 0.003 198.369 0.000 0.641
## .Stst28m (.180) 0.562 0.003 160.580 0.000 0.555
## .Sts303D 0.206 0.004 50.235 0.000 0.198
## ci.upper Std.lv Std.all
## -0.101 -0.108 -0.111
## -0.242 -0.250 -0.254
## -0.179 -0.187 -0.194
## -0.176 -0.184 -0.188
## -0.110 -0.117 -0.119
## -0.077 -0.085 -0.085
## -0.116 -0.123 -0.124
## 0.010 0.002 0.002
## 0.091 0.083 0.085
## 0.147 0.139 0.141
## -0.081 -0.088 -0.092
## 0.243 0.236 0.253
## 0.365 0.358 0.375
## 0.145 0.137 0.135
## 0.195 0.187 0.192
## -0.028 -0.034 -0.037
## -0.160 -0.167 -0.171
## -0.072 -0.080 -0.079
## 0.196 0.189 0.205
## 0.031 0.023 0.023
## -0.097 -0.105 -0.104
## 0.233 0.225 0.229
## 0.251 0.243 0.247
## 0.475 0.468 0.549
## -0.047 -0.054 -0.055
## 0.186 0.178 0.180
## -0.073 -0.081 -0.083
## 0.056 0.048 0.048
## -0.161 -0.169 -0.172
## 0.121 0.113 0.112
## 0.529 0.522 0.653
## 0.653 0.647 0.799
## 0.568 0.562 0.660
## 0.214 0.206 0.203
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.404 0.003 128.671 0.000 0.398
## .Stest20spellng 0.549 0.003 160.794 0.000 0.542
## .Stest21cptlztn 0.515 0.003 162.891 0.000 0.508
## .Stest22puncttn 0.317 0.002 136.085 0.000 0.313
## .Stest23english 0.518 0.003 152.813 0.000 0.512
## .Stest24exprssn 0.651 0.004 155.328 0.000 0.643
## .Stst25wrdfnctn 0.400 0.003 150.762 0.000 0.395
## .Stst26rdngcmpr 0.230 0.002 137.622 0.000 0.227
## .Stst31bstrctrs 0.473 0.003 146.500 0.000 0.467
## .Stst32rthrsnng 0.382 0.002 159.961 0.000 0.377
## .Stst34rthcmptt 0.484 0.003 144.997 0.000 0.477
## .Stest5math 0.243 0.003 94.142 0.000 0.238
## .Stst6physclscn 0.279 0.002 143.336 0.000 0.276
## .Stst33hghschlm 0.172 0.004 47.643 0.000 0.165
## .Stst29vslztn2D 0.556 0.004 128.326 0.000 0.548
## .Stest35tblrdng 0.421 0.004 95.993 0.000 0.412
## .Stst36clrclchc 0.439 0.005 86.797 0.000 0.429
## .Stst37bjctnspc 0.600 0.005 131.669 0.000 0.591
## .Stest1vocab 0.199 0.001 148.496 0.000 0.196
## .Stest2literatr 0.285 0.002 153.426 0.000 0.282
## .Stest3music 0.436 0.003 159.703 0.000 0.431
## .Stest4soclstds 0.295 0.002 152.274 0.000 0.291
## .Stst7blgclscnc 0.468 0.003 159.797 0.000 0.463
## .Stest8aerontcs 0.379 0.003 116.251 0.000 0.372
## .Stest11art 0.376 0.003 141.785 0.000 0.371
## .Stest12law 0.532 0.003 171.648 0.000 0.526
## .Stest13health 0.560 0.003 174.950 0.000 0.554
## .Stest14bible 0.619 0.003 184.414 0.000 0.612
## .Stest15theater 0.416 0.003 153.401 0.000 0.410
## .Stest16mscllns 0.565 0.003 167.837 0.000 0.559
## .Stest9elctrncs 0.228 0.003 80.244 0.000 0.222
## .Stest10mechncs 0.340 0.003 134.410 0.000 0.335
## .Stst28mchnclrs 0.261 0.002 110.547 0.000 0.256
## .Stst30vslztn3D 0.437 0.004 111.276 0.000 0.429
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.410 0.404 0.422
## 0.556 0.549 0.567
## 0.521 0.515 0.558
## 0.322 0.317 0.334
## 0.525 0.518 0.535
## 0.659 0.651 0.651
## 0.405 0.400 0.404
## 0.233 0.230 0.232
## 0.480 0.473 0.490
## 0.386 0.382 0.391
## 0.490 0.484 0.528
## 0.248 0.243 0.281
## 0.283 0.279 0.306
## 0.179 0.172 0.168
## 0.565 0.556 0.586
## 0.429 0.421 0.490
## 0.449 0.439 0.461
## 0.609 0.600 0.586
## 0.201 0.199 0.234
## 0.289 0.285 0.283
## 0.441 0.436 0.428
## 0.298 0.295 0.304
## 0.474 0.468 0.484
## 0.385 0.379 0.522
## 0.381 0.376 0.386
## 0.538 0.532 0.543
## 0.567 0.560 0.585
## 0.625 0.619 0.605
## 0.421 0.416 0.433
## 0.572 0.565 0.552
## 0.234 0.228 0.356
## 0.345 0.340 0.520
## 0.266 0.261 0.361
## 0.445 0.437 0.426
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.309 0.003 98.090 0.000 0.303
## Stst20s (.p2.) 0.351 0.003 134.866 0.000 0.346
## Stst21c (.p3.) 0.325 0.002 136.326 0.000 0.320
## Stst22p (.p4.) 0.374 0.003 146.577 0.000 0.369
## Stst23n (.p5.) 0.292 0.002 132.452 0.000 0.287
## Stst24x (.p6.) 0.250 0.002 118.305 0.000 0.246
## Stst25w (.p7.) 0.276 0.002 123.089 0.000 0.272
## Stst26r (.p8.) 0.147 0.002 91.270 0.000 0.144
## Stst31b (.p9.) 0.179 0.002 97.531 0.000 0.176
## Stst32r (.10.) 0.121 0.002 74.227 0.000 0.117
## Stst34r (.11.) 0.106 0.002 52.041 0.000 0.102
## math =~
## Stst5mt (.12.) 0.301 0.002 121.485 0.000 0.296
## Stst6ph (.13.) 0.113 0.002 47.842 0.000 0.108
## Stst25w (.14.) 0.165 0.003 62.403 0.000 0.160
## Stst32r (.15.) 0.182 0.003 66.536 0.000 0.176
## Stst33h (.16.) 0.540 0.005 113.542 0.000 0.531
## Stst34r (.17.) 0.241 0.003 75.737 0.000 0.235
## speed =~
## Stst19d (.18.) 0.289 0.003 110.068 0.000 0.284
## Sts292D (.19.) 0.217 0.003 73.333 0.000 0.212
## Stst34r (.20.) 0.363 0.003 121.690 0.000 0.357
## Stst35t (.21.) 0.619 0.004 162.581 0.000 0.611
## Stst36c (.22.) 0.702 0.004 188.657 0.000 0.695
## Stst37b (.23.) 0.594 0.004 166.506 0.000 0.587
## info =~
## Stst1vc (.24.) 0.190 0.003 72.982 0.000 0.185
## Stst2lt (.25.) 0.314 0.003 104.474 0.000 0.308
## Stst3ms (.26.) 0.373 0.003 132.686 0.000 0.367
## Stst4sc (.27.) 0.163 0.003 52.609 0.000 0.157
## Stst7bl (.28.) 0.073 0.004 19.852 0.000 0.066
## Stst8rn (.29.) 0.122 0.003 41.452 0.000 0.117
## Stst11r (.30.) 0.433 0.004 121.315 0.000 0.426
## Stst12l (.31.) 0.135 0.003 48.537 0.000 0.130
## Stst13h (.32.) 0.176 0.004 47.035 0.000 0.168
## Stst14b (.33.) 0.228 0.003 81.048 0.000 0.223
## Stst15t (.34.) 0.407 0.003 135.896 0.000 0.401
## Stst16m (.35.) 0.185 0.003 69.868 0.000 0.180
## Stst19d (.36.) 0.246 0.003 71.961 0.000 0.239
## Stst26r (.37.) 0.190 0.002 78.417 0.000 0.186
## science =~
## Stst1vc (.38.) 0.165 0.002 71.228 0.000 0.161
## Stst6ph (.39.) 0.317 0.003 111.860 0.000 0.311
## Stst7bl (.40.) 0.262 0.003 76.213 0.000 0.256
## Stst8rn (.41.) 0.351 0.003 123.376 0.000 0.345
## Stst9lc (.42.) 0.483 0.003 146.694 0.000 0.476
## Stst10m (.43.) 0.388 0.003 118.928 0.000 0.382
## Stst13h (.44.) 0.091 0.003 27.415 0.000 0.085
## Stst28m (.45.) 0.236 0.003 88.015 0.000 0.231
## spatial =~
## Stst28m (.46.) 0.430 0.003 152.854 0.000 0.424
## Sts292D (.47.) 0.474 0.003 138.263 0.000 0.467
## Sts303D (.48.) 0.594 0.004 161.969 0.000 0.587
## Stst31b (.49.) 0.377 0.003 123.842 0.000 0.371
## Stst32r (.50.) 0.127 0.003 49.822 0.000 0.122
## Stst37b (.51.) 0.225 0.003 70.364 0.000 0.218
## g =~
## Stst1vc 0.905 0.004 254.385 0.000 0.898
## Stst2lt (.53.) 0.789 0.003 288.292 0.000 0.783
## Stst3ms (.54.) 0.666 0.003 245.797 0.000 0.661
## Stst4sc (.55.) 0.805 0.003 292.407 0.000 0.799
## Stst5mt (.56.) 0.729 0.003 281.805 0.000 0.724
## Stst6ph (.57.) 0.721 0.003 273.696 0.000 0.716
## Stst7bl (.58.) 0.653 0.003 226.296 0.000 0.647
## Stst8rn (.59.) 0.457 0.003 159.769 0.000 0.452
## Stst9lc (.60.) 0.423 0.003 152.086 0.000 0.417
## Stst10m (.61.) 0.405 0.003 156.406 0.000 0.400
## Stst11r (.62.) 0.641 0.003 217.494 0.000 0.636
## Stst12l (.63.) 0.656 0.003 233.244 0.000 0.650
## Stst13h (.64.) 0.598 0.003 186.383 0.000 0.592
## Stst14b (.65.) 0.593 0.003 210.338 0.000 0.587
## Stst15t (.66.) 0.615 0.003 221.733 0.000 0.610
## Stst16m (.67.) 0.652 0.003 225.278 0.000 0.646
## Stst19d (.68.) 0.561 0.003 193.515 0.000 0.555
## Stst20s (.69.) 0.544 0.003 188.152 0.000 0.539
## Stst21c (.70.) 0.549 0.003 190.636 0.000 0.544
## Stst22p (.71.) 0.702 0.003 250.771 0.000 0.696
## Stst23n (.72.) 0.605 0.003 198.803 0.000 0.599
## Stst24x (.73.) 0.535 0.003 175.363 0.000 0.529
## Stst25w (.74.) 0.696 0.003 275.407 0.000 0.691
## Stst26r (.75.) 0.838 0.003 309.652 0.000 0.833
## Stst28m (.76.) 0.471 0.003 177.652 0.000 0.466
## Sts292D (.77.) 0.348 0.003 116.817 0.000 0.342
## Sts303D (.78.) 0.485 0.003 161.663 0.000 0.479
## Stst31b (.79.) 0.564 0.003 187.894 0.000 0.558
## Stst32r (.80.) 0.729 0.003 279.907 0.000 0.724
## Stst33h (.81.) 0.750 0.003 254.857 0.000 0.744
## Stst34r (.82.) 0.482 0.003 157.042 0.000 0.476
## Stst35t (.83.) 0.235 0.003 79.524 0.000 0.229
## Stst36c (.84.) 0.140 0.003 47.503 0.000 0.134
## Stst37b (.85.) 0.143 0.003 48.425 0.000 0.137
## ci.upper Std.lv Std.all
##
## 0.315 0.305 0.323
## 0.356 0.346 0.380
## 0.329 0.321 0.345
## 0.379 0.370 0.413
## 0.296 0.288 0.316
## 0.254 0.247 0.272
## 0.281 0.273 0.289
## 0.150 0.145 0.160
## 0.183 0.177 0.190
## 0.124 0.119 0.126
## 0.110 0.105 0.114
##
## 0.306 0.306 0.326
## 0.117 0.115 0.126
## 0.171 0.168 0.178
## 0.187 0.185 0.196
## 0.549 0.550 0.583
## 0.248 0.246 0.268
##
## 0.294 0.261 0.276
## 0.223 0.196 0.206
## 0.368 0.327 0.357
## 0.626 0.558 0.682
## 0.710 0.633 0.690
## 0.601 0.535 0.582
##
## 0.195 0.186 0.192
## 0.320 0.308 0.326
## 0.378 0.365 0.386
## 0.169 0.160 0.175
## 0.080 0.072 0.076
## 0.128 0.120 0.129
## 0.440 0.424 0.448
## 0.141 0.132 0.138
## 0.183 0.172 0.185
## 0.234 0.223 0.227
## 0.413 0.398 0.423
## 0.190 0.181 0.194
## 0.253 0.241 0.255
## 0.195 0.186 0.207
##
## 0.170 0.134 0.138
## 0.323 0.257 0.282
## 0.269 0.212 0.225
## 0.357 0.284 0.305
## 0.489 0.391 0.441
## 0.394 0.314 0.417
## 0.098 0.074 0.080
## 0.241 0.191 0.235
##
## 0.435 0.390 0.480
## 0.481 0.431 0.452
## 0.601 0.540 0.582
## 0.383 0.343 0.368
## 0.132 0.115 0.122
## 0.231 0.204 0.222
##
## 0.912 0.811 0.836
## 0.794 0.708 0.750
## 0.671 0.597 0.633
## 0.810 0.722 0.790
## 0.734 0.654 0.695
## 0.726 0.647 0.711
## 0.658 0.585 0.619
## 0.463 0.410 0.441
## 0.428 0.379 0.428
## 0.410 0.363 0.482
## 0.647 0.575 0.608
## 0.661 0.588 0.613
## 0.604 0.537 0.578
## 0.598 0.532 0.539
## 0.621 0.552 0.586
## 0.658 0.585 0.626
## 0.566 0.503 0.533
## 0.550 0.488 0.536
## 0.555 0.493 0.530
## 0.707 0.629 0.704
## 0.611 0.543 0.596
## 0.541 0.480 0.529
## 0.701 0.625 0.661
## 0.843 0.752 0.833
## 0.477 0.423 0.520
## 0.354 0.312 0.328
## 0.491 0.435 0.470
## 0.570 0.506 0.543
## 0.734 0.654 0.692
## 0.756 0.673 0.713
## 0.488 0.432 0.472
## 0.240 0.210 0.258
## 0.146 0.126 0.137
## 0.148 0.128 0.139
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d -0.974 0.016 -59.584 0.000 -1.006
## .Stst20s (.149) -0.250 0.004 -63.145 0.000 -0.258
## .Stst21c (.150) -0.187 0.004 -48.288 0.000 -0.194
## .Stst22p (.151) -0.184 0.004 -46.659 0.000 -0.191
## .Stst23n (.152) -0.117 0.004 -29.337 0.000 -0.125
## .Stst24x (.153) -0.085 0.004 -20.946 0.000 -0.093
## .Stst25w (.154) -0.123 0.004 -31.767 0.000 -0.131
## .Stst26r (.155) 0.002 0.004 0.573 0.567 -0.006
## .Stst31b (.156) 0.083 0.004 21.558 0.000 0.076
## .Stst32r (.157) 0.139 0.004 35.263 0.000 0.132
## .Stst34r (.158) -0.088 0.004 -22.768 0.000 -0.096
## .Stst5mt (.159) 0.236 0.004 65.155 0.000 0.228
## .Stst6ph 0.937 0.010 92.931 0.000 0.918
## .Stst33h (.161) 0.137 0.004 32.764 0.000 0.129
## .Sts292D (.162) 0.187 0.004 50.136 0.000 0.180
## .Stst35t (.163) -0.034 0.003 -9.841 0.000 -0.041
## .Stst36c (.164) -0.167 0.004 -45.708 0.000 -0.174
## .Stst37b (.165) -0.080 0.004 -21.132 0.000 -0.087
## .Stst1vc 0.637 0.009 69.941 0.000 0.619
## .Stst2lt (.167) 0.023 0.004 5.846 0.000 0.015
## .Stst3ms (.168) -0.105 0.004 -26.046 0.000 -0.113
## .Stst4sc (.169) 0.225 0.004 57.487 0.000 0.218
## .Stst7bl 0.804 0.011 72.244 0.000 0.782
## .Stst8rn (.171) 0.468 0.004 132.941 0.000 0.461
## .Stst11r -0.307 0.010 -30.110 0.000 -0.327
## .Stst12l (.173) 0.178 0.004 44.284 0.000 0.170
## .Stst13h 0.493 0.011 45.162 0.000 0.471
## .Stst14b (.175) 0.048 0.004 11.632 0.000 0.040
## .Stst15t (.176) -0.169 0.004 -43.852 0.000 -0.176
## .Stst16m (.177) 0.113 0.004 27.183 0.000 0.105
## .Stst9lc 0.955 0.011 87.894 0.000 0.933
## .Stst10m (.179) 0.647 0.003 198.369 0.000 0.641
## .Stst28m (.180) 0.562 0.003 160.580 0.000 0.555
## .Sts303D 0.450 0.007 65.228 0.000 0.437
## english 2.965 0.034 86.230 0.000 2.898
## math 0.893 0.026 34.894 0.000 0.842
## speed 0.544 0.009 61.850 0.000 0.527
## info 2.303 0.026 87.450 0.000 2.251
## science -2.044 0.022 -91.646 0.000 -2.088
## spatial -0.200 0.013 -14.942 0.000 -0.226
## g -0.908 0.014 -65.356 0.000 -0.935
## ci.upper Std.lv Std.all
## -0.942 -0.974 -1.032
## -0.242 -0.250 -0.275
## -0.179 -0.187 -0.200
## -0.176 -0.184 -0.205
## -0.110 -0.117 -0.129
## -0.077 -0.085 -0.094
## -0.116 -0.123 -0.130
## 0.010 0.002 0.003
## 0.091 0.083 0.090
## 0.147 0.139 0.147
## -0.081 -0.088 -0.097
## 0.243 0.236 0.250
## 0.957 0.937 1.031
## 0.145 0.137 0.145
## 0.195 0.187 0.197
## -0.028 -0.034 -0.042
## -0.160 -0.167 -0.182
## -0.072 -0.080 -0.087
## 0.655 0.637 0.657
## 0.031 0.023 0.025
## -0.097 -0.105 -0.111
## 0.233 0.225 0.246
## 0.825 0.804 0.850
## 0.475 0.468 0.503
## -0.287 -0.307 -0.324
## 0.186 0.178 0.186
## 0.514 0.493 0.530
## 0.056 0.048 0.049
## -0.161 -0.169 -0.179
## 0.121 0.113 0.121
## 0.976 0.955 1.078
## 0.653 0.647 0.859
## 0.568 0.562 0.690
## 0.464 0.450 0.486
## 3.033 3.004 3.004
## 0.943 0.877 0.877
## 0.561 0.603 0.603
## 2.355 2.352 2.352
## -2.000 -2.525 -2.525
## -0.173 -0.220 -0.220
## -0.881 -1.012 -1.012
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.419 0.003 133.223 0.000 0.413
## .Stest20spellng 0.471 0.003 160.417 0.000 0.465
## .Stest21cptlztn 0.520 0.003 162.856 0.000 0.514
## .Stest22puncttn 0.267 0.002 131.629 0.000 0.264
## .Stest23english 0.450 0.003 158.636 0.000 0.445
## .Stest24exprssn 0.532 0.004 147.967 0.000 0.525
## .Stst25wrdfnctn 0.400 0.003 144.763 0.000 0.395
## .Stst26rdngcmpr 0.193 0.001 141.183 0.000 0.191
## .Stst31bstrctrs 0.462 0.003 150.151 0.000 0.456
## .Stst32rthrsnng 0.405 0.002 168.650 0.000 0.400
## .Stst34rthcmptt 0.474 0.003 139.462 0.000 0.467
## .Stest5math 0.363 0.003 108.283 0.000 0.357
## .Stst6physclscn 0.330 0.002 150.955 0.000 0.325
## .Stst33hghschlm 0.136 0.003 40.827 0.000 0.130
## .Stst29vslztn2D 0.586 0.004 148.325 0.000 0.578
## .Stest35tblrdng 0.312 0.004 88.728 0.000 0.306
## .Stst36clrclchc 0.424 0.004 101.176 0.000 0.416
## .Stst37bjctnspc 0.502 0.004 134.516 0.000 0.495
## .Stest1vocab 0.231 0.002 148.516 0.000 0.228
## .Stest2literatr 0.295 0.002 158.188 0.000 0.291
## .Stest3music 0.401 0.003 157.880 0.000 0.396
## .Stest4soclstds 0.289 0.002 159.334 0.000 0.286
## .Stst7blgclscnc 0.501 0.003 172.761 0.000 0.495
## .Stest8aerontcs 0.603 0.003 174.074 0.000 0.596
## .Stest11art 0.386 0.003 142.570 0.000 0.380
## .Stest12law 0.557 0.003 178.017 0.000 0.550
## .Stest13health 0.540 0.003 173.428 0.000 0.534
## .Stest14bible 0.639 0.003 193.036 0.000 0.633
## .Stest15theater 0.424 0.003 154.111 0.000 0.419
## .Stest16mscllns 0.498 0.003 171.912 0.000 0.492
## .Stest9elctrncs 0.487 0.004 112.113 0.000 0.479
## .Stest10mechncs 0.337 0.002 149.997 0.000 0.333
## .Stst28mchnclrs 0.294 0.002 128.799 0.000 0.289
## .Stst30vslztn3D 0.378 0.003 113.908 0.000 0.372
## english 0.974 0.015 65.378 0.000 0.945
## math 1.036 0.017 62.116 0.000 1.004
## speed 0.812 0.010 79.129 0.000 0.792
## info 0.958 0.016 61.423 0.000 0.928
## science 0.655 0.010 62.503 0.000 0.635
## spatial 0.825 0.010 80.913 0.000 0.805
## g 0.805 0.006 126.227 0.000 0.792
## ci.upper Std.lv Std.all
## 0.425 0.419 0.471
## 0.477 0.471 0.568
## 0.526 0.520 0.601
## 0.271 0.267 0.334
## 0.456 0.450 0.544
## 0.539 0.532 0.646
## 0.405 0.400 0.448
## 0.196 0.193 0.237
## 0.468 0.462 0.533
## 0.410 0.405 0.453
## 0.481 0.474 0.565
## 0.370 0.363 0.411
## 0.334 0.330 0.399
## 0.143 0.136 0.153
## 0.593 0.586 0.646
## 0.319 0.312 0.468
## 0.433 0.424 0.505
## 0.510 0.502 0.593
## 0.234 0.231 0.245
## 0.298 0.295 0.331
## 0.406 0.401 0.450
## 0.293 0.289 0.346
## 0.507 0.501 0.560
## 0.610 0.603 0.696
## 0.391 0.386 0.430
## 0.563 0.557 0.605
## 0.546 0.540 0.626
## 0.646 0.639 0.658
## 0.430 0.424 0.478
## 0.504 0.498 0.571
## 0.496 0.487 0.622
## 0.342 0.337 0.594
## 0.298 0.294 0.444
## 0.385 0.378 0.440
## 1.004 1.000 1.000
## 1.069 1.000 1.000
## 0.832 1.000 1.000
## 0.989 1.000 1.000
## 0.676 1.000 1.000
## 0.845 1.000 1.000
## 0.817 1.000 1.000
lavTestScore(scalar2, release = 85:110) # X2 test for released constraints among the 34 intercepts
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 6857.243 26 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p149. == .p337. 129.060 1 0.000
## 2 .p150. == .p338. 105.385 1 0.000
## 3 .p151. == .p339. 0.355 1 0.551
## 4 .p152. == .p340. 7.221 1 0.007
## 5 .p153. == .p341. 42.319 1 0.000
## 6 .p154. == .p342. 29.191 1 0.000
## 7 .p155. == .p343. 134.747 1 0.000
## 8 .p156. == .p344. 193.933 1 0.000
## 9 .p157. == .p345. 12.421 1 0.000
## 10 .p158. == .p346. 1620.334 1 0.000
## 11 .p159. == .p347. 659.566 1 0.000
## 12 .p161. == .p349. 28.348 1 0.000
## 13 .p162. == .p350. 1051.841 1 0.000
## 14 .p163. == .p351. 113.587 1 0.000
## 15 .p164. == .p352. 1.780 1 0.182
## 16 .p165. == .p353. 140.555 1 0.000
## 17 .p167. == .p355. 110.610 1 0.000
## 18 .p168. == .p356. 471.922 1 0.000
## 19 .p169. == .p357. 26.521 1 0.000
## 20 .p171. == .p359. 641.910 1 0.000
## 21 .p173. == .p361. 1217.778 1 0.000
## 22 .p175. == .p363. 1166.449 1 0.000
## 23 .p176. == .p364. 10.100 1 0.001
## 24 .p177. == .p365. 449.422 1 0.000
## 25 .p179. == .p367. 22.994 1 0.000
## 26 .p180. == .p368. 449.276 1 0.000
strict<-cfa(chc.bifactor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("g=~Stest1vocab", "Stest19disguisedwords~1", "Stest6physicalscience~1", "Stest13health~1", "Stest9electronics~1", "Stest30visualization3D~1", "Stest1vocab~1", "Stest11art~1", "Stest7biologicalscience~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 144820.171 1082.000 0.000 0.946 0.044
## srmr aic bic
## 0.039 10348562.670 10350294.970
Mc(strict)
## [1] 0.596396
chc.bifactor<-cfa(chc.bifactor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("g=~Stest1vocab", "Stest19disguisedwords~1", "Stest6physicalscience~1", "Stest13health~1", "Stest9electronics~1", "Stest30visualization3D~1", "Stest1vocab~1", "Stest11art~1", "Stest7biologicalscience~1"))
fitMeasures(chc.bifactor, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 130741.497 1055.000 0.000 0.951 0.042
## srmr aic bic
## 0.057 10334537.995 10336536.045
Mc(chc.bifactor)
## [1] 0.6273042
summary(chc.bifactor, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 106 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 313
## Number of equality constraints 110
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 130741.497 114744.583
## Degrees of freedom 1055 1055
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.139
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 73982.590 64930.429
## 1 56758.907 49814.155
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.306 0.003 101.674 0.000 0.300
## Stst20s (.p2.) 0.349 0.002 166.727 0.000 0.345
## Stst21c (.p3.) 0.323 0.002 169.323 0.000 0.319
## Stst22p (.p4.) 0.372 0.002 192.254 0.000 0.368
## Stst23n (.p5.) 0.290 0.002 162.521 0.000 0.286
## Stst24x (.p6.) 0.249 0.002 140.190 0.000 0.245
## Stst25w (.p7.) 0.275 0.002 144.067 0.000 0.271
## Stst26r (.p8.) 0.146 0.001 99.103 0.000 0.143
## Stst31b (.p9.) 0.178 0.002 105.349 0.000 0.175
## Stst32r (.10.) 0.120 0.002 77.142 0.000 0.116
## Stst34r (.11.) 0.105 0.002 53.521 0.000 0.102
## math =~
## Stst5mt (.12.) 0.303 0.002 125.478 0.000 0.299
## Stst6ph (.13.) 0.115 0.002 49.060 0.000 0.110
## Stst25w (.14.) 0.167 0.003 66.688 0.000 0.162
## Stst32r (.15.) 0.184 0.002 74.427 0.000 0.179
## Stst33h (.16.) 0.547 0.004 152.392 0.000 0.540
## Stst34r (.17.) 0.245 0.003 87.187 0.000 0.239
## speed =~
## Stst19d (.18.) 0.276 0.002 113.334 0.000 0.272
## Sts292D (.19.) 0.207 0.003 75.214 0.000 0.202
## Stst34r (.20.) 0.345 0.003 132.298 0.000 0.340
## Stst35t (.21.) 0.585 0.003 194.251 0.000 0.579
## Stst36c (.22.) 0.669 0.003 223.551 0.000 0.663
## Stst37b (.23.) 0.564 0.003 195.234 0.000 0.558
## info =~
## Stst1vc (.24.) 0.188 0.003 73.756 0.000 0.183
## Stst2lt (.25.) 0.310 0.003 116.869 0.000 0.305
## Stst3ms (.26.) 0.368 0.002 160.881 0.000 0.364
## Stst4sc (.27.) 0.160 0.003 54.832 0.000 0.154
## Stst7bl (.28.) 0.071 0.004 19.579 0.000 0.064
## Stst8rn (.29.) 0.127 0.003 44.473 0.000 0.121
## Stst11r (.30.) 0.428 0.003 137.494 0.000 0.422
## Stst12l (.31.) 0.133 0.003 50.252 0.000 0.128
## Stst13h (.32.) 0.173 0.004 48.568 0.000 0.166
## Stst14b (.33.) 0.225 0.003 88.411 0.000 0.220
## Stst15t (.34.) 0.402 0.003 159.428 0.000 0.397
## Stst16m (.35.) 0.182 0.002 75.086 0.000 0.177
## Stst19d (.36.) 0.243 0.003 75.800 0.000 0.237
## Stst26r (.37.) 0.187 0.002 83.457 0.000 0.183
## science =~
## Stst1vc (.38.) 0.149 0.002 73.663 0.000 0.145
## Stst6ph (.39.) 0.295 0.003 114.647 0.000 0.290
## Stst7bl (.40.) 0.239 0.003 77.756 0.000 0.233
## Stst8rn (.41.) 0.324 0.002 130.820 0.000 0.319
## Stst9lc (.42.) 0.452 0.003 154.796 0.000 0.446
## Stst10m (.43.) 0.349 0.003 137.732 0.000 0.344
## Stst13h (.44.) 0.082 0.003 27.413 0.000 0.076
## Stst28m (.45.) 0.211 0.002 97.398 0.000 0.207
## spatial =~
## Stst28m (.46.) 0.413 0.002 169.904 0.000 0.408
## Sts292D (.47.) 0.453 0.003 150.673 0.000 0.447
## Sts303D (.48.) 0.565 0.003 190.042 0.000 0.559
## Stst31b (.49.) 0.360 0.003 132.022 0.000 0.355
## Stst32r (.50.) 0.121 0.002 50.192 0.000 0.116
## Stst37b (.51.) 0.213 0.003 72.016 0.000 0.208
## g =~
## Stst1vc 0.732 0.003 285.405 0.000 0.727
## Stst2lt (.53.) 0.749 0.002 337.674 0.000 0.745
## Stst3ms (.54.) 0.633 0.002 269.711 0.000 0.628
## Stst4sc (.55.) 0.765 0.002 351.744 0.000 0.761
## Stst5mt (.56.) 0.693 0.002 328.574 0.000 0.689
## Stst6ph (.57.) 0.686 0.002 328.114 0.000 0.682
## Stst7bl (.58.) 0.623 0.003 248.993 0.000 0.618
## Stst8rn (.59.) 0.435 0.003 173.788 0.000 0.430
## Stst9lc (.60.) 0.404 0.002 164.393 0.000 0.400
## Stst10m (.61.) 0.388 0.002 169.175 0.000 0.384
## Stst11r (.62.) 0.610 0.003 235.818 0.000 0.604
## Stst12l (.63.) 0.623 0.002 266.349 0.000 0.619
## Stst13h (.64.) 0.569 0.003 203.959 0.000 0.563
## Stst14b (.65.) 0.563 0.002 228.759 0.000 0.558
## Stst15t (.66.) 0.585 0.002 239.018 0.000 0.580
## Stst16m (.67.) 0.619 0.002 255.444 0.000 0.614
## Stst19d (.68.) 0.533 0.003 206.563 0.000 0.528
## Stst20s (.69.) 0.517 0.003 204.233 0.000 0.512
## Stst21c (.70.) 0.522 0.003 206.636 0.000 0.517
## Stst22p (.71.) 0.666 0.002 289.871 0.000 0.662
## Stst23n (.72.) 0.574 0.003 219.843 0.000 0.569
## Stst24x (.73.) 0.508 0.003 191.049 0.000 0.503
## Stst25w (.74.) 0.661 0.002 309.059 0.000 0.657
## Stst26r (.75.) 0.796 0.002 390.016 0.000 0.792
## Stst28m (.76.) 0.450 0.002 192.518 0.000 0.445
## Sts292D (.77.) 0.330 0.003 118.845 0.000 0.325
## Sts303D (.78.) 0.460 0.003 169.391 0.000 0.455
## Stst31b (.79.) 0.535 0.003 200.222 0.000 0.530
## Stst32r (.80.) 0.692 0.002 328.844 0.000 0.688
## Stst33h (.81.) 0.711 0.002 296.263 0.000 0.706
## Stst34r (.82.) 0.457 0.003 165.310 0.000 0.452
## Stst35t (.83.) 0.223 0.003 80.754 0.000 0.217
## Stst36c (.84.) 0.134 0.003 47.971 0.000 0.128
## Stst37b (.85.) 0.136 0.003 48.678 0.000 0.130
## ci.upper Std.lv Std.all
##
## 0.312 0.306 0.320
## 0.353 0.349 0.360
## 0.327 0.323 0.342
## 0.376 0.372 0.392
## 0.293 0.290 0.300
## 0.252 0.249 0.252
## 0.278 0.275 0.283
## 0.148 0.146 0.152
## 0.182 0.178 0.185
## 0.123 0.120 0.124
## 0.109 0.105 0.112
##
## 0.308 0.303 0.336
## 0.120 0.115 0.125
## 0.172 0.167 0.172
## 0.189 0.184 0.191
## 0.554 0.547 0.554
## 0.250 0.245 0.261
##
## 0.281 0.276 0.289
## 0.213 0.207 0.217
## 0.350 0.345 0.367
## 0.591 0.585 0.647
## 0.674 0.669 0.702
## 0.570 0.564 0.568
##
## 0.193 0.188 0.211
## 0.315 0.310 0.319
## 0.373 0.368 0.373
## 0.166 0.160 0.168
## 0.078 0.071 0.074
## 0.132 0.127 0.152
## 0.434 0.428 0.443
## 0.138 0.133 0.137
## 0.180 0.173 0.181
## 0.230 0.225 0.226
## 0.407 0.402 0.419
## 0.187 0.182 0.184
## 0.249 0.243 0.254
## 0.192 0.187 0.195
##
## 0.153 0.149 0.167
## 0.300 0.295 0.320
## 0.245 0.239 0.249
## 0.329 0.324 0.391
## 0.457 0.452 0.584
## 0.354 0.349 0.444
## 0.088 0.082 0.086
## 0.216 0.211 0.256
##
## 0.417 0.413 0.499
## 0.459 0.453 0.474
## 0.571 0.565 0.573
## 0.365 0.360 0.375
## 0.125 0.121 0.125
## 0.219 0.213 0.215
##
## 0.737 0.732 0.823
## 0.754 0.749 0.771
## 0.637 0.633 0.642
## 0.769 0.765 0.803
## 0.697 0.693 0.767
## 0.690 0.686 0.744
## 0.627 0.623 0.650
## 0.440 0.435 0.524
## 0.409 0.404 0.523
## 0.393 0.388 0.494
## 0.615 0.610 0.632
## 0.628 0.623 0.644
## 0.574 0.569 0.593
## 0.568 0.563 0.567
## 0.590 0.585 0.610
## 0.624 0.619 0.625
## 0.538 0.533 0.556
## 0.522 0.517 0.533
## 0.527 0.522 0.552
## 0.671 0.666 0.702
## 0.580 0.574 0.595
## 0.513 0.508 0.516
## 0.666 0.661 0.682
## 0.800 0.796 0.830
## 0.454 0.450 0.544
## 0.335 0.330 0.345
## 0.465 0.460 0.466
## 0.541 0.535 0.557
## 0.696 0.692 0.720
## 0.716 0.711 0.720
## 0.463 0.457 0.486
## 0.228 0.223 0.246
## 0.139 0.134 0.140
## 0.141 0.136 0.137
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d -0.108 0.004 -27.549 0.000 -0.116
## .Stst20s (.149) -0.250 0.004 -63.180 0.000 -0.258
## .Stst21c (.150) -0.187 0.004 -48.332 0.000 -0.194
## .Stst22p (.151) -0.184 0.004 -46.672 0.000 -0.191
## .Stst23n (.152) -0.117 0.004 -29.325 0.000 -0.125
## .Stst24x (.153) -0.086 0.004 -20.954 0.000 -0.093
## .Stst25w (.154) -0.123 0.004 -31.710 0.000 -0.130
## .Stst26r (.155) 0.002 0.004 0.594 0.552 -0.006
## .Stst31b (.156) 0.084 0.004 21.582 0.000 0.076
## .Stst32r (.157) 0.140 0.004 35.295 0.000 0.132
## .Stst34r (.158) -0.089 0.004 -22.846 0.000 -0.096
## .Stst5mt (.159) 0.236 0.004 65.194 0.000 0.229
## .Stst6ph 0.358 0.004 92.152 0.000 0.350
## .Stst33h (.161) 0.137 0.004 32.761 0.000 0.129
## .Sts292D (.162) 0.187 0.004 50.110 0.000 0.180
## .Stst35t (.163) -0.034 0.003 -9.768 0.000 -0.041
## .Stst36c (.164) -0.167 0.004 -45.782 0.000 -0.174
## .Stst37b (.165) -0.079 0.004 -20.938 0.000 -0.086
## .Stst1vc 0.189 0.004 50.214 0.000 0.181
## .Stst2lt (.167) 0.023 0.004 5.839 0.000 0.015
## .Stst3ms (.168) -0.105 0.004 -26.033 0.000 -0.113
## .Stst4sc (.169) 0.225 0.004 57.470 0.000 0.218
## .Stst7bl 0.243 0.004 61.805 0.000 0.235
## .Stst8rn (.171) 0.469 0.004 133.233 0.000 0.462
## .Stst11r -0.054 0.004 -13.827 0.000 -0.062
## .Stst12l (.173) 0.178 0.004 44.195 0.000 0.170
## .Stst13h -0.081 0.004 -19.852 0.000 -0.089
## .Stst14b (.175) 0.048 0.004 11.660 0.000 0.040
## .Stst15t (.176) -0.169 0.004 -43.879 0.000 -0.176
## .Stst16m (.177) 0.113 0.004 27.027 0.000 0.104
## .Stst9lc 0.522 0.003 156.854 0.000 0.516
## .Stst10m (.179) 0.646 0.003 198.016 0.000 0.640
## .Stst28m (.180) 0.561 0.003 160.582 0.000 0.555
## .Sts303D 0.206 0.004 50.236 0.000 0.198
## ci.upper Std.lv Std.all
## -0.101 -0.108 -0.113
## -0.242 -0.250 -0.258
## -0.179 -0.187 -0.198
## -0.176 -0.184 -0.194
## -0.110 -0.117 -0.122
## -0.078 -0.086 -0.087
## -0.115 -0.123 -0.127
## 0.010 0.002 0.003
## 0.091 0.084 0.087
## 0.147 0.140 0.145
## -0.081 -0.089 -0.094
## 0.243 0.236 0.261
## 0.365 0.358 0.388
## 0.145 0.137 0.139
## 0.195 0.187 0.196
## -0.027 -0.034 -0.038
## -0.160 -0.167 -0.175
## -0.071 -0.079 -0.079
## 0.196 0.189 0.212
## 0.031 0.023 0.024
## -0.097 -0.105 -0.107
## 0.233 0.225 0.237
## 0.251 0.243 0.254
## 0.476 0.469 0.565
## -0.047 -0.054 -0.056
## 0.186 0.178 0.183
## -0.073 -0.081 -0.084
## 0.056 0.048 0.049
## -0.161 -0.169 -0.176
## 0.121 0.113 0.114
## 0.529 0.522 0.676
## 0.653 0.646 0.822
## 0.568 0.561 0.680
## 0.214 0.206 0.209
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.405 0.003 129.406 0.000 0.398
## .Stest20spellng 0.549 0.003 161.300 0.000 0.543
## .Stest21cptlztn 0.515 0.003 163.154 0.000 0.509
## .Stest22puncttn 0.318 0.002 137.068 0.000 0.314
## .Stest23english 0.518 0.003 152.841 0.000 0.512
## .Stest24exprssn 0.651 0.004 155.340 0.000 0.643
## .Stst25wrdfnctn 0.400 0.003 150.961 0.000 0.395
## .Stst26rdngcmpr 0.230 0.002 137.807 0.000 0.227
## .Stst31bstrctrs 0.475 0.003 146.805 0.000 0.469
## .Stst32rthrsnng 0.382 0.002 160.162 0.000 0.377
## .Stst34rthcmptt 0.485 0.003 145.100 0.000 0.478
## .Stest5math 0.243 0.003 95.410 0.000 0.238
## .Stst6physclscn 0.279 0.002 143.630 0.000 0.275
## .Stst33hghschlm 0.169 0.003 51.483 0.000 0.163
## .Stst29vslztn2D 0.558 0.004 128.889 0.000 0.550
## .Stest35tblrdng 0.426 0.004 95.778 0.000 0.418
## .Stst36clrclchc 0.443 0.005 87.383 0.000 0.433
## .Stst37bjctnspc 0.604 0.005 132.468 0.000 0.595
## .Stest1vocab 0.199 0.001 148.486 0.000 0.196
## .Stest2literatr 0.286 0.002 153.773 0.000 0.283
## .Stest3music 0.436 0.003 160.112 0.000 0.431
## .Stest4soclstds 0.296 0.002 153.076 0.000 0.292
## .Stst7blgclscnc 0.469 0.003 160.056 0.000 0.463
## .Stest8aerontcs 0.379 0.003 115.927 0.000 0.373
## .Stest11art 0.376 0.003 142.524 0.000 0.371
## .Stest12law 0.532 0.003 171.849 0.000 0.526
## .Stest13health 0.561 0.003 174.985 0.000 0.554
## .Stest14bible 0.620 0.003 184.557 0.000 0.613
## .Stest15theater 0.416 0.003 153.975 0.000 0.411
## .Stest16mscllns 0.566 0.003 167.989 0.000 0.559
## .Stest9elctrncs 0.230 0.003 79.188 0.000 0.225
## .Stest10mechncs 0.346 0.003 138.470 0.000 0.341
## .Stst28mchnclrs 0.266 0.002 112.806 0.000 0.261
## .Stst30vslztn3D 0.443 0.004 115.414 0.000 0.435
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.411 0.405 0.441
## 0.556 0.549 0.586
## 0.521 0.515 0.578
## 0.323 0.318 0.354
## 0.525 0.518 0.556
## 0.659 0.651 0.671
## 0.405 0.400 0.425
## 0.234 0.230 0.250
## 0.481 0.475 0.515
## 0.386 0.382 0.413
## 0.491 0.485 0.549
## 0.248 0.243 0.298
## 0.283 0.279 0.328
## 0.176 0.169 0.174
## 0.567 0.558 0.610
## 0.435 0.426 0.521
## 0.453 0.443 0.488
## 0.613 0.604 0.613
## 0.202 0.199 0.251
## 0.290 0.286 0.303
## 0.441 0.436 0.449
## 0.299 0.296 0.326
## 0.475 0.469 0.511
## 0.385 0.379 0.550
## 0.381 0.376 0.404
## 0.538 0.532 0.567
## 0.567 0.561 0.609
## 0.626 0.620 0.628
## 0.421 0.416 0.452
## 0.572 0.566 0.576
## 0.236 0.230 0.385
## 0.351 0.346 0.560
## 0.270 0.266 0.389
## 0.450 0.443 0.455
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.306 0.003 101.674 0.000 0.300
## Stst20s (.p2.) 0.349 0.002 166.727 0.000 0.345
## Stst21c (.p3.) 0.323 0.002 169.323 0.000 0.319
## Stst22p (.p4.) 0.372 0.002 192.254 0.000 0.368
## Stst23n (.p5.) 0.290 0.002 162.521 0.000 0.286
## Stst24x (.p6.) 0.249 0.002 140.190 0.000 0.245
## Stst25w (.p7.) 0.275 0.002 144.067 0.000 0.271
## Stst26r (.p8.) 0.146 0.001 99.103 0.000 0.143
## Stst31b (.p9.) 0.178 0.002 105.349 0.000 0.175
## Stst32r (.10.) 0.120 0.002 77.142 0.000 0.116
## Stst34r (.11.) 0.105 0.002 53.521 0.000 0.102
## math =~
## Stst5mt (.12.) 0.303 0.002 125.478 0.000 0.299
## Stst6ph (.13.) 0.115 0.002 49.060 0.000 0.110
## Stst25w (.14.) 0.167 0.003 66.688 0.000 0.162
## Stst32r (.15.) 0.184 0.002 74.427 0.000 0.179
## Stst33h (.16.) 0.547 0.004 152.392 0.000 0.540
## Stst34r (.17.) 0.245 0.003 87.187 0.000 0.239
## speed =~
## Stst19d (.18.) 0.276 0.002 113.334 0.000 0.272
## Sts292D (.19.) 0.207 0.003 75.214 0.000 0.202
## Stst34r (.20.) 0.345 0.003 132.298 0.000 0.340
## Stst35t (.21.) 0.585 0.003 194.251 0.000 0.579
## Stst36c (.22.) 0.669 0.003 223.551 0.000 0.663
## Stst37b (.23.) 0.564 0.003 195.234 0.000 0.558
## info =~
## Stst1vc (.24.) 0.188 0.003 73.756 0.000 0.183
## Stst2lt (.25.) 0.310 0.003 116.869 0.000 0.305
## Stst3ms (.26.) 0.368 0.002 160.881 0.000 0.364
## Stst4sc (.27.) 0.160 0.003 54.832 0.000 0.154
## Stst7bl (.28.) 0.071 0.004 19.579 0.000 0.064
## Stst8rn (.29.) 0.127 0.003 44.473 0.000 0.121
## Stst11r (.30.) 0.428 0.003 137.494 0.000 0.422
## Stst12l (.31.) 0.133 0.003 50.252 0.000 0.128
## Stst13h (.32.) 0.173 0.004 48.568 0.000 0.166
## Stst14b (.33.) 0.225 0.003 88.411 0.000 0.220
## Stst15t (.34.) 0.402 0.003 159.428 0.000 0.397
## Stst16m (.35.) 0.182 0.002 75.086 0.000 0.177
## Stst19d (.36.) 0.243 0.003 75.800 0.000 0.237
## Stst26r (.37.) 0.187 0.002 83.457 0.000 0.183
## science =~
## Stst1vc (.38.) 0.149 0.002 73.663 0.000 0.145
## Stst6ph (.39.) 0.295 0.003 114.647 0.000 0.290
## Stst7bl (.40.) 0.239 0.003 77.756 0.000 0.233
## Stst8rn (.41.) 0.324 0.002 130.820 0.000 0.319
## Stst9lc (.42.) 0.452 0.003 154.796 0.000 0.446
## Stst10m (.43.) 0.349 0.003 137.732 0.000 0.344
## Stst13h (.44.) 0.082 0.003 27.413 0.000 0.076
## Stst28m (.45.) 0.211 0.002 97.398 0.000 0.207
## spatial =~
## Stst28m (.46.) 0.413 0.002 169.904 0.000 0.408
## Sts292D (.47.) 0.453 0.003 150.673 0.000 0.447
## Sts303D (.48.) 0.565 0.003 190.042 0.000 0.559
## Stst31b (.49.) 0.360 0.003 132.022 0.000 0.355
## Stst32r (.50.) 0.121 0.002 50.192 0.000 0.116
## Stst37b (.51.) 0.213 0.003 72.016 0.000 0.208
## g =~
## Stst1vc 0.855 0.003 315.459 0.000 0.850
## Stst2lt (.53.) 0.749 0.002 337.674 0.000 0.745
## Stst3ms (.54.) 0.633 0.002 269.711 0.000 0.628
## Stst4sc (.55.) 0.765 0.002 351.744 0.000 0.761
## Stst5mt (.56.) 0.693 0.002 328.574 0.000 0.689
## Stst6ph (.57.) 0.686 0.002 328.114 0.000 0.682
## Stst7bl (.58.) 0.623 0.003 248.993 0.000 0.618
## Stst8rn (.59.) 0.435 0.003 173.788 0.000 0.430
## Stst9lc (.60.) 0.404 0.002 164.393 0.000 0.400
## Stst10m (.61.) 0.388 0.002 169.175 0.000 0.384
## Stst11r (.62.) 0.610 0.003 235.818 0.000 0.604
## Stst12l (.63.) 0.623 0.002 266.349 0.000 0.619
## Stst13h (.64.) 0.569 0.003 203.959 0.000 0.563
## Stst14b (.65.) 0.563 0.002 228.759 0.000 0.558
## Stst15t (.66.) 0.585 0.002 239.018 0.000 0.580
## Stst16m (.67.) 0.619 0.002 255.444 0.000 0.614
## Stst19d (.68.) 0.533 0.003 206.563 0.000 0.528
## Stst20s (.69.) 0.517 0.003 204.233 0.000 0.512
## Stst21c (.70.) 0.522 0.003 206.636 0.000 0.517
## Stst22p (.71.) 0.666 0.002 289.871 0.000 0.662
## Stst23n (.72.) 0.574 0.003 219.843 0.000 0.569
## Stst24x (.73.) 0.508 0.003 191.049 0.000 0.503
## Stst25w (.74.) 0.661 0.002 309.059 0.000 0.657
## Stst26r (.75.) 0.796 0.002 390.016 0.000 0.792
## Stst28m (.76.) 0.450 0.002 192.518 0.000 0.445
## Sts292D (.77.) 0.330 0.003 118.845 0.000 0.325
## Sts303D (.78.) 0.460 0.003 169.391 0.000 0.455
## Stst31b (.79.) 0.535 0.003 200.222 0.000 0.530
## Stst32r (.80.) 0.692 0.002 328.844 0.000 0.688
## Stst33h (.81.) 0.711 0.002 296.263 0.000 0.706
## Stst34r (.82.) 0.457 0.003 165.310 0.000 0.452
## Stst35t (.83.) 0.223 0.003 80.754 0.000 0.217
## Stst36c (.84.) 0.134 0.003 47.971 0.000 0.128
## Stst37b (.85.) 0.136 0.003 48.678 0.000 0.130
## ci.upper Std.lv Std.all
##
## 0.312 0.306 0.317
## 0.353 0.349 0.376
## 0.327 0.323 0.341
## 0.376 0.372 0.404
## 0.293 0.290 0.311
## 0.252 0.249 0.269
## 0.278 0.275 0.283
## 0.148 0.146 0.155
## 0.182 0.178 0.187
## 0.123 0.120 0.123
## 0.109 0.105 0.113
##
## 0.308 0.303 0.314
## 0.120 0.115 0.122
## 0.172 0.167 0.172
## 0.189 0.184 0.189
## 0.554 0.547 0.564
## 0.250 0.245 0.262
##
## 0.281 0.276 0.287
## 0.213 0.207 0.214
## 0.350 0.345 0.369
## 0.591 0.585 0.698
## 0.674 0.669 0.711
## 0.570 0.564 0.600
##
## 0.193 0.188 0.186
## 0.315 0.310 0.318
## 0.373 0.368 0.380
## 0.166 0.160 0.169
## 0.078 0.071 0.072
## 0.132 0.127 0.133
## 0.434 0.428 0.441
## 0.138 0.133 0.135
## 0.180 0.173 0.183
## 0.230 0.225 0.224
## 0.407 0.402 0.418
## 0.187 0.182 0.190
## 0.249 0.243 0.252
## 0.192 0.187 0.199
##
## 0.153 0.149 0.147
## 0.300 0.295 0.312
## 0.245 0.239 0.245
## 0.329 0.324 0.340
## 0.457 0.452 0.493
## 0.354 0.349 0.447
## 0.088 0.082 0.087
## 0.216 0.211 0.251
##
## 0.417 0.413 0.490
## 0.459 0.453 0.467
## 0.571 0.565 0.594
## 0.365 0.360 0.378
## 0.125 0.121 0.124
## 0.219 0.213 0.227
##
## 0.861 0.855 0.847
## 0.754 0.749 0.768
## 0.637 0.633 0.654
## 0.769 0.765 0.807
## 0.697 0.693 0.716
## 0.690 0.686 0.725
## 0.627 0.623 0.639
## 0.440 0.435 0.456
## 0.409 0.404 0.441
## 0.393 0.388 0.498
## 0.615 0.610 0.629
## 0.628 0.623 0.635
## 0.574 0.569 0.599
## 0.568 0.563 0.561
## 0.590 0.585 0.607
## 0.624 0.619 0.647
## 0.538 0.533 0.553
## 0.522 0.517 0.557
## 0.527 0.522 0.551
## 0.671 0.666 0.723
## 0.580 0.574 0.618
## 0.513 0.508 0.550
## 0.666 0.661 0.682
## 0.800 0.796 0.847
## 0.454 0.450 0.534
## 0.335 0.330 0.340
## 0.465 0.460 0.483
## 0.541 0.535 0.562
## 0.696 0.692 0.712
## 0.716 0.711 0.733
## 0.463 0.457 0.490
## 0.228 0.223 0.266
## 0.139 0.134 0.142
## 0.141 0.136 0.145
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d -0.969 0.016 -60.153 0.000 -1.001
## .Stst20s (.149) -0.250 0.004 -63.180 0.000 -0.258
## .Stst21c (.150) -0.187 0.004 -48.332 0.000 -0.194
## .Stst22p (.151) -0.184 0.004 -46.672 0.000 -0.191
## .Stst23n (.152) -0.117 0.004 -29.325 0.000 -0.125
## .Stst24x (.153) -0.086 0.004 -20.954 0.000 -0.093
## .Stst25w (.154) -0.123 0.004 -31.710 0.000 -0.130
## .Stst26r (.155) 0.002 0.004 0.594 0.552 -0.006
## .Stst31b (.156) 0.084 0.004 21.582 0.000 0.076
## .Stst32r (.157) 0.140 0.004 35.295 0.000 0.132
## .Stst34r (.158) -0.089 0.004 -22.846 0.000 -0.096
## .Stst5mt (.159) 0.236 0.004 65.194 0.000 0.229
## .Stst6ph 0.956 0.010 94.853 0.000 0.936
## .Stst33h (.161) 0.137 0.004 32.761 0.000 0.129
## .Sts292D (.162) 0.187 0.004 50.110 0.000 0.180
## .Stst35t (.163) -0.034 0.003 -9.768 0.000 -0.041
## .Stst36c (.164) -0.167 0.004 -45.782 0.000 -0.174
## .Stst37b (.165) -0.079 0.004 -20.938 0.000 -0.086
## .Stst1vc 0.631 0.009 70.144 0.000 0.613
## .Stst2lt (.167) 0.023 0.004 5.839 0.000 0.015
## .Stst3ms (.168) -0.105 0.004 -26.033 0.000 -0.113
## .Stst4sc (.169) 0.225 0.004 57.470 0.000 0.218
## .Stst7bl 0.812 0.011 72.783 0.000 0.790
## .Stst8rn (.171) 0.469 0.004 133.233 0.000 0.462
## .Stst11r -0.306 0.010 -30.152 0.000 -0.326
## .Stst12l (.173) 0.178 0.004 44.195 0.000 0.170
## .Stst13h 0.492 0.011 45.068 0.000 0.471
## .Stst14b (.175) 0.048 0.004 11.660 0.000 0.040
## .Stst15t (.176) -0.169 0.004 -43.879 0.000 -0.176
## .Stst16m (.177) 0.113 0.004 27.027 0.000 0.104
## .Stst9lc 0.992 0.011 89.970 0.000 0.971
## .Stst10m (.179) 0.646 0.003 198.016 0.000 0.640
## .Stst28m (.180) 0.561 0.003 160.582 0.000 0.555
## .Sts303D 0.450 0.007 65.632 0.000 0.436
## english 2.971 0.031 96.930 0.000 2.911
## math 0.870 0.023 37.737 0.000 0.825
## speed 0.572 0.009 67.034 0.000 0.555
## info 2.320 0.025 93.884 0.000 2.272
## science -2.268 0.022 -102.508 0.000 -2.311
## spatial -0.216 0.014 -15.692 0.000 -0.243
## g -0.949 0.014 -68.376 0.000 -0.976
## ci.upper Std.lv Std.all
## -0.938 -0.969 -1.005
## -0.242 -0.250 -0.270
## -0.179 -0.187 -0.197
## -0.176 -0.184 -0.199
## -0.110 -0.117 -0.126
## -0.078 -0.086 -0.093
## -0.115 -0.123 -0.127
## 0.010 0.002 0.003
## 0.091 0.084 0.088
## 0.147 0.140 0.143
## -0.081 -0.089 -0.095
## 0.243 0.236 0.244
## 0.976 0.956 1.010
## 0.145 0.137 0.141
## 0.195 0.187 0.193
## -0.027 -0.034 -0.041
## -0.160 -0.167 -0.178
## -0.071 -0.079 -0.084
## 0.648 0.631 0.625
## 0.031 0.023 0.024
## -0.097 -0.105 -0.109
## 0.233 0.225 0.238
## 0.834 0.812 0.833
## 0.476 0.469 0.492
## -0.286 -0.306 -0.316
## 0.186 0.178 0.181
## 0.513 0.492 0.518
## 0.056 0.048 0.048
## -0.161 -0.169 -0.175
## 0.121 0.113 0.118
## 1.014 0.992 1.082
## 0.653 0.646 0.829
## 0.568 0.561 0.667
## 0.463 0.450 0.472
## 3.031 2.971 2.971
## 0.915 0.870 0.870
## 0.588 0.572 0.572
## 2.369 2.320 2.320
## -2.224 -2.268 -2.268
## -0.189 -0.216 -0.216
## -0.922 -0.949 -0.949
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.418 0.003 133.571 0.000 0.411
## .Stest20spellng 0.471 0.003 160.629 0.000 0.465
## .Stest21cptlztn 0.520 0.003 162.815 0.000 0.513
## .Stest22puncttn 0.267 0.002 131.599 0.000 0.263
## .Stest23english 0.450 0.003 158.606 0.000 0.445
## .Stest24exprssn 0.532 0.004 148.001 0.000 0.525
## .Stst25wrdfnctn 0.399 0.003 144.817 0.000 0.394
## .Stst26rdngcmpr 0.193 0.001 141.086 0.000 0.190
## .Stst31bstrctrs 0.461 0.003 149.947 0.000 0.455
## .Stst32rthrsnng 0.405 0.002 168.463 0.000 0.400
## .Stst34rthcmptt 0.473 0.003 139.192 0.000 0.466
## .Stest5math 0.363 0.003 108.612 0.000 0.357
## .Stst6physclscn 0.324 0.002 149.322 0.000 0.320
## .Stst33hghschlm 0.137 0.003 41.540 0.000 0.130
## .Stst29vslztn2D 0.583 0.004 147.697 0.000 0.576
## .Stest35tblrdng 0.311 0.004 88.685 0.000 0.305
## .Stst36clrclchc 0.419 0.004 100.586 0.000 0.411
## .Stst37bjctnspc 0.501 0.004 134.085 0.000 0.493
## .Stest1vocab 0.231 0.002 148.737 0.000 0.228
## .Stest2literatr 0.294 0.002 158.101 0.000 0.290
## .Stest3music 0.401 0.003 157.916 0.000 0.396
## .Stest4soclstds 0.288 0.002 158.798 0.000 0.285
## .Stst7blgclscnc 0.499 0.003 172.211 0.000 0.493
## .Stest8aerontcs 0.599 0.003 171.268 0.000 0.592
## .Stest11art 0.385 0.003 143.185 0.000 0.380
## .Stest12law 0.557 0.003 177.796 0.000 0.551
## .Stest13health 0.540 0.003 173.468 0.000 0.534
## .Stest14bible 0.639 0.003 192.949 0.000 0.632
## .Stest15theater 0.423 0.003 155.077 0.000 0.418
## .Stest16mscllns 0.499 0.003 171.763 0.000 0.493
## .Stest9elctrncs 0.474 0.004 109.766 0.000 0.465
## .Stest10mechncs 0.336 0.002 147.625 0.000 0.331
## .Stst28mchnclrs 0.291 0.002 127.135 0.000 0.286
## .Stst30vslztn3D 0.375 0.003 112.808 0.000 0.369
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.424 0.418 0.449
## 0.477 0.471 0.548
## 0.526 0.520 0.580
## 0.271 0.267 0.314
## 0.456 0.450 0.521
## 0.539 0.532 0.625
## 0.405 0.399 0.425
## 0.196 0.193 0.218
## 0.467 0.461 0.507
## 0.409 0.405 0.427
## 0.480 0.473 0.542
## 0.370 0.363 0.389
## 0.328 0.324 0.362
## 0.143 0.137 0.145
## 0.591 0.583 0.620
## 0.318 0.311 0.443
## 0.427 0.419 0.474
## 0.508 0.501 0.567
## 0.234 0.231 0.227
## 0.298 0.294 0.309
## 0.406 0.401 0.428
## 0.292 0.288 0.321
## 0.505 0.499 0.526
## 0.606 0.599 0.659
## 0.391 0.385 0.410
## 0.563 0.557 0.578
## 0.546 0.540 0.600
## 0.645 0.639 0.635
## 0.429 0.423 0.457
## 0.504 0.499 0.545
## 0.482 0.474 0.563
## 0.340 0.336 0.552
## 0.295 0.291 0.411
## 0.382 0.375 0.414
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
standardizedSolution(chc.bifactor) # get the correct SEs for standardized solution
## lhs op rhs group label
## 1 english =~ Stest19disguisedwords 1 .p1.
## 2 english =~ Stest20spelling 1 .p2.
## 3 english =~ Stest21capitalization 1 .p3.
## 4 english =~ Stest22punctuation 1 .p4.
## 5 english =~ Stest23english 1 .p5.
## 6 english =~ Stest24expression 1 .p6.
## 7 english =~ Stest25wordfunctions 1 .p7.
## 8 english =~ Stest26readingcomprehension 1 .p8.
## 9 english =~ Stest31abstractreasoning 1 .p9.
## 10 english =~ Stest32arithreasoning 1 .p10.
## 11 english =~ Stest34arithcomputation 1 .p11.
## 12 math =~ Stest5math 1 .p12.
## 13 math =~ Stest6physicalscience 1 .p13.
## 14 math =~ Stest25wordfunctions 1 .p14.
## 15 math =~ Stest32arithreasoning 1 .p15.
## 16 math =~ Stest33highschoolmath 1 .p16.
## 17 math =~ Stest34arithcomputation 1 .p17.
## 18 speed =~ Stest19disguisedwords 1 .p18.
## 19 speed =~ Stest29visualization2D 1 .p19.
## 20 speed =~ Stest34arithcomputation 1 .p20.
## 21 speed =~ Stest35tablereading 1 .p21.
## 22 speed =~ Stest36clericalchecking 1 .p22.
## 23 speed =~ Stest37objectinspection 1 .p23.
## 24 info =~ Stest1vocab 1 .p24.
## 25 info =~ Stest2literature 1 .p25.
## 26 info =~ Stest3music 1 .p26.
## 27 info =~ Stest4socialstudies 1 .p27.
## 28 info =~ Stest7biologicalscience 1 .p28.
## 29 info =~ Stest8aeronautics 1 .p29.
## 30 info =~ Stest11art 1 .p30.
## 31 info =~ Stest12law 1 .p31.
## 32 info =~ Stest13health 1 .p32.
## 33 info =~ Stest14bible 1 .p33.
## 34 info =~ Stest15theater 1 .p34.
## 35 info =~ Stest16miscellaneous 1 .p35.
## 36 info =~ Stest19disguisedwords 1 .p36.
## 37 info =~ Stest26readingcomprehension 1 .p37.
## 38 science =~ Stest1vocab 1 .p38.
## 39 science =~ Stest6physicalscience 1 .p39.
## 40 science =~ Stest7biologicalscience 1 .p40.
## 41 science =~ Stest8aeronautics 1 .p41.
## 42 science =~ Stest9electronics 1 .p42.
## 43 science =~ Stest10mechanics 1 .p43.
## 44 science =~ Stest13health 1 .p44.
## 45 science =~ Stest28mechanicalreasoning 1 .p45.
## 46 spatial =~ Stest28mechanicalreasoning 1 .p46.
## 47 spatial =~ Stest29visualization2D 1 .p47.
## 48 spatial =~ Stest30visualization3D 1 .p48.
## 49 spatial =~ Stest31abstractreasoning 1 .p49.
## 50 spatial =~ Stest32arithreasoning 1 .p50.
## 51 spatial =~ Stest37objectinspection 1 .p51.
## 52 g =~ Stest1vocab 1
## 53 g =~ Stest2literature 1 .p53.
## 54 g =~ Stest3music 1 .p54.
## 55 g =~ Stest4socialstudies 1 .p55.
## 56 g =~ Stest5math 1 .p56.
## 57 g =~ Stest6physicalscience 1 .p57.
## 58 g =~ Stest7biologicalscience 1 .p58.
## 59 g =~ Stest8aeronautics 1 .p59.
## 60 g =~ Stest9electronics 1 .p60.
## 61 g =~ Stest10mechanics 1 .p61.
## 62 g =~ Stest11art 1 .p62.
## 63 g =~ Stest12law 1 .p63.
## 64 g =~ Stest13health 1 .p64.
## 65 g =~ Stest14bible 1 .p65.
## 66 g =~ Stest15theater 1 .p66.
## 67 g =~ Stest16miscellaneous 1 .p67.
## 68 g =~ Stest19disguisedwords 1 .p68.
## 69 g =~ Stest20spelling 1 .p69.
## 70 g =~ Stest21capitalization 1 .p70.
## 71 g =~ Stest22punctuation 1 .p71.
## 72 g =~ Stest23english 1 .p72.
## 73 g =~ Stest24expression 1 .p73.
## 74 g =~ Stest25wordfunctions 1 .p74.
## 75 g =~ Stest26readingcomprehension 1 .p75.
## 76 g =~ Stest28mechanicalreasoning 1 .p76.
## 77 g =~ Stest29visualization2D 1 .p77.
## 78 g =~ Stest30visualization3D 1 .p78.
## 79 g =~ Stest31abstractreasoning 1 .p79.
## 80 g =~ Stest32arithreasoning 1 .p80.
## 81 g =~ Stest33highschoolmath 1 .p81.
## 82 g =~ Stest34arithcomputation 1 .p82.
## 83 g =~ Stest35tablereading 1 .p83.
## 84 g =~ Stest36clericalchecking 1 .p84.
## 85 g =~ Stest37objectinspection 1 .p85.
## 86 Stest19disguisedwords ~~ Stest19disguisedwords 1
## 87 Stest20spelling ~~ Stest20spelling 1
## 88 Stest21capitalization ~~ Stest21capitalization 1
## 89 Stest22punctuation ~~ Stest22punctuation 1
## 90 Stest23english ~~ Stest23english 1
## est.std se z pvalue ci.lower ci.upper
## 1 0.320 0.003 101.559 0 0.313 0.326
## 2 0.360 0.002 168.575 0 0.356 0.364
## 3 0.342 0.002 169.721 0 0.338 0.346
## 4 0.392 0.002 193.307 0 0.388 0.396
## 5 0.300 0.002 170.634 0 0.296 0.303
## 6 0.252 0.002 150.776 0 0.249 0.255
## 7 0.283 0.002 144.146 0 0.279 0.287
## 8 0.152 0.002 99.677 0 0.149 0.155
## 9 0.185 0.002 109.539 0 0.182 0.189
## 10 0.124 0.002 78.167 0 0.121 0.127
## 11 0.112 0.002 53.109 0 0.108 0.116
## 12 0.336 0.003 132.741 0 0.331 0.341
## 13 0.125 0.003 49.242 0 0.120 0.130
## 14 0.172 0.003 66.279 0 0.167 0.177
## 15 0.191 0.003 74.202 0 0.186 0.196
## 16 0.554 0.004 152.735 0 0.547 0.561
## 17 0.261 0.003 86.857 0 0.255 0.266
## 18 0.289 0.003 114.152 0 0.284 0.294
## 19 0.217 0.003 74.893 0 0.211 0.222
## 20 0.367 0.003 137.514 0 0.362 0.372
## 21 0.647 0.003 229.831 0 0.641 0.652
## 22 0.702 0.003 239.739 0 0.696 0.707
## 23 0.568 0.003 210.320 0 0.563 0.573
## 24 0.211 0.003 72.848 0 0.205 0.216
## 25 0.319 0.003 117.193 0 0.314 0.324
## 26 0.373 0.002 160.567 0 0.369 0.378
## 27 0.168 0.003 55.050 0 0.162 0.174
## 28 0.074 0.004 19.556 0 0.066 0.081
## 29 0.152 0.003 45.392 0 0.146 0.159
## 30 0.443 0.003 140.585 0 0.437 0.450
## 31 0.137 0.003 50.747 0 0.132 0.142
## 32 0.181 0.004 48.668 0 0.173 0.188
## 33 0.226 0.003 88.622 0 0.221 0.231
## 34 0.419 0.003 162.720 0 0.414 0.424
## 35 0.184 0.002 75.768 0 0.179 0.188
## 36 0.254 0.003 75.637 0 0.247 0.260
## 37 0.195 0.002 82.543 0 0.191 0.200
## 38 0.167 0.002 72.866 0 0.163 0.172
## 39 0.320 0.003 115.670 0 0.315 0.325
## 40 0.249 0.003 77.949 0 0.243 0.255
## 41 0.391 0.003 128.695 0 0.385 0.397
## 42 0.584 0.003 167.573 0 0.577 0.591
## 43 0.444 0.003 139.065 0 0.437 0.450
## 44 0.086 0.003 27.386 0 0.080 0.092
## 45 0.256 0.003 94.361 0 0.251 0.261
## 46 0.499 0.003 176.914 0 0.494 0.505
## 47 0.474 0.003 151.367 0 0.468 0.480
## 48 0.573 0.003 194.834 0 0.567 0.578
## 49 0.375 0.003 135.564 0 0.369 0.380
## 50 0.125 0.003 50.111 0 0.121 0.130
## 51 0.215 0.003 72.484 0 0.209 0.221
## 52 0.823 0.001 567.007 0 0.820 0.825
## 53 0.771 0.002 510.552 0 0.768 0.774
## 54 0.642 0.002 328.161 0 0.638 0.646
## 55 0.803 0.001 573.703 0 0.801 0.806
## 56 0.767 0.002 478.692 0 0.764 0.770
## 57 0.744 0.002 458.519 0 0.741 0.747
## 58 0.650 0.002 310.664 0 0.646 0.654
## 59 0.524 0.003 193.253 0 0.518 0.529
## 60 0.523 0.003 193.105 0 0.518 0.528
## 61 0.494 0.003 195.152 0 0.489 0.499
## 62 0.632 0.002 293.096 0 0.628 0.636
## 63 0.644 0.002 331.506 0 0.640 0.647
## 64 0.593 0.002 247.473 0 0.588 0.597
## 65 0.567 0.002 268.181 0 0.563 0.571
## 66 0.610 0.002 289.321 0 0.606 0.614
## 67 0.625 0.002 313.648 0 0.621 0.629
## 68 0.556 0.002 241.520 0 0.552 0.561
## 69 0.533 0.002 237.416 0 0.529 0.538
## 70 0.552 0.002 243.634 0 0.548 0.557
## 71 0.702 0.002 406.690 0 0.699 0.705
## 72 0.595 0.002 286.862 0 0.591 0.599
## 73 0.516 0.002 220.075 0 0.511 0.520
## 74 0.682 0.002 404.268 0 0.679 0.685
## 75 0.830 0.001 718.674 0 0.828 0.832
## 76 0.544 0.002 230.315 0 0.540 0.549
## 77 0.345 0.003 123.670 0 0.340 0.350
## 78 0.466 0.003 184.350 0 0.461 0.471
## 79 0.557 0.002 252.404 0 0.553 0.561
## 80 0.720 0.002 453.789 0 0.717 0.724
## 81 0.720 0.002 399.532 0 0.717 0.724
## 82 0.486 0.002 196.064 0 0.481 0.491
## 83 0.246 0.003 83.455 0 0.240 0.252
## 84 0.140 0.003 48.013 0 0.134 0.146
## 85 0.137 0.003 49.080 0 0.131 0.142
## 86 0.441 0.003 152.387 0 0.435 0.446
## 87 0.586 0.003 224.435 0 0.581 0.591
## 88 0.578 0.003 213.636 0 0.573 0.583
## 89 0.354 0.002 156.783 0 0.349 0.358
## 90 0.556 0.003 212.675 0 0.551 0.561
## [ reached 'max' / getOption("max.print") -- omitted 286 rows ]
# PAR.boot<- bootstrapLavaan(chc.bifactor, R=500, type="ordinary", FUN="coef") # bootstrap model parameters, unstandardized
# describeBy(PAR.boot) # check sd column for the standard errors, as sd is the variability of the parameter estimates across the bootstrap samples
chc.bifactor.lv<-cfa(chc.bifactor.lv.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("g=~Stest1vocab", "Stest19disguisedwords~1", "Stest6physicalscience~1", "Stest13health~1", "Stest9electronics~1", "Stest30visualization3D~1", "Stest1vocab~1", "Stest11art~1", "Stest7biologicalscience~1"))
fitMeasures(chc.bifactor.lv, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 128439.433 1051.000 0.000 0.952 0.042
## srmr aic bic
## 0.038 10332243.932 10334281.353
Mc(chc.bifactor.lv)
## [1] 0.6325093
summary(chc.bifactor.lv, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 113 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 317
## Number of equality constraints 110
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 128439.433 112733.038
## Degrees of freedom 1051 1051
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.139
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 72753.687 63856.900
## 1 55685.747 48876.137
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.307 0.003 102.061 0.000 0.301
## Stst20s (.p2.) 0.348 0.002 166.704 0.000 0.344
## Stst21c (.p3.) 0.323 0.002 169.432 0.000 0.319
## Stst22p (.p4.) 0.372 0.002 192.348 0.000 0.368
## Stst23n (.p5.) 0.290 0.002 162.692 0.000 0.286
## Stst24x (.p6.) 0.249 0.002 140.535 0.000 0.245
## Stst25w (.p7.) 0.274 0.002 143.466 0.000 0.271
## Stst26r (.p8.) 0.146 0.001 99.272 0.000 0.143
## Stst31b (.p9.) 0.178 0.002 105.428 0.000 0.175
## Stst32r (.10.) 0.120 0.002 77.152 0.000 0.117
## Stst34r (.11.) 0.105 0.002 53.430 0.000 0.101
## math =~
## Stst5mt (.12.) 0.303 0.002 125.223 0.000 0.298
## Stst6ph (.13.) 0.114 0.002 48.221 0.000 0.109
## Stst25w (.14.) 0.167 0.003 66.663 0.000 0.162
## Stst32r (.15.) 0.184 0.002 74.268 0.000 0.179
## Stst33h (.16.) 0.546 0.004 151.267 0.000 0.539
## Stst34r (.17.) 0.244 0.003 86.811 0.000 0.238
## speed =~
## Stst19d (.18.) 0.289 0.003 110.064 0.000 0.284
## Sts292D (.19.) 0.217 0.003 73.344 0.000 0.212
## Stst34r (.20.) 0.362 0.003 121.690 0.000 0.357
## Stst35t (.21.) 0.619 0.004 162.591 0.000 0.611
## Stst36c (.22.) 0.702 0.004 188.660 0.000 0.695
## Stst37b (.23.) 0.594 0.004 166.547 0.000 0.587
## info =~
## Stst1vc (.24.) 0.189 0.003 74.331 0.000 0.184
## Stst2lt (.25.) 0.311 0.003 117.500 0.000 0.306
## Stst3ms (.26.) 0.369 0.002 161.539 0.000 0.364
## Stst4sc (.27.) 0.161 0.003 55.129 0.000 0.156
## Stst7bl (.28.) 0.072 0.004 20.020 0.000 0.065
## Stst8rn (.29.) 0.121 0.003 42.258 0.000 0.115
## Stst11r (.30.) 0.429 0.003 137.971 0.000 0.423
## Stst12l (.31.) 0.134 0.003 50.557 0.000 0.128
## Stst13h (.32.) 0.174 0.004 48.746 0.000 0.167
## Stst14b (.33.) 0.225 0.003 88.746 0.000 0.220
## Stst15t (.34.) 0.403 0.003 159.558 0.000 0.398
## Stst16m (.35.) 0.183 0.002 75.479 0.000 0.178
## Stst19d (.36.) 0.243 0.003 76.117 0.000 0.237
## Stst26r (.37.) 0.188 0.002 83.813 0.000 0.184
## science =~
## Stst1vc (.38.) 0.165 0.002 71.338 0.000 0.161
## Stst6ph (.39.) 0.317 0.003 111.867 0.000 0.311
## Stst7bl (.40.) 0.262 0.003 76.305 0.000 0.255
## Stst8rn (.41.) 0.351 0.003 123.374 0.000 0.345
## Stst9lc (.42.) 0.483 0.003 146.682 0.000 0.476
## Stst10m (.43.) 0.388 0.003 119.036 0.000 0.382
## Stst13h (.44.) 0.091 0.003 27.405 0.000 0.085
## Stst28m (.45.) 0.236 0.003 88.075 0.000 0.231
## spatial =~
## Stst28m (.46.) 0.430 0.003 152.883 0.000 0.424
## Sts292D (.47.) 0.474 0.003 138.563 0.000 0.468
## Sts303D (.48.) 0.594 0.004 162.151 0.000 0.587
## Stst31b (.49.) 0.378 0.003 123.969 0.000 0.372
## Stst32r (.50.) 0.127 0.003 49.856 0.000 0.122
## Stst37b (.51.) 0.225 0.003 70.378 0.000 0.219
## g =~
## Stst1vc 0.766 0.003 251.334 0.000 0.760
## Stst2lt (.53.) 0.789 0.003 288.395 0.000 0.784
## Stst3ms (.54.) 0.666 0.003 245.609 0.000 0.661
## Stst4sc (.55.) 0.805 0.003 293.030 0.000 0.800
## Stst5mt (.56.) 0.729 0.003 282.737 0.000 0.724
## Stst6ph (.57.) 0.721 0.003 274.594 0.000 0.716
## Stst7bl (.58.) 0.653 0.003 226.619 0.000 0.647
## Stst8rn (.59.) 0.457 0.003 159.938 0.000 0.452
## Stst9lc (.60.) 0.423 0.003 152.278 0.000 0.418
## Stst10m (.61.) 0.405 0.003 156.561 0.000 0.400
## Stst11r (.62.) 0.641 0.003 217.455 0.000 0.635
## Stst12l (.63.) 0.656 0.003 233.459 0.000 0.651
## Stst13h (.64.) 0.598 0.003 186.578 0.000 0.592
## Stst14b (.65.) 0.593 0.003 210.401 0.000 0.587
## Stst15t (.66.) 0.615 0.003 221.595 0.000 0.610
## Stst16m (.67.) 0.652 0.003 225.397 0.000 0.646
## Stst19d (.68.) 0.561 0.003 193.522 0.000 0.555
## Stst20s (.69.) 0.544 0.003 188.521 0.000 0.539
## Stst21c (.70.) 0.550 0.003 191.132 0.000 0.544
## Stst22p (.71.) 0.702 0.003 251.863 0.000 0.696
## Stst23n (.72.) 0.605 0.003 199.087 0.000 0.599
## Stst24x (.73.) 0.535 0.003 175.527 0.000 0.530
## Stst25w (.74.) 0.696 0.003 277.363 0.000 0.691
## Stst26r (.75.) 0.838 0.003 310.048 0.000 0.833
## Stst28m (.76.) 0.471 0.003 177.802 0.000 0.466
## Sts292D (.77.) 0.348 0.003 116.960 0.000 0.342
## Sts303D (.78.) 0.485 0.003 161.967 0.000 0.479
## Stst31b (.79.) 0.564 0.003 188.313 0.000 0.558
## Stst32r (.80.) 0.729 0.003 281.429 0.000 0.724
## Stst33h (.81.) 0.750 0.003 256.288 0.000 0.744
## Stst34r (.82.) 0.482 0.003 157.979 0.000 0.476
## Stst35t (.83.) 0.235 0.003 79.544 0.000 0.229
## Stst36c (.84.) 0.140 0.003 47.492 0.000 0.134
## Stst37b (.85.) 0.143 0.003 48.394 0.000 0.137
## ci.upper Std.lv Std.all
##
## 0.313 0.307 0.314
## 0.353 0.348 0.354
## 0.326 0.323 0.336
## 0.376 0.372 0.382
## 0.293 0.290 0.294
## 0.252 0.249 0.249
## 0.278 0.274 0.276
## 0.149 0.146 0.147
## 0.181 0.178 0.181
## 0.123 0.120 0.121
## 0.109 0.105 0.110
##
## 0.308 0.303 0.326
## 0.118 0.114 0.119
## 0.172 0.167 0.168
## 0.188 0.184 0.186
## 0.553 0.546 0.538
## 0.249 0.244 0.255
##
## 0.294 0.289 0.296
## 0.223 0.217 0.223
## 0.368 0.362 0.378
## 0.626 0.619 0.668
## 0.710 0.702 0.720
## 0.601 0.594 0.587
##
## 0.194 0.189 0.205
## 0.316 0.311 0.310
## 0.373 0.369 0.366
## 0.167 0.161 0.164
## 0.079 0.072 0.073
## 0.127 0.121 0.142
## 0.435 0.429 0.435
## 0.139 0.134 0.135
## 0.181 0.174 0.177
## 0.230 0.225 0.223
## 0.408 0.403 0.412
## 0.187 0.183 0.181
## 0.250 0.243 0.249
## 0.193 0.188 0.189
##
## 0.170 0.165 0.179
## 0.323 0.317 0.332
## 0.269 0.262 0.266
## 0.357 0.351 0.412
## 0.489 0.483 0.604
## 0.394 0.388 0.479
## 0.098 0.091 0.093
## 0.241 0.236 0.277
##
## 0.435 0.430 0.505
## 0.481 0.474 0.487
## 0.602 0.594 0.587
## 0.384 0.378 0.384
## 0.132 0.127 0.128
## 0.231 0.225 0.222
##
## 0.772 0.766 0.832
## 0.794 0.789 0.787
## 0.671 0.666 0.661
## 0.810 0.805 0.818
## 0.734 0.729 0.783
## 0.726 0.721 0.755
## 0.658 0.653 0.663
## 0.463 0.457 0.537
## 0.428 0.423 0.529
## 0.410 0.405 0.501
## 0.647 0.641 0.651
## 0.662 0.656 0.663
## 0.605 0.598 0.612
## 0.598 0.593 0.587
## 0.621 0.615 0.629
## 0.658 0.652 0.644
## 0.566 0.561 0.574
## 0.550 0.544 0.554
## 0.555 0.550 0.573
## 0.707 0.702 0.720
## 0.611 0.605 0.615
## 0.541 0.535 0.536
## 0.701 0.696 0.701
## 0.844 0.838 0.843
## 0.477 0.471 0.554
## 0.354 0.348 0.357
## 0.491 0.485 0.479
## 0.570 0.564 0.574
## 0.734 0.729 0.738
## 0.756 0.750 0.739
## 0.488 0.482 0.503
## 0.240 0.235 0.253
## 0.146 0.140 0.143
## 0.148 0.143 0.141
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d -0.108 0.004 -27.549 0.000 -0.116
## .Stst20s (.149) -0.250 0.004 -63.143 0.000 -0.258
## .Stst21c (.150) -0.186 0.004 -48.287 0.000 -0.194
## .Stst22p (.151) -0.184 0.004 -46.653 0.000 -0.191
## .Stst23n (.152) -0.117 0.004 -29.339 0.000 -0.125
## .Stst24x (.153) -0.085 0.004 -20.953 0.000 -0.093
## .Stst25w (.154) -0.123 0.004 -31.776 0.000 -0.131
## .Stst26r (.155) 0.002 0.004 0.571 0.568 -0.006
## .Stst31b (.156) 0.083 0.004 21.551 0.000 0.076
## .Stst32r (.157) 0.139 0.004 35.252 0.000 0.132
## .Stst34r (.158) -0.088 0.004 -22.772 0.000 -0.096
## .Stst5mt (.159) 0.236 0.004 65.202 0.000 0.229
## .Stst6ph 0.358 0.004 92.152 0.000 0.350
## .Stst33h (.161) 0.137 0.004 32.769 0.000 0.129
## .Sts292D (.162) 0.187 0.004 50.139 0.000 0.180
## .Stst35t (.163) -0.034 0.003 -9.869 0.000 -0.041
## .Stst36c (.164) -0.167 0.004 -45.707 0.000 -0.174
## .Stst37b (.165) -0.080 0.004 -21.122 0.000 -0.087
## .Stst1vc 0.189 0.004 50.215 0.000 0.181
## .Stst2lt (.167) 0.023 0.004 5.838 0.000 0.015
## .Stst3ms (.168) -0.105 0.004 -26.020 0.000 -0.113
## .Stst4sc (.169) 0.225 0.004 57.482 0.000 0.218
## .Stst7bl 0.243 0.004 61.806 0.000 0.235
## .Stst8rn (.171) 0.468 0.004 132.979 0.000 0.461
## .Stst11r -0.054 0.004 -13.826 0.000 -0.062
## .Stst12l (.173) 0.178 0.004 44.267 0.000 0.170
## .Stst13h -0.081 0.004 -19.852 0.000 -0.089
## .Stst14b (.175) 0.048 0.004 11.683 0.000 0.040
## .Stst15t (.176) -0.169 0.004 -43.894 0.000 -0.177
## .Stst16m (.177) 0.113 0.004 27.209 0.000 0.105
## .Stst9lc 0.522 0.003 156.854 0.000 0.516
## .Stst10m (.179) 0.647 0.003 198.338 0.000 0.641
## .Stst28m (.180) 0.562 0.003 160.581 0.000 0.555
## .Sts303D 0.206 0.004 50.236 0.000 0.198
## ci.upper Std.lv Std.all
## -0.101 -0.108 -0.111
## -0.242 -0.250 -0.254
## -0.179 -0.186 -0.194
## -0.176 -0.184 -0.188
## -0.110 -0.117 -0.119
## -0.077 -0.085 -0.085
## -0.116 -0.123 -0.124
## 0.010 0.002 0.002
## 0.091 0.083 0.085
## 0.147 0.139 0.141
## -0.081 -0.088 -0.092
## 0.243 0.236 0.253
## 0.365 0.358 0.375
## 0.145 0.137 0.135
## 0.195 0.187 0.192
## -0.028 -0.034 -0.037
## -0.160 -0.167 -0.171
## -0.072 -0.080 -0.079
## 0.196 0.189 0.205
## 0.031 0.023 0.023
## -0.097 -0.105 -0.104
## 0.233 0.225 0.229
## 0.251 0.243 0.247
## 0.475 0.468 0.549
## -0.047 -0.054 -0.055
## 0.186 0.178 0.180
## -0.073 -0.081 -0.083
## 0.056 0.048 0.048
## -0.161 -0.169 -0.173
## 0.121 0.113 0.112
## 0.529 0.522 0.653
## 0.653 0.647 0.799
## 0.568 0.562 0.660
## 0.214 0.206 0.203
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english 1.000 1.000
## math 1.000 1.000
## info 1.000 1.000
## .Stst19dsgsdwrd 0.404 0.003 129.230 0.000 0.398
## .Stest20spellng 0.549 0.003 161.335 0.000 0.542
## .Stest21cptlztn 0.515 0.003 163.124 0.000 0.509
## .Stest22puncttn 0.318 0.002 136.962 0.000 0.313
## .Stest23english 0.518 0.003 152.834 0.000 0.512
## .Stest24exprssn 0.651 0.004 155.345 0.000 0.643
## .Stst25wrdfnctn 0.400 0.003 150.924 0.000 0.395
## .Stst26rdngcmpr 0.230 0.002 137.627 0.000 0.227
## .Stst31bstrctrs 0.473 0.003 146.512 0.000 0.467
## .Stst32rthrsnng 0.382 0.002 159.990 0.000 0.377
## .Stst34rthcmptt 0.483 0.003 145.115 0.000 0.477
## .Stest5math 0.244 0.003 95.509 0.000 0.239
## .Stst6physclscn 0.280 0.002 143.412 0.000 0.276
## .Stst33hghschlm 0.169 0.003 51.523 0.000 0.163
## .Stst29vslztn2D 0.556 0.004 128.318 0.000 0.548
## .Stest35tblrdng 0.421 0.004 96.036 0.000 0.412
## .Stst36clrclchc 0.439 0.005 86.792 0.000 0.429
## .Stst37bjctnspc 0.600 0.005 131.665 0.000 0.591
## .Stest1vocab 0.199 0.001 148.489 0.000 0.196
## .Stest2literatr 0.285 0.002 153.566 0.000 0.282
## .Stest3music 0.436 0.003 160.080 0.000 0.431
## .Stest4soclstds 0.295 0.002 152.558 0.000 0.291
## .Stst7blgclscnc 0.468 0.003 159.806 0.000 0.463
## .Stest8aerontcs 0.379 0.003 116.259 0.000 0.373
## .Stest11art 0.376 0.003 142.580 0.000 0.371
## .Stest12law 0.532 0.003 171.650 0.000 0.526
## .Stest13health 0.560 0.003 174.966 0.000 0.554
## .Stest14bible 0.619 0.003 184.449 0.000 0.612
## .Stest15theater 0.416 0.003 153.973 0.000 0.411
## .Stest16mscllns 0.565 0.003 167.844 0.000 0.559
## .Stest9elctrncs 0.228 0.003 80.228 0.000 0.222
## .Stest10mechncs 0.340 0.003 134.416 0.000 0.335
## .Stst28mchnclrs 0.261 0.002 110.549 0.000 0.256
## .Stst30vslztn3D 0.437 0.004 111.259 0.000 0.429
## speed 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 0.410 0.404 0.423
## 0.556 0.549 0.568
## 0.521 0.515 0.559
## 0.322 0.318 0.335
## 0.525 0.518 0.535
## 0.659 0.651 0.651
## 0.405 0.400 0.405
## 0.233 0.230 0.232
## 0.480 0.473 0.490
## 0.386 0.382 0.391
## 0.490 0.483 0.527
## 0.249 0.244 0.281
## 0.283 0.280 0.306
## 0.176 0.169 0.164
## 0.565 0.556 0.586
## 0.429 0.421 0.490
## 0.449 0.439 0.461
## 0.609 0.600 0.586
## 0.201 0.199 0.234
## 0.289 0.285 0.284
## 0.441 0.436 0.429
## 0.298 0.295 0.304
## 0.474 0.468 0.484
## 0.385 0.379 0.522
## 0.382 0.376 0.387
## 0.538 0.532 0.543
## 0.567 0.560 0.586
## 0.625 0.619 0.606
## 0.421 0.416 0.435
## 0.572 0.565 0.552
## 0.234 0.228 0.356
## 0.345 0.340 0.519
## 0.266 0.261 0.361
## 0.445 0.437 0.426
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.307 0.003 102.061 0.000 0.301
## Stst20s (.p2.) 0.348 0.002 166.704 0.000 0.344
## Stst21c (.p3.) 0.323 0.002 169.432 0.000 0.319
## Stst22p (.p4.) 0.372 0.002 192.348 0.000 0.368
## Stst23n (.p5.) 0.290 0.002 162.692 0.000 0.286
## Stst24x (.p6.) 0.249 0.002 140.535 0.000 0.245
## Stst25w (.p7.) 0.274 0.002 143.466 0.000 0.271
## Stst26r (.p8.) 0.146 0.001 99.272 0.000 0.143
## Stst31b (.p9.) 0.178 0.002 105.428 0.000 0.175
## Stst32r (.10.) 0.120 0.002 77.152 0.000 0.117
## Stst34r (.11.) 0.105 0.002 53.430 0.000 0.101
## math =~
## Stst5mt (.12.) 0.303 0.002 125.223 0.000 0.298
## Stst6ph (.13.) 0.114 0.002 48.221 0.000 0.109
## Stst25w (.14.) 0.167 0.003 66.663 0.000 0.162
## Stst32r (.15.) 0.184 0.002 74.268 0.000 0.179
## Stst33h (.16.) 0.546 0.004 151.267 0.000 0.539
## Stst34r (.17.) 0.244 0.003 86.811 0.000 0.238
## speed =~
## Stst19d (.18.) 0.289 0.003 110.064 0.000 0.284
## Sts292D (.19.) 0.217 0.003 73.344 0.000 0.212
## Stst34r (.20.) 0.362 0.003 121.690 0.000 0.357
## Stst35t (.21.) 0.619 0.004 162.591 0.000 0.611
## Stst36c (.22.) 0.702 0.004 188.660 0.000 0.695
## Stst37b (.23.) 0.594 0.004 166.547 0.000 0.587
## info =~
## Stst1vc (.24.) 0.189 0.003 74.331 0.000 0.184
## Stst2lt (.25.) 0.311 0.003 117.500 0.000 0.306
## Stst3ms (.26.) 0.369 0.002 161.539 0.000 0.364
## Stst4sc (.27.) 0.161 0.003 55.129 0.000 0.156
## Stst7bl (.28.) 0.072 0.004 20.020 0.000 0.065
## Stst8rn (.29.) 0.121 0.003 42.258 0.000 0.115
## Stst11r (.30.) 0.429 0.003 137.971 0.000 0.423
## Stst12l (.31.) 0.134 0.003 50.557 0.000 0.128
## Stst13h (.32.) 0.174 0.004 48.746 0.000 0.167
## Stst14b (.33.) 0.225 0.003 88.746 0.000 0.220
## Stst15t (.34.) 0.403 0.003 159.558 0.000 0.398
## Stst16m (.35.) 0.183 0.002 75.479 0.000 0.178
## Stst19d (.36.) 0.243 0.003 76.117 0.000 0.237
## Stst26r (.37.) 0.188 0.002 83.813 0.000 0.184
## science =~
## Stst1vc (.38.) 0.165 0.002 71.338 0.000 0.161
## Stst6ph (.39.) 0.317 0.003 111.867 0.000 0.311
## Stst7bl (.40.) 0.262 0.003 76.305 0.000 0.255
## Stst8rn (.41.) 0.351 0.003 123.374 0.000 0.345
## Stst9lc (.42.) 0.483 0.003 146.682 0.000 0.476
## Stst10m (.43.) 0.388 0.003 119.036 0.000 0.382
## Stst13h (.44.) 0.091 0.003 27.405 0.000 0.085
## Stst28m (.45.) 0.236 0.003 88.075 0.000 0.231
## spatial =~
## Stst28m (.46.) 0.430 0.003 152.883 0.000 0.424
## Sts292D (.47.) 0.474 0.003 138.563 0.000 0.468
## Sts303D (.48.) 0.594 0.004 162.151 0.000 0.587
## Stst31b (.49.) 0.378 0.003 123.969 0.000 0.372
## Stst32r (.50.) 0.127 0.003 49.856 0.000 0.122
## Stst37b (.51.) 0.225 0.003 70.378 0.000 0.219
## g =~
## Stst1vc 0.905 0.004 254.520 0.000 0.898
## Stst2lt (.53.) 0.789 0.003 288.395 0.000 0.784
## Stst3ms (.54.) 0.666 0.003 245.609 0.000 0.661
## Stst4sc (.55.) 0.805 0.003 293.030 0.000 0.800
## Stst5mt (.56.) 0.729 0.003 282.737 0.000 0.724
## Stst6ph (.57.) 0.721 0.003 274.594 0.000 0.716
## Stst7bl (.58.) 0.653 0.003 226.619 0.000 0.647
## Stst8rn (.59.) 0.457 0.003 159.938 0.000 0.452
## Stst9lc (.60.) 0.423 0.003 152.278 0.000 0.418
## Stst10m (.61.) 0.405 0.003 156.561 0.000 0.400
## Stst11r (.62.) 0.641 0.003 217.455 0.000 0.635
## Stst12l (.63.) 0.656 0.003 233.459 0.000 0.651
## Stst13h (.64.) 0.598 0.003 186.578 0.000 0.592
## Stst14b (.65.) 0.593 0.003 210.401 0.000 0.587
## Stst15t (.66.) 0.615 0.003 221.595 0.000 0.610
## Stst16m (.67.) 0.652 0.003 225.397 0.000 0.646
## Stst19d (.68.) 0.561 0.003 193.522 0.000 0.555
## Stst20s (.69.) 0.544 0.003 188.521 0.000 0.539
## Stst21c (.70.) 0.550 0.003 191.132 0.000 0.544
## Stst22p (.71.) 0.702 0.003 251.863 0.000 0.696
## Stst23n (.72.) 0.605 0.003 199.087 0.000 0.599
## Stst24x (.73.) 0.535 0.003 175.527 0.000 0.530
## Stst25w (.74.) 0.696 0.003 277.363 0.000 0.691
## Stst26r (.75.) 0.838 0.003 310.048 0.000 0.833
## Stst28m (.76.) 0.471 0.003 177.802 0.000 0.466
## Sts292D (.77.) 0.348 0.003 116.960 0.000 0.342
## Sts303D (.78.) 0.485 0.003 161.967 0.000 0.479
## Stst31b (.79.) 0.564 0.003 188.313 0.000 0.558
## Stst32r (.80.) 0.729 0.003 281.429 0.000 0.724
## Stst33h (.81.) 0.750 0.003 256.288 0.000 0.744
## Stst34r (.82.) 0.482 0.003 157.979 0.000 0.476
## Stst35t (.83.) 0.235 0.003 79.544 0.000 0.229
## Stst36c (.84.) 0.140 0.003 47.492 0.000 0.134
## Stst37b (.85.) 0.143 0.003 48.394 0.000 0.137
## ci.upper Std.lv Std.all
##
## 0.313 0.307 0.325
## 0.353 0.348 0.382
## 0.326 0.323 0.347
## 0.376 0.372 0.415
## 0.293 0.290 0.318
## 0.252 0.249 0.274
## 0.278 0.274 0.290
## 0.149 0.146 0.161
## 0.181 0.178 0.191
## 0.123 0.120 0.127
## 0.109 0.105 0.115
##
## 0.308 0.303 0.323
## 0.118 0.114 0.125
## 0.172 0.167 0.177
## 0.188 0.184 0.194
## 0.553 0.546 0.579
## 0.249 0.244 0.266
##
## 0.294 0.261 0.276
## 0.223 0.196 0.206
## 0.368 0.327 0.357
## 0.626 0.558 0.682
## 0.710 0.633 0.690
## 0.601 0.535 0.582
##
## 0.194 0.189 0.194
## 0.316 0.311 0.329
## 0.373 0.369 0.390
## 0.167 0.161 0.176
## 0.079 0.072 0.076
## 0.127 0.121 0.130
## 0.435 0.429 0.452
## 0.139 0.134 0.139
## 0.181 0.174 0.187
## 0.230 0.225 0.229
## 0.408 0.403 0.427
## 0.187 0.183 0.195
## 0.250 0.243 0.258
## 0.193 0.188 0.208
##
## 0.170 0.134 0.138
## 0.323 0.256 0.282
## 0.269 0.212 0.224
## 0.357 0.284 0.305
## 0.489 0.391 0.441
## 0.394 0.314 0.417
## 0.098 0.074 0.079
## 0.241 0.191 0.235
##
## 0.435 0.390 0.480
## 0.481 0.430 0.452
## 0.602 0.540 0.582
## 0.384 0.343 0.368
## 0.132 0.115 0.122
## 0.231 0.204 0.222
##
## 0.912 0.811 0.836
## 0.794 0.707 0.749
## 0.671 0.597 0.632
## 0.810 0.722 0.789
## 0.734 0.653 0.696
## 0.726 0.647 0.711
## 0.658 0.585 0.619
## 0.463 0.410 0.441
## 0.428 0.379 0.428
## 0.410 0.363 0.482
## 0.647 0.575 0.606
## 0.662 0.588 0.613
## 0.605 0.536 0.577
## 0.598 0.532 0.539
## 0.621 0.552 0.585
## 0.658 0.585 0.626
## 0.566 0.503 0.532
## 0.550 0.488 0.536
## 0.555 0.493 0.529
## 0.707 0.629 0.703
## 0.611 0.543 0.596
## 0.541 0.480 0.529
## 0.701 0.624 0.661
## 0.844 0.752 0.833
## 0.477 0.423 0.520
## 0.354 0.312 0.328
## 0.491 0.435 0.470
## 0.570 0.506 0.543
## 0.734 0.654 0.692
## 0.756 0.672 0.714
## 0.488 0.432 0.472
## 0.240 0.210 0.257
## 0.146 0.125 0.137
## 0.148 0.128 0.139
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d -0.973 0.016 -60.158 0.000 -1.005
## .Stst20s (.149) -0.250 0.004 -63.143 0.000 -0.258
## .Stst21c (.150) -0.186 0.004 -48.287 0.000 -0.194
## .Stst22p (.151) -0.184 0.004 -46.653 0.000 -0.191
## .Stst23n (.152) -0.117 0.004 -29.339 0.000 -0.125
## .Stst24x (.153) -0.085 0.004 -20.953 0.000 -0.093
## .Stst25w (.154) -0.123 0.004 -31.776 0.000 -0.131
## .Stst26r (.155) 0.002 0.004 0.571 0.568 -0.006
## .Stst31b (.156) 0.083 0.004 21.551 0.000 0.076
## .Stst32r (.157) 0.139 0.004 35.252 0.000 0.132
## .Stst34r (.158) -0.088 0.004 -22.772 0.000 -0.096
## .Stst5mt (.159) 0.236 0.004 65.202 0.000 0.229
## .Stst6ph 0.937 0.010 92.964 0.000 0.917
## .Stst33h (.161) 0.137 0.004 32.769 0.000 0.129
## .Sts292D (.162) 0.187 0.004 50.139 0.000 0.180
## .Stst35t (.163) -0.034 0.003 -9.869 0.000 -0.041
## .Stst36c (.164) -0.167 0.004 -45.707 0.000 -0.174
## .Stst37b (.165) -0.080 0.004 -21.122 0.000 -0.087
## .Stst1vc 0.635 0.009 70.537 0.000 0.618
## .Stst2lt (.167) 0.023 0.004 5.838 0.000 0.015
## .Stst3ms (.168) -0.105 0.004 -26.020 0.000 -0.113
## .Stst4sc (.169) 0.225 0.004 57.482 0.000 0.218
## .Stst7bl 0.803 0.011 72.247 0.000 0.782
## .Stst8rn (.171) 0.468 0.004 132.979 0.000 0.461
## .Stst11r -0.307 0.010 -30.158 0.000 -0.327
## .Stst12l (.173) 0.178 0.004 44.267 0.000 0.170
## .Stst13h 0.493 0.011 45.227 0.000 0.472
## .Stst14b (.175) 0.048 0.004 11.683 0.000 0.040
## .Stst15t (.176) -0.169 0.004 -43.894 0.000 -0.177
## .Stst16m (.177) 0.113 0.004 27.209 0.000 0.105
## .Stst9lc 0.955 0.011 87.873 0.000 0.933
## .Stst10m (.179) 0.647 0.003 198.338 0.000 0.641
## .Stst28m (.180) 0.562 0.003 160.581 0.000 0.555
## .Sts303D 0.450 0.007 65.321 0.000 0.436
## english 2.980 0.031 96.124 0.000 2.920
## math 0.880 0.023 37.572 0.000 0.834
## speed 0.543 0.009 62.020 0.000 0.526
## info 2.323 0.025 92.625 0.000 2.274
## science -2.046 0.022 -92.549 0.000 -2.089
## spatial -0.201 0.013 -15.208 0.000 -0.227
## g -0.906 0.014 -66.471 0.000 -0.932
## ci.upper Std.lv Std.all
## -0.941 -0.973 -1.030
## -0.242 -0.250 -0.274
## -0.179 -0.186 -0.200
## -0.176 -0.184 -0.205
## -0.110 -0.117 -0.129
## -0.077 -0.085 -0.094
## -0.116 -0.123 -0.130
## 0.010 0.002 0.003
## 0.091 0.083 0.090
## 0.147 0.139 0.147
## -0.081 -0.088 -0.097
## 0.243 0.236 0.251
## 0.957 0.937 1.031
## 0.145 0.137 0.146
## 0.195 0.187 0.197
## -0.028 -0.034 -0.042
## -0.160 -0.167 -0.182
## -0.072 -0.080 -0.086
## 0.653 0.635 0.655
## 0.031 0.023 0.025
## -0.097 -0.105 -0.111
## 0.233 0.225 0.246
## 0.825 0.803 0.850
## 0.475 0.468 0.503
## -0.287 -0.307 -0.324
## 0.186 0.178 0.186
## 0.514 0.493 0.530
## 0.056 0.048 0.049
## -0.161 -0.169 -0.179
## 0.121 0.113 0.121
## 0.976 0.955 1.078
## 0.653 0.647 0.859
## 0.568 0.562 0.691
## 0.463 0.450 0.486
## 3.041 2.980 2.980
## 0.926 0.880 0.880
## 0.560 0.603 0.603
## 2.372 2.323 2.323
## -2.002 -2.529 -2.529
## -0.175 -0.221 -0.221
## -0.879 -1.010 -1.010
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english 1.000 1.000
## math 1.000 1.000
## info 1.000 1.000
## .Stst19dsgsdwrd 0.419 0.003 133.780 0.000 0.413
## .Stest20spellng 0.471 0.003 160.620 0.000 0.465
## .Stest21cptlztn 0.520 0.003 162.845 0.000 0.513
## .Stest22puncttn 0.267 0.002 131.605 0.000 0.263
## .Stest23english 0.450 0.003 158.608 0.000 0.445
## .Stest24exprssn 0.532 0.004 147.982 0.000 0.525
## .Stst25wrdfnctn 0.400 0.003 144.795 0.000 0.394
## .Stst26rdngcmpr 0.193 0.001 141.290 0.000 0.191
## .Stst31bstrctrs 0.462 0.003 150.138 0.000 0.456
## .Stst32rthrsnng 0.405 0.002 168.592 0.000 0.400
## .Stst34rthcmptt 0.474 0.003 139.452 0.000 0.467
## .Stest5math 0.364 0.003 108.449 0.000 0.357
## .Stst6physclscn 0.329 0.002 150.951 0.000 0.325
## .Stst33hghschlm 0.137 0.003 41.593 0.000 0.131
## .Stst29vslztn2D 0.586 0.004 148.340 0.000 0.578
## .Stest35tblrdng 0.312 0.004 88.731 0.000 0.305
## .Stst36clrclchc 0.424 0.004 101.184 0.000 0.416
## .Stst37bjctnspc 0.502 0.004 134.506 0.000 0.495
## .Stest1vocab 0.231 0.002 148.563 0.000 0.228
## .Stest2literatr 0.295 0.002 158.172 0.000 0.291
## .Stest3music 0.401 0.003 157.886 0.000 0.396
## .Stest4soclstds 0.289 0.002 159.293 0.000 0.285
## .Stst7blgclscnc 0.501 0.003 172.756 0.000 0.495
## .Stest8aerontcs 0.603 0.003 174.051 0.000 0.596
## .Stest11art 0.385 0.003 143.109 0.000 0.380
## .Stest12law 0.557 0.003 178.026 0.000 0.551
## .Stest13health 0.540 0.003 173.464 0.000 0.534
## .Stest14bible 0.639 0.003 193.046 0.000 0.633
## .Stest15theater 0.424 0.003 154.936 0.000 0.418
## .Stest16mscllns 0.498 0.003 171.914 0.000 0.492
## .Stest9elctrncs 0.487 0.004 112.133 0.000 0.479
## .Stest10mechncs 0.337 0.002 149.995 0.000 0.333
## .Stst28mchnclrs 0.294 0.002 128.834 0.000 0.289
## .Stst30vslztn3D 0.378 0.003 113.928 0.000 0.372
## speed 0.812 0.010 79.132 0.000 0.792
## science 0.654 0.010 62.509 0.000 0.634
## spatial 0.824 0.010 80.963 0.000 0.804
## g 0.804 0.006 127.237 0.000 0.792
## ci.upper Std.lv Std.all
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 0.425 0.419 0.469
## 0.477 0.471 0.567
## 0.526 0.520 0.600
## 0.271 0.267 0.333
## 0.456 0.450 0.544
## 0.539 0.532 0.645
## 0.405 0.400 0.448
## 0.196 0.193 0.237
## 0.468 0.462 0.533
## 0.410 0.405 0.453
## 0.481 0.474 0.566
## 0.370 0.364 0.412
## 0.334 0.329 0.399
## 0.144 0.137 0.155
## 0.593 0.586 0.646
## 0.319 0.312 0.468
## 0.433 0.424 0.505
## 0.510 0.502 0.593
## 0.234 0.231 0.245
## 0.298 0.295 0.330
## 0.406 0.401 0.449
## 0.293 0.289 0.346
## 0.507 0.501 0.561
## 0.610 0.603 0.696
## 0.390 0.385 0.428
## 0.563 0.557 0.605
## 0.546 0.540 0.625
## 0.646 0.639 0.657
## 0.429 0.424 0.476
## 0.504 0.498 0.570
## 0.496 0.487 0.622
## 0.342 0.337 0.594
## 0.298 0.294 0.444
## 0.385 0.378 0.440
## 0.832 1.000 1.000
## 0.675 1.000 1.000
## 0.844 1.000 1.000
## 0.816 1.000 1.000
bifactor.weak<-cfa(chc.bifactor.weak.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("g=~Stest1vocab", "Stest19disguisedwords~1", "Stest6physicalscience~1", "Stest13health~1", "Stest9electronics~1", "Stest30visualization3D~1", "Stest1vocab~1", "Stest11art~1", "Stest7biologicalscience~1"))
fitMeasures(bifactor.weak, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 131076.133 1056.000 0.000 0.951 0.042
## srmr aic bic
## 0.057 10334870.631 10336858.839
Mc(bifactor.weak)
## [1] 0.6265521
summary(bifactor.weak, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 104 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 312
## Number of equality constraints 110
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 131076.133 115019.752
## Degrees of freedom 1056 1056
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.140
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 74118.928 65039.611
## 1 56957.205 49980.141
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.307 0.003 101.141 0.000 0.301
## Stst20s (.p2.) 0.345 0.002 166.854 0.000 0.341
## Stst21c (.p3.) 0.321 0.002 169.198 0.000 0.317
## Stst22p (.p4.) 0.371 0.002 191.515 0.000 0.367
## Stst23n (.p5.) 0.290 0.002 163.981 0.000 0.287
## Stst24x (.p6.) 0.250 0.002 142.729 0.000 0.246
## Stst25w (.p7.) 0.272 0.002 141.551 0.000 0.268
## Stst26r (.p8.) 0.146 0.001 99.676 0.000 0.143
## Stst31b (.p9.) 0.169 0.002 107.379 0.000 0.166
## Stst32r (.10.) 0.118 0.002 76.344 0.000 0.115
## Stst34r (.11.) 0.101 0.002 51.752 0.000 0.097
## math =~
## Stst5mt (.12.) 0.310 0.002 130.613 0.000 0.305
## Stst6ph (.13.) 0.114 0.002 48.130 0.000 0.110
## Stst25w (.14.) 0.166 0.003 66.363 0.000 0.161
## Stst32r (.15.) 0.183 0.002 74.112 0.000 0.178
## Stst33h (.16.) 0.534 0.004 148.968 0.000 0.527
## Stst34r (.17.) 0.242 0.003 85.830 0.000 0.237
## speed =~
## Stst19d (.18.) 0.277 0.002 113.512 0.000 0.272
## Sts292D (.19.) 0.200 0.003 73.060 0.000 0.194
## Stst34r (.20.) 0.345 0.003 132.423 0.000 0.340
## Stst35t (.21.) 0.588 0.003 195.502 0.000 0.582
## Stst36c (.22.) 0.670 0.003 223.706 0.000 0.664
## Stst37b (.23.) 0.559 0.003 193.487 0.000 0.554
## info =~
## Stst1vc (.24.) 0.193 0.002 77.709 0.000 0.188
## Stst2lt (.25.) 0.318 0.002 128.206 0.000 0.313
## Stst3ms (.26.) 0.370 0.002 166.574 0.000 0.365
## Stst4sc (.27.) 0.175 0.003 65.933 0.000 0.170
## Stst7bl (.28.) 0.078 0.003 22.196 0.000 0.071
## Stst8rn (.29.) 0.128 0.003 45.863 0.000 0.122
## Stst11r (.30.) 0.432 0.003 141.826 0.000 0.426
## Stst12l (.31.) 0.144 0.002 59.060 0.000 0.139
## Stst13h (.32.) 0.179 0.003 51.149 0.000 0.172
## Stst14b (.33.) 0.233 0.002 99.322 0.000 0.228
## Stst15t (.34.) 0.400 0.002 161.858 0.000 0.395
## Stst16m (.35.) 0.191 0.002 84.170 0.000 0.186
## Stst19d (.36.) 0.242 0.003 75.866 0.000 0.235
## Stst26r (.37.) 0.195 0.002 92.555 0.000 0.190
## science =~
## Stst1vc (.38.) 0.149 0.002 73.816 0.000 0.145
## Stst6ph (.39.) 0.296 0.003 114.548 0.000 0.291
## Stst7bl (.40.) 0.240 0.003 78.191 0.000 0.234
## Stst8rn (.41.) 0.324 0.003 129.025 0.000 0.319
## Stst9lc (.42.) 0.451 0.003 154.747 0.000 0.445
## Stst10m (.43.) 0.344 0.003 134.487 0.000 0.339
## Stst13h (.44.) 0.083 0.003 27.532 0.000 0.077
## Stst28m (.45.) 0.222 0.002 106.952 0.000 0.218
## spatial =~
## Stst28m (.46.) 0.413 0.002 170.268 0.000 0.408
## Sts292D (.47.) 0.446 0.003 148.735 0.000 0.441
## Sts303D (.48.) 0.562 0.003 188.925 0.000 0.557
## Stst31b (.49.) 0.360 0.003 131.870 0.000 0.354
## Stst32r (.50.) 0.119 0.002 49.580 0.000 0.114
## Stst37b (.51.) 0.217 0.003 73.768 0.000 0.211
## g =~
## Stst1vc 0.731 0.003 284.964 0.000 0.726
## Stst2lt (.53.) 0.746 0.002 340.848 0.000 0.742
## Stst3ms (.54.) 0.631 0.002 271.712 0.000 0.626
## Stst4sc (.55.) 0.760 0.002 354.133 0.000 0.756
## Stst5mt (.56.) 0.690 0.002 329.246 0.000 0.686
## Stst6ph (.57.) 0.686 0.002 327.383 0.000 0.682
## Stst7bl (.58.) 0.621 0.003 248.117 0.000 0.616
## Stst8rn (.59.) 0.434 0.002 174.109 0.000 0.429
## Stst9lc (.60.) 0.405 0.002 164.222 0.000 0.400
## Stst10m (.61.) 0.387 0.002 168.524 0.000 0.382
## Stst11r (.62.) 0.606 0.003 237.037 0.000 0.601
## Stst12l (.63.) 0.620 0.002 266.668 0.000 0.616
## Stst13h (.64.) 0.567 0.003 203.736 0.000 0.561
## Stst14b (.65.) 0.560 0.002 230.100 0.000 0.555
## Stst15t (.66.) 0.584 0.002 240.865 0.000 0.579
## Stst16m (.67.) 0.616 0.002 256.122 0.000 0.611
## Stst19d (.68.) 0.533 0.003 205.899 0.000 0.527
## Stst20s (.69.) 0.518 0.003 204.718 0.000 0.513
## Stst21c (.70.) 0.522 0.003 207.207 0.000 0.518
## Stst22p (.71.) 0.667 0.002 291.129 0.000 0.663
## Stst23n (.72.) 0.575 0.003 219.975 0.000 0.569
## Stst24x (.73.) 0.508 0.003 191.166 0.000 0.503
## Stst25w (.74.) 0.663 0.002 311.563 0.000 0.659
## Stst26r (.75.) 0.794 0.002 391.077 0.000 0.790
## Stst28m (.76.) 0.457 0.002 201.649 0.000 0.452
## Sts292D (.77.) 0.347 0.002 142.541 0.000 0.342
## Sts303D (.78.) 0.469 0.003 178.767 0.000 0.464
## Stst31b (.79.) 0.543 0.003 209.236 0.000 0.538
## Stst32r (.80.) 0.695 0.002 334.926 0.000 0.691
## Stst33h (.81.) 0.715 0.002 300.999 0.000 0.710
## Stst34r (.82.) 0.460 0.003 167.106 0.000 0.455
## Stst35t (.83.) 0.220 0.003 80.192 0.000 0.214
## Stst36c (.84.) 0.133 0.003 47.691 0.000 0.127
## Stst37b (.85.) 0.143 0.003 52.225 0.000 0.138
## ci.upper Std.lv Std.all
##
## 0.313 0.307 0.320
## 0.349 0.345 0.357
## 0.325 0.321 0.340
## 0.375 0.371 0.391
## 0.294 0.290 0.301
## 0.253 0.250 0.253
## 0.275 0.272 0.280
## 0.149 0.146 0.152
## 0.172 0.169 0.175
## 0.121 0.118 0.123
## 0.105 0.101 0.108
##
## 0.314 0.310 0.343
## 0.119 0.114 0.124
## 0.171 0.166 0.171
## 0.187 0.183 0.190
## 0.541 0.534 0.541
## 0.248 0.242 0.258
##
## 0.282 0.277 0.289
## 0.205 0.200 0.208
## 0.350 0.345 0.367
## 0.593 0.588 0.649
## 0.676 0.670 0.703
## 0.565 0.559 0.564
##
## 0.198 0.193 0.217
## 0.323 0.318 0.327
## 0.374 0.370 0.375
## 0.181 0.175 0.184
## 0.085 0.078 0.081
## 0.133 0.128 0.154
## 0.438 0.432 0.448
## 0.149 0.144 0.149
## 0.186 0.179 0.186
## 0.237 0.233 0.234
## 0.405 0.400 0.417
## 0.195 0.191 0.193
## 0.248 0.242 0.252
## 0.199 0.195 0.203
##
## 0.153 0.149 0.168
## 0.301 0.296 0.321
## 0.246 0.240 0.250
## 0.329 0.324 0.391
## 0.456 0.451 0.583
## 0.349 0.344 0.438
## 0.089 0.083 0.086
## 0.227 0.222 0.268
##
## 0.418 0.413 0.497
## 0.452 0.446 0.465
## 0.568 0.562 0.568
## 0.365 0.360 0.373
## 0.124 0.119 0.124
## 0.223 0.217 0.218
##
## 0.736 0.731 0.821
## 0.751 0.746 0.768
## 0.635 0.631 0.640
## 0.764 0.760 0.799
## 0.695 0.690 0.765
## 0.691 0.686 0.744
## 0.626 0.621 0.648
## 0.439 0.434 0.523
## 0.409 0.405 0.523
## 0.391 0.387 0.493
## 0.611 0.606 0.628
## 0.625 0.620 0.641
## 0.572 0.567 0.591
## 0.565 0.560 0.564
## 0.588 0.584 0.609
## 0.621 0.616 0.622
## 0.538 0.533 0.556
## 0.523 0.518 0.535
## 0.527 0.522 0.553
## 0.672 0.667 0.703
## 0.580 0.575 0.595
## 0.513 0.508 0.516
## 0.668 0.663 0.684
## 0.798 0.794 0.828
## 0.461 0.457 0.550
## 0.352 0.347 0.361
## 0.474 0.469 0.474
## 0.548 0.543 0.564
## 0.699 0.695 0.722
## 0.720 0.715 0.724
## 0.466 0.460 0.489
## 0.225 0.220 0.243
## 0.138 0.133 0.139
## 0.148 0.143 0.144
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## spatial 0.000 0.000
## .Stst19d -0.108 0.004 -27.549 0.000 -0.116
## .Stst20s (.150) -0.251 0.004 -63.157 0.000 -0.258
## .Stst21c (.151) -0.187 0.004 -48.331 0.000 -0.195
## .Stst22p (.152) -0.183 0.004 -46.442 0.000 -0.191
## .Stst23n (.153) -0.117 0.004 -29.177 0.000 -0.125
## .Stst24x (.154) -0.085 0.004 -20.817 0.000 -0.093
## .Stst25w (.155) -0.123 0.004 -31.712 0.000 -0.131
## .Stst26r (.156) 0.002 0.004 0.573 0.566 -0.006
## .Stst31b (.157) 0.073 0.004 19.014 0.000 0.066
## .Stst32r (.158) 0.138 0.004 34.675 0.000 0.130
## .Stst34r (.159) -0.088 0.004 -22.665 0.000 -0.096
## .Stst5mt (.160) 0.239 0.004 66.166 0.000 0.232
## .Stst6ph 0.358 0.004 92.151 0.000 0.350
## .Stst33h (.162) 0.135 0.004 32.370 0.000 0.127
## .Sts292D (.163) 0.164 0.004 45.135 0.000 0.157
## .Stst35t (.164) -0.027 0.003 -7.904 0.000 -0.034
## .Stst36c (.165) -0.164 0.004 -44.828 0.000 -0.172
## .Stst37b (.166) -0.094 0.004 -25.974 0.000 -0.101
## .Stst1vc 0.189 0.004 50.214 0.000 0.181
## .Stst2lt (.168) 0.024 0.004 5.896 0.000 0.016
## .Stst3ms (.169) -0.107 0.004 -26.349 0.000 -0.114
## .Stst4sc (.170) 0.228 0.004 58.346 0.000 0.220
## .Stst7bl 0.243 0.004 61.805 0.000 0.235
## .Stst8rn (.172) 0.469 0.004 133.221 0.000 0.462
## .Stst11r -0.054 0.004 -13.827 0.000 -0.062
## .Stst12l (.174) 0.181 0.004 45.233 0.000 0.173
## .Stst13h -0.081 0.004 -19.853 0.000 -0.089
## .Stst14b (.176) 0.046 0.004 11.090 0.000 0.038
## .Stst15t (.177) -0.170 0.004 -44.106 0.000 -0.178
## .Stst16m (.178) 0.116 0.004 27.793 0.000 0.107
## .Stst9lc 0.522 0.003 156.854 0.000 0.516
## .Stst10m (.180) 0.649 0.003 199.887 0.000 0.643
## .Stst28m (.181) 0.549 0.003 159.083 0.000 0.542
## .Sts303D 0.194 0.004 47.734 0.000 0.186
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -0.101 -0.108 -0.113
## -0.243 -0.251 -0.259
## -0.179 -0.187 -0.198
## -0.175 -0.183 -0.193
## -0.109 -0.117 -0.121
## -0.077 -0.085 -0.086
## -0.116 -0.123 -0.127
## 0.010 0.002 0.002
## 0.081 0.073 0.076
## 0.145 0.138 0.143
## -0.081 -0.088 -0.094
## 0.246 0.239 0.265
## 0.365 0.358 0.388
## 0.143 0.135 0.137
## 0.171 0.164 0.171
## -0.021 -0.027 -0.030
## -0.157 -0.164 -0.172
## -0.087 -0.094 -0.094
## 0.196 0.189 0.212
## 0.031 0.024 0.024
## -0.099 -0.107 -0.108
## 0.235 0.228 0.239
## 0.251 0.243 0.254
## 0.476 0.469 0.566
## -0.047 -0.054 -0.056
## 0.189 0.181 0.187
## -0.073 -0.081 -0.084
## 0.054 0.046 0.046
## -0.162 -0.170 -0.177
## 0.124 0.116 0.117
## 0.529 0.522 0.676
## 0.656 0.649 0.827
## 0.555 0.549 0.660
## 0.202 0.194 0.196
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.405 0.003 129.571 0.000 0.399
## .Stest20spellng 0.550 0.003 161.585 0.000 0.544
## .Stest21cptlztn 0.515 0.003 163.240 0.000 0.509
## .Stest22puncttn 0.317 0.002 136.932 0.000 0.313
## .Stest23english 0.518 0.003 152.665 0.000 0.511
## .Stest24exprssn 0.651 0.004 155.183 0.000 0.643
## .Stst25wrdfnctn 0.400 0.003 150.947 0.000 0.395
## .Stst26rdngcmpr 0.230 0.002 137.881 0.000 0.227
## .Stst31bstrctrs 0.475 0.003 147.114 0.000 0.469
## .Stst32rthrsnng 0.381 0.002 159.966 0.000 0.377
## .Stst34rthcmptt 0.485 0.003 145.038 0.000 0.478
## .Stest5math 0.241 0.003 94.869 0.000 0.236
## .Stst6physclscn 0.279 0.002 143.341 0.000 0.275
## .Stst33hghschlm 0.179 0.003 56.109 0.000 0.172
## .Stst29vslztn2D 0.563 0.004 132.009 0.000 0.555
## .Stest35tblrdng 0.426 0.004 95.118 0.000 0.417
## .Stst36clrclchc 0.442 0.005 87.143 0.000 0.432
## .Stst37bjctnspc 0.605 0.005 132.775 0.000 0.596
## .Stest1vocab 0.199 0.001 148.481 0.000 0.196
## .Stest2literatr 0.286 0.002 153.569 0.000 0.282
## .Stest3music 0.437 0.003 160.760 0.000 0.432
## .Stest4soclstds 0.297 0.002 153.887 0.000 0.293
## .Stst7blgclscnc 0.469 0.003 160.178 0.000 0.463
## .Stest8aerontcs 0.379 0.003 115.882 0.000 0.372
## .Stest11art 0.377 0.003 142.956 0.000 0.372
## .Stest12law 0.532 0.003 172.003 0.000 0.525
## .Stest13health 0.561 0.003 174.958 0.000 0.554
## .Stest14bible 0.619 0.003 184.395 0.000 0.613
## .Stest15theater 0.419 0.003 155.754 0.000 0.413
## .Stest16mscllns 0.565 0.003 168.003 0.000 0.559
## .Stest9elctrncs 0.231 0.003 79.601 0.000 0.225
## .Stest10mechncs 0.348 0.003 138.987 0.000 0.343
## .Stst28mchnclrs 0.262 0.002 111.414 0.000 0.258
## .Stst30vslztn3D 0.444 0.004 115.672 0.000 0.437
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.411 0.405 0.441
## 0.557 0.550 0.587
## 0.521 0.515 0.578
## 0.322 0.317 0.352
## 0.524 0.518 0.555
## 0.659 0.651 0.670
## 0.405 0.400 0.425
## 0.234 0.230 0.250
## 0.481 0.475 0.512
## 0.386 0.381 0.412
## 0.492 0.485 0.548
## 0.246 0.241 0.296
## 0.283 0.279 0.328
## 0.185 0.179 0.183
## 0.572 0.563 0.610
## 0.435 0.426 0.520
## 0.452 0.442 0.487
## 0.614 0.605 0.614
## 0.202 0.199 0.251
## 0.289 0.286 0.303
## 0.443 0.437 0.450
## 0.300 0.297 0.328
## 0.475 0.469 0.511
## 0.385 0.379 0.550
## 0.382 0.377 0.405
## 0.538 0.532 0.567
## 0.567 0.561 0.609
## 0.626 0.619 0.627
## 0.424 0.419 0.455
## 0.572 0.565 0.576
## 0.237 0.231 0.386
## 0.353 0.348 0.565
## 0.267 0.262 0.379
## 0.452 0.444 0.453
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.307 0.003 101.141 0.000 0.301
## Stst20s (.p2.) 0.345 0.002 166.854 0.000 0.341
## Stst21c (.p3.) 0.321 0.002 169.198 0.000 0.317
## Stst22p (.p4.) 0.371 0.002 191.515 0.000 0.367
## Stst23n (.p5.) 0.290 0.002 163.981 0.000 0.287
## Stst24x (.p6.) 0.250 0.002 142.729 0.000 0.246
## Stst25w (.p7.) 0.272 0.002 141.551 0.000 0.268
## Stst26r (.p8.) 0.146 0.001 99.676 0.000 0.143
## Stst31b (.p9.) 0.169 0.002 107.379 0.000 0.166
## Stst32r (.10.) 0.118 0.002 76.344 0.000 0.115
## Stst34r (.11.) 0.101 0.002 51.752 0.000 0.097
## math =~
## Stst5mt (.12.) 0.310 0.002 130.613 0.000 0.305
## Stst6ph (.13.) 0.114 0.002 48.130 0.000 0.110
## Stst25w (.14.) 0.166 0.003 66.363 0.000 0.161
## Stst32r (.15.) 0.183 0.002 74.112 0.000 0.178
## Stst33h (.16.) 0.534 0.004 148.968 0.000 0.527
## Stst34r (.17.) 0.242 0.003 85.830 0.000 0.237
## speed =~
## Stst19d (.18.) 0.277 0.002 113.512 0.000 0.272
## Sts292D (.19.) 0.200 0.003 73.060 0.000 0.194
## Stst34r (.20.) 0.345 0.003 132.423 0.000 0.340
## Stst35t (.21.) 0.588 0.003 195.502 0.000 0.582
## Stst36c (.22.) 0.670 0.003 223.706 0.000 0.664
## Stst37b (.23.) 0.559 0.003 193.487 0.000 0.554
## info =~
## Stst1vc (.24.) 0.193 0.002 77.709 0.000 0.188
## Stst2lt (.25.) 0.318 0.002 128.206 0.000 0.313
## Stst3ms (.26.) 0.370 0.002 166.574 0.000 0.365
## Stst4sc (.27.) 0.175 0.003 65.933 0.000 0.170
## Stst7bl (.28.) 0.078 0.003 22.196 0.000 0.071
## Stst8rn (.29.) 0.128 0.003 45.863 0.000 0.122
## Stst11r (.30.) 0.432 0.003 141.826 0.000 0.426
## Stst12l (.31.) 0.144 0.002 59.060 0.000 0.139
## Stst13h (.32.) 0.179 0.003 51.149 0.000 0.172
## Stst14b (.33.) 0.233 0.002 99.322 0.000 0.228
## Stst15t (.34.) 0.400 0.002 161.858 0.000 0.395
## Stst16m (.35.) 0.191 0.002 84.170 0.000 0.186
## Stst19d (.36.) 0.242 0.003 75.866 0.000 0.235
## Stst26r (.37.) 0.195 0.002 92.555 0.000 0.190
## science =~
## Stst1vc (.38.) 0.149 0.002 73.816 0.000 0.145
## Stst6ph (.39.) 0.296 0.003 114.548 0.000 0.291
## Stst7bl (.40.) 0.240 0.003 78.191 0.000 0.234
## Stst8rn (.41.) 0.324 0.003 129.025 0.000 0.319
## Stst9lc (.42.) 0.451 0.003 154.747 0.000 0.445
## Stst10m (.43.) 0.344 0.003 134.487 0.000 0.339
## Stst13h (.44.) 0.083 0.003 27.532 0.000 0.077
## Stst28m (.45.) 0.222 0.002 106.952 0.000 0.218
## spatial =~
## Stst28m (.46.) 0.413 0.002 170.268 0.000 0.408
## Sts292D (.47.) 0.446 0.003 148.735 0.000 0.441
## Sts303D (.48.) 0.562 0.003 188.925 0.000 0.557
## Stst31b (.49.) 0.360 0.003 131.870 0.000 0.354
## Stst32r (.50.) 0.119 0.002 49.580 0.000 0.114
## Stst37b (.51.) 0.217 0.003 73.768 0.000 0.211
## g =~
## Stst1vc 0.854 0.003 314.889 0.000 0.848
## Stst2lt (.53.) 0.746 0.002 340.848 0.000 0.742
## Stst3ms (.54.) 0.631 0.002 271.712 0.000 0.626
## Stst4sc (.55.) 0.760 0.002 354.133 0.000 0.756
## Stst5mt (.56.) 0.690 0.002 329.246 0.000 0.686
## Stst6ph (.57.) 0.686 0.002 327.383 0.000 0.682
## Stst7bl (.58.) 0.621 0.003 248.117 0.000 0.616
## Stst8rn (.59.) 0.434 0.002 174.109 0.000 0.429
## Stst9lc (.60.) 0.405 0.002 164.222 0.000 0.400
## Stst10m (.61.) 0.387 0.002 168.524 0.000 0.382
## Stst11r (.62.) 0.606 0.003 237.037 0.000 0.601
## Stst12l (.63.) 0.620 0.002 266.668 0.000 0.616
## Stst13h (.64.) 0.567 0.003 203.736 0.000 0.561
## Stst14b (.65.) 0.560 0.002 230.100 0.000 0.555
## Stst15t (.66.) 0.584 0.002 240.865 0.000 0.579
## Stst16m (.67.) 0.616 0.002 256.122 0.000 0.611
## Stst19d (.68.) 0.533 0.003 205.899 0.000 0.527
## Stst20s (.69.) 0.518 0.003 204.718 0.000 0.513
## Stst21c (.70.) 0.522 0.003 207.207 0.000 0.518
## Stst22p (.71.) 0.667 0.002 291.129 0.000 0.663
## Stst23n (.72.) 0.575 0.003 219.975 0.000 0.569
## Stst24x (.73.) 0.508 0.003 191.166 0.000 0.503
## Stst25w (.74.) 0.663 0.002 311.563 0.000 0.659
## Stst26r (.75.) 0.794 0.002 391.077 0.000 0.790
## Stst28m (.76.) 0.457 0.002 201.649 0.000 0.452
## Sts292D (.77.) 0.347 0.002 142.541 0.000 0.342
## Sts303D (.78.) 0.469 0.003 178.767 0.000 0.464
## Stst31b (.79.) 0.543 0.003 209.236 0.000 0.538
## Stst32r (.80.) 0.695 0.002 334.926 0.000 0.691
## Stst33h (.81.) 0.715 0.002 300.999 0.000 0.710
## Stst34r (.82.) 0.460 0.003 167.106 0.000 0.455
## Stst35t (.83.) 0.220 0.003 80.192 0.000 0.214
## Stst36c (.84.) 0.133 0.003 47.691 0.000 0.127
## Stst37b (.85.) 0.143 0.003 52.225 0.000 0.138
## ci.upper Std.lv Std.all
##
## 0.313 0.307 0.318
## 0.349 0.345 0.373
## 0.325 0.321 0.339
## 0.375 0.371 0.403
## 0.294 0.290 0.312
## 0.253 0.250 0.270
## 0.275 0.272 0.280
## 0.149 0.146 0.155
## 0.172 0.169 0.176
## 0.121 0.118 0.122
## 0.105 0.101 0.108
##
## 0.314 0.310 0.321
## 0.119 0.114 0.121
## 0.171 0.166 0.171
## 0.187 0.183 0.187
## 0.541 0.534 0.550
## 0.248 0.242 0.259
##
## 0.282 0.277 0.287
## 0.205 0.200 0.205
## 0.350 0.345 0.369
## 0.593 0.588 0.700
## 0.676 0.670 0.712
## 0.565 0.559 0.596
##
## 0.198 0.193 0.191
## 0.323 0.318 0.326
## 0.374 0.370 0.382
## 0.181 0.175 0.185
## 0.085 0.078 0.080
## 0.133 0.128 0.134
## 0.438 0.432 0.446
## 0.149 0.144 0.147
## 0.186 0.179 0.189
## 0.237 0.233 0.232
## 0.405 0.400 0.416
## 0.195 0.191 0.200
## 0.248 0.242 0.250
## 0.199 0.195 0.207
##
## 0.153 0.149 0.148
## 0.301 0.296 0.313
## 0.246 0.240 0.246
## 0.329 0.324 0.340
## 0.456 0.451 0.491
## 0.349 0.344 0.442
## 0.089 0.083 0.087
## 0.227 0.222 0.263
##
## 0.418 0.413 0.488
## 0.452 0.446 0.459
## 0.568 0.562 0.589
## 0.365 0.360 0.376
## 0.124 0.119 0.122
## 0.223 0.217 0.231
##
## 0.859 0.854 0.846
## 0.751 0.746 0.765
## 0.635 0.631 0.652
## 0.764 0.760 0.803
## 0.695 0.690 0.715
## 0.691 0.686 0.726
## 0.626 0.621 0.637
## 0.439 0.434 0.455
## 0.409 0.405 0.441
## 0.391 0.387 0.497
## 0.611 0.606 0.625
## 0.625 0.620 0.632
## 0.572 0.567 0.597
## 0.565 0.560 0.558
## 0.588 0.584 0.606
## 0.621 0.616 0.644
## 0.538 0.533 0.552
## 0.523 0.518 0.559
## 0.527 0.522 0.552
## 0.672 0.667 0.724
## 0.580 0.575 0.618
## 0.513 0.508 0.550
## 0.668 0.663 0.684
## 0.798 0.794 0.845
## 0.461 0.457 0.539
## 0.352 0.347 0.356
## 0.474 0.469 0.491
## 0.548 0.543 0.568
## 0.699 0.695 0.714
## 0.720 0.715 0.737
## 0.466 0.460 0.493
## 0.225 0.220 0.262
## 0.138 0.133 0.141
## 0.148 0.143 0.152
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## spatial 0.000 0.000
## .Stst19d -1.011 0.017 -58.593 0.000 -1.045
## .Stst20s (.150) -0.251 0.004 -63.157 0.000 -0.258
## .Stst21c (.151) -0.187 0.004 -48.331 0.000 -0.195
## .Stst22p (.152) -0.183 0.004 -46.442 0.000 -0.191
## .Stst23n (.153) -0.117 0.004 -29.177 0.000 -0.125
## .Stst24x (.154) -0.085 0.004 -20.817 0.000 -0.093
## .Stst25w (.155) -0.123 0.004 -31.712 0.000 -0.131
## .Stst26r (.156) 0.002 0.004 0.573 0.566 -0.006
## .Stst31b (.157) 0.073 0.004 19.014 0.000 0.066
## .Stst32r (.158) 0.138 0.004 34.675 0.000 0.130
## .Stst34r (.159) -0.088 0.004 -22.665 0.000 -0.096
## .Stst5mt (.160) 0.239 0.004 66.166 0.000 0.232
## .Stst6ph 0.989 0.010 100.145 0.000 0.970
## .Stst33h (.162) 0.135 0.004 32.370 0.000 0.127
## .Sts292D (.163) 0.164 0.004 45.135 0.000 0.157
## .Stst35t (.164) -0.027 0.003 -7.904 0.000 -0.034
## .Stst36c (.165) -0.164 0.004 -44.828 0.000 -0.172
## .Stst37b (.166) -0.094 0.004 -25.974 0.000 -0.101
## .Stst1vc 0.661 0.009 72.679 0.000 0.643
## .Stst2lt (.168) 0.024 0.004 5.896 0.000 0.016
## .Stst3ms (.169) -0.107 0.004 -26.349 0.000 -0.114
## .Stst4sc (.170) 0.228 0.004 58.346 0.000 0.220
## .Stst7bl 0.830 0.011 72.432 0.000 0.808
## .Stst8rn (.172) 0.469 0.004 133.221 0.000 0.462
## .Stst11r -0.327 0.011 -30.492 0.000 -0.348
## .Stst12l (.174) 0.181 0.004 45.233 0.000 0.173
## .Stst13h 0.500 0.011 44.372 0.000 0.478
## .Stst14b (.176) 0.046 0.004 11.090 0.000 0.038
## .Stst15t (.177) -0.170 0.004 -44.106 0.000 -0.178
## .Stst16m (.178) 0.116 0.004 27.793 0.000 0.107
## .Stst9lc 1.004 0.011 91.641 0.000 0.982
## .Stst10m (.180) 0.649 0.003 199.887 0.000 0.643
## .Stst28m (.181) 0.549 0.003 159.083 0.000 0.542
## .Sts303D 0.392 0.007 56.729 0.000 0.378
## english 3.147 0.032 98.829 0.000 3.085
## math 1.031 0.024 42.723 0.000 0.984
## speed 0.580 0.009 65.143 0.000 0.563
## info 2.472 0.026 93.896 0.000 2.421
## science -2.215 0.023 -96.090 0.000 -2.260
## g -1.043 0.014 -75.876 0.000 -1.070
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -0.978 -1.011 -1.048
## -0.243 -0.251 -0.270
## -0.179 -0.187 -0.198
## -0.175 -0.183 -0.198
## -0.109 -0.117 -0.126
## -0.077 -0.085 -0.092
## -0.116 -0.123 -0.127
## 0.010 0.002 0.002
## 0.081 0.073 0.077
## 0.145 0.138 0.141
## -0.081 -0.088 -0.094
## 0.246 0.239 0.247
## 1.008 0.989 1.045
## 0.143 0.135 0.139
## 0.171 0.164 0.169
## -0.021 -0.027 -0.033
## -0.157 -0.164 -0.175
## -0.087 -0.094 -0.100
## 0.678 0.661 0.654
## 0.031 0.024 0.024
## -0.099 -0.107 -0.110
## 0.235 0.228 0.240
## 0.853 0.830 0.852
## 0.476 0.469 0.492
## -0.306 -0.327 -0.337
## 0.189 0.181 0.185
## 0.522 0.500 0.527
## 0.054 0.046 0.046
## -0.162 -0.170 -0.177
## 0.124 0.116 0.121
## 1.025 1.004 1.095
## 0.656 0.649 0.835
## 0.555 0.549 0.648
## 0.405 0.392 0.410
## 3.210 3.147 3.147
## 1.078 1.031 1.031
## 0.597 0.580 0.580
## 2.524 2.472 2.472
## -2.170 -2.215 -2.215
## -1.016 -1.043 -1.043
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.418 0.003 133.657 0.000 0.412
## .Stest20spellng 0.472 0.003 161.013 0.000 0.466
## .Stest21cptlztn 0.520 0.003 162.921 0.000 0.514
## .Stest22puncttn 0.266 0.002 131.528 0.000 0.262
## .Stest23english 0.450 0.003 158.473 0.000 0.444
## .Stest24exprssn 0.532 0.004 147.985 0.000 0.525
## .Stst25wrdfnctn 0.399 0.003 144.954 0.000 0.394
## .Stst26rdngcmpr 0.193 0.001 141.077 0.000 0.190
## .Stst31bstrctrs 0.461 0.003 150.281 0.000 0.455
## .Stst32rthrsnng 0.404 0.002 168.351 0.000 0.399
## .Stst34rthcmptt 0.473 0.003 139.196 0.000 0.466
## .Stest5math 0.361 0.003 106.861 0.000 0.354
## .Stst6physclscn 0.323 0.002 149.041 0.000 0.319
## .Stst33hghschlm 0.146 0.003 46.027 0.000 0.140
## .Stst29vslztn2D 0.588 0.004 148.307 0.000 0.580
## .Stest35tblrdng 0.310 0.004 88.233 0.000 0.304
## .Stst36clrclchc 0.418 0.004 99.999 0.000 0.410
## .Stst37bjctnspc 0.501 0.004 134.517 0.000 0.494
## .Stest1vocab 0.231 0.002 148.751 0.000 0.228
## .Stest2literatr 0.294 0.002 157.940 0.000 0.290
## .Stest3music 0.402 0.003 158.499 0.000 0.397
## .Stest4soclstds 0.289 0.002 159.413 0.000 0.285
## .Stst7blgclscnc 0.499 0.003 172.306 0.000 0.494
## .Stest8aerontcs 0.599 0.004 171.044 0.000 0.592
## .Stest11art 0.386 0.003 143.614 0.000 0.380
## .Stest12law 0.557 0.003 177.949 0.000 0.550
## .Stest13health 0.540 0.003 173.440 0.000 0.534
## .Stest14bible 0.639 0.003 192.886 0.000 0.632
## .Stest15theater 0.426 0.003 156.631 0.000 0.421
## .Stest16mscllns 0.498 0.003 171.769 0.000 0.493
## .Stest9elctrncs 0.475 0.004 110.085 0.000 0.466
## .Stest10mechncs 0.337 0.002 148.737 0.000 0.333
## .Stst28mchnclrs 0.288 0.002 125.796 0.000 0.284
## .Stst30vslztn3D 0.376 0.003 113.035 0.000 0.369
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.424 0.418 0.449
## 0.477 0.472 0.549
## 0.526 0.520 0.580
## 0.270 0.266 0.313
## 0.455 0.450 0.521
## 0.539 0.532 0.624
## 0.405 0.399 0.424
## 0.196 0.193 0.218
## 0.467 0.461 0.504
## 0.409 0.404 0.426
## 0.479 0.473 0.542
## 0.368 0.361 0.387
## 0.328 0.323 0.361
## 0.153 0.146 0.155
## 0.596 0.588 0.621
## 0.317 0.310 0.441
## 0.427 0.418 0.473
## 0.508 0.501 0.568
## 0.234 0.231 0.227
## 0.297 0.294 0.308
## 0.407 0.402 0.429
## 0.292 0.289 0.322
## 0.505 0.499 0.527
## 0.606 0.599 0.659
## 0.391 0.386 0.410
## 0.563 0.557 0.579
## 0.546 0.540 0.600
## 0.645 0.639 0.634
## 0.431 0.426 0.460
## 0.504 0.498 0.545
## 0.483 0.475 0.564
## 0.342 0.337 0.557
## 0.293 0.288 0.402
## 0.382 0.376 0.412
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
tests<-lavTestLRT(configural, metric2, scalar2, chc.bifactor, bifactor.weak)
Td=tests[2:5,"Chisq diff"]
Td
## [1] 7682.5932 5650.4349 1998.6217 251.0064
dfd=tests[2:5,"Df diff"]
dfd
## [1] 77 19 7 1
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.03727822 0.06457533 0.06326862 0.05930748
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.03657566 0.03798536
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.06316428 0.06599736
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.06095056 0.06561788
RMSEA.CI(T=Td[4],df=dfd[4],N=N,G=2)
## [1] 0.05325613 0.06559540
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 0 0 0 0
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 1 1 0 0
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.00 1.00 1.00 0.99 0.00 0.00
round(pvals(T=Td[4],df=dfd[4],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.994 0.439 0.000 0.000
tests<-lavTestLRT(configural, metric2, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 7682.593 28301.000
dfd=tests[2:3,"Df diff"]
dfd
## [1] 77 27
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.03727822 0.12137959
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.03657566 0.03798536
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.1201937 0.1225689
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 0 0 0 0
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 1 1 1 1
tests<-lavTestLRT(configural, metric2, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 7682.593 5650.435 12805.903
dfd=tests[2:4,"Df diff"]
dfd
## [1] 77 19 34
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.03727822 0.06457533 0.07269797
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.03657566 0.03798536
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.06316428 0.06599736
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.07164178 0.07375932
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 0 0 0 0
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 1 1 0 0
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 1 1 0 0
tests<-lavTestLRT(configural, metric)
Td=tests[2,"Chisq diff"]
Td
## [1] 9479.228
dfd=tests[2,"Df diff"]
dfd
## [1] 78
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.0411793
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04048132 0.04188133
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 0 0 0 0
bf.age <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning + Stest34arithcomputation
math =~ Stest5math + Stest6physicalscience + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest13health + Stest28mechanicalreasoning
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest37objectinspection
g=~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
g ~ age
'
bf.age2 <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning + Stest34arithcomputation
math =~ Stest5math + Stest6physicalscience + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest13health + Stest28mechanicalreasoning
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest37objectinspection
g=~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
g ~ age + age2
'
sem.age<-sem(bf.age, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("g=~Stest1vocab", "Stest19disguisedwords~1", "Stest6physicalscience~1", "Stest13health~1", "Stest9electronics~1", "Stest30visualization3D~1", "Stest1vocab~1", "Stest11art~1", "Stest7biologicalscience~1"))
fitMeasures(sem.age, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 154257.444 1121.000 0.000 0.943 0.044
## srmr ecvi aic bic
## 0.057 1.112 10331870.401 10333888.137
Mc(sem.age)
## [1] 0.5765781
summary(sem.age, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 108 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 315
## Number of equality constraints 110
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 154257.444 135356.075
## Degrees of freedom 1121 1121
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.140
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 84705.251 74326.205
## 1 69552.193 61029.870
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.308 0.003 102.309 0.000 0.303
## Stst20s (.p2.) 0.348 0.002 167.133 0.000 0.344
## Stst21c (.p3.) 0.323 0.002 169.079 0.000 0.319
## Stst22p (.p4.) 0.372 0.002 191.794 0.000 0.368
## Stst23n (.p5.) 0.289 0.002 162.499 0.000 0.286
## Stst24x (.p6.) 0.248 0.002 140.197 0.000 0.245
## Stst25w (.p7.) 0.274 0.002 144.124 0.000 0.271
## Stst26r (.p8.) 0.145 0.001 98.937 0.000 0.143
## Stst31b (.p9.) 0.178 0.002 105.098 0.000 0.175
## Stst32r (.10.) 0.119 0.002 77.069 0.000 0.116
## Stst34r (.11.) 0.106 0.002 54.028 0.000 0.102
## math =~
## Stst5mt (.12.) 0.305 0.002 126.263 0.000 0.301
## Stst6ph (.13.) 0.120 0.002 51.048 0.000 0.115
## Stst25w (.14.) 0.168 0.003 67.334 0.000 0.164
## Stst32r (.15.) 0.185 0.002 75.102 0.000 0.181
## Stst33h (.16.) 0.550 0.004 155.787 0.000 0.543
## Stst34r (.17.) 0.245 0.003 87.468 0.000 0.240
## speed =~
## Stst19d (.18.) 0.277 0.002 113.558 0.000 0.272
## Sts292D (.19.) 0.207 0.003 75.190 0.000 0.202
## Stst34r (.20.) 0.345 0.003 132.360 0.000 0.340
## Stst35t (.21.) 0.585 0.003 194.205 0.000 0.579
## Stst36c (.22.) 0.668 0.003 223.462 0.000 0.662
## Stst37b (.23.) 0.564 0.003 195.266 0.000 0.558
## info =~
## Stst1vc (.24.) 0.185 0.003 73.406 0.000 0.180
## Stst2lt (.25.) 0.307 0.003 116.953 0.000 0.301
## Stst3ms (.26.) 0.366 0.002 159.590 0.000 0.362
## Stst4sc (.27.) 0.158 0.003 54.854 0.000 0.152
## Stst7bl (.28.) 0.068 0.004 18.959 0.000 0.061
## Stst8rn (.29.) 0.128 0.003 44.908 0.000 0.122
## Stst11r (.30.) 0.429 0.003 137.127 0.000 0.423
## Stst12l (.31.) 0.130 0.003 49.844 0.000 0.125
## Stst13h (.32.) 0.171 0.004 47.934 0.000 0.164
## Stst14b (.33.) 0.223 0.003 88.553 0.000 0.218
## Stst15t (.34.) 0.400 0.003 158.444 0.000 0.395
## Stst16m (.35.) 0.181 0.002 75.008 0.000 0.176
## Stst19d (.36.) 0.246 0.003 76.400 0.000 0.239
## Stst26r (.37.) 0.186 0.002 83.519 0.000 0.181
## science =~
## Stst1vc (.38.) 0.149 0.002 73.814 0.000 0.145
## Stst6ph (.39.) 0.298 0.003 115.850 0.000 0.293
## Stst7bl (.40.) 0.239 0.003 77.844 0.000 0.233
## Stst8rn (.41.) 0.326 0.002 131.327 0.000 0.321
## Stst9lc (.42.) 0.452 0.003 155.365 0.000 0.446
## Stst10m (.43.) 0.347 0.003 137.494 0.000 0.342
## Stst13h (.44.) 0.082 0.003 27.240 0.000 0.076
## Stst28m (.45.) 0.211 0.002 97.143 0.000 0.206
## spatial =~
## Stst28m (.46.) 0.413 0.002 170.085 0.000 0.408
## Sts292D (.47.) 0.454 0.003 151.201 0.000 0.448
## Sts303D (.48.) 0.565 0.003 190.375 0.000 0.560
## Stst31b (.49.) 0.361 0.003 132.333 0.000 0.355
## Stst32r (.50.) 0.121 0.002 50.337 0.000 0.116
## Stst37b (.51.) 0.213 0.003 71.831 0.000 0.207
## g =~
## Stst1vc 0.725 0.003 285.299 0.000 0.720
## Stst2lt (.53.) 0.743 0.002 343.880 0.000 0.739
## Stst3ms (.54.) 0.627 0.002 270.266 0.000 0.623
## Stst4sc (.55.) 0.757 0.002 351.181 0.000 0.753
## Stst5mt (.56.) 0.684 0.002 323.961 0.000 0.680
## Stst6ph (.57.) 0.677 0.002 317.507 0.000 0.673
## Stst7bl (.58.) 0.617 0.002 250.115 0.000 0.612
## Stst8rn (.59.) 0.429 0.002 172.322 0.000 0.424
## Stst9lc (.60.) 0.400 0.002 164.032 0.000 0.395
## Stst10m (.61.) 0.386 0.002 171.460 0.000 0.381
## Stst11r (.62.) 0.603 0.003 234.850 0.000 0.598
## Stst12l (.63.) 0.618 0.002 269.208 0.000 0.613
## Stst13h (.64.) 0.564 0.003 205.270 0.000 0.558
## Stst14b (.65.) 0.558 0.002 228.893 0.000 0.553
## Stst15t (.66.) 0.580 0.002 240.861 0.000 0.575
## Stst16m (.67.) 0.613 0.002 253.814 0.000 0.608
## Stst19d (.68.) 0.527 0.003 205.466 0.000 0.522
## Stst20s (.69.) 0.512 0.002 205.242 0.000 0.507
## Stst21c (.70.) 0.516 0.003 206.257 0.000 0.511
## Stst22p (.71.) 0.659 0.002 287.799 0.000 0.654
## Stst23n (.72.) 0.569 0.003 220.213 0.000 0.564
## Stst24x (.73.) 0.504 0.003 192.119 0.000 0.499
## Stst25w (.74.) 0.654 0.002 306.604 0.000 0.650
## Stst26r (.75.) 0.788 0.002 389.947 0.000 0.784
## Stst28m (.76.) 0.444 0.002 191.710 0.000 0.440
## Sts292D (.77.) 0.326 0.003 118.297 0.000 0.320
## Sts303D (.78.) 0.455 0.003 169.267 0.000 0.450
## Stst31b (.79.) 0.529 0.003 198.490 0.000 0.524
## Stst32r (.80.) 0.684 0.002 326.120 0.000 0.680
## Stst33h (.81.) 0.702 0.002 291.668 0.000 0.697
## Stst34r (.82.) 0.452 0.003 165.704 0.000 0.447
## Stst35t (.83.) 0.222 0.003 81.515 0.000 0.216
## Stst36c (.84.) 0.133 0.003 48.377 0.000 0.128
## Stst37b (.85.) 0.136 0.003 49.104 0.000 0.130
## ci.upper Std.lv Std.all
##
## 0.314 0.308 0.322
## 0.352 0.348 0.360
## 0.326 0.323 0.342
## 0.375 0.372 0.392
## 0.293 0.289 0.300
## 0.252 0.248 0.252
## 0.278 0.274 0.283
## 0.148 0.145 0.152
## 0.182 0.178 0.186
## 0.122 0.119 0.124
## 0.110 0.106 0.112
##
## 0.310 0.305 0.338
## 0.124 0.120 0.130
## 0.173 0.168 0.174
## 0.190 0.185 0.193
## 0.557 0.550 0.557
## 0.251 0.245 0.261
##
## 0.282 0.277 0.289
## 0.213 0.207 0.216
## 0.350 0.345 0.367
## 0.591 0.585 0.646
## 0.674 0.668 0.701
## 0.569 0.564 0.568
##
## 0.190 0.185 0.208
## 0.312 0.307 0.315
## 0.371 0.366 0.371
## 0.163 0.158 0.166
## 0.075 0.068 0.071
## 0.134 0.128 0.154
## 0.435 0.429 0.444
## 0.135 0.130 0.134
## 0.178 0.171 0.178
## 0.228 0.223 0.224
## 0.404 0.400 0.417
## 0.185 0.181 0.182
## 0.252 0.246 0.256
## 0.190 0.186 0.193
##
## 0.153 0.149 0.167
## 0.303 0.298 0.323
## 0.245 0.239 0.249
## 0.331 0.326 0.392
## 0.458 0.452 0.585
## 0.352 0.347 0.441
## 0.088 0.082 0.085
## 0.215 0.211 0.255
##
## 0.418 0.413 0.500
## 0.460 0.454 0.474
## 0.571 0.565 0.573
## 0.366 0.361 0.375
## 0.126 0.121 0.126
## 0.218 0.213 0.214
##
## 0.730 0.733 0.823
## 0.748 0.751 0.773
## 0.632 0.634 0.643
## 0.761 0.765 0.804
## 0.689 0.692 0.766
## 0.681 0.684 0.741
## 0.621 0.623 0.650
## 0.434 0.434 0.523
## 0.405 0.404 0.522
## 0.390 0.390 0.496
## 0.608 0.610 0.632
## 0.622 0.624 0.645
## 0.569 0.570 0.594
## 0.562 0.564 0.567
## 0.585 0.586 0.611
## 0.617 0.619 0.625
## 0.532 0.533 0.556
## 0.517 0.517 0.534
## 0.521 0.521 0.552
## 0.663 0.666 0.702
## 0.574 0.575 0.595
## 0.509 0.509 0.516
## 0.658 0.661 0.681
## 0.792 0.797 0.830
## 0.449 0.449 0.544
## 0.331 0.329 0.344
## 0.460 0.460 0.466
## 0.534 0.534 0.556
## 0.689 0.692 0.720
## 0.706 0.709 0.718
## 0.458 0.457 0.486
## 0.227 0.224 0.248
## 0.139 0.135 0.141
## 0.141 0.137 0.138
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.117 0.004 31.324 0.000 0.110
## ci.upper Std.lv Std.all
##
## 0.125 0.116 0.144
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## science ~~
## spatial 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d -0.101 0.004 -25.494 0.000 -0.109
## .Stst20s (.145) -0.242 0.004 -61.227 0.000 -0.250
## .Stst21c (.146) -0.179 0.004 -46.353 0.000 -0.187
## .Stst22p (.147) -0.175 0.004 -44.126 0.000 -0.182
## .Stst23n (.148) -0.109 0.004 -27.264 0.000 -0.117
## .Stst24x (.149) -0.078 0.004 -19.130 0.000 -0.086
## .Stst25w (.150) -0.114 0.004 -29.175 0.000 -0.121
## .Stst26r (.151) 0.014 0.004 3.367 0.001 0.006
## .Stst31b (.152) 0.091 0.004 23.354 0.000 0.083
## .Stst32r (.153) 0.149 0.004 37.615 0.000 0.141
## .Stst34r (.154) -0.082 0.004 -21.069 0.000 -0.089
## .Stst5mt (.155) 0.245 0.004 67.388 0.000 0.238
## .Stst6ph 0.367 0.004 93.305 0.000 0.360
## .Stst33h (.157) 0.147 0.004 34.854 0.000 0.139
## .Sts292D (.158) 0.192 0.004 51.260 0.000 0.184
## .Stst35t (.159) -0.031 0.003 -8.970 0.000 -0.038
## .Stst36c (.160) -0.165 0.004 -45.438 0.000 -0.173
## .Stst37b (.161) -0.077 0.004 -20.397 0.000 -0.084
## .Stst1vc 0.199 0.004 52.921 0.000 0.192
## .Stst2lt (.163) 0.035 0.004 8.715 0.000 0.027
## .Stst3ms (.164) -0.097 0.004 -23.941 0.000 -0.105
## .Stst4sc (.165) 0.236 0.004 60.003 0.000 0.228
## .Stst7bl 0.252 0.004 64.146 0.000 0.244
## .Stst8rn (.167) 0.475 0.004 134.622 0.000 0.468
## .Stst11r -0.046 0.004 -11.588 0.000 -0.054
## .Stst12l (.169) 0.188 0.004 46.895 0.000 0.180
## .Stst13h -0.073 0.004 -17.941 0.000 -0.081
## .Stst14b (.171) 0.056 0.004 13.392 0.000 0.048
## .Stst15t (.172) -0.161 0.004 -41.644 0.000 -0.168
## .Stst16m (.173) 0.120 0.004 28.718 0.000 0.112
## .Stst9lc 0.528 0.003 159.102 0.000 0.521
## .Stst10m (.175) 0.652 0.003 202.030 0.000 0.645
## .Stst28m (.176) 0.568 0.003 162.762 0.000 0.561
## .Sts303D 0.212 0.004 51.901 0.000 0.204
## ci.upper Std.lv Std.all
## -0.093 -0.101 -0.105
## -0.235 -0.242 -0.250
## -0.172 -0.179 -0.190
## -0.167 -0.175 -0.184
## -0.101 -0.109 -0.113
## -0.070 -0.078 -0.079
## -0.106 -0.114 -0.117
## 0.022 0.014 0.014
## 0.098 0.091 0.094
## 0.157 0.149 0.155
## -0.074 -0.082 -0.087
## 0.252 0.245 0.271
## 0.375 0.367 0.398
## 0.155 0.147 0.149
## 0.199 0.192 0.201
## -0.024 -0.031 -0.034
## -0.158 -0.165 -0.174
## -0.069 -0.077 -0.077
## 0.207 0.199 0.224
## 0.043 0.035 0.036
## -0.089 -0.097 -0.099
## 0.244 0.236 0.248
## 0.259 0.252 0.263
## 0.482 0.475 0.573
## -0.038 -0.046 -0.047
## 0.196 0.188 0.194
## -0.065 -0.073 -0.076
## 0.064 0.056 0.056
## -0.153 -0.161 -0.168
## 0.128 0.120 0.121
## 0.534 0.528 0.683
## 0.658 0.652 0.829
## 0.575 0.568 0.688
## 0.220 0.212 0.215
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.403 0.003 128.271 0.000 0.396
## .Stest20spellng 0.549 0.003 161.324 0.000 0.542
## .Stest21cptlztn 0.515 0.003 163.182 0.000 0.509
## .Stest22puncttn 0.319 0.002 137.199 0.000 0.314
## .Stest23english 0.518 0.003 152.804 0.000 0.511
## .Stest24exprssn 0.651 0.004 155.298 0.000 0.642
## .Stst25wrdfnctn 0.400 0.003 151.013 0.000 0.395
## .Stst26rdngcmpr 0.230 0.002 137.775 0.000 0.227
## .Stst31bstrctrs 0.475 0.003 146.771 0.000 0.469
## .Stst32rthrsnng 0.382 0.002 160.161 0.000 0.377
## .Stst34rthcmptt 0.485 0.003 145.192 0.000 0.478
## .Stest5math 0.243 0.003 95.382 0.000 0.238
## .Stst6physclscn 0.280 0.002 143.355 0.000 0.276
## .Stst33hghschlm 0.169 0.003 51.677 0.000 0.162
## .Stst29vslztn2D 0.558 0.004 128.826 0.000 0.549
## .Stest35tblrdng 0.426 0.004 95.794 0.000 0.417
## .Stst36clrclchc 0.444 0.005 87.421 0.000 0.434
## .Stst37bjctnspc 0.604 0.005 132.506 0.000 0.595
## .Stest1vocab 0.199 0.001 148.498 0.000 0.196
## .Stest2literatr 0.286 0.002 153.794 0.000 0.282
## .Stest3music 0.436 0.003 160.187 0.000 0.431
## .Stest4soclstds 0.296 0.002 153.110 0.000 0.292
## .Stst7blgclscnc 0.469 0.003 160.003 0.000 0.463
## .Stest8aerontcs 0.379 0.003 115.710 0.000 0.372
## .Stest11art 0.375 0.003 141.843 0.000 0.370
## .Stest12law 0.531 0.003 171.745 0.000 0.525
## .Stest13health 0.561 0.003 175.025 0.000 0.554
## .Stest14bible 0.620 0.003 184.574 0.000 0.613
## .Stest15theater 0.416 0.003 154.224 0.000 0.411
## .Stest16mscllns 0.566 0.003 168.042 0.000 0.560
## .Stest9elctrncs 0.230 0.003 79.226 0.000 0.224
## .Stest10mechncs 0.347 0.002 139.125 0.000 0.342
## .Stst28mchnclrs 0.266 0.002 112.966 0.000 0.261
## .Stst30vslztn3D 0.443 0.004 115.435 0.000 0.435
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.409 0.403 0.438
## 0.556 0.549 0.585
## 0.521 0.515 0.578
## 0.324 0.319 0.354
## 0.525 0.518 0.556
## 0.659 0.651 0.670
## 0.405 0.400 0.425
## 0.233 0.230 0.250
## 0.482 0.475 0.515
## 0.386 0.382 0.413
## 0.491 0.485 0.549
## 0.248 0.243 0.299
## 0.284 0.280 0.329
## 0.175 0.169 0.173
## 0.566 0.558 0.610
## 0.435 0.426 0.521
## 0.453 0.444 0.488
## 0.613 0.604 0.613
## 0.202 0.199 0.251
## 0.289 0.286 0.303
## 0.441 0.436 0.449
## 0.300 0.296 0.327
## 0.474 0.469 0.510
## 0.385 0.379 0.549
## 0.381 0.375 0.403
## 0.537 0.531 0.566
## 0.567 0.561 0.609
## 0.626 0.620 0.628
## 0.422 0.416 0.453
## 0.573 0.566 0.577
## 0.236 0.230 0.385
## 0.352 0.347 0.560
## 0.270 0.266 0.390
## 0.450 0.443 0.455
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 0.979 0.979
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.308 0.003 102.309 0.000 0.303
## Stst20s (.p2.) 0.348 0.002 167.133 0.000 0.344
## Stst21c (.p3.) 0.323 0.002 169.079 0.000 0.319
## Stst22p (.p4.) 0.372 0.002 191.794 0.000 0.368
## Stst23n (.p5.) 0.289 0.002 162.499 0.000 0.286
## Stst24x (.p6.) 0.248 0.002 140.197 0.000 0.245
## Stst25w (.p7.) 0.274 0.002 144.124 0.000 0.271
## Stst26r (.p8.) 0.145 0.001 98.937 0.000 0.143
## Stst31b (.p9.) 0.178 0.002 105.098 0.000 0.175
## Stst32r (.10.) 0.119 0.002 77.069 0.000 0.116
## Stst34r (.11.) 0.106 0.002 54.028 0.000 0.102
## math =~
## Stst5mt (.12.) 0.305 0.002 126.263 0.000 0.301
## Stst6ph (.13.) 0.120 0.002 51.048 0.000 0.115
## Stst25w (.14.) 0.168 0.003 67.334 0.000 0.164
## Stst32r (.15.) 0.185 0.002 75.102 0.000 0.181
## Stst33h (.16.) 0.550 0.004 155.787 0.000 0.543
## Stst34r (.17.) 0.245 0.003 87.468 0.000 0.240
## speed =~
## Stst19d (.18.) 0.277 0.002 113.558 0.000 0.272
## Sts292D (.19.) 0.207 0.003 75.190 0.000 0.202
## Stst34r (.20.) 0.345 0.003 132.360 0.000 0.340
## Stst35t (.21.) 0.585 0.003 194.205 0.000 0.579
## Stst36c (.22.) 0.668 0.003 223.462 0.000 0.662
## Stst37b (.23.) 0.564 0.003 195.266 0.000 0.558
## info =~
## Stst1vc (.24.) 0.185 0.003 73.406 0.000 0.180
## Stst2lt (.25.) 0.307 0.003 116.953 0.000 0.301
## Stst3ms (.26.) 0.366 0.002 159.590 0.000 0.362
## Stst4sc (.27.) 0.158 0.003 54.854 0.000 0.152
## Stst7bl (.28.) 0.068 0.004 18.959 0.000 0.061
## Stst8rn (.29.) 0.128 0.003 44.908 0.000 0.122
## Stst11r (.30.) 0.429 0.003 137.127 0.000 0.423
## Stst12l (.31.) 0.130 0.003 49.844 0.000 0.125
## Stst13h (.32.) 0.171 0.004 47.934 0.000 0.164
## Stst14b (.33.) 0.223 0.003 88.553 0.000 0.218
## Stst15t (.34.) 0.400 0.003 158.444 0.000 0.395
## Stst16m (.35.) 0.181 0.002 75.008 0.000 0.176
## Stst19d (.36.) 0.246 0.003 76.400 0.000 0.239
## Stst26r (.37.) 0.186 0.002 83.519 0.000 0.181
## science =~
## Stst1vc (.38.) 0.149 0.002 73.814 0.000 0.145
## Stst6ph (.39.) 0.298 0.003 115.850 0.000 0.293
## Stst7bl (.40.) 0.239 0.003 77.844 0.000 0.233
## Stst8rn (.41.) 0.326 0.002 131.327 0.000 0.321
## Stst9lc (.42.) 0.452 0.003 155.365 0.000 0.446
## Stst10m (.43.) 0.347 0.003 137.494 0.000 0.342
## Stst13h (.44.) 0.082 0.003 27.240 0.000 0.076
## Stst28m (.45.) 0.211 0.002 97.143 0.000 0.206
## spatial =~
## Stst28m (.46.) 0.413 0.002 170.085 0.000 0.408
## Sts292D (.47.) 0.454 0.003 151.201 0.000 0.448
## Sts303D (.48.) 0.565 0.003 190.375 0.000 0.560
## Stst31b (.49.) 0.361 0.003 132.333 0.000 0.355
## Stst32r (.50.) 0.121 0.002 50.337 0.000 0.116
## Stst37b (.51.) 0.213 0.003 71.831 0.000 0.207
## g =~
## Stst1vc 0.847 0.003 316.234 0.000 0.842
## Stst2lt (.53.) 0.743 0.002 343.880 0.000 0.739
## Stst3ms (.54.) 0.627 0.002 270.266 0.000 0.623
## Stst4sc (.55.) 0.757 0.002 351.181 0.000 0.753
## Stst5mt (.56.) 0.684 0.002 323.961 0.000 0.680
## Stst6ph (.57.) 0.677 0.002 317.507 0.000 0.673
## Stst7bl (.58.) 0.617 0.002 250.115 0.000 0.612
## Stst8rn (.59.) 0.429 0.002 172.322 0.000 0.424
## Stst9lc (.60.) 0.400 0.002 164.032 0.000 0.395
## Stst10m (.61.) 0.386 0.002 171.460 0.000 0.381
## Stst11r (.62.) 0.603 0.003 234.850 0.000 0.598
## Stst12l (.63.) 0.618 0.002 269.208 0.000 0.613
## Stst13h (.64.) 0.564 0.003 205.270 0.000 0.558
## Stst14b (.65.) 0.558 0.002 228.893 0.000 0.553
## Stst15t (.66.) 0.580 0.002 240.861 0.000 0.575
## Stst16m (.67.) 0.613 0.002 253.814 0.000 0.608
## Stst19d (.68.) 0.527 0.003 205.466 0.000 0.522
## Stst20s (.69.) 0.512 0.002 205.242 0.000 0.507
## Stst21c (.70.) 0.516 0.003 206.257 0.000 0.511
## Stst22p (.71.) 0.659 0.002 287.799 0.000 0.654
## Stst23n (.72.) 0.569 0.003 220.213 0.000 0.564
## Stst24x (.73.) 0.504 0.003 192.119 0.000 0.499
## Stst25w (.74.) 0.654 0.002 306.604 0.000 0.650
## Stst26r (.75.) 0.788 0.002 389.947 0.000 0.784
## Stst28m (.76.) 0.444 0.002 191.710 0.000 0.440
## Sts292D (.77.) 0.326 0.003 118.297 0.000 0.320
## Sts303D (.78.) 0.455 0.003 169.267 0.000 0.450
## Stst31b (.79.) 0.529 0.003 198.490 0.000 0.524
## Stst32r (.80.) 0.684 0.002 326.120 0.000 0.680
## Stst33h (.81.) 0.702 0.002 291.668 0.000 0.697
## Stst34r (.82.) 0.452 0.003 165.704 0.000 0.447
## Stst35t (.83.) 0.222 0.003 81.515 0.000 0.216
## Stst36c (.84.) 0.133 0.003 48.377 0.000 0.128
## Stst37b (.85.) 0.136 0.003 49.104 0.000 0.130
## ci.upper Std.lv Std.all
##
## 0.314 0.308 0.320
## 0.352 0.348 0.376
## 0.326 0.323 0.341
## 0.375 0.372 0.403
## 0.293 0.289 0.311
## 0.252 0.248 0.269
## 0.278 0.274 0.283
## 0.148 0.145 0.155
## 0.182 0.178 0.187
## 0.122 0.119 0.122
## 0.110 0.106 0.113
##
## 0.310 0.305 0.316
## 0.124 0.120 0.127
## 0.173 0.168 0.174
## 0.190 0.185 0.191
## 0.557 0.550 0.567
## 0.251 0.245 0.262
##
## 0.282 0.277 0.287
## 0.213 0.207 0.214
## 0.350 0.345 0.369
## 0.591 0.585 0.697
## 0.674 0.668 0.711
## 0.569 0.564 0.600
##
## 0.190 0.185 0.184
## 0.312 0.307 0.314
## 0.371 0.366 0.378
## 0.163 0.158 0.166
## 0.075 0.068 0.070
## 0.134 0.128 0.134
## 0.435 0.429 0.442
## 0.135 0.130 0.133
## 0.178 0.171 0.180
## 0.228 0.223 0.222
## 0.404 0.400 0.415
## 0.185 0.181 0.189
## 0.252 0.246 0.255
## 0.190 0.186 0.197
##
## 0.153 0.149 0.147
## 0.303 0.298 0.315
## 0.245 0.239 0.245
## 0.331 0.326 0.342
## 0.458 0.452 0.493
## 0.352 0.347 0.444
## 0.088 0.082 0.086
## 0.215 0.211 0.250
##
## 0.418 0.413 0.491
## 0.460 0.454 0.468
## 0.571 0.565 0.594
## 0.366 0.361 0.378
## 0.126 0.121 0.124
## 0.218 0.213 0.226
##
## 0.852 0.856 0.848
## 0.748 0.751 0.770
## 0.632 0.634 0.655
## 0.761 0.765 0.807
## 0.689 0.692 0.715
## 0.681 0.684 0.723
## 0.621 0.623 0.640
## 0.434 0.434 0.455
## 0.405 0.404 0.441
## 0.390 0.390 0.500
## 0.608 0.610 0.629
## 0.622 0.624 0.636
## 0.569 0.570 0.601
## 0.562 0.564 0.562
## 0.585 0.586 0.609
## 0.617 0.619 0.647
## 0.532 0.533 0.552
## 0.517 0.517 0.558
## 0.521 0.522 0.551
## 0.663 0.666 0.723
## 0.574 0.575 0.618
## 0.509 0.509 0.551
## 0.658 0.661 0.682
## 0.792 0.797 0.848
## 0.449 0.449 0.534
## 0.331 0.329 0.340
## 0.460 0.460 0.483
## 0.534 0.535 0.561
## 0.689 0.692 0.711
## 0.706 0.709 0.731
## 0.458 0.457 0.490
## 0.227 0.224 0.267
## 0.139 0.135 0.143
## 0.141 0.137 0.146
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.124 0.003 35.790 0.000 0.117
## ci.upper Std.lv Std.all
##
## 0.130 0.122 0.145
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## science ~~
## spatial 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d -0.980 0.016 -60.158 0.000 -1.012
## .Stst20s (.145) -0.242 0.004 -61.227 0.000 -0.250
## .Stst21c (.146) -0.179 0.004 -46.353 0.000 -0.187
## .Stst22p (.147) -0.175 0.004 -44.126 0.000 -0.182
## .Stst23n (.148) -0.109 0.004 -27.264 0.000 -0.117
## .Stst24x (.149) -0.078 0.004 -19.130 0.000 -0.086
## .Stst25w (.150) -0.114 0.004 -29.175 0.000 -0.121
## .Stst26r (.151) 0.014 0.004 3.367 0.001 0.006
## .Stst31b (.152) 0.091 0.004 23.354 0.000 0.083
## .Stst32r (.153) 0.149 0.004 37.615 0.000 0.141
## .Stst34r (.154) -0.082 0.004 -21.069 0.000 -0.089
## .Stst5mt (.155) 0.245 0.004 67.388 0.000 0.238
## .Stst6ph 0.969 0.010 96.046 0.000 0.949
## .Stst33h (.157) 0.147 0.004 34.854 0.000 0.139
## .Sts292D (.158) 0.192 0.004 51.260 0.000 0.184
## .Stst35t (.159) -0.031 0.003 -8.970 0.000 -0.038
## .Stst36c (.160) -0.165 0.004 -45.438 0.000 -0.173
## .Stst37b (.161) -0.077 0.004 -20.397 0.000 -0.084
## .Stst1vc 0.644 0.009 71.449 0.000 0.627
## .Stst2lt (.163) 0.035 0.004 8.715 0.000 0.027
## .Stst3ms (.164) -0.097 0.004 -23.941 0.000 -0.105
## .Stst4sc (.165) 0.236 0.004 60.003 0.000 0.228
## .Stst7bl 0.827 0.011 73.654 0.000 0.805
## .Stst8rn (.167) 0.475 0.004 134.622 0.000 0.468
## .Stst11r -0.307 0.010 -29.928 0.000 -0.327
## .Stst12l (.169) 0.188 0.004 46.895 0.000 0.180
## .Stst13h 0.502 0.011 45.749 0.000 0.481
## .Stst14b (.171) 0.056 0.004 13.392 0.000 0.048
## .Stst15t (.172) -0.161 0.004 -41.644 0.000 -0.168
## .Stst16m (.173) 0.120 0.004 28.718 0.000 0.112
## .Stst9lc 1.003 0.011 90.840 0.000 0.982
## .Stst10m (.175) 0.652 0.003 202.030 0.000 0.645
## .Stst28m (.176) 0.568 0.003 162.762 0.000 0.561
## .Sts303D 0.456 0.007 66.457 0.000 0.443
## english 2.966 0.030 97.811 0.000 2.906
## math 0.855 0.022 38.220 0.000 0.811
## speed 0.573 0.009 67.247 0.000 0.556
## info 2.332 0.025 94.425 0.000 2.284
## science -2.283 0.022 -103.445 0.000 -2.326
## spatial -0.221 0.014 -16.146 0.000 -0.248
## .g -0.942 0.014 -67.986 0.000 -0.969
## ci.upper Std.lv Std.all
## -0.948 -0.980 -1.015
## -0.235 -0.242 -0.262
## -0.172 -0.179 -0.190
## -0.167 -0.175 -0.189
## -0.101 -0.109 -0.117
## -0.070 -0.078 -0.084
## -0.106 -0.114 -0.117
## 0.022 0.014 0.015
## 0.098 0.091 0.095
## 0.157 0.149 0.153
## -0.074 -0.082 -0.088
## 0.252 0.245 0.253
## 0.989 0.969 1.024
## 0.155 0.147 0.152
## 0.199 0.192 0.198
## -0.024 -0.031 -0.037
## -0.158 -0.165 -0.176
## -0.069 -0.077 -0.082
## 0.662 0.644 0.638
## 0.043 0.035 0.036
## -0.089 -0.097 -0.100
## 0.244 0.236 0.249
## 0.849 0.827 0.849
## 0.482 0.475 0.499
## -0.287 -0.307 -0.317
## 0.196 0.188 0.191
## 0.524 0.502 0.529
## 0.064 0.056 0.055
## -0.153 -0.161 -0.167
## 0.128 0.120 0.126
## 1.025 1.003 1.094
## 0.658 0.652 0.836
## 0.575 0.568 0.675
## 0.470 0.456 0.479
## 3.025 2.966 2.966
## 0.899 0.855 0.855
## 0.590 0.573 0.573
## 2.381 2.332 2.332
## -2.240 -2.283 -2.283
## -0.194 -0.221 -0.221
## -0.915 -0.932 -0.932
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.416 0.003 132.413 0.000 0.410
## .Stest20spellng 0.470 0.003 160.643 0.000 0.465
## .Stest21cptlztn 0.520 0.003 162.828 0.000 0.514
## .Stest22puncttn 0.267 0.002 131.707 0.000 0.263
## .Stest23english 0.450 0.003 158.606 0.000 0.445
## .Stest24exprssn 0.532 0.004 148.039 0.000 0.525
## .Stst25wrdfnctn 0.400 0.003 144.845 0.000 0.394
## .Stst26rdngcmpr 0.193 0.001 141.176 0.000 0.190
## .Stst31bstrctrs 0.461 0.003 149.898 0.000 0.455
## .Stst32rthrsnng 0.405 0.002 168.490 0.000 0.400
## .Stst34rthcmptt 0.473 0.003 139.260 0.000 0.466
## .Stest5math 0.364 0.003 108.682 0.000 0.357
## .Stst6physclscn 0.324 0.002 148.860 0.000 0.320
## .Stst33hghschlm 0.137 0.003 41.653 0.000 0.130
## .Stst29vslztn2D 0.583 0.004 147.626 0.000 0.576
## .Stest35tblrdng 0.311 0.004 88.691 0.000 0.304
## .Stst36clrclchc 0.419 0.004 100.639 0.000 0.411
## .Stst37bjctnspc 0.501 0.004 134.125 0.000 0.493
## .Stest1vocab 0.231 0.002 148.694 0.000 0.228
## .Stest2literatr 0.293 0.002 158.135 0.000 0.290
## .Stest3music 0.401 0.003 158.000 0.000 0.396
## .Stest4soclstds 0.288 0.002 158.843 0.000 0.284
## .Stst7blgclscnc 0.499 0.003 172.129 0.000 0.493
## .Stest8aerontcs 0.598 0.003 170.952 0.000 0.591
## .Stest11art 0.384 0.003 142.507 0.000 0.379
## .Stest12law 0.556 0.003 177.735 0.000 0.550
## .Stest13health 0.540 0.003 173.498 0.000 0.534
## .Stest14bible 0.639 0.003 192.981 0.000 0.633
## .Stest15theater 0.424 0.003 155.355 0.000 0.418
## .Stest16mscllns 0.499 0.003 171.785 0.000 0.493
## .Stest9elctrncs 0.473 0.004 109.773 0.000 0.465
## .Stest10mechncs 0.336 0.002 148.321 0.000 0.332
## .Stst28mchnclrs 0.291 0.002 127.227 0.000 0.286
## .Stst30vslztn3D 0.375 0.003 112.827 0.000 0.368
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.422 0.416 0.446
## 0.476 0.470 0.547
## 0.526 0.520 0.580
## 0.271 0.267 0.315
## 0.456 0.450 0.521
## 0.539 0.532 0.624
## 0.405 0.400 0.425
## 0.195 0.193 0.218
## 0.467 0.461 0.507
## 0.409 0.405 0.428
## 0.480 0.473 0.542
## 0.370 0.364 0.389
## 0.328 0.324 0.362
## 0.143 0.137 0.145
## 0.591 0.583 0.620
## 0.318 0.311 0.442
## 0.427 0.419 0.474
## 0.508 0.501 0.567
## 0.234 0.231 0.226
## 0.297 0.293 0.308
## 0.406 0.401 0.428
## 0.292 0.288 0.321
## 0.504 0.499 0.526
## 0.605 0.598 0.658
## 0.390 0.384 0.409
## 0.562 0.556 0.577
## 0.546 0.540 0.600
## 0.646 0.639 0.635
## 0.429 0.424 0.457
## 0.505 0.499 0.545
## 0.482 0.473 0.563
## 0.341 0.336 0.552
## 0.295 0.291 0.411
## 0.381 0.375 0.414
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 0.979 0.979
sem.age2<-sem(bf.age2, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("g=~Stest1vocab", "Stest19disguisedwords~1", "Stest6physicalscience~1", "Stest13health~1", "Stest9electronics~1", "Stest30visualization3D~1", "Stest1vocab~1", "Stest11art~1", "Stest7biologicalscience~1"))
fitMeasures(sem.age2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea
## 156890.750 1187.000 0.000 0.942 0.043
## srmr ecvi aic bic
## 0.055 1.131 10331002.618 10333040.039
Mc(sem.age2)
## [1] 0.5712799
summary(sem.age2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 112 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 317
## Number of equality constraints 110
##
## Number of observations per group:
## 0 68858
## 1 70195
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 156890.750 137803.236
## Degrees of freedom 1187 1187
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.139
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 85916.044 75463.397
## 1 70974.706 62339.839
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.308 0.003 102.247 0.000 0.302
## Stst20s (.p2.) 0.348 0.002 167.072 0.000 0.344
## Stst21c (.p3.) 0.322 0.002 169.053 0.000 0.319
## Stst22p (.p4.) 0.372 0.002 191.745 0.000 0.368
## Stst23n (.p5.) 0.289 0.002 162.500 0.000 0.286
## Stst24x (.p6.) 0.248 0.002 140.220 0.000 0.245
## Stst25w (.p7.) 0.274 0.002 144.059 0.000 0.271
## Stst26r (.p8.) 0.145 0.001 98.966 0.000 0.143
## Stst31b (.p9.) 0.178 0.002 105.114 0.000 0.175
## Stst32r (.10.) 0.119 0.002 77.067 0.000 0.116
## Stst34r (.11.) 0.106 0.002 53.944 0.000 0.102
## math =~
## Stst5mt (.12.) 0.305 0.002 126.219 0.000 0.301
## Stst6ph (.13.) 0.120 0.002 51.229 0.000 0.116
## Stst25w (.14.) 0.168 0.003 67.297 0.000 0.163
## Stst32r (.15.) 0.186 0.002 75.136 0.000 0.181
## Stst33h (.16.) 0.550 0.004 155.601 0.000 0.543
## Stst34r (.17.) 0.245 0.003 87.463 0.000 0.240
## speed =~
## Stst19d (.18.) 0.277 0.002 113.608 0.000 0.272
## Sts292D (.19.) 0.207 0.003 75.182 0.000 0.202
## Stst34r (.20.) 0.345 0.003 132.356 0.000 0.340
## Stst35t (.21.) 0.585 0.003 194.199 0.000 0.579
## Stst36c (.22.) 0.668 0.003 223.447 0.000 0.662
## Stst37b (.23.) 0.564 0.003 195.253 0.000 0.558
## info =~
## Stst1vc (.24.) 0.185 0.003 73.461 0.000 0.180
## Stst2lt (.25.) 0.307 0.003 117.164 0.000 0.302
## Stst3ms (.26.) 0.366 0.002 159.766 0.000 0.362
## Stst4sc (.27.) 0.158 0.003 55.013 0.000 0.153
## Stst7bl (.28.) 0.067 0.004 18.657 0.000 0.060
## Stst8rn (.29.) 0.128 0.003 45.062 0.000 0.123
## Stst11r (.30.) 0.429 0.003 137.253 0.000 0.423
## Stst12l (.31.) 0.130 0.003 49.988 0.000 0.125
## Stst13h (.32.) 0.170 0.004 47.806 0.000 0.163
## Stst14b (.33.) 0.223 0.003 88.688 0.000 0.218
## Stst15t (.34.) 0.400 0.003 158.707 0.000 0.395
## Stst16m (.35.) 0.181 0.002 75.114 0.000 0.176
## Stst19d (.36.) 0.246 0.003 76.376 0.000 0.239
## Stst26r (.37.) 0.186 0.002 83.641 0.000 0.181
## science =~
## Stst1vc (.38.) 0.149 0.002 73.826 0.000 0.145
## Stst6ph (.39.) 0.299 0.003 116.042 0.000 0.294
## Stst7bl (.40.) 0.238 0.003 77.703 0.000 0.232
## Stst8rn (.41.) 0.326 0.002 131.424 0.000 0.321
## Stst9lc (.42.) 0.453 0.003 155.510 0.000 0.447
## Stst10m (.43.) 0.346 0.003 137.457 0.000 0.341
## Stst13h (.44.) 0.081 0.003 27.153 0.000 0.076
## Stst28m (.45.) 0.210 0.002 97.069 0.000 0.206
## spatial =~
## Stst28m (.46.) 0.413 0.002 170.065 0.000 0.408
## Sts292D (.47.) 0.454 0.003 151.150 0.000 0.448
## Sts303D (.48.) 0.565 0.003 190.364 0.000 0.560
## Stst31b (.49.) 0.361 0.003 132.338 0.000 0.355
## Stst32r (.50.) 0.121 0.002 50.351 0.000 0.116
## Stst37b (.51.) 0.213 0.003 71.809 0.000 0.207
## g =~
## Stst1vc 0.723 0.003 285.250 0.000 0.718
## Stst2lt (.53.) 0.741 0.002 343.541 0.000 0.737
## Stst3ms (.54.) 0.625 0.002 269.990 0.000 0.620
## Stst4sc (.55.) 0.754 0.002 349.525 0.000 0.750
## Stst5mt (.56.) 0.682 0.002 323.959 0.000 0.678
## Stst6ph (.57.) 0.674 0.002 316.422 0.000 0.670
## Stst7bl (.58.) 0.615 0.002 251.125 0.000 0.610
## Stst8rn (.59.) 0.428 0.002 172.114 0.000 0.423
## Stst9lc (.60.) 0.398 0.002 163.706 0.000 0.393
## Stst10m (.61.) 0.385 0.002 171.498 0.000 0.380
## Stst11r (.62.) 0.601 0.003 234.681 0.000 0.596
## Stst12l (.63.) 0.616 0.002 268.432 0.000 0.611
## Stst13h (.64.) 0.562 0.003 205.603 0.000 0.557
## Stst14b (.65.) 0.556 0.002 228.610 0.000 0.551
## Stst15t (.66.) 0.578 0.002 240.856 0.000 0.573
## Stst16m (.67.) 0.610 0.002 253.586 0.000 0.606
## Stst19d (.68.) 0.525 0.003 205.863 0.000 0.520
## Stst20s (.69.) 0.510 0.002 205.268 0.000 0.505
## Stst21c (.70.) 0.514 0.002 206.365 0.000 0.510
## Stst22p (.71.) 0.657 0.002 287.747 0.000 0.652
## Stst23n (.72.) 0.567 0.003 220.143 0.000 0.562
## Stst24x (.73.) 0.502 0.003 192.203 0.000 0.497
## Stst25w (.74.) 0.652 0.002 306.920 0.000 0.648
## Stst26r (.75.) 0.786 0.002 389.376 0.000 0.782
## Stst28m (.76.) 0.443 0.002 191.821 0.000 0.438
## Sts292D (.77.) 0.325 0.003 118.455 0.000 0.320
## Sts303D (.78.) 0.453 0.003 169.203 0.000 0.448
## Stst31b (.79.) 0.527 0.003 198.501 0.000 0.522
## Stst32r (.80.) 0.682 0.002 325.957 0.000 0.678
## Stst33h (.81.) 0.699 0.002 291.902 0.000 0.695
## Stst34r (.82.) 0.451 0.003 165.802 0.000 0.446
## Stst35t (.83.) 0.221 0.003 81.655 0.000 0.216
## Stst36c (.84.) 0.133 0.003 48.521 0.000 0.128
## Stst37b (.85.) 0.135 0.003 49.248 0.000 0.130
## ci.upper Std.lv Std.all
##
## 0.314 0.308 0.322
## 0.352 0.348 0.359
## 0.326 0.322 0.341
## 0.375 0.372 0.391
## 0.293 0.289 0.299
## 0.251 0.248 0.252
## 0.278 0.274 0.283
## 0.148 0.145 0.151
## 0.182 0.178 0.185
## 0.122 0.119 0.124
## 0.109 0.106 0.112
##
## 0.310 0.305 0.338
## 0.125 0.120 0.130
## 0.173 0.168 0.174
## 0.190 0.186 0.193
## 0.557 0.550 0.557
## 0.251 0.245 0.261
##
## 0.282 0.277 0.289
## 0.212 0.207 0.216
## 0.350 0.345 0.367
## 0.591 0.585 0.646
## 0.674 0.668 0.701
## 0.569 0.564 0.568
##
## 0.190 0.185 0.208
## 0.312 0.307 0.315
## 0.371 0.366 0.371
## 0.164 0.158 0.166
## 0.074 0.067 0.070
## 0.134 0.128 0.155
## 0.435 0.429 0.444
## 0.135 0.130 0.135
## 0.177 0.170 0.177
## 0.228 0.223 0.225
## 0.405 0.400 0.417
## 0.186 0.181 0.182
## 0.252 0.246 0.256
## 0.190 0.186 0.193
##
## 0.153 0.149 0.167
## 0.304 0.299 0.324
## 0.244 0.238 0.248
## 0.331 0.326 0.392
## 0.458 0.453 0.585
## 0.351 0.346 0.440
## 0.087 0.081 0.085
## 0.215 0.210 0.255
##
## 0.418 0.413 0.500
## 0.460 0.454 0.474
## 0.571 0.565 0.573
## 0.366 0.361 0.375
## 0.126 0.121 0.126
## 0.218 0.213 0.214
##
## 0.728 0.734 0.824
## 0.745 0.752 0.773
## 0.629 0.634 0.643
## 0.759 0.766 0.804
## 0.686 0.693 0.767
## 0.678 0.684 0.742
## 0.620 0.624 0.651
## 0.432 0.434 0.523
## 0.403 0.404 0.523
## 0.389 0.391 0.496
## 0.606 0.610 0.632
## 0.620 0.625 0.645
## 0.567 0.571 0.594
## 0.560 0.564 0.568
## 0.583 0.587 0.612
## 0.615 0.620 0.625
## 0.530 0.534 0.556
## 0.515 0.518 0.535
## 0.519 0.522 0.553
## 0.661 0.667 0.702
## 0.572 0.575 0.596
## 0.507 0.510 0.517
## 0.656 0.662 0.682
## 0.789 0.798 0.831
## 0.447 0.450 0.544
## 0.330 0.330 0.345
## 0.459 0.460 0.466
## 0.532 0.535 0.557
## 0.686 0.693 0.720
## 0.704 0.710 0.719
## 0.456 0.458 0.487
## 0.227 0.225 0.248
## 0.138 0.135 0.142
## 0.141 0.137 0.138
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.108 0.004 29.061 0.000 0.100
## age2 -0.055 0.003 -21.283 0.000 -0.060
## ci.upper Std.lv Std.all
##
## 0.115 0.106 0.131
## -0.050 -0.054 -0.097
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## science ~~
## spatial 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d -0.057 0.004 -12.727 0.000 -0.066
## .Stst20s (.148) -0.200 0.004 -44.815 0.000 -0.209
## .Stst21c (.149) -0.137 0.004 -31.317 0.000 -0.145
## .Stst22p (.150) -0.120 0.005 -25.426 0.000 -0.129
## .Stst23n (.151) -0.062 0.005 -13.567 0.000 -0.071
## .Stst24x (.152) -0.036 0.004 -7.971 0.000 -0.045
## .Stst25w (.153) -0.059 0.005 -12.635 0.000 -0.069
## .Stst26r (.154) 0.079 0.005 15.582 0.000 0.069
## .Stst31b (.155) 0.135 0.004 30.880 0.000 0.126
## .Stst32r (.156) 0.206 0.005 43.090 0.000 0.197
## .Stst34r (.157) -0.044 0.004 -10.266 0.000 -0.053
## .Stst5mt (.158) 0.302 0.005 67.025 0.000 0.293
## .Stst6ph 0.424 0.005 89.776 0.000 0.414
## .Stst33h (.160) 0.205 0.005 40.276 0.000 0.195
## .Sts292D (.161) 0.219 0.004 55.365 0.000 0.211
## .Stst35t (.162) -0.013 0.004 -3.548 0.000 -0.020
## .Stst36c (.163) -0.154 0.004 -41.935 0.000 -0.162
## .Stst37b (.164) -0.065 0.004 -17.174 0.000 -0.073
## .Stst1vc 0.259 0.005 55.496 0.000 0.250
## .Stst2lt (.166) 0.097 0.005 19.479 0.000 0.087
## .Stst3ms (.167) -0.045 0.005 -9.533 0.000 -0.054
## .Stst4sc (.168) 0.299 0.005 61.216 0.000 0.289
## .Stst7bl 0.303 0.005 66.314 0.000 0.294
## .Stst8rn (.170) 0.511 0.004 131.969 0.000 0.503
## .Stst11r 0.004 0.005 0.947 0.344 -0.005
## .Stst12l (.172) 0.239 0.005 50.612 0.000 0.230
## .Stst13h -0.026 0.005 -5.687 0.000 -0.035
## .Stst14b (.174) 0.102 0.005 21.584 0.000 0.093
## .Stst15t (.175) -0.113 0.004 -25.030 0.000 -0.121
## .Stst16m (.176) 0.171 0.005 35.430 0.000 0.162
## .Stst9lc 0.561 0.004 154.385 0.000 0.554
## .Stst10m (.178) 0.684 0.004 191.921 0.000 0.677
## .Stst28m (.179) 0.605 0.004 155.850 0.000 0.597
## .Sts303D 0.250 0.004 55.749 0.000 0.241
## ci.upper Std.lv Std.all
## -0.048 -0.057 -0.059
## -0.191 -0.200 -0.206
## -0.128 -0.137 -0.145
## -0.111 -0.120 -0.126
## -0.053 -0.062 -0.064
## -0.027 -0.036 -0.036
## -0.050 -0.059 -0.061
## 0.089 0.079 0.083
## 0.143 0.135 0.140
## 0.215 0.206 0.214
## -0.036 -0.044 -0.047
## 0.311 0.302 0.334
## 0.433 0.424 0.459
## 0.215 0.205 0.208
## 0.227 0.219 0.229
## -0.006 -0.013 -0.014
## -0.147 -0.154 -0.162
## -0.058 -0.065 -0.066
## 0.269 0.259 0.291
## 0.106 0.097 0.099
## -0.036 -0.045 -0.046
## 0.308 0.299 0.313
## 0.312 0.303 0.316
## 0.519 0.511 0.615
## 0.013 0.004 0.004
## 0.248 0.239 0.247
## -0.017 -0.026 -0.027
## 0.111 0.102 0.103
## -0.104 -0.113 -0.117
## 0.181 0.171 0.173
## 0.568 0.561 0.725
## 0.691 0.684 0.869
## 0.613 0.605 0.732
## 0.259 0.250 0.254
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.403 0.003 128.362 0.000 0.397
## .Stest20spellng 0.549 0.003 161.322 0.000 0.543
## .Stest21cptlztn 0.515 0.003 163.186 0.000 0.509
## .Stest22puncttn 0.319 0.002 137.209 0.000 0.315
## .Stest23english 0.518 0.003 152.795 0.000 0.511
## .Stest24exprssn 0.651 0.004 155.290 0.000 0.642
## .Stst25wrdfnctn 0.400 0.003 151.015 0.000 0.395
## .Stst26rdngcmpr 0.230 0.002 137.794 0.000 0.227
## .Stst31bstrctrs 0.475 0.003 146.766 0.000 0.469
## .Stst32rthrsnng 0.382 0.002 160.162 0.000 0.377
## .Stst34rthcmptt 0.485 0.003 145.185 0.000 0.478
## .Stest5math 0.243 0.003 95.293 0.000 0.238
## .Stst6physclscn 0.280 0.002 143.315 0.000 0.276
## .Stst33hghschlm 0.169 0.003 51.782 0.000 0.163
## .Stst29vslztn2D 0.558 0.004 128.836 0.000 0.549
## .Stest35tblrdng 0.426 0.004 95.801 0.000 0.417
## .Stst36clrclchc 0.444 0.005 87.422 0.000 0.434
## .Stst37bjctnspc 0.604 0.005 132.509 0.000 0.595
## .Stest1vocab 0.199 0.001 148.484 0.000 0.196
## .Stest2literatr 0.286 0.002 153.783 0.000 0.282
## .Stest3music 0.436 0.003 160.180 0.000 0.431
## .Stest4soclstds 0.296 0.002 153.186 0.000 0.292
## .Stst7blgclscnc 0.468 0.003 159.956 0.000 0.463
## .Stest8aerontcs 0.378 0.003 115.685 0.000 0.372
## .Stest11art 0.375 0.003 141.811 0.000 0.370
## .Stest12law 0.531 0.003 171.760 0.000 0.525
## .Stest13health 0.561 0.003 175.028 0.000 0.554
## .Stest14bible 0.620 0.003 184.565 0.000 0.613
## .Stest15theater 0.416 0.003 154.238 0.000 0.411
## .Stest16mscllns 0.566 0.003 168.045 0.000 0.560
## .Stest9elctrncs 0.230 0.003 79.164 0.000 0.224
## .Stest10mechncs 0.347 0.002 139.215 0.000 0.342
## .Stst28mchnclrs 0.266 0.002 113.001 0.000 0.261
## .Stst30vslztn3D 0.443 0.004 115.423 0.000 0.435
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.409 0.403 0.438
## 0.556 0.549 0.585
## 0.521 0.515 0.578
## 0.324 0.319 0.354
## 0.525 0.518 0.555
## 0.659 0.651 0.669
## 0.405 0.400 0.425
## 0.233 0.230 0.250
## 0.482 0.475 0.515
## 0.386 0.382 0.413
## 0.491 0.485 0.548
## 0.248 0.243 0.298
## 0.284 0.280 0.328
## 0.175 0.169 0.173
## 0.566 0.558 0.609
## 0.435 0.426 0.521
## 0.453 0.444 0.488
## 0.613 0.604 0.613
## 0.201 0.199 0.251
## 0.289 0.286 0.302
## 0.441 0.436 0.448
## 0.300 0.296 0.326
## 0.474 0.468 0.509
## 0.385 0.378 0.549
## 0.380 0.375 0.403
## 0.537 0.531 0.566
## 0.567 0.561 0.608
## 0.626 0.620 0.627
## 0.422 0.416 0.452
## 0.573 0.566 0.576
## 0.236 0.230 0.384
## 0.352 0.347 0.560
## 0.271 0.266 0.389
## 0.450 0.443 0.454
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 0.970 0.970
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.308 0.003 102.247 0.000 0.302
## Stst20s (.p2.) 0.348 0.002 167.072 0.000 0.344
## Stst21c (.p3.) 0.322 0.002 169.053 0.000 0.319
## Stst22p (.p4.) 0.372 0.002 191.745 0.000 0.368
## Stst23n (.p5.) 0.289 0.002 162.500 0.000 0.286
## Stst24x (.p6.) 0.248 0.002 140.220 0.000 0.245
## Stst25w (.p7.) 0.274 0.002 144.059 0.000 0.271
## Stst26r (.p8.) 0.145 0.001 98.966 0.000 0.143
## Stst31b (.p9.) 0.178 0.002 105.114 0.000 0.175
## Stst32r (.10.) 0.119 0.002 77.067 0.000 0.116
## Stst34r (.11.) 0.106 0.002 53.944 0.000 0.102
## math =~
## Stst5mt (.12.) 0.305 0.002 126.219 0.000 0.301
## Stst6ph (.13.) 0.120 0.002 51.229 0.000 0.116
## Stst25w (.14.) 0.168 0.003 67.297 0.000 0.163
## Stst32r (.15.) 0.186 0.002 75.136 0.000 0.181
## Stst33h (.16.) 0.550 0.004 155.601 0.000 0.543
## Stst34r (.17.) 0.245 0.003 87.463 0.000 0.240
## speed =~
## Stst19d (.18.) 0.277 0.002 113.608 0.000 0.272
## Sts292D (.19.) 0.207 0.003 75.182 0.000 0.202
## Stst34r (.20.) 0.345 0.003 132.356 0.000 0.340
## Stst35t (.21.) 0.585 0.003 194.199 0.000 0.579
## Stst36c (.22.) 0.668 0.003 223.447 0.000 0.662
## Stst37b (.23.) 0.564 0.003 195.253 0.000 0.558
## info =~
## Stst1vc (.24.) 0.185 0.003 73.461 0.000 0.180
## Stst2lt (.25.) 0.307 0.003 117.164 0.000 0.302
## Stst3ms (.26.) 0.366 0.002 159.766 0.000 0.362
## Stst4sc (.27.) 0.158 0.003 55.013 0.000 0.153
## Stst7bl (.28.) 0.067 0.004 18.657 0.000 0.060
## Stst8rn (.29.) 0.128 0.003 45.062 0.000 0.123
## Stst11r (.30.) 0.429 0.003 137.253 0.000 0.423
## Stst12l (.31.) 0.130 0.003 49.988 0.000 0.125
## Stst13h (.32.) 0.170 0.004 47.806 0.000 0.163
## Stst14b (.33.) 0.223 0.003 88.688 0.000 0.218
## Stst15t (.34.) 0.400 0.003 158.707 0.000 0.395
## Stst16m (.35.) 0.181 0.002 75.114 0.000 0.176
## Stst19d (.36.) 0.246 0.003 76.376 0.000 0.239
## Stst26r (.37.) 0.186 0.002 83.641 0.000 0.181
## science =~
## Stst1vc (.38.) 0.149 0.002 73.826 0.000 0.145
## Stst6ph (.39.) 0.299 0.003 116.042 0.000 0.294
## Stst7bl (.40.) 0.238 0.003 77.703 0.000 0.232
## Stst8rn (.41.) 0.326 0.002 131.424 0.000 0.321
## Stst9lc (.42.) 0.453 0.003 155.510 0.000 0.447
## Stst10m (.43.) 0.346 0.003 137.457 0.000 0.341
## Stst13h (.44.) 0.081 0.003 27.153 0.000 0.076
## Stst28m (.45.) 0.210 0.002 97.069 0.000 0.206
## spatial =~
## Stst28m (.46.) 0.413 0.002 170.065 0.000 0.408
## Sts292D (.47.) 0.454 0.003 151.150 0.000 0.448
## Sts303D (.48.) 0.565 0.003 190.364 0.000 0.560
## Stst31b (.49.) 0.361 0.003 132.338 0.000 0.355
## Stst32r (.50.) 0.121 0.002 50.351 0.000 0.116
## Stst37b (.51.) 0.213 0.003 71.809 0.000 0.207
## g =~
## Stst1vc 0.844 0.003 316.128 0.000 0.839
## Stst2lt (.53.) 0.741 0.002 343.541 0.000 0.737
## Stst3ms (.54.) 0.625 0.002 269.990 0.000 0.620
## Stst4sc (.55.) 0.754 0.002 349.525 0.000 0.750
## Stst5mt (.56.) 0.682 0.002 323.959 0.000 0.678
## Stst6ph (.57.) 0.674 0.002 316.422 0.000 0.670
## Stst7bl (.58.) 0.615 0.002 251.125 0.000 0.610
## Stst8rn (.59.) 0.428 0.002 172.114 0.000 0.423
## Stst9lc (.60.) 0.398 0.002 163.706 0.000 0.393
## Stst10m (.61.) 0.385 0.002 171.498 0.000 0.380
## Stst11r (.62.) 0.601 0.003 234.681 0.000 0.596
## Stst12l (.63.) 0.616 0.002 268.432 0.000 0.611
## Stst13h (.64.) 0.562 0.003 205.603 0.000 0.557
## Stst14b (.65.) 0.556 0.002 228.610 0.000 0.551
## Stst15t (.66.) 0.578 0.002 240.856 0.000 0.573
## Stst16m (.67.) 0.610 0.002 253.586 0.000 0.606
## Stst19d (.68.) 0.525 0.003 205.863 0.000 0.520
## Stst20s (.69.) 0.510 0.002 205.268 0.000 0.505
## Stst21c (.70.) 0.514 0.002 206.365 0.000 0.510
## Stst22p (.71.) 0.657 0.002 287.747 0.000 0.652
## Stst23n (.72.) 0.567 0.003 220.143 0.000 0.562
## Stst24x (.73.) 0.502 0.003 192.203 0.000 0.497
## Stst25w (.74.) 0.652 0.002 306.920 0.000 0.648
## Stst26r (.75.) 0.786 0.002 389.376 0.000 0.782
## Stst28m (.76.) 0.443 0.002 191.821 0.000 0.438
## Sts292D (.77.) 0.325 0.003 118.455 0.000 0.320
## Sts303D (.78.) 0.453 0.003 169.203 0.000 0.448
## Stst31b (.79.) 0.527 0.003 198.501 0.000 0.522
## Stst32r (.80.) 0.682 0.002 325.957 0.000 0.678
## Stst33h (.81.) 0.699 0.002 291.902 0.000 0.695
## Stst34r (.82.) 0.451 0.003 165.802 0.000 0.446
## Stst35t (.83.) 0.221 0.003 81.655 0.000 0.216
## Stst36c (.84.) 0.133 0.003 48.521 0.000 0.128
## Stst37b (.85.) 0.135 0.003 49.248 0.000 0.130
## ci.upper Std.lv Std.all
##
## 0.314 0.308 0.320
## 0.352 0.348 0.376
## 0.326 0.322 0.341
## 0.375 0.372 0.404
## 0.293 0.289 0.311
## 0.251 0.248 0.269
## 0.278 0.274 0.283
## 0.148 0.145 0.155
## 0.182 0.178 0.187
## 0.122 0.119 0.123
## 0.109 0.106 0.113
##
## 0.310 0.305 0.316
## 0.125 0.120 0.127
## 0.173 0.168 0.174
## 0.190 0.186 0.191
## 0.557 0.550 0.567
## 0.251 0.245 0.262
##
## 0.282 0.277 0.287
## 0.212 0.207 0.214
## 0.350 0.345 0.369
## 0.591 0.585 0.697
## 0.674 0.668 0.711
## 0.569 0.564 0.600
##
## 0.190 0.185 0.184
## 0.312 0.307 0.315
## 0.371 0.366 0.378
## 0.164 0.158 0.167
## 0.074 0.067 0.069
## 0.134 0.128 0.135
## 0.435 0.429 0.443
## 0.135 0.130 0.133
## 0.177 0.170 0.179
## 0.228 0.223 0.223
## 0.405 0.400 0.415
## 0.186 0.181 0.189
## 0.252 0.246 0.254
## 0.190 0.186 0.198
##
## 0.153 0.149 0.148
## 0.304 0.299 0.316
## 0.244 0.238 0.244
## 0.331 0.326 0.342
## 0.458 0.453 0.494
## 0.351 0.346 0.444
## 0.087 0.081 0.086
## 0.215 0.210 0.250
##
## 0.418 0.413 0.491
## 0.460 0.454 0.468
## 0.571 0.565 0.594
## 0.366 0.361 0.379
## 0.126 0.121 0.124
## 0.218 0.213 0.226
##
## 0.850 0.855 0.847
## 0.745 0.750 0.770
## 0.629 0.633 0.654
## 0.759 0.764 0.807
## 0.686 0.691 0.715
## 0.678 0.683 0.722
## 0.620 0.623 0.640
## 0.432 0.433 0.454
## 0.403 0.403 0.440
## 0.389 0.390 0.500
## 0.606 0.609 0.628
## 0.620 0.623 0.636
## 0.567 0.569 0.600
## 0.560 0.563 0.561
## 0.583 0.586 0.608
## 0.615 0.618 0.647
## 0.530 0.532 0.552
## 0.515 0.517 0.558
## 0.519 0.521 0.551
## 0.661 0.665 0.722
## 0.572 0.574 0.618
## 0.507 0.509 0.551
## 0.656 0.660 0.681
## 0.789 0.796 0.847
## 0.447 0.449 0.534
## 0.330 0.329 0.339
## 0.459 0.459 0.483
## 0.532 0.534 0.560
## 0.686 0.691 0.711
## 0.704 0.708 0.730
## 0.456 0.457 0.489
## 0.227 0.224 0.267
## 0.138 0.135 0.143
## 0.141 0.137 0.146
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.105 0.004 28.278 0.000 0.098
## age2 -0.042 0.003 -15.752 0.000 -0.047
## ci.upper Std.lv Std.all
##
## 0.112 0.104 0.123
## -0.037 -0.041 -0.068
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## science ~~
## spatial 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d -0.936 0.017 -56.678 0.000 -0.968
## .Stst20s (.148) -0.200 0.004 -44.815 0.000 -0.209
## .Stst21c (.149) -0.137 0.004 -31.317 0.000 -0.145
## .Stst22p (.150) -0.120 0.005 -25.426 0.000 -0.129
## .Stst23n (.151) -0.062 0.005 -13.567 0.000 -0.071
## .Stst24x (.152) -0.036 0.004 -7.971 0.000 -0.045
## .Stst25w (.153) -0.059 0.005 -12.635 0.000 -0.069
## .Stst26r (.154) 0.079 0.005 15.582 0.000 0.069
## .Stst31b (.155) 0.135 0.004 30.880 0.000 0.126
## .Stst32r (.156) 0.206 0.005 43.090 0.000 0.197
## .Stst34r (.157) -0.044 0.004 -10.266 0.000 -0.053
## .Stst5mt (.158) 0.302 0.005 67.025 0.000 0.293
## .Stst6ph 1.026 0.010 98.341 0.000 1.006
## .Stst33h (.160) 0.205 0.005 40.276 0.000 0.195
## .Sts292D (.161) 0.219 0.004 55.365 0.000 0.211
## .Stst35t (.162) -0.013 0.004 -3.548 0.000 -0.020
## .Stst36c (.163) -0.154 0.004 -41.935 0.000 -0.162
## .Stst37b (.164) -0.065 0.004 -17.174 0.000 -0.073
## .Stst1vc 0.716 0.010 73.923 0.000 0.697
## .Stst2lt (.166) 0.097 0.005 19.479 0.000 0.087
## .Stst3ms (.167) -0.045 0.005 -9.533 0.000 -0.054
## .Stst4sc (.168) 0.299 0.005 61.216 0.000 0.289
## .Stst7bl 0.881 0.012 76.152 0.000 0.858
## .Stst8rn (.170) 0.511 0.004 131.969 0.000 0.503
## .Stst11r -0.257 0.011 -24.336 0.000 -0.278
## .Stst12l (.172) 0.239 0.005 50.612 0.000 0.230
## .Stst13h 0.551 0.011 48.873 0.000 0.529
## .Stst14b (.174) 0.102 0.005 21.584 0.000 0.093
## .Stst15t (.175) -0.113 0.004 -25.030 0.000 -0.121
## .Stst16m (.176) 0.171 0.005 35.430 0.000 0.162
## .Stst9lc 1.038 0.011 92.932 0.000 1.016
## .Stst10m (.178) 0.684 0.004 191.921 0.000 0.677
## .Stst28m (.179) 0.605 0.004 155.850 0.000 0.597
## .Sts303D 0.494 0.007 69.292 0.000 0.480
## english 2.969 0.030 97.712 0.000 2.910
## math 0.858 0.022 38.220 0.000 0.814
## speed 0.574 0.009 67.277 0.000 0.557
## info 2.333 0.025 94.428 0.000 2.285
## science -2.283 0.022 -103.382 0.000 -2.326
## spatial -0.220 0.014 -16.080 0.000 -0.247
## .g -0.973 0.015 -65.069 0.000 -1.002
## ci.upper Std.lv Std.all
## -0.904 -0.936 -0.970
## -0.191 -0.200 -0.216
## -0.128 -0.137 -0.144
## -0.111 -0.120 -0.130
## -0.053 -0.062 -0.067
## -0.027 -0.036 -0.039
## -0.050 -0.059 -0.061
## 0.089 0.079 0.084
## 0.143 0.135 0.141
## 0.215 0.206 0.212
## -0.036 -0.044 -0.047
## 0.311 0.302 0.312
## 1.047 1.026 1.085
## 0.215 0.205 0.212
## 0.227 0.219 0.226
## -0.006 -0.013 -0.015
## -0.147 -0.154 -0.164
## -0.058 -0.065 -0.070
## 0.735 0.716 0.709
## 0.106 0.097 0.099
## -0.036 -0.045 -0.047
## 0.308 0.299 0.315
## 0.903 0.881 0.905
## 0.519 0.511 0.536
## -0.237 -0.257 -0.266
## 0.248 0.239 0.244
## 0.573 0.551 0.581
## 0.111 0.102 0.102
## -0.104 -0.113 -0.117
## 0.181 0.171 0.179
## 1.060 1.038 1.132
## 0.691 0.684 0.877
## 0.613 0.605 0.720
## 0.508 0.494 0.519
## 3.029 2.969 2.969
## 0.902 0.858 0.858
## 0.590 0.574 0.574
## 2.382 2.333 2.333
## -2.240 -2.283 -2.283
## -0.193 -0.220 -0.220
## -0.943 -0.960 -0.960
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.416 0.003 132.458 0.000 0.410
## .Stest20spellng 0.470 0.003 160.653 0.000 0.465
## .Stest21cptlztn 0.520 0.003 162.829 0.000 0.514
## .Stest22puncttn 0.267 0.002 131.706 0.000 0.263
## .Stest23english 0.450 0.003 158.617 0.000 0.445
## .Stest24exprssn 0.532 0.004 148.039 0.000 0.525
## .Stst25wrdfnctn 0.399 0.003 144.840 0.000 0.394
## .Stst26rdngcmpr 0.193 0.001 141.176 0.000 0.190
## .Stst31bstrctrs 0.461 0.003 149.896 0.000 0.455
## .Stst32rthrsnng 0.405 0.002 168.511 0.000 0.400
## .Stst34rthcmptt 0.473 0.003 139.256 0.000 0.466
## .Stest5math 0.364 0.003 108.629 0.000 0.357
## .Stst6physclscn 0.324 0.002 148.804 0.000 0.320
## .Stst33hghschlm 0.137 0.003 41.761 0.000 0.130
## .Stst29vslztn2D 0.583 0.004 147.634 0.000 0.576
## .Stest35tblrdng 0.311 0.004 88.695 0.000 0.304
## .Stst36clrclchc 0.419 0.004 100.642 0.000 0.411
## .Stst37bjctnspc 0.501 0.004 134.130 0.000 0.493
## .Stest1vocab 0.231 0.002 148.654 0.000 0.228
## .Stest2literatr 0.293 0.002 158.125 0.000 0.290
## .Stest3music 0.401 0.003 157.994 0.000 0.396
## .Stest4soclstds 0.288 0.002 158.881 0.000 0.285
## .Stst7blgclscnc 0.498 0.003 172.066 0.000 0.493
## .Stest8aerontcs 0.598 0.003 170.906 0.000 0.591
## .Stest11art 0.384 0.003 142.496 0.000 0.379
## .Stest12law 0.556 0.003 177.733 0.000 0.550
## .Stest13health 0.540 0.003 173.503 0.000 0.534
## .Stest14bible 0.639 0.003 192.980 0.000 0.633
## .Stest15theater 0.424 0.003 155.368 0.000 0.418
## .Stest16mscllns 0.499 0.003 171.789 0.000 0.493
## .Stest9elctrncs 0.473 0.004 109.729 0.000 0.465
## .Stest10mechncs 0.336 0.002 148.410 0.000 0.332
## .Stst28mchnclrs 0.291 0.002 127.246 0.000 0.286
## .Stst30vslztn3D 0.375 0.003 112.815 0.000 0.368
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.422 0.416 0.447
## 0.476 0.470 0.548
## 0.526 0.520 0.581
## 0.271 0.267 0.315
## 0.456 0.450 0.521
## 0.539 0.532 0.624
## 0.405 0.399 0.426
## 0.195 0.193 0.219
## 0.467 0.461 0.508
## 0.409 0.405 0.428
## 0.480 0.473 0.543
## 0.370 0.364 0.389
## 0.328 0.324 0.363
## 0.143 0.137 0.145
## 0.591 0.583 0.620
## 0.318 0.311 0.443
## 0.427 0.419 0.474
## 0.508 0.501 0.567
## 0.234 0.231 0.227
## 0.297 0.293 0.309
## 0.406 0.401 0.429
## 0.292 0.288 0.321
## 0.504 0.498 0.526
## 0.605 0.598 0.658
## 0.390 0.384 0.409
## 0.562 0.556 0.578
## 0.546 0.540 0.600
## 0.646 0.639 0.635
## 0.429 0.424 0.457
## 0.505 0.499 0.546
## 0.482 0.473 0.563
## 0.341 0.336 0.553
## 0.295 0.291 0.412
## 0.381 0.375 0.414
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 0.975 0.975
MGCFA FOR BLACKS
dmale<- subset(db, sex==0)
dfemale<- subset(db, sex==1)
datamale<- select(dmale, starts_with("Stest"), -Stest17memsentences, -Stest18memwords, -Stest27creativity)
datafemale<- select(dfemale, starts_with("Stest"), -Stest17memsentences, -Stest18memwords, -Stest27creativity)
datagroup<- select(db, starts_with("Stest"), -Stest17memsentences, -Stest18memwords, -Stest27creativity)
dgroup<- select(db, starts_with("Stest"), wb, age, age2, sex, BY_WTA, -Stest17memsentences, -Stest18memwords, -Stest27creativity)
describeBy(dgroup$age)
## Warning in describeBy(dgroup$age): no grouping variable requested
## vars n mean sd median trimmed mad min max range skew
## X1 1 6085 -0.13 1.37 0.03 -0.19 1.48 -3.94 5.11 9.05 0.3
## kurtosis se
## X1 -0.15 0.02
dgroup_design <- svydesign(ids = ~1, weights = ~BY_WTA, data = dgroup)
weighted_mean <- svymean(~age, dgroup_design)
weighted_variance <- svyvar(~age, dgroup_design)
weighted_sd <- sqrt(weighted_variance)
weighted_mean # prior to mean centering
## mean SE
## age -0.12297 0.0187
weighted_sd # 1.37
## variance SE
## age 1.372 0.0345
describeBy(datamale)
## Warning in describeBy(datamale): no grouping variable requested
## vars n mean sd median trimmed mad
## Stest1vocab 1 2443 -1.11 1.06 -1.31 -1.15 1.13
## Stest2literature 2 2443 -0.99 0.97 -1.16 -1.07 0.98
## Stest3music 3 2443 -0.88 0.91 -0.97 -0.97 1.01
## Stest4socialstudies 4 2443 -1.03 1.12 -1.29 -1.10 1.16
## Stest5math 5 2443 -0.79 1.05 -0.70 -0.76 1.13
## Stest6physicalscience 6 2443 -0.71 0.89 -0.77 -0.79 1.08
## Stest7biologicalscience 7 2443 -0.60 0.97 -0.57 -0.64 1.27
## Stest8aeronautics 8 2443 -0.49 1.01 -0.22 -0.51 0.96
## Stest9electronics 9 2443 -0.62 1.11 -0.51 -0.58 1.17
## Stest10mechanics 10 2443 -0.63 0.89 -0.61 -0.65 0.77
## Stest11art 11 2443 -1.00 0.96 -1.08 -1.08 1.20
## Stest12law 12 2443 -0.75 0.94 -1.06 -0.80 0.83
## Stest13health 13 2443 -1.16 1.10 -1.18 -1.20 1.58
## Stest14bible 14 2443 -0.70 0.87 -0.79 -0.79 0.90
## Stest15theater 15 2443 -1.00 0.83 -0.88 -1.08 0.84
## Stest16miscellaneous 16 2443 -0.84 1.05 -1.15 -0.89 0.87
## Stest19disguisedwords 17 2443 -0.97 0.88 -1.18 -1.07 0.87
## Stest20spelling 18 2443 -0.83 1.00 -0.93 -0.85 1.00
## Stest21capitalization 19 2443 -1.14 0.95 -1.41 -1.24 0.92
## Stest22punctuation 20 2443 -1.21 1.00 -1.28 -1.23 1.01
## Stest23english 21 2443 -1.04 1.18 -1.03 -1.01 0.95
## Stest24expression 22 2443 -0.95 1.17 -0.90 -0.92 1.36
## Stest25wordfunctions 23 2443 -0.86 0.78 -0.93 -0.91 0.77
## Stest26readingcomprehension 24 2443 -1.26 1.08 -1.46 -1.34 1.19
## Stest28mechanicalreasoning 25 2443 -0.69 0.90 -0.76 -0.75 1.05
## Stest29visualization2D 26 2443 -0.49 1.10 -0.45 -0.53 1.36
## Stest30visualization3D 27 2443 -0.69 0.95 -0.65 -0.73 0.93
## Stest31abstractreasoning 28 2443 -1.02 1.14 -0.90 -1.04 1.60
## Stest32arithreasoning 29 2443 -1.03 0.85 -1.18 -1.11 0.85
## Stest33highschoolmath 30 2443 -0.85 0.80 -0.93 -0.94 0.60
## Stest34arithcomputation 31 2443 -1.14 1.14 -1.18 -1.19 1.21
## Stest35tablereading 32 2443 -0.68 1.65 -0.49 -0.60 1.29
## Stest36clericalchecking 33 2443 0.00 1.30 -0.41 -0.09 1.18
## Stest37objectinspection 34 2443 -0.28 1.24 -0.51 -0.35 1.08
## min max range skew kurtosis se
## Stest1vocab -3.08 1.73 4.81 0.35 -0.60 0.02
## Stest2literature -2.70 2.13 4.83 0.64 -0.11 0.02
## Stest3music -1.99 2.10 4.09 0.86 0.10 0.02
## Stest4socialstudies -2.86 1.65 4.51 0.48 -0.71 0.02
## Stest5math -3.10 1.58 4.68 -0.29 -0.19 0.02
## Stest6physicalscience -1.99 2.15 4.14 0.77 0.09 0.02
## Stest7biologicalscience -2.28 2.00 4.28 0.31 -0.55 0.02
## Stest8aeronautics -1.97 1.69 3.66 -0.05 -0.90 0.02
## Stest9electronics -3.22 1.82 5.03 -0.39 -0.04 0.02
## Stest10mechanics -2.42 2.23 4.65 0.23 -0.43 0.02
## Stest11art -2.29 2.14 4.44 0.65 -0.29 0.02
## Stest12law -2.19 2.32 4.51 0.61 0.08 0.02
## Stest13health -2.78 1.49 4.27 0.39 -0.73 0.02
## Stest14bible -2.00 2.24 4.24 0.85 0.41 0.02
## Stest15theater -2.01 1.95 3.96 0.78 0.23 0.02
## Stest16miscellaneous -2.32 2.94 5.26 0.44 -0.47 0.02
## Stest19disguisedwords -2.20 2.04 4.24 1.06 0.73 0.02
## Stest20spelling -2.95 2.09 5.04 0.23 -0.31 0.02
## Stest21capitalization -2.21 1.79 4.01 0.81 -0.23 0.02
## Stest22punctuation -4.01 1.91 5.92 0.18 -0.22 0.02
## Stest23english -5.18 2.49 7.66 -0.25 0.22 0.02
## Stest24expression -3.65 1.40 5.06 -0.18 -0.67 0.02
## Stest25wordfunctions -2.61 1.67 4.28 0.48 0.45 0.02
## Stest26readingcomprehension -3.16 1.55 4.71 0.59 -0.58 0.02
## Stest28mechanicalreasoning -2.41 2.08 4.50 0.54 -0.18 0.02
## Stest29visualization2D -2.28 1.92 4.21 0.22 -0.96 0.02
## Stest30visualization3D -2.54 2.18 4.72 0.35 -0.47 0.02
## Stest31abstractreasoning -3.05 1.97 5.03 0.15 -0.85 0.02
## Stest32arithreasoning -2.33 1.97 4.30 0.90 0.54 0.02
## Stest33highschoolmath -2.15 2.52 4.67 1.11 1.41 0.02
## Stest34arithcomputation -3.94 3.20 7.14 0.53 0.72 0.02
## Stest35tablereading -4.82 3.61 8.43 -0.44 0.55 0.03
## Stest36clericalchecking -2.66 2.63 5.29 0.56 -0.89 0.03
## Stest37objectinspection -3.28 2.40 5.69 0.42 -0.54 0.03
describeBy(datafemale)
## Warning in describeBy(datafemale): no grouping variable requested
## vars n mean sd median trimmed mad
## Stest1vocab 1 3642 -1.31 0.92 -1.31 -1.36 0.75
## Stest2literature 2 3642 -0.99 0.90 -1.16 -1.06 0.98
## Stest3music 3 3642 -0.78 0.92 -0.97 -0.86 1.01
## Stest4socialstudies 4 3642 -1.23 0.91 -1.29 -1.29 0.87
## Stest5math 5 3642 -0.94 0.99 -0.70 -0.91 1.04
## Stest6physicalscience 6 3642 -1.01 0.69 -1.02 -1.07 0.72
## Stest7biologicalscience 7 3642 -0.82 0.85 -1.00 -0.85 0.63
## Stest8aeronautics 8 3642 -0.92 0.83 -0.87 -0.96 0.96
## Stest9electronics 9 3642 -1.14 0.96 -0.89 -1.06 0.72
## Stest10mechanics 10 3642 -1.36 0.61 -1.39 -1.39 0.77
## Stest11art 11 3642 -1.00 0.98 -1.08 -1.09 1.20
## Stest12law 12 3642 -0.88 0.82 -1.06 -0.91 0.83
## Stest13health 13 3642 -0.96 1.11 -1.18 -0.99 1.58
## Stest14bible 14 3642 -0.55 0.87 -0.79 -0.61 0.90
## Stest15theater 15 3642 -0.81 0.90 -0.88 -0.89 0.84
## Stest16miscellaneous 16 3642 -0.92 0.92 -1.15 -0.96 0.87
## Stest19disguisedwords 17 3642 -0.84 0.95 -1.03 -0.94 0.87
## Stest20spelling 18 3642 -0.42 0.97 -0.26 -0.42 1.00
## Stest21capitalization 19 3642 -0.86 1.02 -1.14 -0.94 1.18
## Stest22punctuation 20 3642 -0.90 0.98 -1.05 -0.92 1.01
## Stest23english 21 3642 -0.70 1.09 -0.71 -0.68 0.95
## Stest24expression 22 3642 -0.67 1.08 -0.44 -0.64 1.36
## Stest25wordfunctions 23 3642 -0.78 0.80 -0.93 -0.83 0.77
## Stest26readingcomprehension 24 3642 -1.19 0.98 -1.36 -1.25 1.04
## Stest28mechanicalreasoning 25 3642 -1.30 0.62 -1.47 -1.35 0.70
## Stest29visualization2D 26 3642 -0.90 0.99 -1.00 -0.98 1.08
## Stest30visualization3D 27 3642 -0.96 0.77 -0.97 -0.99 0.93
## Stest31abstractreasoning 28 3642 -1.20 1.10 -1.26 -1.24 1.06
## Stest32arithreasoning 29 3642 -1.17 0.74 -1.18 -1.24 0.85
## Stest33highschoolmath 30 3642 -0.92 0.70 -1.13 -0.98 0.60
## Stest34arithcomputation 31 3642 -1.01 1.13 -1.08 -1.04 1.06
## Stest35tablereading 32 3642 -0.50 1.59 -0.28 -0.41 1.18
## Stest36clericalchecking 33 3642 0.30 1.28 0.02 0.25 1.40
## Stest37objectinspection 34 3642 -0.20 1.13 -0.37 -0.25 1.08
## min max range skew kurtosis se
## Stest1vocab -3.08 1.73 4.81 0.54 -0.03 0.02
## Stest2literature -2.70 2.35 5.05 0.67 0.27 0.01
## Stest3music -1.99 2.10 4.09 0.73 -0.11 0.02
## Stest4socialstudies -2.86 1.65 4.51 0.57 -0.10 0.02
## Stest5math -3.10 1.58 4.68 -0.35 -0.13 0.02
## Stest6physicalscience -1.99 1.91 3.90 0.91 0.77 0.01
## Stest7biologicalscience -2.28 2.00 4.28 0.40 -0.22 0.01
## Stest8aeronautics -1.97 1.69 3.66 0.07 -1.01 0.01
## Stest9electronics -3.22 1.64 4.85 -0.61 -0.10 0.02
## Stest10mechanics -2.42 1.46 3.88 0.48 0.04 0.01
## Stest11art -2.29 2.14 4.44 0.74 -0.04 0.02
## Stest12law -2.19 2.32 4.51 0.48 0.04 0.01
## Stest13health -2.78 1.49 4.27 0.21 -0.81 0.02
## Stest14bible -2.00 2.24 4.24 0.63 0.12 0.01
## Stest15theater -2.01 1.95 3.96 0.71 0.13 0.01
## Stest16miscellaneous -2.32 2.35 4.67 0.39 -0.32 0.02
## Stest19disguisedwords -2.20 2.04 4.24 0.84 -0.01 0.02
## Stest20spelling -2.95 2.09 5.04 0.00 -0.39 0.02
## Stest21capitalization -2.21 1.79 4.01 0.56 -0.57 0.02
## Stest22punctuation -3.78 1.91 5.69 0.12 -0.30 0.02
## Stest23english -5.18 2.49 7.66 -0.24 0.09 0.02
## Stest24expression -3.65 1.40 5.06 -0.28 -0.44 0.02
## Stest25wordfunctions -2.61 1.79 4.40 0.55 0.41 0.01
## Stest26readingcomprehension -3.16 1.55 4.71 0.54 -0.41 0.02
## Stest28mechanicalreasoning -2.41 1.37 3.79 0.74 0.69 0.01
## Stest29visualization2D -2.28 1.92 4.21 0.62 -0.43 0.02
## Stest30visualization3D -2.54 2.18 4.72 0.47 0.13 0.01
## Stest31abstractreasoning -3.05 1.97 5.03 0.26 -0.79 0.02
## Stest32arithreasoning -2.33 1.97 4.30 0.97 1.13 0.01
## Stest33highschoolmath -2.15 2.32 4.47 0.95 1.27 0.01
## Stest34arithcomputation -3.94 3.30 7.24 0.41 0.57 0.02
## Stest35tablereading -4.82 3.61 8.43 -0.57 0.88 0.03
## Stest36clericalchecking -2.66 2.63 5.29 0.35 -1.07 0.02
## Stest37objectinspection -3.28 2.40 5.69 0.32 -0.39 0.02
scree(datamale)
VSS.scree(datafemale)
scree(datamale)
VSS.scree(datafemale)
malecor<- cor(datamale) # fa.parallel requires cor matrix if n.obs is to be used
femalecor<- cor(datafemale) # fa.parallel requires cor matrix if n.obs is to be used
eigen(malecor) # all eigenvalues different from zero
## eigen() decomposition
## $values
## [1] 15.4295414 1.9922302 1.4306193 1.2695300 0.8629413 0.8303971
## [7] 0.7012036 0.6576196 0.6015821 0.5802333 0.5550347 0.5514279
## [13] 0.5355076 0.5096965 0.5004802 0.4815809 0.4691915 0.4606554
## [19] 0.4562679 0.4457202 0.4351771 0.4181434 0.4111521 0.3949951
## [25] 0.3868495 0.3685303 0.3594665 0.3416078 0.3295348 0.3132991
## [31] 0.2865017 0.2301844 0.2195756 0.1835219
##
## $vectors
## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.22024187 -0.085145693 -0.058727771 -0.059667371 -0.0450239900
## [2,] -0.20876220 -0.103099027 -0.108678952 -0.077122104 0.0183615271
## [3,] -0.18798265 -0.079938031 -0.119633113 -0.077507670 -0.0303572165
## [4,] -0.21713451 -0.090781971 -0.109964297 -0.027588253 0.0480641896
## [5,] -0.17873298 -0.013393109 -0.034950632 -0.010207807 0.3858883502
## [6,] -0.20037107 -0.086092083 0.019733356 -0.156498707 0.1335431503
## [7,] -0.18025733 -0.083309597 -0.022131677 -0.080871919 -0.0993460960
## [8,] -0.15177971 -0.102731243 -0.059332672 -0.315480382 -0.0003051381
## [9,] -0.15993061 -0.065930087 0.021749346 -0.312023715 0.1179922216
## [10,] -0.18005160 -0.069551702 0.018775833 -0.149529928 -0.0838511839
## [11,] -0.19091639 -0.086074892 -0.096542146 -0.119234912 -0.1238912698
## [12,] -0.17512095 -0.103175950 -0.090574270 -0.071373361 0.0151827424
## [13,] -0.19045036 -0.077661084 -0.122076960 -0.046762173 -0.0741707047
## [14,] -0.17144502 -0.078311134 -0.149106853 -0.013906507 -0.0167842323
## [15,] -0.17524709 -0.121428732 -0.166051120 -0.023826682 -0.1285062410
## [16,] -0.18174670 -0.074936560 -0.156636868 -0.094731788 -0.0539702295
## [17,] -0.17682434 0.100546343 -0.099560432 0.124153499 -0.1699833435
## [18,] -0.16054017 -0.011239231 -0.136145981 0.362715067 -0.0963696681
## [19,] -0.17939342 0.022962393 0.072936123 0.239552031 -0.1533577467
## [20,] -0.18969473 0.030282615 0.092088906 0.263909360 -0.0643024703
## [21,] -0.17714846 0.032636999 0.062516080 0.227567539 -0.2807598191
## [22,] -0.14925574 -0.023093934 0.103777190 0.278937557 -0.3054816572
## [23,] -0.14637814 0.039177699 0.128416794 0.252630880 0.3242995055
## [24,] -0.22504897 -0.078438013 -0.008322061 0.065661242 -0.0331280624
## [25,] -0.16845928 0.105138178 0.329272783 -0.225714305 -0.0564613633
## [26,] -0.11730781 0.294309804 0.323323230 -0.091218176 -0.2318732382
## [27,] -0.12899919 0.142952103 0.447965460 -0.201952448 -0.0020782671
## [28,] -0.16588671 0.117869117 0.335857704 0.006964685 -0.0046959742
## [29,] -0.18088780 -0.004031267 0.141369502 0.088031439 0.3224364405
## [,6] [,7] [,8] [,9]
## [1,] -0.1075637350 -0.006868000 0.0135065593 0.004928500
## [2,] 0.1332257169 -0.064047554 -0.0313871220 -0.110932838
## [3,] 0.2482137852 -0.123411526 0.0540163701 -0.033428508
## [4,] 0.0008653766 0.108505582 -0.0867137850 -0.052191698
## [5,] -0.1124700383 -0.018369617 0.0364618137 -0.083039398
## [6,] -0.1534691687 0.028621245 0.0160784501 -0.157289482
## [7,] -0.1723560362 0.101593166 -0.1625124672 -0.441613782
## [8,] -0.1426353780 -0.092920351 0.4833199697 0.003016460
## [9,] -0.4114901327 -0.134757704 -0.0527234320 0.120183234
## [10,] -0.3879933748 0.020616858 -0.0518130386 0.179600157
## [11,] 0.2467172714 -0.069389430 -0.1007298500 0.029206934
## [12,] 0.1599788352 0.222529546 0.0898464026 0.290523221
## [13,] 0.0298335278 0.123201650 -0.2555370391 -0.030625226
## [14,] 0.2142702909 0.136747032 -0.1643759671 -0.381490437
## [15,] 0.3094867492 -0.040295730 0.1215798773 0.310744278
## [16,] 0.1430834618 0.020335003 -0.2065636753 0.163623140
## [17,] 0.0270517097 -0.403924980 0.0746167873 0.112940813
## [18,] -0.2556017538 -0.189523704 -0.1737593609 0.133857473
## [19,] -0.0559358424 -0.049527235 -0.1485151023 0.056959362
## [20,] -0.0888556846 -0.043442887 0.0005508254 0.011543172
## [21,] -0.1558973561 0.016426569 0.1775389149 -0.086443810
## [22,] -0.0501126796 0.315600597 0.4850019449 -0.184594441
## [23,] 0.1959168286 -0.465566774 0.1643328723 -0.160136112
## [24,] 0.0757378710 -0.023303006 0.0384431028 -0.012376911
## [25,] -0.0746338616 -0.056424235 0.1160505771 0.080806059
## [26,] 0.0365358794 -0.098945921 -0.2379258022 0.197334045
## [27,] 0.1988911677 -0.033045248 -0.0684295993 -0.068614713
## [28,] 0.1291249125 0.102886199 -0.1353354221 0.009061009
## [29,] 0.0944334058 0.140700239 0.1472804234 0.105561154
## [,10] [,11] [,12] [,13] [,14]
## [1,] 0.032602194 -0.022709404 -0.056153686 0.007147062 0.07333946
## [2,] -0.026717266 0.008171498 -0.095885690 -0.038806099 -0.01821667
## [3,] -0.045671127 0.153951159 -0.272423900 0.010900300 -0.06097894
## [4,] 0.012103563 -0.054020780 -0.062608554 -0.030811703 -0.01489226
## [5,] 0.072217411 0.218987320 -0.293817277 -0.074614013 -0.13741328
## [6,] -0.003007576 -0.013961298 -0.057049552 0.015374942 -0.08139651
## [7,] 0.141273344 -0.101419290 0.134109671 -0.136780700 0.41718057
## [8,] -0.249867969 -0.499461220 -0.018309193 -0.379478426 -0.13279326
## [9,] 0.090899804 0.205131778 -0.060607047 0.249032261 -0.31614124
## [10,] 0.131969334 0.033074508 0.174329948 0.184848840 0.19575594
## [11,] -0.007910740 0.018549412 -0.110842252 -0.027011754 0.15517245
## [12,] 0.104039831 0.087691117 0.457224940 0.238460130 -0.20271537
## [13,] 0.091439873 -0.129373875 -0.047962186 -0.007793876 0.16530556
## [14,] 0.057475742 0.036723485 0.398713133 -0.135450083 -0.47838126
## [15,] 0.078426549 0.065748037 -0.077592558 -0.105010925 0.08547130
## [16,] -0.032637947 -0.102023336 -0.099411262 0.276938703 0.10841716
## [17,] -0.077726709 0.224570292 -0.011475294 -0.003459892 0.06198043
## [18,] -0.174357105 0.067055200 0.029732154 -0.171002527 -0.22960971
## [19,] -0.337496903 -0.146171738 -0.025569303 0.029029936 -0.01470475
## [20,] -0.178426576 -0.097579272 0.165930641 0.067818676 -0.01867092
## [21,] -0.045550320 0.057615129 0.112125487 0.023484828 -0.01068406
## [22,] 0.317309250 0.224965938 -0.231720768 0.061341590 -0.05484567
## [23,] 0.312497031 -0.358241695 0.196892929 0.309647575 0.02614242
## [24,] 0.004662131 -0.014975566 -0.005359795 -0.033126849 0.05810494
## [25,] -0.066718613 0.038824257 0.192781657 0.078894854 0.19762206
## [26,] 0.543249315 -0.249122830 -0.196137485 -0.247021583 -0.24836999
## [27,] -0.154482473 0.361269068 0.215457301 -0.269617342 0.04307100
## [28,] -0.280302939 -0.064014043 -0.130804918 0.064553488 -0.08686473
## [29,] -0.013678222 0.084406654 -0.005940691 -0.019023848 0.27708655
## [,15] [,16] [,17] [,18] [,19]
## [1,] 0.012326567 -0.0001649009 -0.073647051 -0.058973053 -0.022798844
## [2,] 0.078905229 -0.0801237036 -0.028494824 -0.081226378 -0.042297377
## [3,] 0.141072144 -0.0740560808 -0.126272165 -0.312315719 -0.293125168
## [4,] 0.037632408 -0.0732066318 -0.037126671 -0.053298073 -0.146390998
## [5,] -0.115622976 0.3208951695 -0.366017028 0.050539862 0.080834336
## [6,] 0.121344470 -0.0308747924 0.110628693 -0.019099244 -0.013784345
## [7,] 0.082250409 -0.0340722356 -0.152255424 -0.212382087 0.005053037
## [8,] -0.210413041 -0.0358160358 0.024648405 0.155676534 -0.068406317
## [9,] 0.297078988 -0.2045164054 0.081336561 0.099030711 0.069143243
## [10,] -0.065389446 0.0382494285 -0.006540654 -0.144267549 0.144032758
## [11,] 0.133493410 0.0868648456 -0.050516378 0.122505774 0.310122224
## [12,] -0.342036856 -0.0723921383 -0.239103682 0.037859911 -0.048764643
## [13,] -0.122887576 0.2087510937 -0.041543191 0.352132529 0.118188341
## [14,] 0.052751090 0.1024768985 0.369314938 -0.057041042 0.109197838
## [15,] -0.064465122 -0.2266804537 -0.101651893 -0.084581425 0.453729601
## [16,] -0.048255179 0.0195587970 0.144563556 0.257667849 -0.588963156
## [17,] 0.004542823 0.3779194605 0.363032955 0.029911411 0.043121718
## [18,] -0.167464991 0.0089125754 -0.143869964 -0.124147155 -0.064416682
## [19,] 0.176511323 -0.3220655244 0.013236023 -0.057163551 0.100113263
## [20,] 0.059692278 -0.2258111308 -0.088924519 -0.084783161 -0.021261342
## [21,] -0.053919501 0.4070402391 -0.196254100 -0.002620986 -0.140083672
## [22,] 0.062363287 -0.2134546515 0.103225983 0.254280864 -0.035613881
## [23,] 0.139233962 -0.0243135274 -0.166220488 0.115651052 0.023388861
## [24,] 0.035836390 0.0245416589 0.081625654 -0.014179152 -0.002421644
## [25,] -0.007727840 0.1244194768 0.213414161 0.004761451 0.089187725
## [26,] -0.132064888 0.0049589923 0.055768284 -0.204824436 -0.085152984
## [27,] 0.017149090 -0.1165653841 -0.312260476 0.124242313 -0.182587269
## [28,] 0.100439571 0.0431351548 0.033163894 0.338853476 0.120768740
## [29,] -0.196542555 -0.0606740686 0.363595734 -0.331423250 -0.143149122
## [,20] [,21] [,22] [,23] [,24]
## [1,] -0.043492925 0.073535354 6.364436e-02 -0.037325946 0.007992572
## [2,] -0.047405885 0.076970613 4.352992e-02 -0.115853505 0.224407945
## [3,] -0.167060605 0.124517616 1.771104e-01 -0.084341171 0.014812203
## [4,] -0.025475348 -0.007609075 1.039867e-01 -0.071409307 0.137469715
## [5,] 0.214039914 0.248801386 -5.371008e-02 0.390412611 -0.029118756
## [6,] 0.143315734 -0.117103916 -4.052527e-02 -0.162613227 -0.154374557
## [7,] 0.114946751 -0.093580526 -3.766393e-01 -0.156504709 -0.095000609
## [8,] -0.068310287 -0.067517744 4.262373e-05 0.059271430 0.060176947
## [9,] 0.039010278 -0.245946963 6.927191e-02 -0.173487254 -0.033834215
## [10,] -0.341935486 0.296435903 9.711630e-02 0.273110626 0.256916984
## [11,] -0.021621688 -0.094794161 3.548236e-02 -0.023705911 0.206936634
## [12,] 0.244860427 -0.096371326 -1.997529e-01 -0.158349804 0.228122367
## [13,] 0.031195258 -0.217760264 4.002534e-02 0.112905806 -0.008430273
## [14,] -0.099235423 0.164176035 1.081761e-01 0.207461985 -0.084870876
## [15,] -0.027436924 0.071169936 6.406562e-02 -0.054546801 -0.436231237
## [16,] 0.031539986 0.078049061 -1.111690e-01 0.189549380 -0.326606088
## [17,] 0.029977036 -0.316254289 -1.133983e-01 0.006698982 0.142490986
## [18,] -0.381945122 -0.036389338 -4.137321e-01 -0.037620873 -0.119648196
## [19,] 0.456033875 -0.037153043 3.867188e-02 0.433936662 0.209954533
## [20,] 0.091251058 0.093929647 1.414364e-01 -0.029947719 -0.235854086
## [21,] 0.231725473 0.070516755 4.544919e-01 -0.308056251 -0.059461319
## [22,] -0.106883492 -0.037462961 -1.801701e-01 0.163347097 0.016392852
## [23,] -0.165077582 -0.050676088 -6.567815e-03 0.047272093 0.012421839
## [24,] 0.010076694 -0.020390724 -8.361075e-03 -0.068517918 0.118159684
## [25,] -0.008680280 0.201956373 4.637076e-03 0.089973286 -0.367637226
## [26,] 0.166305203 0.021973555 -2.312871e-02 -0.017191853 0.043130913
## [27,] -0.205585961 -0.318482227 8.578709e-02 0.189944333 -0.006720633
## [28,] -0.107596385 0.452316938 -2.551522e-01 -0.368562437 0.204239559
## [29,] -0.003476552 -0.019534838 2.145639e-02 0.008858399 0.224424621
## [,25] [,26] [,27] [,28] [,29]
## [1,] -0.0813379505 0.017943702 -0.059268162 -0.057492344 -0.099170447
## [2,] -0.0636773590 0.095313865 0.073774232 -0.113405897 -0.161667402
## [3,] -0.1142917367 -0.407239046 -0.280317776 -0.091481662 0.146505279
## [4,] -0.0852441498 0.025481035 0.046394260 -0.029461934 -0.066112741
## [5,] -0.0840420915 0.079819614 -0.049278745 0.170003757 0.166906340
## [6,] -0.1798703531 -0.088920902 0.091587923 -0.114097730 -0.503532978
## [7,] -0.1083433479 0.175947813 -0.121930350 0.085298393 0.265049763
## [8,] 0.0008525678 0.030803643 0.002394222 0.069361462 0.099639477
## [9,] 0.2682214338 0.122691342 -0.101414850 0.073389115 0.259676138
## [10,] -0.0775482277 0.055260719 0.119524104 0.053849096 -0.283013075
## [11,] 0.1149372395 -0.168111468 0.632712793 -0.003868648 0.322294878
## [12,] -0.2099762664 -0.123373399 -0.056899873 -0.046053360 0.106655711
## [13,] 0.4005924764 -0.396426183 -0.386708161 0.036078424 -0.226413878
## [14,] 0.0572859041 0.083258633 -0.020960302 0.028880578 0.075496681
## [15,] 0.0461611892 0.352555503 -0.179782087 0.020769324 -0.108546161
## [16,] 0.0050998185 0.262082765 0.202119999 0.033784748 0.030901052
## [17,] -0.3663495452 0.093972967 -0.178656248 0.236794098 -0.019680309
## [18,] 0.2285492298 -0.069108054 0.076953470 -0.225482340 0.049883905
## [19,] -0.0276543255 0.074671905 -0.123747449 -0.296220984 0.030239521
## [20,] -0.0129995857 -0.310672974 0.142241997 0.700726038 -0.022730315
## [21,] 0.2269800526 0.224506291 0.074880901 -0.176535975 0.004313352
## [22,] -0.0108899497 -0.064088366 0.051741385 -0.022318864 0.008589996
## [23,] 0.0482634698 0.061453765 -0.044423942 -0.116108036 -0.011705310
## [24,] 0.0266346647 -0.012725201 0.047494864 0.030542726 -0.097294265
## [25,] -0.1239956106 -0.321185227 -0.054297241 -0.343970465 0.274426225
## [26,] 0.0016486064 -0.018991085 0.058283756 0.051617105 -0.014962070
## [27,] 0.0267922003 0.139024976 0.034704421 0.034910983 -0.152515467
## [28,] -0.0064280193 0.133175972 -0.197420675 0.101170324 -0.005156581
## [29,] 0.4423578444 0.119850318 -0.101910890 0.110904648 0.129637290
## [,30] [,31] [,32] [,33]
## [1,] 0.0919982724 -0.158036337 0.4158995197 0.773563562
## [2,] 0.2689885282 -0.531955714 -0.6079377422 0.049503265
## [3,] -0.3353430422 0.193416399 -0.0423490713 -0.026291799
## [4,] 0.1973606889 -0.186154476 0.4859556347 -0.580504435
## [5,] 0.1735962523 0.042906851 -0.0231468480 -0.029881563
## [6,] 0.2917642881 0.564939026 -0.1251268608 0.006190220
## [7,] -0.1599820914 0.021839034 -0.0631914163 -0.037622022
## [8,] -0.1322048076 0.020635568 -0.0364130799 -0.022026553
## [9,] -0.0738394452 -0.101714469 -0.0025550723 -0.016097434
## [10,] -0.3002111229 0.071237296 -0.0799243047 -0.114530536
## [11,] 0.0274093819 0.229637215 -0.0004111940 0.061787818
## [12,] 0.0120875287 0.053882743 -0.0470498154 0.034414008
## [13,] -0.0378051780 -0.076910588 -0.0834163665 -0.029016795
## [14,] -0.0787126916 0.038853197 0.0260501327 0.064492633
## [15,] 0.0007421373 0.056489987 0.0004051126 -0.098548899
## [16,] -0.0906103882 0.021470730 -0.0547993298 0.026371922
## [17,] -0.0367177849 -0.012410142 -0.0151359313 -0.037524298
## [18,] 0.1529782296 0.066886750 -0.0226148566 -0.017383457
## [19,] -0.0795487534 0.069366168 -0.0103250444 0.008142220
## [20,] 0.0893459823 -0.083719843 -0.0842897650 0.014122903
## [21,] -0.1026293813 0.061476270 -0.0704881862 -0.048422991
## [22,] -0.0220294417 -0.026002271 -0.0424591389 -0.011234438
## [23,] -0.0279288094 0.051103976 0.0208410446 -0.017568579
## [24,] 0.1606948074 -0.160653886 0.3707680450 -0.047984094
## [25,] 0.2726009373 -0.166230382 -0.0160013115 -0.099799098
## [26,] -0.0010857039 0.002553071 -0.0246967021 0.008213822
## [27,] -0.0355543454 0.004304592 0.0334892558 0.024330084
## [28,] -0.0746945126 0.109538572 0.0258876039 -0.005375860
## [29,] 0.1761975446 0.189603060 -0.0656091632 0.061959455
## [,34]
## [1,] -2.498776e-01
## [2,] -9.788535e-03
## [3,] 7.577362e-02
## [4,] -4.114393e-01
## [5,] 5.641255e-02
## [6,] 1.424667e-02
## [7,] 3.275377e-02
## [8,] 7.655150e-03
## [9,] 4.620540e-02
## [10,] 4.988445e-02
## [11,] -8.296738e-02
## [12,] 8.992243e-03
## [13,] -4.416537e-02
## [14,] -2.116328e-02
## [15,] -1.883361e-02
## [16,] 4.289382e-02
## [17,] -1.251432e-01
## [18,] -1.270702e-02
## [19,] -8.287048e-04
## [20,] -5.051914e-02
## [21,] -9.624278e-03
## [22,] -5.724749e-02
## [23,] -5.324912e-02
## [24,] 8.319458e-01
## [25,] -1.979983e-02
## [26,] -4.283701e-03
## [27,] -1.543998e-03
## [28,] -4.474362e-02
## [29,] -9.332698e-02
## [ reached getOption("max.print") -- omitted 5 rows ]
eigen(femalecor) # all eigenvalues different from zero
## eigen() decomposition
## $values
## [1] 13.3649545 1.9702789 1.4509868 1.2672664 1.0740497 0.8537717
## [7] 0.7984894 0.7540629 0.7140611 0.6844476 0.6761208 0.6434187
## [13] 0.6121904 0.6003574 0.5633101 0.5542226 0.5438415 0.5245232
## [19] 0.5199726 0.4987226 0.4813443 0.4746945 0.4669883 0.4473728
## [25] 0.4392394 0.4204262 0.4024514 0.3868779 0.3773670 0.3322831
## [31] 0.3208035 0.2899127 0.2694387 0.2217512
##
## $vectors
## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.22657751 -0.081365525 0.103283410 0.013665026 0.007722882
## [2,] -0.21758374 -0.116697064 0.146334053 -0.013617245 -0.099080623
## [3,] -0.20429548 -0.100573304 0.121922530 0.029908362 -0.090397400
## [4,] -0.22121881 -0.111312630 0.121803717 0.004393635 0.015550726
## [5,] -0.16032552 -0.025281490 -0.012465230 -0.175568324 0.383848027
## [6,] -0.18230401 -0.075695945 0.024919665 -0.223553292 0.229557176
## [7,] -0.16125666 -0.096398081 0.103030804 -0.055845596 0.028148638
## [8,] -0.08296528 -0.042923439 0.228290596 -0.287993697 -0.142241688
## [9,] -0.09203796 -0.061869908 0.237508970 -0.378123037 0.332110012
## [10,] -0.15208968 -0.047694764 0.135773748 -0.209211555 0.009838069
## [11,] -0.19940865 -0.097495174 0.144669900 -0.008763479 -0.255465142
## [12,] -0.16396957 -0.085337149 0.106258607 -0.012075448 -0.179143867
## [13,] -0.19448442 -0.085734842 0.117484874 0.078559638 -0.113683475
## [14,] -0.17999204 -0.067780513 0.123437143 0.052635451 -0.023926241
## [15,] -0.18604868 -0.095606432 0.148226442 0.067258958 -0.207886458
## [16,] -0.18207528 -0.065074009 0.119123190 0.001505474 -0.117251381
## [17,] -0.19818858 0.141959070 0.043332022 0.133317555 -0.069021759
## [18,] -0.17519665 0.038876141 0.035424925 0.341106634 0.180782145
## [19,] -0.19361740 0.025965733 -0.113309610 0.206526700 0.006331174
## [20,] -0.20959105 0.030966903 -0.188237158 0.177238593 0.103939695
## [21,] -0.18794814 0.024764256 -0.135847036 0.220517630 0.002129137
## [22,] -0.14805144 -0.006806240 -0.199693269 0.246125627 -0.113972510
## [23,] -0.16840798 -0.005769157 -0.206288112 -0.022098823 0.249617202
## [24,] -0.23815474 -0.069424330 0.001427493 0.079634764 -0.057856818
## [25,] -0.14729689 0.031724054 -0.194469658 -0.286896021 -0.133678510
## [26,] -0.11390252 0.211530905 -0.299291660 -0.257652143 -0.227062846
## [27,] -0.12166043 0.100553622 -0.351532252 -0.325004653 -0.231449669
## [28,] -0.17406087 0.059922974 -0.325214944 -0.042155756 -0.136793593
## [29,] -0.17482146 -0.038325750 -0.208554881 -0.085805783 0.154499322
## [,6] [,7] [,8] [,9]
## [1,] 0.007668276 0.003441247 -0.0183971396 0.0166440844
## [2,] 0.049897500 0.082052989 0.0493917931 -0.0160931740
## [3,] 0.094123862 0.034066145 0.0244419739 0.0271952875
## [4,] 0.081398259 0.080583288 -0.0502454652 -0.0490891826
## [5,] 0.029247854 0.197110873 -0.0581753435 -0.0962940755
## [6,] 0.061367779 0.079339828 -0.1352291954 -0.1000327568
## [7,] 0.099531010 0.255183208 -0.6096067665 0.0716428141
## [8,] -0.885978767 -0.035228552 -0.0970646746 -0.0530920560
## [9,] 0.200257687 -0.613588703 0.0680043205 -0.2334111873
## [10,] 0.069023083 -0.259890733 -0.0929116404 0.4356693005
## [11,] 0.077119634 0.071723194 0.1183540209 0.0478054250
## [12,] 0.088491633 0.098267803 0.3393595632 -0.4577864626
## [13,] 0.027422625 -0.009524301 -0.1257211932 0.0946079865
## [14,] 0.071500401 0.168563437 -0.2132206980 -0.2361014701
## [15,] 0.024807936 -0.044610099 0.2833943806 -0.0343687414
## [16,] 0.121742830 0.061942133 0.1254950422 0.1669140216
## [17,] -0.067460133 -0.117471512 0.0995878865 0.1650272506
## [18,] -0.074937573 -0.202172867 -0.0347004789 0.1851563723
## [19,] -0.037414956 -0.129850326 0.0256360081 0.0862812355
## [20,] -0.077206677 -0.096072184 -0.0384166211 -0.0048743627
## [21,] -0.049031462 -0.225860761 -0.1650795436 0.0321067550
## [22,] -0.116326942 -0.310445511 -0.1735672710 -0.3583796429
## [23,] -0.153831880 0.180272167 0.2374815508 0.0183306658
## [24,] -0.022921991 0.028667020 0.0027386429 -0.0241939833
## [25,] 0.012700445 -0.030583958 0.1795242102 0.4113709366
## [26,] 0.036934069 -0.188345768 -0.1115792906 -0.2016946953
## [27,] 0.115353607 0.001069539 -0.1343970106 0.0003084686
## [28,] 0.060043303 0.022608680 -0.0045264990 -0.0306819231
## [29,] -0.099630964 0.151697440 0.2539567632 -0.0203509374
## [,10] [,11] [,12] [,13] [,14]
## [1,] 0.030392158 0.058286089 0.025044159 0.039804227 -0.025381127
## [2,] 0.006410586 0.056437693 0.106382341 -0.126140739 -0.052399526
## [3,] -0.118791537 0.046467796 0.192468256 -0.179877943 -0.025124861
## [4,] -0.033611793 0.017463105 -0.047008099 -0.067539427 -0.032009346
## [5,] 0.031043191 0.426133680 0.325032026 -0.250290311 -0.043460126
## [6,] 0.041986715 -0.066875115 -0.021487365 -0.064818938 0.100279165
## [7,] 0.067486902 -0.173124107 0.129151962 0.237464735 0.134045553
## [8,] -0.119329668 -0.039993991 -0.028750622 -0.053457761 -0.019667304
## [9,] -0.139095046 -0.301951255 0.045725368 -0.028877684 0.032627093
## [10,] 0.410118120 0.395172317 -0.403757563 0.033954897 -0.222488107
## [11,] -0.041053324 0.051026877 0.079510925 -0.181656702 0.029199497
## [12,] 0.142561069 -0.014184612 -0.191731066 0.257062974 -0.028007291
## [13,] -0.057844928 -0.051617961 -0.036762130 0.095845531 0.043742843
## [14,] 0.027969420 -0.166790303 -0.184191145 0.259891396 -0.026263028
## [15,] -0.016043593 0.091376009 0.076897660 -0.134175652 0.115483194
## [16,] -0.231254324 0.048369115 -0.201758276 0.040468848 -0.045868160
## [17,] -0.112306161 0.026730606 0.252522223 0.194207271 -0.042889213
## [18,] -0.189428903 0.032918530 0.044469745 0.127569870 -0.065461084
## [19,] -0.153729202 -0.154140106 -0.023698478 -0.107020607 0.038072072
## [20,] -0.106498561 -0.040096423 0.004262885 0.047488660 0.003435301
## [21,] 0.050531004 -0.050328281 0.061559908 0.001057408 -0.050915765
## [22,] 0.539635903 0.035845369 0.115540315 -0.189049950 -0.026372871
## [23,] 0.164356880 -0.028785433 0.125842159 0.260162741 -0.313658714
## [24,] 0.003287491 -0.017232579 0.008960832 0.029512784 -0.003318251
## [25,] 0.299535604 -0.347777911 0.147160913 0.046702392 0.426628719
## [26,] -0.237435228 0.498243242 -0.010351577 0.381840705 0.330248405
## [27,] -0.222083770 -0.186434755 -0.065288953 -0.121746184 -0.621145596
## [28,] -0.106273515 -0.044673568 0.012911680 -0.248743916 0.060860325
## [29,] 0.159415351 -0.147601929 -0.122921765 0.194462886 -0.027803311
## [,15] [,16] [,17] [,18] [,19]
## [1,] 0.062530228 -0.06392560 -0.065077311 0.045501001 -0.0650390496
## [2,] 0.060359159 -0.04414302 -0.060804731 -0.025193906 -0.0111098684
## [3,] 0.088706065 -0.12596852 0.018931744 0.070851198 -0.0732840119
## [4,] 0.071667581 -0.02286275 -0.056874742 -0.025488462 -0.0226063263
## [5,] -0.250777448 -0.16151910 -0.093533467 -0.035343656 0.0582888566
## [6,] -0.009368999 0.02557112 0.203905745 -0.042429583 -0.0763674611
## [7,] -0.197285061 0.37107619 -0.147762565 -0.032474151 -0.0364088716
## [8,] -0.060722600 -0.01283495 0.009530373 0.006326971 0.0096697247
## [9,] 0.089020793 0.10635311 -0.046176228 0.064783140 0.0941725413
## [10,] 0.039014244 0.02482458 -0.036585830 0.143343422 -0.1338856631
## [11,] 0.136697989 0.04860152 -0.031380568 0.019016988 -0.0908377695
## [12,] -0.567227970 0.01923534 -0.058346454 0.103476348 -0.2153211723
## [13,] 0.084476514 0.19279288 -0.024082776 -0.202644453 0.0811207979
## [14,] 0.342590586 -0.58701077 0.020428430 0.136781690 0.1386814768
## [15,] 0.092790752 0.14280804 0.044229417 0.045074728 -0.1132840657
## [16,] -0.187241416 0.13019122 0.431473357 -0.237220861 0.6128441775
## [17,] 0.089172279 -0.10683473 -0.058253941 -0.023625906 -0.0115118506
## [18,] -0.138889140 -0.09411013 -0.011986796 -0.089279520 -0.2209704217
## [19,] -0.109792735 0.21208438 -0.144125372 0.282106460 -0.0265039205
## [20,] -0.072687436 0.02552850 0.003529160 0.106044936 -0.0311869225
## [21,] -0.222765619 -0.07743339 0.195095704 0.120845783 0.0006891897
## [22,] 0.044928330 0.02069279 0.193179689 -0.267773622 0.1709211719
## [23,] 0.125326910 0.18274692 -0.036239022 0.450666465 0.3746307340
## [24,] 0.097531027 -0.04481098 -0.074944392 -0.008466129 -0.0198535457
## [25,] -0.225286242 -0.33951073 -0.034132691 -0.022351472 0.0704774745
## [26,] 0.098362067 0.04044985 -0.036103409 0.035758227 0.0497864496
## [27,] -0.143847351 -0.12448442 0.009465467 -0.160029809 -0.1363102996
## [28,] 0.155108577 0.08188902 -0.281412369 0.019833581 0.0696276955
## [29,] 0.335210921 0.27965248 0.016849750 -0.388996616 -0.2861838501
## [,20] [,21] [,22] [,23] [,24]
## [1,] 0.050788359 -0.02218361 -0.0141016132 0.001501657 -0.041507805
## [2,] 0.051684520 0.03048044 0.1754839643 -0.173086585 0.168825544
## [3,] 0.007847249 -0.03288882 0.2447351371 -0.168721963 0.244144881
## [4,] 0.019724265 -0.01770769 0.0574584599 -0.126910044 0.201902238
## [5,] -0.247386817 0.27665536 -0.0978751083 0.076878522 -0.170520869
## [6,] 0.473163107 -0.43598083 -0.4527766241 -0.214059405 0.068631008
## [7,] 0.028267130 -0.05030406 0.3240376658 0.194719275 -0.044128229
## [8,] -0.074997345 -0.03114198 0.0253303894 -0.023011906 0.014039843
## [9,] -0.086816515 0.11611171 0.1000073400 0.062196071 0.001964129
## [10,] -0.129887514 -0.11906152 0.0243038035 -0.016773234 -0.040070771
## [11,] 0.142692967 0.07848523 0.0830016895 -0.101023613 -0.037935567
## [12,] -0.155472510 -0.06595959 -0.0687557831 -0.044594400 0.084753475
## [13,] -0.259264954 0.20909206 -0.6577311590 0.128282674 -0.024140368
## [14,] -0.153007421 0.06442333 -0.0127818670 0.050210394 -0.140775594
## [15,] 0.243445491 -0.03850539 0.0126985251 0.560756012 -0.362734319
## [16,] -0.097311197 -0.01652481 0.1384737254 -0.065671768 0.022945667
## [17,] 0.074325215 -0.10594431 -0.0844477892 0.029527376 -0.118131207
## [18,] 0.063289630 0.17353765 -0.0875006401 0.165851427 0.558106638
## [19,] -0.171574809 -0.06824029 -0.0072310296 -0.172035623 -0.125529539
## [20,] -0.048595017 -0.02586761 0.0174214860 -0.034637048 -0.151670438
## [21,] 0.165134597 0.18410593 0.0198248868 -0.410158240 -0.419524675
## [22,] -0.024446870 -0.08016730 0.0907662337 0.164336398 0.162525254
## [23,] 0.153967742 -0.02758457 -0.0031952860 0.160765994 0.162020128
## [24,] 0.043752092 0.02258660 -0.0293917107 0.019176201 -0.046580410
## [25,] -0.004828545 0.08047353 0.0006685759 0.076243666 0.091937018
## [26,] 0.139609982 0.09244855 0.0528619683 -0.048664102 0.093121475
## [27,] 0.149760758 0.08356735 -0.0069429745 0.209960213 -0.030968855
## [28,] -0.429693044 -0.43072999 -0.0693250761 -0.050286192 0.066819751
## [29,] -0.071235221 0.30190938 0.1315723572 -0.240950021 -0.078539338
## [,25] [,26] [,27] [,28]
## [1,] -0.0189664474 -0.021017170 -0.1787642141 -0.0956943114
## [2,] -0.0085382851 -0.027509810 0.0249630437 -0.0228824131
## [3,] 0.0672819683 -0.008750047 0.3132531449 0.3635485108
## [4,] -0.0317162280 -0.087841090 0.1108228112 0.1956745358
## [5,] -0.1474842562 0.031320120 -0.1773235033 0.1619145680
## [6,] -0.1600481689 0.110565398 -0.0929315880 0.0784667290
## [7,] 0.0717338522 0.017743495 -0.0448696762 -0.0650816256
## [8,] 0.0077122296 0.051768469 0.0025809473 0.0265756290
## [9,] 0.1030563158 -0.032994957 -0.0494026383 -0.0537190849
## [10,] -0.0073967825 0.049799510 0.0228097348 -0.0595208993
## [11,] 0.1032843443 -0.361370197 -0.0817258219 -0.2740953170
## [12,] 0.1040004112 -0.034802681 -0.0480757579 -0.0474525199
## [13,] 0.1606881672 -0.259765232 0.3008510313 0.1416778149
## [14,] -0.1357722588 0.186912802 0.0501332209 -0.1455000671
## [15,] -0.0472818665 0.387814958 0.1296408488 0.1190273523
## [16,] -0.1040044943 0.145048220 -0.1750175511 0.0084335165
## [17,] 0.0647793543 -0.279917404 -0.5476240132 -0.0524888055
## [18,] 0.0229156363 0.350665062 -0.0446870532 -0.1536245768
## [19,] -0.6489190078 -0.112242107 0.1750248233 -0.1082966018
## [20,] -0.1169933535 0.063524019 -0.0008392539 0.0015766888
## [21,] 0.4326647024 0.148502501 0.1210867972 0.0872043895
## [22,] -0.1229195235 -0.149282358 -0.0124470788 -0.0235640856
## [23,] 0.1483115717 -0.103412682 0.1226321754 0.0925385532
## [24,] -0.0250354755 -0.044020279 -0.1128421320 -0.0675994068
## [25,] -0.0659091906 -0.015658792 0.0460995766 0.1019912316
## [26,] -0.0741198849 -0.027959990 0.1102877707 0.0477837469
## [27,] -0.0702064104 -0.071430053 0.0575301305 -0.0276279926
## [28,] 0.3335713341 0.318988748 -0.1616984007 0.0005033992
## [29,] -0.0985669810 0.163292858 -0.1283383147 0.1450426994
## [,29] [,30] [,31] [,32]
## [1,] -0.0228890576 0.296083474 0.0096674007 0.8604866919
## [2,] 0.1709474072 0.163113275 0.4469819535 -0.1182234345
## [3,] -0.5208449234 -0.251910269 -0.2274596153 0.1145879689
## [4,] 0.1626429004 0.319701542 0.3648343719 -0.2227047712
## [5,] 0.0825113954 -0.025769974 -0.1162536676 -0.0645486629
## [6,] 0.0150383587 -0.087927313 -0.0987819454 -0.0527250617
## [7,] -0.0622582535 -0.026623590 -0.0566439042 -0.0601064143
## [8,] 0.0180424592 -0.011648862 -0.0284636980 -0.0150494149
## [9,] 0.0009668235 -0.017087086 -0.0004541133 -0.0139541263
## [10,] -0.0729643727 -0.083150087 0.0001445532 -0.0935583017
## [11,] 0.4631052502 -0.337726068 -0.3752673926 -0.0418533728
## [12,] -0.1023992219 -0.038708356 -0.0306906640 -0.0361744033
## [13,] -0.0418569610 -0.025948306 0.0362159451 0.0391711368
## [14,] -0.0039393948 -0.060902145 -0.1323768376 -0.1280743017
## [15,] -0.0041698435 0.069225273 0.0247582651 -0.0946131629
## [16,] 0.0045019695 -0.020393626 -0.0540290644 0.0376602795
## [17,] -0.4310683849 0.059132747 0.0733699452 -0.2809704693
## [18,] 0.1609744625 -0.005918515 -0.1764566964 -0.0578630416
## [19,] -0.0399003224 0.221095295 -0.2049727425 -0.0869916449
## [20,] 0.0678516750 -0.678396359 0.5200987383 0.1727855131
## [21,] 0.0847526716 0.195966141 -0.0913696659 -0.0625857420
## [22,] -0.0311938905 -0.005217020 -0.0562935091 -0.0006939667
## [23,] 0.0945796590 0.013991259 -0.0794223442 -0.0080893341
## [24,] 0.0627361790 0.070601508 0.1080520834 0.0212904806
## [25,] 0.0855412003 0.004056702 0.0270722338 0.0259194628
## [26,] 0.0484768993 0.047605368 -0.0279042775 0.0077895728
## [27,] -0.0336118474 0.033843770 0.0072121734 0.0140739960
## [28,] 0.0949405765 0.039401077 -0.0862333201 -0.0195843137
## [29,] -0.0533353818 -0.019277183 -0.1070179540 -0.0250721393
## [,33] [,34]
## [1,] -0.0626328109 0.158680535
## [2,] 0.6867358071 0.128128932
## [3,] -0.0011493361 -0.091944932
## [4,] -0.6625514208 0.125423551
## [5,] -0.0015221917 -0.003465585
## [6,] 0.0761532039 0.007274855
## [7,] 0.0181741049 0.019057474
## [8,] -0.0239600845 0.008444155
## [9,] 0.0116165362 -0.028658339
## [10,] 0.0074823563 -0.019876052
## [11,] -0.1158368840 0.096585167
## [12,] -0.0007901573 0.009529396
## [13,] 0.1151630716 0.048288321
## [14,] 0.0329363121 0.113013450
## [15,] -0.0201426769 0.073662198
## [16,] -0.0237669889 -0.021362277
## [17,] -0.0338863462 0.147833916
## [18,] 0.0087952130 0.023844509
## [19,] 0.0640257737 0.035792271
## [20,] -0.1067636752 0.074339320
## [21,] 0.0102004815 0.016056828
## [22,] -0.0098465107 0.045888040
## [23,] 0.0304881143 0.020938551
## [24,] -0.0170629337 -0.927860476
## [25,] -0.0295432673 0.008998886
## [26,] 0.0274069342 0.005107252
## [27,] 0.0051591845 0.018256856
## [28,] 0.0031955528 0.031879608
## [29,] 0.0120463729 0.057700086
## [ reached getOption("max.print") -- omitted 5 rows ]
mpa<- fa.parallel(malecor, n.obs=2443, n.iter=1000)
## Parallel analysis suggests that the number of factors = 6 and the number of components = 4
fpa<- fa.parallel(femalecor, n.obs=3642, n.iter=1000)
## Parallel analysis suggests that the number of factors = 6 and the number of components = 4
mqqnorm(datafemale, main = "Multi-normal Q-Q Plot")
## 4858 4367
## 2415 1924
mqqnorm(datamale, main = "Multi-normal Q-Q Plot")
## [1] 2159 2079
mqqnorm(datagroup, main = "Multi-normal Q-Q Plot")
## [1] 2159 4858
mvn(data = datamale, mvnTest = "mardia")
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 13163.5402108666 0 NO
## 2 Mardia Kurtosis 13.4805655631301 0 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value
## 1 Anderson-Darling Stest1vocab 17.2962 <0.001
## 2 Anderson-Darling Stest2literature 28.6087 <0.001
## 3 Anderson-Darling Stest3music 62.5931 <0.001
## 4 Anderson-Darling Stest4socialstudies 31.6788 <0.001
## 5 Anderson-Darling Stest5math 19.8829 <0.001
## 6 Anderson-Darling Stest6physicalscience 39.4139 <0.001
## 7 Anderson-Darling Stest7biologicalscience 26.7368 <0.001
## 8 Anderson-Darling Stest8aeronautics 66.5155 <0.001
## 9 Anderson-Darling Stest9electronics 22.3116 <0.001
## 10 Anderson-Darling Stest10mechanics 11.9673 <0.001
## 11 Anderson-Darling Stest11art 49.6799 <0.001
## 12 Anderson-Darling Stest12law 51.1701 <0.001
## 13 Anderson-Darling Stest13health 43.6321 <0.001
## 14 Anderson-Darling Stest14bible 44.8686 <0.001
## 15 Anderson-Darling Stest15theater 78.1606 <0.001
## 16 Anderson-Darling Stest16miscellaneous 46.7119 <0.001
## 17 Anderson-Darling Stest19disguisedwords 60.6622 <0.001
## 18 Anderson-Darling Stest20spelling 13.5916 <0.001
## 19 Anderson-Darling Stest21capitalization 79.2095 <0.001
## 20 Anderson-Darling Stest22punctuation 7.0268 <0.001
## 21 Anderson-Darling Stest23english 9.7213 <0.001
## 22 Anderson-Darling Stest24expression 21.4125 <0.001
## 23 Anderson-Darling Stest25wordfunctions 23.0605 <0.001
## 24 Anderson-Darling Stest26readingcomprehension 39.6555 <0.001
## 25 Anderson-Darling Stest28mechanicalreasoning 22.9034 <0.001
## 26 Anderson-Darling Stest29visualization2D 22.3567 <0.001
## 27 Anderson-Darling Stest30visualization3D 19.6763 <0.001
## 28 Anderson-Darling Stest31abstractreasoning 21.9210 <0.001
## 29 Anderson-Darling Stest32arithreasoning 48.8610 <0.001
## 30 Anderson-Darling Stest33highschoolmath 49.4632 <0.001
## 31 Anderson-Darling Stest34arithcomputation 5.6482 <0.001
## 32 Anderson-Darling Stest35tablereading 26.8353 <0.001
## 33 Anderson-Darling Stest36clericalchecking 70.2704 <0.001
## 34 Anderson-Darling Stest37objectinspection 26.1694 <0.001
## Normality
## 1 NO
## 2 NO
## 3 NO
## 4 NO
## 5 NO
## 6 NO
## 7 NO
## 8 NO
## 9 NO
## 10 NO
## 11 NO
## 12 NO
## 13 NO
## 14 NO
## 15 NO
## 16 NO
## 17 NO
## 18 NO
## 19 NO
## 20 NO
## 21 NO
## 22 NO
## 23 NO
## 24 NO
## 25 NO
## 26 NO
## 27 NO
## 28 NO
## 29 NO
## 30 NO
## 31 NO
## 32 NO
## 33 NO
## 34 NO
##
## $Descriptives
## n Mean Std.Dev Median
## Stest1vocab 2443 -1.1095892563 1.0621130 -1.3076552
## Stest2literature 2443 -0.9945907006 0.9693893 -1.1585876
## Stest3music 2443 -0.8760449097 0.9107866 -0.9699066
## Stest4socialstudies 2443 -1.0337270784 1.1153862 -1.2899342
## Stest5math 2443 -0.7896922969 1.0531123 -0.7002896
## Stest6physicalscience 2443 -0.7052279449 0.8948063 -0.7738134
## Stest7biologicalscience 2443 -0.6026174421 0.9747421 -0.5677824
## Stest8aeronautics 2443 -0.4869574146 1.0100620 -0.2229884
## Stest9electronics 2443 -0.6218183114 1.1050936 -0.5117613
## Stest10mechanics 2443 -0.6318496885 0.8917348 -0.6123728
## Stest11art 2443 -1.0040464783 0.9595535 -1.0845879
## Stest12law 2443 -0.7453417674 0.9366330 -1.0623025
## Stest13health 2443 -1.1566211046 1.1020137 -1.1789320
## Stest14bible 2443 -0.7012685645 0.8651236 -0.7850621
## Stest15theater 2443 -0.9981830125 0.8264665 -0.8782804
## Stest16miscellaneous 2443 -0.8382264779 1.0478540 -1.1533921
## Stest19disguisedwords 2443 -0.9650082562 0.8800368 -1.1766655
## Stest20spelling 2443 -0.8272665823 1.0004359 -0.9333158
## Stest21capitalization 2443 -1.1436734095 0.9454176 -1.4082177
## Stest22punctuation 2443 -1.2064543525 0.9968915 -1.2766891
## Stest23english 2443 -1.0353461760 1.1804729 -1.0251536
## Stest24expression 2443 -0.9498035005 1.1681145 -0.8965657
## Stest25wordfunctions 2443 -0.8645041762 0.7783038 -0.9300168
## Stest26readingcomprehension 2443 -1.2550031376 1.0826988 -1.4556234
## Stest28mechanicalreasoning 2443 -0.6930350339 0.8982447 -0.7570797
## Stest29visualization2D 2443 -0.4859242630 1.0960685 -0.4541734
## Stest30visualization3D 2443 -0.6885105790 0.9516764 -0.6518204
## Stest31abstractreasoning 2443 -1.0209400576 1.1409325 -0.8992617
## Stest32arithreasoning 2443 -1.0263748677 0.8487616 -1.1815940
## Stest33highschoolmath 2443 -0.8535754828 0.8021980 -0.9288142
## Stest34arithcomputation 2443 -1.1433319274 1.1393281 -1.1848340
## Stest35tablereading 2443 -0.6809154199 1.6458126 -0.4864526
## Stest36clericalchecking 2443 0.0003385028 1.2952453 -0.4144503
## Stest37objectinspection 2443 -0.2813571657 1.2386776 -0.5141888
## Min Max 25th 75th
## Stest1vocab -3.081020 1.732398 -1.9409997 -0.29430412
## Stest2literature -2.695306 2.134379 -1.8171810 -0.49999415
## Stest3music -1.992064 2.096567 -1.6513451 -0.28846803
## Stest4socialstudies -2.857168 1.648629 -1.8776468 -0.31041310
## Stest5math -3.103322 1.578247 -1.4629972 -0.19790688
## Stest6physicalscience -1.991504 2.148645 -1.5044280 -0.28673699
## Stest7biologicalscience -2.278375 1.998107 -1.4230789 -0.14013417
## Stest8aeronautics -1.969735 1.691277 -0.8676605 0.23441370
## Stest9electronics -3.215139 1.816802 -1.3697967 0.05341212
## Stest10mechanics -2.422555 2.232198 -1.3881650 -0.09517808
## Stest11art -2.294194 2.141029 -1.8909920 -0.27818370
## Stest12law -2.188608 2.316614 -1.6254553 0.06400306
## Stest13health -2.782038 1.492912 -2.2476696 -0.11019449
## Stest14bible -1.996349 2.243155 -1.3907055 -0.17941857
## Stest15theater -2.009254 1.949153 -1.4437671 -0.31279372
## Stest16miscellaneous -2.321753 2.935870 -1.7375724 0.01496852
## Stest19disguisedwords -2.200294 2.040453 -1.6153635 -0.44550220
## Stest20spelling -2.949489 2.090944 -1.6053734 -0.26125817
## Stest21capitalization -2.212520 1.792646 -1.9895058 -0.34408038
## Stest22punctuation -4.007462 1.909213 -1.9593824 -0.59399588
## Stest23english -5.175212 2.486434 -1.6636241 -0.38668319
## Stest24expression -3.654018 1.401311 -1.8157166 0.02258511
## Stest25wordfunctions -2.609127 1.665905 -1.4507123 -0.49105015
## Stest26readingcomprehension -3.158804 1.549990 -2.1569331 -0.55393946
## Stest28mechanicalreasoning -2.414006 2.083365 -1.4671908 -0.04696863
## Stest29visualization2D -2.283595 1.924074 -1.5518262 0.27759518
## Stest30visualization3D -2.538855 2.178732 -1.2808320 -0.02280880
## Stest31abstractreasoning -3.053322 1.972819 -1.9762918 -0.18124158
## Stest32arithreasoning -2.327215 1.968863 -1.7544044 -0.60878369
## Stest33highschoolmath -2.147432 2.523936 -1.3350200 -0.52260833
## Stest34arithcomputation -3.938878 3.201236 -2.0008470 -0.47082264
## Stest35tablereading -4.815108 3.610163 -1.6444251 0.38398259
## Stest36clericalchecking -2.661621 2.630104 -0.9943653 0.99909258
## Stest37objectinspection -3.283883 2.401279 -1.2430558 0.50622493
## Skew Kurtosis
## Stest1vocab 0.34510687 -0.59976692
## Stest2literature 0.63787571 -0.10633742
## Stest3music 0.85660701 0.09551652
## Stest4socialstudies 0.47628668 -0.71164871
## Stest5math -0.28834814 -0.19402440
## Stest6physicalscience 0.76509425 0.08850632
## Stest7biologicalscience 0.30504439 -0.54731463
## Stest8aeronautics -0.04590821 -0.89545568
## Stest9electronics -0.39215567 -0.03900773
## Stest10mechanics 0.22994082 -0.42619009
## Stest11art 0.65101238 -0.28537963
## Stest12law 0.60619691 0.08045298
## Stest13health 0.39011295 -0.73203792
## Stest14bible 0.84828024 0.41410836
## Stest15theater 0.78321829 0.23119127
## Stest16miscellaneous 0.43761686 -0.47478304
## Stest19disguisedwords 1.06086785 0.72556634
## Stest20spelling 0.23127394 -0.31405639
## Stest21capitalization 0.80707774 -0.23153238
## Stest22punctuation 0.18223440 -0.22045506
## Stest23english -0.25160293 0.21859560
## Stest24expression -0.18049493 -0.66948911
## Stest25wordfunctions 0.47884776 0.45276250
## Stest26readingcomprehension 0.58767258 -0.57755544
## Stest28mechanicalreasoning 0.54024097 -0.17789919
## Stest29visualization2D 0.22119256 -0.96147180
## Stest30visualization3D 0.35150508 -0.46924804
## Stest31abstractreasoning 0.15046639 -0.84825866
## Stest32arithreasoning 0.89612583 0.54144588
## Stest33highschoolmath 1.10968463 1.40578035
## Stest34arithcomputation 0.53147902 0.72304444
## Stest35tablereading -0.44457343 0.54651004
## Stest36clericalchecking 0.56498656 -0.88599275
## Stest37objectinspection 0.42282433 -0.54254508
mvn(data = datafemale, mvnTest = "mardia")
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 15103.4680787055 0 NO
## 2 Mardia Kurtosis 13.5647517677615 0 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value
## 1 Anderson-Darling Stest1vocab 29.6155 <0.001
## 2 Anderson-Darling Stest2literature 36.2554 <0.001
## 3 Anderson-Darling Stest3music 71.8574 <0.001
## 4 Anderson-Darling Stest4socialstudies 30.9935 <0.001
## 5 Anderson-Darling Stest5math 40.5679 <0.001
## 6 Anderson-Darling Stest6physicalscience 65.7130 <0.001
## 7 Anderson-Darling Stest7biologicalscience 47.3995 <0.001
## 8 Anderson-Darling Stest8aeronautics 197.6227 <0.001
## 9 Anderson-Darling Stest9electronics 86.2056 <0.001
## 10 Anderson-Darling Stest10mechanics 37.8697 <0.001
## 11 Anderson-Darling Stest11art 77.7074 <0.001
## 12 Anderson-Darling Stest12law 80.0334 <0.001
## 13 Anderson-Darling Stest13health 50.0620 <0.001
## 14 Anderson-Darling Stest14bible 41.6359 <0.001
## 15 Anderson-Darling Stest15theater 95.1835 <0.001
## 16 Anderson-Darling Stest16miscellaneous 71.5141 <0.001
## 17 Anderson-Darling Stest19disguisedwords 77.7550 <0.001
## 18 Anderson-Darling Stest20spelling 18.8864 <0.001
## 19 Anderson-Darling Stest21capitalization 76.8646 <0.001
## 20 Anderson-Darling Stest22punctuation 10.1089 <0.001
## 21 Anderson-Darling Stest23english 14.3929 <0.001
## 22 Anderson-Darling Stest24expression 34.0889 <0.001
## 23 Anderson-Darling Stest25wordfunctions 41.3657 <0.001
## 24 Anderson-Darling Stest26readingcomprehension 36.4058 <0.001
## 25 Anderson-Darling Stest28mechanicalreasoning 44.7846 <0.001
## 26 Anderson-Darling Stest29visualization2D 55.7612 <0.001
## 27 Anderson-Darling Stest30visualization3D 34.3835 <0.001
## 28 Anderson-Darling Stest31abstractreasoning 35.9934 <0.001
## 29 Anderson-Darling Stest32arithreasoning 66.7532 <0.001
## 30 Anderson-Darling Stest33highschoolmath 51.9887 <0.001
## 31 Anderson-Darling Stest34arithcomputation 5.6984 <0.001
## 32 Anderson-Darling Stest35tablereading 49.6425 <0.001
## 33 Anderson-Darling Stest36clericalchecking 76.8501 <0.001
## 34 Anderson-Darling Stest37objectinspection 24.2471 <0.001
## Normality
## 1 NO
## 2 NO
## 3 NO
## 4 NO
## 5 NO
## 6 NO
## 7 NO
## 8 NO
## 9 NO
## 10 NO
## 11 NO
## 12 NO
## 13 NO
## 14 NO
## 15 NO
## 16 NO
## 17 NO
## 18 NO
## 19 NO
## 20 NO
## 21 NO
## 22 NO
## 23 NO
## 24 NO
## 25 NO
## 26 NO
## 27 NO
## 28 NO
## 29 NO
## 30 NO
## 31 NO
## 32 NO
## 33 NO
## 34 NO
##
## $Descriptives
## n Mean Std.Dev Median
## Stest1vocab 3642 -1.3059162 0.9248888 -1.30765522
## Stest2literature 3642 -0.9914377 0.8950670 -1.15858756
## Stest3music 3642 -0.7758781 0.9190758 -0.96990659
## Stest4socialstudies 3642 -1.2338847 0.9052924 -1.28993419
## Stest5math 3642 -0.9443045 0.9910145 -0.70028957
## Stest6physicalscience 3642 -1.0069200 0.6944041 -1.01735162
## Stest7biologicalscience 3642 -0.8155413 0.8470220 -0.99543064
## Stest8aeronautics 3642 -0.9192058 0.8332552 -0.86766055
## Stest9electronics 3642 -1.1383580 0.9596358 -0.88657622
## Stest10mechanics 3642 -1.3599053 0.6125667 -1.38816500
## Stest11art 3642 -0.9996741 0.9816871 -1.08458787
## Stest12law 3642 -0.8765951 0.8238857 -1.06230250
## Stest13health 3642 -0.9642748 1.1081972 -1.17893204
## Stest14bible 3642 -0.5514187 0.8738003 -0.78506205
## Stest15theater 3642 -0.8146204 0.8967290 -0.87828039
## Stest16miscellaneous 3642 -0.9185651 0.9190418 -1.15339212
## Stest19disguisedwords 3642 -0.8405552 0.9511804 -1.03043286
## Stest20spelling 3642 -0.4191234 0.9671101 -0.26125817
## Stest21capitalization 3642 -0.8593189 1.0230130 -1.13661640
## Stest22punctuation 3642 -0.9019139 0.9821093 -1.04912472
## Stest23english 3642 -0.7026752 1.0872635 -0.70591842
## Stest24expression 3642 -0.6723303 1.0808223 -0.43699031
## Stest25wordfunctions 3642 -0.7847425 0.7999295 -0.93001676
## Stest26readingcomprehension 3642 -1.1869173 0.9780501 -1.35543630
## Stest28mechanicalreasoning 3642 -1.3049688 0.6162571 -1.46719079
## Stest29visualization2D 3642 -0.8971626 0.9881316 -1.00299976
## Stest30visualization3D 3642 -0.9572589 0.7740721 -0.96632617
## Stest31abstractreasoning 3642 -1.2023797 1.0962782 -1.25827171
## Stest32arithreasoning 3642 -1.1661807 0.7435679 -1.18159405
## Stest33highschoolmath 3642 -0.9221779 0.7029660 -1.13191711
## Stest34arithcomputation 3642 -1.0090058 1.1311203 -1.08283240
## Stest35tablereading 3642 -0.5028674 1.5899830 -0.27888648
## Stest36clericalchecking 3642 0.3031985 1.2764551 0.02048598
## Stest37objectinspection 3642 -0.2015085 1.1318854 -0.36841545
## Min Max 25th 75th
## Stest1vocab -3.081020 1.732398 -2.0676685 -0.80097967
## Stest2literature -2.695306 2.353911 -1.5976498 -0.49999415
## Stest3music -1.992064 2.096567 -1.6513451 -0.28846803
## Stest4socialstudies -2.857168 1.648629 -1.8776468 -0.70222154
## Stest5math -3.103322 1.578247 -1.4629972 -0.19790688
## Stest6physicalscience -1.991504 1.905107 -1.5044280 -0.53027520
## Stest7biologicalscience -2.278375 1.998107 -1.4230789 -0.14013417
## Stest8aeronautics -1.969735 1.691277 -1.9697348 -0.22298844
## Stest9electronics -3.215139 1.639827 -2.0508576 -0.51176132
## Stest10mechanics -2.422555 1.456406 -1.9053598 -0.87097023
## Stest11art -2.294194 2.141029 -1.8909920 -0.27818370
## Stest12law -2.188608 2.316614 -1.6254553 -0.49914972
## Stest13health -2.782038 1.492912 -1.7133008 -0.11019449
## Stest14bible -1.996349 2.243155 -1.0878838 -0.17941857
## Stest15theater -2.009254 1.949153 -1.4437671 -0.31279372
## Stest16miscellaneous -2.321753 2.351690 -1.7375724 -0.56921180
## Stest19disguisedwords -2.200294 2.040453 -1.6153635 -0.29926954
## Stest20spelling -2.949489 2.090944 -0.9333158 0.07477064
## Stest21capitalization -2.212520 1.792646 -1.7779803 -0.34408038
## Stest22punctuation -3.779898 1.909213 -1.5042536 -0.13886704
## Stest23english -5.175212 2.486434 -1.3443889 -0.06744796
## Stest24expression -3.654018 1.401311 -1.3561412 0.02258511
## Stest25wordfunctions -2.609127 1.788020 -1.1772477 -0.29229762
## Stest26readingcomprehension -3.158804 1.549990 -1.9565589 -0.55393946
## Stest28mechanicalreasoning -2.414006 1.373254 -1.7038945 -0.99378340
## Stest29visualization2D -2.283595 1.924074 -1.7347683 -0.27123122
## Stest30visualization3D -2.538855 2.178732 -1.5953378 -0.33731459
## Stest31abstractreasoning -3.053322 1.972819 -1.9762918 -0.27099409
## Stest32arithreasoning -2.327215 1.968863 -1.7544044 -0.89518887
## Stest33highschoolmath -2.147432 2.320833 -1.3350200 -0.52260833
## Stest34arithcomputation -3.938878 3.303237 -1.7968438 -0.36882102
## Stest35tablereading -4.815108 3.610163 -1.2852414 0.38398259
## Stest36clericalchecking -2.661621 2.630104 -0.7768972 1.45215119
## Stest37objectinspection -3.283883 2.401279 -0.9515090 0.50622493
## Skew Kurtosis
## Stest1vocab 0.535868058 -0.032645035
## Stest2literature 0.673434928 0.274137992
## Stest3music 0.725301546 -0.105540451
## Stest4socialstudies 0.572053653 -0.098694006
## Stest5math -0.352819327 -0.127331788
## Stest6physicalscience 0.914860918 0.771630247
## Stest7biologicalscience 0.397118046 -0.215019721
## Stest8aeronautics 0.071124573 -1.006045714
## Stest9electronics -0.605525468 -0.097425179
## Stest10mechanics 0.480307205 0.038007067
## Stest11art 0.744167443 -0.036572557
## Stest12law 0.484289110 0.044593284
## Stest13health 0.213760783 -0.813486890
## Stest14bible 0.632584515 0.118689706
## Stest15theater 0.713945372 0.126181418
## Stest16miscellaneous 0.394486339 -0.315192047
## Stest19disguisedwords 0.836665160 -0.007085817
## Stest20spelling 0.002357536 -0.387807405
## Stest21capitalization 0.563701708 -0.574558620
## Stest22punctuation 0.123386844 -0.302025868
## Stest23english -0.236414541 0.093257874
## Stest24expression -0.278535675 -0.439309073
## Stest25wordfunctions 0.548651694 0.412662989
## Stest26readingcomprehension 0.537123619 -0.413658623
## Stest28mechanicalreasoning 0.737112611 0.694206093
## Stest29visualization2D 0.616914647 -0.425638201
## Stest30visualization3D 0.467354756 0.133077169
## Stest31abstractreasoning 0.261892929 -0.790686145
## Stest32arithreasoning 0.967723776 1.133224623
## Stest33highschoolmath 0.952540727 1.271246103
## Stest34arithcomputation 0.406086185 0.574457758
## Stest35tablereading -0.573971387 0.882021013
## Stest36clericalchecking 0.351036496 -1.067695471
## Stest37objectinspection 0.324476372 -0.392041976
mvn(data = datagroup, mvnTest = "mardia")
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 21668.2674061215 0 NO
## 2 Mardia Kurtosis 21.0641034945153 0 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value
## 1 Anderson-Darling Stest1vocab 48.2718 <0.001
## 2 Anderson-Darling Stest2literature 63.8638 <0.001
## 3 Anderson-Darling Stest3music 132.7303 <0.001
## 4 Anderson-Darling Stest4socialstudies 65.7229 <0.001
## 5 Anderson-Darling Stest5math 58.4651 <0.001
## 6 Anderson-Darling Stest6physicalscience 117.1058 <0.001
## 7 Anderson-Darling Stest7biologicalscience 74.0470 <0.001
## 8 Anderson-Darling Stest8aeronautics 234.9478 <0.001
## 9 Anderson-Darling Stest9electronics 85.6461 <0.001
## 10 Anderson-Darling Stest10mechanics 70.7622 <0.001
## 11 Anderson-Darling Stest11art 126.7407 <0.001
## 12 Anderson-Darling Stest12law 130.1874 <0.001
## 13 Anderson-Darling Stest13health 91.9635 <0.001
## 14 Anderson-Darling Stest14bible 84.0249 <0.001
## 15 Anderson-Darling Stest15theater 171.8744 <0.001
## 16 Anderson-Darling Stest16miscellaneous 116.3917 <0.001
## 17 Anderson-Darling Stest19disguisedwords 139.9232 <0.001
## 18 Anderson-Darling Stest20spelling 30.1780 <0.001
## 19 Anderson-Darling Stest21capitalization 152.5606 <0.001
## 20 Anderson-Darling Stest22punctuation 16.1634 <0.001
## 21 Anderson-Darling Stest23english 23.6787 <0.001
## 22 Anderson-Darling Stest24expression 55.2359 <0.001
## 23 Anderson-Darling Stest25wordfunctions 64.1826 <0.001
## 24 Anderson-Darling Stest26readingcomprehension 72.4436 <0.001
## 25 Anderson-Darling Stest28mechanicalreasoning 97.9184 <0.001
## 26 Anderson-Darling Stest29visualization2D 78.4859 <0.001
## 27 Anderson-Darling Stest30visualization3D 57.8360 <0.001
## 28 Anderson-Darling Stest31abstractreasoning 57.5540 <0.001
## 29 Anderson-Darling Stest32arithreasoning 119.2201 <0.001
## 30 Anderson-Darling Stest33highschoolmath 102.6981 <0.001
## 31 Anderson-Darling Stest34arithcomputation 10.6258 <0.001
## 32 Anderson-Darling Stest35tablereading 76.0593 <0.001
## 33 Anderson-Darling Stest36clericalchecking 141.1956 <0.001
## 34 Anderson-Darling Stest37objectinspection 47.7660 <0.001
## Normality
## 1 NO
## 2 NO
## 3 NO
## 4 NO
## 5 NO
## 6 NO
## 7 NO
## 8 NO
## 9 NO
## 10 NO
## 11 NO
## 12 NO
## 13 NO
## 14 NO
## 15 NO
## 16 NO
## 17 NO
## 18 NO
## 19 NO
## 20 NO
## 21 NO
## 22 NO
## 23 NO
## 24 NO
## 25 NO
## 26 NO
## 27 NO
## 28 NO
## 29 NO
## 30 NO
## 31 NO
## 32 NO
## 33 NO
## 34 NO
##
## $Descriptives
## n Mean Std.Dev Median
## Stest1vocab 6085 -1.2270951 0.9869065 -1.3076552
## Stest2literature 6085 -0.9927036 0.9255459 -1.1585876
## Stest3music 6085 -0.8160930 0.9169976 -0.9699066
## Stest4socialstudies 6085 -1.1535256 0.9997235 -1.2899342
## Stest5math 6085 -0.8822309 1.0191384 -0.7002896
## Stest6physicalscience 6085 -0.8857970 0.7948740 -1.0173516
## Stest7biologicalscience 6085 -0.7300568 0.9064303 -0.9954306
## Stest8aeronautics 6085 -0.7456672 0.9326940 -0.8676605
## Stest9electronics 6085 -0.9309782 1.0513899 -0.8865762
## Stest10mechanics 6085 -1.0676062 0.8192249 -1.1295676
## Stest11art 6085 -1.0014295 0.9727845 -1.0845879
## Stest12law 6085 -0.8238996 0.8732055 -1.0623025
## Stest13health 6085 -1.0414978 1.1096419 -1.1789320
## Stest14bible 6085 -0.6115803 0.8733510 -0.7850621
## Stest15theater 6085 -0.8883170 0.8737799 -0.8782804
## Stest16miscellaneous 6085 -0.8863108 0.9735215 -1.1533921
## Stest19disguisedwords 6085 -0.8905205 0.9252168 -1.1766655
## Stest20spelling 6085 -0.5829844 1.0007505 -0.5972870
## Stest21capitalization 6085 -0.9734813 1.0022519 -1.1366164
## Stest22punctuation 6085 -1.0241805 0.9992056 -1.0491247
## Stest23english 6085 -0.8362356 1.1372716 -0.7059184
## Stest24expression 6085 -0.7837300 1.1248490 -0.8965657
## Stest25wordfunctions 6085 -0.8167652 0.7922195 -0.9300168
## Stest26readingcomprehension 6085 -1.2142523 1.0218114 -1.3554363
## Stest28mechanicalreasoning 6085 -1.0592902 0.8007023 -1.2304871
## Stest29visualization2D 6085 -0.7320590 1.0522279 -0.8200576
## Stest30visualization3D 6085 -0.8493621 0.8599248 -0.9663262
## Stest31abstractreasoning 6085 -1.1295355 1.1178724 -1.2582717
## Stest32arithreasoning 6085 -1.1100516 0.7904001 -1.1815940
## Stest33highschoolmath 6085 -0.8946355 0.7450916 -0.9288142
## Stest34arithcomputation 6085 -1.0629350 1.1362390 -1.0828324
## Stest35tablereading 6085 -0.5743500 1.6148560 -0.2788865
## Stest36clericalchecking 6085 0.1816066 1.2924821 -0.1244928
## Stest37objectinspection 6085 -0.2335661 1.1764773 -0.3684154
## Min Max 25th 75th
## Stest1vocab -3.081020 1.732398 -2.0676685 -0.54764189
## Stest2literature -2.695306 2.353911 -1.5976498 -0.49999415
## Stest3music -1.992064 2.096567 -1.6513451 -0.28846803
## Stest4socialstudies -2.857168 1.648629 -1.8776468 -0.50631732
## Stest5math -3.103322 1.578247 -1.4629972 -0.19790688
## Stest6physicalscience -1.991504 2.148645 -1.5044280 -0.53027520
## Stest7biologicalscience -2.278375 1.998107 -1.4230789 -0.14013417
## Stest8aeronautics -1.969735 1.691277 -1.9697348 -0.22298844
## Stest9electronics -3.215139 1.816802 -1.3697967 -0.20551524
## Stest10mechanics -2.422555 2.232198 -1.6467624 -0.61237285
## Stest11art -2.294194 2.141029 -1.8909920 -0.27818370
## Stest12law -2.188608 2.316614 -1.6254553 -0.49914972
## Stest13health -2.782038 1.492912 -1.7133008 -0.11019449
## Stest14bible -1.996349 2.243155 -1.3907055 -0.17941857
## Stest15theater -2.009254 1.949153 -1.4437671 -0.31279372
## Stest16miscellaneous -2.321753 2.935870 -1.7375724 0.01496852
## Stest19disguisedwords -2.200294 2.040453 -1.6153635 -0.29926954
## Stest20spelling -2.949489 2.090944 -1.2693446 0.07477064
## Stest21capitalization -2.212520 1.792646 -1.8990475 -0.34408038
## Stest22punctuation -4.007462 1.909213 -1.7318180 -0.36643146
## Stest23english -5.175212 2.486434 -1.6636241 -0.06744796
## Stest24expression -3.654018 1.401311 -1.3561412 0.02258511
## Stest25wordfunctions -2.609127 1.788020 -1.4507123 -0.49105015
## Stest26readingcomprehension -3.158804 1.549990 -2.0567460 -0.55393946
## Stest28mechanicalreasoning -2.414006 2.083365 -1.7038945 -0.52037602
## Stest29visualization2D -2.283595 1.924074 -1.5518262 0.09465304
## Stest30visualization3D -2.538855 2.178732 -1.5953378 -0.33731459
## Stest31abstractreasoning -3.053322 1.972819 -1.9762918 -0.18124158
## Stest32arithreasoning -2.327215 1.968863 -1.7544044 -0.60878369
## Stest33highschoolmath -2.147432 2.523936 -1.3350200 -0.52260833
## Stest34arithcomputation -3.938878 3.303237 -1.8988454 -0.36882102
## Stest35tablereading -4.815108 3.610163 -1.2852414 0.38398259
## Stest36clericalchecking -2.661621 2.630104 -0.8493866 1.25280540
## Stest37objectinspection -3.283883 2.401279 -1.0972824 0.50622493
## Skew Kurtosis
## Stest1vocab 0.47717287 -0.279692892
## Stest2literature 0.65838400 0.111610278
## Stest3music 0.77540391 -0.036745822
## Stest4socialstudies 0.58144787 -0.301113235
## Stest5math -0.30838742 -0.143546296
## Stest6physicalscience 0.94368855 0.704239904
## Stest7biologicalscience 0.39477216 -0.316576081
## Stest8aeronautics 0.13673454 -0.806627133
## Stest9electronics -0.35663855 0.009260749
## Stest10mechanics 0.67315403 0.205473093
## Stest11art 0.70873541 -0.128100196
## Stest12law 0.57216405 0.164709927
## Stest13health 0.28201206 -0.797594285
## Stest14bible 0.71245506 0.200747281
## Stest15theater 0.75154286 0.196907631
## Stest16miscellaneous 0.43365270 -0.335660266
## Stest19disguisedwords 0.92528173 0.250022067
## Stest20spelling 0.07162174 -0.414024867
## Stest21capitalization 0.66079326 -0.454749236
## Stest22punctuation 0.13503261 -0.273717815
## Stest23english -0.27221625 0.192916265
## Stest24expression -0.25731040 -0.526773408
## Stest25wordfunctions 0.52426120 0.439729052
## Stest26readingcomprehension 0.55267240 -0.482674838
## Stest28mechanicalreasoning 0.89527624 0.740797816
## Stest29visualization2D 0.46617489 -0.713633533
## Stest30visualization3D 0.49007612 -0.054286745
## Stest31abstractreasoning 0.22160144 -0.814732513
## Stest32arithreasoning 0.96214821 0.927072761
## Stest33highschoolmath 1.05266420 1.466811245
## Stest34arithcomputation 0.45360729 0.616927016
## Stest35tablereading -0.52240978 0.729341191
## Stest36clericalchecking 0.42520016 -1.016922782
## Stest37objectinspection 0.36212399 -0.456683319
mvn(data = datamale, mvnTest = "hz", multivariatePlot = "qq", multivariateOutlierMethod = "quan") # time consuming
## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 1.000159 0 NO
##
## $univariateNormality
## Test Variable Statistic p value
## 1 Anderson-Darling Stest1vocab 17.2962 <0.001
## 2 Anderson-Darling Stest2literature 28.6087 <0.001
## 3 Anderson-Darling Stest3music 62.5931 <0.001
## 4 Anderson-Darling Stest4socialstudies 31.6788 <0.001
## 5 Anderson-Darling Stest5math 19.8829 <0.001
## 6 Anderson-Darling Stest6physicalscience 39.4139 <0.001
## 7 Anderson-Darling Stest7biologicalscience 26.7368 <0.001
## 8 Anderson-Darling Stest8aeronautics 66.5155 <0.001
## 9 Anderson-Darling Stest9electronics 22.3116 <0.001
## 10 Anderson-Darling Stest10mechanics 11.9673 <0.001
## 11 Anderson-Darling Stest11art 49.6799 <0.001
## 12 Anderson-Darling Stest12law 51.1701 <0.001
## 13 Anderson-Darling Stest13health 43.6321 <0.001
## 14 Anderson-Darling Stest14bible 44.8686 <0.001
## 15 Anderson-Darling Stest15theater 78.1606 <0.001
## 16 Anderson-Darling Stest16miscellaneous 46.7119 <0.001
## 17 Anderson-Darling Stest19disguisedwords 60.6622 <0.001
## 18 Anderson-Darling Stest20spelling 13.5916 <0.001
## 19 Anderson-Darling Stest21capitalization 79.2095 <0.001
## 20 Anderson-Darling Stest22punctuation 7.0268 <0.001
## 21 Anderson-Darling Stest23english 9.7213 <0.001
## 22 Anderson-Darling Stest24expression 21.4125 <0.001
## 23 Anderson-Darling Stest25wordfunctions 23.0605 <0.001
## 24 Anderson-Darling Stest26readingcomprehension 39.6555 <0.001
## 25 Anderson-Darling Stest28mechanicalreasoning 22.9034 <0.001
## 26 Anderson-Darling Stest29visualization2D 22.3567 <0.001
## 27 Anderson-Darling Stest30visualization3D 19.6763 <0.001
## 28 Anderson-Darling Stest31abstractreasoning 21.9210 <0.001
## 29 Anderson-Darling Stest32arithreasoning 48.8610 <0.001
## 30 Anderson-Darling Stest33highschoolmath 49.4632 <0.001
## 31 Anderson-Darling Stest34arithcomputation 5.6482 <0.001
## 32 Anderson-Darling Stest35tablereading 26.8353 <0.001
## 33 Anderson-Darling Stest36clericalchecking 70.2704 <0.001
## 34 Anderson-Darling Stest37objectinspection 26.1694 <0.001
## Normality
## 1 NO
## 2 NO
## 3 NO
## 4 NO
## 5 NO
## 6 NO
## 7 NO
## 8 NO
## 9 NO
## 10 NO
## 11 NO
## 12 NO
## 13 NO
## 14 NO
## 15 NO
## 16 NO
## 17 NO
## 18 NO
## 19 NO
## 20 NO
## 21 NO
## 22 NO
## 23 NO
## 24 NO
## 25 NO
## 26 NO
## 27 NO
## 28 NO
## 29 NO
## 30 NO
## 31 NO
## 32 NO
## 33 NO
## 34 NO
##
## $Descriptives
## n Mean Std.Dev Median
## Stest1vocab 2443 -1.1095892563 1.0621130 -1.3076552
## Stest2literature 2443 -0.9945907006 0.9693893 -1.1585876
## Stest3music 2443 -0.8760449097 0.9107866 -0.9699066
## Stest4socialstudies 2443 -1.0337270784 1.1153862 -1.2899342
## Stest5math 2443 -0.7896922969 1.0531123 -0.7002896
## Stest6physicalscience 2443 -0.7052279449 0.8948063 -0.7738134
## Stest7biologicalscience 2443 -0.6026174421 0.9747421 -0.5677824
## Stest8aeronautics 2443 -0.4869574146 1.0100620 -0.2229884
## Stest9electronics 2443 -0.6218183114 1.1050936 -0.5117613
## Stest10mechanics 2443 -0.6318496885 0.8917348 -0.6123728
## Stest11art 2443 -1.0040464783 0.9595535 -1.0845879
## Stest12law 2443 -0.7453417674 0.9366330 -1.0623025
## Stest13health 2443 -1.1566211046 1.1020137 -1.1789320
## Stest14bible 2443 -0.7012685645 0.8651236 -0.7850621
## Stest15theater 2443 -0.9981830125 0.8264665 -0.8782804
## Stest16miscellaneous 2443 -0.8382264779 1.0478540 -1.1533921
## Stest19disguisedwords 2443 -0.9650082562 0.8800368 -1.1766655
## Stest20spelling 2443 -0.8272665823 1.0004359 -0.9333158
## Stest21capitalization 2443 -1.1436734095 0.9454176 -1.4082177
## Stest22punctuation 2443 -1.2064543525 0.9968915 -1.2766891
## Stest23english 2443 -1.0353461760 1.1804729 -1.0251536
## Stest24expression 2443 -0.9498035005 1.1681145 -0.8965657
## Stest25wordfunctions 2443 -0.8645041762 0.7783038 -0.9300168
## Stest26readingcomprehension 2443 -1.2550031376 1.0826988 -1.4556234
## Stest28mechanicalreasoning 2443 -0.6930350339 0.8982447 -0.7570797
## Stest29visualization2D 2443 -0.4859242630 1.0960685 -0.4541734
## Stest30visualization3D 2443 -0.6885105790 0.9516764 -0.6518204
## Stest31abstractreasoning 2443 -1.0209400576 1.1409325 -0.8992617
## Stest32arithreasoning 2443 -1.0263748677 0.8487616 -1.1815940
## Stest33highschoolmath 2443 -0.8535754828 0.8021980 -0.9288142
## Stest34arithcomputation 2443 -1.1433319274 1.1393281 -1.1848340
## Stest35tablereading 2443 -0.6809154199 1.6458126 -0.4864526
## Stest36clericalchecking 2443 0.0003385028 1.2952453 -0.4144503
## Stest37objectinspection 2443 -0.2813571657 1.2386776 -0.5141888
## Min Max 25th 75th
## Stest1vocab -3.081020 1.732398 -1.9409997 -0.29430412
## Stest2literature -2.695306 2.134379 -1.8171810 -0.49999415
## Stest3music -1.992064 2.096567 -1.6513451 -0.28846803
## Stest4socialstudies -2.857168 1.648629 -1.8776468 -0.31041310
## Stest5math -3.103322 1.578247 -1.4629972 -0.19790688
## Stest6physicalscience -1.991504 2.148645 -1.5044280 -0.28673699
## Stest7biologicalscience -2.278375 1.998107 -1.4230789 -0.14013417
## Stest8aeronautics -1.969735 1.691277 -0.8676605 0.23441370
## Stest9electronics -3.215139 1.816802 -1.3697967 0.05341212
## Stest10mechanics -2.422555 2.232198 -1.3881650 -0.09517808
## Stest11art -2.294194 2.141029 -1.8909920 -0.27818370
## Stest12law -2.188608 2.316614 -1.6254553 0.06400306
## Stest13health -2.782038 1.492912 -2.2476696 -0.11019449
## Stest14bible -1.996349 2.243155 -1.3907055 -0.17941857
## Stest15theater -2.009254 1.949153 -1.4437671 -0.31279372
## Stest16miscellaneous -2.321753 2.935870 -1.7375724 0.01496852
## Stest19disguisedwords -2.200294 2.040453 -1.6153635 -0.44550220
## Stest20spelling -2.949489 2.090944 -1.6053734 -0.26125817
## Stest21capitalization -2.212520 1.792646 -1.9895058 -0.34408038
## Stest22punctuation -4.007462 1.909213 -1.9593824 -0.59399588
## Stest23english -5.175212 2.486434 -1.6636241 -0.38668319
## Stest24expression -3.654018 1.401311 -1.8157166 0.02258511
## Stest25wordfunctions -2.609127 1.665905 -1.4507123 -0.49105015
## Stest26readingcomprehension -3.158804 1.549990 -2.1569331 -0.55393946
## Stest28mechanicalreasoning -2.414006 2.083365 -1.4671908 -0.04696863
## Stest29visualization2D -2.283595 1.924074 -1.5518262 0.27759518
## Stest30visualization3D -2.538855 2.178732 -1.2808320 -0.02280880
## Stest31abstractreasoning -3.053322 1.972819 -1.9762918 -0.18124158
## Stest32arithreasoning -2.327215 1.968863 -1.7544044 -0.60878369
## Stest33highschoolmath -2.147432 2.523936 -1.3350200 -0.52260833
## Stest34arithcomputation -3.938878 3.201236 -2.0008470 -0.47082264
## Stest35tablereading -4.815108 3.610163 -1.6444251 0.38398259
## Stest36clericalchecking -2.661621 2.630104 -0.9943653 0.99909258
## Stest37objectinspection -3.283883 2.401279 -1.2430558 0.50622493
## Skew Kurtosis
## Stest1vocab 0.34510687 -0.59976692
## Stest2literature 0.63787571 -0.10633742
## Stest3music 0.85660701 0.09551652
## Stest4socialstudies 0.47628668 -0.71164871
## Stest5math -0.28834814 -0.19402440
## Stest6physicalscience 0.76509425 0.08850632
## Stest7biologicalscience 0.30504439 -0.54731463
## Stest8aeronautics -0.04590821 -0.89545568
## Stest9electronics -0.39215567 -0.03900773
## Stest10mechanics 0.22994082 -0.42619009
## Stest11art 0.65101238 -0.28537963
## Stest12law 0.60619691 0.08045298
## Stest13health 0.39011295 -0.73203792
## Stest14bible 0.84828024 0.41410836
## Stest15theater 0.78321829 0.23119127
## Stest16miscellaneous 0.43761686 -0.47478304
## Stest19disguisedwords 1.06086785 0.72556634
## Stest20spelling 0.23127394 -0.31405639
## Stest21capitalization 0.80707774 -0.23153238
## Stest22punctuation 0.18223440 -0.22045506
## Stest23english -0.25160293 0.21859560
## Stest24expression -0.18049493 -0.66948911
## Stest25wordfunctions 0.47884776 0.45276250
## Stest26readingcomprehension 0.58767258 -0.57755544
## Stest28mechanicalreasoning 0.54024097 -0.17789919
## Stest29visualization2D 0.22119256 -0.96147180
## Stest30visualization3D 0.35150508 -0.46924804
## Stest31abstractreasoning 0.15046639 -0.84825866
## Stest32arithreasoning 0.89612583 0.54144588
## Stest33highschoolmath 1.10968463 1.40578035
## Stest34arithcomputation 0.53147902 0.72304444
## Stest35tablereading -0.44457343 0.54651004
## Stest36clericalchecking 0.56498656 -0.88599275
## Stest37objectinspection 0.42282433 -0.54254508
mvn(data = datafemale, mvnTest = "hz", multivariatePlot = "qq", multivariateOutlierMethod = "quan") # time consuming
## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 1.000111 0 NO
##
## $univariateNormality
## Test Variable Statistic p value
## 1 Anderson-Darling Stest1vocab 29.6155 <0.001
## 2 Anderson-Darling Stest2literature 36.2554 <0.001
## 3 Anderson-Darling Stest3music 71.8574 <0.001
## 4 Anderson-Darling Stest4socialstudies 30.9935 <0.001
## 5 Anderson-Darling Stest5math 40.5679 <0.001
## 6 Anderson-Darling Stest6physicalscience 65.7130 <0.001
## 7 Anderson-Darling Stest7biologicalscience 47.3995 <0.001
## 8 Anderson-Darling Stest8aeronautics 197.6227 <0.001
## 9 Anderson-Darling Stest9electronics 86.2056 <0.001
## 10 Anderson-Darling Stest10mechanics 37.8697 <0.001
## 11 Anderson-Darling Stest11art 77.7074 <0.001
## 12 Anderson-Darling Stest12law 80.0334 <0.001
## 13 Anderson-Darling Stest13health 50.0620 <0.001
## 14 Anderson-Darling Stest14bible 41.6359 <0.001
## 15 Anderson-Darling Stest15theater 95.1835 <0.001
## 16 Anderson-Darling Stest16miscellaneous 71.5141 <0.001
## 17 Anderson-Darling Stest19disguisedwords 77.7550 <0.001
## 18 Anderson-Darling Stest20spelling 18.8864 <0.001
## 19 Anderson-Darling Stest21capitalization 76.8646 <0.001
## 20 Anderson-Darling Stest22punctuation 10.1089 <0.001
## 21 Anderson-Darling Stest23english 14.3929 <0.001
## 22 Anderson-Darling Stest24expression 34.0889 <0.001
## 23 Anderson-Darling Stest25wordfunctions 41.3657 <0.001
## 24 Anderson-Darling Stest26readingcomprehension 36.4058 <0.001
## 25 Anderson-Darling Stest28mechanicalreasoning 44.7846 <0.001
## 26 Anderson-Darling Stest29visualization2D 55.7612 <0.001
## 27 Anderson-Darling Stest30visualization3D 34.3835 <0.001
## 28 Anderson-Darling Stest31abstractreasoning 35.9934 <0.001
## 29 Anderson-Darling Stest32arithreasoning 66.7532 <0.001
## 30 Anderson-Darling Stest33highschoolmath 51.9887 <0.001
## 31 Anderson-Darling Stest34arithcomputation 5.6984 <0.001
## 32 Anderson-Darling Stest35tablereading 49.6425 <0.001
## 33 Anderson-Darling Stest36clericalchecking 76.8501 <0.001
## 34 Anderson-Darling Stest37objectinspection 24.2471 <0.001
## Normality
## 1 NO
## 2 NO
## 3 NO
## 4 NO
## 5 NO
## 6 NO
## 7 NO
## 8 NO
## 9 NO
## 10 NO
## 11 NO
## 12 NO
## 13 NO
## 14 NO
## 15 NO
## 16 NO
## 17 NO
## 18 NO
## 19 NO
## 20 NO
## 21 NO
## 22 NO
## 23 NO
## 24 NO
## 25 NO
## 26 NO
## 27 NO
## 28 NO
## 29 NO
## 30 NO
## 31 NO
## 32 NO
## 33 NO
## 34 NO
##
## $Descriptives
## n Mean Std.Dev Median
## Stest1vocab 3642 -1.3059162 0.9248888 -1.30765522
## Stest2literature 3642 -0.9914377 0.8950670 -1.15858756
## Stest3music 3642 -0.7758781 0.9190758 -0.96990659
## Stest4socialstudies 3642 -1.2338847 0.9052924 -1.28993419
## Stest5math 3642 -0.9443045 0.9910145 -0.70028957
## Stest6physicalscience 3642 -1.0069200 0.6944041 -1.01735162
## Stest7biologicalscience 3642 -0.8155413 0.8470220 -0.99543064
## Stest8aeronautics 3642 -0.9192058 0.8332552 -0.86766055
## Stest9electronics 3642 -1.1383580 0.9596358 -0.88657622
## Stest10mechanics 3642 -1.3599053 0.6125667 -1.38816500
## Stest11art 3642 -0.9996741 0.9816871 -1.08458787
## Stest12law 3642 -0.8765951 0.8238857 -1.06230250
## Stest13health 3642 -0.9642748 1.1081972 -1.17893204
## Stest14bible 3642 -0.5514187 0.8738003 -0.78506205
## Stest15theater 3642 -0.8146204 0.8967290 -0.87828039
## Stest16miscellaneous 3642 -0.9185651 0.9190418 -1.15339212
## Stest19disguisedwords 3642 -0.8405552 0.9511804 -1.03043286
## Stest20spelling 3642 -0.4191234 0.9671101 -0.26125817
## Stest21capitalization 3642 -0.8593189 1.0230130 -1.13661640
## Stest22punctuation 3642 -0.9019139 0.9821093 -1.04912472
## Stest23english 3642 -0.7026752 1.0872635 -0.70591842
## Stest24expression 3642 -0.6723303 1.0808223 -0.43699031
## Stest25wordfunctions 3642 -0.7847425 0.7999295 -0.93001676
## Stest26readingcomprehension 3642 -1.1869173 0.9780501 -1.35543630
## Stest28mechanicalreasoning 3642 -1.3049688 0.6162571 -1.46719079
## Stest29visualization2D 3642 -0.8971626 0.9881316 -1.00299976
## Stest30visualization3D 3642 -0.9572589 0.7740721 -0.96632617
## Stest31abstractreasoning 3642 -1.2023797 1.0962782 -1.25827171
## Stest32arithreasoning 3642 -1.1661807 0.7435679 -1.18159405
## Stest33highschoolmath 3642 -0.9221779 0.7029660 -1.13191711
## Stest34arithcomputation 3642 -1.0090058 1.1311203 -1.08283240
## Stest35tablereading 3642 -0.5028674 1.5899830 -0.27888648
## Stest36clericalchecking 3642 0.3031985 1.2764551 0.02048598
## Stest37objectinspection 3642 -0.2015085 1.1318854 -0.36841545
## Min Max 25th 75th
## Stest1vocab -3.081020 1.732398 -2.0676685 -0.80097967
## Stest2literature -2.695306 2.353911 -1.5976498 -0.49999415
## Stest3music -1.992064 2.096567 -1.6513451 -0.28846803
## Stest4socialstudies -2.857168 1.648629 -1.8776468 -0.70222154
## Stest5math -3.103322 1.578247 -1.4629972 -0.19790688
## Stest6physicalscience -1.991504 1.905107 -1.5044280 -0.53027520
## Stest7biologicalscience -2.278375 1.998107 -1.4230789 -0.14013417
## Stest8aeronautics -1.969735 1.691277 -1.9697348 -0.22298844
## Stest9electronics -3.215139 1.639827 -2.0508576 -0.51176132
## Stest10mechanics -2.422555 1.456406 -1.9053598 -0.87097023
## Stest11art -2.294194 2.141029 -1.8909920 -0.27818370
## Stest12law -2.188608 2.316614 -1.6254553 -0.49914972
## Stest13health -2.782038 1.492912 -1.7133008 -0.11019449
## Stest14bible -1.996349 2.243155 -1.0878838 -0.17941857
## Stest15theater -2.009254 1.949153 -1.4437671 -0.31279372
## Stest16miscellaneous -2.321753 2.351690 -1.7375724 -0.56921180
## Stest19disguisedwords -2.200294 2.040453 -1.6153635 -0.29926954
## Stest20spelling -2.949489 2.090944 -0.9333158 0.07477064
## Stest21capitalization -2.212520 1.792646 -1.7779803 -0.34408038
## Stest22punctuation -3.779898 1.909213 -1.5042536 -0.13886704
## Stest23english -5.175212 2.486434 -1.3443889 -0.06744796
## Stest24expression -3.654018 1.401311 -1.3561412 0.02258511
## Stest25wordfunctions -2.609127 1.788020 -1.1772477 -0.29229762
## Stest26readingcomprehension -3.158804 1.549990 -1.9565589 -0.55393946
## Stest28mechanicalreasoning -2.414006 1.373254 -1.7038945 -0.99378340
## Stest29visualization2D -2.283595 1.924074 -1.7347683 -0.27123122
## Stest30visualization3D -2.538855 2.178732 -1.5953378 -0.33731459
## Stest31abstractreasoning -3.053322 1.972819 -1.9762918 -0.27099409
## Stest32arithreasoning -2.327215 1.968863 -1.7544044 -0.89518887
## Stest33highschoolmath -2.147432 2.320833 -1.3350200 -0.52260833
## Stest34arithcomputation -3.938878 3.303237 -1.7968438 -0.36882102
## Stest35tablereading -4.815108 3.610163 -1.2852414 0.38398259
## Stest36clericalchecking -2.661621 2.630104 -0.7768972 1.45215119
## Stest37objectinspection -3.283883 2.401279 -0.9515090 0.50622493
## Skew Kurtosis
## Stest1vocab 0.535868058 -0.032645035
## Stest2literature 0.673434928 0.274137992
## Stest3music 0.725301546 -0.105540451
## Stest4socialstudies 0.572053653 -0.098694006
## Stest5math -0.352819327 -0.127331788
## Stest6physicalscience 0.914860918 0.771630247
## Stest7biologicalscience 0.397118046 -0.215019721
## Stest8aeronautics 0.071124573 -1.006045714
## Stest9electronics -0.605525468 -0.097425179
## Stest10mechanics 0.480307205 0.038007067
## Stest11art 0.744167443 -0.036572557
## Stest12law 0.484289110 0.044593284
## Stest13health 0.213760783 -0.813486890
## Stest14bible 0.632584515 0.118689706
## Stest15theater 0.713945372 0.126181418
## Stest16miscellaneous 0.394486339 -0.315192047
## Stest19disguisedwords 0.836665160 -0.007085817
## Stest20spelling 0.002357536 -0.387807405
## Stest21capitalization 0.563701708 -0.574558620
## Stest22punctuation 0.123386844 -0.302025868
## Stest23english -0.236414541 0.093257874
## Stest24expression -0.278535675 -0.439309073
## Stest25wordfunctions 0.548651694 0.412662989
## Stest26readingcomprehension 0.537123619 -0.413658623
## Stest28mechanicalreasoning 0.737112611 0.694206093
## Stest29visualization2D 0.616914647 -0.425638201
## Stest30visualization3D 0.467354756 0.133077169
## Stest31abstractreasoning 0.261892929 -0.790686145
## Stest32arithreasoning 0.967723776 1.133224623
## Stest33highschoolmath 0.952540727 1.271246103
## Stest34arithcomputation 0.406086185 0.574457758
## Stest35tablereading -0.573971387 0.882021013
## Stest36clericalchecking 0.351036496 -1.067695471
## Stest37objectinspection 0.324476372 -0.392041976
mvn(data = datagroup, mvnTest = "hz", multivariatePlot = "qq", multivariateOutlierMethod = "quan") # time consuming
## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 1.000212 0 NO
##
## $univariateNormality
## Test Variable Statistic p value
## 1 Anderson-Darling Stest1vocab 48.2718 <0.001
## 2 Anderson-Darling Stest2literature 63.8638 <0.001
## 3 Anderson-Darling Stest3music 132.7303 <0.001
## 4 Anderson-Darling Stest4socialstudies 65.7229 <0.001
## 5 Anderson-Darling Stest5math 58.4651 <0.001
## 6 Anderson-Darling Stest6physicalscience 117.1058 <0.001
## 7 Anderson-Darling Stest7biologicalscience 74.0470 <0.001
## 8 Anderson-Darling Stest8aeronautics 234.9478 <0.001
## 9 Anderson-Darling Stest9electronics 85.6461 <0.001
## 10 Anderson-Darling Stest10mechanics 70.7622 <0.001
## 11 Anderson-Darling Stest11art 126.7407 <0.001
## 12 Anderson-Darling Stest12law 130.1874 <0.001
## 13 Anderson-Darling Stest13health 91.9635 <0.001
## 14 Anderson-Darling Stest14bible 84.0249 <0.001
## 15 Anderson-Darling Stest15theater 171.8744 <0.001
## 16 Anderson-Darling Stest16miscellaneous 116.3917 <0.001
## 17 Anderson-Darling Stest19disguisedwords 139.9232 <0.001
## 18 Anderson-Darling Stest20spelling 30.1780 <0.001
## 19 Anderson-Darling Stest21capitalization 152.5606 <0.001
## 20 Anderson-Darling Stest22punctuation 16.1634 <0.001
## 21 Anderson-Darling Stest23english 23.6787 <0.001
## 22 Anderson-Darling Stest24expression 55.2359 <0.001
## 23 Anderson-Darling Stest25wordfunctions 64.1826 <0.001
## 24 Anderson-Darling Stest26readingcomprehension 72.4436 <0.001
## 25 Anderson-Darling Stest28mechanicalreasoning 97.9184 <0.001
## 26 Anderson-Darling Stest29visualization2D 78.4859 <0.001
## 27 Anderson-Darling Stest30visualization3D 57.8360 <0.001
## 28 Anderson-Darling Stest31abstractreasoning 57.5540 <0.001
## 29 Anderson-Darling Stest32arithreasoning 119.2201 <0.001
## 30 Anderson-Darling Stest33highschoolmath 102.6981 <0.001
## 31 Anderson-Darling Stest34arithcomputation 10.6258 <0.001
## 32 Anderson-Darling Stest35tablereading 76.0593 <0.001
## 33 Anderson-Darling Stest36clericalchecking 141.1956 <0.001
## 34 Anderson-Darling Stest37objectinspection 47.7660 <0.001
## Normality
## 1 NO
## 2 NO
## 3 NO
## 4 NO
## 5 NO
## 6 NO
## 7 NO
## 8 NO
## 9 NO
## 10 NO
## 11 NO
## 12 NO
## 13 NO
## 14 NO
## 15 NO
## 16 NO
## 17 NO
## 18 NO
## 19 NO
## 20 NO
## 21 NO
## 22 NO
## 23 NO
## 24 NO
## 25 NO
## 26 NO
## 27 NO
## 28 NO
## 29 NO
## 30 NO
## 31 NO
## 32 NO
## 33 NO
## 34 NO
##
## $Descriptives
## n Mean Std.Dev Median
## Stest1vocab 6085 -1.2270951 0.9869065 -1.3076552
## Stest2literature 6085 -0.9927036 0.9255459 -1.1585876
## Stest3music 6085 -0.8160930 0.9169976 -0.9699066
## Stest4socialstudies 6085 -1.1535256 0.9997235 -1.2899342
## Stest5math 6085 -0.8822309 1.0191384 -0.7002896
## Stest6physicalscience 6085 -0.8857970 0.7948740 -1.0173516
## Stest7biologicalscience 6085 -0.7300568 0.9064303 -0.9954306
## Stest8aeronautics 6085 -0.7456672 0.9326940 -0.8676605
## Stest9electronics 6085 -0.9309782 1.0513899 -0.8865762
## Stest10mechanics 6085 -1.0676062 0.8192249 -1.1295676
## Stest11art 6085 -1.0014295 0.9727845 -1.0845879
## Stest12law 6085 -0.8238996 0.8732055 -1.0623025
## Stest13health 6085 -1.0414978 1.1096419 -1.1789320
## Stest14bible 6085 -0.6115803 0.8733510 -0.7850621
## Stest15theater 6085 -0.8883170 0.8737799 -0.8782804
## Stest16miscellaneous 6085 -0.8863108 0.9735215 -1.1533921
## Stest19disguisedwords 6085 -0.8905205 0.9252168 -1.1766655
## Stest20spelling 6085 -0.5829844 1.0007505 -0.5972870
## Stest21capitalization 6085 -0.9734813 1.0022519 -1.1366164
## Stest22punctuation 6085 -1.0241805 0.9992056 -1.0491247
## Stest23english 6085 -0.8362356 1.1372716 -0.7059184
## Stest24expression 6085 -0.7837300 1.1248490 -0.8965657
## Stest25wordfunctions 6085 -0.8167652 0.7922195 -0.9300168
## Stest26readingcomprehension 6085 -1.2142523 1.0218114 -1.3554363
## Stest28mechanicalreasoning 6085 -1.0592902 0.8007023 -1.2304871
## Stest29visualization2D 6085 -0.7320590 1.0522279 -0.8200576
## Stest30visualization3D 6085 -0.8493621 0.8599248 -0.9663262
## Stest31abstractreasoning 6085 -1.1295355 1.1178724 -1.2582717
## Stest32arithreasoning 6085 -1.1100516 0.7904001 -1.1815940
## Stest33highschoolmath 6085 -0.8946355 0.7450916 -0.9288142
## Stest34arithcomputation 6085 -1.0629350 1.1362390 -1.0828324
## Stest35tablereading 6085 -0.5743500 1.6148560 -0.2788865
## Stest36clericalchecking 6085 0.1816066 1.2924821 -0.1244928
## Stest37objectinspection 6085 -0.2335661 1.1764773 -0.3684154
## Min Max 25th 75th
## Stest1vocab -3.081020 1.732398 -2.0676685 -0.54764189
## Stest2literature -2.695306 2.353911 -1.5976498 -0.49999415
## Stest3music -1.992064 2.096567 -1.6513451 -0.28846803
## Stest4socialstudies -2.857168 1.648629 -1.8776468 -0.50631732
## Stest5math -3.103322 1.578247 -1.4629972 -0.19790688
## Stest6physicalscience -1.991504 2.148645 -1.5044280 -0.53027520
## Stest7biologicalscience -2.278375 1.998107 -1.4230789 -0.14013417
## Stest8aeronautics -1.969735 1.691277 -1.9697348 -0.22298844
## Stest9electronics -3.215139 1.816802 -1.3697967 -0.20551524
## Stest10mechanics -2.422555 2.232198 -1.6467624 -0.61237285
## Stest11art -2.294194 2.141029 -1.8909920 -0.27818370
## Stest12law -2.188608 2.316614 -1.6254553 -0.49914972
## Stest13health -2.782038 1.492912 -1.7133008 -0.11019449
## Stest14bible -1.996349 2.243155 -1.3907055 -0.17941857
## Stest15theater -2.009254 1.949153 -1.4437671 -0.31279372
## Stest16miscellaneous -2.321753 2.935870 -1.7375724 0.01496852
## Stest19disguisedwords -2.200294 2.040453 -1.6153635 -0.29926954
## Stest20spelling -2.949489 2.090944 -1.2693446 0.07477064
## Stest21capitalization -2.212520 1.792646 -1.8990475 -0.34408038
## Stest22punctuation -4.007462 1.909213 -1.7318180 -0.36643146
## Stest23english -5.175212 2.486434 -1.6636241 -0.06744796
## Stest24expression -3.654018 1.401311 -1.3561412 0.02258511
## Stest25wordfunctions -2.609127 1.788020 -1.4507123 -0.49105015
## Stest26readingcomprehension -3.158804 1.549990 -2.0567460 -0.55393946
## Stest28mechanicalreasoning -2.414006 2.083365 -1.7038945 -0.52037602
## Stest29visualization2D -2.283595 1.924074 -1.5518262 0.09465304
## Stest30visualization3D -2.538855 2.178732 -1.5953378 -0.33731459
## Stest31abstractreasoning -3.053322 1.972819 -1.9762918 -0.18124158
## Stest32arithreasoning -2.327215 1.968863 -1.7544044 -0.60878369
## Stest33highschoolmath -2.147432 2.523936 -1.3350200 -0.52260833
## Stest34arithcomputation -3.938878 3.303237 -1.8988454 -0.36882102
## Stest35tablereading -4.815108 3.610163 -1.2852414 0.38398259
## Stest36clericalchecking -2.661621 2.630104 -0.8493866 1.25280540
## Stest37objectinspection -3.283883 2.401279 -1.0972824 0.50622493
## Skew Kurtosis
## Stest1vocab 0.47717287 -0.279692892
## Stest2literature 0.65838400 0.111610278
## Stest3music 0.77540391 -0.036745822
## Stest4socialstudies 0.58144787 -0.301113235
## Stest5math -0.30838742 -0.143546296
## Stest6physicalscience 0.94368855 0.704239904
## Stest7biologicalscience 0.39477216 -0.316576081
## Stest8aeronautics 0.13673454 -0.806627133
## Stest9electronics -0.35663855 0.009260749
## Stest10mechanics 0.67315403 0.205473093
## Stest11art 0.70873541 -0.128100196
## Stest12law 0.57216405 0.164709927
## Stest13health 0.28201206 -0.797594285
## Stest14bible 0.71245506 0.200747281
## Stest15theater 0.75154286 0.196907631
## Stest16miscellaneous 0.43365270 -0.335660266
## Stest19disguisedwords 0.92528173 0.250022067
## Stest20spelling 0.07162174 -0.414024867
## Stest21capitalization 0.66079326 -0.454749236
## Stest22punctuation 0.13503261 -0.273717815
## Stest23english -0.27221625 0.192916265
## Stest24expression -0.25731040 -0.526773408
## Stest25wordfunctions 0.52426120 0.439729052
## Stest26readingcomprehension 0.55267240 -0.482674838
## Stest28mechanicalreasoning 0.89527624 0.740797816
## Stest29visualization2D 0.46617489 -0.713633533
## Stest30visualization3D 0.49007612 -0.054286745
## Stest31abstractreasoning 0.22160144 -0.814732513
## Stest32arithreasoning 0.96214821 0.927072761
## Stest33highschoolmath 1.05266420 1.466811245
## Stest34arithcomputation 0.45360729 0.616927016
## Stest35tablereading -0.52240978 0.729341191
## Stest36clericalchecking 0.42520016 -1.016922782
## Stest37objectinspection 0.36212399 -0.456683319
# standardized loadings for Jensen's MCV
FAmale<-fa(r=datamale, nfactors=6, max.iter=100, warnings=TRUE, rotate="none", fm="pa", weight=dmale$BY_WTA)
print(FAmale, digits=2, cutoff=.10)
## Factor Analysis using method = pa
## Call: fa(r = datamale, nfactors = 6, rotate = "none", max.iter = 100,
## warnings = TRUE, fm = "pa", weight = dmale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 PA3 PA4 PA5 PA6 h2
## Stest1vocab 0.87 -0.12 0.07 0.06 -0.02 0.11 0.78
## Stest2literature 0.82 -0.15 0.12 0.08 0.05 -0.10 0.72
## Stest3music 0.73 -0.11 0.11 0.07 0.11 -0.12 0.59
## Stest4socialstudies 0.85 -0.13 0.13 0.02 -0.05 -0.03 0.76
## Stest5math 0.68 -0.02 0.03 0.01 -0.23 -0.07 0.53
## Stest6physicalscience 0.78 -0.12 -0.01 0.14 -0.16 0.04 0.67
## Stest7biologicalscience 0.70 -0.11 0.03 0.08 -0.02 0.13 0.52
## Stest8aeronautics 0.58 -0.13 0.06 0.23 -0.04 0.04 0.41
## Stest9electronics 0.62 -0.10 -0.01 0.24 -0.19 0.16 0.52
## Stest10mechanics 0.70 -0.08 -0.01 0.14 -0.10 0.26 0.60
## Stest11art 0.74 -0.12 0.11 0.12 0.17 -0.10 0.63
## Stest12law 0.67 -0.12 0.08 0.05 0.02 -0.07 0.48
## Stest13health 0.74 -0.10 0.12 0.04 0.03 0.02 0.57
## Stest14bible 0.66 -0.09 0.14 0.00 0.06 -0.08 0.48
## Stest15theater 0.68 -0.15 0.15 0.02 0.17 -0.12 0.55
## Stest16miscellaneous 0.71 -0.09 0.15 0.07 0.06 -0.05 0.54
## Stest19disguisedwords 0.69 0.13 0.09 -0.11 0.12 0.04 0.53
## Stest20spelling 0.62 0.00 0.11 -0.35 -0.01 0.16 0.54
## Stest21capitalization 0.70 0.04 -0.08 -0.22 0.09 0.07 0.56
## Stest22punctuation 0.74 0.06 -0.12 -0.27 0.03 0.08 0.65
## Stest23english 0.69 0.07 -0.05 -0.20 0.11 0.19 0.57
## Stest24expression 0.56 -0.01 -0.10 -0.21 0.08 0.06 0.38
## Stest25wordfunctions 0.56 0.04 -0.11 -0.17 -0.05 -0.14 0.38
## Stest26readingcomprehension 0.89 -0.10 0.01 -0.08 0.08 -0.04 0.81
## Stest28mechanicalreasoning 0.65 0.13 -0.35 0.24 0.02 0.08 0.63
## Stest29visualization2D 0.45 0.33 -0.27 0.10 0.10 0.05 0.41
## Stest30visualization3D 0.50 0.17 -0.41 0.20 0.09 -0.08 0.50
## Stest31abstractreasoning 0.65 0.16 -0.34 0.02 0.08 -0.06 0.57
## Stest32arithreasoning 0.70 0.01 -0.16 -0.08 -0.13 -0.17 0.56
## Stest33highschoolmath 0.73 0.05 -0.16 -0.15 -0.28 -0.21 0.70
## Stest34arithcomputation 0.59 0.38 0.11 -0.19 -0.16 0.00 0.56
## Stest35tablereading 0.38 0.52 0.17 0.05 -0.02 -0.07 0.45
## Stest36clericalchecking 0.17 0.56 0.38 0.07 -0.05 0.02 0.50
## Stest37objectinspection 0.25 0.59 0.13 0.20 0.07 0.01 0.48
## u2 com
## Stest1vocab 0.22 1.1
## Stest2literature 0.28 1.2
## Stest3music 0.41 1.2
## Stest4socialstudies 0.24 1.1
## Stest5math 0.47 1.2
## Stest6physicalscience 0.33 1.2
## Stest7biologicalscience 0.48 1.2
## Stest8aeronautics 0.59 1.5
## Stest9electronics 0.48 1.7
## Stest10mechanics 0.40 1.5
## Stest11art 0.37 1.3
## Stest12law 0.52 1.1
## Stest13health 0.43 1.1
## Stest14bible 0.52 1.2
## Stest15theater 0.45 1.4
## Stest16miscellaneous 0.46 1.2
## Stest19disguisedwords 0.47 1.2
## Stest20spelling 0.46 1.8
## Stest21capitalization 0.44 1.3
## Stest22punctuation 0.35 1.4
## Stest23english 0.43 1.4
## Stest24expression 0.62 1.4
## Stest25wordfunctions 0.62 1.5
## Stest26readingcomprehension 0.19 1.1
## Stest28mechanicalreasoning 0.37 2.0
## Stest29visualization2D 0.59 2.8
## Stest30visualization3D 0.50 2.7
## Stest31abstractreasoning 0.43 1.7
## Stest32arithreasoning 0.44 1.3
## Stest33highschoolmath 0.30 1.7
## Stest34arithcomputation 0.44 2.2
## Stest35tablereading 0.55 2.2
## Stest36clericalchecking 0.50 2.0
## Stest37objectinspection 0.52 1.8
##
## PA1 PA2 PA3 PA4 PA5 PA6
## SS loadings 15.08 1.50 0.95 0.79 0.42 0.39
## Proportion Var 0.44 0.04 0.03 0.02 0.01 0.01
## Cumulative Var 0.44 0.49 0.52 0.54 0.55 0.56
## Proportion Explained 0.79 0.08 0.05 0.04 0.02 0.02
## Cumulative Proportion 0.79 0.87 0.92 0.96 0.98 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 6 factors are sufficient.
##
## df null model = 561 with the objective function = 21.05 0.1 with Chi Square = 51157.71
## df of the model are 372 and the objective function was 0.44
## 0.1
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.02
## 0.1
## The harmonic n.obs is 2443 with the empirical chi square 409.88 with prob < 0.086
## 0.1The total n.obs was 2443 with Likelihood Chi Square = 1064.2 with prob < 6.2e-68
## 0.1
## Tucker Lewis Index of factoring reliability = 0.979
## RMSEA index = 0.028 and the 90 % confidence intervals are 0.026 0.03 0.1
## BIC = -1837.76
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA2 PA3 PA4
## Correlation of (regression) scores with factors 0.99 0.87 0.82 0.80
## Multiple R square of scores with factors 0.98 0.76 0.68 0.65
## Minimum correlation of possible factor scores 0.95 0.51 0.36 0.29
## PA5 PA6
## Correlation of (regression) scores with factors 0.72 0.70
## Multiple R square of scores with factors 0.52 0.50
## Minimum correlation of possible factor scores 0.04 -0.01
FAfemale<-fa(r=datafemale, nfactors=6, max.iter=100, warnings=TRUE, rotate="none", fm="pa", weight=dfemale$BY_WTA)
print(FAfemale, digits=2, cutoff=.10)
## Factor Analysis using method = pa
## Call: fa(r = datafemale, nfactors = 6, rotate = "none", max.iter = 100,
## warnings = TRUE, fm = "pa", weight = dfemale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 PA3 PA4 PA5 PA6 h2
## Stest1vocab 0.82 -0.11 0.13 0.01 0.02 0.04 0.70
## Stest2literature 0.79 -0.15 0.18 0.05 -0.09 -0.06 0.70
## Stest3music 0.73 -0.13 0.14 0.00 -0.08 -0.01 0.58
## Stest4socialstudies 0.80 -0.15 0.15 0.03 0.05 0.03 0.69
## Stest5math 0.57 -0.02 -0.03 0.16 0.26 -0.01 0.41
## Stest6physicalscience 0.65 -0.09 0.01 0.21 0.20 0.09 0.53
## Stest7biologicalscience 0.56 -0.09 0.10 0.06 0.05 0.17 0.37
## Stest8aeronautics 0.29 -0.03 0.14 0.15 -0.03 0.00 0.13
## Stest9electronics 0.32 -0.05 0.15 0.23 0.18 0.08 0.22
## Stest10mechanics 0.54 -0.05 0.11 0.16 0.05 0.10 0.34
## Stest11art 0.72 -0.13 0.17 0.04 -0.24 -0.11 0.63
## Stest12law 0.58 -0.08 0.10 0.04 -0.08 -0.07 0.37
## Stest13health 0.70 -0.10 0.12 -0.06 -0.05 0.07 0.52
## Stest14bible 0.64 -0.07 0.13 -0.02 0.01 0.08 0.44
## Stest15theater 0.66 -0.11 0.16 -0.04 -0.16 -0.13 0.52
## Stest16miscellaneous 0.64 -0.06 0.11 0.02 -0.06 -0.04 0.44
## Stest19disguisedwords 0.71 0.18 0.05 -0.13 -0.06 -0.05 0.57
## Stest20spelling 0.62 0.05 0.05 -0.34 0.15 0.02 0.53
## Stest21capitalization 0.70 0.02 -0.11 -0.20 -0.04 0.01 0.54
## Stest22punctuation 0.76 0.03 -0.22 -0.21 0.06 0.05 0.68
## Stest23english 0.67 0.03 -0.14 -0.22 -0.02 0.15 0.55
## Stest24expression 0.52 -0.01 -0.15 -0.20 -0.07 0.06 0.34
## Stest25wordfunctions 0.60 -0.02 -0.21 0.02 0.16 -0.14 0.45
## Stest26readingcomprehension 0.87 -0.09 0.01 -0.09 -0.06 -0.02 0.78
## Stest28mechanicalreasoning 0.53 0.02 -0.18 0.20 -0.10 -0.02 0.36
## Stest29visualization2D 0.40 0.21 -0.27 0.18 -0.15 0.07 0.34
## Stest30visualization3D 0.44 0.09 -0.34 0.25 -0.19 0.09 0.42
## Stest31abstractreasoning 0.62 0.05 -0.34 0.03 -0.16 0.00 0.54
## Stest32arithreasoning 0.62 -0.05 -0.21 0.08 0.11 -0.15 0.48
## Stest33highschoolmath 0.68 0.01 -0.21 0.09 0.25 -0.16 0.60
## Stest34arithcomputation 0.56 0.40 0.01 -0.12 0.21 -0.01 0.53
## Stest35tablereading 0.40 0.53 0.13 -0.01 0.00 -0.02 0.46
## Stest36clericalchecking 0.15 0.62 0.26 0.06 0.02 -0.04 0.48
## Stest37objectinspection 0.29 0.60 0.08 0.11 -0.12 0.03 0.48
## u2 com
## Stest1vocab 0.30 1.1
## Stest2literature 0.30 1.2
## Stest3music 0.42 1.2
## Stest4socialstudies 0.31 1.2
## Stest5math 0.59 1.6
## Stest6physicalscience 0.47 1.5
## Stest7biologicalscience 0.63 1.4
## Stest8aeronautics 0.87 2.0
## Stest9electronics 0.78 3.2
## Stest10mechanics 0.66 1.4
## Stest11art 0.37 1.5
## Stest12law 0.63 1.2
## Stest13health 0.48 1.1
## Stest14bible 0.56 1.1
## Stest15theater 0.48 1.4
## Stest16miscellaneous 0.56 1.1
## Stest19disguisedwords 0.43 1.2
## Stest20spelling 0.47 1.7
## Stest21capitalization 0.46 1.2
## Stest22punctuation 0.32 1.4
## Stest23english 0.45 1.4
## Stest24expression 0.66 1.6
## Stest25wordfunctions 0.55 1.5
## Stest26readingcomprehension 0.22 1.1
## Stest28mechanicalreasoning 0.64 1.7
## Stest29visualization2D 0.66 3.3
## Stest30visualization3D 0.58 3.2
## Stest31abstractreasoning 0.46 1.7
## Stest32arithreasoning 0.52 1.5
## Stest33highschoolmath 0.40 1.6
## Stest34arithcomputation 0.47 2.3
## Stest35tablereading 0.54 2.0
## Stest36clericalchecking 0.52 1.5
## Stest37objectinspection 0.52 1.7
##
## PA1 PA2 PA3 PA4 PA5 PA6
## SS loadings 12.86 1.44 0.94 0.68 0.55 0.22
## Proportion Var 0.38 0.04 0.03 0.02 0.02 0.01
## Cumulative Var 0.38 0.42 0.45 0.47 0.48 0.49
## Proportion Explained 0.77 0.09 0.06 0.04 0.03 0.01
## Cumulative Proportion 0.77 0.86 0.91 0.95 0.99 1.00
##
## Mean item complexity = 1.6
## Test of the hypothesis that 6 factors are sufficient.
##
## df null model = 561 with the objective function = 16.8 0.1 with Chi Square = 60957.22
## df of the model are 372 and the objective function was 0.35
## 0.1
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.02
## 0.1
## The harmonic n.obs is 3642 with the empirical chi square 628.39 with prob < 2e-15
## 0.1The total n.obs was 3642 with Likelihood Chi Square = 1267.25 with prob < 4.9e-98
## 0.1
## Tucker Lewis Index of factoring reliability = 0.978
## RMSEA index = 0.026 and the 90 % confidence intervals are 0.024 0.027 0.1
## BIC = -1783.26
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA2 PA3 PA4
## Correlation of (regression) scores with factors 0.98 0.86 0.81 0.75
## Multiple R square of scores with factors 0.97 0.74 0.66 0.57
## Minimum correlation of possible factor scores 0.94 0.48 0.32 0.14
## PA5 PA6
## Correlation of (regression) scores with factors 0.73 0.55
## Multiple R square of scores with factors 0.53 0.31
## Minimum correlation of possible factor scores 0.06 -0.38
FA<-fa(r=datagroup, nfactors=6, max.iter=100, warnings=TRUE, rotate="none", fm="pa", weight=dgroup$BY_WTA)
print(FA, digits=2, cutoff=.10)
## Factor Analysis using method = pa
## Call: fa(r = datagroup, nfactors = 6, rotate = "none", max.iter = 100,
## warnings = TRUE, fm = "pa", weight = dgroup$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 PA3 PA4 PA5 PA6 h2
## Stest1vocab 0.84 -0.12 -0.04 0.12 -0.02 0.08 0.74
## Stest2literature 0.80 -0.09 -0.13 0.15 0.09 -0.11 0.71
## Stest3music 0.73 -0.03 -0.15 0.11 0.12 -0.09 0.58
## Stest4socialstudies 0.83 -0.13 -0.07 0.14 -0.05 -0.03 0.73
## Stest5math 0.62 -0.07 0.07 0.02 -0.23 -0.12 0.46
## Stest6physicalscience 0.71 -0.23 0.13 0.07 -0.16 -0.01 0.60
## Stest7biologicalscience 0.62 -0.15 0.02 0.10 -0.04 0.09 0.43
## Stest8aeronautics 0.43 -0.24 0.15 0.18 0.00 0.05 0.30
## Stest9electronics 0.46 -0.27 0.21 0.18 -0.16 0.08 0.39
## Stest10mechanics 0.58 -0.33 0.27 0.13 -0.09 0.22 0.59
## Stest11art 0.72 -0.07 -0.11 0.15 0.24 -0.09 0.63
## Stest12law 0.62 -0.10 -0.04 0.11 0.06 -0.04 0.42
## Stest13health 0.70 0.00 -0.16 0.10 0.05 0.03 0.54
## Stest14bible 0.64 0.03 -0.15 0.11 0.03 -0.04 0.45
## Stest15theater 0.65 0.01 -0.20 0.13 0.17 -0.07 0.52
## Stest16miscellaneous 0.67 -0.05 -0.06 0.13 0.06 -0.03 0.48
## Stest19disguisedwords 0.69 0.24 -0.04 0.02 0.06 0.06 0.55
## Stest20spelling 0.60 0.25 -0.28 -0.04 -0.15 0.16 0.55
## Stest21capitalization 0.68 0.17 -0.16 -0.17 0.03 0.08 0.56
## Stest22punctuation 0.74 0.19 -0.15 -0.25 -0.06 0.08 0.67
## Stest23english 0.67 0.17 -0.14 -0.17 0.01 0.20 0.56
## Stest24expression 0.53 0.11 -0.15 -0.19 0.03 0.11 0.36
## Stest25wordfunctions 0.58 0.06 -0.05 -0.21 -0.11 -0.14 0.41
## Stest26readingcomprehension 0.88 -0.01 -0.15 -0.02 0.06 -0.01 0.79
## Stest28mechanicalreasoning 0.56 -0.26 0.41 -0.13 0.08 0.08 0.58
## Stest29visualization2D 0.43 0.03 0.38 -0.20 0.14 0.05 0.39
## Stest30visualization3D 0.47 -0.10 0.34 -0.27 0.19 -0.05 0.46
## Stest31abstractreasoning 0.63 0.00 0.17 -0.32 0.16 -0.04 0.55
## Stest32arithreasoning 0.66 -0.08 0.07 -0.18 -0.11 -0.14 0.51
## Stest33highschoolmath 0.70 -0.01 0.07 -0.20 -0.25 -0.22 0.65
## Stest34arithcomputation 0.56 0.40 0.11 0.00 -0.21 0.00 0.54
## Stest35tablereading 0.39 0.46 0.26 0.15 0.00 -0.04 0.45
## Stest36clericalchecking 0.15 0.54 0.27 0.32 -0.05 -0.01 0.49
## Stest37objectinspection 0.27 0.46 0.39 0.15 0.13 -0.03 0.48
## u2 com
## Stest1vocab 0.26 1.1
## Stest2literature 0.29 1.2
## Stest3music 0.42 1.2
## Stest4socialstudies 0.27 1.1
## Stest5math 0.54 1.4
## Stest6physicalscience 0.40 1.4
## Stest7biologicalscience 0.57 1.2
## Stest8aeronautics 0.70 2.3
## Stest9electronics 0.61 2.9
## Stest10mechanics 0.41 2.6
## Stest11art 0.37 1.4
## Stest12law 0.58 1.1
## Stest13health 0.46 1.2
## Stest14bible 0.55 1.2
## Stest15theater 0.48 1.4
## Stest16miscellaneous 0.52 1.1
## Stest19disguisedwords 0.45 1.3
## Stest20spelling 0.45 2.2
## Stest21capitalization 0.44 1.4
## Stest22punctuation 0.33 1.5
## Stest23english 0.44 1.6
## Stest24expression 0.64 1.6
## Stest25wordfunctions 0.59 1.5
## Stest26readingcomprehension 0.21 1.1
## Stest28mechanicalreasoning 0.42 2.5
## Stest29visualization2D 0.61 2.7
## Stest30visualization3D 0.54 3.0
## Stest31abstractreasoning 0.45 1.8
## Stest32arithreasoning 0.49 1.4
## Stest33highschoolmath 0.35 1.7
## Stest34arithcomputation 0.46 2.2
## Stest35tablereading 0.55 2.8
## Stest36clericalchecking 0.51 2.4
## Stest37objectinspection 0.52 3.1
##
## PA1 PA2 PA3 PA4 PA5 PA6
## SS loadings 13.56 1.57 1.28 0.90 0.51 0.32
## Proportion Var 0.40 0.05 0.04 0.03 0.01 0.01
## Cumulative Var 0.40 0.44 0.48 0.51 0.52 0.53
## Proportion Explained 0.75 0.09 0.07 0.05 0.03 0.02
## Cumulative Proportion 0.75 0.83 0.90 0.95 0.98 1.00
##
## Mean item complexity = 1.8
## Test of the hypothesis that 6 factors are sufficient.
##
## df null model = 561 with the objective function = 18.64 0.1 with Chi Square = 113178.9
## df of the model are 372 and the objective function was 0.31
## 0.1
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
## 0.1
## The harmonic n.obs is 6085 with the empirical chi square 829.32 with prob < 6.7e-37
## 0.1The total n.obs was 6085 with Likelihood Chi Square = 1882.91 with prob < 5.8e-200
## 0.1
## Tucker Lewis Index of factoring reliability = 0.98
## RMSEA index = 0.026 and the 90 % confidence intervals are 0.025 0.027 0.1
## BIC = -1358.54
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA2 PA3 PA4
## Correlation of (regression) scores with factors 0.99 0.87 0.85 0.81
## Multiple R square of scores with factors 0.97 0.77 0.73 0.66
## Minimum correlation of possible factor scores 0.94 0.53 0.46 0.33
## PA5 PA6
## Correlation of (regression) scores with factors 0.73 0.66
## Multiple R square of scores with factors 0.53 0.43
## Minimum correlation of possible factor scores 0.07 -0.14
# EFA: The rotate options "promax" and "Promax" differ slightly. Because unlike "Promax", the "promax" performs a Kaiser normalization before rotation, which is recommended according to Kaizer.
male5<-fa(datamale, nfactors=5, rotate="promax", fm="minres", weight=dmale$BY_WTA)
print(male5, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datamale, nfactors = 5, rotate = "promax", fm = "minres",
## weight = dmale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR4 MR3 MR2 MR5 h2 u2 com
## Stest1vocab 0.63 0.18 -0.01 0.00 0.20 0.78 0.22 1.4
## Stest2literature 0.78 0.06 0.00 -0.01 0.04 0.71 0.29 1.0
## Stest3music 0.73 0.04 0.04 0.02 -0.05 0.58 0.42 1.0
## Stest4socialstudies 0.66 0.23 -0.09 0.01 0.15 0.76 0.24 1.4
## Stest5math 0.32 0.26 -0.03 0.04 0.25 0.49 0.51 2.9
## Stest6physicalscience 0.52 0.06 0.07 -0.03 0.34 0.68 0.32 1.8
## Stest7biologicalscience 0.50 0.12 0.02 -0.03 0.20 0.51 0.49 1.4
## Stest8aeronautics 0.62 -0.20 0.06 0.01 0.23 0.41 0.59 1.5
## Stest9electronics 0.45 -0.12 0.07 0.00 0.45 0.52 0.48 2.2
## Stest10mechanics 0.42 0.07 0.05 -0.01 0.34 0.55 0.45 2.0
## Stest11art 0.83 -0.07 0.09 0.02 -0.09 0.63 0.37 1.1
## Stest12law 0.61 0.08 0.00 -0.01 0.04 0.48 0.52 1.0
## Stest13health 0.62 0.14 -0.05 0.03 0.08 0.57 0.43 1.2
## Stest14bible 0.61 0.15 -0.06 0.03 -0.02 0.48 0.52 1.2
## Stest15theater 0.77 0.06 -0.03 -0.01 -0.14 0.55 0.45 1.1
## Stest16miscellaneous 0.69 0.05 -0.04 0.05 0.02 0.54 0.46 1.0
## Stest19disguisedwords 0.32 0.39 0.02 0.17 -0.10 0.52 0.48 2.5
## Stest20spelling 0.10 0.78 -0.26 0.00 0.00 0.51 0.49 1.3
## Stest21capitalization 0.13 0.63 0.09 -0.04 -0.08 0.55 0.45 1.2
## Stest22punctuation 0.03 0.75 0.09 -0.05 -0.03 0.64 0.36 1.0
## Stest23english 0.13 0.58 0.07 0.00 -0.03 0.52 0.48 1.1
## Stest24expression 0.08 0.55 0.08 -0.10 -0.07 0.37 0.63 1.2
## Stest25wordfunctions 0.05 0.50 0.12 -0.05 -0.03 0.35 0.65 1.2
## Stest26readingcomprehension 0.56 0.39 0.06 -0.07 -0.03 0.81 0.19 1.8
## Stest28mechanicalreasoning 0.15 -0.06 0.63 -0.01 0.19 0.62 0.38 1.3
## Stest29visualization2D -0.10 0.10 0.55 0.17 -0.01 0.40 0.60 1.3
## Stest30visualization3D 0.03 -0.07 0.74 -0.03 0.01 0.51 0.49 1.0
## Stest31abstractreasoning 0.02 0.27 0.56 -0.04 -0.04 0.57 0.43 1.5
## Stest32arithreasoning 0.16 0.41 0.20 -0.07 0.09 0.51 0.49 2.0
## Stest33highschoolmath 0.06 0.53 0.13 -0.04 0.15 0.57 0.43 1.3
## Stest34arithcomputation -0.11 0.61 -0.08 0.38 0.08 0.56 0.44 1.8
## Stest35tablereading 0.02 0.10 0.08 0.58 -0.02 0.44 0.56 1.1
## Stest36clericalchecking 0.03 -0.03 -0.18 0.75 0.03 0.50 0.50 1.1
## Stest37objectinspection 0.01 -0.19 0.25 0.65 -0.03 0.48 0.52 1.5
##
## MR1 MR4 MR3 MR2 MR5
## SS loadings 8.36 5.21 2.22 1.58 1.31
## Proportion Var 0.25 0.15 0.07 0.05 0.04
## Cumulative Var 0.25 0.40 0.46 0.51 0.55
## Proportion Explained 0.45 0.28 0.12 0.08 0.07
## Cumulative Proportion 0.45 0.73 0.85 0.93 1.00
##
## With factor correlations of
## MR1 MR4 MR3 MR2 MR5
## MR1 1.00 0.78 0.60 0.28 0.46
## MR4 0.78 1.00 0.64 0.37 0.49
## MR3 0.60 0.64 1.00 0.34 0.43
## MR2 0.28 0.37 0.34 1.00 0.18
## MR5 0.46 0.49 0.43 0.18 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 5 factors are sufficient.
##
## df null model = 561 with the objective function = 21.05 0.1 with Chi Square = 51157.71
## df of the model are 401 and the objective function was 0.68
## 0.1
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.02
## 0.1
## The harmonic n.obs is 2443 with the empirical chi square 743.12 with prob < 8.7e-23
## 0.1The total n.obs was 2443 with Likelihood Chi Square = 1642.71 with prob < 1.3e-149
## 0.1
## Tucker Lewis Index of factoring reliability = 0.966
## RMSEA index = 0.036 and the 90 % confidence intervals are 0.034 0.037 0.1
## BIC = -1485.48
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR4 MR3 MR2
## Correlation of (regression) scores with factors 0.97 0.96 0.91 0.87
## Multiple R square of scores with factors 0.95 0.92 0.83 0.76
## Minimum correlation of possible factor scores 0.90 0.83 0.66 0.53
## MR5
## Correlation of (regression) scores with factors 0.82
## Multiple R square of scores with factors 0.67
## Minimum correlation of possible factor scores 0.34
male6<-fa(datamale, nfactors=6, rotate="promax", fm="minres", weight=dmale$BY_WTA)
print(male6, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datamale, nfactors = 6, rotate = "promax", fm = "minres",
## weight = dmale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR4 MR3 MR5 MR2 MR6 h2
## Stest1vocab 0.59 0.22 0.00 -0.02 -0.01 0.23 0.78
## Stest2literature 0.82 -0.02 -0.01 0.06 0.00 0.01 0.72
## Stest3music 0.78 -0.02 0.03 0.01 0.02 -0.06 0.59
## Stest4socialstudies 0.67 0.11 -0.10 0.14 0.01 0.11 0.76
## Stest5math 0.32 -0.01 -0.06 0.40 0.05 0.16 0.53
## Stest6physicalscience 0.49 -0.03 0.06 0.19 -0.03 0.29 0.67
## Stest7biologicalscience 0.46 0.18 0.03 -0.05 -0.03 0.24 0.52
## Stest8aeronautics 0.60 -0.15 0.06 -0.04 0.00 0.23 0.41
## Stest9electronics 0.37 -0.09 0.07 0.06 0.00 0.44 0.52
## Stest10mechanics 0.32 0.21 0.07 -0.10 -0.02 0.43 0.60
## Stest11art 0.87 -0.04 0.08 -0.10 0.02 -0.07 0.63
## Stest12law 0.63 0.01 -0.01 0.07 -0.01 0.02 0.48
## Stest13health 0.62 0.15 -0.05 -0.02 0.03 0.09 0.57
## Stest14bible 0.64 0.08 -0.07 0.04 0.04 -0.04 0.48
## Stest15theater 0.82 0.05 -0.04 -0.07 -0.01 -0.12 0.55
## Stest16miscellaneous 0.72 0.03 -0.04 -0.01 0.05 0.02 0.54
## Stest19disguisedwords 0.33 0.41 0.03 -0.07 0.16 -0.05 0.53
## Stest20spelling 0.07 0.77 -0.25 0.02 0.00 0.05 0.54
## Stest21capitalization 0.13 0.60 0.11 0.01 -0.05 -0.03 0.56
## Stest22punctuation 0.03 0.66 0.10 0.10 -0.06 0.00 0.65
## Stest23english 0.08 0.70 0.09 -0.13 -0.01 0.06 0.57
## Stest24expression 0.08 0.53 0.10 0.01 -0.10 -0.03 0.38
## Stest25wordfunctions 0.09 0.22 0.10 0.35 -0.05 -0.10 0.37
## Stest26readingcomprehension 0.59 0.30 0.06 0.07 -0.07 -0.03 0.81
## Stest28mechanicalreasoning 0.10 -0.02 0.63 0.00 -0.01 0.22 0.63
## Stest29visualization2D -0.12 0.14 0.56 -0.05 0.16 0.03 0.41
## Stest30visualization3D 0.05 -0.14 0.72 0.09 -0.03 0.00 0.50
## Stest31abstractreasoning 0.04 0.15 0.55 0.14 -0.04 -0.05 0.57
## Stest32arithreasoning 0.19 0.06 0.17 0.46 -0.06 -0.02 0.56
## Stest33highschoolmath 0.04 0.06 0.08 0.72 -0.03 0.01 0.70
## Stest34arithcomputation -0.11 0.37 -0.08 0.32 0.39 0.03 0.56
## Stest35tablereading 0.04 0.00 0.07 0.10 0.59 -0.05 0.45
## Stest36clericalchecking 0.03 -0.03 -0.18 -0.02 0.75 0.02 0.50
## Stest37objectinspection 0.01 -0.11 0.25 -0.13 0.65 0.00 0.48
## u2 com
## Stest1vocab 0.22 1.6
## Stest2literature 0.28 1.0
## Stest3music 0.41 1.0
## Stest4socialstudies 0.24 1.2
## Stest5math 0.47 2.3
## Stest6physicalscience 0.33 2.0
## Stest7biologicalscience 0.48 1.9
## Stest8aeronautics 0.59 1.5
## Stest9electronics 0.48 2.2
## Stest10mechanics 0.40 2.6
## Stest11art 0.37 1.1
## Stest12law 0.52 1.0
## Stest13health 0.43 1.2
## Stest14bible 0.52 1.1
## Stest15theater 0.45 1.1
## Stest16miscellaneous 0.46 1.0
## Stest19disguisedwords 0.47 2.4
## Stest20spelling 0.46 1.2
## Stest21capitalization 0.44 1.2
## Stest22punctuation 0.35 1.1
## Stest23english 0.43 1.2
## Stest24expression 0.62 1.2
## Stest25wordfunctions 0.63 2.3
## Stest26readingcomprehension 0.19 1.6
## Stest28mechanicalreasoning 0.37 1.3
## Stest29visualization2D 0.59 1.4
## Stest30visualization3D 0.50 1.1
## Stest31abstractreasoning 0.43 1.3
## Stest32arithreasoning 0.44 1.7
## Stest33highschoolmath 0.30 1.1
## Stest34arithcomputation 0.44 3.2
## Stest35tablereading 0.55 1.1
## Stest36clericalchecking 0.50 1.1
## Stest37objectinspection 0.52 1.4
##
## MR1 MR4 MR3 MR5 MR2 MR6
## SS loadings 8.38 3.83 2.19 1.85 1.59 1.28
## Proportion Var 0.25 0.11 0.06 0.05 0.05 0.04
## Cumulative Var 0.25 0.36 0.42 0.48 0.53 0.56
## Proportion Explained 0.44 0.20 0.11 0.10 0.08 0.07
## Cumulative Proportion 0.44 0.64 0.75 0.85 0.93 1.00
##
## With factor correlations of
## MR1 MR4 MR3 MR5 MR2 MR6
## MR1 1.00 0.77 0.60 0.70 0.30 0.50
## MR4 0.77 1.00 0.61 0.73 0.38 0.41
## MR3 0.60 0.61 1.00 0.57 0.35 0.39
## MR5 0.70 0.73 0.57 1.00 0.32 0.42
## MR2 0.30 0.38 0.35 0.32 1.00 0.18
## MR6 0.50 0.41 0.39 0.42 0.18 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 6 factors are sufficient.
##
## df null model = 561 with the objective function = 21.05 0.1 with Chi Square = 51157.71
## df of the model are 372 and the objective function was 0.44
## 0.1
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.02
## 0.1
## The harmonic n.obs is 2443 with the empirical chi square 409.88 with prob < 0.086
## 0.1The total n.obs was 2443 with Likelihood Chi Square = 1064.31 with prob < 6e-68
## 0.1
## Tucker Lewis Index of factoring reliability = 0.979
## RMSEA index = 0.028 and the 90 % confidence intervals are 0.026 0.03 0.1
## BIC = -1837.66
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR4 MR3 MR5
## Correlation of (regression) scores with factors 0.98 0.95 0.91 0.91
## Multiple R square of scores with factors 0.95 0.90 0.83 0.83
## Minimum correlation of possible factor scores 0.91 0.80 0.66 0.66
## MR2 MR6
## Correlation of (regression) scores with factors 0.88 0.83
## Multiple R square of scores with factors 0.77 0.68
## Minimum correlation of possible factor scores 0.53 0.37
male7<-fa(datamale, nfactors=7, rotate="promax", fm="minres", weight=dmale$BY_WTA)
print(male7, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datamale, nfactors = 7, rotate = "promax", fm = "minres",
## weight = dmale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR4 MR3 MR5 MR2 MR6 MR7
## Stest1vocab 0.60 0.22 0.00 -0.02 -0.01 0.22 0.00
## Stest2literature 0.82 -0.01 -0.01 0.08 0.00 0.02 -0.05
## Stest3music 0.75 0.00 0.03 0.06 0.04 -0.03 -0.13
## Stest4socialstudies 0.75 0.05 -0.10 0.08 -0.01 0.07 0.16
## Stest5math 0.30 0.00 -0.06 0.39 0.06 0.17 0.04
## Stest6physicalscience 0.50 -0.04 0.06 0.16 -0.03 0.28 0.06
## Stest7biologicalscience 0.50 0.15 0.03 -0.09 -0.05 0.20 0.08
## Stest8aeronautics 0.57 -0.13 0.06 -0.01 0.02 0.24 -0.08
## Stest9electronics 0.34 -0.06 0.07 0.08 0.01 0.45 -0.03
## Stest10mechanics 0.32 0.21 0.07 -0.10 -0.02 0.41 0.03
## Stest11art 0.88 -0.04 0.08 -0.09 0.02 -0.06 -0.07
## Stest12law 0.67 -0.01 -0.01 0.04 -0.02 0.01 0.05
## Stest13health 0.70 0.09 -0.05 -0.08 0.00 0.05 0.13
## Stest14bible 0.69 0.05 -0.07 0.01 0.02 -0.06 0.05
## Stest15theater 0.81 0.06 -0.04 -0.04 0.00 -0.11 -0.11
## Stest16miscellaneous 0.75 0.01 -0.04 -0.03 0.04 0.00 0.02
## Stest19disguisedwords 0.24 0.51 0.03 0.01 0.20 0.00 -0.25
## Stest20spelling 0.04 0.80 -0.25 0.05 0.01 0.06 -0.04
## Stest21capitalization 0.15 0.58 0.12 0.00 -0.05 -0.04 0.01
## Stest22punctuation 0.03 0.64 0.11 0.10 -0.06 0.00 0.02
## Stest23english 0.08 0.69 0.10 -0.11 -0.01 0.05 -0.03
## Stest24expression 0.11 0.50 0.10 -0.01 -0.11 -0.05 0.04
## Stest25wordfunctions 0.03 0.26 0.10 0.40 -0.02 -0.06 -0.10
## Stest26readingcomprehension 0.59 0.30 0.06 0.08 -0.06 -0.02 -0.05
## Stest28mechanicalreasoning 0.06 0.01 0.65 0.03 0.00 0.24 -0.10
## Stest29visualization2D -0.11 0.12 0.57 -0.05 0.16 0.02 0.01
## Stest30visualization3D 0.04 -0.13 0.73 0.09 -0.02 0.01 -0.05
## Stest31abstractreasoning 0.08 0.11 0.57 0.11 -0.05 -0.07 0.07
## Stest32arithreasoning 0.18 0.06 0.18 0.44 -0.06 -0.01 0.05
## Stest33highschoolmath 0.05 0.05 0.09 0.66 -0.03 0.02 0.12
## Stest34arithcomputation -0.04 0.30 -0.09 0.23 0.35 -0.03 0.33
## Stest35tablereading 0.09 -0.04 0.08 0.05 0.55 -0.08 0.17
## Stest36clericalchecking -0.04 0.02 -0.19 0.02 0.78 0.07 -0.05
## Stest37objectinspection 0.01 -0.11 0.26 -0.12 0.63 0.00 0.03
## h2 u2 com
## Stest1vocab 0.78 0.22 1.5
## Stest2literature 0.72 0.28 1.0
## Stest3music 0.60 0.40 1.1
## Stest4socialstudies 0.79 0.21 1.2
## Stest5math 0.53 0.47 2.4
## Stest6physicalscience 0.67 0.33 1.9
## Stest7biologicalscience 0.53 0.47 1.7
## Stest8aeronautics 0.42 0.58 1.5
## Stest9electronics 0.53 0.47 2.0
## Stest10mechanics 0.60 0.40 2.7
## Stest11art 0.63 0.37 1.1
## Stest12law 0.48 0.52 1.0
## Stest13health 0.59 0.41 1.2
## Stest14bible 0.48 0.52 1.1
## Stest15theater 0.55 0.45 1.1
## Stest16miscellaneous 0.54 0.46 1.0
## Stest19disguisedwords 0.59 0.41 2.3
## Stest20spelling 0.55 0.45 1.2
## Stest21capitalization 0.56 0.44 1.2
## Stest22punctuation 0.64 0.36 1.1
## Stest23english 0.57 0.43 1.1
## Stest24expression 0.38 0.62 1.3
## Stest25wordfunctions 0.40 0.60 2.1
## Stest26readingcomprehension 0.81 0.19 1.6
## Stest28mechanicalreasoning 0.64 0.36 1.3
## Stest29visualization2D 0.41 0.59 1.4
## Stest30visualization3D 0.50 0.50 1.1
## Stest31abstractreasoning 0.58 0.42 1.3
## Stest32arithreasoning 0.56 0.44 1.8
## Stest33highschoolmath 0.70 0.30 1.1
## Stest34arithcomputation 0.61 0.39 3.9
## Stest35tablereading 0.46 0.54 1.4
## Stest36clericalchecking 0.55 0.45 1.2
## Stest37objectinspection 0.47 0.53 1.5
##
## MR1 MR4 MR3 MR5 MR2 MR6 MR7
## SS loadings 8.53 3.74 2.25 1.73 1.57 1.23 0.37
## Proportion Var 0.25 0.11 0.07 0.05 0.05 0.04 0.01
## Cumulative Var 0.25 0.36 0.43 0.48 0.52 0.56 0.57
## Proportion Explained 0.44 0.19 0.12 0.09 0.08 0.06 0.02
## Cumulative Proportion 0.44 0.63 0.75 0.84 0.92 0.98 1.00
##
## With factor correlations of
## MR1 MR4 MR3 MR5 MR2 MR6 MR7
## MR1 1.00 0.78 0.62 0.70 0.29 0.50 0.34
## MR4 0.78 1.00 0.62 0.69 0.35 0.38 0.43
## MR3 0.62 0.62 1.00 0.55 0.33 0.37 0.38
## MR5 0.70 0.69 0.55 1.00 0.27 0.37 0.29
## MR2 0.29 0.35 0.33 0.27 1.00 0.12 0.22
## MR6 0.50 0.38 0.37 0.37 0.12 1.00 0.24
## MR7 0.34 0.43 0.38 0.29 0.22 0.24 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 7 factors are sufficient.
##
## df null model = 561 with the objective function = 21.05 0.1 with Chi Square = 51157.71
## df of the model are 344 and the objective function was 0.34
## 0.1
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
## 0.1
## The harmonic n.obs is 2443 with the empirical chi square 294.56 with prob < 0.97
## 0.1The total n.obs was 2443 with Likelihood Chi Square = 824.79 with prob < 1.8e-41
## 0.1
## Tucker Lewis Index of factoring reliability = 0.984
## RMSEA index = 0.024 and the 90 % confidence intervals are 0.022 0.026 0.1
## BIC = -1858.75
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR4 MR3 MR5
## Correlation of (regression) scores with factors 0.98 0.95 0.91 0.90
## Multiple R square of scores with factors 0.96 0.90 0.83 0.80
## Minimum correlation of possible factor scores 0.91 0.80 0.67 0.61
## MR2 MR6 MR7
## Correlation of (regression) scores with factors 0.88 0.82 0.72
## Multiple R square of scores with factors 0.77 0.68 0.52
## Minimum correlation of possible factor scores 0.54 0.35 0.05
female5<-fa(datafemale, nfactors=5, rotate="promax", fm="minres", weight=dfemale$BY_WTA)
print(female5, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datafemale, nfactors = 5, rotate = "promax", fm = "minres",
## weight = dfemale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR4 MR3 MR5 MR2 h2 u2 com
## Stest1vocab 0.57 0.24 -0.05 0.16 -0.02 0.70 0.30 1.5
## Stest2literature 0.74 0.08 0.00 0.06 -0.03 0.69 0.31 1.0
## Stest3music 0.64 0.16 -0.01 0.02 -0.03 0.58 0.42 1.1
## Stest4socialstudies 0.58 0.20 -0.08 0.21 -0.05 0.69 0.31 1.6
## Stest5math 0.03 0.13 0.03 0.52 -0.01 0.42 0.58 1.1
## Stest6physicalscience 0.21 0.04 0.07 0.49 -0.04 0.52 0.48 1.4
## Stest7biologicalscience 0.38 0.11 -0.03 0.19 -0.03 0.34 0.66 1.7
## Stest8aeronautics 0.35 -0.18 0.03 0.12 0.05 0.13 0.87 1.8
## Stest9electronics 0.20 -0.18 -0.07 0.44 0.04 0.21 0.79 1.9
## Stest10mechanics 0.38 -0.05 0.04 0.25 0.03 0.33 0.67 1.8
## Stest11art 0.81 0.01 0.10 -0.14 -0.01 0.61 0.39 1.1
## Stest12law 0.51 0.07 0.04 0.02 0.00 0.36 0.64 1.1
## Stest13health 0.55 0.25 -0.05 0.00 -0.02 0.52 0.48 1.4
## Stest14bible 0.47 0.21 -0.08 0.09 0.01 0.43 0.57 1.6
## Stest15theater 0.68 0.13 0.00 -0.11 -0.01 0.50 0.50 1.1
## Stest16miscellaneous 0.51 0.13 0.02 0.04 0.02 0.44 0.56 1.1
## Stest19disguisedwords 0.33 0.43 0.03 -0.09 0.22 0.57 0.43 2.5
## Stest20spelling 0.13 0.77 -0.30 0.01 0.06 0.53 0.47 1.4
## Stest21capitalization 0.20 0.59 0.08 -0.09 0.00 0.55 0.45 1.3
## Stest22punctuation 0.02 0.73 0.12 0.03 -0.04 0.68 0.32 1.1
## Stest23english 0.14 0.62 0.07 -0.08 -0.01 0.52 0.48 1.2
## Stest24expression 0.12 0.50 0.11 -0.15 -0.06 0.33 0.67 1.4
## Stest25wordfunctions -0.06 0.37 0.17 0.29 -0.07 0.43 0.57 2.5
## Stest26readingcomprehension 0.52 0.41 0.06 -0.01 -0.05 0.78 0.22 2.0
## Stest28mechanicalreasoning 0.16 -0.04 0.45 0.10 0.00 0.36 0.64 1.4
## Stest29visualization2D -0.04 -0.01 0.57 -0.02 0.14 0.33 0.67 1.1
## Stest30visualization3D 0.00 -0.09 0.69 0.01 0.01 0.41 0.59 1.0
## Stest31abstractreasoning 0.06 0.28 0.54 -0.09 -0.04 0.54 0.46 1.6
## Stest32arithreasoning 0.02 0.28 0.24 0.27 -0.10 0.45 0.55 3.2
## Stest33highschoolmath -0.10 0.36 0.17 0.44 -0.05 0.57 0.43 2.4
## Stest34arithcomputation -0.17 0.55 -0.10 0.21 0.39 0.53 0.47 2.4
## Stest35tablereading 0.03 0.18 0.03 0.00 0.58 0.46 0.54 1.2
## Stest36clericalchecking -0.01 -0.06 -0.08 0.04 0.71 0.48 0.52 1.0
## Stest37objectinspection 0.02 -0.06 0.24 -0.08 0.64 0.48 0.52 1.3
##
## MR1 MR4 MR3 MR5 MR2
## SS loadings 6.11 4.96 1.91 1.90 1.56
## Proportion Var 0.18 0.15 0.06 0.06 0.05
## Cumulative Var 0.18 0.33 0.38 0.44 0.48
## Proportion Explained 0.37 0.30 0.12 0.12 0.09
## Cumulative Proportion 0.37 0.67 0.79 0.91 1.00
##
## With factor correlations of
## MR1 MR4 MR3 MR5 MR2
## MR1 1.00 0.71 0.58 0.67 0.24
## MR4 0.71 1.00 0.66 0.61 0.27
## MR3 0.58 0.66 1.00 0.54 0.23
## MR5 0.67 0.61 0.54 1.00 0.24
## MR2 0.24 0.27 0.23 0.24 1.00
##
## Mean item complexity = 1.6
## Test of the hypothesis that 5 factors are sufficient.
##
## df null model = 561 with the objective function = 16.8 0.1 with Chi Square = 60957.22
## df of the model are 401 and the objective function was 0.42
## 0.1
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.02
## 0.1
## The harmonic n.obs is 3642 with the empirical chi square 790.53 with prob < 9.4e-28
## 0.1The total n.obs was 3642 with Likelihood Chi Square = 1506.76 with prob < 1.5e-127
## 0.1
## Tucker Lewis Index of factoring reliability = 0.974
## RMSEA index = 0.028 and the 90 % confidence intervals are 0.026 0.029 0.1
## BIC = -1781.56
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR4 MR3 MR5
## Correlation of (regression) scores with factors 0.96 0.95 0.89 0.89
## Multiple R square of scores with factors 0.93 0.90 0.79 0.78
## Minimum correlation of possible factor scores 0.85 0.81 0.59 0.57
## MR2
## Correlation of (regression) scores with factors 0.87
## Multiple R square of scores with factors 0.75
## Minimum correlation of possible factor scores 0.50
female6<-fa(datafemale, nfactors=6, rotate="promax", fm="minres", weight=dfemale$BY_WTA)
print(female6, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datafemale, nfactors = 6, rotate = "promax", fm = "minres",
## weight = dfemale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR6 MR3 MR4 MR2 MR5 h2
## Stest1vocab 0.51 0.25 -0.03 0.19 -0.02 0.01 0.70
## Stest2literature 0.78 0.02 -0.03 0.06 -0.02 0.04 0.70
## Stest3music 0.64 0.14 -0.02 0.04 -0.03 -0.01 0.58
## Stest4socialstudies 0.52 0.20 -0.07 0.24 -0.05 0.02 0.69
## Stest5math -0.02 0.08 0.01 0.42 0.00 0.27 0.41
## Stest6physicalscience 0.08 0.08 0.09 0.50 -0.06 0.12 0.53
## Stest7biologicalscience 0.20 0.24 0.05 0.33 -0.06 -0.14 0.37
## Stest8aeronautics 0.33 -0.17 0.02 0.14 0.05 -0.01 0.13
## Stest9electronics 0.08 -0.13 -0.03 0.48 0.03 0.03 0.22
## Stest10mechanics 0.26 0.02 0.08 0.33 0.01 -0.05 0.34
## Stest11art 0.92 -0.07 0.04 -0.14 0.01 -0.01 0.63
## Stest12law 0.57 0.01 0.00 0.00 0.01 0.05 0.37
## Stest13health 0.49 0.30 -0.01 0.08 -0.03 -0.10 0.52
## Stest14bible 0.38 0.27 -0.04 0.17 0.00 -0.08 0.44
## Stest15theater 0.81 0.02 -0.07 -0.15 0.02 0.05 0.52
## Stest16miscellaneous 0.53 0.09 0.00 0.04 0.02 0.03 0.44
## Stest19disguisedwords 0.38 0.36 0.00 -0.12 0.23 0.05 0.57
## Stest20spelling 0.10 0.73 -0.26 -0.01 0.06 0.05 0.53
## Stest21capitalization 0.21 0.55 0.07 -0.11 0.00 0.05 0.54
## Stest22punctuation -0.02 0.70 0.13 -0.01 -0.05 0.11 0.68
## Stest23english 0.02 0.71 0.14 -0.01 -0.04 -0.09 0.55
## Stest24expression 0.09 0.52 0.13 -0.12 -0.07 -0.03 0.34
## Stest25wordfunctions 0.03 0.20 0.08 0.09 -0.05 0.41 0.45
## Stest26readingcomprehension 0.53 0.36 0.04 -0.02 -0.05 0.06 0.78
## Stest28mechanicalreasoning 0.18 -0.08 0.40 0.06 0.00 0.12 0.36
## Stest29visualization2D -0.09 0.03 0.56 0.01 0.13 -0.01 0.34
## Stest30visualization3D -0.05 -0.04 0.68 0.04 -0.01 0.00 0.42
## Stest31abstractreasoning 0.10 0.24 0.49 -0.13 -0.04 0.11 0.54
## Stest32arithreasoning 0.13 0.09 0.14 0.07 -0.07 0.41 0.48
## Stest33highschoolmath -0.02 0.15 0.07 0.21 -0.02 0.51 0.60
## Stest34arithcomputation -0.18 0.47 -0.10 0.12 0.40 0.17 0.53
## Stest35tablereading 0.05 0.14 0.02 -0.01 0.59 0.00 0.46
## Stest36clericalchecking 0.02 -0.09 -0.09 0.03 0.73 -0.02 0.49
## Stest37objectinspection 0.01 -0.03 0.24 -0.03 0.64 -0.10 0.48
## u2 com
## Stest1vocab 0.30 1.8
## Stest2literature 0.30 1.0
## Stest3music 0.42 1.1
## Stest4socialstudies 0.31 1.8
## Stest5math 0.59 1.8
## Stest6physicalscience 0.47 1.3
## Stest7biologicalscience 0.63 3.1
## Stest8aeronautics 0.87 2.0
## Stest9electronics 0.78 1.2
## Stest10mechanics 0.66 2.1
## Stest11art 0.37 1.1
## Stest12law 0.63 1.0
## Stest13health 0.48 1.8
## Stest14bible 0.56 2.4
## Stest15theater 0.48 1.1
## Stest16miscellaneous 0.56 1.1
## Stest19disguisedwords 0.43 2.9
## Stest20spelling 0.47 1.3
## Stest21capitalization 0.46 1.4
## Stest22punctuation 0.32 1.1
## Stest23english 0.45 1.1
## Stest24expression 0.66 1.4
## Stest25wordfunctions 0.55 1.7
## Stest26readingcomprehension 0.22 1.8
## Stest28mechanicalreasoning 0.64 1.7
## Stest29visualization2D 0.66 1.2
## Stest30visualization3D 0.58 1.0
## Stest31abstractreasoning 0.46 1.8
## Stest32arithreasoning 0.52 1.7
## Stest33highschoolmath 0.40 1.6
## Stest34arithcomputation 0.47 2.8
## Stest35tablereading 0.54 1.1
## Stest36clericalchecking 0.51 1.1
## Stest37objectinspection 0.52 1.4
##
## MR1 MR6 MR3 MR4 MR2 MR5
## SS loadings 5.99 4.43 1.71 1.65 1.59 1.35
## Proportion Var 0.18 0.13 0.05 0.05 0.05 0.04
## Cumulative Var 0.18 0.31 0.36 0.40 0.45 0.49
## Proportion Explained 0.36 0.26 0.10 0.10 0.10 0.08
## Cumulative Proportion 0.36 0.62 0.73 0.82 0.92 1.00
##
## With factor correlations of
## MR1 MR6 MR3 MR4 MR2 MR5
## MR1 1.00 0.76 0.61 0.71 0.27 0.56
## MR6 0.76 1.00 0.60 0.57 0.33 0.64
## MR3 0.61 0.60 1.00 0.45 0.28 0.58
## MR4 0.71 0.57 0.45 1.00 0.27 0.49
## MR2 0.27 0.33 0.28 0.27 1.00 0.23
## MR5 0.56 0.64 0.58 0.49 0.23 1.00
##
## Mean item complexity = 1.6
## Test of the hypothesis that 6 factors are sufficient.
##
## df null model = 561 with the objective function = 16.8 0.1 with Chi Square = 60957.22
## df of the model are 372 and the objective function was 0.35
## 0.1
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.02
## 0.1
## The harmonic n.obs is 3642 with the empirical chi square 628.38 with prob < 2e-15
## 0.1The total n.obs was 3642 with Likelihood Chi Square = 1267.2 with prob < 5e-98
## 0.1
## Tucker Lewis Index of factoring reliability = 0.978
## RMSEA index = 0.026 and the 90 % confidence intervals are 0.024 0.027 0.1
## BIC = -1783.31
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR6 MR3 MR4
## Correlation of (regression) scores with factors 0.97 0.95 0.88 0.87
## Multiple R square of scores with factors 0.93 0.90 0.78 0.76
## Minimum correlation of possible factor scores 0.87 0.80 0.55 0.53
## MR2 MR5
## Correlation of (regression) scores with factors 0.87 0.85
## Multiple R square of scores with factors 0.76 0.72
## Minimum correlation of possible factor scores 0.52 0.45
female7<-fa(datafemale, nfactors=7, rotate="promax", fm="minres", weight=dfemale$BY_WTA)
print(female7, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datafemale, nfactors = 7, rotate = "promax", fm = "minres",
## weight = dfemale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR7 MR5 MR3 MR2 MR4 MR6
## Stest1vocab 0.52 0.23 0.02 -0.03 -0.03 0.17 0.06
## Stest2literature 0.83 -0.06 0.06 -0.04 0.00 0.00 0.06
## Stest3music 0.67 0.10 0.00 -0.02 -0.02 0.03 0.05
## Stest4socialstudies 0.64 0.01 0.10 -0.09 -0.01 0.07 0.24
## Stest5math 0.01 0.01 0.40 0.00 0.01 0.28 0.07
## Stest6physicalscience 0.14 -0.02 0.22 0.08 -0.03 0.34 0.19
## Stest7biologicalscience 0.29 0.11 -0.11 0.03 -0.02 0.19 0.28
## Stest8aeronautics 0.29 -0.09 -0.03 0.03 0.04 0.18 -0.03
## Stest9electronics 0.00 -0.03 0.05 -0.02 0.00 0.48 0.04
## Stest10mechanics 0.19 0.12 -0.07 0.10 -0.02 0.37 0.03
## Stest11art 0.94 -0.11 -0.03 0.03 0.02 -0.13 -0.01
## Stest12law 0.60 -0.06 0.07 0.00 0.02 -0.04 0.03
## Stest13health 0.52 0.25 -0.11 -0.01 -0.02 0.06 0.11
## Stest14bible 0.50 0.09 -0.04 -0.06 0.04 0.03 0.26
## Stest15theater 0.78 0.06 0.02 -0.06 0.00 -0.08 -0.11
## Stest16miscellaneous 0.55 0.05 0.05 -0.01 0.03 0.02 0.03
## Stest19disguisedwords 0.28 0.51 0.00 0.03 0.18 0.03 -0.22
## Stest20spelling 0.06 0.78 0.05 -0.25 0.03 0.05 -0.05
## Stest21capitalization 0.22 0.51 0.05 0.08 -0.01 -0.08 -0.01
## Stest22punctuation -0.01 0.64 0.15 0.14 -0.06 -0.02 0.02
## Stest23english 0.01 0.70 -0.12 0.16 -0.05 0.03 0.06
## Stest24expression 0.11 0.47 -0.05 0.14 -0.07 -0.10 0.04
## Stest25wordfunctions 0.02 0.16 0.52 0.08 -0.06 0.03 -0.10
## Stest26readingcomprehension 0.58 0.27 0.09 0.04 -0.04 -0.05 0.06
## Stest28mechanicalreasoning 0.12 0.00 0.12 0.43 -0.02 0.12 -0.10
## Stest29visualization2D -0.12 0.06 -0.02 0.58 0.12 0.04 -0.03
## Stest30visualization3D -0.04 -0.07 0.01 0.68 0.00 0.02 0.05
## Stest31abstractreasoning 0.15 0.13 0.14 0.49 -0.02 -0.18 0.03
## Stest32arithreasoning 0.15 0.03 0.52 0.14 -0.07 -0.01 -0.06
## Stest33highschoolmath 0.02 0.03 0.69 0.05 0.00 0.06 -0.03
## Stest34arithcomputation -0.11 0.32 0.29 -0.11 0.43 0.00 0.08
## Stest35tablereading 0.10 0.03 0.04 0.01 0.63 -0.08 0.04
## Stest36clericalchecking -0.06 0.01 -0.04 -0.08 0.72 0.12 -0.16
## Stest37objectinspection 0.05 -0.13 -0.10 0.24 0.68 -0.07 0.05
## h2 u2 com
## Stest1vocab 0.70 0.30 1.7
## Stest2literature 0.70 0.30 1.0
## Stest3music 0.58 0.42 1.1
## Stest4socialstudies 0.71 0.29 1.4
## Stest5math 0.41 0.59 1.9
## Stest6physicalscience 0.53 0.47 3.0
## Stest7biologicalscience 0.37 0.63 3.4
## Stest8aeronautics 0.13 0.87 2.1
## Stest9electronics 0.25 0.75 1.1
## Stest10mechanics 0.37 0.63 2.0
## Stest11art 0.63 0.37 1.1
## Stest12law 0.37 0.63 1.1
## Stest13health 0.52 0.48 1.7
## Stest14bible 0.46 0.54 1.6
## Stest15theater 0.52 0.48 1.1
## Stest16miscellaneous 0.44 0.56 1.0
## Stest19disguisedwords 0.61 0.39 2.3
## Stest20spelling 0.54 0.46 1.3
## Stest21capitalization 0.54 0.46 1.5
## Stest22punctuation 0.68 0.32 1.2
## Stest23english 0.55 0.45 1.2
## Stest24expression 0.34 0.66 1.5
## Stest25wordfunctions 0.45 0.55 1.4
## Stest26readingcomprehension 0.78 0.22 1.5
## Stest28mechanicalreasoning 0.38 0.62 1.6
## Stest29visualization2D 0.34 0.66 1.2
## Stest30visualization3D 0.42 0.58 1.0
## Stest31abstractreasoning 0.54 0.46 1.9
## Stest32arithreasoning 0.47 0.53 1.4
## Stest33highschoolmath 0.61 0.39 1.0
## Stest34arithcomputation 0.54 0.46 3.1
## Stest35tablereading 0.47 0.53 1.1
## Stest36clericalchecking 0.50 0.50 1.2
## Stest37objectinspection 0.49 0.51 1.4
##
## MR1 MR7 MR5 MR3 MR2 MR4 MR6
## SS loadings 6.35 3.59 2.03 1.70 1.64 1.03 0.62
## Proportion Var 0.19 0.11 0.06 0.05 0.05 0.03 0.02
## Cumulative Var 0.19 0.29 0.35 0.40 0.45 0.48 0.50
## Proportion Explained 0.37 0.21 0.12 0.10 0.10 0.06 0.04
## Cumulative Proportion 0.37 0.59 0.71 0.81 0.90 0.96 1.00
##
## With factor correlations of
## MR1 MR7 MR5 MR3 MR2 MR4 MR6
## MR1 1.00 0.76 0.68 0.62 0.31 0.63 0.42
## MR7 0.76 1.00 0.75 0.60 0.40 0.39 0.52
## MR5 0.68 0.75 1.00 0.63 0.30 0.49 0.56
## MR3 0.62 0.60 0.63 1.00 0.30 0.35 0.33
## MR2 0.31 0.40 0.30 0.30 1.00 0.28 0.17
## MR4 0.63 0.39 0.49 0.35 0.28 1.00 0.25
## MR6 0.42 0.52 0.56 0.33 0.17 0.25 1.00
##
## Mean item complexity = 1.6
## Test of the hypothesis that 7 factors are sufficient.
##
## df null model = 561 with the objective function = 16.8 0.1 with Chi Square = 60957.22
## df of the model are 344 and the objective function was 0.28
## 0.1
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
## 0.1
## The harmonic n.obs is 3642 with the empirical chi square 484.86 with prob < 8e-07
## 0.1The total n.obs was 3642 with Likelihood Chi Square = 1024.82 with prob < 7.8e-69
## 0.1
## Tucker Lewis Index of factoring reliability = 0.982
## RMSEA index = 0.023 and the 90 % confidence intervals are 0.022 0.025 0.1
## BIC = -1796.08
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR7 MR5 MR3
## Correlation of (regression) scores with factors 0.97 0.95 0.91 0.88
## Multiple R square of scores with factors 0.94 0.90 0.83 0.78
## Minimum correlation of possible factor scores 0.87 0.79 0.66 0.56
## MR2 MR4 MR6
## Correlation of (regression) scores with factors 0.88 0.82 0.73
## Multiple R square of scores with factors 0.78 0.67 0.54
## Minimum correlation of possible factor scores 0.55 0.33 0.08
START MGCFA
datamale<- select(dmale, starts_with("Stest"), age, -Stest17memsentences, -Stest18memwords, -Stest27creativity)
datafemale<- select(dfemale, starts_with("Stest"), age, -Stest17memsentences, -Stest18memwords, -Stest27creativity)
# within-group CFA
chc.model <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest9electronics + Stest10mechanics
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning
'
chc.highorder.model <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest9electronics + Stest10mechanics
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning
g =~ english + math + speed + info + science + spatial
'
chc.bifactor.model <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest9electronics + Stest10mechanics
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning
g =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
'
maleCFA<-cfa(chc.model, data=datamale, meanstructure=TRUE)
fitMeasures(maleCFA, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 2532.434 501.000 0.000 0.960 0.041 0.034
## aic bic
## 189304.428 190046.953
Mc(maleCFA)
## [1] 0.6597221
maleCFA2<-cfa(chc.highorder.model, data=datamale, meanstructure=TRUE)
fitMeasures(maleCFA2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 2810.645 510.000 0.000 0.955 0.043 0.037
## aic bic
## 189564.638 190254.955
Mc(maleCFA2)
## [1] 0.6243417
maleCFA3<-cfa(chc.bifactor.model, data=datamale, meanstructure=TRUE, orthogonal=TRUE, std.lv=T)
fitMeasures(maleCFA3, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 2355.223 482.000 0.000 0.963 0.040 0.028
## aic bic
## 189165.216 190017.960
Mc(maleCFA3)
## [1] 0.681443
femaleCFA<-cfa(chc.model, data=datafemale, meanstructure=TRUE)
fitMeasures(femaleCFA, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 2906.120 501.000 0.000 0.961 0.036 0.034
## aic bic
## 274218.002 275011.639
Mc(femaleCFA)
## [1] 0.7187204
femaleCFA2<-cfa(chc.highorder.model, data=datafemale, meanstructure=TRUE)
fitMeasures(femaleCFA2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 3263.813 510.000 0.000 0.955 0.039 0.037
## aic bic
## 274557.694 275295.529
Mc(femaleCFA2)
## [1] 0.685116
femaleCFA3<-cfa(chc.bifactor.model, data=datafemale, meanstructure=TRUE, orthogonal=TRUE, std.lv=T)
fitMeasures(femaleCFA3, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 2601.074 482.000 0.000 0.965 0.035 0.025
## aic bic
## 273950.955 274862.398
Mc(femaleCFA3)
## [1] 0.7475145
# CHC common factor model
chc.factor.model <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest9electronics + Stest10mechanics
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
'
chc.factor.reduced <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest9electronics + Stest10mechanics
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
info ~ 0*1
'
baseline<-cfa(chc.factor.model, data=dgroup, meanstructure=TRUE, sampling.weights="BY_WTA")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 6177.434 500.000 0.000 0.950 0.043 0.039
## aic bic
## 468801.202 469667.255
Mc(baseline)
## [1] 0.6271389
configural<-cfa(chc.factor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T)
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 5467.973 1000.000 0.000 0.960 0.038 0.035
## aic bic
## 462404.376 464136.481
Mc(configural)
## [1] 0.6926777
summary(configural, standardized=T)
## lavaan 0.6-18 ended normally after 70 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 258
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 5467.973 4877.285
## Degrees of freedom 1000 1000
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.121
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 2506.159 2235.427
## 1 2961.814 2641.858
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv
## english =~
## Stest1vocab 0.139 0.027 5.168 0.000 0.139
## Stst19dsgsdwrd 0.386 0.033 11.591 0.000 0.386
## Stest20spellng 0.676 0.019 35.397 0.000 0.676
## Stest21cptlztn 0.716 0.016 45.632 0.000 0.716
## Stest22puncttn 0.807 0.018 45.390 0.000 0.807
## Stest23english 0.885 0.021 41.370 0.000 0.885
## Stest24exprssn 0.717 0.021 33.953 0.000 0.717
## Stst25wrdfnctn 0.180 0.038 4.749 0.000 0.180
## Stst26rdngcmpr 0.370 0.028 13.203 0.000 0.370
## Stst31bstrctrs 0.286 0.033 8.568 0.000 0.286
## Stst34rthcmptt 0.276 0.049 5.582 0.000 0.276
## math =~
## Stest5math 0.411 0.037 11.196 0.000 0.411
## Stst25wrdfnctn 0.311 0.039 7.983 0.000 0.311
## Stst32rthrsnng 0.650 0.018 36.408 0.000 0.650
## Stst33hghschlm 0.644 0.018 34.998 0.000 0.644
## Stst34rthcmptt 0.294 0.051 5.749 0.000 0.294
## speed =~
## Stst19dsgsdwrd 0.157 0.017 9.037 0.000 0.157
## Stst34rthcmptt 0.459 0.030 15.237 0.000 0.459
## Stest35tblrdng 1.159 0.046 25.325 0.000 1.159
## Stst36clrclchc 0.827 0.032 25.818 0.000 0.827
## Stst37bjctnspc 0.742 0.033 22.267 0.000 0.742
## info =~
## Stest1vocab 0.411 0.049 8.326 0.000 0.411
## Stest2literatr 0.817 0.017 48.872 0.000 0.817
## Stest3music 0.680 0.017 40.203 0.000 0.680
## Stest4soclstds 0.971 0.016 62.592 0.000 0.971
## Stst7blgclscnc 0.261 0.061 4.297 0.000 0.261
## Stest8aerontcs 0.611 0.019 31.818 0.000 0.611
## Stest11art 0.733 0.016 47.050 0.000 0.733
## Stest12law 0.646 0.019 34.417 0.000 0.646
## Stest13health 0.824 0.017 47.809 0.000 0.824
## Stest14bible 0.594 0.018 33.573 0.000 0.594
## Stest15theater 0.578 0.017 34.960 0.000 0.578
## Stest16mscllns 0.766 0.018 42.703 0.000 0.766
## Stst19dsgsdwrd 0.194 0.032 5.991 0.000 0.194
## Stst26rdngcmpr 0.636 0.028 22.894 0.000 0.636
## science =~
## Stest1vocab 0.429 0.047 9.122 0.000 0.429
## Stest5math 0.375 0.038 9.937 0.000 0.375
## Stst6physclscn 0.737 0.017 44.141 0.000 0.737
## Stst7blgclscnc 0.460 0.062 7.463 0.000 0.460
## Stest9elctrncs 0.763 0.020 37.690 0.000 0.763
## Stest10mechncs 0.666 0.016 40.705 0.000 0.666
## spatial =~
## Stst28mchnclrs 0.722 0.018 39.676 0.000 0.722
## Stst29vslztn2D 0.652 0.022 29.533 0.000 0.652
## Stst30vslztn3D 0.640 0.019 33.903 0.000 0.640
## Stst31bstrctrs 0.616 0.035 17.675 0.000 0.616
## Stst37bjctnspc 0.124 0.030 4.203 0.000 0.124
## Std.all
##
## 0.131
## 0.442
## 0.678
## 0.759
## 0.808
## 0.744
## 0.616
## 0.231
## 0.344
## 0.250
## 0.241
##
## 0.392
## 0.399
## 0.774
## 0.821
## 0.257
##
## 0.179
## 0.401
## 0.695
## 0.638
## 0.599
##
## 0.385
## 0.848
## 0.757
## 0.877
## 0.267
## 0.603
## 0.771
## 0.691
## 0.754
## 0.688
## 0.706
## 0.732
## 0.222
## 0.591
##
## 0.402
## 0.358
## 0.828
## 0.472
## 0.687
## 0.743
##
## 0.802
## 0.598
## 0.676
## 0.540
## 0.100
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv
## english ~~
## math 0.831 0.013 65.536 0.000 0.831
## speed 0.315 0.027 11.551 0.000 0.315
## info 0.833 0.010 86.338 0.000 0.833
## science 0.789 0.013 62.272 0.000 0.789
## spatial 0.687 0.017 39.286 0.000 0.687
## math ~~
## speed 0.306 0.028 11.033 0.000 0.306
## info 0.810 0.013 64.457 0.000 0.810
## science 0.792 0.013 58.802 0.000 0.792
## spatial 0.727 0.018 40.832 0.000 0.727
## speed ~~
## info 0.297 0.026 11.198 0.000 0.297
## science 0.270 0.028 9.702 0.000 0.270
## spatial 0.351 0.031 11.325 0.000 0.351
## info ~~
## science 0.914 0.008 121.150 0.000 0.914
## spatial 0.663 0.017 39.657 0.000 0.663
## science ~~
## spatial 0.729 0.017 43.640 0.000 0.729
## Std.all
##
## 0.831
## 0.315
## 0.833
## 0.789
## 0.687
##
## 0.306
## 0.810
## 0.792
## 0.727
##
## 0.297
## 0.270
## 0.351
##
## 0.914
## 0.663
##
## 0.729
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv
## .Stest1vocab -1.155 0.023 -50.360 0.000 -1.155
## .Stst19dsgsdwrd -0.992 0.018 -53.776 0.000 -0.992
## .Stest20spellng -0.848 0.021 -39.900 0.000 -0.848
## .Stest21cptlztn -1.167 0.020 -58.007 0.000 -1.167
## .Stest22puncttn -1.226 0.021 -57.496 0.000 -1.226
## .Stest23english -1.062 0.026 -41.362 0.000 -1.062
## .Stest24exprssn -0.965 0.025 -38.928 0.000 -0.965
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.871
## .Stst26rdngcmpr -1.292 0.023 -56.802 0.000 -1.292
## .Stst31bstrctrs -1.070 0.024 -43.766 0.000 -1.070
## .Stst34rthcmptt -1.153 0.025 -46.702 0.000 -1.153
## .Stest5math -0.814 0.022 -36.442 0.000 -0.814
## .Stst32rthrsnng -1.052 0.018 -59.194 0.000 -1.052
## .Stst33hghschlm -0.875 0.016 -53.483 0.000 -0.875
## .Stest35tblrdng -0.712 0.037 -19.463 0.000 -0.712
## .Stst36clrclchc -0.032 0.028 -1.139 0.255 -0.032
## .Stst37bjctnspc -0.318 0.027 -11.957 0.000 -0.318
## .Stest2literatr -1.041 0.021 -50.624 0.000 -1.041
## .Stest3music -0.921 0.019 -48.386 0.000 -0.921
## .Stest4soclstds -1.083 0.023 -46.133 0.000 -1.083
## .Stst7blgclscnc -0.617 0.021 -29.442 0.000 -0.617
## .Stest8aerontcs -0.517 0.022 -23.664 0.000 -0.517
## .Stest11art -1.040 0.020 -51.542 0.000 -1.040
## .Stest12law -0.778 0.020 -39.122 0.000 -0.778
## .Stest13health -1.200 0.023 -51.595 0.000 -1.200
## .Stest14bible -0.720 0.018 -39.356 0.000 -0.720
## .Stest15theater -1.025 0.017 -59.426 0.000 -1.025
## .Stest16mscllns -0.887 0.022 -39.478 0.000 -0.887
## .Stst6physclscn -0.732 0.019 -38.793 0.000 -0.732
## .Stest9elctrncs -0.668 0.024 -27.887 0.000 -0.668
## .Stest10mechncs -0.656 0.019 -33.970 0.000 -0.656
## .Stst28mchnclrs -0.715 0.019 -36.895 0.000 -0.715
## .Stst29vslztn2D -0.512 0.023 -22.047 0.000 -0.512
## .Stst30vslztn3D -0.723 0.020 -35.874 0.000 -0.723
## Std.all
## -1.083
## -1.136
## -0.851
## -1.236
## -1.229
## -0.893
## -0.829
## -1.119
## -1.202
## -0.937
## -1.006
## -0.777
## -1.253
## -1.115
## -0.427
## -0.025
## -0.257
## -1.080
## -1.026
## -0.978
## -0.633
## -0.510
## -1.093
## -0.832
## -1.098
## -0.834
## -1.254
## -0.848
## -0.822
## -0.601
## -0.732
## -0.795
## -0.469
## -0.763
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv
## .Stest1vocab 0.255 0.009 27.925 0.000 0.255
## .Stst19dsgsdwrd 0.370 0.013 27.820 0.000 0.370
## .Stest20spellng 0.537 0.017 30.724 0.000 0.537
## .Stest21cptlztn 0.378 0.015 24.854 0.000 0.378
## .Stest22puncttn 0.345 0.013 27.580 0.000 0.345
## .Stest23english 0.631 0.024 26.774 0.000 0.631
## .Stest24exprssn 0.842 0.026 32.424 0.000 0.842
## .Stst25wrdfnctn 0.384 0.012 32.654 0.000 0.384
## .Stst26rdngcmpr 0.223 0.009 24.858 0.000 0.223
## .Stst31bstrctrs 0.600 0.023 26.173 0.000 0.600
## .Stst34rthcmptt 0.641 0.029 21.900 0.000 0.641
## .Stest5math 0.543 0.020 27.199 0.000 0.543
## .Stst32rthrsnng 0.282 0.011 25.871 0.000 0.282
## .Stst33hghschlm 0.201 0.009 21.898 0.000 0.201
## .Stest35tblrdng 1.439 0.087 16.560 0.000 1.439
## .Stst36clrclchc 0.994 0.049 20.248 0.000 0.994
## .Stst37bjctnspc 0.903 0.039 23.336 0.000 0.903
## .Stest2literatr 0.260 0.009 29.086 0.000 0.260
## .Stest3music 0.345 0.012 29.047 0.000 0.345
## .Stest4soclstds 0.282 0.010 27.036 0.000 0.282
## .Stst7blgclscnc 0.451 0.014 31.985 0.000 0.451
## .Stest8aerontcs 0.655 0.018 36.968 0.000 0.655
## .Stest11art 0.367 0.012 29.969 0.000 0.367
## .Stest12law 0.458 0.014 33.104 0.000 0.458
## .Stest13health 0.515 0.016 31.938 0.000 0.515
## .Stest14bible 0.392 0.013 29.174 0.000 0.392
## .Stest15theater 0.335 0.011 30.878 0.000 0.335
## .Stest16mscllns 0.508 0.016 31.051 0.000 0.508
## .Stst6physclscn 0.249 0.011 23.237 0.000 0.249
## .Stest9elctrncs 0.652 0.027 24.505 0.000 0.652
## .Stest10mechncs 0.360 0.013 27.782 0.000 0.360
## .Stst28mchnclrs 0.288 0.016 18.381 0.000 0.288
## .Stst29vslztn2D 0.764 0.027 28.061 0.000 0.764
## .Stst30vslztn3D 0.488 0.017 27.999 0.000 0.488
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## Std.all
## 0.224
## 0.486
## 0.540
## 0.424
## 0.347
## 0.446
## 0.621
## 0.634
## 0.193
## 0.460
## 0.489
## 0.495
## 0.400
## 0.327
## 0.517
## 0.592
## 0.588
## 0.280
## 0.427
## 0.230
## 0.475
## 0.637
## 0.406
## 0.523
## 0.431
## 0.526
## 0.501
## 0.464
## 0.314
## 0.528
## 0.448
## 0.356
## 0.642
## 0.543
## 1.000
## 1.000
## 1.000
## 1.000
## 1.000
## 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv
## english =~
## Stest1vocab 0.127 0.024 5.300 0.000 0.127
## Stst19dsgsdwrd 0.387 0.030 12.700 0.000 0.387
## Stest20spellng 0.643 0.015 42.930 0.000 0.643
## Stest21cptlztn 0.758 0.014 55.895 0.000 0.758
## Stest22puncttn 0.814 0.014 58.255 0.000 0.814
## Stest23english 0.792 0.016 48.012 0.000 0.792
## Stest24exprssn 0.611 0.017 35.932 0.000 0.611
## Stst25wrdfnctn 0.099 0.031 3.215 0.001 0.099
## Stst26rdngcmpr 0.344 0.021 16.050 0.000 0.344
## Stst31bstrctrs 0.308 0.029 10.553 0.000 0.308
## Stst34rthcmptt 0.284 0.043 6.622 0.000 0.284
## math =~
## Stest5math 0.290 0.035 8.191 0.000 0.290
## Stst25wrdfnctn 0.447 0.032 13.930 0.000 0.447
## Stst32rthrsnng 0.516 0.015 33.619 0.000 0.516
## Stst33hghschlm 0.537 0.014 38.176 0.000 0.537
## Stst34rthcmptt 0.230 0.042 5.537 0.000 0.230
## speed =~
## Stst19dsgsdwrd 0.211 0.016 13.467 0.000 0.211
## Stst34rthcmptt 0.493 0.027 18.500 0.000 0.493
## Stest35tblrdng 1.145 0.037 30.664 0.000 1.145
## Stst36clrclchc 0.804 0.026 31.386 0.000 0.804
## Stst37bjctnspc 0.708 0.025 28.515 0.000 0.708
## info =~
## Stest1vocab 0.485 0.035 13.748 0.000 0.485
## Stest2literatr 0.741 0.014 54.745 0.000 0.741
## Stest3music 0.692 0.013 51.520 0.000 0.692
## Stest4soclstds 0.740 0.012 59.973 0.000 0.740
## Stst7blgclscnc 0.299 0.038 7.809 0.000 0.299
## Stest8aerontcs 0.256 0.015 16.761 0.000 0.256
## Stest11art 0.728 0.014 50.934 0.000 0.728
## Stest12law 0.489 0.014 34.149 0.000 0.489
## Stest13health 0.786 0.014 55.281 0.000 0.786
## Stest14bible 0.578 0.014 41.045 0.000 0.578
## Stest15theater 0.609 0.015 41.691 0.000 0.609
## Stest16mscllns 0.601 0.014 43.120 0.000 0.601
## Stst19dsgsdwrd 0.242 0.029 8.326 0.000 0.242
## Stst26rdngcmpr 0.547 0.021 25.635 0.000 0.547
## science =~
## Stest1vocab 0.196 0.030 6.624 0.000 0.196
## Stest5math 0.357 0.035 10.129 0.000 0.357
## Stst6physclscn 0.509 0.013 38.005 0.000 0.509
## Stst7blgclscnc 0.213 0.041 5.189 0.000 0.213
## Stest9elctrncs 0.390 0.018 21.779 0.000 0.390
## Stest10mechncs 0.362 0.011 31.762 0.000 0.362
## spatial =~
## Stst28mchnclrs 0.382 0.013 29.049 0.000 0.382
## Stst29vslztn2D 0.548 0.019 29.149 0.000 0.548
## Stst30vslztn3D 0.472 0.015 31.616 0.000 0.472
## Stst31bstrctrs 0.537 0.031 17.374 0.000 0.537
## Stst37bjctnspc 0.124 0.024 5.211 0.000 0.124
## Std.all
##
## 0.139
## 0.412
## 0.667
## 0.750
## 0.825
## 0.726
## 0.566
## 0.124
## 0.355
## 0.282
## 0.245
##
## 0.294
## 0.560
## 0.699
## 0.773
## 0.199
##
## 0.224
## 0.427
## 0.705
## 0.628
## 0.616
##
## 0.527
## 0.831
## 0.764
## 0.828
## 0.354
## 0.308
## 0.755
## 0.601
## 0.713
## 0.662
## 0.690
## 0.660
## 0.258
## 0.564
##
## 0.213
## 0.362
## 0.736
## 0.253
## 0.406
## 0.591
##
## 0.624
## 0.554
## 0.611
## 0.491
## 0.108
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv
## english ~~
## math 0.825 0.011 73.123 0.000 0.825
## speed 0.336 0.024 13.972 0.000 0.336
## info 0.831 0.008 107.185 0.000 0.831
## science 0.711 0.015 48.546 0.000 0.711
## spatial 0.686 0.017 41.286 0.000 0.686
## math ~~
## speed 0.268 0.024 11.121 0.000 0.268
## info 0.772 0.012 63.947 0.000 0.772
## science 0.809 0.016 49.137 0.000 0.809
## spatial 0.746 0.019 40.262 0.000 0.746
## speed ~~
## info 0.296 0.022 13.533 0.000 0.296
## science 0.293 0.025 11.765 0.000 0.293
## spatial 0.317 0.028 11.496 0.000 0.317
## info ~~
## science 0.853 0.011 76.882 0.000 0.853
## spatial 0.642 0.018 35.976 0.000 0.642
## science ~~
## spatial 0.633 0.022 28.717 0.000 0.633
## Std.all
##
## 0.825
## 0.336
## 0.831
## 0.711
## 0.686
##
## 0.268
## 0.772
## 0.809
## 0.746
##
## 0.296
## 0.293
## 0.317
##
## 0.853
## 0.642
##
## 0.633
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv
## .Stest1vocab -1.339 0.016 -83.554 0.000 -1.339
## .Stst19dsgsdwrd -0.878 0.016 -54.059 0.000 -0.878
## .Stest20spellng -0.450 0.017 -26.686 0.000 -0.450
## .Stest21cptlztn -0.899 0.017 -51.477 0.000 -0.899
## .Stest22puncttn -0.929 0.017 -53.286 0.000 -0.929
## .Stest23english -0.744 0.019 -38.449 0.000 -0.744
## .Stest24exprssn -0.704 0.019 -37.099 0.000 -0.704
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.788
## .Stst26rdngcmpr -1.226 0.017 -72.842 0.000 -1.226
## .Stst31bstrctrs -1.260 0.019 -65.843 0.000 -1.260
## .Stst34rthcmptt -1.004 0.021 -47.990 0.000 -1.004
## .Stest5math -0.965 0.017 -55.615 0.000 -0.965
## .Stst32rthrsnng -1.184 0.013 -92.849 0.000 -1.184
## .Stst33hghschlm -0.942 0.012 -78.389 0.000 -0.942
## .Stest35tblrdng -0.524 0.029 -17.830 0.000 -0.524
## .Stst36clrclchc 0.300 0.023 13.284 0.000 0.300
## .Stst37bjctnspc -0.217 0.021 -10.567 0.000 -0.217
## .Stest2literatr -1.034 0.016 -66.363 0.000 -1.034
## .Stest3music -0.825 0.016 -52.646 0.000 -0.825
## .Stest4soclstds -1.273 0.015 -82.694 0.000 -1.273
## .Stst7blgclscnc -0.831 0.015 -55.991 0.000 -0.831
## .Stest8aerontcs -0.942 0.014 -64.960 0.000 -0.942
## .Stest11art -1.046 0.017 -63.114 0.000 -1.046
## .Stest12law -0.897 0.014 -63.710 0.000 -0.897
## .Stest13health -1.020 0.019 -52.885 0.000 -1.020
## .Stest14bible -0.565 0.015 -36.958 0.000 -0.565
## .Stest15theater -0.856 0.015 -56.660 0.000 -0.856
## .Stest16mscllns -0.949 0.016 -60.013 0.000 -0.949
## .Stst6physclscn -1.022 0.012 -84.927 0.000 -1.022
## .Stest9elctrncs -1.154 0.017 -68.546 0.000 -1.154
## .Stest10mechncs -1.373 0.011 -128.778 0.000 -1.373
## .Stst28mchnclrs -1.323 0.011 -124.285 0.000 -1.323
## .Stst29vslztn2D -0.916 0.017 -52.801 0.000 -0.916
## .Stst30vslztn3D -0.982 0.014 -72.639 0.000 -0.982
## Std.all
## -1.455
## -0.935
## -0.467
## -0.889
## -0.942
## -0.682
## -0.652
## -0.989
## -1.265
## -1.152
## -0.868
## -0.978
## -1.604
## -1.356
## -0.323
## 0.234
## -0.189
## -1.160
## -0.911
## -1.425
## -0.984
## -1.133
## -1.085
## -1.101
## -0.926
## -0.647
## -0.970
## -1.042
## -1.477
## -1.202
## -2.245
## -2.162
## -0.926
## -1.270
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv
## .Stest1vocab 0.257 0.007 35.154 0.000 0.257
## .Stst19dsgsdwrd 0.388 0.011 35.855 0.000 0.388
## .Stest20spellng 0.515 0.014 36.858 0.000 0.515
## .Stest21cptlztn 0.448 0.014 32.323 0.000 0.448
## .Stest22puncttn 0.310 0.011 29.331 0.000 0.310
## .Stest23english 0.563 0.017 33.325 0.000 0.563
## .Stest24exprssn 0.794 0.021 37.646 0.000 0.794
## .Stst25wrdfnctn 0.354 0.010 33.792 0.000 0.354
## .Stst26rdngcmpr 0.210 0.007 29.436 0.000 0.210
## .Stst31bstrctrs 0.586 0.018 31.940 0.000 0.586
## .Stst34rthcmptt 0.698 0.026 26.510 0.000 0.698
## .Stest5math 0.594 0.017 35.602 0.000 0.594
## .Stst32rthrsnng 0.279 0.008 33.726 0.000 0.279
## .Stst33hghschlm 0.194 0.007 27.570 0.000 0.194
## .Stest35tblrdng 1.326 0.071 18.602 0.000 1.326
## .Stst36clrclchc 0.994 0.037 26.541 0.000 0.994
## .Stst37bjctnspc 0.747 0.029 25.908 0.000 0.747
## .Stest2literatr 0.246 0.007 35.902 0.000 0.246
## .Stest3music 0.342 0.009 37.630 0.000 0.342
## .Stest4soclstds 0.250 0.007 34.768 0.000 0.250
## .Stst7blgclscnc 0.470 0.012 39.301 0.000 0.470
## .Stest8aerontcs 0.626 0.011 58.944 0.000 0.626
## .Stest11art 0.399 0.011 36.856 0.000 0.399
## .Stest12law 0.424 0.011 40.342 0.000 0.424
## .Stest13health 0.596 0.015 40.467 0.000 0.596
## .Stest14bible 0.428 0.012 34.528 0.000 0.428
## .Stest15theater 0.407 0.011 38.421 0.000 0.407
## .Stest16mscllns 0.468 0.012 38.004 0.000 0.468
## .Stst6physclscn 0.219 0.007 30.026 0.000 0.219
## .Stest9elctrncs 0.770 0.020 38.972 0.000 0.770
## .Stest10mechncs 0.243 0.006 37.444 0.000 0.243
## .Stst28mchnclrs 0.229 0.007 32.889 0.000 0.229
## .Stst29vslztn2D 0.677 0.020 33.785 0.000 0.677
## .Stst30vslztn3D 0.374 0.011 33.057 0.000 0.374
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## Std.all
## 0.303
## 0.440
## 0.555
## 0.438
## 0.319
## 0.473
## 0.680
## 0.556
## 0.224
## 0.490
## 0.522
## 0.610
## 0.511
## 0.403
## 0.503
## 0.606
## 0.567
## 0.310
## 0.416
## 0.314
## 0.658
## 0.905
## 0.429
## 0.639
## 0.491
## 0.562
## 0.523
## 0.564
## 0.458
## 0.835
## 0.650
## 0.611
## 0.693
## 0.627
## 1.000
## 1.000
## 1.000
## 1.000
## 1.000
## 1.000
modificationIndices(configural, sort=T, maximum.number=30)
## lhs op rhs block group
## 1005 english =~ Stest35tablereading 2 2
## 1034 math =~ Stest35tablereading 2 2
## 1094 info =~ Stest35tablereading 2 2
## 1144 spatial =~ Stest35tablereading 2 2
## 1115 science =~ Stest35tablereading 2 2
## 315 math =~ Stest35tablereading 1 1
## 1006 english =~ Stest36clericalchecking 2 2
## 425 spatial =~ Stest35tablereading 1 1
## 286 english =~ Stest35tablereading 1 1
## 1133 spatial =~ Stest20spelling 2 2
## 1145 spatial =~ Stest36clericalchecking 2 2
## 1035 math =~ Stest36clericalchecking 2 2
## 375 info =~ Stest35tablereading 1 1
## 1128 science =~ Stest28mechanicalreasoning 2 2
## 396 science =~ Stest35tablereading 1 1
## 409 science =~ Stest28mechanicalreasoning 1 1
## 1100 info =~ Stest28mechanicalreasoning 2 2
## 414 spatial =~ Stest20spelling 1 1
## 1051 math =~ Stest28mechanicalreasoning 2 2
## 1095 info =~ Stest36clericalchecking 2 2
## 426 spatial =~ Stest36clericalchecking 1 1
## 317 math =~ Stest37objectinspection 1 1
## 362 speed =~ Stest29visualization2D 1 1
## 1116 science =~ Stest36clericalchecking 2 2
## 402 science =~ Stest8aeronautics 1 1
## 1206 Stest19disguisedwords ~~ Stest36clericalchecking 2 2
## 1048 math =~ Stest6physicalscience 2 2
## 988 Stest6physicalscience ~~ Stest10mechanics 1 1
## 1120 science =~ Stest4socialstudies 2 2
## 1447 Stest34arithcomputation ~~ Stest33highschoolmath 2 2
## level mi epc sepc.lv sepc.all sepc.nox
## 1005 1 283.761 0.560 0.560 0.345 0.345
## 1034 1 264.686 0.547 0.547 0.337 0.337
## 1094 1 242.239 0.474 0.474 0.292 0.292
## 1144 1 212.872 0.544 0.544 0.335 0.335
## 1115 1 207.606 0.467 0.467 0.288 0.288
## 315 1 188.320 0.573 0.573 0.344 0.344
## 1006 1 155.511 -0.303 -0.303 -0.237 -0.237
## 425 1 155.364 0.559 0.559 0.335 0.335
## 286 1 154.825 0.506 0.506 0.303 0.303
## 1133 1 147.133 -0.303 -0.303 -0.314 -0.314
## 1145 1 136.084 -0.313 -0.313 -0.245 -0.245
## 1035 1 135.759 -0.285 -0.285 -0.222 -0.222
## 375 1 134.842 0.439 0.439 0.263 0.263
## 1128 1 134.764 0.207 0.207 0.339 0.339
## 396 1 128.096 0.440 0.440 0.264 0.264
## 409 1 122.918 0.352 0.352 0.392 0.392
## 1100 1 110.303 0.172 0.172 0.282 0.282
## 414 1 106.962 -0.290 -0.290 -0.291 -0.291
## 1051 1 106.139 0.250 0.250 0.408 0.408
## 1095 1 102.417 -0.230 -0.230 -0.179 -0.179
## 426 1 102.019 -0.330 -0.330 -0.254 -0.254
## 317 1 87.705 -0.398 -0.398 -0.321 -0.321
## 362 1 86.456 0.232 0.232 0.213 0.213
## 1116 1 83.626 -0.221 -0.221 -0.172 -0.172
## 402 1 76.288 0.547 0.547 0.539 0.539
## 1206 1 72.809 0.108 0.108 0.173 0.173
## 1048 1 72.579 0.279 0.279 0.403 0.403
## 988 1 70.428 -0.073 -0.073 -0.243 -0.243
## 1120 1 69.074 0.230 0.230 0.258 0.258
## 1447 1 67.207 0.067 0.067 0.181 0.181
metric<-cfa(chc.factor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 6283.722 1040.000 0.000 0.953 0.041 0.052
## aic bic
## 463140.125 464603.686
Mc(metric)
## [1] 0.6498955
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 97 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 264
## Number of equality constraints 46
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 6283.722 5605.333
## Degrees of freedom 1040 1040
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.121
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 2928.844 2612.646
## 1 3354.878 2992.687
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.142 0.018 8.037 0.000 0.107
## Stst19d (.p2.) 0.399 0.023 17.648 0.000 0.355
## Stst20s (.p3.) 0.658 0.015 44.762 0.000 0.629
## Stst21c (.p4.) 0.742 0.013 55.549 0.000 0.715
## Stst22p (.p5.) 0.813 0.015 54.326 0.000 0.784
## Stst23n (.p6.) 0.828 0.017 48.077 0.000 0.794
## Stst24x (.p7.) 0.653 0.016 39.950 0.000 0.621
## Stst25w (.p8.) 0.158 0.024 6.559 0.000 0.111
## Stst26r (.p9.) 0.351 0.018 19.921 0.000 0.316
## Stst31b (.10.) 0.335 0.021 15.991 0.000 0.294
## Stst34r (.11.) 0.279 0.032 8.757 0.000 0.216
## math =~
## Stst5mt (.12.) 0.416 0.027 15.617 0.000 0.364
## Stst25w (.13.) 0.396 0.026 15.038 0.000 0.344
## Stst32r (.14.) 0.622 0.017 36.291 0.000 0.588
## Stst33h (.15.) 0.635 0.017 36.322 0.000 0.600
## Stst34r (.16.) 0.283 0.035 8.119 0.000 0.215
## speed =~
## Stst19d (.17.) 0.188 0.012 16.167 0.000 0.166
## Stst34r (.18.) 0.477 0.021 22.643 0.000 0.436
## Stst35t (.19.) 1.147 0.035 32.664 0.000 1.079
## Stst36c (.20.) 0.810 0.025 32.526 0.000 0.761
## Stst37b (.21.) 0.719 0.024 29.469 0.000 0.671
## info =~
## Stst1vc (.22.) 0.506 0.030 16.880 0.000 0.447
## Stst2lt (.23.) 0.830 0.014 57.446 0.000 0.802
## Stst3ms (.24.) 0.736 0.014 53.634 0.000 0.709
## Stst4sc (.25.) 0.894 0.016 57.626 0.000 0.864
## Stst7bl (.26.) 0.301 0.031 9.606 0.000 0.240
## Stst8rn (.27.) 0.432 0.016 27.495 0.000 0.401
## Stst11r (.28.) 0.781 0.014 57.613 0.000 0.754
## Stst12l (.29.) 0.596 0.015 40.897 0.000 0.567
## Stst13h (.30.) 0.858 0.015 57.034 0.000 0.828
## Stst14b (.31.) 0.626 0.014 45.476 0.000 0.599
## Stst15t (.32.) 0.632 0.013 47.599 0.000 0.606
## Stst16m (.33.) 0.719 0.015 47.998 0.000 0.690
## Stst19d (.34.) 0.225 0.023 9.673 0.000 0.179
## Stst26r (.35.) 0.632 0.019 32.666 0.000 0.594
## science =~
## Stst1vc (.36.) 0.342 0.027 12.486 0.000 0.288
## Stst5mt (.37.) 0.404 0.030 13.454 0.000 0.345
## Stst6ph (.38.) 0.767 0.015 50.789 0.000 0.737
## Stst7bl (.39.) 0.412 0.037 11.042 0.000 0.339
## Stst9lc (.40.) 0.722 0.019 37.615 0.000 0.684
## Stst10m (.41.) 0.628 0.015 41.156 0.000 0.599
## spatial =~
## Stst28m (.42.) 0.641 0.019 34.370 0.000 0.604
## Sts292D (.43.) 0.713 0.018 40.035 0.000 0.678
## Sts303D (.44.) 0.663 0.016 40.893 0.000 0.631
## Stst31b (.45.) 0.642 0.025 25.565 0.000 0.593
## Stst37b (.46.) 0.150 0.022 6.782 0.000 0.107
## ci.upper Std.lv Std.all
##
## 0.176 0.142 0.132
## 0.444 0.399 0.437
## 0.686 0.658 0.667
## 0.768 0.742 0.772
## 0.843 0.813 0.812
## 0.862 0.828 0.718
## 0.685 0.653 0.577
## 0.205 0.158 0.194
## 0.385 0.351 0.332
## 0.376 0.335 0.283
## 0.341 0.279 0.243
##
## 0.468 0.416 0.389
## 0.448 0.396 0.485
## 0.655 0.622 0.756
## 0.669 0.635 0.815
## 0.351 0.283 0.247
##
## 0.211 0.188 0.206
## 0.519 0.477 0.416
## 1.216 1.147 0.689
## 0.858 0.810 0.630
## 0.767 0.719 0.582
##
## 0.564 0.506 0.469
## 0.859 0.830 0.853
## 0.763 0.736 0.782
## 0.925 0.894 0.853
## 0.362 0.301 0.311
## 0.463 0.432 0.461
## 0.807 0.781 0.791
## 0.624 0.596 0.658
## 0.887 0.858 0.767
## 0.653 0.626 0.708
## 0.658 0.632 0.738
## 0.749 0.719 0.709
## 0.270 0.225 0.246
## 0.670 0.632 0.598
##
## 0.395 0.342 0.317
## 0.463 0.404 0.378
## 0.796 0.767 0.843
## 0.485 0.412 0.425
## 0.759 0.722 0.665
## 0.658 0.628 0.719
##
## 0.677 0.641 0.745
## 0.748 0.713 0.639
## 0.694 0.663 0.694
## 0.692 0.642 0.543
## 0.194 0.150 0.122
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.831 0.013 65.545 0.000 0.806
## speed 0.300 0.026 11.451 0.000 0.249
## info 0.832 0.010 86.977 0.000 0.813
## science 0.783 0.012 62.902 0.000 0.759
## spatial 0.675 0.018 38.496 0.000 0.641
## math ~~
## speed 0.297 0.026 11.325 0.000 0.246
## info 0.809 0.012 65.431 0.000 0.785
## science 0.791 0.014 57.287 0.000 0.764
## spatial 0.718 0.018 40.703 0.000 0.684
## speed ~~
## info 0.287 0.025 11.371 0.000 0.238
## science 0.260 0.027 9.573 0.000 0.207
## spatial 0.348 0.029 12.101 0.000 0.292
## info ~~
## science 0.908 0.008 119.428 0.000 0.893
## spatial 0.651 0.017 38.402 0.000 0.618
## science ~~
## spatial 0.710 0.018 40.316 0.000 0.676
## ci.upper Std.lv Std.all
##
## 0.856 0.831 0.831
## 0.351 0.300 0.300
## 0.851 0.832 0.832
## 0.808 0.783 0.783
## 0.709 0.675 0.675
##
## 0.349 0.297 0.297
## 0.833 0.809 0.809
## 0.818 0.791 0.791
## 0.753 0.718 0.718
##
## 0.337 0.287 0.287
## 0.313 0.260 0.260
## 0.404 0.348 0.348
##
## 0.923 0.908 0.908
## 0.684 0.651 0.651
##
## 0.745 0.710 0.710
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -1.155 0.023 -50.360 0.000 -1.200
## .Stst19dsgsdwrd -0.992 0.018 -53.776 0.000 -1.028
## .Stest20spellng -0.848 0.021 -39.900 0.000 -0.890
## .Stest21cptlztn -1.167 0.020 -58.007 0.000 -1.206
## .Stest22puncttn -1.226 0.021 -57.496 0.000 -1.268
## .Stest23english -1.062 0.026 -41.362 0.000 -1.113
## .Stest24exprssn -0.965 0.025 -38.928 0.000 -1.014
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.903
## .Stst26rdngcmpr -1.292 0.023 -56.802 0.000 -1.337
## .Stst31bstrctrs -1.070 0.024 -43.766 0.000 -1.118
## .Stst34rthcmptt -1.153 0.025 -46.702 0.000 -1.201
## .Stest5math -0.814 0.022 -36.442 0.000 -0.857
## .Stst32rthrsnng -1.052 0.018 -59.194 0.000 -1.087
## .Stst33hghschlm -0.875 0.016 -53.483 0.000 -0.907
## .Stest35tblrdng -0.712 0.037 -19.463 0.000 -0.784
## .Stst36clrclchc -0.032 0.028 -1.139 0.255 -0.086
## .Stst37bjctnspc -0.318 0.027 -11.957 0.000 -0.370
## .Stest2literatr -1.041 0.021 -50.624 0.000 -1.081
## .Stest3music -0.921 0.019 -48.386 0.000 -0.959
## .Stest4soclstds -1.083 0.023 -46.133 0.000 -1.129
## .Stst7blgclscnc -0.617 0.021 -29.442 0.000 -0.658
## .Stest8aerontcs -0.517 0.022 -23.664 0.000 -0.560
## .Stest11art -1.040 0.020 -51.542 0.000 -1.079
## .Stest12law -0.778 0.020 -39.122 0.000 -0.817
## .Stest13health -1.200 0.023 -51.595 0.000 -1.245
## .Stest14bible -0.720 0.018 -39.356 0.000 -0.756
## .Stest15theater -1.025 0.017 -59.426 0.000 -1.059
## .Stest16mscllns -0.887 0.022 -39.478 0.000 -0.931
## .Stst6physclscn -0.732 0.019 -38.793 0.000 -0.769
## .Stest9elctrncs -0.668 0.024 -27.887 0.000 -0.715
## .Stest10mechncs -0.656 0.019 -33.970 0.000 -0.694
## .Stst28mchnclrs -0.715 0.019 -36.895 0.000 -0.753
## .Stst29vslztn2D -0.512 0.023 -22.047 0.000 -0.557
## .Stst30vslztn3D -0.723 0.020 -35.874 0.000 -0.762
## ci.upper Std.lv Std.all
## -1.110 -1.155 -1.072
## -0.956 -0.992 -1.087
## -0.806 -0.848 -0.861
## -1.128 -1.167 -1.215
## -1.184 -1.226 -1.224
## -1.012 -1.062 -0.921
## -0.916 -0.965 -0.853
## -0.838 -0.871 -1.067
## -1.248 -1.292 -1.223
## -1.022 -1.070 -0.905
## -1.104 -1.153 -1.006
## -0.770 -0.814 -0.761
## -1.017 -1.052 -1.279
## -0.843 -0.875 -1.124
## -0.640 -0.712 -0.428
## 0.023 -0.032 -0.025
## -0.266 -0.318 -0.258
## -1.000 -1.041 -1.069
## -0.884 -0.921 -0.980
## -1.037 -1.083 -1.033
## -0.576 -0.617 -0.636
## -0.475 -0.517 -0.551
## -1.000 -1.040 -1.054
## -0.739 -0.778 -0.860
## -1.154 -1.200 -1.073
## -0.684 -0.720 -0.814
## -0.991 -1.025 -1.197
## -0.843 -0.887 -0.874
## -0.695 -0.732 -0.805
## -0.621 -0.668 -0.616
## -0.618 -0.656 -0.751
## -0.677 -0.715 -0.831
## -0.466 -0.512 -0.458
## -0.683 -0.723 -0.757
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.259 0.009 28.075 0.000 0.241
## .Stst19dsgsdwrd 0.369 0.013 27.576 0.000 0.343
## .Stest20spellng 0.539 0.017 31.385 0.000 0.505
## .Stest21cptlztn 0.372 0.015 24.715 0.000 0.343
## .Stest22puncttn 0.342 0.012 27.964 0.000 0.318
## .Stest23english 0.646 0.024 26.796 0.000 0.599
## .Stest24exprssn 0.855 0.026 33.402 0.000 0.804
## .Stst25wrdfnctn 0.380 0.012 32.200 0.000 0.357
## .Stst26rdngcmpr 0.225 0.009 25.280 0.000 0.208
## .Stst31bstrctrs 0.583 0.022 26.332 0.000 0.540
## .Stst34rthcmptt 0.637 0.030 21.287 0.000 0.578
## .Stest5math 0.540 0.020 27.023 0.000 0.501
## .Stst32rthrsnng 0.290 0.011 27.076 0.000 0.269
## .Stst33hghschlm 0.203 0.009 22.566 0.000 0.186
## .Stest35tblrdng 1.455 0.076 19.105 0.000 1.306
## .Stst36clrclchc 0.997 0.042 23.773 0.000 0.914
## .Stst37bjctnspc 0.909 0.035 26.179 0.000 0.841
## .Stest2literatr 0.259 0.009 29.288 0.000 0.241
## .Stest3music 0.344 0.012 28.750 0.000 0.320
## .Stest4soclstds 0.299 0.011 27.851 0.000 0.278
## .Stst7blgclscnc 0.454 0.014 32.335 0.000 0.427
## .Stest8aerontcs 0.694 0.018 39.169 0.000 0.659
## .Stest11art 0.364 0.012 29.797 0.000 0.340
## .Stest12law 0.463 0.014 33.421 0.000 0.436
## .Stest13health 0.514 0.016 31.841 0.000 0.482
## .Stest14bible 0.391 0.013 29.048 0.000 0.364
## .Stest15theater 0.334 0.011 30.532 0.000 0.313
## .Stest16mscllns 0.513 0.016 31.237 0.000 0.481
## .Stst6physclscn 0.239 0.010 22.965 0.000 0.218
## .Stest9elctrncs 0.656 0.027 24.550 0.000 0.604
## .Stest10mechncs 0.369 0.013 28.401 0.000 0.344
## .Stst28mchnclrs 0.330 0.016 20.703 0.000 0.299
## .Stst29vslztn2D 0.738 0.026 27.973 0.000 0.686
## .Stst30vslztn3D 0.472 0.017 27.857 0.000 0.439
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.277 0.259 0.223
## 0.396 0.369 0.443
## 0.572 0.539 0.555
## 0.402 0.372 0.404
## 0.366 0.342 0.341
## 0.693 0.646 0.485
## 0.905 0.855 0.667
## 0.403 0.380 0.570
## 0.243 0.225 0.202
## 0.626 0.583 0.417
## 0.695 0.637 0.485
## 0.579 0.540 0.473
## 0.311 0.290 0.429
## 0.221 0.203 0.335
## 1.605 1.455 0.525
## 1.079 0.997 0.603
## 0.977 0.909 0.597
## 0.276 0.259 0.273
## 0.367 0.344 0.388
## 0.320 0.299 0.272
## 0.482 0.454 0.483
## 0.729 0.694 0.788
## 0.388 0.364 0.374
## 0.490 0.463 0.566
## 0.546 0.514 0.411
## 0.417 0.391 0.499
## 0.356 0.334 0.455
## 0.545 0.513 0.498
## 0.259 0.239 0.289
## 0.709 0.656 0.558
## 0.395 0.369 0.483
## 0.361 0.330 0.445
## 0.790 0.738 0.592
## 0.506 0.472 0.518
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.142 0.018 8.037 0.000 0.107
## Stst19d (.p2.) 0.399 0.023 17.648 0.000 0.355
## Stst20s (.p3.) 0.658 0.015 44.762 0.000 0.629
## Stst21c (.p4.) 0.742 0.013 55.549 0.000 0.715
## Stst22p (.p5.) 0.813 0.015 54.326 0.000 0.784
## Stst23n (.p6.) 0.828 0.017 48.077 0.000 0.794
## Stst24x (.p7.) 0.653 0.016 39.950 0.000 0.621
## Stst25w (.p8.) 0.158 0.024 6.559 0.000 0.111
## Stst26r (.p9.) 0.351 0.018 19.921 0.000 0.316
## Stst31b (.10.) 0.335 0.021 15.991 0.000 0.294
## Stst34r (.11.) 0.279 0.032 8.757 0.000 0.216
## math =~
## Stst5mt (.12.) 0.416 0.027 15.617 0.000 0.364
## Stst25w (.13.) 0.396 0.026 15.038 0.000 0.344
## Stst32r (.14.) 0.622 0.017 36.291 0.000 0.588
## Stst33h (.15.) 0.635 0.017 36.322 0.000 0.600
## Stst34r (.16.) 0.283 0.035 8.119 0.000 0.215
## speed =~
## Stst19d (.17.) 0.188 0.012 16.167 0.000 0.166
## Stst34r (.18.) 0.477 0.021 22.643 0.000 0.436
## Stst35t (.19.) 1.147 0.035 32.664 0.000 1.079
## Stst36c (.20.) 0.810 0.025 32.526 0.000 0.761
## Stst37b (.21.) 0.719 0.024 29.469 0.000 0.671
## info =~
## Stst1vc (.22.) 0.506 0.030 16.880 0.000 0.447
## Stst2lt (.23.) 0.830 0.014 57.446 0.000 0.802
## Stst3ms (.24.) 0.736 0.014 53.634 0.000 0.709
## Stst4sc (.25.) 0.894 0.016 57.626 0.000 0.864
## Stst7bl (.26.) 0.301 0.031 9.606 0.000 0.240
## Stst8rn (.27.) 0.432 0.016 27.495 0.000 0.401
## Stst11r (.28.) 0.781 0.014 57.613 0.000 0.754
## Stst12l (.29.) 0.596 0.015 40.897 0.000 0.567
## Stst13h (.30.) 0.858 0.015 57.034 0.000 0.828
## Stst14b (.31.) 0.626 0.014 45.476 0.000 0.599
## Stst15t (.32.) 0.632 0.013 47.599 0.000 0.606
## Stst16m (.33.) 0.719 0.015 47.998 0.000 0.690
## Stst19d (.34.) 0.225 0.023 9.673 0.000 0.179
## Stst26r (.35.) 0.632 0.019 32.666 0.000 0.594
## science =~
## Stst1vc (.36.) 0.342 0.027 12.486 0.000 0.288
## Stst5mt (.37.) 0.404 0.030 13.454 0.000 0.345
## Stst6ph (.38.) 0.767 0.015 50.789 0.000 0.737
## Stst7bl (.39.) 0.412 0.037 11.042 0.000 0.339
## Stst9lc (.40.) 0.722 0.019 37.615 0.000 0.684
## Stst10m (.41.) 0.628 0.015 41.156 0.000 0.599
## spatial =~
## Stst28m (.42.) 0.641 0.019 34.370 0.000 0.604
## Sts292D (.43.) 0.713 0.018 40.035 0.000 0.678
## Sts303D (.44.) 0.663 0.016 40.893 0.000 0.631
## Stst31b (.45.) 0.642 0.025 25.565 0.000 0.593
## Stst37b (.46.) 0.150 0.022 6.782 0.000 0.107
## ci.upper Std.lv Std.all
##
## 0.176 0.141 0.155
## 0.444 0.397 0.436
## 0.686 0.654 0.674
## 0.768 0.738 0.739
## 0.843 0.809 0.823
## 0.862 0.824 0.741
## 0.685 0.650 0.590
## 0.205 0.157 0.204
## 0.385 0.349 0.355
## 0.376 0.333 0.314
## 0.341 0.277 0.240
##
## 0.468 0.359 0.370
## 0.448 0.341 0.441
## 0.655 0.536 0.714
## 0.669 0.547 0.782
## 0.351 0.244 0.211
##
## 0.211 0.189 0.208
## 0.519 0.480 0.415
## 1.216 1.153 0.709
## 0.858 0.814 0.632
## 0.767 0.723 0.628
##
## 0.564 0.445 0.489
## 0.859 0.732 0.827
## 0.763 0.648 0.739
## 0.925 0.788 0.846
## 0.362 0.265 0.312
## 0.463 0.381 0.431
## 0.807 0.688 0.734
## 0.624 0.525 0.628
## 0.887 0.756 0.698
## 0.653 0.551 0.644
## 0.658 0.557 0.655
## 0.749 0.634 0.680
## 0.270 0.198 0.217
## 0.670 0.557 0.567
##
## 0.395 0.213 0.233
## 0.463 0.251 0.259
## 0.796 0.477 0.706
## 0.485 0.256 0.302
## 0.759 0.449 0.456
## 0.658 0.391 0.625
##
## 0.677 0.438 0.689
## 0.748 0.488 0.503
## 0.694 0.453 0.590
## 0.692 0.439 0.414
## 0.194 0.103 0.089
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.703 0.035 20.083 0.000 0.635
## speed 0.347 0.025 13.791 0.000 0.298
## info 0.729 0.028 26.470 0.000 0.675
## science 0.441 0.021 21.454 0.000 0.401
## spatial 0.471 0.022 21.059 0.000 0.427
## math ~~
## speed 0.240 0.021 11.217 0.000 0.198
## info 0.587 0.031 18.939 0.000 0.526
## science 0.431 0.025 16.960 0.000 0.381
## spatial 0.443 0.027 16.667 0.000 0.390
## speed ~~
## info 0.270 0.021 13.039 0.000 0.229
## science 0.187 0.017 11.170 0.000 0.155
## spatial 0.222 0.020 11.182 0.000 0.183
## info ~~
## science 0.472 0.022 21.315 0.000 0.429
## spatial 0.393 0.020 19.755 0.000 0.354
## science ~~
## spatial 0.276 0.016 16.795 0.000 0.244
## ci.upper Std.lv Std.all
##
## 0.772 0.820 0.820
## 0.396 0.347 0.347
## 0.783 0.832 0.832
## 0.482 0.713 0.713
## 0.515 0.692 0.692
##
## 0.282 0.277 0.277
## 0.648 0.773 0.773
## 0.481 0.804 0.804
## 0.495 0.751 0.751
##
## 0.311 0.305 0.305
## 0.220 0.300 0.300
## 0.261 0.323 0.323
##
## 0.516 0.862 0.862
## 0.432 0.652 0.652
##
## 0.308 0.648 0.648
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -1.339 0.016 -83.554 0.000 -1.370
## .Stst19dsgsdwrd -0.878 0.016 -54.059 0.000 -0.910
## .Stest20spellng -0.450 0.017 -26.686 0.000 -0.483
## .Stest21cptlztn -0.899 0.017 -51.477 0.000 -0.934
## .Stest22puncttn -0.929 0.017 -53.286 0.000 -0.963
## .Stest23english -0.744 0.019 -38.449 0.000 -0.781
## .Stest24exprssn -0.704 0.019 -37.099 0.000 -0.742
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.816
## .Stst26rdngcmpr -1.226 0.017 -72.842 0.000 -1.259
## .Stst31bstrctrs -1.260 0.019 -65.843 0.000 -1.297
## .Stst34rthcmptt -1.004 0.021 -47.990 0.000 -1.045
## .Stest5math -0.965 0.017 -55.615 0.000 -0.999
## .Stst32rthrsnng -1.184 0.013 -92.849 0.000 -1.209
## .Stst33hghschlm -0.942 0.012 -78.389 0.000 -0.966
## .Stest35tblrdng -0.524 0.029 -17.830 0.000 -0.582
## .Stst36clrclchc 0.300 0.023 13.284 0.000 0.256
## .Stst37bjctnspc -0.217 0.021 -10.567 0.000 -0.257
## .Stest2literatr -1.034 0.016 -66.363 0.000 -1.065
## .Stest3music -0.825 0.016 -52.646 0.000 -0.856
## .Stest4soclstds -1.273 0.015 -82.694 0.000 -1.303
## .Stst7blgclscnc -0.831 0.015 -55.991 0.000 -0.860
## .Stest8aerontcs -0.942 0.014 -64.960 0.000 -0.970
## .Stest11art -1.046 0.017 -63.114 0.000 -1.078
## .Stest12law -0.897 0.014 -63.710 0.000 -0.925
## .Stest13health -1.020 0.019 -52.885 0.000 -1.057
## .Stest14bible -0.565 0.015 -36.958 0.000 -0.595
## .Stest15theater -0.856 0.015 -56.660 0.000 -0.885
## .Stest16mscllns -0.949 0.016 -60.013 0.000 -0.980
## .Stst6physclscn -1.022 0.012 -84.927 0.000 -1.046
## .Stest9elctrncs -1.154 0.017 -68.546 0.000 -1.187
## .Stest10mechncs -1.373 0.011 -128.778 0.000 -1.394
## .Stst28mchnclrs -1.323 0.011 -124.285 0.000 -1.344
## .Stst29vslztn2D -0.916 0.017 -52.801 0.000 -0.950
## .Stst30vslztn3D -0.982 0.014 -72.639 0.000 -1.008
## ci.upper Std.lv Std.all
## -1.307 -1.339 -1.468
## -0.846 -0.878 -0.963
## -0.417 -0.450 -0.464
## -0.865 -0.899 -0.901
## -0.895 -0.929 -0.945
## -0.706 -0.744 -0.668
## -0.667 -0.704 -0.640
## -0.761 -0.788 -1.020
## -1.193 -1.226 -1.248
## -1.222 -1.260 -1.186
## -0.963 -1.004 -0.868
## -0.931 -0.965 -0.995
## -1.159 -1.184 -1.578
## -0.919 -0.942 -1.347
## -0.466 -0.524 -0.322
## 0.344 0.300 0.233
## -0.176 -0.217 -0.188
## -1.004 -1.034 -1.170
## -0.795 -0.825 -0.942
## -1.243 -1.273 -1.366
## -0.802 -0.831 -0.979
## -0.913 -0.942 -1.065
## -1.013 -1.046 -1.116
## -0.870 -0.897 -1.074
## -0.982 -1.020 -0.942
## -0.535 -0.565 -0.659
## -0.826 -0.856 -1.006
## -0.918 -0.949 -1.018
## -0.998 -1.022 -1.513
## -1.121 -1.154 -1.173
## -1.352 -1.373 -2.196
## -1.303 -1.323 -2.081
## -0.882 -0.916 -0.944
## -0.955 -0.982 -1.278
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.257 0.007 35.738 0.000 0.243
## .Stst19dsgsdwrd 0.394 0.011 36.038 0.000 0.372
## .Stest20spellng 0.515 0.014 37.188 0.000 0.488
## .Stest21cptlztn 0.453 0.014 33.185 0.000 0.426
## .Stest22puncttn 0.312 0.010 29.990 0.000 0.292
## .Stest23english 0.559 0.017 33.197 0.000 0.526
## .Stest24exprssn 0.790 0.021 37.613 0.000 0.749
## .Stst25wrdfnctn 0.368 0.010 36.067 0.000 0.348
## .Stst26rdngcmpr 0.210 0.007 29.484 0.000 0.196
## .Stst31bstrctrs 0.621 0.017 36.094 0.000 0.587
## .Stst34rthcmptt 0.702 0.027 26.088 0.000 0.649
## .Stest5math 0.603 0.017 35.982 0.000 0.570
## .Stst32rthrsnng 0.276 0.008 33.571 0.000 0.260
## .Stst33hghschlm 0.190 0.007 28.384 0.000 0.177
## .Stest35tblrdng 1.313 0.066 19.965 0.000 1.184
## .Stst36clrclchc 0.997 0.034 29.627 0.000 0.931
## .Stst37bjctnspc 0.743 0.027 27.419 0.000 0.690
## .Stest2literatr 0.247 0.007 36.099 0.000 0.233
## .Stest3music 0.348 0.009 38.148 0.000 0.331
## .Stest4soclstds 0.247 0.007 34.302 0.000 0.233
## .Stst7blgclscnc 0.467 0.012 39.462 0.000 0.444
## .Stest8aerontcs 0.637 0.011 55.774 0.000 0.614
## .Stest11art 0.405 0.011 37.359 0.000 0.384
## .Stest12law 0.423 0.011 40.177 0.000 0.403
## .Stest13health 0.599 0.015 41.147 0.000 0.571
## .Stest14bible 0.430 0.012 34.741 0.000 0.406
## .Stest15theater 0.414 0.011 38.998 0.000 0.393
## .Stest16mscllns 0.467 0.012 37.926 0.000 0.443
## .Stst6physclscn 0.229 0.007 31.834 0.000 0.215
## .Stest9elctrncs 0.765 0.020 38.725 0.000 0.727
## .Stest10mechncs 0.238 0.006 37.599 0.000 0.226
## .Stst28mchnclrs 0.212 0.007 31.325 0.000 0.199
## .Stst29vslztn2D 0.703 0.019 36.804 0.000 0.666
## .Stst30vslztn3D 0.385 0.011 34.748 0.000 0.363
## english 0.990 0.041 24.449 0.000 0.911
## math 0.742 0.051 14.632 0.000 0.643
## speed 1.010 0.060 16.757 0.000 0.892
## info 0.776 0.032 24.045 0.000 0.713
## science 0.387 0.022 17.585 0.000 0.344
## spatial 0.468 0.027 17.022 0.000 0.414
## ci.upper Std.lv Std.all
## 0.271 0.257 0.310
## 0.415 0.394 0.473
## 0.542 0.515 0.546
## 0.480 0.453 0.454
## 0.333 0.312 0.323
## 0.591 0.559 0.451
## 0.832 0.790 0.652
## 0.388 0.368 0.616
## 0.224 0.210 0.217
## 0.655 0.621 0.551
## 0.755 0.702 0.525
## 0.636 0.603 0.642
## 0.292 0.276 0.490
## 0.203 0.190 0.389
## 1.442 1.313 0.497
## 1.063 0.997 0.601
## 0.797 0.743 0.561
## 0.260 0.247 0.316
## 0.366 0.348 0.453
## 0.261 0.247 0.284
## 0.491 0.467 0.649
## 0.659 0.637 0.814
## 0.426 0.405 0.461
## 0.444 0.423 0.606
## 0.628 0.599 0.512
## 0.454 0.430 0.586
## 0.434 0.414 0.571
## 0.491 0.467 0.537
## 0.243 0.229 0.502
## 0.804 0.765 0.792
## 0.251 0.238 0.609
## 0.225 0.212 0.525
## 0.741 0.703 0.747
## 0.407 0.385 0.652
## 1.070 1.000 1.000
## 0.842 1.000 1.000
## 1.129 1.000 1.000
## 0.839 1.000 1.000
## 0.430 1.000 1.000
## 0.522 1.000 1.000
lavTestScore(metric, release = 1:46)
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 794.486 46 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p142. 3.873 1 0.049
## 2 .p2. == .p143. 30.348 1 0.000
## 3 .p3. == .p144. 2.861 1 0.091
## 4 .p4. == .p145. 7.422 1 0.006
## 5 .p5. == .p146. 0.384 1 0.535
## 6 .p6. == .p147. 19.813 1 0.000
## 7 .p7. == .p148. 17.947 1 0.000
## 8 .p8. == .p149. 32.867 1 0.000
## 9 .p9. == .p150. 9.445 1 0.002
## 10 .p10. == .p151. 31.781 1 0.000
## 11 .p11. == .p152. 0.258 1 0.611
## 12 .p12. == .p153. 8.716 1 0.003
## 13 .p13. == .p154. 51.089 1 0.000
## 14 .p14. == .p155. 15.016 1 0.000
## 15 .p15. == .p156. 3.930 1 0.047
## 16 .p16. == .p157. 0.473 1 0.491
## 17 .p17. == .p158. 20.560 1 0.000
## 18 .p18. == .p159. 0.786 1 0.375
## 19 .p19. == .p160. 0.179 1 0.672
## 20 .p20. == .p161. 2.435 1 0.119
## 21 .p21. == .p162. 0.666 1 0.415
## 22 .p22. == .p163. 5.683 1 0.017
## 23 .p23. == .p164. 3.311 1 0.069
## 24 .p24. == .p165. 43.835 1 0.000
## 25 .p25. == .p166. 91.393 1 0.000
## 26 .p26. == .p167. 0.561 1 0.454
## 27 .p27. == .p168. 195.354 1 0.000
## 28 .p28. == .p169. 30.154 1 0.000
## 29 .p29. == .p170. 23.658 1 0.000
## 30 .p30. == .p171. 11.194 1 0.001
## 31 .p31. == .p172. 12.713 1 0.000
## 32 .p32. == .p173. 45.188 1 0.000
## 33 .p33. == .p174. 19.052 1 0.000
## 34 .p34. == .p175. 31.809 1 0.000
## 35 .p35. == .p176. 10.102 1 0.001
## 36 .p36. == .p177. 2.704 1 0.100
## 37 .p37. == .p178. 16.597 1 0.000
## 38 .p38. == .p179. 31.833 1 0.000
## 39 .p39. == .p180. 1.457 1 0.227
## 40 .p40. == .p181. 24.613 1 0.000
## 41 .p41. == .p182. 22.087 1 0.000
## 42 .p42. == .p183. 99.187 1 0.000
## 43 .p43. == .p184. 20.766 1 0.000
## 44 .p44. == .p185. 2.183 1 0.140
## 45 .p45. == .p186. 40.540 1 0.000
## 46 .p46. == .p187. 0.181 1 0.670
metric2<-cfa(chc.factor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings"), group.partial=c("info=~Stest8aeronautics", "spatial=~Stest28mechanicalreasoning", "info=~Stest4socialstudies"))
fitMeasures(metric2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 5861.962 1037.000 0.000 0.957 0.039 0.044
## aic bic
## 462724.365 464208.067
Mc(metric2)
## [1] 0.6726509
scalar<-cfa(chc.factor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts"), group.partial=c("info=~Stest8aeronautics", "spatial=~Stest28mechanicalreasoning", "info=~Stest4socialstudies"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 7847.420 1065.000 0.000 0.939 0.046 0.056
## aic bic
## 464653.824 465949.545
Mc(scalar)
## [1] 0.5726972
summary(scalar, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 112 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 270
## Number of equality constraints 77
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 7847.420 7008.811
## Degrees of freedom 1065 1065
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.120
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 3901.518 3484.585
## 1 3945.902 3524.226
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.133 0.018 7.546 0.000 0.099
## Stst19d (.p2.) 0.357 0.021 16.776 0.000 0.316
## Stst20s (.p3.) 0.688 0.015 45.118 0.000 0.658
## Stst21c (.p4.) 0.759 0.014 53.893 0.000 0.732
## Stst22p (.p5.) 0.835 0.016 51.714 0.000 0.803
## Stst23n (.p6.) 0.851 0.018 46.393 0.000 0.815
## Stst24x (.p7.) 0.672 0.017 39.208 0.000 0.638
## Stst25w (.p8.) 0.200 0.020 9.856 0.000 0.160
## Stst26r (.p9.) 0.320 0.017 19.175 0.000 0.288
## Stst31b (.10.) 0.394 0.017 23.216 0.000 0.361
## Stst34r (.11.) 0.265 0.028 9.416 0.000 0.209
## math =~
## Stst5mt (.12.) 0.517 0.026 20.096 0.000 0.467
## Stst25w (.13.) 0.364 0.023 15.867 0.000 0.319
## Stst32r (.14.) 0.636 0.018 35.098 0.000 0.601
## Stst33h (.15.) 0.649 0.018 36.149 0.000 0.614
## Stst34r (.16.) 0.312 0.031 10.215 0.000 0.252
## speed =~
## Stst19d (.17.) 0.187 0.012 16.129 0.000 0.164
## Stst34r (.18.) 0.477 0.021 22.487 0.000 0.435
## Stst35t (.19.) 1.141 0.035 32.167 0.000 1.071
## Stst36c (.20.) 0.822 0.024 33.694 0.000 0.774
## Stst37b (.21.) 0.729 0.023 31.499 0.000 0.683
## info =~
## Stst1vc (.22.) 0.500 0.027 18.546 0.000 0.447
## Stst2lt (.23.) 0.824 0.016 52.073 0.000 0.793
## Stst3ms (.24.) 0.733 0.015 50.122 0.000 0.704
## Stst4sc 1.019 0.019 54.429 0.000 0.982
## Stst7bl (.26.) 0.330 0.021 15.510 0.000 0.288
## Stst8rn 0.677 0.022 30.355 0.000 0.633
## Stst11r (.28.) 0.778 0.015 52.275 0.000 0.749
## Stst12l (.29.) 0.589 0.016 37.537 0.000 0.558
## Stst13h (.30.) 0.855 0.016 53.262 0.000 0.824
## Stst14b (.31.) 0.623 0.014 43.984 0.000 0.595
## Stst15t (.32.) 0.632 0.014 45.919 0.000 0.605
## Stst16m (.33.) 0.712 0.016 43.647 0.000 0.680
## Stst19d (.34.) 0.274 0.022 12.515 0.000 0.231
## Stst26r (.35.) 0.663 0.020 33.483 0.000 0.624
## science =~
## Stst1vc (.36.) 0.376 0.019 19.542 0.000 0.338
## Stst5mt (.37.) 0.295 0.025 11.583 0.000 0.245
## Stst6ph (.38.) 0.736 0.017 43.032 0.000 0.703
## Stst7bl (.39.) 0.386 0.025 15.444 0.000 0.337
## Stst9lc (.40.) 0.752 0.019 38.799 0.000 0.714
## Stst10m (.41.) 0.730 0.016 44.347 0.000 0.698
## spatial =~
## Stst28m 0.760 0.021 35.444 0.000 0.718
## Sts292D (.43.) 0.668 0.019 35.234 0.000 0.631
## Sts303D (.44.) 0.586 0.018 33.217 0.000 0.552
## Stst31b (.45.) 0.556 0.020 27.605 0.000 0.517
## Stst37b (.46.) 0.133 0.019 7.013 0.000 0.096
## ci.upper Std.lv Std.all
##
## 0.168 0.133 0.122
## 0.399 0.357 0.388
## 0.718 0.688 0.682
## 0.787 0.759 0.780
## 0.867 0.835 0.820
## 0.887 0.851 0.727
## 0.706 0.672 0.588
## 0.239 0.200 0.242
## 0.353 0.320 0.301
## 0.427 0.394 0.335
## 0.320 0.265 0.228
##
## 0.568 0.517 0.484
## 0.409 0.364 0.443
## 0.672 0.636 0.762
## 0.684 0.649 0.821
## 0.372 0.312 0.269
##
## 0.210 0.187 0.203
## 0.518 0.477 0.412
## 1.210 1.141 0.685
## 0.870 0.822 0.635
## 0.774 0.729 0.590
##
## 0.553 0.500 0.456
## 0.855 0.824 0.850
## 0.761 0.733 0.779
## 1.056 1.019 0.883
## 0.372 0.330 0.339
## 0.721 0.677 0.630
## 0.807 0.778 0.789
## 0.619 0.589 0.650
## 0.887 0.855 0.763
## 0.651 0.623 0.702
## 0.659 0.632 0.733
## 0.744 0.712 0.702
## 0.317 0.274 0.297
## 0.702 0.663 0.624
##
## 0.413 0.376 0.343
## 0.345 0.295 0.276
## 0.770 0.736 0.819
## 0.435 0.386 0.396
## 0.790 0.752 0.681
## 0.762 0.730 0.758
##
## 0.802 0.760 0.817
## 0.706 0.668 0.607
## 0.621 0.586 0.630
## 0.596 0.556 0.473
## 0.171 0.133 0.108
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.839 0.012 70.251 0.000 0.815
## speed 0.316 0.026 12.011 0.000 0.265
## info 0.840 0.009 90.364 0.000 0.822
## science 0.794 0.012 64.771 0.000 0.770
## spatial 0.693 0.017 39.617 0.000 0.658
## math ~~
## speed 0.310 0.026 11.778 0.000 0.258
## info 0.825 0.012 69.702 0.000 0.802
## science 0.806 0.014 59.115 0.000 0.779
## spatial 0.731 0.017 41.843 0.000 0.696
## speed ~~
## info 0.297 0.026 11.510 0.000 0.246
## science 0.269 0.028 9.737 0.000 0.215
## spatial 0.353 0.029 12.341 0.000 0.297
## info ~~
## science 0.919 0.007 124.256 0.000 0.904
## spatial 0.676 0.017 39.134 0.000 0.642
## science ~~
## spatial 0.747 0.018 42.492 0.000 0.712
## ci.upper Std.lv Std.all
##
## 0.862 0.839 0.839
## 0.368 0.316 0.316
## 0.858 0.840 0.840
## 0.818 0.794 0.794
## 0.727 0.693 0.693
##
## 0.361 0.310 0.310
## 0.848 0.825 0.825
## 0.832 0.806 0.806
## 0.765 0.731 0.731
##
## 0.348 0.297 0.297
## 0.324 0.269 0.269
## 0.410 0.353 0.353
##
## 0.933 0.919 0.919
## 0.710 0.676 0.676
##
## 0.781 0.747 0.747
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.102) -1.378 0.027 -51.844 0.000 -1.430
## .Stst19d (.103) -1.180 0.019 -60.837 0.000 -1.218
## .Stst20s (.104) -0.902 0.022 -40.601 0.000 -0.945
## .Stst21c (.105) -1.330 0.022 -61.773 0.000 -1.372
## .Stst22p (.106) -1.405 0.024 -58.060 0.000 -1.452
## .Stst23n (.107) -1.235 0.027 -46.314 0.000 -1.287
## .Stst24x (.108) -1.096 0.023 -47.120 0.000 -1.141
## .Stst25w (.109) -0.955 0.016 -58.111 0.000 -0.987
## .Stst26r (.110) -1.545 0.026 -59.636 0.000 -1.596
## .Stst31b (.111) -1.214 0.028 -43.608 0.000 -1.268
## .Stst34r (.112) -1.323 0.026 -50.076 0.000 -1.374
## .Stst5mt (.113) -0.928 0.023 -40.248 0.000 -0.973
## .Stst32r (.114) -1.216 0.018 -69.131 0.000 -1.250
## .Stst33h (.115) -1.001 0.017 -57.724 0.000 -1.035
## .Stst35t (.116) -0.855 0.037 -23.171 0.000 -0.927
## .Stst36c (.117) -0.015 0.027 -0.565 0.572 -0.069
## .Stst37b (.118) -0.385 0.026 -14.924 0.000 -0.435
## .Stst2lt (.119) -1.229 0.023 -53.994 0.000 -1.273
## .Stst3ms (.120) -1.034 0.021 -49.985 0.000 -1.075
## .Stst4sc (.121) -1.407 0.024 -59.266 0.000 -1.453
## .Stst7bl (.122) -0.760 0.022 -34.695 0.000 -0.803
## .Stst8rn (.123) -0.875 0.015 -57.745 0.000 -0.904
## .Stst11r (.124) -1.224 0.022 -56.202 0.000 -1.267
## .Stst12l (.125) -0.989 0.018 -55.030 0.000 -1.025
## .Stst13h (.126) -1.297 0.025 -51.611 0.000 -1.346
## .Stst14b (.127) -0.775 0.019 -40.936 0.000 -0.812
## .Stst15t (.128) -1.078 0.018 -58.480 0.000 -1.115
## .Stst16m (.129) -1.091 0.021 -51.151 0.000 -1.133
## .Stst6ph (.130) -0.785 0.021 -37.423 0.000 -0.826
## .Stst9lc (.131) -0.838 0.023 -35.783 0.000 -0.884
## .Stst10m (.132) -0.997 0.023 -43.898 0.000 -1.041
## .Stst28m (.133) -0.953 0.030 -32.223 0.000 -1.011
## .Sts292D (.134) -0.586 0.024 -24.110 0.000 -0.634
## .Sts303D (.135) -0.722 0.021 -34.497 0.000 -0.763
## ci.upper Std.lv Std.all
## -1.326 -1.378 -1.257
## -1.142 -1.180 -1.282
## -0.858 -0.902 -0.893
## -1.288 -1.330 -1.366
## -1.358 -1.405 -1.380
## -1.182 -1.235 -1.055
## -1.050 -1.096 -0.959
## -0.922 -0.955 -1.159
## -1.494 -1.545 -1.453
## -1.159 -1.214 -1.032
## -1.271 -1.323 -1.142
## -0.883 -0.928 -0.868
## -1.181 -1.216 -1.455
## -0.967 -1.001 -1.266
## -0.782 -0.855 -0.513
## 0.038 -0.015 -0.012
## -0.334 -0.385 -0.312
## -1.184 -1.229 -1.267
## -0.994 -1.034 -1.100
## -1.360 -1.407 -1.219
## -0.717 -0.760 -0.781
## -0.845 -0.875 -0.814
## -1.181 -1.224 -1.241
## -0.954 -0.989 -1.093
## -1.247 -1.297 -1.156
## -0.738 -0.775 -0.872
## -1.042 -1.078 -1.251
## -1.049 -1.091 -1.076
## -0.744 -0.785 -0.873
## -0.792 -0.838 -0.759
## -0.952 -0.997 -1.035
## -0.895 -0.953 -1.024
## -0.538 -0.586 -0.532
## -0.681 -0.722 -0.775
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.256 0.009 28.260 0.000 0.238
## .Stst19dsgsdwrd 0.374 0.014 27.219 0.000 0.347
## .Stest20spellng 0.546 0.018 31.080 0.000 0.511
## .Stest21cptlztn 0.372 0.015 24.513 0.000 0.342
## .Stest22puncttn 0.339 0.012 27.998 0.000 0.315
## .Stest23english 0.645 0.024 26.899 0.000 0.598
## .Stest24exprssn 0.854 0.026 33.362 0.000 0.804
## .Stst25wrdfnctn 0.384 0.012 32.441 0.000 0.360
## .Stst26rdngcmpr 0.231 0.009 25.371 0.000 0.213
## .Stst31bstrctrs 0.615 0.022 27.890 0.000 0.572
## .Stst34rthcmptt 0.636 0.030 21.194 0.000 0.577
## .Stest5math 0.541 0.020 26.720 0.000 0.501
## .Stst32rthrsnng 0.293 0.011 26.894 0.000 0.272
## .Stst33hghschlm 0.204 0.009 23.091 0.000 0.187
## .Stest35tblrdng 1.470 0.075 19.717 0.000 1.324
## .Stst36clrclchc 1.000 0.042 23.547 0.000 0.917
## .Stst37bjctnspc 0.908 0.035 26.002 0.000 0.839
## .Stest2literatr 0.261 0.009 29.754 0.000 0.244
## .Stest3music 0.347 0.012 29.114 0.000 0.324
## .Stest4soclstds 0.293 0.011 26.120 0.000 0.271
## .Stst7blgclscnc 0.456 0.014 32.954 0.000 0.429
## .Stest8aerontcs 0.698 0.019 35.790 0.000 0.659
## .Stest11art 0.367 0.012 29.971 0.000 0.343
## .Stest12law 0.474 0.014 32.717 0.000 0.445
## .Stest13health 0.526 0.016 32.425 0.000 0.495
## .Stest14bible 0.400 0.014 29.639 0.000 0.374
## .Stest15theater 0.344 0.011 31.175 0.000 0.323
## .Stest16mscllns 0.521 0.017 30.880 0.000 0.488
## .Stst6physclscn 0.267 0.011 23.850 0.000 0.245
## .Stest9elctrncs 0.655 0.027 24.269 0.000 0.602
## .Stest10mechncs 0.394 0.016 25.024 0.000 0.364
## .Stst28mchnclrs 0.288 0.017 16.688 0.000 0.254
## .Stst29vslztn2D 0.766 0.027 28.637 0.000 0.714
## .Stst30vslztn3D 0.523 0.018 29.158 0.000 0.488
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.273 0.256 0.213
## 0.401 0.374 0.441
## 0.580 0.546 0.535
## 0.401 0.372 0.392
## 0.363 0.339 0.327
## 0.692 0.645 0.471
## 0.904 0.854 0.654
## 0.407 0.384 0.565
## 0.248 0.231 0.204
## 0.658 0.615 0.444
## 0.695 0.636 0.474
## 0.580 0.541 0.474
## 0.314 0.293 0.420
## 0.221 0.204 0.327
## 1.616 1.470 0.530
## 1.084 1.000 0.597
## 0.976 0.908 0.595
## 0.279 0.261 0.278
## 0.371 0.347 0.393
## 0.315 0.293 0.220
## 0.483 0.456 0.481
## 0.736 0.698 0.604
## 0.391 0.367 0.377
## 0.502 0.474 0.578
## 0.558 0.526 0.418
## 0.427 0.400 0.508
## 0.366 0.344 0.463
## 0.554 0.521 0.507
## 0.289 0.267 0.330
## 0.708 0.655 0.537
## 0.425 0.394 0.425
## 0.321 0.288 0.332
## 0.819 0.766 0.632
## 0.559 0.523 0.604
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.133 0.018 7.546 0.000 0.099
## Stst19d (.p2.) 0.357 0.021 16.776 0.000 0.316
## Stst20s (.p3.) 0.688 0.015 45.118 0.000 0.658
## Stst21c (.p4.) 0.759 0.014 53.893 0.000 0.732
## Stst22p (.p5.) 0.835 0.016 51.714 0.000 0.803
## Stst23n (.p6.) 0.851 0.018 46.393 0.000 0.815
## Stst24x (.p7.) 0.672 0.017 39.208 0.000 0.638
## Stst25w (.p8.) 0.200 0.020 9.856 0.000 0.160
## Stst26r (.p9.) 0.320 0.017 19.175 0.000 0.288
## Stst31b (.10.) 0.394 0.017 23.216 0.000 0.361
## Stst34r (.11.) 0.265 0.028 9.416 0.000 0.209
## math =~
## Stst5mt (.12.) 0.517 0.026 20.096 0.000 0.467
## Stst25w (.13.) 0.364 0.023 15.867 0.000 0.319
## Stst32r (.14.) 0.636 0.018 35.098 0.000 0.601
## Stst33h (.15.) 0.649 0.018 36.149 0.000 0.614
## Stst34r (.16.) 0.312 0.031 10.215 0.000 0.252
## speed =~
## Stst19d (.17.) 0.187 0.012 16.129 0.000 0.164
## Stst34r (.18.) 0.477 0.021 22.487 0.000 0.435
## Stst35t (.19.) 1.141 0.035 32.167 0.000 1.071
## Stst36c (.20.) 0.822 0.024 33.694 0.000 0.774
## Stst37b (.21.) 0.729 0.023 31.499 0.000 0.683
## info =~
## Stst1vc (.22.) 0.500 0.027 18.546 0.000 0.447
## Stst2lt (.23.) 0.824 0.016 52.073 0.000 0.793
## Stst3ms (.24.) 0.733 0.015 50.122 0.000 0.704
## Stst4sc 0.796 0.017 45.936 0.000 0.762
## Stst7bl (.26.) 0.330 0.021 15.510 0.000 0.288
## Stst8rn 0.244 0.017 14.078 0.000 0.210
## Stst11r (.28.) 0.778 0.015 52.275 0.000 0.749
## Stst12l (.29.) 0.589 0.016 37.537 0.000 0.558
## Stst13h (.30.) 0.855 0.016 53.262 0.000 0.824
## Stst14b (.31.) 0.623 0.014 43.984 0.000 0.595
## Stst15t (.32.) 0.632 0.014 45.919 0.000 0.605
## Stst16m (.33.) 0.712 0.016 43.647 0.000 0.680
## Stst19d (.34.) 0.274 0.022 12.515 0.000 0.231
## Stst26r (.35.) 0.663 0.020 33.483 0.000 0.624
## science =~
## Stst1vc (.36.) 0.376 0.019 19.542 0.000 0.338
## Stst5mt (.37.) 0.295 0.025 11.583 0.000 0.245
## Stst6ph (.38.) 0.736 0.017 43.032 0.000 0.703
## Stst7bl (.39.) 0.386 0.025 15.444 0.000 0.337
## Stst9lc (.40.) 0.752 0.019 38.799 0.000 0.714
## Stst10m (.41.) 0.730 0.016 44.347 0.000 0.698
## spatial =~
## Stst28m 0.599 0.033 18.005 0.000 0.534
## Sts292D (.43.) 0.668 0.019 35.234 0.000 0.631
## Sts303D (.44.) 0.586 0.018 33.217 0.000 0.552
## Stst31b (.45.) 0.556 0.020 27.605 0.000 0.517
## Stst37b (.46.) 0.133 0.019 7.013 0.000 0.096
## ci.upper Std.lv Std.all
##
## 0.168 0.129 0.141
## 0.399 0.345 0.379
## 0.718 0.665 0.678
## 0.787 0.733 0.737
## 0.867 0.806 0.823
## 0.887 0.822 0.740
## 0.706 0.649 0.590
## 0.239 0.193 0.249
## 0.353 0.309 0.312
## 0.427 0.380 0.354
## 0.320 0.255 0.222
##
## 0.568 0.435 0.447
## 0.409 0.306 0.396
## 0.672 0.535 0.712
## 0.684 0.545 0.781
## 0.372 0.262 0.227
##
## 0.210 0.187 0.206
## 0.518 0.477 0.414
## 1.210 1.143 0.704
## 0.870 0.823 0.636
## 0.774 0.730 0.633
##
## 0.553 0.455 0.498
## 0.855 0.750 0.834
## 0.761 0.667 0.749
## 0.830 0.725 0.820
## 0.372 0.300 0.352
## 0.278 0.222 0.267
## 0.807 0.708 0.745
## 0.619 0.536 0.634
## 0.887 0.778 0.708
## 0.651 0.567 0.653
## 0.659 0.575 0.666
## 0.744 0.648 0.688
## 0.317 0.249 0.274
## 0.702 0.604 0.610
##
## 0.413 0.218 0.239
## 0.345 0.172 0.176
## 0.770 0.428 0.650
## 0.435 0.224 0.263
## 0.790 0.437 0.447
## 0.762 0.424 0.654
##
## 0.664 0.442 0.691
## 0.706 0.493 0.507
## 0.621 0.432 0.567
## 0.596 0.410 0.382
## 0.171 0.098 0.085
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.665 0.034 19.685 0.000 0.598
## speed 0.337 0.024 13.840 0.000 0.289
## info 0.731 0.029 24.970 0.000 0.673
## science 0.399 0.020 20.177 0.000 0.360
## spatial 0.490 0.027 18.085 0.000 0.437
## math ~~
## speed 0.235 0.021 11.296 0.000 0.194
## info 0.595 0.032 18.601 0.000 0.532
## science 0.395 0.024 16.359 0.000 0.347
## spatial 0.463 0.031 15.121 0.000 0.403
## speed ~~
## info 0.277 0.021 13.000 0.000 0.236
## science 0.176 0.016 10.966 0.000 0.144
## spatial 0.240 0.023 10.321 0.000 0.195
## info ~~
## science 0.458 0.023 20.123 0.000 0.413
## spatial 0.438 0.025 17.475 0.000 0.389
## science ~~
## spatial 0.279 0.018 15.605 0.000 0.244
## ci.upper Std.lv Std.all
##
## 0.731 0.819 0.819
## 0.385 0.349 0.349
## 0.788 0.831 0.831
## 0.438 0.710 0.710
## 0.543 0.688 0.688
##
## 0.275 0.279 0.279
## 0.658 0.778 0.778
## 0.442 0.808 0.808
## 0.523 0.747 0.747
##
## 0.319 0.304 0.304
## 0.207 0.301 0.301
## 0.286 0.325 0.325
##
## 0.503 0.866 0.866
## 0.487 0.653 0.653
##
## 0.314 0.651 0.651
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.102) -1.378 0.027 -51.844 0.000 -1.430
## .Stst19d (.103) -1.180 0.019 -60.837 0.000 -1.218
## .Stst20s (.104) -0.902 0.022 -40.601 0.000 -0.945
## .Stst21c (.105) -1.330 0.022 -61.773 0.000 -1.372
## .Stst22p (.106) -1.405 0.024 -58.060 0.000 -1.452
## .Stst23n (.107) -1.235 0.027 -46.314 0.000 -1.287
## .Stst24x (.108) -1.096 0.023 -47.120 0.000 -1.141
## .Stst25w (.109) -0.955 0.016 -58.111 0.000 -0.987
## .Stst26r (.110) -1.545 0.026 -59.636 0.000 -1.596
## .Stst31b (.111) -1.214 0.028 -43.608 0.000 -1.268
## .Stst34r (.112) -1.323 0.026 -50.076 0.000 -1.374
## .Stst5mt (.113) -0.928 0.023 -40.248 0.000 -0.973
## .Stst32r (.114) -1.216 0.018 -69.131 0.000 -1.250
## .Stst33h (.115) -1.001 0.017 -57.724 0.000 -1.035
## .Stst35t (.116) -0.855 0.037 -23.171 0.000 -0.927
## .Stst36c (.117) -0.015 0.027 -0.565 0.572 -0.069
## .Stst37b (.118) -0.385 0.026 -14.924 0.000 -0.435
## .Stst2lt (.119) -1.229 0.023 -53.994 0.000 -1.273
## .Stst3ms (.120) -1.034 0.021 -49.985 0.000 -1.075
## .Stst4sc (.121) -1.407 0.024 -59.266 0.000 -1.453
## .Stst7bl (.122) -0.760 0.022 -34.695 0.000 -0.803
## .Stst8rn (.123) -0.875 0.015 -57.745 0.000 -0.904
## .Stst11r (.124) -1.224 0.022 -56.202 0.000 -1.267
## .Stst12l (.125) -0.989 0.018 -55.030 0.000 -1.025
## .Stst13h (.126) -1.297 0.025 -51.611 0.000 -1.346
## .Stst14b (.127) -0.775 0.019 -40.936 0.000 -0.812
## .Stst15t (.128) -1.078 0.018 -58.480 0.000 -1.115
## .Stst16m (.129) -1.091 0.021 -51.151 0.000 -1.133
## .Stst6ph (.130) -0.785 0.021 -37.423 0.000 -0.826
## .Stst9lc (.131) -0.838 0.023 -35.783 0.000 -0.884
## .Stst10m (.132) -0.997 0.023 -43.898 0.000 -1.041
## .Stst28m (.133) -0.953 0.030 -32.223 0.000 -1.011
## .Sts292D (.134) -0.586 0.024 -24.110 0.000 -0.634
## .Sts303D (.135) -0.722 0.021 -34.497 0.000 -0.763
## english 0.579 0.034 17.173 0.000 0.513
## math 0.087 0.032 2.762 0.006 0.025
## speed 0.319 0.038 8.417 0.000 0.245
## info 0.234 0.033 7.154 0.000 0.170
## science -0.414 0.034 -12.238 0.000 -0.480
## spatial -0.538 0.039 -13.858 0.000 -0.614
## ci.upper Std.lv Std.all
## -1.326 -1.378 -1.506
## -1.142 -1.180 -1.296
## -0.858 -0.902 -0.921
## -1.288 -1.330 -1.336
## -1.358 -1.405 -1.434
## -1.182 -1.235 -1.112
## -1.050 -1.096 -0.996
## -0.922 -0.955 -1.233
## -1.494 -1.545 -1.560
## -1.159 -1.214 -1.131
## -1.271 -1.323 -1.147
## -0.883 -0.928 -0.954
## -1.181 -1.216 -1.619
## -0.967 -1.001 -1.434
## -0.782 -0.855 -0.527
## 0.038 -0.015 -0.012
## -0.334 -0.385 -0.334
## -1.184 -1.229 -1.366
## -0.994 -1.034 -1.162
## -1.360 -1.407 -1.592
## -0.717 -0.760 -0.892
## -0.845 -0.875 -1.051
## -1.181 -1.224 -1.288
## -0.954 -0.989 -1.171
## -1.247 -1.297 -1.179
## -0.738 -0.775 -0.892
## -1.042 -1.078 -1.248
## -1.049 -1.091 -1.158
## -0.744 -0.785 -1.192
## -0.792 -0.838 -0.856
## -0.952 -0.997 -1.536
## -0.895 -0.953 -1.491
## -0.538 -0.586 -0.603
## -0.681 -0.722 -0.946
## 0.645 0.599 0.599
## 0.149 0.104 0.104
## 0.393 0.319 0.319
## 0.298 0.257 0.257
## -0.348 -0.712 -0.712
## -0.462 -0.730 -0.730
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.256 0.007 35.325 0.000 0.242
## .Stst19dsgsdwrd 0.397 0.011 36.554 0.000 0.375
## .Stest20spellng 0.518 0.014 36.878 0.000 0.491
## .Stest21cptlztn 0.453 0.014 33.484 0.000 0.426
## .Stest22puncttn 0.310 0.010 29.986 0.000 0.290
## .Stest23english 0.558 0.017 33.040 0.000 0.524
## .Stest24exprssn 0.789 0.021 37.553 0.000 0.748
## .Stst25wrdfnctn 0.372 0.010 36.960 0.000 0.352
## .Stst26rdngcmpr 0.210 0.007 29.234 0.000 0.196
## .Stst31bstrctrs 0.625 0.018 34.921 0.000 0.589
## .Stst34rthcmptt 0.702 0.027 26.113 0.000 0.650
## .Stest5math 0.606 0.017 35.969 0.000 0.573
## .Stst32rthrsnng 0.278 0.008 33.590 0.000 0.262
## .Stst33hghschlm 0.190 0.007 28.376 0.000 0.177
## .Stest35tblrdng 1.327 0.066 20.126 0.000 1.198
## .Stst36clrclchc 0.996 0.034 29.643 0.000 0.930
## .Stst37bjctnspc 0.739 0.027 27.622 0.000 0.687
## .Stest2literatr 0.246 0.007 36.083 0.000 0.233
## .Stest3music 0.348 0.009 37.736 0.000 0.330
## .Stest4soclstds 0.255 0.007 34.847 0.000 0.241
## .Stst7blgclscnc 0.470 0.012 39.176 0.000 0.446
## .Stest8aerontcs 0.643 0.011 57.576 0.000 0.621
## .Stest11art 0.401 0.011 37.296 0.000 0.380
## .Stest12law 0.426 0.011 40.139 0.000 0.405
## .Stest13health 0.603 0.015 40.403 0.000 0.573
## .Stest14bible 0.433 0.013 33.976 0.000 0.408
## .Stest15theater 0.416 0.011 38.211 0.000 0.395
## .Stest16mscllns 0.467 0.012 37.886 0.000 0.443
## .Stst6physclscn 0.250 0.008 31.707 0.000 0.235
## .Stest9elctrncs 0.767 0.020 38.844 0.000 0.729
## .Stest10mechncs 0.241 0.007 34.739 0.000 0.227
## .Stst28mchnclrs 0.213 0.008 26.917 0.000 0.198
## .Stst29vslztn2D 0.702 0.020 34.369 0.000 0.662
## .Stst30vslztn3D 0.394 0.012 32.561 0.000 0.371
## english 0.932 0.040 23.372 0.000 0.854
## math 0.706 0.048 14.579 0.000 0.611
## speed 1.003 0.059 16.880 0.000 0.887
## info 0.828 0.037 22.468 0.000 0.756
## science 0.338 0.021 16.391 0.000 0.298
## spatial 0.544 0.049 11.166 0.000 0.448
## ci.upper Std.lv Std.all
## 0.270 0.256 0.306
## 0.418 0.397 0.478
## 0.546 0.518 0.540
## 0.479 0.453 0.457
## 0.330 0.310 0.323
## 0.591 0.558 0.452
## 0.831 0.789 0.652
## 0.392 0.372 0.620
## 0.224 0.210 0.214
## 0.660 0.625 0.542
## 0.755 0.702 0.529
## 0.639 0.606 0.641
## 0.294 0.278 0.493
## 0.204 0.190 0.390
## 1.457 1.327 0.504
## 1.062 0.996 0.595
## 0.791 0.739 0.556
## 0.260 0.246 0.304
## 0.366 0.348 0.439
## 0.270 0.255 0.327
## 0.493 0.470 0.646
## 0.665 0.643 0.929
## 0.422 0.401 0.445
## 0.447 0.426 0.598
## 0.632 0.603 0.499
## 0.458 0.433 0.574
## 0.437 0.416 0.557
## 0.492 0.467 0.527
## 0.266 0.250 0.577
## 0.806 0.767 0.800
## 0.254 0.241 0.572
## 0.229 0.213 0.522
## 0.742 0.702 0.743
## 0.418 0.394 0.678
## 1.011 1.000 1.000
## 0.801 1.000 1.000
## 1.120 1.000 1.000
## 0.901 1.000 1.000
## 0.378 1.000 1.000
## 0.639 1.000 1.000
lavTestScore(scalar, release = 44:77) # X2 test for released constraints among the 34 intercepts
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 1876.184 34 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p102. == .p243. 0.027 1 0.870
## 2 .p103. == .p244. 23.226 1 0.000
## 3 .p104. == .p245. 64.461 1 0.000
## 4 .p105. == .p246. 1.945 1 0.163
## 5 .p106. == .p247. 2.431 1 0.119
## 6 .p107. == .p248. 0.030 1 0.861
## 7 .p108. == .p249. 0.083 1 0.774
## 8 .p109. == .p250. 13.257 1 0.000
## 9 .p110. == .p251. 31.307 1 0.000
## 10 .p111. == .p252. 25.008 1 0.000
## 11 .p112. == .p253. 3.731 1 0.053
## 12 .p113. == .p254. 38.459 1 0.000
## 13 .p114. == .p255. 28.372 1 0.000
## 14 .p115. == .p256. 0.468 1 0.494
## 15 .p116. == .p257. 13.781 1 0.000
## 16 .p117. == .p258. 37.267 1 0.000
## 17 .p118. == .p259. 1.373 1 0.241
## 18 .p119. == .p260. 0.069 1 0.792
## 19 .p120. == .p261. 41.296 1 0.000
## 20 .p121. == .p262. 136.834 1 0.000
## 21 .p122. == .p263. 5.937 1 0.015
## 22 .p123. == .p264. 269.881 1 0.000
## 23 .p124. == .p265. 0.385 1 0.535
## 24 .p125. == .p266. 50.910 1 0.000
## 25 .p126. == .p267. 91.256 1 0.000
## 26 .p127. == .p268. 89.111 1 0.000
## 27 .p128. == .p269. 119.552 1 0.000
## 28 .p129. == .p270. 13.298 1 0.000
## 29 .p130. == .p271. 322.137 1 0.000
## 30 .p131. == .p272. 0.253 1 0.615
## 31 .p132. == .p273. 458.032 1 0.000
## 32 .p133. == .p274. 299.417 1 0.000
## 33 .p134. == .p275. 18.164 1 0.000
## 34 .p135. == .p276. 130.341 1 0.000
scalar2<-cfa(chc.factor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts"), group.partial=c("info=~Stest8aeronautics", "spatial=~Stest28mechanicalreasoning", "info=~Stest4socialstudies", "Stest10mechanics~1", "Stest8aeronautics~1", "Stest28mechanicalreasoning~1", "Stest4socialstudies~1", "Stest15theater~1"))
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 6406.859 1060.000 0.000 0.952 0.041 0.045
## aic bic
## 463223.262 464552.551
Mc(scalar2)
## [1] 0.6444103
summary(scalar2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 118 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 270
## Number of equality constraints 72
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 6406.859 5716.206
## Degrees of freedom 1060 1060
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.121
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 3001.454 2677.900
## 1 3405.405 3038.306
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.113 0.018 6.431 0.000 0.078
## Stst19d (.p2.) 0.354 0.021 16.860 0.000 0.313
## Stst20s (.p3.) 0.675 0.015 46.487 0.000 0.647
## Stst21c (.p4.) 0.745 0.013 56.579 0.000 0.719
## Stst22p (.p5.) 0.819 0.015 54.509 0.000 0.790
## Stst23n (.p6.) 0.835 0.017 48.076 0.000 0.801
## Stst24x (.p7.) 0.659 0.016 40.223 0.000 0.627
## Stst25w (.p8.) 0.198 0.020 10.082 0.000 0.160
## Stst26r (.p9.) 0.312 0.016 18.949 0.000 0.280
## Stst31b (.10.) 0.315 0.018 17.592 0.000 0.280
## Stst34r (.11.) 0.265 0.027 9.728 0.000 0.211
## math =~
## Stst5mt (.12.) 0.454 0.026 17.721 0.000 0.404
## Stst25w (.13.) 0.355 0.022 15.949 0.000 0.311
## Stst32r (.14.) 0.625 0.017 36.145 0.000 0.591
## Stst33h (.15.) 0.637 0.017 37.100 0.000 0.603
## Stst34r (.16.) 0.303 0.030 10.238 0.000 0.245
## speed =~
## Stst19d (.17.) 0.186 0.012 16.129 0.000 0.164
## Stst34r (.18.) 0.476 0.021 22.565 0.000 0.435
## Stst35t (.19.) 1.138 0.035 32.121 0.000 1.069
## Stst36c (.20.) 0.822 0.025 33.414 0.000 0.774
## Stst37b (.21.) 0.719 0.023 30.820 0.000 0.674
## info =~
## Stst1vc (.22.) 0.454 0.028 16.200 0.000 0.399
## Stst2lt (.23.) 0.806 0.015 54.929 0.000 0.777
## Stst3ms (.24.) 0.716 0.014 52.918 0.000 0.690
## Stst4sc 0.970 0.016 62.479 0.000 0.940
## Stst7bl (.26.) 0.259 0.024 10.822 0.000 0.212
## Stst8rn 0.611 0.019 31.822 0.000 0.573
## Stst11r (.28.) 0.760 0.014 55.241 0.000 0.733
## Stst12l (.29.) 0.575 0.015 38.830 0.000 0.546
## Stst13h (.30.) 0.836 0.015 56.597 0.000 0.807
## Stst14b (.31.) 0.610 0.013 45.685 0.000 0.583
## Stst15t (.32.) 0.617 0.013 46.524 0.000 0.591
## Stst16m (.33.) 0.696 0.015 45.560 0.000 0.666
## Stst19d (.34.) 0.264 0.022 12.283 0.000 0.222
## Stst26r (.35.) 0.650 0.019 34.191 0.000 0.613
## science =~
## Stst1vc (.36.) 0.428 0.021 19.915 0.000 0.386
## Stst5mt (.37.) 0.353 0.027 13.288 0.000 0.301
## Stst6ph (.38.) 0.752 0.015 49.690 0.000 0.723
## Stst7bl (.39.) 0.455 0.028 16.171 0.000 0.400
## Stst9lc (.40.) 0.746 0.019 39.806 0.000 0.709
## Stst10m (.41.) 0.631 0.015 41.450 0.000 0.601
## spatial =~
## Stst28m 0.723 0.018 39.953 0.000 0.687
## Sts292D (.43.) 0.675 0.018 36.799 0.000 0.639
## Sts303D (.44.) 0.599 0.017 35.224 0.000 0.565
## Stst31b (.45.) 0.621 0.022 28.675 0.000 0.578
## Stst37b (.46.) 0.141 0.019 7.317 0.000 0.103
## ci.upper Std.lv Std.all
##
## 0.147 0.113 0.104
## 0.395 0.354 0.389
## 0.704 0.675 0.675
## 0.771 0.745 0.774
## 0.849 0.819 0.816
## 0.869 0.835 0.721
## 0.691 0.659 0.581
## 0.237 0.198 0.243
## 0.344 0.312 0.299
## 0.350 0.315 0.271
## 0.318 0.265 0.230
##
## 0.504 0.454 0.428
## 0.399 0.355 0.435
## 0.659 0.625 0.757
## 0.670 0.637 0.817
## 0.361 0.303 0.264
##
## 0.209 0.186 0.205
## 0.517 0.476 0.414
## 1.208 1.138 0.684
## 0.870 0.822 0.635
## 0.765 0.719 0.584
##
## 0.509 0.454 0.419
## 0.835 0.806 0.845
## 0.743 0.716 0.773
## 1.001 0.970 0.877
## 0.306 0.259 0.267
## 0.648 0.611 0.602
## 0.787 0.760 0.782
## 0.604 0.575 0.641
## 0.865 0.836 0.756
## 0.636 0.610 0.694
## 0.643 0.617 0.730
## 0.726 0.696 0.694
## 0.307 0.264 0.291
## 0.687 0.650 0.623
##
## 0.470 0.428 0.395
## 0.405 0.353 0.333
## 0.782 0.752 0.834
## 0.510 0.455 0.469
## 0.783 0.746 0.676
## 0.661 0.631 0.722
##
## 0.758 0.723 0.804
## 0.711 0.675 0.612
## 0.632 0.599 0.646
## 0.663 0.621 0.535
## 0.179 0.141 0.114
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.828 0.013 66.140 0.000 0.803
## speed 0.304 0.026 11.621 0.000 0.253
## info 0.832 0.009 87.665 0.000 0.813
## science 0.786 0.012 64.109 0.000 0.761
## spatial 0.682 0.017 39.858 0.000 0.648
## math ~~
## speed 0.297 0.026 11.307 0.000 0.246
## info 0.812 0.012 66.257 0.000 0.788
## science 0.793 0.014 58.096 0.000 0.766
## spatial 0.722 0.017 41.841 0.000 0.689
## speed ~~
## info 0.286 0.025 11.295 0.000 0.236
## science 0.259 0.027 9.557 0.000 0.206
## spatial 0.343 0.029 12.040 0.000 0.287
## info ~~
## science 0.913 0.007 124.586 0.000 0.899
## spatial 0.662 0.016 40.504 0.000 0.630
## science ~~
## spatial 0.729 0.017 43.307 0.000 0.696
## ci.upper Std.lv Std.all
##
## 0.852 0.828 0.828
## 0.356 0.304 0.304
## 0.850 0.832 0.832
## 0.810 0.786 0.786
## 0.715 0.682 0.682
##
## 0.349 0.297 0.297
## 0.836 0.812 0.812
## 0.820 0.793 0.793
## 0.756 0.722 0.722
##
## 0.336 0.286 0.286
## 0.312 0.259 0.259
## 0.399 0.343 0.343
##
## 0.928 0.913 0.913
## 0.694 0.662 0.662
##
## 0.762 0.729 0.729
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.102) -1.177 0.022 -53.099 0.000 -1.220
## .Stst19d (.103) -1.032 0.016 -64.006 0.000 -1.063
## .Stst20s (.104) -0.760 0.019 -40.430 0.000 -0.797
## .Stst21c (.105) -1.174 0.018 -64.231 0.000 -1.210
## .Stst22p (.106) -1.233 0.020 -61.469 0.000 -1.272
## .Stst23n (.107) -1.059 0.022 -47.205 0.000 -1.103
## .Stst24x (.108) -0.957 0.020 -47.962 0.000 -0.996
## .Stst25w (.109) -0.840 0.014 -59.143 0.000 -0.868
## .Stst26r (.110) -1.331 0.021 -61.960 0.000 -1.373
## .Stst31b (.111) -1.068 0.023 -46.237 0.000 -1.113
## .Stst34r (.112) -1.167 0.022 -52.488 0.000 -1.211
## .Stst5mt (.113) -0.775 0.019 -40.149 0.000 -0.813
## .Stst32r (.114) -1.086 0.016 -67.310 0.000 -1.118
## .Stst33h (.115) -0.869 0.016 -55.273 0.000 -0.900
## .Stst35t (.116) -0.762 0.033 -23.066 0.000 -0.827
## .Stst36c (.117) 0.051 0.025 2.019 0.043 0.001
## .Stst37b (.118) -0.316 0.023 -13.695 0.000 -0.362
## .Stst2lt (.119) -1.046 0.019 -54.349 0.000 -1.083
## .Stst3ms (.120) -0.872 0.018 -49.262 0.000 -0.906
## .Stst4sc -1.083 0.023 -46.133 0.000 -1.129
## .Stst7bl (.122) -0.622 0.019 -31.943 0.000 -0.660
## .Stst8rn -0.517 0.022 -23.664 0.000 -0.560
## .Stst11r (.124) -1.051 0.019 -56.662 0.000 -1.087
## .Stst12l (.125) -0.859 0.016 -53.844 0.000 -0.890
## .Stst13h (.126) -1.106 0.021 -51.869 0.000 -1.148
## .Stst14b (.127) -0.636 0.016 -38.782 0.000 -0.668
## .Stst15t -1.025 0.017 -59.426 0.000 -1.059
## .Stst16m (.129) -0.933 0.019 -50.091 0.000 -0.970
## .Stst6ph (.130) -0.697 0.019 -37.205 0.000 -0.734
## .Stst9lc (.131) -0.748 0.021 -34.788 0.000 -0.790
## .Stst10m -0.656 0.019 -33.970 0.000 -0.694
## .Stst28m -0.715 0.019 -36.895 0.000 -0.753
## .Sts292D (.134) -0.552 0.021 -26.310 0.000 -0.593
## .Sts303D (.135) -0.695 0.018 -38.230 0.000 -0.730
## ci.upper Std.lv Std.all
## -1.133 -1.177 -1.087
## -1.000 -1.032 -1.134
## -0.723 -0.760 -0.760
## -1.138 -1.174 -1.220
## -1.194 -1.233 -1.227
## -1.015 -1.059 -0.915
## -0.918 -0.957 -0.843
## -0.812 -0.840 -1.030
## -1.289 -1.331 -1.277
## -1.022 -1.068 -0.920
## -1.124 -1.167 -1.017
## -0.737 -0.775 -0.731
## -1.055 -1.086 -1.316
## -0.838 -0.869 -1.115
## -0.697 -0.762 -0.458
## 0.101 0.051 0.039
## -0.271 -0.316 -0.257
## -1.008 -1.046 -1.096
## -0.837 -0.872 -0.940
## -1.037 -1.083 -0.978
## -0.584 -0.622 -0.641
## -0.475 -0.517 -0.510
## -1.015 -1.051 -1.082
## -0.828 -0.859 -0.957
## -1.064 -1.106 -1.000
## -0.604 -0.636 -0.725
## -0.991 -1.025 -1.212
## -0.897 -0.933 -0.931
## -0.660 -0.697 -0.773
## -0.705 -0.748 -0.677
## -0.618 -0.656 -0.750
## -0.677 -0.715 -0.795
## -0.511 -0.552 -0.501
## -0.659 -0.695 -0.750
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.254 0.009 27.853 0.000 0.236
## .Stst19dsgsdwrd 0.373 0.014 27.195 0.000 0.346
## .Stest20spellng 0.545 0.018 31.071 0.000 0.510
## .Stest21cptlztn 0.371 0.015 24.547 0.000 0.341
## .Stest22puncttn 0.338 0.012 27.909 0.000 0.314
## .Stest23english 0.644 0.024 26.833 0.000 0.597
## .Stest24exprssn 0.854 0.026 33.322 0.000 0.804
## .Stst25wrdfnctn 0.383 0.012 32.416 0.000 0.360
## .Stst26rdngcmpr 0.230 0.009 25.339 0.000 0.213
## .Stst31bstrctrs 0.597 0.022 27.024 0.000 0.554
## .Stst34rthcmptt 0.635 0.030 21.214 0.000 0.576
## .Stest5math 0.541 0.020 26.868 0.000 0.501
## .Stst32rthrsnng 0.291 0.011 26.782 0.000 0.270
## .Stst33hghschlm 0.202 0.009 22.759 0.000 0.185
## .Stest35tblrdng 1.470 0.075 19.619 0.000 1.323
## .Stst36clrclchc 0.998 0.043 23.420 0.000 0.915
## .Stst37bjctnspc 0.910 0.035 26.113 0.000 0.842
## .Stest2literatr 0.261 0.009 29.702 0.000 0.244
## .Stest3music 0.346 0.012 29.098 0.000 0.323
## .Stest4soclstds 0.284 0.010 27.097 0.000 0.264
## .Stst7blgclscnc 0.452 0.014 32.520 0.000 0.424
## .Stest8aerontcs 0.656 0.018 37.020 0.000 0.621
## .Stest11art 0.366 0.012 29.905 0.000 0.342
## .Stest12law 0.474 0.015 32.647 0.000 0.445
## .Stest13health 0.525 0.016 32.382 0.000 0.493
## .Stest14bible 0.399 0.013 29.600 0.000 0.373
## .Stest15theater 0.335 0.011 30.768 0.000 0.313
## .Stest16mscllns 0.520 0.017 30.791 0.000 0.487
## .Stst6physclscn 0.247 0.010 23.807 0.000 0.227
## .Stest9elctrncs 0.662 0.027 24.813 0.000 0.610
## .Stest10mechncs 0.366 0.013 28.573 0.000 0.341
## .Stst28mchnclrs 0.286 0.015 18.584 0.000 0.256
## .Stst29vslztn2D 0.760 0.027 28.520 0.000 0.708
## .Stst30vslztn3D 0.501 0.017 29.131 0.000 0.467
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.272 0.254 0.217
## 0.400 0.373 0.451
## 0.579 0.545 0.544
## 0.401 0.371 0.401
## 0.362 0.338 0.335
## 0.691 0.644 0.480
## 0.904 0.854 0.663
## 0.406 0.383 0.576
## 0.248 0.230 0.212
## 0.640 0.597 0.443
## 0.694 0.635 0.482
## 0.580 0.541 0.480
## 0.312 0.291 0.427
## 0.220 0.202 0.333
## 1.616 1.470 0.532
## 1.082 0.998 0.597
## 0.978 0.910 0.600
## 0.278 0.261 0.287
## 0.370 0.346 0.403
## 0.305 0.284 0.232
## 0.479 0.452 0.480
## 0.690 0.656 0.638
## 0.390 0.366 0.388
## 0.502 0.474 0.589
## 0.557 0.525 0.429
## 0.426 0.399 0.518
## 0.356 0.335 0.467
## 0.554 0.520 0.518
## 0.267 0.247 0.304
## 0.715 0.662 0.544
## 0.391 0.366 0.479
## 0.317 0.286 0.354
## 0.813 0.760 0.625
## 0.534 0.501 0.583
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.113 0.018 6.431 0.000 0.078
## Stst19d (.p2.) 0.354 0.021 16.860 0.000 0.313
## Stst20s (.p3.) 0.675 0.015 46.487 0.000 0.647
## Stst21c (.p4.) 0.745 0.013 56.579 0.000 0.719
## Stst22p (.p5.) 0.819 0.015 54.509 0.000 0.790
## Stst23n (.p6.) 0.835 0.017 48.076 0.000 0.801
## Stst24x (.p7.) 0.659 0.016 40.223 0.000 0.627
## Stst25w (.p8.) 0.198 0.020 10.082 0.000 0.160
## Stst26r (.p9.) 0.312 0.016 18.949 0.000 0.280
## Stst31b (.10.) 0.315 0.018 17.592 0.000 0.280
## Stst34r (.11.) 0.265 0.027 9.728 0.000 0.211
## math =~
## Stst5mt (.12.) 0.454 0.026 17.721 0.000 0.404
## Stst25w (.13.) 0.355 0.022 15.949 0.000 0.311
## Stst32r (.14.) 0.625 0.017 36.145 0.000 0.591
## Stst33h (.15.) 0.637 0.017 37.100 0.000 0.603
## Stst34r (.16.) 0.303 0.030 10.238 0.000 0.245
## speed =~
## Stst19d (.17.) 0.186 0.012 16.129 0.000 0.164
## Stst34r (.18.) 0.476 0.021 22.565 0.000 0.435
## Stst35t (.19.) 1.138 0.035 32.121 0.000 1.069
## Stst36c (.20.) 0.822 0.025 33.414 0.000 0.774
## Stst37b (.21.) 0.719 0.023 30.820 0.000 0.674
## info =~
## Stst1vc (.22.) 0.454 0.028 16.200 0.000 0.399
## Stst2lt (.23.) 0.806 0.015 54.929 0.000 0.777
## Stst3ms (.24.) 0.716 0.014 52.918 0.000 0.690
## Stst4sc 0.797 0.016 48.569 0.000 0.765
## Stst7bl (.26.) 0.259 0.024 10.822 0.000 0.212
## Stst8rn 0.275 0.016 17.072 0.000 0.244
## Stst11r (.28.) 0.760 0.014 55.241 0.000 0.733
## Stst12l (.29.) 0.575 0.015 38.830 0.000 0.546
## Stst13h (.30.) 0.836 0.015 56.597 0.000 0.807
## Stst14b (.31.) 0.610 0.013 45.685 0.000 0.583
## Stst15t (.32.) 0.617 0.013 46.524 0.000 0.591
## Stst16m (.33.) 0.696 0.015 45.560 0.000 0.666
## Stst19d (.34.) 0.264 0.022 12.283 0.000 0.222
## Stst26r (.35.) 0.650 0.019 34.191 0.000 0.613
## science =~
## Stst1vc (.36.) 0.428 0.021 19.915 0.000 0.386
## Stst5mt (.37.) 0.353 0.027 13.288 0.000 0.301
## Stst6ph (.38.) 0.752 0.015 49.690 0.000 0.723
## Stst7bl (.39.) 0.455 0.028 16.171 0.000 0.400
## Stst9lc (.40.) 0.746 0.019 39.806 0.000 0.709
## Stst10m (.41.) 0.631 0.015 41.450 0.000 0.601
## spatial =~
## Stst28m 0.468 0.021 21.954 0.000 0.426
## Sts292D (.43.) 0.675 0.018 36.799 0.000 0.639
## Sts303D (.44.) 0.599 0.017 35.224 0.000 0.565
## Stst31b (.45.) 0.621 0.022 28.675 0.000 0.578
## Stst37b (.46.) 0.141 0.019 7.317 0.000 0.103
## ci.upper Std.lv Std.all
##
## 0.147 0.111 0.122
## 0.395 0.349 0.383
## 0.704 0.666 0.679
## 0.771 0.734 0.737
## 0.849 0.807 0.824
## 0.869 0.823 0.741
## 0.691 0.650 0.590
## 0.237 0.195 0.252
## 0.344 0.307 0.311
## 0.350 0.310 0.288
## 0.318 0.261 0.226
##
## 0.504 0.389 0.401
## 0.399 0.304 0.393
## 0.659 0.536 0.713
## 0.670 0.546 0.782
## 0.361 0.260 0.225
##
## 0.209 0.187 0.206
## 0.517 0.478 0.414
## 1.208 1.143 0.704
## 0.870 0.825 0.638
## 0.765 0.722 0.627
##
## 0.509 0.421 0.463
## 0.835 0.748 0.833
## 0.743 0.665 0.748
## 0.829 0.740 0.828
## 0.306 0.240 0.283
## 0.307 0.256 0.307
## 0.787 0.706 0.744
## 0.604 0.534 0.633
## 0.865 0.776 0.707
## 0.636 0.566 0.652
## 0.643 0.573 0.667
## 0.726 0.646 0.687
## 0.307 0.245 0.270
## 0.687 0.603 0.610
##
## 0.470 0.265 0.291
## 0.405 0.219 0.225
## 0.782 0.466 0.694
## 0.510 0.282 0.332
## 0.783 0.462 0.465
## 0.661 0.391 0.625
##
## 0.509 0.382 0.624
## 0.711 0.551 0.557
## 0.632 0.489 0.626
## 0.663 0.507 0.470
## 0.179 0.115 0.100
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.690 0.034 20.222 0.000 0.623
## speed 0.340 0.025 13.601 0.000 0.291
## info 0.760 0.029 26.100 0.000 0.703
## science 0.438 0.021 21.232 0.000 0.398
## spatial 0.552 0.026 21.427 0.000 0.502
## math ~~
## speed 0.235 0.021 11.003 0.000 0.193
## info 0.617 0.032 19.157 0.000 0.554
## science 0.428 0.025 17.081 0.000 0.379
## spatial 0.519 0.030 17.340 0.000 0.460
## speed ~~
## info 0.281 0.022 12.799 0.000 0.238
## science 0.185 0.017 11.037 0.000 0.152
## spatial 0.264 0.024 10.993 0.000 0.217
## info ~~
## science 0.498 0.023 21.243 0.000 0.452
## spatial 0.488 0.024 20.232 0.000 0.441
## science ~~
## spatial 0.320 0.018 17.351 0.000 0.284
## ci.upper Std.lv Std.all
##
## 0.757 0.816 0.816
## 0.389 0.344 0.344
## 0.817 0.831 0.831
## 0.479 0.718 0.718
## 0.603 0.686 0.686
##
## 0.277 0.273 0.273
## 0.680 0.775 0.775
## 0.477 0.806 0.806
## 0.578 0.741 0.741
##
## 0.324 0.301 0.301
## 0.218 0.297 0.297
## 0.311 0.322 0.322
##
## 0.544 0.866 0.866
## 0.536 0.644 0.644
##
## 0.356 0.632 0.632
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.102) -1.177 0.022 -53.099 0.000 -1.220
## .Stst19d (.103) -1.032 0.016 -64.006 0.000 -1.063
## .Stst20s (.104) -0.760 0.019 -40.430 0.000 -0.797
## .Stst21c (.105) -1.174 0.018 -64.231 0.000 -1.210
## .Stst22p (.106) -1.233 0.020 -61.469 0.000 -1.272
## .Stst23n (.107) -1.059 0.022 -47.205 0.000 -1.103
## .Stst24x (.108) -0.957 0.020 -47.962 0.000 -0.996
## .Stst25w (.109) -0.840 0.014 -59.143 0.000 -0.868
## .Stst26r (.110) -1.331 0.021 -61.960 0.000 -1.373
## .Stst31b (.111) -1.068 0.023 -46.237 0.000 -1.113
## .Stst34r (.112) -1.167 0.022 -52.488 0.000 -1.211
## .Stst5mt (.113) -0.775 0.019 -40.149 0.000 -0.813
## .Stst32r (.114) -1.086 0.016 -67.310 0.000 -1.118
## .Stst33h (.115) -0.869 0.016 -55.273 0.000 -0.900
## .Stst35t (.116) -0.762 0.033 -23.066 0.000 -0.827
## .Stst36c (.117) 0.051 0.025 2.019 0.043 0.001
## .Stst37b (.118) -0.316 0.023 -13.695 0.000 -0.362
## .Stst2lt (.119) -1.046 0.019 -54.349 0.000 -1.083
## .Stst3ms (.120) -0.872 0.018 -49.262 0.000 -0.906
## .Stst4sc -1.287 0.021 -62.419 0.000 -1.327
## .Stst7bl (.122) -0.622 0.019 -31.943 0.000 -0.660
## .Stst8rn -0.947 0.015 -62.244 0.000 -0.977
## .Stst11r (.124) -1.051 0.019 -56.662 0.000 -1.087
## .Stst12l (.125) -0.859 0.016 -53.844 0.000 -0.890
## .Stst13h (.126) -1.106 0.021 -51.869 0.000 -1.148
## .Stst14b (.127) -0.636 0.016 -38.782 0.000 -0.668
## .Stst15t -0.867 0.018 -47.873 0.000 -0.902
## .Stst16m (.129) -0.933 0.019 -50.091 0.000 -0.970
## .Stst6ph (.130) -0.697 0.019 -37.205 0.000 -0.734
## .Stst9lc (.131) -0.748 0.021 -34.788 0.000 -0.790
## .Stst10m -1.082 0.019 -56.544 0.000 -1.119
## .Stst28m -1.088 0.020 -54.805 0.000 -1.127
## .Sts292D (.134) -0.552 0.021 -26.310 0.000 -0.593
## .Sts303D (.135) -0.695 0.018 -38.230 0.000 -0.730
## english 0.376 0.031 11.950 0.000 0.314
## math -0.121 0.028 -4.324 0.000 -0.176
## speed 0.235 0.036 6.606 0.000 0.166
## info 0.018 0.028 0.628 0.530 -0.038
## science -0.462 0.027 -17.334 0.000 -0.514
## spatial -0.503 0.034 -14.732 0.000 -0.569
## ci.upper Std.lv Std.all
## -1.133 -1.177 -1.293
## -1.000 -1.032 -1.133
## -0.723 -0.760 -0.776
## -1.138 -1.174 -1.179
## -1.194 -1.233 -1.258
## -1.015 -1.059 -0.954
## -0.918 -0.957 -0.870
## -0.812 -0.840 -1.084
## -1.289 -1.331 -1.347
## -1.022 -1.068 -0.989
## -1.124 -1.167 -1.013
## -0.737 -0.775 -0.799
## -1.055 -1.086 -1.446
## -0.838 -0.869 -1.244
## -0.697 -0.762 -0.469
## 0.101 0.051 0.039
## -0.271 -0.316 -0.275
## -1.008 -1.046 -1.165
## -0.837 -0.872 -0.981
## -1.247 -1.287 -1.441
## -0.584 -0.622 -0.733
## -0.917 -0.947 -1.139
## -1.015 -1.051 -1.108
## -0.828 -0.859 -1.018
## -1.064 -1.106 -1.008
## -0.604 -0.636 -0.733
## -0.831 -0.867 -1.008
## -0.897 -0.933 -0.992
## -0.660 -0.697 -1.037
## -0.705 -0.748 -0.753
## -1.044 -1.082 -1.730
## -1.050 -1.088 -1.778
## -0.511 -0.552 -0.558
## -0.659 -0.695 -0.890
## 0.438 0.381 0.381
## -0.066 -0.142 -0.142
## 0.305 0.235 0.235
## 0.074 0.019 0.019
## -0.410 -0.746 -0.746
## -0.436 -0.615 -0.615
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.255 0.007 35.220 0.000 0.241
## .Stst19dsgsdwrd 0.397 0.011 36.529 0.000 0.375
## .Stest20spellng 0.517 0.014 36.828 0.000 0.490
## .Stest21cptlztn 0.453 0.014 33.444 0.000 0.426
## .Stest22puncttn 0.309 0.010 29.888 0.000 0.289
## .Stest23english 0.557 0.017 33.009 0.000 0.523
## .Stest24exprssn 0.789 0.021 37.552 0.000 0.748
## .Stst25wrdfnctn 0.372 0.010 36.986 0.000 0.352
## .Stst26rdngcmpr 0.210 0.007 29.250 0.000 0.196
## .Stst31bstrctrs 0.596 0.017 34.409 0.000 0.562
## .Stst34rthcmptt 0.701 0.027 26.093 0.000 0.649
## .Stest5math 0.605 0.017 36.188 0.000 0.572
## .Stst32rthrsnng 0.277 0.008 33.447 0.000 0.261
## .Stst33hghschlm 0.190 0.007 28.195 0.000 0.176
## .Stest35tblrdng 1.328 0.066 19.976 0.000 1.198
## .Stst36clrclchc 0.993 0.034 29.189 0.000 0.926
## .Stst37bjctnspc 0.740 0.027 27.702 0.000 0.687
## .Stest2literatr 0.246 0.007 36.088 0.000 0.233
## .Stest3music 0.347 0.009 37.775 0.000 0.329
## .Stest4soclstds 0.250 0.007 34.804 0.000 0.236
## .Stst7blgclscnc 0.467 0.012 39.283 0.000 0.444
## .Stest8aerontcs 0.626 0.011 58.938 0.000 0.605
## .Stest11art 0.402 0.011 37.283 0.000 0.381
## .Stest12law 0.426 0.011 40.146 0.000 0.406
## .Stest13health 0.602 0.015 40.468 0.000 0.573
## .Stest14bible 0.432 0.013 34.016 0.000 0.408
## .Stest15theater 0.410 0.011 38.824 0.000 0.390
## .Stest16mscllns 0.468 0.012 37.933 0.000 0.443
## .Stst6physclscn 0.234 0.007 32.094 0.000 0.220
## .Stest9elctrncs 0.772 0.020 38.129 0.000 0.733
## .Stest10mechncs 0.238 0.006 37.659 0.000 0.226
## .Stst28mchnclrs 0.229 0.007 32.845 0.000 0.215
## .Stst29vslztn2D 0.676 0.019 34.782 0.000 0.638
## .Stst30vslztn3D 0.370 0.011 33.400 0.000 0.349
## english 0.971 0.040 24.141 0.000 0.892
## math 0.735 0.050 14.784 0.000 0.638
## speed 1.008 0.060 16.835 0.000 0.891
## info 0.862 0.037 23.451 0.000 0.790
## science 0.384 0.022 17.647 0.000 0.341
## spatial 0.667 0.042 15.980 0.000 0.585
## ci.upper Std.lv Std.all
## 0.269 0.255 0.308
## 0.418 0.397 0.479
## 0.545 0.517 0.539
## 0.479 0.453 0.457
## 0.329 0.309 0.322
## 0.590 0.557 0.451
## 0.830 0.789 0.652
## 0.392 0.372 0.620
## 0.225 0.210 0.215
## 0.629 0.596 0.511
## 0.754 0.701 0.528
## 0.638 0.605 0.642
## 0.293 0.277 0.491
## 0.203 0.190 0.389
## 1.459 1.328 0.504
## 1.060 0.993 0.593
## 0.792 0.740 0.557
## 0.260 0.246 0.305
## 0.365 0.347 0.440
## 0.264 0.250 0.314
## 0.490 0.467 0.647
## 0.647 0.626 0.906
## 0.423 0.402 0.446
## 0.447 0.426 0.599
## 0.632 0.602 0.500
## 0.457 0.432 0.575
## 0.431 0.410 0.555
## 0.492 0.468 0.528
## 0.249 0.234 0.519
## 0.812 0.772 0.784
## 0.251 0.238 0.610
## 0.243 0.229 0.611
## 0.714 0.676 0.690
## 0.392 0.370 0.608
## 1.050 1.000 1.000
## 0.833 1.000 1.000
## 1.125 1.000 1.000
## 0.934 1.000 1.000
## 0.426 1.000 1.000
## 0.749 1.000 1.000
lavTestScore(scalar2, release = 44:72) # X2 test for released constraints among the 34 intercepts
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 542.303 29 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p102. == .p243. 18.353 1 0.000
## 2 .p103. == .p244. 22.711 1 0.000
## 3 .p104. == .p245. 67.368 1 0.000
## 4 .p105. == .p246. 0.736 1 0.391
## 5 .p106. == .p247. 0.767 1 0.381
## 6 .p107. == .p248. 0.074 1 0.785
## 7 .p108. == .p249. 0.325 1 0.568
## 8 .p109. == .p250. 15.117 1 0.000
## 9 .p110. == .p251. 37.246 1 0.000
## 10 .p111. == .p252. 0.070 1 0.791
## 11 .p112. == .p253. 2.455 1 0.117
## 12 .p113. == .p254. 16.946 1 0.000
## 13 .p114. == .p255. 24.516 1 0.000
## 14 .p115. == .p256. 1.599 1 0.206
## 15 .p116. == .p257. 11.010 1 0.001
## 16 .p117. == .p258. 39.896 1 0.000
## 17 .p118. == .p259. 0.022 1 0.883
## 18 .p119. == .p260. 0.472 1 0.492
## 19 .p120. == .p261. 33.596 1 0.000
## 20 .p122. == .p263. 0.483 1 0.487
## 21 .p124. == .p265. 1.754 1 0.185
## 22 .p125. == .p266. 57.696 1 0.000
## 23 .p126. == .p267. 80.655 1 0.000
## 24 .p127. == .p268. 79.927 1 0.000
## 25 .p129. == .p270. 17.625 1 0.000
## 26 .p130. == .p271. 54.587 1 0.000
## 27 .p131. == .p272. 56.247 1 0.000
## 28 .p134. == .p275. 14.148 1 0.000
## 29 .p135. == .p276. 11.298 1 0.001
strict<-cfa(chc.factor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("info=~Stest8aeronautics", "spatial=~Stest28mechanicalreasoning", "info=~Stest4socialstudies", "Stest10mechanics~1", "Stest8aeronautics~1", "Stest28mechanicalreasoning~1", "Stest4socialstudies~1", "Stest15theater~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 6781.027 1094.000 0.000 0.949 0.041 0.047
## aic bic
## 463529.430 464630.458
Mc(strict)
## [1] 0.6266447
chc.cov<-cfa(chc.factor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("info=~Stest8aeronautics", "spatial=~Stest28mechanicalreasoning", "info=~Stest4socialstudies", "Stest10mechanics~1", "Stest8aeronautics~1", "Stest28mechanicalreasoning~1", "Stest4socialstudies~1", "Stest15theater~1"))
fitMeasures(chc.cov, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 6919.081 1075.000 0.000 0.948 0.042 0.079
## aic bic
## 463705.485 464934.070
Mc(chc.cov)
## [1] 0.6186084
chc.vcov<-cfa(chc.factor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "lv.variances", "lv.covariances"), group.partial=c("info=~Stest8aeronautics", "spatial=~Stest28mechanicalreasoning", "info=~Stest4socialstudies", "Stest10mechanics~1", "Stest8aeronautics~1", "Stest28mechanicalreasoning~1", "Stest4socialstudies~1", "Stest15theater~1"))
fitMeasures(chc.vcov, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 7027.745 1081.000 0.000 0.947 0.043 0.081
## aic bic
## 463802.149 464990.453
Mc(chc.vcov)
## [1] 0.613411
summary(chc.vcov, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 74 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 264
## Number of equality constraints 87
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 7027.745 6259.395
## Degrees of freedom 1081 1081
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.123
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 3343.018 2977.523
## 1 3684.727 3281.873
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.113 0.018 6.386 0.000 0.078
## Stst19d (.p2.) 0.351 0.021 16.847 0.000 0.310
## Stst20s (.p3.) 0.670 0.011 58.294 0.000 0.647
## Stst21c (.p4.) 0.737 0.010 72.637 0.000 0.717
## Stst22p (.p5.) 0.812 0.011 74.942 0.000 0.791
## Stst23n (.p6.) 0.829 0.013 64.051 0.000 0.804
## Stst24x (.p7.) 0.654 0.013 49.488 0.000 0.628
## Stst25w (.p8.) 0.195 0.019 10.277 0.000 0.157
## Stst26r (.p9.) 0.310 0.016 19.704 0.000 0.279
## Stst31b (.10.) 0.313 0.017 17.917 0.000 0.279
## Stst34r (.11.) 0.259 0.027 9.699 0.000 0.207
## math =~
## Stst5mt (.12.) 0.392 0.023 16.803 0.000 0.346
## Stst25w (.13.) 0.328 0.020 16.020 0.000 0.287
## Stst32r (.14.) 0.573 0.012 48.853 0.000 0.550
## Stst33h (.15.) 0.584 0.011 52.119 0.000 0.562
## Stst34r (.16.) 0.281 0.027 10.453 0.000 0.228
## speed =~
## Stst19d (.17.) 0.187 0.012 16.080 0.000 0.164
## Stst34r (.18.) 0.477 0.020 24.020 0.000 0.438
## Stst35t (.19.) 1.139 0.029 39.437 0.000 1.082
## Stst36c (.20.) 0.825 0.020 42.043 0.000 0.787
## Stst37b (.21.) 0.722 0.019 37.972 0.000 0.684
## info =~
## Stst1vc (.22.) 0.428 0.028 15.288 0.000 0.373
## Stst2lt (.23.) 0.772 0.011 73.309 0.000 0.752
## Stst3ms (.24.) 0.685 0.011 64.563 0.000 0.665
## Stst4sc 0.911 0.013 72.140 0.000 0.886
## Stst7bl (.26.) 0.254 0.024 10.710 0.000 0.208
## Stst8rn 0.572 0.017 34.342 0.000 0.540
## Stst11r (.28.) 0.727 0.011 68.798 0.000 0.706
## Stst12l (.29.) 0.552 0.012 47.464 0.000 0.530
## Stst13h (.30.) 0.799 0.011 72.956 0.000 0.778
## Stst14b (.31.) 0.583 0.011 52.691 0.000 0.562
## Stst15t (.32.) 0.590 0.011 53.842 0.000 0.568
## Stst16m (.33.) 0.668 0.011 59.739 0.000 0.646
## Stst19d (.34.) 0.252 0.020 12.378 0.000 0.212
## Stst26r (.35.) 0.623 0.016 39.084 0.000 0.592
## science =~
## Stst1vc (.36.) 0.345 0.019 17.982 0.000 0.308
## Stst5mt (.37.) 0.307 0.022 13.663 0.000 0.263
## Stst6ph (.38.) 0.599 0.011 55.278 0.000 0.577
## Stst7bl (.39.) 0.354 0.024 14.878 0.000 0.307
## Stst9lc (.40.) 0.591 0.014 42.729 0.000 0.564
## Stst10m (.41.) 0.479 0.010 47.198 0.000 0.459
## spatial =~
## Stst28m 0.675 0.016 43.370 0.000 0.645
## Sts292D (.43.) 0.605 0.014 44.764 0.000 0.578
## Sts303D (.44.) 0.533 0.012 45.105 0.000 0.510
## Stst31b (.45.) 0.556 0.018 30.362 0.000 0.520
## Stst37b (.46.) 0.127 0.017 7.349 0.000 0.093
## ci.upper Std.lv Std.all
##
## 0.148 0.113 0.115
## 0.392 0.351 0.390
## 0.692 0.670 0.671
## 0.757 0.737 0.771
## 0.834 0.812 0.813
## 0.854 0.829 0.719
## 0.680 0.654 0.578
## 0.232 0.195 0.244
## 0.341 0.310 0.305
## 0.347 0.313 0.281
## 0.312 0.259 0.229
##
## 0.438 0.392 0.396
## 0.368 0.328 0.411
## 0.596 0.573 0.725
## 0.606 0.584 0.788
## 0.334 0.281 0.248
##
## 0.209 0.187 0.207
## 0.516 0.477 0.421
## 1.196 1.139 0.685
## 0.864 0.825 0.637
## 0.759 0.722 0.587
##
## 0.483 0.428 0.435
## 0.793 0.772 0.835
## 0.706 0.685 0.759
## 0.935 0.911 0.862
## 0.301 0.254 0.283
## 0.605 0.572 0.577
## 0.748 0.727 0.769
## 0.575 0.552 0.627
## 0.821 0.799 0.741
## 0.605 0.583 0.678
## 0.611 0.590 0.714
## 0.690 0.668 0.680
## 0.292 0.252 0.279
## 0.654 0.623 0.613
##
## 0.383 0.345 0.351
## 0.351 0.307 0.310
## 0.620 0.599 0.765
## 0.401 0.354 0.394
## 0.619 0.591 0.584
## 0.499 0.479 0.609
##
## 0.706 0.675 0.783
## 0.631 0.605 0.568
## 0.556 0.533 0.598
## 0.592 0.556 0.499
## 0.160 0.127 0.103
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math (.87.) 0.820 0.008 100.439 0.000 0.804
## speed (.88.) 0.328 0.018 18.107 0.000 0.292
## info (.89.) 0.831 0.006 138.073 0.000 0.819
## science (.90.) 0.734 0.010 75.721 0.000 0.715
## spatial (.91.) 0.679 0.012 56.559 0.000 0.656
## math ~~
## speed (.92.) 0.281 0.018 15.329 0.000 0.245
## info (.93.) 0.790 0.009 91.203 0.000 0.773
## science (.94.) 0.792 0.011 73.075 0.000 0.771
## spatial (.95.) 0.729 0.013 56.809 0.000 0.704
## speed ~~
## info (.96.) 0.294 0.017 17.310 0.000 0.261
## science (.97.) 0.271 0.018 14.801 0.000 0.235
## spatial (.98.) 0.329 0.021 15.985 0.000 0.289
## info ~~
## science (.99.) 0.875 0.007 129.631 0.000 0.862
## spatial (.100) 0.648 0.012 53.248 0.000 0.625
## science ~~
## spatial (.101) 0.677 0.014 49.944 0.000 0.650
## ci.upper Std.lv Std.all
##
## 0.836 0.820 0.820
## 0.363 0.328 0.328
## 0.843 0.831 0.831
## 0.753 0.734 0.734
## 0.703 0.679 0.679
##
## 0.317 0.281 0.281
## 0.807 0.790 0.790
## 0.813 0.792 0.792
## 0.754 0.729 0.729
##
## 0.328 0.294 0.294
## 0.307 0.271 0.271
## 0.369 0.329 0.329
##
## 0.889 0.875 0.875
## 0.672 0.648 0.648
##
## 0.703 0.677 0.677
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.102) -1.176 0.022 -52.582 0.000 -1.220
## .Stst19d (.103) -1.031 0.016 -64.058 0.000 -1.063
## .Stst20s (.104) -0.760 0.019 -40.423 0.000 -0.797
## .Stst21c (.105) -1.173 0.018 -64.312 0.000 -1.209
## .Stst22p (.106) -1.233 0.020 -61.462 0.000 -1.272
## .Stst23n (.107) -1.059 0.022 -47.170 0.000 -1.104
## .Stst24x (.108) -0.957 0.020 -47.959 0.000 -0.996
## .Stst25w (.109) -0.840 0.014 -58.804 0.000 -0.868
## .Stst26r (.110) -1.331 0.021 -61.975 0.000 -1.373
## .Stst31b (.111) -1.067 0.023 -46.172 0.000 -1.113
## .Stst34r (.112) -1.167 0.022 -52.586 0.000 -1.211
## .Stst5mt (.113) -0.769 0.019 -39.740 0.000 -0.807
## .Stst32r (.114) -1.087 0.016 -67.766 0.000 -1.119
## .Stst33h (.115) -0.870 0.016 -55.488 0.000 -0.900
## .Stst35t (.116) -0.762 0.033 -23.076 0.000 -0.827
## .Stst36c (.117) 0.051 0.025 1.991 0.046 0.001
## .Stst37b (.118) -0.316 0.023 -13.675 0.000 -0.362
## .Stst2lt (.119) -1.045 0.019 -54.338 0.000 -1.083
## .Stst3ms (.120) -0.872 0.018 -49.297 0.000 -0.906
## .Stst4sc -1.083 0.023 -46.133 0.000 -1.129
## .Stst7bl (.122) -0.626 0.020 -31.797 0.000 -0.664
## .Stst8rn -0.517 0.022 -23.664 0.000 -0.560
## .Stst11r (.124) -1.051 0.019 -56.720 0.000 -1.087
## .Stst12l (.125) -0.859 0.016 -53.806 0.000 -0.890
## .Stst13h (.126) -1.106 0.021 -51.930 0.000 -1.148
## .Stst14b (.127) -0.636 0.016 -38.801 0.000 -0.668
## .Stst15t -1.025 0.017 -59.426 0.000 -1.059
## .Stst16m (.129) -0.933 0.019 -50.046 0.000 -0.970
## .Stst6ph (.130) -0.697 0.019 -37.226 0.000 -0.734
## .Stst9lc (.131) -0.750 0.022 -34.413 0.000 -0.793
## .Stst10m -0.656 0.019 -33.970 0.000 -0.694
## .Stst28m -0.715 0.019 -36.895 0.000 -0.753
## .Sts292D (.134) -0.552 0.021 -26.234 0.000 -0.593
## .Sts303D (.135) -0.695 0.018 -38.324 0.000 -0.731
## ci.upper Std.lv Std.all
## -1.132 -1.176 -1.195
## -1.000 -1.031 -1.144
## -0.723 -0.760 -0.762
## -1.138 -1.173 -1.227
## -1.194 -1.233 -1.233
## -1.015 -1.059 -0.919
## -0.918 -0.957 -0.846
## -0.812 -0.840 -1.054
## -1.289 -1.331 -1.310
## -1.022 -1.067 -0.957
## -1.124 -1.167 -1.029
## -0.731 -0.769 -0.777
## -1.056 -1.087 -1.377
## -0.839 -0.870 -1.173
## -0.697 -0.762 -0.458
## 0.100 0.051 0.039
## -0.271 -0.316 -0.257
## -1.008 -1.045 -1.130
## -0.837 -0.872 -0.965
## -1.037 -1.083 -1.025
## -0.587 -0.626 -0.697
## -0.475 -0.517 -0.521
## -1.014 -1.051 -1.111
## -0.827 -0.859 -0.974
## -1.064 -1.106 -1.025
## -0.604 -0.636 -0.740
## -0.991 -1.025 -1.242
## -0.896 -0.933 -0.950
## -0.660 -0.697 -0.891
## -0.707 -0.750 -0.741
## -0.618 -0.656 -0.834
## -0.677 -0.715 -0.829
## -0.511 -0.552 -0.518
## -0.660 -0.695 -0.780
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.257 0.009 28.104 0.000 0.239
## .Stst19dsgsdwrd 0.373 0.014 27.162 0.000 0.346
## .Stest20spellng 0.546 0.017 31.239 0.000 0.512
## .Stest21cptlztn 0.372 0.015 24.573 0.000 0.342
## .Stest22puncttn 0.340 0.012 28.170 0.000 0.316
## .Stest23english 0.643 0.024 26.866 0.000 0.596
## .Stest24exprssn 0.853 0.026 33.297 0.000 0.803
## .Stst25wrdfnctn 0.385 0.012 32.527 0.000 0.362
## .Stst26rdngcmpr 0.227 0.009 25.330 0.000 0.209
## .Stst31bstrctrs 0.600 0.022 27.863 0.000 0.558
## .Stst34rthcmptt 0.637 0.030 21.124 0.000 0.578
## .Stest5math 0.540 0.020 26.634 0.000 0.501
## .Stst32rthrsnng 0.296 0.011 27.298 0.000 0.274
## .Stst33hghschlm 0.208 0.009 23.705 0.000 0.191
## .Stest35tblrdng 1.471 0.075 19.652 0.000 1.324
## .Stst36clrclchc 0.996 0.042 23.876 0.000 0.914
## .Stst37bjctnspc 0.914 0.034 26.529 0.000 0.847
## .Stest2literatr 0.260 0.009 29.572 0.000 0.243
## .Stest3music 0.346 0.012 29.057 0.000 0.323
## .Stest4soclstds 0.287 0.011 27.242 0.000 0.266
## .Stst7blgclscnc 0.458 0.014 32.845 0.000 0.431
## .Stest8aerontcs 0.657 0.018 37.153 0.000 0.622
## .Stest11art 0.365 0.012 29.872 0.000 0.341
## .Stest12law 0.472 0.014 32.662 0.000 0.444
## .Stest13health 0.525 0.016 32.228 0.000 0.493
## .Stest14bible 0.399 0.013 29.585 0.000 0.372
## .Stest15theater 0.334 0.011 30.629 0.000 0.313
## .Stest16mscllns 0.518 0.017 30.815 0.000 0.485
## .Stst6physclscn 0.254 0.011 23.947 0.000 0.233
## .Stest9elctrncs 0.675 0.028 24.479 0.000 0.621
## .Stest10mechncs 0.390 0.013 29.815 0.000 0.364
## .Stst28mchnclrs 0.288 0.015 19.057 0.000 0.259
## .Stst29vslztn2D 0.769 0.026 29.922 0.000 0.719
## .Stst30vslztn3D 0.510 0.017 30.688 0.000 0.478
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.275 0.257 0.266
## 0.400 0.373 0.459
## 0.581 0.546 0.549
## 0.401 0.372 0.406
## 0.363 0.340 0.340
## 0.690 0.643 0.483
## 0.903 0.853 0.666
## 0.408 0.385 0.607
## 0.245 0.227 0.220
## 0.643 0.600 0.482
## 0.696 0.637 0.495
## 0.580 0.540 0.552
## 0.317 0.296 0.474
## 0.225 0.208 0.379
## 1.617 1.471 0.531
## 1.077 0.996 0.594
## 0.982 0.914 0.605
## 0.277 0.260 0.304
## 0.370 0.346 0.424
## 0.307 0.287 0.257
## 0.486 0.458 0.569
## 0.692 0.657 0.667
## 0.389 0.365 0.408
## 0.500 0.472 0.607
## 0.557 0.525 0.451
## 0.425 0.399 0.540
## 0.355 0.334 0.490
## 0.551 0.518 0.537
## 0.275 0.254 0.415
## 0.729 0.675 0.659
## 0.415 0.390 0.629
## 0.318 0.288 0.387
## 0.819 0.769 0.678
## 0.543 0.510 0.642
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.113 0.018 6.386 0.000 0.078
## Stst19d (.p2.) 0.351 0.021 16.847 0.000 0.310
## Stst20s (.p3.) 0.670 0.011 58.294 0.000 0.647
## Stst21c (.p4.) 0.737 0.010 72.637 0.000 0.717
## Stst22p (.p5.) 0.812 0.011 74.942 0.000 0.791
## Stst23n (.p6.) 0.829 0.013 64.051 0.000 0.804
## Stst24x (.p7.) 0.654 0.013 49.488 0.000 0.628
## Stst25w (.p8.) 0.195 0.019 10.277 0.000 0.157
## Stst26r (.p9.) 0.310 0.016 19.704 0.000 0.279
## Stst31b (.10.) 0.313 0.017 17.917 0.000 0.279
## Stst34r (.11.) 0.259 0.027 9.699 0.000 0.207
## math =~
## Stst5mt (.12.) 0.392 0.023 16.803 0.000 0.346
## Stst25w (.13.) 0.328 0.020 16.020 0.000 0.287
## Stst32r (.14.) 0.573 0.012 48.853 0.000 0.550
## Stst33h (.15.) 0.584 0.011 52.119 0.000 0.562
## Stst34r (.16.) 0.281 0.027 10.453 0.000 0.228
## speed =~
## Stst19d (.17.) 0.187 0.012 16.080 0.000 0.164
## Stst34r (.18.) 0.477 0.020 24.020 0.000 0.438
## Stst35t (.19.) 1.139 0.029 39.437 0.000 1.082
## Stst36c (.20.) 0.825 0.020 42.043 0.000 0.787
## Stst37b (.21.) 0.722 0.019 37.972 0.000 0.684
## info =~
## Stst1vc (.22.) 0.428 0.028 15.288 0.000 0.373
## Stst2lt (.23.) 0.772 0.011 73.309 0.000 0.752
## Stst3ms (.24.) 0.685 0.011 64.563 0.000 0.665
## Stst4sc 0.776 0.012 66.935 0.000 0.753
## Stst7bl (.26.) 0.254 0.024 10.710 0.000 0.208
## Stst8rn 0.268 0.016 17.171 0.000 0.237
## Stst11r (.28.) 0.727 0.011 68.798 0.000 0.706
## Stst12l (.29.) 0.552 0.012 47.464 0.000 0.530
## Stst13h (.30.) 0.799 0.011 72.956 0.000 0.778
## Stst14b (.31.) 0.583 0.011 52.691 0.000 0.562
## Stst15t (.32.) 0.590 0.011 53.842 0.000 0.568
## Stst16m (.33.) 0.668 0.011 59.739 0.000 0.646
## Stst19d (.34.) 0.252 0.020 12.378 0.000 0.212
## Stst26r (.35.) 0.623 0.016 39.084 0.000 0.592
## science =~
## Stst1vc (.36.) 0.345 0.019 17.982 0.000 0.308
## Stst5mt (.37.) 0.307 0.022 13.663 0.000 0.263
## Stst6ph (.38.) 0.599 0.011 55.278 0.000 0.577
## Stst7bl (.39.) 0.354 0.024 14.878 0.000 0.307
## Stst9lc (.40.) 0.591 0.014 42.729 0.000 0.564
## Stst10m (.41.) 0.479 0.010 47.198 0.000 0.459
## spatial =~
## Stst28m 0.399 0.013 29.615 0.000 0.372
## Sts292D (.43.) 0.605 0.014 44.764 0.000 0.578
## Sts303D (.44.) 0.533 0.012 45.105 0.000 0.510
## Stst31b (.45.) 0.556 0.018 30.362 0.000 0.520
## Stst37b (.46.) 0.127 0.017 7.349 0.000 0.093
## ci.upper Std.lv Std.all
##
## 0.148 0.113 0.115
## 0.392 0.351 0.384
## 0.692 0.670 0.682
## 0.757 0.737 0.738
## 0.834 0.812 0.825
## 0.854 0.829 0.744
## 0.680 0.654 0.593
## 0.232 0.195 0.247
## 0.341 0.310 0.308
## 0.347 0.313 0.282
## 0.312 0.259 0.223
##
## 0.438 0.392 0.384
## 0.368 0.328 0.416
## 0.596 0.573 0.738
## 0.606 0.584 0.806
## 0.334 0.281 0.242
##
## 0.209 0.187 0.204
## 0.516 0.477 0.411
## 1.196 1.139 0.702
## 0.864 0.825 0.638
## 0.759 0.722 0.625
##
## 0.483 0.428 0.436
## 0.793 0.772 0.841
## 0.706 0.685 0.758
## 0.798 0.776 0.841
## 0.301 0.254 0.282
## 0.299 0.268 0.321
## 0.748 0.727 0.753
## 0.575 0.552 0.646
## 0.821 0.799 0.717
## 0.605 0.583 0.663
## 0.611 0.590 0.677
## 0.690 0.668 0.699
## 0.292 0.252 0.275
## 0.654 0.623 0.618
##
## 0.383 0.345 0.352
## 0.351 0.307 0.301
## 0.620 0.599 0.786
## 0.401 0.354 0.393
## 0.619 0.591 0.558
## 0.499 0.479 0.701
##
## 0.425 0.399 0.638
## 0.631 0.605 0.596
## 0.556 0.533 0.663
## 0.592 0.556 0.501
## 0.160 0.127 0.110
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math (.87.) 0.820 0.008 100.439 0.000 0.804
## speed (.88.) 0.328 0.018 18.107 0.000 0.292
## info (.89.) 0.831 0.006 138.073 0.000 0.819
## science (.90.) 0.734 0.010 75.721 0.000 0.715
## spatial (.91.) 0.679 0.012 56.559 0.000 0.656
## math ~~
## speed (.92.) 0.281 0.018 15.329 0.000 0.245
## info (.93.) 0.790 0.009 91.203 0.000 0.773
## science (.94.) 0.792 0.011 73.075 0.000 0.771
## spatial (.95.) 0.729 0.013 56.809 0.000 0.704
## speed ~~
## info (.96.) 0.294 0.017 17.310 0.000 0.261
## science (.97.) 0.271 0.018 14.801 0.000 0.235
## spatial (.98.) 0.329 0.021 15.985 0.000 0.289
## info ~~
## science (.99.) 0.875 0.007 129.631 0.000 0.862
## spatial (.100) 0.648 0.012 53.248 0.000 0.625
## science ~~
## spatial (.101) 0.677 0.014 49.944 0.000 0.650
## ci.upper Std.lv Std.all
##
## 0.836 0.820 0.820
## 0.363 0.328 0.328
## 0.843 0.831 0.831
## 0.753 0.734 0.734
## 0.703 0.679 0.679
##
## 0.317 0.281 0.281
## 0.807 0.790 0.790
## 0.813 0.792 0.792
## 0.754 0.729 0.729
##
## 0.328 0.294 0.294
## 0.307 0.271 0.271
## 0.369 0.329 0.329
##
## 0.889 0.875 0.875
## 0.672 0.648 0.648
##
## 0.703 0.677 0.677
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.102) -1.176 0.022 -52.582 0.000 -1.220
## .Stst19d (.103) -1.031 0.016 -64.058 0.000 -1.063
## .Stst20s (.104) -0.760 0.019 -40.423 0.000 -0.797
## .Stst21c (.105) -1.173 0.018 -64.312 0.000 -1.209
## .Stst22p (.106) -1.233 0.020 -61.462 0.000 -1.272
## .Stst23n (.107) -1.059 0.022 -47.170 0.000 -1.104
## .Stst24x (.108) -0.957 0.020 -47.959 0.000 -0.996
## .Stst25w (.109) -0.840 0.014 -58.804 0.000 -0.868
## .Stst26r (.110) -1.331 0.021 -61.975 0.000 -1.373
## .Stst31b (.111) -1.067 0.023 -46.172 0.000 -1.113
## .Stst34r (.112) -1.167 0.022 -52.586 0.000 -1.211
## .Stst5mt (.113) -0.769 0.019 -39.740 0.000 -0.807
## .Stst32r (.114) -1.087 0.016 -67.766 0.000 -1.119
## .Stst33h (.115) -0.870 0.016 -55.488 0.000 -0.900
## .Stst35t (.116) -0.762 0.033 -23.076 0.000 -0.827
## .Stst36c (.117) 0.051 0.025 1.991 0.046 0.001
## .Stst37b (.118) -0.316 0.023 -13.675 0.000 -0.362
## .Stst2lt (.119) -1.045 0.019 -54.338 0.000 -1.083
## .Stst3ms (.120) -0.872 0.018 -49.297 0.000 -0.906
## .Stst4sc -1.287 0.021 -61.579 0.000 -1.328
## .Stst7bl (.122) -0.626 0.020 -31.797 0.000 -0.664
## .Stst8rn -0.947 0.015 -62.042 0.000 -0.977
## .Stst11r (.124) -1.051 0.019 -56.720 0.000 -1.087
## .Stst12l (.125) -0.859 0.016 -53.806 0.000 -0.890
## .Stst13h (.126) -1.106 0.021 -51.930 0.000 -1.148
## .Stst14b (.127) -0.636 0.016 -38.801 0.000 -0.668
## .Stst15t -0.866 0.018 -47.955 0.000 -0.902
## .Stst16m (.129) -0.933 0.019 -50.046 0.000 -0.970
## .Stst6ph (.130) -0.697 0.019 -37.226 0.000 -0.734
## .Stst9lc (.131) -0.750 0.022 -34.413 0.000 -0.793
## .Stst10m -1.097 0.019 -58.341 0.000 -1.133
## .Stst28m -1.099 0.019 -58.990 0.000 -1.136
## .Sts292D (.134) -0.552 0.021 -26.234 0.000 -0.593
## .Sts303D (.135) -0.695 0.018 -38.324 0.000 -0.731
## english 0.379 0.030 12.440 0.000 0.319
## math -0.130 0.032 -4.107 0.000 -0.193
## speed 0.236 0.035 6.794 0.000 0.168
## info 0.018 0.030 0.614 0.539 -0.040
## science -0.577 0.036 -16.196 0.000 -0.646
## spatial -0.563 0.039 -14.405 0.000 -0.639
## ci.upper Std.lv Std.all
## -1.132 -1.176 -1.198
## -1.000 -1.031 -1.127
## -0.723 -0.760 -0.774
## -1.138 -1.173 -1.175
## -1.194 -1.233 -1.253
## -1.015 -1.059 -0.951
## -0.918 -0.957 -0.868
## -0.812 -0.840 -1.066
## -1.289 -1.331 -1.320
## -1.022 -1.067 -0.961
## -1.124 -1.167 -1.005
## -0.731 -0.769 -0.754
## -1.056 -1.087 -1.401
## -0.839 -0.870 -1.199
## -0.697 -0.762 -0.470
## 0.100 0.051 0.039
## -0.271 -0.316 -0.274
## -1.008 -1.045 -1.139
## -0.837 -0.872 -0.963
## -1.246 -1.287 -1.395
## -0.587 -0.626 -0.694
## -0.917 -0.947 -1.134
## -1.014 -1.051 -1.088
## -0.827 -0.859 -1.004
## -1.064 -1.106 -0.992
## -0.604 -0.636 -0.723
## -0.831 -0.866 -0.994
## -0.896 -0.933 -0.976
## -0.660 -0.697 -0.915
## -0.707 -0.750 -0.707
## -1.060 -1.097 -1.605
## -1.063 -1.099 -1.761
## -0.511 -0.552 -0.544
## -0.660 -0.695 -0.864
## 0.439 0.379 0.379
## -0.068 -0.130 -0.130
## 0.304 0.236 0.236
## 0.076 0.018 0.018
## -0.507 -0.577 -0.577
## -0.486 -0.563 -0.563
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.252 0.007 34.808 0.000 0.238
## .Stst19dsgsdwrd 0.398 0.011 36.525 0.000 0.377
## .Stest20spellng 0.517 0.014 36.849 0.000 0.489
## .Stest21cptlztn 0.454 0.013 33.614 0.000 0.427
## .Stest22puncttn 0.309 0.010 29.951 0.000 0.289
## .Stest23english 0.555 0.017 32.925 0.000 0.522
## .Stest24exprssn 0.788 0.021 37.556 0.000 0.747
## .Stst25wrdfnctn 0.371 0.010 36.948 0.000 0.351
## .Stst26rdngcmpr 0.211 0.007 29.311 0.000 0.197
## .Stst31bstrctrs 0.590 0.017 34.750 0.000 0.557
## .Stst34rthcmptt 0.700 0.027 25.874 0.000 0.647
## .Stest5math 0.601 0.016 36.514 0.000 0.569
## .Stst32rthrsnng 0.275 0.008 33.023 0.000 0.258
## .Stst33hghschlm 0.185 0.007 27.689 0.000 0.172
## .Stest35tblrdng 1.335 0.067 19.981 0.000 1.204
## .Stst36clrclchc 0.991 0.034 29.523 0.000 0.925
## .Stst37bjctnspc 0.735 0.027 27.746 0.000 0.683
## .Stest2literatr 0.246 0.007 36.115 0.000 0.233
## .Stest3music 0.349 0.009 37.778 0.000 0.331
## .Stest4soclstds 0.249 0.007 34.700 0.000 0.235
## .Stst7blgclscnc 0.465 0.012 38.835 0.000 0.442
## .Stest8aerontcs 0.626 0.011 58.911 0.000 0.605
## .Stest11art 0.403 0.011 37.371 0.000 0.382
## .Stest12law 0.426 0.011 40.259 0.000 0.405
## .Stest13health 0.604 0.015 40.605 0.000 0.575
## .Stest14bible 0.433 0.013 33.996 0.000 0.408
## .Stest15theater 0.412 0.011 38.867 0.000 0.391
## .Stest16mscllns 0.467 0.012 38.012 0.000 0.443
## .Stst6physclscn 0.222 0.007 30.983 0.000 0.208
## .Stest9elctrncs 0.775 0.021 37.631 0.000 0.734
## .Stest10mechncs 0.237 0.006 36.964 0.000 0.225
## .Stst28mchnclrs 0.231 0.007 33.405 0.000 0.217
## .Stst29vslztn2D 0.665 0.019 34.733 0.000 0.627
## .Stst30vslztn3D 0.363 0.011 33.268 0.000 0.341
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.267 0.252 0.262
## 0.419 0.398 0.475
## 0.544 0.517 0.535
## 0.480 0.454 0.455
## 0.329 0.309 0.319
## 0.588 0.555 0.447
## 0.829 0.788 0.648
## 0.391 0.371 0.598
## 0.225 0.211 0.207
## 0.623 0.590 0.478
## 0.753 0.700 0.518
## 0.634 0.601 0.578
## 0.291 0.275 0.456
## 0.198 0.185 0.351
## 1.466 1.335 0.507
## 1.056 0.991 0.593
## 0.787 0.735 0.552
## 0.260 0.246 0.292
## 0.367 0.349 0.426
## 0.263 0.249 0.293
## 0.489 0.465 0.572
## 0.647 0.626 0.897
## 0.425 0.403 0.433
## 0.447 0.426 0.583
## 0.633 0.604 0.486
## 0.458 0.433 0.560
## 0.433 0.412 0.542
## 0.491 0.467 0.511
## 0.236 0.222 0.382
## 0.815 0.775 0.689
## 0.250 0.237 0.508
## 0.245 0.231 0.593
## 0.703 0.665 0.645
## 0.384 0.363 0.561
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
chc.reduced<-cfa(chc.factor.reduced, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "lv.variances", "lv.covariances"), group.partial=c("info=~Stest8aeronautics", "spatial=~Stest28mechanicalreasoning", "info=~Stest4socialstudies", "Stest10mechanics~1", "Stest8aeronautics~1", "Stest28mechanicalreasoning~1", "Stest4socialstudies~1", "Stest15theater~1"))
fitMeasures(chc.reduced, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 7028.184 1082.000 0.000 0.947 0.043 0.081
## aic bic
## 463800.587 464982.178
Mc(chc.reduced)
## [1] 0.6134393
summary(chc.reduced, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 70 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 263
## Number of equality constraints 87
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 7028.184 6259.556
## Degrees of freedom 1082 1082
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.123
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 3343.154 2977.534
## 1 3685.030 3282.022
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.113 0.018 6.394 0.000 0.078
## Stst19d (.p2.) 0.351 0.021 16.865 0.000 0.310
## Stst20s (.p3.) 0.670 0.011 58.289 0.000 0.647
## Stst21c (.p4.) 0.737 0.010 72.639 0.000 0.717
## Stst22p (.p5.) 0.812 0.011 74.941 0.000 0.791
## Stst23n (.p6.) 0.829 0.013 64.057 0.000 0.804
## Stst24x (.p7.) 0.654 0.013 49.496 0.000 0.628
## Stst25w (.p8.) 0.195 0.019 10.279 0.000 0.157
## Stst26r (.p9.) 0.311 0.016 19.755 0.000 0.280
## Stst31b (.10.) 0.313 0.017 17.917 0.000 0.279
## Stst34r (.11.) 0.259 0.027 9.696 0.000 0.207
## math =~
## Stst5mt (.12.) 0.392 0.023 16.799 0.000 0.346
## Stst25w (.13.) 0.328 0.020 16.021 0.000 0.287
## Stst32r (.14.) 0.573 0.012 48.864 0.000 0.550
## Stst33h (.15.) 0.584 0.011 52.130 0.000 0.562
## Stst34r (.16.) 0.281 0.027 10.456 0.000 0.228
## speed =~
## Stst19d (.17.) 0.187 0.012 16.082 0.000 0.164
## Stst34r (.18.) 0.477 0.020 24.020 0.000 0.438
## Stst35t (.19.) 1.139 0.029 39.435 0.000 1.082
## Stst36c (.20.) 0.825 0.020 42.044 0.000 0.787
## Stst37b (.21.) 0.722 0.019 37.973 0.000 0.684
## info =~
## Stst1vc (.22.) 0.428 0.028 15.337 0.000 0.374
## Stst2lt (.23.) 0.772 0.011 73.344 0.000 0.752
## Stst3ms (.24.) 0.685 0.011 64.550 0.000 0.665
## Stst4sc 0.911 0.013 72.124 0.000 0.886
## Stst7bl (.26.) 0.255 0.024 10.729 0.000 0.208
## Stst8rn 0.572 0.017 34.349 0.000 0.540
## Stst11r (.28.) 0.727 0.011 68.825 0.000 0.706
## Stst12l (.29.) 0.552 0.012 47.578 0.000 0.530
## Stst13h (.30.) 0.799 0.011 72.948 0.000 0.778
## Stst14b (.31.) 0.583 0.011 52.685 0.000 0.562
## Stst15t (.32.) 0.590 0.011 53.854 0.000 0.568
## Stst16m (.33.) 0.668 0.011 59.828 0.000 0.646
## Stst19d (.34.) 0.252 0.020 12.387 0.000 0.212
## Stst26r (.35.) 0.623 0.016 39.051 0.000 0.592
## science =~
## Stst1vc (.36.) 0.345 0.019 17.985 0.000 0.307
## Stst5mt (.37.) 0.307 0.022 13.663 0.000 0.263
## Stst6ph (.38.) 0.599 0.011 55.322 0.000 0.578
## Stst7bl (.39.) 0.354 0.024 14.855 0.000 0.307
## Stst9lc (.40.) 0.591 0.014 42.799 0.000 0.564
## Stst10m (.41.) 0.479 0.010 47.209 0.000 0.459
## spatial =~
## Stst28m 0.675 0.016 43.380 0.000 0.645
## Sts292D (.43.) 0.605 0.014 44.764 0.000 0.578
## Sts303D (.44.) 0.533 0.012 45.107 0.000 0.510
## Stst31b (.45.) 0.556 0.018 30.366 0.000 0.520
## Stst37b (.46.) 0.127 0.017 7.350 0.000 0.093
## ci.upper Std.lv Std.all
##
## 0.148 0.113 0.115
## 0.392 0.351 0.390
## 0.692 0.670 0.671
## 0.757 0.737 0.770
## 0.834 0.812 0.813
## 0.854 0.829 0.719
## 0.680 0.654 0.578
## 0.232 0.195 0.244
## 0.341 0.311 0.306
## 0.347 0.313 0.281
## 0.312 0.259 0.229
##
## 0.438 0.392 0.396
## 0.368 0.328 0.411
## 0.596 0.573 0.725
## 0.606 0.584 0.788
## 0.334 0.281 0.248
##
## 0.209 0.187 0.207
## 0.516 0.477 0.421
## 1.196 1.139 0.685
## 0.864 0.825 0.637
## 0.759 0.722 0.587
##
## 0.483 0.428 0.435
## 0.793 0.772 0.835
## 0.706 0.685 0.759
## 0.935 0.911 0.862
## 0.301 0.255 0.284
## 0.605 0.572 0.577
## 0.748 0.727 0.769
## 0.575 0.552 0.627
## 0.821 0.799 0.741
## 0.605 0.583 0.678
## 0.611 0.590 0.714
## 0.690 0.668 0.680
## 0.292 0.252 0.279
## 0.654 0.623 0.613
##
## 0.382 0.345 0.350
## 0.351 0.307 0.311
## 0.620 0.599 0.765
## 0.400 0.354 0.394
## 0.619 0.591 0.584
## 0.499 0.479 0.609
##
## 0.706 0.675 0.783
## 0.631 0.605 0.568
## 0.556 0.533 0.598
## 0.592 0.556 0.499
## 0.160 0.127 0.103
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math (.88.) 0.820 0.008 100.457 0.000 0.804
## speed (.89.) 0.328 0.018 18.106 0.000 0.292
## info (.90.) 0.831 0.006 138.088 0.000 0.819
## science (.91.) 0.734 0.010 75.722 0.000 0.715
## spatial (.92.) 0.679 0.012 56.564 0.000 0.656
## math ~~
## speed (.93.) 0.281 0.018 15.328 0.000 0.245
## info (.94.) 0.790 0.009 91.216 0.000 0.773
## science (.95.) 0.792 0.011 73.073 0.000 0.771
## spatial (.96.) 0.729 0.013 56.811 0.000 0.704
## speed ~~
## info (.97.) 0.294 0.017 17.308 0.000 0.261
## science (.98.) 0.271 0.018 14.800 0.000 0.235
## spatial (.99.) 0.329 0.021 15.985 0.000 0.289
## info ~~
## science (.100) 0.875 0.007 129.569 0.000 0.862
## spatial (.101) 0.648 0.012 53.255 0.000 0.625
## science ~~
## spatial (.102) 0.677 0.014 49.946 0.000 0.650
## ci.upper Std.lv Std.all
##
## 0.836 0.820 0.820
## 0.363 0.328 0.328
## 0.843 0.831 0.831
## 0.753 0.734 0.734
## 0.703 0.679 0.679
##
## 0.317 0.281 0.281
## 0.807 0.790 0.790
## 0.813 0.792 0.792
## 0.754 0.729 0.729
##
## 0.328 0.294 0.294
## 0.307 0.271 0.271
## 0.369 0.329 0.329
##
## 0.889 0.875 0.875
## 0.672 0.648 0.648
##
## 0.703 0.677 0.677
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## info 0.000 0.000
## .Stst1vc (.103) -1.168 0.016 -70.914 0.000 -1.200
## .Stst19d (.104) -1.025 0.013 -79.687 0.000 -1.051
## .Stst20s (.105) -0.755 0.016 -46.479 0.000 -0.786
## .Stst21c (.106) -1.168 0.015 -75.779 0.000 -1.198
## .Stst22p (.107) -1.226 0.017 -73.193 0.000 -1.259
## .Stst23n (.108) -1.053 0.019 -55.033 0.000 -1.090
## .Stst24x (.109) -0.952 0.018 -53.772 0.000 -0.987
## .Stst25w (.110) -0.835 0.013 -66.269 0.000 -0.860
## .Stst26r (.111) -1.322 0.014 -94.011 0.000 -1.349
## .Stst31b (.112) -1.061 0.020 -51.987 0.000 -1.101
## .Stst34r (.113) -1.161 0.020 -58.371 0.000 -1.200
## .Stst5mt (.114) -0.764 0.016 -47.291 0.000 -0.795
## .Stst32r (.115) -1.083 0.014 -78.758 0.000 -1.110
## .Stst33h (.116) -0.865 0.013 -65.181 0.000 -0.891
## .Stst35t (.117) -0.759 0.032 -23.416 0.000 -0.822
## .Stst36c (.118) 0.053 0.025 2.119 0.034 0.004
## .Stst37b (.119) -0.314 0.023 -13.876 0.000 -0.358
## .Stst2lt (.120) -1.037 0.012 -83.277 0.000 -1.061
## .Stst3ms (.121) -0.864 0.012 -70.897 0.000 -0.888
## .Stst4sc -1.074 0.017 -61.791 0.000 -1.108
## .Stst7bl (.123) -0.620 0.016 -37.943 0.000 -0.652
## .Stst8rn -0.512 0.019 -26.295 0.000 -0.550
## .Stst11r (.125) -1.043 0.013 -81.571 0.000 -1.068
## .Stst12l (.126) -0.853 0.012 -73.371 0.000 -0.875
## .Stst13h (.127) -1.098 0.015 -73.051 0.000 -1.127
## .Stst14b (.128) -0.630 0.012 -52.948 0.000 -0.653
## .Stst15t -1.019 0.014 -71.344 0.000 -1.047
## .Stst16m (.130) -0.926 0.013 -71.030 0.000 -0.951
## .Stst6ph (.131) -0.692 0.015 -45.021 0.000 -0.722
## .Stst9lc (.132) -0.745 0.019 -40.262 0.000 -0.781
## .Stst10m -0.652 0.017 -38.665 0.000 -0.685
## .Stst28m -0.711 0.017 -40.624 0.000 -0.745
## .Sts292D (.135) -0.548 0.020 -27.638 0.000 -0.587
## .Sts303D (.136) -0.692 0.017 -41.027 0.000 -0.725
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -1.135 -1.168 -1.186
## -1.000 -1.025 -1.138
## -0.723 -0.755 -0.757
## -1.137 -1.168 -1.221
## -1.194 -1.226 -1.227
## -1.015 -1.053 -0.913
## -0.917 -0.952 -0.841
## -0.811 -0.835 -1.049
## -1.294 -1.322 -1.301
## -1.021 -1.061 -0.951
## -1.122 -1.161 -1.024
## -0.732 -0.764 -0.772
## -1.056 -1.083 -1.371
## -0.839 -0.865 -1.167
## -0.695 -0.759 -0.456
## 0.102 0.053 0.041
## -0.269 -0.314 -0.255
## -1.013 -1.037 -1.120
## -0.840 -0.864 -0.956
## -1.039 -1.074 -1.016
## -0.588 -0.620 -0.691
## -0.474 -0.512 -0.516
## -1.018 -1.043 -1.103
## -0.830 -0.853 -0.967
## -1.068 -1.098 -1.017
## -0.606 -0.630 -0.733
## -0.991 -1.019 -1.235
## -0.900 -0.926 -0.943
## -0.662 -0.692 -0.884
## -0.709 -0.745 -0.736
## -0.619 -0.652 -0.828
## -0.676 -0.711 -0.824
## -0.509 -0.548 -0.514
## -0.659 -0.692 -0.776
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.257 0.009 28.109 0.000 0.239
## .Stst19dsgsdwrd 0.373 0.014 27.151 0.000 0.346
## .Stest20spellng 0.546 0.017 31.239 0.000 0.512
## .Stest21cptlztn 0.372 0.015 24.578 0.000 0.342
## .Stest22puncttn 0.340 0.012 28.173 0.000 0.316
## .Stest23english 0.643 0.024 26.866 0.000 0.596
## .Stest24exprssn 0.853 0.026 33.299 0.000 0.803
## .Stst25wrdfnctn 0.385 0.012 32.526 0.000 0.362
## .Stst26rdngcmpr 0.227 0.009 25.319 0.000 0.209
## .Stst31bstrctrs 0.600 0.022 27.863 0.000 0.558
## .Stst34rthcmptt 0.637 0.030 21.123 0.000 0.578
## .Stest5math 0.540 0.020 26.636 0.000 0.501
## .Stst32rthrsnng 0.296 0.011 27.298 0.000 0.274
## .Stst33hghschlm 0.208 0.009 23.705 0.000 0.191
## .Stest35tblrdng 1.471 0.075 19.650 0.000 1.324
## .Stst36clrclchc 0.996 0.042 23.875 0.000 0.914
## .Stst37bjctnspc 0.914 0.034 26.530 0.000 0.847
## .Stest2literatr 0.260 0.009 29.564 0.000 0.243
## .Stest3music 0.346 0.012 29.121 0.000 0.323
## .Stest4soclstds 0.287 0.011 27.242 0.000 0.266
## .Stst7blgclscnc 0.458 0.014 32.851 0.000 0.431
## .Stest8aerontcs 0.657 0.018 37.154 0.000 0.622
## .Stest11art 0.365 0.012 29.867 0.000 0.341
## .Stest12law 0.472 0.014 32.623 0.000 0.443
## .Stest13health 0.526 0.016 32.287 0.000 0.494
## .Stest14bible 0.399 0.013 29.677 0.000 0.373
## .Stest15theater 0.334 0.011 30.629 0.000 0.313
## .Stest16mscllns 0.518 0.017 30.806 0.000 0.485
## .Stst6physclscn 0.254 0.011 23.911 0.000 0.233
## .Stest9elctrncs 0.675 0.028 24.484 0.000 0.621
## .Stest10mechncs 0.390 0.013 29.815 0.000 0.364
## .Stst28mchnclrs 0.288 0.015 19.057 0.000 0.259
## .Stst29vslztn2D 0.769 0.026 29.922 0.000 0.719
## .Stst30vslztn3D 0.510 0.017 30.689 0.000 0.478
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.275 0.257 0.266
## 0.400 0.373 0.459
## 0.581 0.546 0.549
## 0.401 0.372 0.406
## 0.363 0.340 0.340
## 0.690 0.643 0.483
## 0.903 0.853 0.666
## 0.408 0.385 0.607
## 0.244 0.227 0.220
## 0.643 0.600 0.482
## 0.696 0.637 0.495
## 0.580 0.540 0.552
## 0.317 0.296 0.474
## 0.225 0.208 0.379
## 1.617 1.471 0.531
## 1.077 0.996 0.594
## 0.982 0.914 0.605
## 0.277 0.260 0.304
## 0.370 0.346 0.424
## 0.307 0.287 0.257
## 0.486 0.458 0.569
## 0.692 0.657 0.667
## 0.389 0.365 0.408
## 0.500 0.472 0.607
## 0.557 0.526 0.451
## 0.425 0.399 0.540
## 0.355 0.334 0.490
## 0.550 0.518 0.537
## 0.274 0.254 0.414
## 0.729 0.675 0.659
## 0.415 0.390 0.629
## 0.318 0.288 0.387
## 0.819 0.769 0.678
## 0.543 0.510 0.642
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.113 0.018 6.394 0.000 0.078
## Stst19d (.p2.) 0.351 0.021 16.865 0.000 0.310
## Stst20s (.p3.) 0.670 0.011 58.289 0.000 0.647
## Stst21c (.p4.) 0.737 0.010 72.639 0.000 0.717
## Stst22p (.p5.) 0.812 0.011 74.941 0.000 0.791
## Stst23n (.p6.) 0.829 0.013 64.057 0.000 0.804
## Stst24x (.p7.) 0.654 0.013 49.496 0.000 0.628
## Stst25w (.p8.) 0.195 0.019 10.279 0.000 0.157
## Stst26r (.p9.) 0.311 0.016 19.755 0.000 0.280
## Stst31b (.10.) 0.313 0.017 17.917 0.000 0.279
## Stst34r (.11.) 0.259 0.027 9.696 0.000 0.207
## math =~
## Stst5mt (.12.) 0.392 0.023 16.799 0.000 0.346
## Stst25w (.13.) 0.328 0.020 16.021 0.000 0.287
## Stst32r (.14.) 0.573 0.012 48.864 0.000 0.550
## Stst33h (.15.) 0.584 0.011 52.130 0.000 0.562
## Stst34r (.16.) 0.281 0.027 10.456 0.000 0.228
## speed =~
## Stst19d (.17.) 0.187 0.012 16.082 0.000 0.164
## Stst34r (.18.) 0.477 0.020 24.020 0.000 0.438
## Stst35t (.19.) 1.139 0.029 39.435 0.000 1.082
## Stst36c (.20.) 0.825 0.020 42.044 0.000 0.787
## Stst37b (.21.) 0.722 0.019 37.973 0.000 0.684
## info =~
## Stst1vc (.22.) 0.428 0.028 15.337 0.000 0.374
## Stst2lt (.23.) 0.772 0.011 73.344 0.000 0.752
## Stst3ms (.24.) 0.685 0.011 64.550 0.000 0.665
## Stst4sc 0.776 0.012 66.962 0.000 0.753
## Stst7bl (.26.) 0.255 0.024 10.729 0.000 0.208
## Stst8rn 0.268 0.016 17.170 0.000 0.237
## Stst11r (.28.) 0.727 0.011 68.825 0.000 0.706
## Stst12l (.29.) 0.552 0.012 47.578 0.000 0.530
## Stst13h (.30.) 0.799 0.011 72.948 0.000 0.778
## Stst14b (.31.) 0.583 0.011 52.685 0.000 0.562
## Stst15t (.32.) 0.590 0.011 53.854 0.000 0.568
## Stst16m (.33.) 0.668 0.011 59.828 0.000 0.646
## Stst19d (.34.) 0.252 0.020 12.387 0.000 0.212
## Stst26r (.35.) 0.623 0.016 39.051 0.000 0.592
## science =~
## Stst1vc (.36.) 0.345 0.019 17.985 0.000 0.307
## Stst5mt (.37.) 0.307 0.022 13.663 0.000 0.263
## Stst6ph (.38.) 0.599 0.011 55.322 0.000 0.578
## Stst7bl (.39.) 0.354 0.024 14.855 0.000 0.307
## Stst9lc (.40.) 0.591 0.014 42.799 0.000 0.564
## Stst10m (.41.) 0.479 0.010 47.209 0.000 0.459
## spatial =~
## Stst28m 0.399 0.013 29.612 0.000 0.372
## Sts292D (.43.) 0.605 0.014 44.764 0.000 0.578
## Sts303D (.44.) 0.533 0.012 45.107 0.000 0.510
## Stst31b (.45.) 0.556 0.018 30.366 0.000 0.520
## Stst37b (.46.) 0.127 0.017 7.350 0.000 0.093
## ci.upper Std.lv Std.all
##
## 0.148 0.113 0.115
## 0.392 0.351 0.384
## 0.692 0.670 0.682
## 0.757 0.737 0.738
## 0.834 0.812 0.825
## 0.854 0.829 0.744
## 0.680 0.654 0.593
## 0.232 0.195 0.247
## 0.341 0.311 0.308
## 0.347 0.313 0.282
## 0.312 0.259 0.223
##
## 0.438 0.392 0.384
## 0.368 0.328 0.416
## 0.596 0.573 0.738
## 0.606 0.584 0.806
## 0.334 0.281 0.242
##
## 0.209 0.187 0.204
## 0.516 0.477 0.411
## 1.196 1.139 0.702
## 0.864 0.825 0.638
## 0.759 0.722 0.625
##
## 0.483 0.428 0.436
## 0.793 0.772 0.841
## 0.706 0.685 0.758
## 0.798 0.776 0.841
## 0.301 0.255 0.283
## 0.299 0.268 0.321
## 0.748 0.727 0.753
## 0.575 0.552 0.646
## 0.821 0.799 0.717
## 0.605 0.583 0.663
## 0.611 0.590 0.677
## 0.690 0.668 0.699
## 0.292 0.252 0.275
## 0.654 0.623 0.618
##
## 0.382 0.345 0.351
## 0.351 0.307 0.301
## 0.620 0.599 0.786
## 0.400 0.354 0.392
## 0.619 0.591 0.558
## 0.499 0.479 0.701
##
## 0.425 0.399 0.638
## 0.631 0.605 0.596
## 0.556 0.533 0.663
## 0.592 0.556 0.501
## 0.160 0.127 0.110
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math (.88.) 0.820 0.008 100.457 0.000 0.804
## speed (.89.) 0.328 0.018 18.106 0.000 0.292
## info (.90.) 0.831 0.006 138.088 0.000 0.819
## science (.91.) 0.734 0.010 75.722 0.000 0.715
## spatial (.92.) 0.679 0.012 56.564 0.000 0.656
## math ~~
## speed (.93.) 0.281 0.018 15.328 0.000 0.245
## info (.94.) 0.790 0.009 91.216 0.000 0.773
## science (.95.) 0.792 0.011 73.073 0.000 0.771
## spatial (.96.) 0.729 0.013 56.811 0.000 0.704
## speed ~~
## info (.97.) 0.294 0.017 17.308 0.000 0.261
## science (.98.) 0.271 0.018 14.800 0.000 0.235
## spatial (.99.) 0.329 0.021 15.985 0.000 0.289
## info ~~
## science (.100) 0.875 0.007 129.569 0.000 0.862
## spatial (.101) 0.648 0.012 53.255 0.000 0.625
## science ~~
## spatial (.102) 0.677 0.014 49.946 0.000 0.650
## ci.upper Std.lv Std.all
##
## 0.836 0.820 0.820
## 0.363 0.328 0.328
## 0.843 0.831 0.831
## 0.753 0.734 0.734
## 0.703 0.679 0.679
##
## 0.317 0.281 0.281
## 0.807 0.790 0.790
## 0.813 0.792 0.792
## 0.754 0.729 0.729
##
## 0.328 0.294 0.294
## 0.307 0.271 0.271
## 0.369 0.329 0.329
##
## 0.889 0.875 0.875
## 0.672 0.648 0.648
##
## 0.703 0.677 0.677
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## info 0.000 0.000
## .Stst1vc (.103) -1.168 0.016 -70.914 0.000 -1.200
## .Stst19d (.104) -1.025 0.013 -79.687 0.000 -1.051
## .Stst20s (.105) -0.755 0.016 -46.479 0.000 -0.786
## .Stst21c (.106) -1.168 0.015 -75.779 0.000 -1.198
## .Stst22p (.107) -1.226 0.017 -73.193 0.000 -1.259
## .Stst23n (.108) -1.053 0.019 -55.033 0.000 -1.090
## .Stst24x (.109) -0.952 0.018 -53.772 0.000 -0.987
## .Stst25w (.110) -0.835 0.013 -66.269 0.000 -0.860
## .Stst26r (.111) -1.322 0.014 -94.011 0.000 -1.349
## .Stst31b (.112) -1.061 0.020 -51.987 0.000 -1.101
## .Stst34r (.113) -1.161 0.020 -58.371 0.000 -1.200
## .Stst5mt (.114) -0.764 0.016 -47.291 0.000 -0.795
## .Stst32r (.115) -1.083 0.014 -78.758 0.000 -1.110
## .Stst33h (.116) -0.865 0.013 -65.181 0.000 -0.891
## .Stst35t (.117) -0.759 0.032 -23.416 0.000 -0.822
## .Stst36c (.118) 0.053 0.025 2.119 0.034 0.004
## .Stst37b (.119) -0.314 0.023 -13.876 0.000 -0.358
## .Stst2lt (.120) -1.037 0.012 -83.277 0.000 -1.061
## .Stst3ms (.121) -0.864 0.012 -70.897 0.000 -0.888
## .Stst4sc -1.278 0.014 -93.222 0.000 -1.305
## .Stst7bl (.123) -0.620 0.016 -37.943 0.000 -0.652
## .Stst8rn -0.944 0.014 -66.087 0.000 -0.972
## .Stst11r (.125) -1.043 0.013 -81.571 0.000 -1.068
## .Stst12l (.126) -0.853 0.012 -73.371 0.000 -0.875
## .Stst13h (.127) -1.098 0.015 -73.051 0.000 -1.127
## .Stst14b (.128) -0.630 0.012 -52.948 0.000 -0.653
## .Stst15t -0.860 0.014 -61.799 0.000 -0.887
## .Stst16m (.130) -0.926 0.013 -71.030 0.000 -0.951
## .Stst6ph (.131) -0.692 0.015 -45.021 0.000 -0.722
## .Stst9lc (.132) -0.745 0.019 -40.262 0.000 -0.781
## .Stst10m -1.093 0.017 -65.175 0.000 -1.125
## .Stst28m -1.097 0.018 -59.810 0.000 -1.133
## .Sts292D (.135) -0.548 0.020 -27.638 0.000 -0.587
## .Sts303D (.136) -0.692 0.017 -41.027 0.000 -0.725
## english 0.366 0.021 17.303 0.000 0.324
## math -0.144 0.024 -6.084 0.000 -0.190
## speed 0.231 0.034 6.862 0.000 0.165
## science -0.591 0.026 -22.706 0.000 -0.642
## spatial -0.573 0.035 -16.468 0.000 -0.642
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -1.135 -1.168 -1.189
## -1.000 -1.025 -1.121
## -0.723 -0.755 -0.768
## -1.137 -1.168 -1.169
## -1.194 -1.226 -1.246
## -1.015 -1.053 -0.945
## -0.917 -0.952 -0.863
## -0.811 -0.835 -1.060
## -1.294 -1.322 -1.311
## -1.021 -1.061 -0.955
## -1.122 -1.161 -1.000
## -0.732 -0.764 -0.749
## -1.056 -1.083 -1.395
## -0.839 -0.865 -1.193
## -0.695 -0.759 -0.468
## 0.102 0.053 0.041
## -0.269 -0.314 -0.272
## -1.013 -1.037 -1.130
## -0.840 -0.864 -0.955
## -1.251 -1.278 -1.386
## -0.588 -0.620 -0.688
## -0.916 -0.944 -1.130
## -1.018 -1.043 -1.080
## -0.830 -0.853 -0.997
## -1.068 -1.098 -0.985
## -0.606 -0.630 -0.716
## -0.832 -0.860 -0.986
## -0.900 -0.926 -0.969
## -0.662 -0.692 -0.909
## -0.709 -0.745 -0.703
## -1.060 -1.093 -1.599
## -1.061 -1.097 -1.756
## -0.509 -0.548 -0.540
## -0.659 -0.692 -0.860
## 0.407 0.366 0.366
## -0.097 -0.144 -0.144
## 0.297 0.231 0.231
## -0.540 -0.591 -0.591
## -0.505 -0.573 -0.573
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.252 0.007 34.810 0.000 0.238
## .Stst19dsgsdwrd 0.398 0.011 36.540 0.000 0.377
## .Stest20spellng 0.517 0.014 36.849 0.000 0.489
## .Stest21cptlztn 0.454 0.013 33.611 0.000 0.427
## .Stest22puncttn 0.309 0.010 29.954 0.000 0.289
## .Stest23english 0.555 0.017 32.927 0.000 0.522
## .Stest24exprssn 0.788 0.021 37.556 0.000 0.747
## .Stst25wrdfnctn 0.371 0.010 36.948 0.000 0.351
## .Stst26rdngcmpr 0.211 0.007 29.323 0.000 0.197
## .Stst31bstrctrs 0.590 0.017 34.750 0.000 0.557
## .Stst34rthcmptt 0.700 0.027 25.874 0.000 0.647
## .Stest5math 0.601 0.016 36.511 0.000 0.569
## .Stst32rthrsnng 0.275 0.008 33.022 0.000 0.258
## .Stst33hghschlm 0.185 0.007 27.690 0.000 0.172
## .Stest35tblrdng 1.335 0.067 19.983 0.000 1.204
## .Stst36clrclchc 0.991 0.034 29.521 0.000 0.925
## .Stst37bjctnspc 0.735 0.027 27.746 0.000 0.683
## .Stest2literatr 0.246 0.007 36.118 0.000 0.233
## .Stest3music 0.349 0.009 37.746 0.000 0.331
## .Stest4soclstds 0.249 0.007 34.701 0.000 0.235
## .Stst7blgclscnc 0.465 0.012 38.835 0.000 0.442
## .Stest8aerontcs 0.626 0.011 58.911 0.000 0.605
## .Stest11art 0.403 0.011 37.378 0.000 0.382
## .Stest12law 0.426 0.011 40.270 0.000 0.405
## .Stest13health 0.604 0.015 40.588 0.000 0.575
## .Stest14bible 0.433 0.013 33.969 0.000 0.408
## .Stest15theater 0.412 0.011 38.867 0.000 0.391
## .Stest16mscllns 0.467 0.012 38.013 0.000 0.443
## .Stst6physclscn 0.221 0.007 31.004 0.000 0.207
## .Stest9elctrncs 0.775 0.021 37.627 0.000 0.734
## .Stest10mechncs 0.237 0.006 36.967 0.000 0.225
## .Stst28mchnclrs 0.231 0.007 33.406 0.000 0.217
## .Stst29vslztn2D 0.665 0.019 34.733 0.000 0.627
## .Stst30vslztn3D 0.363 0.011 33.268 0.000 0.341
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.267 0.252 0.262
## 0.419 0.398 0.475
## 0.544 0.517 0.535
## 0.480 0.454 0.455
## 0.329 0.309 0.319
## 0.588 0.555 0.447
## 0.829 0.788 0.648
## 0.391 0.371 0.598
## 0.225 0.211 0.207
## 0.623 0.590 0.478
## 0.753 0.700 0.518
## 0.634 0.601 0.578
## 0.291 0.275 0.456
## 0.198 0.185 0.351
## 1.466 1.335 0.507
## 1.056 0.991 0.593
## 0.787 0.735 0.552
## 0.260 0.246 0.292
## 0.367 0.349 0.426
## 0.263 0.249 0.293
## 0.489 0.465 0.572
## 0.647 0.626 0.897
## 0.425 0.403 0.433
## 0.447 0.426 0.583
## 0.633 0.604 0.486
## 0.458 0.433 0.560
## 0.433 0.412 0.542
## 0.491 0.467 0.511
## 0.235 0.221 0.382
## 0.815 0.775 0.689
## 0.250 0.237 0.508
## 0.245 0.231 0.593
## 0.703 0.665 0.645
## 0.384 0.363 0.561
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
# PAR.boot<- bootstrapLavaan(chc.reduced, R=500, type="ordinary", FUN="coef") # bootstrap model parameters, unstandardized
# describeBy(PAR.boot) # check sd column for the standard errors, as sd is the variability of the parameter estimates across the bootstrap samples
tests<-lavTestLRT(configural, metric2, scalar2, chc.cov, chc.vcov, chc.reduced)
Td=tests[2:6,"Chisq diff"]
Td
## [1] 353.5995092 486.9539180 430.6437455 83.8050105 0.3756798
dfd=tests[2:6,"Df diff"]
dfd
## [1] 37 23 15 6 1
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
## Warning in sqrt((ld) * G/(N - G)): NaNs produced
RMSEAD
## [1] 0.05304083 0.08143847 0.09544893 0.06529565 NaN
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04806910 0.05815053
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.07522310 0.08780691
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.08778676 0.10331658
RMSEA.CI(T=Td[4],df=dfd[4],N=N,G=2)
## [1] 0.05330758 0.07805071
RMSEA.CI(T=Td[5],df=dfd[5],N=N,G=2)
## [1] NA 0.04055778
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.846 0.012 0.000 0.000
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 1.000 0.655 0.000
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 1.000 1.000 0.174
round(pvals(T=Td[4],df=dfd[4],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.981 0.776 0.028 0.000
round(pvals(T=Td[5],df=dfd[5],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 0.460 0.402 0.016 0.003 0.000 0.000
tests<-lavTestLRT(configural, metric2, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 353.5995 1847.4370
dfd=tests[2:3,"Df diff"]
dfd
## [1] 37 28
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.05304083 0.14616574
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04806910 0.05815053
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.1405364 0.1518501
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.846 0.012 0.000 0.000
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 1 1 1 1
tests<-lavTestLRT(configural, metric2, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 353.5995 486.9539 317.2100
dfd=tests[2:4,"Df diff"]
dfd
## [1] 37 23 34
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.05304083 0.08143847 0.05233243
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04806910 0.05815053
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.07522310 0.08780691
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.04714676 0.05767069
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.846 0.012 0.000 0.000
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 1.000 0.655 0.000
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.775 0.009 0.000 0.000
tests<-lavTestLRT(configural, metric)
Td=tests[2,"Chisq diff"]
Td
## [1] 729.0518
dfd=tests[2,"Df diff"]
dfd
## [1] 40
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.07525789
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.07052122 0.08008469
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 1.000 0.053 0.000
# CHC higher order models
chc.hof.model <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest9electronics + Stest10mechanics
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g =~ english + math + speed + info + science + spatial
'
chc.hof.weak.model <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest9electronics + Stest10mechanics
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g =~ english + math + speed + info + science + spatial
math ~ 0*1
'
baseline<-cfa(chc.hof.model, data=dgroup, meanstructure=TRUE, sampling.weights="BY_WTA")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 7271.603 509.000 0.000 0.940 0.047 0.044
## aic bic
## 469877.372 470683.002
Mc(baseline)
## [1] 0.5736307
configural<-cfa(chc.hof.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T)
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 6060.994 1018.000 0.000 0.955 0.040 0.038
## aic bic
## 462961.398 464572.657
Mc(configural)
## [1] 0.6607054
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 142 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 240
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 6060.994 5399.657
## Degrees of freedom 1018 1018
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.122
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 2768.964 2466.833
## 1 3292.030 2932.825
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stest1vocab 0.043 0.014 3.094 0.002 0.016
## Stst19dsgsdwrd 0.180 0.016 11.235 0.000 0.149
## Stest20spellng 0.319 0.014 23.198 0.000 0.292
## Stest21cptlztn 0.337 0.013 26.321 0.000 0.312
## Stest22puncttn 0.379 0.014 26.946 0.000 0.352
## Stest23english 0.418 0.017 25.024 0.000 0.385
## Stest24exprssn 0.337 0.014 23.711 0.000 0.309
## Stst25wrdfnctn 0.094 0.016 5.918 0.000 0.063
## Stst26rdngcmpr 0.166 0.013 12.877 0.000 0.141
## Stst31bstrctrs 0.132 0.016 8.415 0.000 0.101
## Stst34rthcmptt 0.139 0.022 6.167 0.000 0.094
## math =~
## Stest5math 0.205 0.019 10.986 0.000 0.168
## Stst25wrdfnctn 0.138 0.016 8.531 0.000 0.107
## Stst32rthrsnng 0.306 0.014 21.981 0.000 0.279
## Stst33hghschlm 0.304 0.015 20.346 0.000 0.275
## Stst34rthcmptt 0.136 0.023 5.830 0.000 0.090
## speed =~
## Stst19dsgsdwrd 0.152 0.017 9.195 0.000 0.119
## Stst34rthcmptt 0.442 0.029 15.328 0.000 0.386
## Stest35tblrdng 1.081 0.040 26.705 0.000 1.002
## Stst36clrclchc 0.808 0.034 23.697 0.000 0.741
## Stst37bjctnspc 0.692 0.031 21.983 0.000 0.631
## info =~
## Stest1vocab 0.161 0.016 9.822 0.000 0.129
## Stest2literatr 0.280 0.013 21.340 0.000 0.254
## Stest3music 0.233 0.012 20.035 0.000 0.210
## Stest4soclstds 0.332 0.015 22.136 0.000 0.302
## Stst7blgclscnc 0.103 0.018 5.838 0.000 0.069
## Stest8aerontcs 0.209 0.011 19.411 0.000 0.187
## Stest11art 0.251 0.012 20.726 0.000 0.228
## Stest12law 0.221 0.011 20.099 0.000 0.200
## Stest13health 0.282 0.013 21.383 0.000 0.256
## Stest14bible 0.203 0.010 19.777 0.000 0.183
## Stest15theater 0.198 0.010 19.377 0.000 0.178
## Stest16mscllns 0.262 0.013 20.350 0.000 0.237
## Stst19dsgsdwrd 0.068 0.012 5.887 0.000 0.046
## Stst26rdngcmpr 0.223 0.012 18.061 0.000 0.199
## science =~
## Stest1vocab 0.145 0.016 9.111 0.000 0.113
## Stest5math 0.123 0.016 7.839 0.000 0.092
## Stst6physclscn 0.257 0.014 17.776 0.000 0.229
## Stst7blgclscnc 0.147 0.018 8.250 0.000 0.112
## Stest9elctrncs 0.265 0.017 16.010 0.000 0.233
## Stest10mechncs 0.232 0.014 16.869 0.000 0.205
## spatial =~
## Stst28mchnclrs 0.474 0.014 32.693 0.000 0.445
## Stst29vslztn2D 0.423 0.019 22.846 0.000 0.386
## Stst30vslztn3D 0.423 0.016 25.951 0.000 0.391
## Stst31bstrctrs 0.410 0.022 18.478 0.000 0.366
## Stst37bjctnspc 0.106 0.019 5.533 0.000 0.068
## g =~
## english 1.878 0.083 22.756 0.000 1.716
## math 1.865 0.098 19.110 0.000 1.674
## speed 0.329 0.033 10.049 0.000 0.265
## info 2.746 0.143 19.222 0.000 2.466
## science 2.691 0.172 15.614 0.000 2.353
## spatial 1.151 0.053 21.638 0.000 1.046
## ci.upper Std.lv Std.all
##
## 0.070 0.091 0.085
## 0.211 0.383 0.439
## 0.346 0.679 0.681
## 0.362 0.716 0.759
## 0.407 0.807 0.809
## 0.451 0.889 0.748
## 0.365 0.717 0.616
## 0.125 0.199 0.257
## 0.192 0.354 0.329
## 0.162 0.280 0.246
## 0.183 0.295 0.258
##
## 0.241 0.433 0.413
## 0.170 0.293 0.377
## 0.334 0.648 0.772
## 0.334 0.644 0.820
## 0.182 0.288 0.252
##
## 0.184 0.160 0.183
## 0.499 0.466 0.407
## 1.160 1.138 0.682
## 0.875 0.850 0.656
## 0.754 0.729 0.590
##
## 0.193 0.471 0.442
## 0.305 0.817 0.849
## 0.256 0.681 0.758
## 0.361 0.969 0.875
## 0.138 0.302 0.310
## 0.230 0.609 0.601
## 0.275 0.735 0.773
## 0.243 0.646 0.691
## 0.308 0.823 0.753
## 0.223 0.594 0.688
## 0.218 0.579 0.708
## 0.287 0.766 0.732
## 0.091 0.200 0.229
## 0.247 0.652 0.606
##
## 0.176 0.415 0.389
## 0.154 0.353 0.337
## 0.285 0.738 0.829
## 0.182 0.421 0.433
## 0.298 0.762 0.686
## 0.259 0.667 0.744
##
## 0.502 0.722 0.803
## 0.459 0.644 0.591
## 0.455 0.645 0.680
## 0.453 0.624 0.548
## 0.143 0.161 0.131
##
## 2.040 0.883 0.883
## 2.057 0.881 0.881
## 0.393 0.312 0.312
## 3.026 0.940 0.940
## 3.028 0.937 0.937
## 1.255 0.755 0.755
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -1.155 0.023 -50.360 0.000 -1.200
## .Stst19dsgsdwrd -0.992 0.018 -53.776 0.000 -1.028
## .Stest20spellng -0.848 0.021 -39.900 0.000 -0.890
## .Stest21cptlztn -1.167 0.020 -58.007 0.000 -1.206
## .Stest22puncttn -1.226 0.021 -57.496 0.000 -1.268
## .Stest23english -1.062 0.026 -41.362 0.000 -1.113
## .Stest24exprssn -0.965 0.025 -38.928 0.000 -1.014
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.903
## .Stst26rdngcmpr -1.292 0.023 -56.802 0.000 -1.337
## .Stst31bstrctrs -1.070 0.024 -43.766 0.000 -1.118
## .Stst34rthcmptt -1.153 0.025 -46.702 0.000 -1.201
## .Stest5math -0.814 0.022 -36.442 0.000 -0.857
## .Stst32rthrsnng -1.052 0.018 -59.194 0.000 -1.087
## .Stst33hghschlm -0.875 0.016 -53.483 0.000 -0.907
## .Stest35tblrdng -0.712 0.037 -19.463 0.000 -0.784
## .Stst36clrclchc -0.032 0.028 -1.139 0.255 -0.086
## .Stst37bjctnspc -0.318 0.027 -11.957 0.000 -0.370
## .Stest2literatr -1.041 0.021 -50.624 0.000 -1.081
## .Stest3music -0.921 0.019 -48.386 0.000 -0.959
## .Stest4soclstds -1.083 0.023 -46.133 0.000 -1.129
## .Stst7blgclscnc -0.617 0.021 -29.442 0.000 -0.658
## .Stest8aerontcs -0.517 0.022 -23.664 0.000 -0.560
## .Stest11art -1.040 0.020 -51.542 0.000 -1.079
## .Stest12law -0.778 0.020 -39.122 0.000 -0.817
## .Stest13health -1.200 0.023 -51.595 0.000 -1.245
## .Stest14bible -0.720 0.018 -39.356 0.000 -0.756
## .Stest15theater -1.025 0.017 -59.426 0.000 -1.059
## .Stest16mscllns -0.887 0.022 -39.478 0.000 -0.931
## .Stst6physclscn -0.732 0.019 -38.793 0.000 -0.769
## .Stest9elctrncs -0.668 0.024 -27.887 0.000 -0.715
## .Stest10mechncs -0.656 0.019 -33.970 0.000 -0.694
## .Stst28mchnclrs -0.715 0.019 -36.895 0.000 -0.753
## .Stst29vslztn2D -0.512 0.023 -22.047 0.000 -0.557
## .Stst30vslztn3D -0.723 0.020 -35.874 0.000 -0.762
## ci.upper Std.lv Std.all
## -1.110 -1.155 -1.084
## -0.956 -0.992 -1.137
## -0.806 -0.848 -0.851
## -1.128 -1.167 -1.236
## -1.184 -1.226 -1.229
## -1.012 -1.062 -0.893
## -0.916 -0.965 -0.829
## -0.838 -0.871 -1.120
## -1.248 -1.292 -1.202
## -1.022 -1.070 -0.938
## -1.104 -1.153 -1.009
## -0.770 -0.814 -0.776
## -1.017 -1.052 -1.253
## -0.843 -0.875 -1.115
## -0.640 -0.712 -0.427
## 0.023 -0.032 -0.025
## -0.266 -0.318 -0.258
## -1.000 -1.041 -1.080
## -0.884 -0.921 -1.026
## -1.037 -1.083 -0.978
## -0.576 -0.617 -0.634
## -0.475 -0.517 -0.510
## -1.000 -1.040 -1.093
## -0.739 -0.778 -0.832
## -1.154 -1.200 -1.098
## -0.684 -0.720 -0.834
## -0.991 -1.025 -1.254
## -0.843 -0.887 -0.848
## -0.695 -0.732 -0.822
## -0.621 -0.668 -0.601
## -0.618 -0.656 -0.732
## -0.677 -0.715 -0.795
## -0.466 -0.512 -0.469
## -0.683 -0.723 -0.763
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.255 0.009 28.008 0.000 0.237
## .Stst19dsgsdwrd 0.370 0.013 27.845 0.000 0.344
## .Stest20spellng 0.533 0.017 30.714 0.000 0.499
## .Stest21cptlztn 0.378 0.015 24.818 0.000 0.348
## .Stest22puncttn 0.344 0.013 27.335 0.000 0.320
## .Stest23english 0.624 0.023 26.690 0.000 0.578
## .Stest24exprssn 0.841 0.026 32.445 0.000 0.790
## .Stst25wrdfnctn 0.388 0.012 33.051 0.000 0.365
## .Stst26rdngcmpr 0.223 0.009 24.945 0.000 0.205
## .Stst31bstrctrs 0.598 0.023 26.133 0.000 0.553
## .Stst34rthcmptt 0.638 0.029 21.861 0.000 0.580
## .Stest5math 0.534 0.020 27.144 0.000 0.495
## .Stst32rthrsnng 0.285 0.011 25.456 0.000 0.263
## .Stst33hghschlm 0.202 0.009 21.581 0.000 0.183
## .Stest35tblrdng 1.488 0.090 16.571 0.000 1.312
## .Stst36clrclchc 0.955 0.050 19.204 0.000 0.858
## .Stst37bjctnspc 0.912 0.037 24.425 0.000 0.838
## .Stest2literatr 0.260 0.009 28.999 0.000 0.242
## .Stest3music 0.343 0.012 28.907 0.000 0.320
## .Stest4soclstds 0.287 0.011 27.060 0.000 0.266
## .Stst7blgclscnc 0.455 0.014 32.371 0.000 0.427
## .Stest8aerontcs 0.657 0.018 37.026 0.000 0.622
## .Stest11art 0.364 0.012 29.921 0.000 0.341
## .Stest12law 0.457 0.014 33.061 0.000 0.430
## .Stest13health 0.517 0.016 31.638 0.000 0.485
## .Stest14bible 0.391 0.013 29.162 0.000 0.365
## .Stest15theater 0.334 0.011 30.777 0.000 0.313
## .Stest16mscllns 0.508 0.016 31.043 0.000 0.476
## .Stst6physclscn 0.248 0.011 23.351 0.000 0.227
## .Stest9elctrncs 0.655 0.027 24.213 0.000 0.602
## .Stest10mechncs 0.358 0.013 26.990 0.000 0.332
## .Stst28mchnclrs 0.287 0.015 18.582 0.000 0.257
## .Stst29vslztn2D 0.774 0.027 28.527 0.000 0.721
## .Stst30vslztn3D 0.482 0.018 27.347 0.000 0.448
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.273 0.255 0.225
## 0.396 0.370 0.486
## 0.567 0.533 0.537
## 0.408 0.378 0.424
## 0.369 0.344 0.346
## 0.670 0.624 0.441
## 0.892 0.841 0.620
## 0.411 0.388 0.642
## 0.241 0.223 0.193
## 0.643 0.598 0.460
## 0.695 0.638 0.488
## 0.572 0.534 0.485
## 0.307 0.285 0.404
## 0.220 0.202 0.327
## 1.664 1.488 0.535
## 1.053 0.955 0.569
## 0.985 0.912 0.598
## 0.277 0.260 0.280
## 0.366 0.343 0.425
## 0.308 0.287 0.234
## 0.482 0.455 0.480
## 0.692 0.657 0.639
## 0.388 0.364 0.403
## 0.484 0.457 0.523
## 0.549 0.517 0.433
## 0.418 0.391 0.526
## 0.355 0.334 0.499
## 0.540 0.508 0.464
## 0.269 0.248 0.313
## 0.708 0.655 0.530
## 0.385 0.358 0.446
## 0.318 0.287 0.355
## 0.827 0.774 0.651
## 0.517 0.482 0.537
## 1.000 0.221 0.221
## 1.000 0.223 0.223
## 1.000 0.902 0.902
## 1.000 0.117 0.117
## 1.000 0.121 0.121
## 1.000 0.430 0.430
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stest1vocab 0.039 0.011 3.434 0.001 0.017
## Stst19dsgsdwrd 0.168 0.014 11.790 0.000 0.140
## Stest20spellng 0.287 0.011 26.271 0.000 0.266
## Stest21cptlztn 0.339 0.012 29.345 0.000 0.316
## Stest22puncttn 0.365 0.012 29.335 0.000 0.341
## Stest23english 0.356 0.013 27.151 0.000 0.330
## Stest24exprssn 0.273 0.011 24.032 0.000 0.251
## Stst25wrdfnctn 0.059 0.013 4.496 0.000 0.033
## Stst26rdngcmpr 0.149 0.010 15.191 0.000 0.129
## Stst31bstrctrs 0.137 0.013 10.228 0.000 0.110
## Stst34rthcmptt 0.148 0.019 7.907 0.000 0.111
## math =~
## Stest5math 0.145 0.018 8.178 0.000 0.110
## Stst25wrdfnctn 0.189 0.014 13.175 0.000 0.161
## Stst32rthrsnng 0.235 0.011 20.527 0.000 0.213
## Stst33hghschlm 0.245 0.012 19.693 0.000 0.221
## Stst34rthcmptt 0.087 0.019 4.551 0.000 0.049
## speed =~
## Stst19dsgsdwrd 0.202 0.015 13.511 0.000 0.172
## Stst34rthcmptt 0.463 0.025 18.767 0.000 0.415
## Stest35tblrdng 1.075 0.032 33.927 0.000 1.013
## Stst36clrclchc 0.764 0.028 27.694 0.000 0.710
## Stst37bjctnspc 0.663 0.024 27.223 0.000 0.615
## info =~
## Stest1vocab 0.219 0.014 15.516 0.000 0.191
## Stest2literatr 0.312 0.011 28.981 0.000 0.291
## Stest3music 0.292 0.010 28.397 0.000 0.271
## Stest4soclstds 0.311 0.010 30.060 0.000 0.291
## Stst7blgclscnc 0.124 0.014 8.690 0.000 0.096
## Stest8aerontcs 0.108 0.007 15.246 0.000 0.094
## Stest11art 0.308 0.011 27.274 0.000 0.286
## Stest12law 0.207 0.008 24.422 0.000 0.190
## Stest13health 0.330 0.011 28.880 0.000 0.308
## Stest14bible 0.243 0.009 26.517 0.000 0.225
## Stest15theater 0.257 0.010 26.312 0.000 0.238
## Stest16mscllns 0.254 0.009 27.773 0.000 0.236
## Stst19dsgsdwrd 0.108 0.012 8.942 0.000 0.085
## Stst26rdngcmpr 0.236 0.011 22.174 0.000 0.215
## science =~
## Stest1vocab 0.099 0.013 7.315 0.000 0.072
## Stest5math 0.161 0.019 8.498 0.000 0.124
## Stst6physclscn 0.250 0.012 20.759 0.000 0.226
## Stst7blgclscnc 0.110 0.017 6.327 0.000 0.076
## Stest9elctrncs 0.186 0.012 14.959 0.000 0.162
## Stest10mechncs 0.175 0.009 20.107 0.000 0.158
## spatial =~
## Stst28mchnclrs 0.254 0.009 27.776 0.000 0.236
## Stst29vslztn2D 0.358 0.017 21.110 0.000 0.325
## Stst30vslztn3D 0.312 0.014 22.475 0.000 0.285
## Stst31bstrctrs 0.357 0.020 17.641 0.000 0.317
## Stst37bjctnspc 0.092 0.016 5.728 0.000 0.060
## g =~
## english 2.000 0.078 25.504 0.000 1.847
## math 1.957 0.106 18.387 0.000 1.748
## speed 0.355 0.028 12.893 0.000 0.301
## info 2.154 0.086 25.136 0.000 1.986
## science 1.801 0.100 17.930 0.000 1.604
## spatial 1.137 0.057 20.122 0.000 1.026
## ci.upper Std.lv Std.all
##
## 0.062 0.088 0.096
## 0.196 0.375 0.399
## 0.309 0.643 0.667
## 0.361 0.758 0.749
## 0.390 0.817 0.829
## 0.381 0.795 0.729
## 0.296 0.611 0.566
## 0.085 0.132 0.166
## 0.168 0.332 0.343
## 0.163 0.306 0.280
## 0.184 0.331 0.286
##
## 0.180 0.319 0.323
## 0.217 0.415 0.521
## 0.258 0.517 0.701
## 0.270 0.539 0.776
## 0.124 0.191 0.165
##
## 0.231 0.214 0.228
## 0.511 0.491 0.425
## 1.137 1.141 0.702
## 0.818 0.811 0.633
## 0.711 0.704 0.614
##
## 0.246 0.519 0.565
## 0.333 0.742 0.832
## 0.312 0.692 0.764
## 0.331 0.738 0.827
## 0.152 0.294 0.348
## 0.121 0.255 0.307
## 0.330 0.731 0.758
## 0.223 0.491 0.602
## 0.353 0.784 0.712
## 0.261 0.577 0.661
## 0.276 0.610 0.691
## 0.271 0.602 0.661
## 0.132 0.257 0.274
## 0.257 0.561 0.579
##
## 0.125 0.203 0.221
## 0.198 0.332 0.337
## 0.273 0.515 0.744
## 0.143 0.226 0.267
## 0.211 0.384 0.400
## 0.192 0.360 0.589
##
## 0.272 0.385 0.628
## 0.391 0.542 0.548
## 0.340 0.473 0.612
## 0.397 0.540 0.494
## 0.123 0.139 0.121
##
## 2.154 0.894 0.894
## 2.165 0.890 0.890
## 0.409 0.335 0.335
## 2.322 0.907 0.907
## 1.998 0.874 0.874
## 1.248 0.751 0.751
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -1.339 0.016 -83.554 0.000 -1.370
## .Stst19dsgsdwrd -0.878 0.016 -54.059 0.000 -0.910
## .Stest20spellng -0.450 0.017 -26.686 0.000 -0.483
## .Stest21cptlztn -0.899 0.017 -51.477 0.000 -0.934
## .Stest22puncttn -0.929 0.017 -53.286 0.000 -0.963
## .Stest23english -0.744 0.019 -38.449 0.000 -0.781
## .Stest24exprssn -0.704 0.019 -37.099 0.000 -0.742
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.816
## .Stst26rdngcmpr -1.226 0.017 -72.842 0.000 -1.259
## .Stst31bstrctrs -1.260 0.019 -65.843 0.000 -1.297
## .Stst34rthcmptt -1.004 0.021 -47.990 0.000 -1.045
## .Stest5math -0.965 0.017 -55.615 0.000 -0.999
## .Stst32rthrsnng -1.184 0.013 -92.849 0.000 -1.209
## .Stst33hghschlm -0.942 0.012 -78.389 0.000 -0.966
## .Stest35tblrdng -0.524 0.029 -17.830 0.000 -0.582
## .Stst36clrclchc 0.300 0.023 13.284 0.000 0.256
## .Stst37bjctnspc -0.217 0.021 -10.567 0.000 -0.257
## .Stest2literatr -1.034 0.016 -66.363 0.000 -1.065
## .Stest3music -0.825 0.016 -52.646 0.000 -0.856
## .Stest4soclstds -1.273 0.015 -82.694 0.000 -1.303
## .Stst7blgclscnc -0.831 0.015 -55.991 0.000 -0.860
## .Stest8aerontcs -0.942 0.014 -64.960 0.000 -0.970
## .Stest11art -1.046 0.017 -63.114 0.000 -1.078
## .Stest12law -0.897 0.014 -63.710 0.000 -0.925
## .Stest13health -1.020 0.019 -52.885 0.000 -1.057
## .Stest14bible -0.565 0.015 -36.958 0.000 -0.595
## .Stest15theater -0.856 0.015 -56.660 0.000 -0.885
## .Stest16mscllns -0.949 0.016 -60.013 0.000 -0.980
## .Stst6physclscn -1.022 0.012 -84.927 0.000 -1.046
## .Stest9elctrncs -1.154 0.017 -68.546 0.000 -1.187
## .Stest10mechncs -1.373 0.011 -128.778 0.000 -1.394
## .Stst28mchnclrs -1.323 0.011 -124.285 0.000 -1.344
## .Stst29vslztn2D -0.916 0.017 -52.801 0.000 -0.950
## .Stst30vslztn3D -0.982 0.014 -72.639 0.000 -1.008
## ci.upper Std.lv Std.all
## -1.307 -1.339 -1.457
## -0.846 -0.878 -0.936
## -0.417 -0.450 -0.467
## -0.865 -0.899 -0.889
## -0.895 -0.929 -0.942
## -0.706 -0.744 -0.682
## -0.667 -0.704 -0.652
## -0.761 -0.788 -0.989
## -1.193 -1.226 -1.266
## -1.222 -1.260 -1.153
## -0.963 -1.004 -0.869
## -0.931 -0.965 -0.978
## -1.159 -1.184 -1.604
## -0.919 -0.942 -1.356
## -0.466 -0.524 -0.323
## 0.344 0.300 0.234
## -0.176 -0.217 -0.189
## -1.004 -1.034 -1.160
## -0.795 -0.825 -0.911
## -1.243 -1.273 -1.425
## -0.802 -0.831 -0.985
## -0.913 -0.942 -1.133
## -1.013 -1.046 -1.085
## -0.870 -0.897 -1.101
## -0.982 -1.020 -0.926
## -0.535 -0.565 -0.647
## -0.826 -0.856 -0.970
## -0.918 -0.949 -1.042
## -0.998 -1.022 -1.477
## -1.121 -1.154 -1.202
## -1.352 -1.373 -2.245
## -1.303 -1.323 -2.162
## -0.882 -0.916 -0.926
## -0.955 -0.982 -1.270
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.256 0.007 34.900 0.000 0.242
## .Stst19dsgsdwrd 0.390 0.011 35.827 0.000 0.369
## .Stest20spellng 0.515 0.014 36.795 0.000 0.488
## .Stest21cptlztn 0.449 0.014 32.463 0.000 0.422
## .Stest22puncttn 0.304 0.010 28.961 0.000 0.283
## .Stest23english 0.558 0.017 33.267 0.000 0.525
## .Stest24exprssn 0.794 0.021 37.533 0.000 0.752
## .Stst25wrdfnctn 0.358 0.010 34.153 0.000 0.338
## .Stst26rdngcmpr 0.210 0.007 29.444 0.000 0.196
## .Stst31bstrctrs 0.587 0.018 31.978 0.000 0.551
## .Stst34rthcmptt 0.695 0.026 26.583 0.000 0.644
## .Stest5math 0.596 0.017 35.649 0.000 0.564
## .Stst32rthrsnng 0.278 0.008 33.023 0.000 0.261
## .Stst33hghschlm 0.192 0.007 26.427 0.000 0.178
## .Stest35tblrdng 1.336 0.072 18.524 0.000 1.194
## .Stst36clrclchc 0.984 0.038 26.140 0.000 0.910
## .Stst37bjctnspc 0.750 0.028 26.427 0.000 0.695
## .Stest2literatr 0.245 0.007 35.313 0.000 0.231
## .Stest3music 0.342 0.009 37.328 0.000 0.324
## .Stest4soclstds 0.252 0.007 34.518 0.000 0.238
## .Stst7blgclscnc 0.470 0.012 39.352 0.000 0.446
## .Stest8aerontcs 0.626 0.011 58.940 0.000 0.605
## .Stest11art 0.395 0.011 36.602 0.000 0.374
## .Stest12law 0.423 0.011 40.251 0.000 0.403
## .Stest13health 0.599 0.015 40.457 0.000 0.570
## .Stest14bible 0.429 0.012 34.410 0.000 0.405
## .Stest15theater 0.406 0.011 38.191 0.000 0.385
## .Stest16mscllns 0.467 0.012 37.969 0.000 0.443
## .Stst6physclscn 0.214 0.008 28.071 0.000 0.199
## .Stest9elctrncs 0.774 0.020 38.760 0.000 0.735
## .Stest10mechncs 0.244 0.007 36.786 0.000 0.231
## .Stst28mchnclrs 0.227 0.007 32.537 0.000 0.213
## .Stst29vslztn2D 0.684 0.020 34.095 0.000 0.645
## .Stst30vslztn3D 0.374 0.011 32.834 0.000 0.351
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.271 0.256 0.304
## 0.412 0.390 0.443
## 0.543 0.515 0.555
## 0.476 0.449 0.439
## 0.325 0.304 0.313
## 0.591 0.558 0.469
## 0.835 0.794 0.680
## 0.379 0.358 0.564
## 0.224 0.210 0.224
## 0.623 0.587 0.492
## 0.746 0.695 0.520
## 0.629 0.596 0.613
## 0.294 0.278 0.509
## 0.207 0.192 0.398
## 1.477 1.336 0.507
## 1.058 0.984 0.599
## 0.806 0.750 0.571
## 0.259 0.245 0.308
## 0.360 0.342 0.416
## 0.267 0.252 0.316
## 0.493 0.470 0.660
## 0.647 0.626 0.906
## 0.417 0.395 0.426
## 0.444 0.423 0.637
## 0.628 0.599 0.493
## 0.453 0.429 0.563
## 0.427 0.406 0.522
## 0.491 0.467 0.563
## 0.229 0.214 0.447
## 0.813 0.774 0.840
## 0.257 0.244 0.653
## 0.240 0.227 0.605
## 0.723 0.684 0.700
## 0.396 0.374 0.625
## 1.000 0.200 0.200
## 1.000 0.207 0.207
## 1.000 0.888 0.888
## 1.000 0.177 0.177
## 1.000 0.236 0.236
## 1.000 0.436 0.436
## 1.000 1.000 1.000
metric<-cfa(chc.hof.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 7254.521 1063.000 0.000 0.944 0.044 0.066
## aic bic
## 464064.924 465374.073
Mc(metric)
## [1] 0.6011947
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 136 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 247
## Number of equality constraints 52
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 7254.521 6463.601
## Degrees of freedom 1063 1063
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.122
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 3424.630 3051.262
## 1 3829.891 3412.340
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.043 0.008 5.192 0.000 0.027
## Stst19d (.p2.) 0.171 0.011 15.226 0.000 0.149
## Stst20s (.p3.) 0.293 0.012 23.583 0.000 0.268
## Stst21c (.p4.) 0.328 0.013 25.202 0.000 0.302
## Stst22p (.p5.) 0.362 0.014 25.387 0.000 0.334
## Stst23n (.p6.) 0.370 0.015 24.312 0.000 0.341
## Stst24x (.p7.) 0.291 0.012 23.399 0.000 0.267
## Stst25w (.p8.) 0.080 0.010 7.858 0.000 0.060
## Stst26r (.p9.) 0.152 0.008 17.915 0.000 0.136
## Stst31b (.10.) 0.143 0.010 13.883 0.000 0.123
## Stst34r (.11.) 0.141 0.014 9.776 0.000 0.113
## math =~
## Stst5mt (.12.) 0.198 0.014 13.954 0.000 0.170
## Stst25w (.13.) 0.170 0.012 14.633 0.000 0.147
## Stst32r (.14.) 0.284 0.014 20.526 0.000 0.257
## Stst33h (.15.) 0.290 0.015 19.815 0.000 0.261
## Stst34r (.16.) 0.115 0.016 7.078 0.000 0.083
## speed =~
## Stst19d (.17.) 0.182 0.011 16.176 0.000 0.160
## Stst34r (.18.) 0.455 0.020 22.454 0.000 0.415
## Stst35t (.19.) 1.080 0.032 33.516 0.000 1.016
## Stst36c (.20.) 0.783 0.026 29.609 0.000 0.731
## Stst37b (.21.) 0.676 0.024 28.354 0.000 0.629
## info =~
## Stst1vc (.22.) 0.190 0.012 15.592 0.000 0.166
## Stst2lt (.23.) 0.294 0.013 21.796 0.000 0.267
## Stst3ms (.24.) 0.260 0.012 21.352 0.000 0.236
## Stst4sc (.25.) 0.315 0.014 22.032 0.000 0.287
## Stst7bl (.26.) 0.111 0.011 10.000 0.000 0.090
## Stst8rn (.27.) 0.152 0.008 18.659 0.000 0.136
## Stst11r (.28.) 0.276 0.013 21.486 0.000 0.251
## Stst12l (.29.) 0.211 0.010 20.887 0.000 0.191
## Stst13h (.30.) 0.302 0.014 21.773 0.000 0.275
## Stst14b (.31.) 0.221 0.010 21.096 0.000 0.200
## Stst15t (.32.) 0.223 0.011 20.922 0.000 0.203
## Stst16m (.33.) 0.254 0.012 21.021 0.000 0.231
## Stst19d (.34.) 0.085 0.009 9.646 0.000 0.068
## Stst26r (.35.) 0.227 0.011 20.596 0.000 0.206
## science =~
## Stst1vc (.36.) 0.160 0.014 11.709 0.000 0.133
## Stst5mt (.37.) 0.173 0.015 11.208 0.000 0.142
## Stst6ph (.38.) 0.344 0.014 25.236 0.000 0.317
## Stst7bl (.39.) 0.179 0.016 11.388 0.000 0.148
## Stst9lc (.40.) 0.320 0.015 21.261 0.000 0.290
## Stst10m (.41.) 0.273 0.012 22.476 0.000 0.249
## spatial =~
## Stst28m (.42.) 0.430 0.014 30.958 0.000 0.403
## Sts292D (.43.) 0.481 0.017 29.089 0.000 0.448
## Sts303D (.44.) 0.453 0.015 30.250 0.000 0.424
## Stst31b (.45.) 0.450 0.018 25.019 0.000 0.415
## Stst37b (.46.) 0.124 0.015 8.057 0.000 0.093
## g =~
## english (.47.) 2.186 0.092 23.829 0.000 2.006
## math (.48.) 1.988 0.101 19.625 0.000 1.789
## speed (.49.) 0.379 0.024 15.506 0.000 0.331
## info (.50.) 2.691 0.138 19.567 0.000 2.421
## science (.51.) 1.726 0.093 18.653 0.000 1.544
## spatial (.52.) 0.985 0.041 23.952 0.000 0.905
## ci.upper Std.lv Std.all
##
## 0.059 0.104 0.099
## 0.193 0.411 0.435
## 0.317 0.703 0.693
## 0.353 0.788 0.790
## 0.390 0.871 0.830
## 0.400 0.890 0.744
## 0.315 0.700 0.604
## 0.100 0.193 0.233
## 0.169 0.366 0.335
## 0.163 0.344 0.294
## 0.169 0.339 0.289
##
## 0.226 0.441 0.425
## 0.193 0.379 0.458
## 0.311 0.631 0.761
## 0.319 0.646 0.820
## 0.147 0.255 0.218
##
## 0.204 0.195 0.206
## 0.494 0.486 0.414
## 1.143 1.155 0.689
## 0.835 0.837 0.647
## 0.723 0.723 0.584
##
## 0.214 0.547 0.521
## 0.320 0.843 0.856
## 0.284 0.746 0.787
## 0.343 0.905 0.854
## 0.133 0.320 0.343
## 0.168 0.437 0.463
## 0.302 0.793 0.797
## 0.231 0.605 0.665
## 0.329 0.867 0.770
## 0.241 0.634 0.712
## 0.244 0.641 0.744
## 0.278 0.730 0.714
## 0.102 0.244 0.259
## 0.249 0.653 0.599
##
## 0.187 0.319 0.304
## 0.203 0.344 0.332
## 0.370 0.686 0.817
## 0.209 0.356 0.382
## 0.349 0.638 0.618
## 0.297 0.544 0.663
##
## 0.457 0.604 0.718
## 0.513 0.675 0.617
## 0.482 0.636 0.683
## 0.485 0.632 0.540
## 0.154 0.173 0.140
##
## 2.365 0.909 0.909
## 2.186 0.893 0.893
## 0.427 0.355 0.355
## 2.960 0.937 0.937
## 1.907 0.865 0.865
## 1.066 0.702 0.702
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -1.155 0.023 -50.360 0.000 -1.200
## .Stst19dsgsdwrd -0.992 0.018 -53.776 0.000 -1.028
## .Stest20spellng -0.848 0.021 -39.900 0.000 -0.890
## .Stest21cptlztn -1.167 0.020 -58.007 0.000 -1.206
## .Stest22puncttn -1.226 0.021 -57.496 0.000 -1.268
## .Stest23english -1.062 0.026 -41.362 0.000 -1.113
## .Stest24exprssn -0.965 0.025 -38.928 0.000 -1.014
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.903
## .Stst26rdngcmpr -1.292 0.023 -56.802 0.000 -1.337
## .Stst31bstrctrs -1.070 0.024 -43.766 0.000 -1.118
## .Stst34rthcmptt -1.153 0.025 -46.702 0.000 -1.201
## .Stest5math -0.814 0.022 -36.442 0.000 -0.857
## .Stst32rthrsnng -1.052 0.018 -59.194 0.000 -1.087
## .Stst33hghschlm -0.875 0.016 -53.483 0.000 -0.907
## .Stest35tblrdng -0.712 0.037 -19.463 0.000 -0.784
## .Stst36clrclchc -0.032 0.028 -1.139 0.255 -0.086
## .Stst37bjctnspc -0.318 0.027 -11.957 0.000 -0.370
## .Stest2literatr -1.041 0.021 -50.624 0.000 -1.081
## .Stest3music -0.921 0.019 -48.386 0.000 -0.959
## .Stest4soclstds -1.083 0.023 -46.133 0.000 -1.129
## .Stst7blgclscnc -0.617 0.021 -29.442 0.000 -0.658
## .Stest8aerontcs -0.517 0.022 -23.664 0.000 -0.560
## .Stest11art -1.040 0.020 -51.542 0.000 -1.079
## .Stest12law -0.778 0.020 -39.122 0.000 -0.817
## .Stest13health -1.200 0.023 -51.595 0.000 -1.245
## .Stest14bible -0.720 0.018 -39.356 0.000 -0.756
## .Stest15theater -1.025 0.017 -59.426 0.000 -1.059
## .Stest16mscllns -0.887 0.022 -39.478 0.000 -0.931
## .Stst6physclscn -0.732 0.019 -38.793 0.000 -0.769
## .Stest9elctrncs -0.668 0.024 -27.887 0.000 -0.715
## .Stest10mechncs -0.656 0.019 -33.970 0.000 -0.694
## .Stst28mchnclrs -0.715 0.019 -36.895 0.000 -0.753
## .Stst29vslztn2D -0.512 0.023 -22.047 0.000 -0.557
## .Stst30vslztn3D -0.723 0.020 -35.874 0.000 -0.762
## ci.upper Std.lv Std.all
## -1.110 -1.155 -1.100
## -0.956 -0.992 -1.050
## -0.806 -0.848 -0.836
## -1.128 -1.167 -1.171
## -1.184 -1.226 -1.169
## -1.012 -1.062 -0.888
## -0.916 -0.965 -0.833
## -0.838 -0.871 -1.053
## -1.248 -1.292 -1.185
## -1.022 -1.070 -0.915
## -1.104 -1.153 -0.982
## -0.770 -0.814 -0.783
## -1.017 -1.052 -1.268
## -0.843 -0.875 -1.112
## -0.640 -0.712 -0.425
## 0.023 -0.032 -0.025
## -0.266 -0.318 -0.257
## -1.000 -1.041 -1.057
## -0.884 -0.921 -0.972
## -1.037 -1.083 -1.022
## -0.576 -0.617 -0.661
## -0.475 -0.517 -0.549
## -1.000 -1.040 -1.044
## -0.739 -0.778 -0.855
## -1.154 -1.200 -1.065
## -0.684 -0.720 -0.809
## -0.991 -1.025 -1.189
## -0.843 -0.887 -0.867
## -0.695 -0.732 -0.872
## -0.621 -0.668 -0.648
## -0.618 -0.656 -0.799
## -0.677 -0.715 -0.850
## -0.466 -0.512 -0.467
## -0.683 -0.723 -0.777
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.258 0.009 27.993 0.000 0.240
## .Stst19dsgsdwrd 0.371 0.013 27.559 0.000 0.345
## .Stest20spellng 0.536 0.017 31.366 0.000 0.502
## .Stest21cptlztn 0.373 0.015 24.724 0.000 0.344
## .Stest22puncttn 0.342 0.012 27.839 0.000 0.318
## .Stest23english 0.638 0.024 26.916 0.000 0.591
## .Stest24exprssn 0.851 0.026 33.367 0.000 0.801
## .Stst25wrdfnctn 0.384 0.012 32.499 0.000 0.361
## .Stst26rdngcmpr 0.223 0.009 25.266 0.000 0.205
## .Stst31bstrctrs 0.573 0.022 26.066 0.000 0.530
## .Stst34rthcmptt 0.635 0.030 21.297 0.000 0.576
## .Stest5math 0.531 0.020 26.796 0.000 0.492
## .Stst32rthrsnng 0.290 0.011 26.851 0.000 0.269
## .Stst33hghschlm 0.203 0.009 22.598 0.000 0.186
## .Stest35tblrdng 1.479 0.078 19.067 0.000 1.327
## .Stst36clrclchc 0.971 0.042 23.041 0.000 0.889
## .Stst37bjctnspc 0.918 0.034 26.723 0.000 0.851
## .Stest2literatr 0.259 0.009 29.122 0.000 0.241
## .Stest3music 0.341 0.012 28.541 0.000 0.318
## .Stest4soclstds 0.304 0.011 27.883 0.000 0.282
## .Stst7blgclscnc 0.456 0.014 32.586 0.000 0.429
## .Stest8aerontcs 0.698 0.018 39.340 0.000 0.664
## .Stest11art 0.361 0.012 29.729 0.000 0.338
## .Stest12law 0.463 0.014 33.335 0.000 0.435
## .Stest13health 0.517 0.016 31.500 0.000 0.485
## .Stest14bible 0.390 0.013 29.056 0.000 0.364
## .Stest15theater 0.332 0.011 30.314 0.000 0.310
## .Stest16mscllns 0.512 0.016 31.254 0.000 0.480
## .Stst6physclscn 0.235 0.011 21.593 0.000 0.213
## .Stest9elctrncs 0.658 0.028 23.502 0.000 0.603
## .Stest10mechncs 0.378 0.014 27.820 0.000 0.351
## .Stst28mchnclrs 0.343 0.016 21.688 0.000 0.312
## .Stst29vslztn2D 0.743 0.026 28.384 0.000 0.692
## .Stst30vslztn3D 0.462 0.017 27.036 0.000 0.429
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.276 0.258 0.234
## 0.398 0.371 0.416
## 0.569 0.536 0.520
## 0.403 0.373 0.376
## 0.366 0.342 0.311
## 0.684 0.638 0.446
## 0.901 0.851 0.635
## 0.407 0.384 0.562
## 0.240 0.223 0.187
## 0.616 0.573 0.419
## 0.693 0.635 0.461
## 0.570 0.531 0.492
## 0.311 0.290 0.421
## 0.221 0.203 0.328
## 1.631 1.479 0.526
## 1.054 0.971 0.581
## 0.985 0.918 0.599
## 0.276 0.259 0.267
## 0.365 0.341 0.380
## 0.325 0.304 0.270
## 0.484 0.456 0.524
## 0.733 0.698 0.786
## 0.385 0.361 0.365
## 0.490 0.463 0.558
## 0.549 0.517 0.407
## 0.416 0.390 0.492
## 0.353 0.332 0.446
## 0.545 0.512 0.490
## 0.256 0.235 0.333
## 0.713 0.658 0.618
## 0.405 0.378 0.561
## 0.374 0.343 0.485
## 0.794 0.743 0.620
## 0.496 0.462 0.533
## 1.000 0.173 0.173
## 1.000 0.202 0.202
## 1.000 0.874 0.874
## 1.000 0.121 0.121
## 1.000 0.251 0.251
## 1.000 0.507 0.507
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.043 0.008 5.192 0.000 0.027
## Stst19d (.p2.) 0.171 0.011 15.226 0.000 0.149
## Stst20s (.p3.) 0.293 0.012 23.583 0.000 0.268
## Stst21c (.p4.) 0.328 0.013 25.202 0.000 0.302
## Stst22p (.p5.) 0.362 0.014 25.387 0.000 0.334
## Stst23n (.p6.) 0.370 0.015 24.312 0.000 0.341
## Stst24x (.p7.) 0.291 0.012 23.399 0.000 0.267
## Stst25w (.p8.) 0.080 0.010 7.858 0.000 0.060
## Stst26r (.p9.) 0.152 0.008 17.915 0.000 0.136
## Stst31b (.10.) 0.143 0.010 13.883 0.000 0.123
## Stst34r (.11.) 0.141 0.014 9.776 0.000 0.113
## math =~
## Stst5mt (.12.) 0.198 0.014 13.954 0.000 0.170
## Stst25w (.13.) 0.170 0.012 14.633 0.000 0.147
## Stst32r (.14.) 0.284 0.014 20.526 0.000 0.257
## Stst33h (.15.) 0.290 0.015 19.815 0.000 0.261
## Stst34r (.16.) 0.115 0.016 7.078 0.000 0.083
## speed =~
## Stst19d (.17.) 0.182 0.011 16.176 0.000 0.160
## Stst34r (.18.) 0.455 0.020 22.454 0.000 0.415
## Stst35t (.19.) 1.080 0.032 33.516 0.000 1.016
## Stst36c (.20.) 0.783 0.026 29.609 0.000 0.731
## Stst37b (.21.) 0.676 0.024 28.354 0.000 0.629
## info =~
## Stst1vc (.22.) 0.190 0.012 15.592 0.000 0.166
## Stst2lt (.23.) 0.294 0.013 21.796 0.000 0.267
## Stst3ms (.24.) 0.260 0.012 21.352 0.000 0.236
## Stst4sc (.25.) 0.315 0.014 22.032 0.000 0.287
## Stst7bl (.26.) 0.111 0.011 10.000 0.000 0.090
## Stst8rn (.27.) 0.152 0.008 18.659 0.000 0.136
## Stst11r (.28.) 0.276 0.013 21.486 0.000 0.251
## Stst12l (.29.) 0.211 0.010 20.887 0.000 0.191
## Stst13h (.30.) 0.302 0.014 21.773 0.000 0.275
## Stst14b (.31.) 0.221 0.010 21.096 0.000 0.200
## Stst15t (.32.) 0.223 0.011 20.922 0.000 0.203
## Stst16m (.33.) 0.254 0.012 21.021 0.000 0.231
## Stst19d (.34.) 0.085 0.009 9.646 0.000 0.068
## Stst26r (.35.) 0.227 0.011 20.596 0.000 0.206
## science =~
## Stst1vc (.36.) 0.160 0.014 11.709 0.000 0.133
## Stst5mt (.37.) 0.173 0.015 11.208 0.000 0.142
## Stst6ph (.38.) 0.344 0.014 25.236 0.000 0.317
## Stst7bl (.39.) 0.179 0.016 11.388 0.000 0.148
## Stst9lc (.40.) 0.320 0.015 21.261 0.000 0.290
## Stst10m (.41.) 0.273 0.012 22.476 0.000 0.249
## spatial =~
## Stst28m (.42.) 0.430 0.014 30.958 0.000 0.403
## Sts292D (.43.) 0.481 0.017 29.089 0.000 0.448
## Sts303D (.44.) 0.453 0.015 30.250 0.000 0.424
## Stst31b (.45.) 0.450 0.018 25.019 0.000 0.415
## Stst37b (.46.) 0.124 0.015 8.057 0.000 0.093
## g =~
## english (.47.) 2.186 0.092 23.829 0.000 2.006
## math (.48.) 1.988 0.101 19.625 0.000 1.789
## speed (.49.) 0.379 0.024 15.506 0.000 0.331
## info (.50.) 2.691 0.138 19.567 0.000 2.421
## science (.51.) 1.726 0.093 18.653 0.000 1.544
## spatial (.52.) 0.985 0.041 23.952 0.000 0.905
## ci.upper Std.lv Std.all
##
## 0.059 0.092 0.100
## 0.193 0.363 0.410
## 0.317 0.621 0.655
## 0.353 0.695 0.717
## 0.390 0.769 0.811
## 0.400 0.786 0.727
## 0.315 0.618 0.571
## 0.100 0.170 0.223
## 0.169 0.323 0.339
## 0.163 0.304 0.286
## 0.169 0.299 0.264
##
## 0.226 0.369 0.375
## 0.193 0.317 0.415
## 0.311 0.529 0.709
## 0.319 0.540 0.779
## 0.147 0.214 0.189
##
## 0.204 0.190 0.215
## 0.494 0.476 0.420
## 1.143 1.130 0.698
## 0.835 0.819 0.639
## 0.723 0.707 0.619
##
## 0.214 0.469 0.510
## 0.320 0.723 0.825
## 0.284 0.640 0.735
## 0.343 0.777 0.842
## 0.133 0.274 0.317
## 0.168 0.375 0.425
## 0.302 0.681 0.732
## 0.231 0.519 0.624
## 0.329 0.744 0.692
## 0.241 0.544 0.638
## 0.244 0.550 0.650
## 0.278 0.626 0.676
## 0.102 0.210 0.237
## 0.249 0.560 0.588
##
## 0.187 0.250 0.272
## 0.203 0.270 0.274
## 0.370 0.537 0.752
## 0.209 0.279 0.323
## 0.349 0.500 0.493
## 0.297 0.426 0.656
##
## 0.457 0.451 0.701
## 0.513 0.504 0.514
## 0.482 0.475 0.609
## 0.485 0.472 0.445
## 0.154 0.130 0.113
##
## 2.365 0.854 0.854
## 2.186 0.885 0.885
## 0.427 0.301 0.301
## 2.960 0.906 0.906
## 1.907 0.916 0.916
## 1.066 0.779 0.779
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -1.339 0.016 -83.554 0.000 -1.370
## .Stst19dsgsdwrd -0.878 0.016 -54.059 0.000 -0.910
## .Stest20spellng -0.450 0.017 -26.686 0.000 -0.483
## .Stest21cptlztn -0.899 0.017 -51.477 0.000 -0.934
## .Stest22puncttn -0.929 0.017 -53.286 0.000 -0.963
## .Stest23english -0.744 0.019 -38.449 0.000 -0.781
## .Stest24exprssn -0.704 0.019 -37.099 0.000 -0.742
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.816
## .Stst26rdngcmpr -1.226 0.017 -72.842 0.000 -1.259
## .Stst31bstrctrs -1.260 0.019 -65.843 0.000 -1.297
## .Stst34rthcmptt -1.004 0.021 -47.990 0.000 -1.045
## .Stest5math -0.965 0.017 -55.615 0.000 -0.999
## .Stst32rthrsnng -1.184 0.013 -92.849 0.000 -1.209
## .Stst33hghschlm -0.942 0.012 -78.389 0.000 -0.966
## .Stest35tblrdng -0.524 0.029 -17.830 0.000 -0.582
## .Stst36clrclchc 0.300 0.023 13.284 0.000 0.256
## .Stst37bjctnspc -0.217 0.021 -10.567 0.000 -0.257
## .Stest2literatr -1.034 0.016 -66.363 0.000 -1.065
## .Stest3music -0.825 0.016 -52.646 0.000 -0.856
## .Stest4soclstds -1.273 0.015 -82.694 0.000 -1.303
## .Stst7blgclscnc -0.831 0.015 -55.991 0.000 -0.860
## .Stest8aerontcs -0.942 0.014 -64.960 0.000 -0.970
## .Stest11art -1.046 0.017 -63.114 0.000 -1.078
## .Stest12law -0.897 0.014 -63.710 0.000 -0.925
## .Stest13health -1.020 0.019 -52.885 0.000 -1.057
## .Stest14bible -0.565 0.015 -36.958 0.000 -0.595
## .Stest15theater -0.856 0.015 -56.660 0.000 -0.885
## .Stest16mscllns -0.949 0.016 -60.013 0.000 -0.980
## .Stst6physclscn -1.022 0.012 -84.927 0.000 -1.046
## .Stest9elctrncs -1.154 0.017 -68.546 0.000 -1.187
## .Stest10mechncs -1.373 0.011 -128.778 0.000 -1.394
## .Stst28mchnclrs -1.323 0.011 -124.285 0.000 -1.344
## .Stst29vslztn2D -0.916 0.017 -52.801 0.000 -0.950
## .Stst30vslztn3D -0.982 0.014 -72.639 0.000 -1.008
## ci.upper Std.lv Std.all
## -1.307 -1.339 -1.456
## -0.846 -0.878 -0.992
## -0.417 -0.450 -0.475
## -0.865 -0.899 -0.928
## -0.895 -0.929 -0.980
## -0.706 -0.744 -0.688
## -0.667 -0.704 -0.651
## -0.761 -0.788 -1.032
## -1.193 -1.226 -1.286
## -1.222 -1.260 -1.187
## -0.963 -1.004 -0.886
## -0.931 -0.965 -0.979
## -1.159 -1.184 -1.588
## -0.919 -0.942 -1.359
## -0.466 -0.524 -0.324
## 0.344 0.300 0.234
## -0.176 -0.217 -0.190
## -1.004 -1.034 -1.181
## -0.795 -0.825 -0.948
## -1.243 -1.273 -1.380
## -0.802 -0.831 -0.960
## -0.913 -0.942 -1.070
## -1.013 -1.046 -1.125
## -0.870 -0.897 -1.079
## -0.982 -1.020 -0.948
## -0.535 -0.565 -0.662
## -0.826 -0.856 -1.011
## -0.918 -0.949 -1.024
## -0.998 -1.022 -1.432
## -1.121 -1.154 -1.139
## -1.352 -1.373 -2.113
## -1.303 -1.323 -2.057
## -0.882 -0.916 -0.933
## -0.955 -0.982 -1.258
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.257 0.007 35.507 0.000 0.242
## .Stst19dsgsdwrd 0.397 0.011 36.027 0.000 0.375
## .Stest20spellng 0.514 0.014 36.966 0.000 0.486
## .Stest21cptlztn 0.456 0.014 33.384 0.000 0.429
## .Stest22puncttn 0.307 0.010 29.305 0.000 0.286
## .Stest23english 0.550 0.017 32.878 0.000 0.517
## .Stest24exprssn 0.788 0.021 37.407 0.000 0.746
## .Stst25wrdfnctn 0.372 0.010 36.467 0.000 0.352
## .Stst26rdngcmpr 0.210 0.007 29.494 0.000 0.196
## .Stst31bstrctrs 0.621 0.017 35.939 0.000 0.587
## .Stst34rthcmptt 0.698 0.027 26.147 0.000 0.645
## .Stest5math 0.600 0.017 36.063 0.000 0.567
## .Stst32rthrsnng 0.277 0.008 32.980 0.000 0.260
## .Stst33hghschlm 0.189 0.007 27.477 0.000 0.176
## .Stest35tblrdng 1.341 0.067 20.015 0.000 1.209
## .Stst36clrclchc 0.975 0.034 28.833 0.000 0.909
## .Stst37bjctnspc 0.745 0.027 28.016 0.000 0.693
## .Stest2literatr 0.245 0.007 35.509 0.000 0.231
## .Stest3music 0.349 0.009 37.899 0.000 0.331
## .Stest4soclstds 0.248 0.007 34.002 0.000 0.233
## .Stst7blgclscnc 0.469 0.012 39.247 0.000 0.445
## .Stest8aerontcs 0.635 0.011 55.864 0.000 0.613
## .Stest11art 0.402 0.011 37.102 0.000 0.380
## .Stest12law 0.422 0.011 40.125 0.000 0.401
## .Stest13health 0.603 0.015 41.235 0.000 0.575
## .Stest14bible 0.431 0.012 34.610 0.000 0.407
## .Stest15theater 0.413 0.011 38.865 0.000 0.393
## .Stest16mscllns 0.465 0.012 37.912 0.000 0.441
## .Stst6physclscn 0.221 0.007 30.859 0.000 0.207
## .Stest9elctrncs 0.777 0.020 38.490 0.000 0.737
## .Stest10mechncs 0.241 0.006 37.264 0.000 0.228
## .Stst28mchnclrs 0.210 0.007 31.660 0.000 0.197
## .Stst29vslztn2D 0.708 0.019 36.994 0.000 0.671
## .Stst30vslztn3D 0.383 0.011 34.701 0.000 0.362
## .english 1.216 0.111 10.948 0.000 0.998
## .math 0.752 0.100 7.485 0.000 0.555
## .speed 0.996 0.063 15.728 0.000 0.872
## .info 1.081 0.114 9.471 0.000 0.858
## .science 0.391 0.053 7.335 0.000 0.287
## .spatial 0.432 0.036 11.900 0.000 0.361
## g 0.688 0.031 21.901 0.000 0.627
## ci.upper Std.lv Std.all
## 0.271 0.257 0.304
## 0.419 0.397 0.506
## 0.541 0.514 0.571
## 0.483 0.456 0.485
## 0.327 0.307 0.342
## 0.582 0.550 0.471
## 0.829 0.788 0.674
## 0.392 0.372 0.638
## 0.224 0.210 0.231
## 0.655 0.621 0.551
## 0.750 0.698 0.544
## 0.633 0.600 0.618
## 0.293 0.277 0.497
## 0.203 0.189 0.393
## 1.472 1.341 0.512
## 1.041 0.975 0.592
## 0.797 0.745 0.571
## 0.258 0.245 0.319
## 0.367 0.349 0.460
## 0.262 0.248 0.291
## 0.492 0.469 0.626
## 0.658 0.635 0.819
## 0.423 0.402 0.464
## 0.442 0.422 0.610
## 0.632 0.603 0.522
## 0.455 0.431 0.593
## 0.434 0.413 0.577
## 0.489 0.465 0.542
## 0.235 0.221 0.434
## 0.816 0.777 0.757
## 0.253 0.241 0.570
## 0.223 0.210 0.508
## 0.746 0.708 0.736
## 0.405 0.383 0.629
## 1.433 0.270 0.270
## 0.948 0.217 0.217
## 1.120 0.910 0.910
## 1.305 0.178 0.178
## 0.496 0.160 0.160
## 0.503 0.393 0.393
## 0.750 1.000 1.000
lavTestScore(metric, release = 1:52)
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 1132.144 52 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p135. 0.010 1 0.922
## 2 .p2. == .p136. 51.271 1 0.000
## 3 .p3. == .p137. 0.002 1 0.969
## 4 .p4. == .p138. 23.845 1 0.000
## 5 .p5. == .p139. 14.846 1 0.000
## 6 .p6. == .p140. 4.629 1 0.031
## 7 .p7. == .p141. 7.702 1 0.006
## 8 .p8. == .p142. 41.210 1 0.000
## 9 .p9. == .p143. 0.235 1 0.628
## 10 .p10. == .p144. 22.497 1 0.000
## 11 .p11. == .p145. 1.302 1 0.254
## 12 .p12. == .p146. 0.376 1 0.540
## 13 .p13. == .p147. 59.882 1 0.000
## 14 .p14. == .p148. 6.881 1 0.009
## 15 .p15. == .p149. 0.049 1 0.825
## 16 .p16. == .p150. 0.279 1 0.597
## 17 .p17. == .p151. 29.649 1 0.000
## 18 .p18. == .p152. 1.521 1 0.217
## 19 .p19. == .p153. 0.019 1 0.890
## 20 .p20. == .p154. 1.975 1 0.160
## 21 .p21. == .p155. 0.105 1 0.746
## 22 .p22. == .p156. 0.011 1 0.916
## 23 .p23. == .p157. 5.857 1 0.016
## 24 .p24. == .p158. 46.578 1 0.000
## 25 .p25. == .p159. 74.753 1 0.000
## 26 .p26. == .p160. 12.383 1 0.000
## 27 .p27. == .p161. 182.648 1 0.000
## 28 .p28. == .p162. 34.555 1 0.000
## 29 .p29. == .p163. 20.378 1 0.000
## 30 .p30. == .p164. 12.920 1 0.000
## 31 .p31. == .p165. 13.885 1 0.000
## 32 .p32. == .p166. 47.451 1 0.000
## 33 .p33. == .p167. 15.919 1 0.000
## 34 .p34. == .p168. 56.665 1 0.000
## 35 .p35. == .p169. 0.449 1 0.503
## 36 .p36. == .p170. 0.600 1 0.439
## 37 .p37. == .p171. 2.227 1 0.136
## 38 .p38. == .p172. 9.766 1 0.002
## 39 .p39. == .p173. 14.472 1 0.000
## 40 .p40. == .p174. 88.145 1 0.000
## 41 .p41. == .p175. 101.544 1 0.000
## 42 .p42. == .p176. 110.436 1 0.000
## 43 .p43. == .p177. 7.498 1 0.006
## 44 .p44. == .p178. 0.859 1 0.354
## 45 .p45. == .p179. 27.914 1 0.000
## 46 .p46. == .p180. 0.139 1 0.710
## 47 .p47. == .p181. 125.600 1 0.000
## 48 .p48. == .p182. 2.760 1 0.097
## 49 .p49. == .p183. 10.697 1 0.001
## 50 .p50. == .p184. 13.340 1 0.000
## 51 .p51. == .p185. 270.289 1 0.000
## 52 .p52. == .p186. 23.530 1 0.000
metric2<-cfa(chc.hof.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings"), group.partial=c("g=~science", "info=~Stest8aeronautics", "spatial=~Stest28mechanicalreasoning", "info=~Stest4socialstudies"))
fitMeasures(metric2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 6494.654 1059.000 0.000 0.951 0.041 0.048
## aic bic
## 463313.057 464649.060
Mc(metric2)
## [1] 0.6397249
summary(metric2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 150 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 247
## Number of equality constraints 48
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 6494.654 5786.531
## Degrees of freedom 1059 1059
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.122
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 2994.292 2667.820
## 1 3500.361 3118.711
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.044 0.009 5.037 0.000 0.027
## Stst19d (.p2.) 0.179 0.012 15.497 0.000 0.156
## Stst20s (.p3.) 0.310 0.012 25.951 0.000 0.286
## Stst21c (.p4.) 0.347 0.012 27.869 0.000 0.323
## Stst22p (.p5.) 0.383 0.014 28.213 0.000 0.357
## Stst23n (.p6.) 0.392 0.015 26.915 0.000 0.363
## Stst24x (.p7.) 0.308 0.012 25.638 0.000 0.284
## Stst25w (.p8.) 0.083 0.011 7.771 0.000 0.062
## Stst26r (.p9.) 0.160 0.009 17.965 0.000 0.142
## Stst31b (.10.) 0.142 0.011 13.228 0.000 0.121
## Stst34r (.11.) 0.147 0.015 9.755 0.000 0.118
## math =~
## Stst5mt (.12.) 0.209 0.014 14.730 0.000 0.181
## Stst25w (.13.) 0.180 0.012 14.977 0.000 0.156
## Stst32r (.14.) 0.296 0.014 21.841 0.000 0.269
## Stst33h (.15.) 0.303 0.014 20.982 0.000 0.274
## Stst34r (.16.) 0.122 0.017 7.195 0.000 0.089
## speed =~
## Stst19d (.17.) 0.182 0.011 16.195 0.000 0.160
## Stst34r (.18.) 0.456 0.020 22.443 0.000 0.416
## Stst35t (.19.) 1.083 0.032 33.484 0.000 1.019
## Stst36c (.20.) 0.785 0.026 29.678 0.000 0.733
## Stst37b (.21.) 0.677 0.024 28.379 0.000 0.631
## info =~
## Stst1vc (.22.) 0.182 0.011 16.632 0.000 0.161
## Stst2lt (.23.) 0.277 0.012 23.247 0.000 0.254
## Stst3ms (.24.) 0.247 0.011 22.813 0.000 0.225
## Stst4sc 0.334 0.014 24.306 0.000 0.307
## Stst7bl (.26.) 0.101 0.010 10.272 0.000 0.082
## Stst8rn 0.210 0.010 20.641 0.000 0.190
## Stst11r (.28.) 0.262 0.011 23.023 0.000 0.240
## Stst12l (.29.) 0.198 0.009 22.027 0.000 0.181
## Stst13h (.30.) 0.287 0.012 23.316 0.000 0.263
## Stst14b (.31.) 0.209 0.009 22.404 0.000 0.191
## Stst15t (.32.) 0.213 0.010 22.297 0.000 0.194
## Stst16m (.33.) 0.240 0.011 22.270 0.000 0.219
## Stst19d (.34.) 0.082 0.008 9.918 0.000 0.066
## Stst26r (.35.) 0.215 0.010 20.929 0.000 0.195
## science =~
## Stst1vc (.36.) 0.126 0.011 11.257 0.000 0.104
## Stst5mt (.37.) 0.134 0.013 10.356 0.000 0.109
## Stst6ph (.38.) 0.271 0.015 18.176 0.000 0.242
## Stst7bl (.39.) 0.147 0.013 11.396 0.000 0.121
## Stst9lc (.40.) 0.253 0.015 16.479 0.000 0.223
## Stst10m (.41.) 0.222 0.013 17.332 0.000 0.197
## spatial =~
## Stst28m 0.486 0.014 35.548 0.000 0.459
## Sts292D (.43.) 0.428 0.017 25.140 0.000 0.394
## Sts303D (.44.) 0.397 0.015 25.683 0.000 0.366
## Stst31b (.45.) 0.415 0.019 22.190 0.000 0.378
## Stst37b (.46.) 0.109 0.014 7.934 0.000 0.082
## g =~
## english (.47.) 1.984 0.079 25.037 0.000 1.829
## math (.48.) 1.796 0.089 20.139 0.000 1.621
## speed (.49.) 0.360 0.023 15.323 0.000 0.314
## info (.50.) 2.710 0.129 21.047 0.000 2.458
## science 2.658 0.167 15.886 0.000 2.330
## spatial (.52.) 1.077 0.048 22.670 0.000 0.984
## ci.upper Std.lv Std.all
##
## 0.061 0.098 0.091
## 0.202 0.398 0.429
## 0.333 0.688 0.685
## 0.371 0.771 0.784
## 0.410 0.852 0.825
## 0.420 0.870 0.737
## 0.331 0.684 0.595
## 0.104 0.185 0.227
## 0.177 0.355 0.337
## 0.164 0.316 0.275
## 0.177 0.327 0.283
##
## 0.237 0.430 0.405
## 0.203 0.370 0.455
## 0.322 0.608 0.747
## 0.331 0.622 0.810
## 0.156 0.251 0.218
##
## 0.204 0.194 0.209
## 0.496 0.485 0.419
## 1.146 1.151 0.688
## 0.837 0.834 0.646
## 0.724 0.720 0.584
##
## 0.203 0.526 0.491
## 0.301 0.802 0.844
## 0.268 0.712 0.773
## 0.361 0.965 0.874
## 0.121 0.293 0.304
## 0.230 0.607 0.600
## 0.285 0.758 0.783
## 0.216 0.573 0.643
## 0.311 0.829 0.756
## 0.228 0.605 0.695
## 0.231 0.615 0.729
## 0.261 0.693 0.694
## 0.099 0.238 0.257
## 0.235 0.622 0.590
##
## 0.148 0.358 0.334
## 0.160 0.381 0.359
## 0.300 0.770 0.844
## 0.172 0.417 0.432
## 0.283 0.717 0.661
## 0.247 0.631 0.721
##
## 0.513 0.714 0.803
## 0.461 0.628 0.581
## 0.427 0.583 0.637
## 0.452 0.610 0.530
## 0.136 0.161 0.130
##
## 2.139 0.893 0.893
## 1.971 0.874 0.874
## 0.406 0.339 0.339
## 2.963 0.938 0.938
## 2.986 0.936 0.936
## 1.170 0.733 0.733
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -1.155 0.023 -50.360 0.000 -1.200
## .Stst19dsgsdwrd -0.992 0.018 -53.776 0.000 -1.028
## .Stest20spellng -0.848 0.021 -39.900 0.000 -0.890
## .Stest21cptlztn -1.167 0.020 -58.007 0.000 -1.206
## .Stest22puncttn -1.226 0.021 -57.496 0.000 -1.268
## .Stest23english -1.062 0.026 -41.362 0.000 -1.113
## .Stest24exprssn -0.965 0.025 -38.928 0.000 -1.014
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.903
## .Stst26rdngcmpr -1.292 0.023 -56.802 0.000 -1.337
## .Stst31bstrctrs -1.070 0.024 -43.766 0.000 -1.118
## .Stst34rthcmptt -1.153 0.025 -46.702 0.000 -1.201
## .Stest5math -0.814 0.022 -36.442 0.000 -0.857
## .Stst32rthrsnng -1.052 0.018 -59.194 0.000 -1.087
## .Stst33hghschlm -0.875 0.016 -53.483 0.000 -0.907
## .Stest35tblrdng -0.712 0.037 -19.463 0.000 -0.784
## .Stst36clrclchc -0.032 0.028 -1.139 0.255 -0.086
## .Stst37bjctnspc -0.318 0.027 -11.957 0.000 -0.370
## .Stest2literatr -1.041 0.021 -50.624 0.000 -1.081
## .Stest3music -0.921 0.019 -48.386 0.000 -0.959
## .Stest4soclstds -1.083 0.023 -46.133 0.000 -1.129
## .Stst7blgclscnc -0.617 0.021 -29.442 0.000 -0.658
## .Stest8aerontcs -0.517 0.022 -23.664 0.000 -0.560
## .Stest11art -1.040 0.020 -51.542 0.000 -1.079
## .Stest12law -0.778 0.020 -39.122 0.000 -0.817
## .Stest13health -1.200 0.023 -51.595 0.000 -1.245
## .Stest14bible -0.720 0.018 -39.356 0.000 -0.756
## .Stest15theater -1.025 0.017 -59.426 0.000 -1.059
## .Stest16mscllns -0.887 0.022 -39.478 0.000 -0.931
## .Stst6physclscn -0.732 0.019 -38.793 0.000 -0.769
## .Stest9elctrncs -0.668 0.024 -27.887 0.000 -0.715
## .Stest10mechncs -0.656 0.019 -33.970 0.000 -0.694
## .Stst28mchnclrs -0.715 0.019 -36.895 0.000 -0.753
## .Stst29vslztn2D -0.512 0.023 -22.047 0.000 -0.557
## .Stst30vslztn3D -0.723 0.020 -35.874 0.000 -0.762
## ci.upper Std.lv Std.all
## -1.110 -1.155 -1.078
## -0.956 -0.992 -1.071
## -0.806 -0.848 -0.845
## -1.128 -1.167 -1.187
## -1.184 -1.226 -1.188
## -1.012 -1.062 -0.900
## -0.916 -0.965 -0.840
## -0.838 -0.871 -1.071
## -1.248 -1.292 -1.227
## -1.022 -1.070 -0.930
## -1.104 -1.153 -0.997
## -0.770 -0.814 -0.766
## -1.017 -1.052 -1.292
## -0.843 -0.875 -1.139
## -0.640 -0.712 -0.425
## 0.023 -0.032 -0.025
## -0.266 -0.318 -0.258
## -1.000 -1.041 -1.095
## -0.884 -0.921 -1.000
## -1.037 -1.083 -0.981
## -0.576 -0.617 -0.640
## -0.475 -0.517 -0.511
## -1.000 -1.040 -1.074
## -0.739 -0.778 -0.872
## -1.154 -1.200 -1.093
## -0.684 -0.720 -0.827
## -0.991 -1.025 -1.216
## -0.843 -0.887 -0.888
## -0.695 -0.732 -0.802
## -0.621 -0.668 -0.616
## -0.618 -0.656 -0.750
## -0.677 -0.715 -0.804
## -0.466 -0.512 -0.473
## -0.683 -0.723 -0.790
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.258 0.009 28.037 0.000 0.240
## .Stst19dsgsdwrd 0.371 0.013 27.624 0.000 0.345
## .Stest20spellng 0.535 0.017 31.298 0.000 0.501
## .Stest21cptlztn 0.372 0.015 24.691 0.000 0.343
## .Stest22puncttn 0.340 0.012 27.683 0.000 0.316
## .Stest23english 0.636 0.024 26.826 0.000 0.589
## .Stest24exprssn 0.852 0.026 33.388 0.000 0.802
## .Stst25wrdfnctn 0.384 0.012 32.535 0.000 0.361
## .Stst26rdngcmpr 0.227 0.009 25.387 0.000 0.209
## .Stst31bstrctrs 0.598 0.022 26.588 0.000 0.554
## .Stst34rthcmptt 0.635 0.030 21.267 0.000 0.576
## .Stest5math 0.530 0.020 26.899 0.000 0.492
## .Stst32rthrsnng 0.293 0.011 26.716 0.000 0.271
## .Stst33hghschlm 0.203 0.009 22.351 0.000 0.185
## .Stest35tblrdng 1.478 0.077 19.094 0.000 1.326
## .Stst36clrclchc 0.971 0.042 23.040 0.000 0.888
## .Stst37bjctnspc 0.921 0.034 26.787 0.000 0.853
## .Stest2literatr 0.260 0.009 29.595 0.000 0.243
## .Stest3music 0.341 0.012 28.794 0.000 0.318
## .Stest4soclstds 0.288 0.011 27.094 0.000 0.267
## .Stst7blgclscnc 0.455 0.014 32.481 0.000 0.428
## .Stest8aerontcs 0.657 0.018 37.037 0.000 0.622
## .Stest11art 0.363 0.012 29.886 0.000 0.339
## .Stest12law 0.466 0.014 33.425 0.000 0.439
## .Stest13health 0.517 0.016 31.836 0.000 0.485
## .Stest14bible 0.391 0.013 29.161 0.000 0.365
## .Stest15theater 0.333 0.011 30.638 0.000 0.312
## .Stest16mscllns 0.517 0.017 31.326 0.000 0.485
## .Stst6physclscn 0.239 0.010 23.129 0.000 0.219
## .Stest9elctrncs 0.663 0.027 24.342 0.000 0.609
## .Stest10mechncs 0.368 0.013 27.842 0.000 0.342
## .Stst28mchnclrs 0.281 0.016 17.925 0.000 0.250
## .Stst29vslztn2D 0.774 0.026 29.409 0.000 0.722
## .Stst30vslztn3D 0.497 0.017 28.498 0.000 0.463
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.276 0.258 0.225
## 0.397 0.371 0.433
## 0.568 0.535 0.530
## 0.402 0.372 0.385
## 0.364 0.340 0.319
## 0.682 0.636 0.456
## 0.902 0.852 0.646
## 0.407 0.384 0.580
## 0.244 0.227 0.204
## 0.642 0.598 0.452
## 0.693 0.635 0.475
## 0.569 0.530 0.470
## 0.314 0.293 0.442
## 0.221 0.203 0.344
## 1.629 1.478 0.527
## 1.054 0.971 0.582
## 0.988 0.921 0.605
## 0.278 0.260 0.288
## 0.364 0.341 0.402
## 0.309 0.288 0.237
## 0.483 0.455 0.490
## 0.692 0.657 0.641
## 0.387 0.363 0.387
## 0.494 0.466 0.586
## 0.549 0.517 0.429
## 0.418 0.391 0.517
## 0.354 0.333 0.469
## 0.550 0.517 0.519
## 0.260 0.239 0.288
## 0.716 0.663 0.563
## 0.394 0.368 0.480
## 0.311 0.281 0.355
## 0.825 0.774 0.662
## 0.531 0.497 0.594
## 1.000 0.203 0.203
## 1.000 0.237 0.237
## 1.000 0.885 0.885
## 1.000 0.120 0.120
## 1.000 0.124 0.124
## 1.000 0.463 0.463
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.044 0.009 5.037 0.000 0.027
## Stst19d (.p2.) 0.179 0.012 15.497 0.000 0.156
## Stst20s (.p3.) 0.310 0.012 25.951 0.000 0.286
## Stst21c (.p4.) 0.347 0.012 27.869 0.000 0.323
## Stst22p (.p5.) 0.383 0.014 28.213 0.000 0.357
## Stst23n (.p6.) 0.392 0.015 26.915 0.000 0.363
## Stst24x (.p7.) 0.308 0.012 25.638 0.000 0.284
## Stst25w (.p8.) 0.083 0.011 7.771 0.000 0.062
## Stst26r (.p9.) 0.160 0.009 17.965 0.000 0.142
## Stst31b (.10.) 0.142 0.011 13.228 0.000 0.121
## Stst34r (.11.) 0.147 0.015 9.755 0.000 0.118
## math =~
## Stst5mt (.12.) 0.209 0.014 14.730 0.000 0.181
## Stst25w (.13.) 0.180 0.012 14.977 0.000 0.156
## Stst32r (.14.) 0.296 0.014 21.841 0.000 0.269
## Stst33h (.15.) 0.303 0.014 20.982 0.000 0.274
## Stst34r (.16.) 0.122 0.017 7.195 0.000 0.089
## speed =~
## Stst19d (.17.) 0.182 0.011 16.195 0.000 0.160
## Stst34r (.18.) 0.456 0.020 22.443 0.000 0.416
## Stst35t (.19.) 1.083 0.032 33.484 0.000 1.019
## Stst36c (.20.) 0.785 0.026 29.678 0.000 0.733
## Stst37b (.21.) 0.677 0.024 28.379 0.000 0.631
## info =~
## Stst1vc (.22.) 0.182 0.011 16.632 0.000 0.161
## Stst2lt (.23.) 0.277 0.012 23.247 0.000 0.254
## Stst3ms (.24.) 0.247 0.011 22.813 0.000 0.225
## Stst4sc 0.273 0.012 22.491 0.000 0.249
## Stst7bl (.26.) 0.101 0.010 10.272 0.000 0.082
## Stst8rn 0.095 0.007 14.210 0.000 0.081
## Stst11r (.28.) 0.262 0.011 23.023 0.000 0.240
## Stst12l (.29.) 0.198 0.009 22.027 0.000 0.181
## Stst13h (.30.) 0.287 0.012 23.316 0.000 0.263
## Stst14b (.31.) 0.209 0.009 22.404 0.000 0.191
## Stst15t (.32.) 0.213 0.010 22.297 0.000 0.194
## Stst16m (.33.) 0.240 0.011 22.270 0.000 0.219
## Stst19d (.34.) 0.082 0.008 9.918 0.000 0.066
## Stst26r (.35.) 0.215 0.010 20.929 0.000 0.195
## science =~
## Stst1vc (.36.) 0.126 0.011 11.257 0.000 0.104
## Stst5mt (.37.) 0.134 0.013 10.356 0.000 0.109
## Stst6ph (.38.) 0.271 0.015 18.176 0.000 0.242
## Stst7bl (.39.) 0.147 0.013 11.396 0.000 0.121
## Stst9lc (.40.) 0.253 0.015 16.479 0.000 0.223
## Stst10m (.41.) 0.222 0.013 17.332 0.000 0.197
## spatial =~
## Stst28m 0.301 0.016 19.312 0.000 0.271
## Sts292D (.43.) 0.428 0.017 25.140 0.000 0.394
## Sts303D (.44.) 0.397 0.015 25.683 0.000 0.366
## Stst31b (.45.) 0.415 0.019 22.190 0.000 0.378
## Stst37b (.46.) 0.109 0.014 7.934 0.000 0.082
## g =~
## english (.47.) 1.984 0.079 25.037 0.000 1.829
## math (.48.) 1.796 0.089 20.139 0.000 1.621
## speed (.49.) 0.360 0.023 15.323 0.000 0.314
## info (.50.) 2.710 0.129 21.047 0.000 2.458
## science 1.694 0.105 16.176 0.000 1.489
## spatial (.52.) 1.077 0.048 22.670 0.000 0.984
## ci.upper Std.lv Std.all
##
## 0.061 0.091 0.099
## 0.202 0.368 0.408
## 0.333 0.637 0.664
## 0.371 0.714 0.727
## 0.410 0.788 0.818
## 0.420 0.806 0.735
## 0.331 0.633 0.580
## 0.104 0.171 0.221
## 0.177 0.329 0.334
## 0.164 0.293 0.270
## 0.177 0.303 0.264
##
## 0.237 0.384 0.394
## 0.203 0.330 0.427
## 0.322 0.542 0.718
## 0.331 0.555 0.787
## 0.156 0.224 0.196
##
## 0.204 0.191 0.211
## 0.496 0.477 0.416
## 1.146 1.133 0.699
## 0.837 0.821 0.639
## 0.724 0.709 0.618
##
## 0.203 0.494 0.540
## 0.301 0.753 0.836
## 0.268 0.669 0.751
## 0.297 0.741 0.828
## 0.121 0.276 0.324
## 0.108 0.257 0.309
## 0.285 0.712 0.749
## 0.216 0.539 0.638
## 0.311 0.779 0.709
## 0.228 0.568 0.655
## 0.231 0.577 0.670
## 0.261 0.651 0.690
## 0.099 0.224 0.248
## 0.235 0.584 0.594
##
## 0.148 0.222 0.242
## 0.160 0.236 0.242
## 0.300 0.476 0.707
## 0.172 0.258 0.303
## 0.283 0.444 0.451
## 0.247 0.390 0.625
##
## 0.332 0.388 0.631
## 0.461 0.550 0.554
## 0.427 0.510 0.644
## 0.452 0.534 0.492
## 0.136 0.141 0.123
##
## 2.139 0.881 0.881
## 1.971 0.894 0.894
## 0.406 0.314 0.314
## 2.963 0.912 0.912
## 1.899 0.880 0.880
## 1.170 0.764 0.764
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -1.339 0.016 -83.554 0.000 -1.370
## .Stst19dsgsdwrd -0.878 0.016 -54.059 0.000 -0.910
## .Stest20spellng -0.450 0.017 -26.686 0.000 -0.483
## .Stest21cptlztn -0.899 0.017 -51.477 0.000 -0.934
## .Stest22puncttn -0.929 0.017 -53.286 0.000 -0.963
## .Stest23english -0.744 0.019 -38.449 0.000 -0.781
## .Stest24exprssn -0.704 0.019 -37.099 0.000 -0.742
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.816
## .Stst26rdngcmpr -1.226 0.017 -72.842 0.000 -1.259
## .Stst31bstrctrs -1.260 0.019 -65.843 0.000 -1.297
## .Stst34rthcmptt -1.004 0.021 -47.990 0.000 -1.045
## .Stest5math -0.965 0.017 -55.615 0.000 -0.999
## .Stst32rthrsnng -1.184 0.013 -92.849 0.000 -1.209
## .Stst33hghschlm -0.942 0.012 -78.389 0.000 -0.966
## .Stest35tblrdng -0.524 0.029 -17.830 0.000 -0.582
## .Stst36clrclchc 0.300 0.023 13.284 0.000 0.256
## .Stst37bjctnspc -0.217 0.021 -10.567 0.000 -0.257
## .Stest2literatr -1.034 0.016 -66.363 0.000 -1.065
## .Stest3music -0.825 0.016 -52.646 0.000 -0.856
## .Stest4soclstds -1.273 0.015 -82.694 0.000 -1.303
## .Stst7blgclscnc -0.831 0.015 -55.991 0.000 -0.860
## .Stest8aerontcs -0.942 0.014 -64.960 0.000 -0.970
## .Stest11art -1.046 0.017 -63.114 0.000 -1.078
## .Stest12law -0.897 0.014 -63.710 0.000 -0.925
## .Stest13health -1.020 0.019 -52.885 0.000 -1.057
## .Stest14bible -0.565 0.015 -36.958 0.000 -0.595
## .Stest15theater -0.856 0.015 -56.660 0.000 -0.885
## .Stest16mscllns -0.949 0.016 -60.013 0.000 -0.980
## .Stst6physclscn -1.022 0.012 -84.927 0.000 -1.046
## .Stest9elctrncs -1.154 0.017 -68.546 0.000 -1.187
## .Stest10mechncs -1.373 0.011 -128.778 0.000 -1.394
## .Stst28mchnclrs -1.323 0.011 -124.285 0.000 -1.344
## .Stst29vslztn2D -0.916 0.017 -52.801 0.000 -0.950
## .Stst30vslztn3D -0.982 0.014 -72.639 0.000 -1.008
## ci.upper Std.lv Std.all
## -1.307 -1.339 -1.464
## -0.846 -0.878 -0.974
## -0.417 -0.450 -0.470
## -0.865 -0.899 -0.916
## -0.895 -0.929 -0.964
## -0.706 -0.744 -0.679
## -0.667 -0.704 -0.646
## -0.761 -0.788 -1.020
## -1.193 -1.226 -1.247
## -1.222 -1.260 -1.162
## -0.963 -1.004 -0.876
## -0.931 -0.965 -0.991
## -1.159 -1.184 -1.567
## -0.919 -0.942 -1.336
## -0.466 -0.524 -0.324
## 0.344 0.300 0.233
## -0.176 -0.217 -0.189
## -1.004 -1.034 -1.148
## -0.795 -0.825 -0.927
## -1.243 -1.273 -1.422
## -0.802 -0.831 -0.977
## -0.913 -0.942 -1.133
## -1.013 -1.046 -1.099
## -0.870 -0.897 -1.063
## -0.982 -1.020 -0.928
## -0.535 -0.565 -0.651
## -0.826 -0.856 -0.993
## -0.918 -0.949 -1.006
## -0.998 -1.022 -1.518
## -1.121 -1.154 -1.174
## -1.352 -1.373 -2.198
## -1.303 -1.323 -2.153
## -0.882 -0.916 -0.921
## -0.955 -0.982 -1.239
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.256 0.007 35.454 0.000 0.242
## .Stst19dsgsdwrd 0.396 0.011 36.059 0.000 0.374
## .Stest20spellng 0.514 0.014 37.030 0.000 0.487
## .Stest21cptlztn 0.455 0.014 33.409 0.000 0.429
## .Stest22puncttn 0.308 0.010 29.517 0.000 0.287
## .Stest23english 0.551 0.017 32.996 0.000 0.519
## .Stest24exprssn 0.789 0.021 37.480 0.000 0.747
## .Stst25wrdfnctn 0.371 0.010 36.436 0.000 0.351
## .Stst26rdngcmpr 0.209 0.007 29.410 0.000 0.195
## .Stst31bstrctrs 0.594 0.017 34.100 0.000 0.560
## .Stst34rthcmptt 0.698 0.027 26.119 0.000 0.645
## .Stest5math 0.603 0.017 36.026 0.000 0.570
## .Stst32rthrsnng 0.276 0.008 33.151 0.000 0.260
## .Stst33hghschlm 0.189 0.007 27.613 0.000 0.176
## .Stest35tblrdng 1.341 0.067 19.958 0.000 1.210
## .Stst36clrclchc 0.975 0.034 28.723 0.000 0.908
## .Stst37bjctnspc 0.744 0.027 27.990 0.000 0.692
## .Stest2literatr 0.244 0.007 35.485 0.000 0.231
## .Stest3music 0.346 0.009 37.778 0.000 0.328
## .Stest4soclstds 0.251 0.007 34.507 0.000 0.237
## .Stst7blgclscnc 0.468 0.012 39.475 0.000 0.445
## .Stest8aerontcs 0.626 0.011 58.915 0.000 0.605
## .Stest11art 0.398 0.011 36.981 0.000 0.377
## .Stest12law 0.422 0.011 39.966 0.000 0.402
## .Stest13health 0.600 0.015 40.945 0.000 0.571
## .Stest14bible 0.429 0.012 34.558 0.000 0.405
## .Stest15theater 0.410 0.011 38.657 0.000 0.389
## .Stest16mscllns 0.465 0.012 37.724 0.000 0.441
## .Stst6physclscn 0.227 0.007 30.910 0.000 0.212
## .Stest9elctrncs 0.770 0.020 38.544 0.000 0.730
## .Stest10mechncs 0.238 0.006 37.076 0.000 0.225
## .Stst28mchnclrs 0.228 0.007 33.069 0.000 0.214
## .Stst29vslztn2D 0.685 0.019 35.412 0.000 0.647
## .Stst30vslztn3D 0.367 0.011 33.073 0.000 0.345
## .english 0.949 0.084 11.251 0.000 0.784
## .math 0.675 0.088 7.694 0.000 0.503
## .speed 0.986 0.063 15.734 0.000 0.863
## .info 1.245 0.128 9.706 0.000 0.994
## .science 0.694 0.102 6.791 0.000 0.494
## .spatial 0.690 0.069 10.028 0.000 0.555
## g 0.833 0.036 23.239 0.000 0.763
## ci.upper Std.lv Std.all
## 0.271 0.256 0.307
## 0.417 0.396 0.487
## 0.541 0.514 0.559
## 0.482 0.455 0.472
## 0.328 0.308 0.331
## 0.584 0.551 0.459
## 0.830 0.789 0.663
## 0.391 0.371 0.621
## 0.223 0.209 0.216
## 0.628 0.594 0.505
## 0.750 0.698 0.531
## 0.636 0.603 0.636
## 0.293 0.276 0.484
## 0.203 0.189 0.381
## 1.473 1.341 0.511
## 1.042 0.975 0.591
## 0.796 0.744 0.566
## 0.258 0.244 0.301
## 0.363 0.346 0.435
## 0.266 0.251 0.314
## 0.491 0.468 0.646
## 0.647 0.626 0.905
## 0.419 0.398 0.440
## 0.443 0.422 0.593
## 0.628 0.600 0.497
## 0.454 0.429 0.571
## 0.430 0.410 0.551
## 0.489 0.465 0.524
## 0.241 0.227 0.500
## 0.809 0.770 0.796
## 0.251 0.238 0.610
## 0.241 0.228 0.602
## 0.723 0.685 0.693
## 0.389 0.367 0.585
## 1.114 0.224 0.224
## 0.847 0.201 0.201
## 1.109 0.901 0.901
## 1.497 0.169 0.169
## 0.895 0.225 0.225
## 0.825 0.417 0.417
## 0.904 1.000 1.000
lavTestScore(metric2, release = 1:48)
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 430.585 48 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p135. 1.174 1 0.279
## 2 .p2. == .p136. 35.477 1 0.000
## 3 .p3. == .p137. 0.125 1 0.724
## 4 .p4. == .p138. 19.458 1 0.000
## 5 .p5. == .p139. 10.104 1 0.001
## 6 .p6. == .p140. 7.273 1 0.007
## 7 .p7. == .p141. 9.427 1 0.002
## 8 .p8. == .p142. 26.187 1 0.000
## 9 .p9. == .p143. 17.011 1 0.000
## 10 .p10. == .p144. 3.515 1 0.061
## 11 .p11. == .p145. 0.082 1 0.775
## 12 .p12. == .p146. 6.223 1 0.013
## 13 .p13. == .p147. 44.243 1 0.000
## 14 .p14. == .p148. 20.439 1 0.000
## 15 .p15. == .p149. 9.151 1 0.002
## 16 .p16. == .p150. 0.084 1 0.772
## 17 .p17. == .p151. 24.236 1 0.000
## 18 .p18. == .p152. 0.796 1 0.372
## 19 .p19. == .p153. 0.002 1 0.968
## 20 .p20. == .p154. 1.696 1 0.193
## 21 .p21. == .p155. 0.472 1 0.492
## 22 .p22. == .p156. 1.957 1 0.162
## 23 .p23. == .p157. 3.181 1 0.074
## 24 .p24. == .p158. 15.339 1 0.000
## 25 .p26. == .p160. 2.250 1 0.134
## 26 .p28. == .p162. 8.824 1 0.003
## 27 .p29. == .p163. 44.124 1 0.000
## 28 .p30. == .p164. 0.770 1 0.380
## 29 .p31. == .p165. 2.208 1 0.137
## 30 .p32. == .p166. 21.355 1 0.000
## 31 .p33. == .p167. 41.181 1 0.000
## 32 .p34. == .p168. 39.845 1 0.000
## 33 .p35. == .p169. 21.576 1 0.000
## 34 .p36. == .p170. 0.556 1 0.456
## 35 .p37. == .p171. 12.151 1 0.000
## 36 .p38. == .p172. 43.353 1 0.000
## 37 .p39. == .p173. 2.904 1 0.088
## 38 .p40. == .p174. 24.985 1 0.000
## 39 .p41. == .p175. 21.060 1 0.000
## 40 .p43. == .p177. 0.266 1 0.606
## 41 .p44. == .p178. 26.797 1 0.000
## 42 .p45. == .p179. 3.720 1 0.054
## 43 .p46. == .p180. 0.011 1 0.916
## 44 .p47. == .p181. 30.735 1 0.000
## 45 .p48. == .p182. 5.608 1 0.018
## 46 .p49. == .p183. 3.897 1 0.048
## 47 .p50. == .p184. 2.381 1 0.123
## 48 .p52. == .p186. 11.930 1 0.001
scalar<-cfa(chc.hof.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts"), group.partial=c("g=~science", "info=~Stest8aeronautics", "spatial=~Stest28mechanicalreasoning", "info=~Stest4socialstudies"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov)
## does not appear to be positive definite! The smallest eigenvalue
## (= 1.733635e-14) is close to zero. This may be a symptom that the
## model is not identified.
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 8481.311 1086.000 0.000 0.934 0.047 0.061
## aic bic
## 465245.714 466400.450
Mc(scalar)
## [1] 0.5445655
summary(scalar, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 178 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 254
## Number of equality constraints 82
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 8481.311 7557.073
## Degrees of freedom 1086 1086
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.122
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 4219.555 3759.736
## 1 4261.755 3797.337
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.042 0.008 5.401 0.000 0.027
## Stst19d (.p2.) 0.161 0.011 14.890 0.000 0.140
## Stst20s (.p3.) 0.317 0.012 26.655 0.000 0.293
## Stst21c (.p4.) 0.348 0.012 28.569 0.000 0.324
## Stst22p (.p5.) 0.384 0.013 28.741 0.000 0.358
## Stst23n (.p6.) 0.393 0.014 27.325 0.000 0.365
## Stst24x (.p7.) 0.309 0.012 25.918 0.000 0.286
## Stst25w (.p8.) 0.096 0.009 10.341 0.000 0.078
## Stst26r (.p9.) 0.145 0.008 17.053 0.000 0.128
## Stst31b (.10.) 0.177 0.009 18.930 0.000 0.159
## Stst34r (.11.) 0.134 0.013 10.205 0.000 0.108
## math =~
## Stst5mt (.12.) 0.248 0.013 18.670 0.000 0.222
## Stst25w (.13.) 0.163 0.011 14.799 0.000 0.141
## Stst32r (.14.) 0.291 0.013 21.834 0.000 0.264
## Stst33h (.15.) 0.297 0.014 21.185 0.000 0.269
## Stst34r (.16.) 0.134 0.015 9.042 0.000 0.105
## speed =~
## Stst19d (.17.) 0.179 0.011 15.999 0.000 0.157
## Stst34r (.18.) 0.452 0.020 22.334 0.000 0.412
## Stst35t (.19.) 1.073 0.032 33.013 0.000 1.009
## Stst36c (.20.) 0.792 0.026 30.630 0.000 0.742
## Stst37b (.21.) 0.687 0.023 29.935 0.000 0.642
## info =~
## Stst1vc (.22.) 0.182 0.011 16.971 0.000 0.161
## Stst2lt (.23.) 0.271 0.012 22.445 0.000 0.248
## Stst3ms (.24.) 0.241 0.011 22.106 0.000 0.220
## Stst4sc 0.336 0.014 23.285 0.000 0.308
## Stst7bl (.26.) 0.111 0.008 13.605 0.000 0.095
## Stst8rn 0.224 0.011 20.312 0.000 0.202
## Stst11r (.28.) 0.257 0.012 22.241 0.000 0.234
## Stst12l (.29.) 0.194 0.009 21.244 0.000 0.176
## Stst13h (.30.) 0.281 0.012 22.631 0.000 0.257
## Stst14b (.31.) 0.205 0.009 21.813 0.000 0.187
## Stst15t (.32.) 0.208 0.010 21.684 0.000 0.190
## Stst16m (.33.) 0.234 0.011 21.536 0.000 0.213
## Stst19d (.34.) 0.093 0.008 11.758 0.000 0.078
## Stst26r (.35.) 0.221 0.010 21.212 0.000 0.201
## science =~
## Stst1vc (.36.) 0.123 0.009 13.075 0.000 0.104
## Stst5mt (.37.) 0.092 0.010 8.830 0.000 0.071
## Stst6ph (.38.) 0.249 0.014 17.184 0.000 0.220
## Stst7bl (.39.) 0.130 0.011 12.275 0.000 0.109
## Stst9lc (.40.) 0.253 0.016 15.778 0.000 0.221
## Stst10m (.41.) 0.247 0.015 16.424 0.000 0.218
## spatial =~
## Stst28m 0.510 0.014 36.581 0.000 0.483
## Sts292D (.43.) 0.417 0.018 23.165 0.000 0.382
## Sts303D (.44.) 0.368 0.016 23.068 0.000 0.337
## Stst31b (.45.) 0.357 0.017 20.818 0.000 0.324
## Stst37b (.46.) 0.098 0.013 7.805 0.000 0.074
## g =~
## english (.47.) 2.036 0.081 25.141 0.000 1.878
## math (.48.) 1.894 0.093 20.343 0.000 1.712
## speed (.49.) 0.375 0.024 15.467 0.000 0.328
## info (.50.) 2.868 0.141 20.385 0.000 2.592
## science 2.795 0.189 14.804 0.000 2.425
## spatial (.52.) 1.097 0.058 18.957 0.000 0.984
## ci.upper Std.lv Std.all
##
## 0.057 0.096 0.087
## 0.182 0.365 0.389
## 0.340 0.719 0.698
## 0.372 0.789 0.791
## 0.411 0.872 0.832
## 0.421 0.892 0.746
## 0.333 0.702 0.605
## 0.115 0.219 0.266
## 0.161 0.328 0.305
## 0.195 0.401 0.346
## 0.160 0.304 0.261
##
## 0.274 0.532 0.501
## 0.184 0.349 0.424
## 0.317 0.622 0.752
## 0.324 0.636 0.814
## 0.163 0.287 0.246
##
## 0.201 0.191 0.204
## 0.492 0.483 0.414
## 1.137 1.146 0.684
## 0.843 0.846 0.651
## 0.732 0.734 0.593
##
## 0.203 0.552 0.502
## 0.295 0.824 0.850
## 0.263 0.733 0.780
## 0.364 1.021 0.882
## 0.127 0.336 0.345
## 0.246 0.680 0.632
## 0.280 0.780 0.791
## 0.212 0.589 0.650
## 0.305 0.854 0.762
## 0.223 0.623 0.702
## 0.227 0.633 0.734
## 0.256 0.712 0.702
## 0.109 0.283 0.302
## 0.241 0.671 0.623
##
## 0.141 0.364 0.331
## 0.112 0.272 0.256
## 0.277 0.738 0.819
## 0.151 0.386 0.396
## 0.284 0.750 0.678
## 0.277 0.734 0.761
##
## 0.538 0.758 0.822
## 0.452 0.619 0.573
## 0.399 0.546 0.600
## 0.391 0.531 0.457
## 0.123 0.146 0.118
##
## 2.195 0.898 0.898
## 2.077 0.884 0.884
## 0.423 0.351 0.351
## 3.144 0.944 0.944
## 3.165 0.942 0.942
## 1.211 0.739 0.739
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.94.) -1.391 0.026 -53.839 0.000 -1.441
## .Stst19d (.95.) -1.197 0.019 -63.619 0.000 -1.234
## .Stst20s (.96.) -0.920 0.022 -41.997 0.000 -0.963
## .Stst21c (.97.) -1.348 0.021 -63.872 0.000 -1.389
## .Stst22p (.98.) -1.427 0.024 -59.968 0.000 -1.474
## .Stst23n (.99.) -1.259 0.026 -47.836 0.000 -1.310
## .Stst24x (.100) -1.113 0.023 -48.456 0.000 -1.158
## .Stst25w (.101) -0.966 0.016 -61.183 0.000 -0.996
## .Stst26r (.102) -1.566 0.025 -61.769 0.000 -1.615
## .Stst31b (.103) -1.227 0.028 -43.998 0.000 -1.281
## .Stst34r (.104) -1.347 0.025 -53.196 0.000 -1.396
## .Stst5mt (.105) -0.941 0.022 -42.708 0.000 -0.985
## .Stst32r (.106) -1.221 0.017 -73.260 0.000 -1.253
## .Stst33h (.107) -1.006 0.016 -61.288 0.000 -1.038
## .Stst35t (.108) -0.866 0.036 -24.272 0.000 -0.936
## .Stst36c (.109) -0.028 0.027 -1.068 0.285 -0.081
## .Stst37b (.110) -0.389 0.025 -15.483 0.000 -0.438
## .Stst2lt (.111) -1.245 0.022 -55.686 0.000 -1.289
## .Stst3ms (.112) -1.049 0.020 -51.581 0.000 -1.089
## .Stst4sc (.113) -1.424 0.023 -61.220 0.000 -1.469
## .Stst7bl (.114) -0.772 0.021 -36.155 0.000 -0.814
## .Stst8rn (.115) -0.882 0.015 -58.847 0.000 -0.912
## .Stst11r (.116) -1.240 0.021 -57.911 0.000 -1.282
## .Stst12l (.117) -1.001 0.018 -56.687 0.000 -1.036
## .Stst13h (.118) -1.313 0.025 -53.076 0.000 -1.362
## .Stst14b (.119) -0.787 0.019 -42.293 0.000 -0.824
## .Stst15t (.120) -1.091 0.018 -60.046 0.000 -1.127
## .Stst16m (.121) -1.105 0.021 -52.645 0.000 -1.147
## .Stst6ph (.122) -0.791 0.020 -39.416 0.000 -0.830
## .Stst9lc (.123) -0.845 0.022 -37.648 0.000 -0.889
## .Stst10m (.124) -1.003 0.022 -45.946 0.000 -1.045
## .Stst28m (.125) -0.977 0.027 -35.780 0.000 -1.030
## .Sts292D (.126) -0.599 0.024 -24.690 0.000 -0.646
## .Sts303D (.127) -0.731 0.021 -34.887 0.000 -0.772
## ci.upper Std.lv Std.all
## -1.340 -1.391 -1.265
## -1.160 -1.197 -1.276
## -0.877 -0.920 -0.894
## -1.307 -1.348 -1.352
## -1.380 -1.427 -1.361
## -1.207 -1.259 -1.052
## -1.068 -1.113 -0.960
## -0.935 -0.966 -1.173
## -1.516 -1.566 -1.453
## -1.172 -1.227 -1.057
## -1.297 -1.347 -1.154
## -0.898 -0.941 -0.887
## -1.188 -1.221 -1.476
## -0.974 -1.006 -1.288
## -0.796 -0.866 -0.517
## 0.024 -0.028 -0.022
## -0.340 -0.389 -0.314
## -1.201 -1.245 -1.283
## -1.009 -1.049 -1.117
## -1.378 -1.424 -1.230
## -0.730 -0.772 -0.792
## -0.853 -0.882 -0.819
## -1.198 -1.240 -1.258
## -0.967 -1.001 -1.105
## -1.265 -1.313 -1.172
## -0.751 -0.787 -0.887
## -1.056 -1.091 -1.266
## -1.064 -1.105 -1.091
## -0.752 -0.791 -0.878
## -0.801 -0.845 -0.765
## -0.960 -1.003 -1.039
## -0.923 -0.977 -1.060
## -0.551 -0.599 -0.554
## -0.690 -0.731 -0.803
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.256 0.009 28.238 0.000 0.239
## .Stst19dsgsdwrd 0.375 0.014 27.239 0.000 0.348
## .Stest20spellng 0.542 0.017 31.070 0.000 0.508
## .Stest21cptlztn 0.372 0.015 24.512 0.000 0.342
## .Stest22puncttn 0.338 0.012 27.724 0.000 0.314
## .Stest23english 0.636 0.024 26.909 0.000 0.589
## .Stest24exprssn 0.852 0.026 33.380 0.000 0.802
## .Stst25wrdfnctn 0.387 0.012 32.689 0.000 0.364
## .Stst26rdngcmpr 0.230 0.009 25.445 0.000 0.212
## .Stst31bstrctrs 0.621 0.022 27.885 0.000 0.577
## .Stst34rthcmptt 0.636 0.030 21.035 0.000 0.576
## .Stest5math 0.529 0.020 26.645 0.000 0.490
## .Stst32rthrsnng 0.297 0.011 26.699 0.000 0.275
## .Stst33hghschlm 0.206 0.009 22.977 0.000 0.188
## .Stest35tblrdng 1.491 0.076 19.732 0.000 1.343
## .Stst36clrclchc 0.975 0.043 22.809 0.000 0.891
## .Stst37bjctnspc 0.917 0.035 26.548 0.000 0.849
## .Stest2literatr 0.261 0.009 29.725 0.000 0.244
## .Stest3music 0.345 0.012 28.997 0.000 0.322
## .Stest4soclstds 0.297 0.011 26.172 0.000 0.275
## .Stst7blgclscnc 0.457 0.014 32.924 0.000 0.430
## .Stest8aerontcs 0.697 0.019 35.821 0.000 0.659
## .Stest11art 0.364 0.012 29.914 0.000 0.340
## .Stest12law 0.474 0.014 32.678 0.000 0.445
## .Stest13health 0.528 0.016 32.201 0.000 0.496
## .Stest14bible 0.400 0.014 29.632 0.000 0.374
## .Stest15theater 0.342 0.011 31.084 0.000 0.321
## .Stest16mscllns 0.521 0.017 30.890 0.000 0.488
## .Stst6physclscn 0.267 0.011 23.877 0.000 0.245
## .Stest9elctrncs 0.659 0.028 23.891 0.000 0.605
## .Stest10mechncs 0.392 0.016 24.273 0.000 0.361
## .Stst28mchnclrs 0.276 0.018 15.344 0.000 0.241
## .Stst29vslztn2D 0.784 0.027 29.485 0.000 0.732
## .Stst30vslztn3D 0.530 0.018 28.961 0.000 0.495
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.274 0.256 0.212
## 0.402 0.375 0.426
## 0.576 0.542 0.512
## 0.401 0.372 0.374
## 0.362 0.338 0.308
## 0.682 0.636 0.444
## 0.902 0.852 0.634
## 0.410 0.387 0.571
## 0.247 0.230 0.198
## 0.664 0.621 0.461
## 0.695 0.636 0.467
## 0.568 0.529 0.470
## 0.319 0.297 0.434
## 0.224 0.206 0.338
## 1.639 1.491 0.532
## 1.058 0.975 0.576
## 0.984 0.917 0.598
## 0.279 0.261 0.278
## 0.368 0.345 0.391
## 0.319 0.297 0.222
## 0.485 0.457 0.482
## 0.735 0.697 0.601
## 0.388 0.364 0.374
## 0.502 0.474 0.577
## 0.560 0.528 0.420
## 0.426 0.400 0.508
## 0.364 0.342 0.461
## 0.554 0.521 0.507
## 0.289 0.267 0.329
## 0.714 0.659 0.540
## 0.424 0.392 0.421
## 0.311 0.276 0.325
## 0.836 0.784 0.672
## 0.566 0.530 0.640
## 1.000 0.194 0.194
## 1.000 0.218 0.218
## 1.000 0.876 0.876
## 1.000 0.108 0.108
## 1.000 0.113 0.113
## 1.000 0.454 0.454
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.042 0.008 5.401 0.000 0.027
## Stst19d (.p2.) 0.161 0.011 14.890 0.000 0.140
## Stst20s (.p3.) 0.317 0.012 26.655 0.000 0.293
## Stst21c (.p4.) 0.348 0.012 28.569 0.000 0.324
## Stst22p (.p5.) 0.384 0.013 28.741 0.000 0.358
## Stst23n (.p6.) 0.393 0.014 27.325 0.000 0.365
## Stst24x (.p7.) 0.309 0.012 25.918 0.000 0.286
## Stst25w (.p8.) 0.096 0.009 10.341 0.000 0.078
## Stst26r (.p9.) 0.145 0.008 17.053 0.000 0.128
## Stst31b (.10.) 0.177 0.009 18.930 0.000 0.159
## Stst34r (.11.) 0.134 0.013 10.205 0.000 0.108
## math =~
## Stst5mt (.12.) 0.248 0.013 18.670 0.000 0.222
## Stst25w (.13.) 0.163 0.011 14.799 0.000 0.141
## Stst32r (.14.) 0.291 0.013 21.834 0.000 0.264
## Stst33h (.15.) 0.297 0.014 21.185 0.000 0.269
## Stst34r (.16.) 0.134 0.015 9.042 0.000 0.105
## speed =~
## Stst19d (.17.) 0.179 0.011 15.999 0.000 0.157
## Stst34r (.18.) 0.452 0.020 22.334 0.000 0.412
## Stst35t (.19.) 1.073 0.032 33.013 0.000 1.009
## Stst36c (.20.) 0.792 0.026 30.630 0.000 0.742
## Stst37b (.21.) 0.687 0.023 29.935 0.000 0.642
## info =~
## Stst1vc (.22.) 0.182 0.011 16.971 0.000 0.161
## Stst2lt (.23.) 0.271 0.012 22.445 0.000 0.248
## Stst3ms (.24.) 0.241 0.011 22.106 0.000 0.220
## Stst4sc 0.261 0.012 21.715 0.000 0.237
## Stst7bl (.26.) 0.111 0.008 13.605 0.000 0.095
## Stst8rn 0.079 0.007 12.040 0.000 0.066
## Stst11r (.28.) 0.257 0.012 22.241 0.000 0.234
## Stst12l (.29.) 0.194 0.009 21.244 0.000 0.176
## Stst13h (.30.) 0.281 0.012 22.631 0.000 0.257
## Stst14b (.31.) 0.205 0.009 21.813 0.000 0.187
## Stst15t (.32.) 0.208 0.010 21.684 0.000 0.190
## Stst16m (.33.) 0.234 0.011 21.536 0.000 0.213
## Stst19d (.34.) 0.093 0.008 11.758 0.000 0.078
## Stst26r (.35.) 0.221 0.010 21.212 0.000 0.201
## science =~
## Stst1vc (.36.) 0.123 0.009 13.075 0.000 0.104
## Stst5mt (.37.) 0.092 0.010 8.830 0.000 0.071
## Stst6ph (.38.) 0.249 0.014 17.184 0.000 0.220
## Stst7bl (.39.) 0.130 0.011 12.275 0.000 0.109
## Stst9lc (.40.) 0.253 0.016 15.778 0.000 0.221
## Stst10m (.41.) 0.247 0.015 16.424 0.000 0.218
## spatial =~
## Stst28m 0.357 0.022 16.080 0.000 0.314
## Sts292D (.43.) 0.417 0.018 23.165 0.000 0.382
## Sts303D (.44.) 0.368 0.016 23.068 0.000 0.337
## Stst31b (.45.) 0.357 0.017 20.818 0.000 0.324
## Stst37b (.46.) 0.098 0.013 7.805 0.000 0.074
## g =~
## english (.47.) 2.036 0.081 25.141 0.000 1.878
## math (.48.) 1.894 0.093 20.343 0.000 1.712
## speed (.49.) 0.375 0.024 15.467 0.000 0.328
## info (.50.) 2.868 0.141 20.385 0.000 2.592
## science 1.724 0.114 15.147 0.000 1.501
## spatial (.52.) 1.097 0.058 18.957 0.000 0.984
## ci.upper Std.lv Std.all
##
## 0.057 0.086 0.095
## 0.182 0.329 0.366
## 0.340 0.648 0.669
## 0.372 0.712 0.726
## 0.411 0.787 0.818
## 0.421 0.805 0.735
## 0.333 0.633 0.581
## 0.115 0.197 0.255
## 0.161 0.296 0.301
## 0.195 0.362 0.335
## 0.160 0.275 0.240
##
## 0.274 0.463 0.473
## 0.184 0.303 0.392
## 0.317 0.542 0.716
## 0.324 0.553 0.785
## 0.163 0.250 0.218
##
## 0.201 0.187 0.208
## 0.492 0.473 0.413
## 1.137 1.123 0.695
## 0.843 0.829 0.643
## 0.732 0.719 0.627
##
## 0.203 0.505 0.553
## 0.295 0.754 0.836
## 0.263 0.670 0.751
## 0.284 0.724 0.819
## 0.127 0.307 0.361
## 0.092 0.220 0.265
## 0.280 0.713 0.749
## 0.212 0.538 0.637
## 0.305 0.781 0.708
## 0.223 0.569 0.654
## 0.227 0.579 0.668
## 0.256 0.651 0.690
## 0.109 0.259 0.288
## 0.241 0.614 0.625
##
## 0.141 0.211 0.231
## 0.112 0.157 0.161
## 0.277 0.428 0.651
## 0.151 0.224 0.262
## 0.284 0.434 0.443
## 0.277 0.425 0.656
##
## 0.401 0.446 0.694
## 0.452 0.521 0.528
## 0.399 0.460 0.593
## 0.391 0.447 0.413
## 0.123 0.123 0.107
##
## 2.195 0.879 0.879
## 2.077 0.897 0.897
## 0.423 0.317 0.317
## 3.144 0.912 0.912
## 1.947 0.885 0.885
## 1.211 0.776 0.776
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.94.) -1.391 0.026 -53.839 0.000 -1.441
## .Stst19d (.95.) -1.197 0.019 -63.619 0.000 -1.234
## .Stst20s (.96.) -0.920 0.022 -41.997 0.000 -0.963
## .Stst21c (.97.) -1.348 0.021 -63.872 0.000 -1.389
## .Stst22p (.98.) -1.427 0.024 -59.968 0.000 -1.474
## .Stst23n (.99.) -1.259 0.026 -47.836 0.000 -1.310
## .Stst24x (.100) -1.113 0.023 -48.456 0.000 -1.158
## .Stst25w (.101) -0.966 0.016 -61.183 0.000 -0.996
## .Stst26r (.102) -1.566 0.025 -61.769 0.000 -1.615
## .Stst31b (.103) -1.227 0.028 -43.998 0.000 -1.281
## .Stst34r (.104) -1.347 0.025 -53.196 0.000 -1.396
## .Stst5mt (.105) -0.941 0.022 -42.708 0.000 -0.985
## .Stst32r (.106) -1.221 0.017 -73.260 0.000 -1.253
## .Stst33h (.107) -1.006 0.016 -61.288 0.000 -1.038
## .Stst35t (.108) -0.866 0.036 -24.272 0.000 -0.936
## .Stst36c (.109) -0.028 0.027 -1.068 0.285 -0.081
## .Stst37b (.110) -0.389 0.025 -15.483 0.000 -0.438
## .Stst2lt (.111) -1.245 0.022 -55.686 0.000 -1.289
## .Stst3ms (.112) -1.049 0.020 -51.581 0.000 -1.089
## .Stst4sc (.113) -1.424 0.023 -61.220 0.000 -1.469
## .Stst7bl (.114) -0.772 0.021 -36.155 0.000 -0.814
## .Stst8rn (.115) -0.882 0.015 -58.847 0.000 -0.912
## .Stst11r (.116) -1.240 0.021 -57.911 0.000 -1.282
## .Stst12l (.117) -1.001 0.018 -56.687 0.000 -1.036
## .Stst13h (.118) -1.313 0.025 -53.076 0.000 -1.362
## .Stst14b (.119) -0.787 0.019 -42.293 0.000 -0.824
## .Stst15t (.120) -1.091 0.018 -60.046 0.000 -1.127
## .Stst16m (.121) -1.105 0.021 -52.645 0.000 -1.147
## .Stst6ph (.122) -0.791 0.020 -39.416 0.000 -0.830
## .Stst9lc (.123) -0.845 0.022 -37.648 0.000 -0.889
## .Stst10m (.124) -1.003 0.022 -45.946 0.000 -1.045
## .Stst28m (.125) -0.977 0.027 -35.780 0.000 -1.030
## .Sts292D (.126) -0.599 0.024 -24.690 0.000 -0.646
## .Sts303D (.127) -0.731 0.021 -34.887 0.000 -0.772
## .english 1.133 0.049 23.356 0.000 1.038
## .math 0.035 0.038 0.915 0.360 -0.040
## .speed 0.317 0.037 8.637 0.000 0.245
## .info 0.520 0.041 12.697 0.000 0.440
## .science -1.355 0.078 -17.344 0.000 -1.508
## .spatial -0.924 0.052 -17.629 0.000 -1.027
## g 0.089 0.032 2.765 0.006 0.026
## ci.upper Std.lv Std.all
## -1.340 -1.391 -1.523
## -1.160 -1.197 -1.331
## -0.877 -0.920 -0.950
## -1.307 -1.348 -1.375
## -1.380 -1.427 -1.484
## -1.207 -1.259 -1.150
## -1.068 -1.113 -1.021
## -0.935 -0.966 -1.247
## -1.516 -1.566 -1.593
## -1.172 -1.227 -1.133
## -1.297 -1.347 -1.177
## -0.898 -0.941 -0.961
## -1.188 -1.221 -1.613
## -0.974 -1.006 -1.428
## -0.796 -0.866 -0.536
## 0.024 -0.028 -0.022
## -0.340 -0.389 -0.339
## -1.201 -1.245 -1.381
## -1.009 -1.049 -1.175
## -1.378 -1.424 -1.611
## -0.730 -0.772 -0.906
## -0.853 -0.882 -1.061
## -1.198 -1.240 -1.302
## -0.967 -1.001 -1.184
## -1.265 -1.313 -1.191
## -0.751 -0.787 -0.904
## -1.056 -1.091 -1.260
## -1.064 -1.105 -1.172
## -0.752 -0.791 -1.203
## -0.801 -0.845 -0.863
## -0.960 -1.003 -1.547
## -0.923 -0.977 -1.519
## -0.551 -0.599 -0.607
## -0.690 -0.731 -0.944
## 1.228 0.554 0.554
## 0.110 0.019 0.019
## 0.389 0.303 0.303
## 0.600 0.187 0.187
## -1.202 -0.788 -0.788
## -0.821 -0.739 -0.739
## 0.152 0.101 0.101
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.256 0.007 35.227 0.000 0.242
## .Stst19dsgsdwrd 0.399 0.011 36.551 0.000 0.377
## .Stest20spellng 0.518 0.014 36.748 0.000 0.490
## .Stest21cptlztn 0.455 0.013 33.725 0.000 0.429
## .Stest22puncttn 0.306 0.010 29.580 0.000 0.286
## .Stest23english 0.551 0.017 32.859 0.000 0.518
## .Stest24exprssn 0.788 0.021 37.394 0.000 0.747
## .Stst25wrdfnctn 0.374 0.010 37.156 0.000 0.354
## .Stst26rdngcmpr 0.210 0.007 29.319 0.000 0.196
## .Stst31bstrctrs 0.621 0.018 35.194 0.000 0.586
## .Stst34rthcmptt 0.700 0.027 26.212 0.000 0.647
## .Stest5math 0.604 0.017 35.811 0.000 0.571
## .Stst32rthrsnng 0.279 0.008 33.327 0.000 0.263
## .Stst33hghschlm 0.190 0.007 27.764 0.000 0.177
## .Stest35tblrdng 1.352 0.067 20.125 0.000 1.220
## .Stst36clrclchc 0.976 0.034 28.957 0.000 0.910
## .Stst37bjctnspc 0.740 0.026 28.091 0.000 0.689
## .Stest2literatr 0.245 0.007 35.547 0.000 0.231
## .Stest3music 0.347 0.009 37.486 0.000 0.329
## .Stest4soclstds 0.257 0.007 34.632 0.000 0.243
## .Stst7blgclscnc 0.471 0.012 39.174 0.000 0.447
## .Stest8aerontcs 0.643 0.011 57.674 0.000 0.621
## .Stest11art 0.398 0.011 37.032 0.000 0.377
## .Stest12law 0.425 0.011 40.081 0.000 0.404
## .Stest13health 0.605 0.015 40.428 0.000 0.576
## .Stest14bible 0.433 0.013 33.863 0.000 0.408
## .Stest15theater 0.415 0.011 38.067 0.000 0.394
## .Stest16mscllns 0.466 0.012 37.861 0.000 0.442
## .Stst6physclscn 0.249 0.008 30.912 0.000 0.234
## .Stest9elctrncs 0.771 0.020 38.634 0.000 0.732
## .Stest10mechncs 0.239 0.007 34.005 0.000 0.225
## .Stst28mchnclrs 0.215 0.008 28.545 0.000 0.200
## .Stst29vslztn2D 0.702 0.020 35.160 0.000 0.663
## .Stst30vslztn3D 0.389 0.012 33.211 0.000 0.366
## .english 0.953 0.084 11.318 0.000 0.788
## .math 0.677 0.088 7.680 0.000 0.504
## .speed 0.985 0.062 15.801 0.000 0.863
## .info 1.299 0.138 9.445 0.000 1.029
## .science 0.641 0.102 6.292 0.000 0.441
## .spatial 0.622 0.078 7.973 0.000 0.469
## g 0.780 0.036 21.870 0.000 0.710
## ci.upper Std.lv Std.all
## 0.270 0.256 0.307
## 0.420 0.399 0.493
## 0.545 0.518 0.552
## 0.481 0.455 0.473
## 0.326 0.306 0.331
## 0.584 0.551 0.460
## 0.829 0.788 0.663
## 0.394 0.374 0.624
## 0.224 0.210 0.218
## 0.655 0.621 0.530
## 0.752 0.700 0.535
## 0.637 0.604 0.630
## 0.296 0.279 0.488
## 0.204 0.190 0.383
## 1.484 1.352 0.518
## 1.042 0.976 0.587
## 0.792 0.740 0.563
## 0.258 0.245 0.301
## 0.365 0.347 0.436
## 0.272 0.257 0.329
## 0.494 0.471 0.648
## 0.664 0.643 0.930
## 0.419 0.398 0.439
## 0.446 0.425 0.595
## 0.635 0.605 0.498
## 0.458 0.433 0.572
## 0.437 0.415 0.553
## 0.490 0.466 0.524
## 0.265 0.249 0.577
## 0.810 0.771 0.803
## 0.253 0.239 0.569
## 0.229 0.215 0.519
## 0.741 0.702 0.721
## 0.412 0.389 0.648
## 1.118 0.228 0.228
## 0.850 0.195 0.195
## 1.107 0.900 0.900
## 1.568 0.168 0.168
## 0.841 0.217 0.217
## 0.775 0.398 0.398
## 0.850 1.000 1.000
lavTestScore(scalar, release = 49:82) # X2 test for released constraints among the 34 intercepts
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 1870.563 34 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p94. == .p228. 0.984 1 0.321
## 2 .p95. == .p229. 22.736 1 0.000
## 3 .p96. == .p230. 64.881 1 0.000
## 4 .p97. == .p231. 1.773 1 0.183
## 5 .p98. == .p232. 2.647 1 0.104
## 6 .p99. == .p233. 0.079 1 0.779
## 7 .p100. == .p234. 0.071 1 0.790
## 8 .p101. == .p235. 10.898 1 0.001
## 9 .p102. == .p236. 31.273 1 0.000
## 10 .p103. == .p237. 33.346 1 0.000
## 11 .p104. == .p238. 7.343 1 0.007
## 12 .p105. == .p239. 33.179 1 0.000
## 13 .p106. == .p240. 25.997 1 0.000
## 14 .p107. == .p241. 0.951 1 0.329
## 15 .p108. == .p242. 14.016 1 0.000
## 16 .p109. == .p243. 34.970 1 0.000
## 17 .p110. == .p244. 3.526 1 0.060
## 18 .p111. == .p245. 0.004 1 0.949
## 19 .p112. == .p246. 39.740 1 0.000
## 20 .p113. == .p247. 128.978 1 0.000
## 21 .p114. == .p248. 4.703 1 0.030
## 22 .p115. == .p249. 257.061 1 0.000
## 23 .p116. == .p250. 0.598 1 0.439
## 24 .p117. == .p251. 52.507 1 0.000
## 25 .p118. == .p252. 88.591 1 0.000
## 26 .p119. == .p253. 87.230 1 0.000
## 27 .p120. == .p254. 117.717 1 0.000
## 28 .p121. == .p255. 14.195 1 0.000
## 29 .p122. == .p256. 327.321 1 0.000
## 30 .p123. == .p257. 0.364 1 0.546
## 31 .p124. == .p258. 456.887 1 0.000
## 32 .p125. == .p259. 305.502 1 0.000
## 33 .p126. == .p260. 15.182 1 0.000
## 34 .p127. == .p261. 125.922 1 0.000
scalar2<-cfa(chc.hof.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts"), group.partial=c("g=~science", "info=~Stest8aeronautics", "spatial=~Stest28mechanicalreasoning", "info=~Stest4socialstudies", "Stest10mechanics~1", "Stest8aeronautics~1", "Stest28mechanicalreasoning~1", "Stest4socialstudies~1", "Stest15theater~1"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov)
## does not appear to be positive definite! The smallest eigenvalue
## (= 4.871606e-15) is close to zero. This may be a symptom that the
## model is not identified.
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 7028.391 1081.000 0.000 0.947 0.043 0.049
## aic bic
## 463802.794 464991.098
Mc(scalar2)
## [1] 0.6133785
summary(scalar2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 172 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 254
## Number of equality constraints 77
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 7028.391 6256.646
## Degrees of freedom 1081 1081
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.123
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 3282.726 2922.269
## 1 3745.665 3334.376
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.029 0.008 3.669 0.000 0.014
## Stst19d (.p2.) 0.162 0.011 14.808 0.000 0.141
## Stst20s (.p3.) 0.317 0.012 26.637 0.000 0.294
## Stst21c (.p4.) 0.348 0.012 28.538 0.000 0.324
## Stst22p (.p5.) 0.385 0.013 28.743 0.000 0.359
## Stst23n (.p6.) 0.394 0.014 27.297 0.000 0.366
## Stst24x (.p7.) 0.310 0.012 25.900 0.000 0.286
## Stst25w (.p8.) 0.097 0.009 10.493 0.000 0.079
## Stst26r (.p9.) 0.143 0.009 16.742 0.000 0.127
## Stst31b (.10.) 0.146 0.009 15.451 0.000 0.127
## Stst34r (.11.) 0.136 0.013 10.403 0.000 0.110
## math =~
## Stst5mt (.12.) 0.226 0.014 16.618 0.000 0.199
## Stst25w (.13.) 0.165 0.011 15.007 0.000 0.143
## Stst32r (.14.) 0.297 0.013 22.194 0.000 0.270
## Stst33h (.15.) 0.303 0.014 21.495 0.000 0.275
## Stst34r (.16.) 0.136 0.015 9.136 0.000 0.107
## speed =~
## Stst19d (.17.) 0.179 0.011 16.024 0.000 0.157
## Stst34r (.18.) 0.453 0.020 22.408 0.000 0.413
## Stst35t (.19.) 1.074 0.033 32.925 0.000 1.010
## Stst36c (.20.) 0.796 0.026 30.518 0.000 0.745
## Stst37b (.21.) 0.681 0.023 29.477 0.000 0.635
## info =~
## Stst1vc (.22.) 0.176 0.011 16.269 0.000 0.155
## Stst2lt (.23.) 0.274 0.012 22.908 0.000 0.251
## Stst3ms (.24.) 0.244 0.011 22.549 0.000 0.223
## Stst4sc 0.330 0.014 23.939 0.000 0.303
## Stst7bl (.26.) 0.093 0.009 10.923 0.000 0.077
## Stst8rn 0.208 0.010 20.410 0.000 0.188
## Stst11r (.28.) 0.259 0.011 22.683 0.000 0.237
## Stst12l (.29.) 0.196 0.009 21.617 0.000 0.178
## Stst13h (.30.) 0.284 0.012 23.089 0.000 0.260
## Stst14b (.31.) 0.207 0.009 22.213 0.000 0.189
## Stst15t (.32.) 0.210 0.010 22.001 0.000 0.192
## Stst16m (.33.) 0.237 0.011 21.930 0.000 0.215
## Stst19d (.34.) 0.094 0.008 11.687 0.000 0.078
## Stst26r (.35.) 0.224 0.010 21.612 0.000 0.204
## science =~
## Stst1vc (.36.) 0.144 0.010 14.108 0.000 0.124
## Stst5mt (.37.) 0.116 0.011 10.210 0.000 0.094
## Stst6ph (.38.) 0.264 0.015 18.146 0.000 0.236
## Stst7bl (.39.) 0.155 0.012 13.338 0.000 0.132
## Stst9lc (.40.) 0.260 0.016 16.575 0.000 0.229
## Stst10m (.41.) 0.221 0.013 17.199 0.000 0.196
## spatial =~
## Stst28m 0.487 0.014 35.966 0.000 0.460
## Sts292D (.43.) 0.436 0.017 25.852 0.000 0.403
## Sts303D (.44.) 0.391 0.015 25.973 0.000 0.362
## Stst31b (.45.) 0.411 0.017 23.923 0.000 0.377
## Stst37b (.46.) 0.108 0.013 8.286 0.000 0.082
## g =~
## english (.47.) 1.972 0.078 25.418 0.000 1.820
## math (.48.) 1.793 0.087 20.522 0.000 1.621
## speed (.49.) 0.358 0.023 15.286 0.000 0.312
## info (.50.) 2.745 0.132 20.842 0.000 2.487
## science 2.677 0.169 15.882 0.000 2.347
## spatial (.52.) 1.075 0.047 22.895 0.000 0.983
## ci.upper Std.lv Std.all
##
## 0.045 0.064 0.060
## 0.183 0.358 0.388
## 0.341 0.702 0.690
## 0.372 0.770 0.784
## 0.411 0.852 0.826
## 0.422 0.871 0.738
## 0.333 0.685 0.596
## 0.116 0.215 0.265
## 0.160 0.317 0.302
## 0.164 0.322 0.280
## 0.162 0.301 0.261
##
## 0.253 0.464 0.441
## 0.187 0.339 0.417
## 0.323 0.609 0.746
## 0.331 0.622 0.810
## 0.165 0.279 0.242
##
## 0.201 0.191 0.206
## 0.493 0.481 0.417
## 1.137 1.140 0.682
## 0.847 0.845 0.651
## 0.726 0.723 0.586
##
## 0.198 0.515 0.477
## 0.297 0.801 0.843
## 0.265 0.712 0.772
## 0.357 0.965 0.874
## 0.110 0.273 0.282
## 0.228 0.607 0.599
## 0.282 0.757 0.782
## 0.213 0.572 0.639
## 0.308 0.829 0.752
## 0.225 0.605 0.692
## 0.229 0.614 0.729
## 0.258 0.691 0.692
## 0.109 0.274 0.296
## 0.244 0.654 0.622
##
## 0.164 0.411 0.380
## 0.139 0.333 0.316
## 0.293 0.756 0.836
## 0.178 0.443 0.458
## 0.291 0.743 0.673
## 0.246 0.632 0.723
##
## 0.513 0.715 0.804
## 0.469 0.640 0.589
## 0.421 0.575 0.630
## 0.444 0.603 0.525
## 0.133 0.158 0.128
##
## 2.124 0.892 0.892
## 1.964 0.873 0.873
## 0.404 0.337 0.337
## 3.003 0.940 0.940
## 3.007 0.937 0.937
## 1.167 0.732 0.732
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.94.) -1.172 0.022 -52.858 0.000 -1.215
## .Stst19d (.95.) -1.031 0.016 -64.193 0.000 -1.062
## .Stst20s (.96.) -0.761 0.019 -40.474 0.000 -0.798
## .Stst21c (.97.) -1.174 0.018 -64.403 0.000 -1.210
## .Stst22p (.98.) -1.234 0.020 -61.526 0.000 -1.273
## .Stst23n (.99.) -1.061 0.022 -47.196 0.000 -1.105
## .Stst24x (.100) -0.958 0.020 -47.998 0.000 -0.997
## .Stst25w (.101) -0.842 0.014 -59.591 0.000 -0.870
## .Stst26r (.102) -1.330 0.021 -61.998 0.000 -1.372
## .Stst31b (.103) -1.066 0.023 -46.074 0.000 -1.111
## .Stst34r (.104) -1.175 0.022 -53.367 0.000 -1.218
## .Stst5mt (.105) -0.779 0.020 -39.921 0.000 -0.817
## .Stst32r (.106) -1.085 0.016 -67.607 0.000 -1.117
## .Stst33h (.107) -0.868 0.016 -55.422 0.000 -0.898
## .Stst35t (.108) -0.763 0.033 -23.176 0.000 -0.827
## .Stst36c (.109) 0.047 0.025 1.852 0.064 -0.003
## .Stst37b (.110) -0.310 0.023 -13.383 0.000 -0.355
## .Stst2lt (.111) -1.046 0.019 -54.429 0.000 -1.083
## .Stst3ms (.112) -0.872 0.018 -49.325 0.000 -0.907
## .Stst4sc -1.083 0.023 -46.133 0.000 -1.129
## .Stst7bl (.114) -0.626 0.019 -32.411 0.000 -0.664
## .Stst8rn -0.517 0.022 -23.664 0.000 -0.560
## .Stst11r (.116) -1.051 0.019 -56.671 0.000 -1.088
## .Stst12l (.117) -0.859 0.016 -53.903 0.000 -0.890
## .Stst13h (.118) -1.106 0.021 -51.960 0.000 -1.148
## .Stst14b (.119) -0.636 0.016 -38.855 0.000 -0.668
## .Stst15t -1.025 0.017 -59.426 0.000 -1.059
## .Stst16m (.121) -0.933 0.019 -50.160 0.000 -0.970
## .Stst6ph (.122) -0.697 0.019 -37.256 0.000 -0.734
## .Stst9lc (.123) -0.750 0.021 -34.981 0.000 -0.792
## .Stst10m -0.656 0.019 -33.970 0.000 -0.694
## .Stst28m -0.715 0.019 -36.895 0.000 -0.753
## .Sts292D (.126) -0.556 0.021 -26.693 0.000 -0.597
## .Sts303D (.127) -0.696 0.018 -38.383 0.000 -0.732
## ci.upper Std.lv Std.all
## -1.128 -1.172 -1.085
## -0.999 -1.031 -1.117
## -0.724 -0.761 -0.748
## -1.138 -1.174 -1.195
## -1.195 -1.234 -1.197
## -1.017 -1.061 -0.899
## -0.919 -0.958 -0.833
## -0.814 -0.842 -1.036
## -1.288 -1.330 -1.265
## -1.020 -1.066 -0.927
## -1.132 -1.175 -1.018
## -0.741 -0.779 -0.740
## -1.054 -1.085 -1.331
## -0.837 -0.868 -1.130
## -0.698 -0.763 -0.456
## 0.097 0.047 0.036
## -0.264 -0.310 -0.251
## -1.008 -1.046 -1.101
## -0.837 -0.872 -0.945
## -1.037 -1.083 -0.980
## -0.589 -0.626 -0.647
## -0.475 -0.517 -0.511
## -1.015 -1.051 -1.086
## -0.828 -0.859 -0.960
## -1.065 -1.106 -1.004
## -0.604 -0.636 -0.728
## -0.991 -1.025 -1.216
## -0.897 -0.933 -0.934
## -0.661 -0.697 -0.772
## -0.708 -0.750 -0.679
## -0.618 -0.656 -0.750
## -0.677 -0.715 -0.804
## -0.515 -0.556 -0.511
## -0.660 -0.696 -0.763
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.255 0.009 27.897 0.000 0.237
## .Stst19dsgsdwrd 0.374 0.014 27.215 0.000 0.347
## .Stest20spellng 0.542 0.017 31.055 0.000 0.507
## .Stest21cptlztn 0.371 0.015 24.536 0.000 0.342
## .Stest22puncttn 0.337 0.012 27.654 0.000 0.313
## .Stest23english 0.636 0.024 26.850 0.000 0.589
## .Stest24exprssn 0.852 0.026 33.351 0.000 0.802
## .Stst25wrdfnctn 0.386 0.012 32.655 0.000 0.363
## .Stst26rdngcmpr 0.229 0.009 25.416 0.000 0.212
## .Stst31bstrctrs 0.599 0.022 26.990 0.000 0.555
## .Stst34rthcmptt 0.634 0.030 21.054 0.000 0.575
## .Stest5math 0.530 0.020 26.764 0.000 0.492
## .Stst32rthrsnng 0.295 0.011 26.544 0.000 0.273
## .Stst33hghschlm 0.203 0.009 22.578 0.000 0.186
## .Stest35tblrdng 1.494 0.076 19.655 0.000 1.345
## .Stst36clrclchc 0.972 0.043 22.675 0.000 0.888
## .Stst37bjctnspc 0.918 0.034 26.610 0.000 0.850
## .Stest2literatr 0.261 0.009 29.672 0.000 0.244
## .Stest3music 0.344 0.012 28.979 0.000 0.321
## .Stest4soclstds 0.289 0.011 27.098 0.000 0.268
## .Stst7blgclscnc 0.454 0.014 32.542 0.000 0.426
## .Stest8aerontcs 0.658 0.018 37.065 0.000 0.623
## .Stest11art 0.363 0.012 29.855 0.000 0.339
## .Stest12law 0.474 0.015 32.621 0.000 0.445
## .Stest13health 0.527 0.016 32.158 0.000 0.495
## .Stest14bible 0.399 0.013 29.601 0.000 0.373
## .Stest15theater 0.333 0.011 30.674 0.000 0.312
## .Stest16mscllns 0.521 0.017 30.812 0.000 0.487
## .Stst6physclscn 0.245 0.010 23.830 0.000 0.225
## .Stest9elctrncs 0.667 0.027 24.448 0.000 0.613
## .Stest10mechncs 0.366 0.013 27.864 0.000 0.340
## .Stst28mchnclrs 0.280 0.016 17.926 0.000 0.249
## .Stst29vslztn2D 0.773 0.027 29.101 0.000 0.721
## .Stst30vslztn3D 0.501 0.017 28.849 0.000 0.467
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.273 0.255 0.218
## 0.401 0.374 0.439
## 0.576 0.542 0.524
## 0.401 0.371 0.385
## 0.361 0.337 0.317
## 0.682 0.636 0.456
## 0.902 0.852 0.645
## 0.409 0.386 0.584
## 0.247 0.229 0.207
## 0.642 0.599 0.454
## 0.693 0.634 0.476
## 0.569 0.530 0.478
## 0.316 0.295 0.443
## 0.221 0.203 0.345
## 1.643 1.494 0.535
## 1.056 0.972 0.576
## 0.985 0.918 0.603
## 0.278 0.261 0.289
## 0.367 0.344 0.404
## 0.310 0.289 0.237
## 0.481 0.454 0.484
## 0.692 0.658 0.641
## 0.387 0.363 0.388
## 0.502 0.474 0.592
## 0.559 0.527 0.434
## 0.425 0.399 0.522
## 0.354 0.333 0.469
## 0.554 0.521 0.521
## 0.265 0.245 0.301
## 0.720 0.667 0.547
## 0.391 0.366 0.478
## 0.310 0.280 0.354
## 0.825 0.773 0.653
## 0.535 0.501 0.603
## 1.000 0.205 0.205
## 1.000 0.237 0.237
## 1.000 0.886 0.886
## 1.000 0.117 0.117
## 1.000 0.122 0.122
## 1.000 0.464 0.464
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.029 0.008 3.669 0.000 0.014
## Stst19d (.p2.) 0.162 0.011 14.808 0.000 0.141
## Stst20s (.p3.) 0.317 0.012 26.637 0.000 0.294
## Stst21c (.p4.) 0.348 0.012 28.538 0.000 0.324
## Stst22p (.p5.) 0.385 0.013 28.743 0.000 0.359
## Stst23n (.p6.) 0.394 0.014 27.297 0.000 0.366
## Stst24x (.p7.) 0.310 0.012 25.900 0.000 0.286
## Stst25w (.p8.) 0.097 0.009 10.493 0.000 0.079
## Stst26r (.p9.) 0.143 0.009 16.742 0.000 0.127
## Stst31b (.10.) 0.146 0.009 15.451 0.000 0.127
## Stst34r (.11.) 0.136 0.013 10.403 0.000 0.110
## math =~
## Stst5mt (.12.) 0.226 0.014 16.618 0.000 0.199
## Stst25w (.13.) 0.165 0.011 15.007 0.000 0.143
## Stst32r (.14.) 0.297 0.013 22.194 0.000 0.270
## Stst33h (.15.) 0.303 0.014 21.495 0.000 0.275
## Stst34r (.16.) 0.136 0.015 9.136 0.000 0.107
## speed =~
## Stst19d (.17.) 0.179 0.011 16.024 0.000 0.157
## Stst34r (.18.) 0.453 0.020 22.408 0.000 0.413
## Stst35t (.19.) 1.074 0.033 32.925 0.000 1.010
## Stst36c (.20.) 0.796 0.026 30.518 0.000 0.745
## Stst37b (.21.) 0.681 0.023 29.477 0.000 0.635
## info =~
## Stst1vc (.22.) 0.176 0.011 16.269 0.000 0.155
## Stst2lt (.23.) 0.274 0.012 22.908 0.000 0.251
## Stst3ms (.24.) 0.244 0.011 22.549 0.000 0.223
## Stst4sc 0.269 0.012 22.210 0.000 0.246
## Stst7bl (.26.) 0.093 0.009 10.923 0.000 0.077
## Stst8rn 0.093 0.007 14.122 0.000 0.080
## Stst11r (.28.) 0.259 0.011 22.683 0.000 0.237
## Stst12l (.29.) 0.196 0.009 21.617 0.000 0.178
## Stst13h (.30.) 0.284 0.012 23.089 0.000 0.260
## Stst14b (.31.) 0.207 0.009 22.213 0.000 0.189
## Stst15t (.32.) 0.210 0.010 22.001 0.000 0.192
## Stst16m (.33.) 0.237 0.011 21.930 0.000 0.215
## Stst19d (.34.) 0.094 0.008 11.687 0.000 0.078
## Stst26r (.35.) 0.224 0.010 21.612 0.000 0.204
## science =~
## Stst1vc (.36.) 0.144 0.010 14.108 0.000 0.124
## Stst5mt (.37.) 0.116 0.011 10.210 0.000 0.094
## Stst6ph (.38.) 0.264 0.015 18.146 0.000 0.236
## Stst7bl (.39.) 0.155 0.012 13.338 0.000 0.132
## Stst9lc (.40.) 0.260 0.016 16.575 0.000 0.229
## Stst10m (.41.) 0.221 0.013 17.199 0.000 0.196
## spatial =~
## Stst28m 0.301 0.016 19.376 0.000 0.271
## Sts292D (.43.) 0.436 0.017 25.852 0.000 0.403
## Sts303D (.44.) 0.391 0.015 25.973 0.000 0.362
## Stst31b (.45.) 0.411 0.017 23.923 0.000 0.377
## Stst37b (.46.) 0.108 0.013 8.286 0.000 0.082
## g =~
## english (.47.) 1.972 0.078 25.418 0.000 1.820
## math (.48.) 1.793 0.087 20.522 0.000 1.621
## speed (.49.) 0.358 0.023 15.286 0.000 0.312
## info (.50.) 2.745 0.132 20.842 0.000 2.487
## science 1.711 0.106 16.095 0.000 1.503
## spatial (.52.) 1.075 0.047 22.895 0.000 0.983
## ci.upper Std.lv Std.all
##
## 0.045 0.060 0.066
## 0.183 0.332 0.369
## 0.341 0.650 0.671
## 0.372 0.713 0.727
## 0.411 0.789 0.819
## 0.422 0.807 0.736
## 0.333 0.634 0.581
## 0.116 0.200 0.258
## 0.160 0.294 0.299
## 0.164 0.298 0.275
## 0.162 0.279 0.244
##
## 0.253 0.414 0.424
## 0.187 0.302 0.390
## 0.323 0.543 0.718
## 0.331 0.555 0.787
## 0.165 0.249 0.218
##
## 0.201 0.188 0.209
## 0.493 0.474 0.414
## 1.137 1.123 0.694
## 0.847 0.832 0.645
## 0.726 0.712 0.621
##
## 0.198 0.485 0.533
## 0.297 0.753 0.836
## 0.265 0.670 0.751
## 0.293 0.740 0.828
## 0.110 0.257 0.302
## 0.106 0.256 0.308
## 0.282 0.712 0.748
## 0.213 0.538 0.636
## 0.308 0.780 0.708
## 0.225 0.569 0.654
## 0.229 0.578 0.670
## 0.258 0.650 0.689
## 0.109 0.257 0.286
## 0.244 0.615 0.626
##
## 0.164 0.254 0.279
## 0.139 0.206 0.211
## 0.293 0.467 0.697
## 0.178 0.274 0.322
## 0.291 0.459 0.462
## 0.246 0.391 0.625
##
## 0.332 0.388 0.631
## 0.469 0.562 0.563
## 0.421 0.504 0.639
## 0.444 0.529 0.488
## 0.133 0.139 0.121
##
## 2.124 0.880 0.880
## 1.964 0.894 0.894
## 0.404 0.313 0.313
## 3.003 0.913 0.913
## 1.920 0.885 0.885
## 1.167 0.763 0.763
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.94.) -1.172 0.022 -52.858 0.000 -1.215
## .Stst19d (.95.) -1.031 0.016 -64.193 0.000 -1.062
## .Stst20s (.96.) -0.761 0.019 -40.474 0.000 -0.798
## .Stst21c (.97.) -1.174 0.018 -64.403 0.000 -1.210
## .Stst22p (.98.) -1.234 0.020 -61.526 0.000 -1.273
## .Stst23n (.99.) -1.061 0.022 -47.196 0.000 -1.105
## .Stst24x (.100) -0.958 0.020 -47.998 0.000 -0.997
## .Stst25w (.101) -0.842 0.014 -59.591 0.000 -0.870
## .Stst26r (.102) -1.330 0.021 -61.998 0.000 -1.372
## .Stst31b (.103) -1.066 0.023 -46.074 0.000 -1.111
## .Stst34r (.104) -1.175 0.022 -53.367 0.000 -1.218
## .Stst5mt (.105) -0.779 0.020 -39.921 0.000 -0.817
## .Stst32r (.106) -1.085 0.016 -67.607 0.000 -1.117
## .Stst33h (.107) -0.868 0.016 -55.422 0.000 -0.898
## .Stst35t (.108) -0.763 0.033 -23.176 0.000 -0.827
## .Stst36c (.109) 0.047 0.025 1.852 0.064 -0.003
## .Stst37b (.110) -0.310 0.023 -13.383 0.000 -0.355
## .Stst2lt (.111) -1.046 0.019 -54.429 0.000 -1.083
## .Stst3ms (.112) -0.872 0.018 -49.325 0.000 -0.907
## .Stst4sc -1.287 0.020 -62.830 0.000 -1.327
## .Stst7bl (.114) -0.626 0.019 -32.411 0.000 -0.664
## .Stst8rn -0.947 0.015 -62.317 0.000 -0.977
## .Stst11r (.116) -1.051 0.019 -56.671 0.000 -1.088
## .Stst12l (.117) -0.859 0.016 -53.903 0.000 -0.890
## .Stst13h (.118) -1.106 0.021 -51.960 0.000 -1.148
## .Stst14b (.119) -0.636 0.016 -38.855 0.000 -0.668
## .Stst15t -0.867 0.018 -47.929 0.000 -0.902
## .Stst16m (.121) -0.933 0.019 -50.160 0.000 -0.970
## .Stst6ph (.122) -0.697 0.019 -37.256 0.000 -0.734
## .Stst9lc (.123) -0.750 0.021 -34.981 0.000 -0.792
## .Stst10m -1.083 0.019 -56.831 0.000 -1.121
## .Stst28m -1.093 0.019 -56.737 0.000 -1.131
## .Sts292D (.126) -0.556 0.021 -26.693 0.000 -0.597
## .Sts303D (.127) -0.696 0.018 -38.383 0.000 -0.732
## .english 1.040 0.046 22.576 0.000 0.949
## .math -0.048 0.037 -1.311 0.190 -0.120
## .speed 0.294 0.036 8.075 0.000 0.222
## .info 0.381 0.039 9.879 0.000 0.305
## .science -1.106 0.068 -16.345 0.000 -1.238
## .spatial -0.636 0.045 -14.043 0.000 -0.725
## g -0.119 0.028 -4.209 0.000 -0.175
## ci.upper Std.lv Std.all
## -1.128 -1.172 -1.288
## -0.999 -1.031 -1.146
## -0.724 -0.761 -0.785
## -1.138 -1.174 -1.196
## -1.195 -1.234 -1.281
## -1.017 -1.061 -0.968
## -0.919 -0.958 -0.878
## -0.814 -0.842 -1.087
## -1.288 -1.330 -1.354
## -1.020 -1.066 -0.983
## -1.132 -1.175 -1.026
## -0.741 -0.779 -0.798
## -1.054 -1.085 -1.434
## -0.837 -0.868 -1.231
## -0.698 -0.763 -0.472
## 0.097 0.047 0.037
## -0.264 -0.310 -0.270
## -1.008 -1.046 -1.161
## -0.837 -0.872 -0.978
## -1.247 -1.287 -1.439
## -0.589 -0.626 -0.737
## -0.917 -0.947 -1.139
## -1.015 -1.051 -1.105
## -0.828 -0.859 -1.017
## -1.065 -1.106 -1.005
## -0.604 -0.636 -0.731
## -0.831 -0.867 -1.006
## -0.897 -0.933 -0.990
## -0.661 -0.697 -1.040
## -0.708 -0.750 -0.755
## -1.046 -1.083 -1.733
## -1.055 -1.093 -1.778
## -0.515 -0.556 -0.556
## -0.660 -0.696 -0.882
## 1.130 0.508 0.508
## 0.024 -0.026 -0.026
## 0.365 0.281 0.281
## 0.457 0.139 0.139
## -0.973 -0.626 -0.626
## -0.547 -0.494 -0.494
## -0.064 -0.131 -0.131
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.255 0.007 35.076 0.000 0.241
## .Stst19dsgsdwrd 0.399 0.011 36.515 0.000 0.377
## .Stest20spellng 0.516 0.014 36.708 0.000 0.489
## .Stest21cptlztn 0.455 0.014 33.697 0.000 0.429
## .Stest22puncttn 0.305 0.010 29.467 0.000 0.285
## .Stest23english 0.550 0.017 32.842 0.000 0.517
## .Stest24exprssn 0.788 0.021 37.417 0.000 0.747
## .Stst25wrdfnctn 0.374 0.010 37.157 0.000 0.354
## .Stst26rdngcmpr 0.210 0.007 29.338 0.000 0.196
## .Stst31bstrctrs 0.595 0.017 34.301 0.000 0.561
## .Stst34rthcmptt 0.698 0.027 26.182 0.000 0.646
## .Stest5math 0.604 0.017 36.123 0.000 0.571
## .Stst32rthrsnng 0.278 0.008 33.137 0.000 0.261
## .Stst33hghschlm 0.189 0.007 27.555 0.000 0.176
## .Stest35tblrdng 1.354 0.068 19.988 0.000 1.222
## .Stst36clrclchc 0.972 0.034 28.515 0.000 0.905
## .Stst37bjctnspc 0.741 0.026 28.176 0.000 0.690
## .Stest2literatr 0.245 0.007 35.575 0.000 0.231
## .Stest3music 0.347 0.009 37.530 0.000 0.329
## .Stest4soclstds 0.252 0.007 34.577 0.000 0.238
## .Stst7blgclscnc 0.468 0.012 39.307 0.000 0.444
## .Stest8aerontcs 0.626 0.011 58.928 0.000 0.605
## .Stest11art 0.398 0.011 37.035 0.000 0.377
## .Stest12law 0.425 0.011 40.089 0.000 0.404
## .Stest13health 0.605 0.015 40.482 0.000 0.576
## .Stest14bible 0.433 0.013 33.904 0.000 0.408
## .Stest15theater 0.409 0.011 38.644 0.000 0.389
## .Stest16mscllns 0.466 0.012 37.906 0.000 0.442
## .Stst6physclscn 0.231 0.007 31.191 0.000 0.217
## .Stest9elctrncs 0.776 0.020 37.884 0.000 0.736
## .Stest10mechncs 0.238 0.006 37.081 0.000 0.225
## .Stst28mchnclrs 0.227 0.007 33.016 0.000 0.214
## .Stst29vslztn2D 0.682 0.020 34.982 0.000 0.644
## .Stst30vslztn3D 0.369 0.011 33.299 0.000 0.347
## .english 0.944 0.083 11.342 0.000 0.781
## .math 0.672 0.087 7.742 0.000 0.502
## .speed 0.987 0.062 15.800 0.000 0.864
## .info 1.253 0.131 9.600 0.000 0.997
## .science 0.675 0.100 6.739 0.000 0.479
## .spatial 0.694 0.069 10.024 0.000 0.559
## g 0.835 0.036 23.210 0.000 0.765
## ci.upper Std.lv Std.all
## 0.269 0.255 0.308
## 0.420 0.399 0.493
## 0.544 0.516 0.550
## 0.481 0.455 0.472
## 0.326 0.305 0.329
## 0.583 0.550 0.458
## 0.829 0.788 0.662
## 0.394 0.374 0.623
## 0.224 0.210 0.218
## 0.629 0.595 0.506
## 0.750 0.698 0.533
## 0.636 0.604 0.634
## 0.294 0.278 0.485
## 0.203 0.189 0.380
## 1.487 1.354 0.518
## 1.039 0.972 0.584
## 0.793 0.741 0.564
## 0.258 0.245 0.302
## 0.365 0.347 0.436
## 0.267 0.252 0.315
## 0.491 0.468 0.648
## 0.647 0.626 0.905
## 0.420 0.398 0.440
## 0.446 0.425 0.595
## 0.634 0.605 0.499
## 0.458 0.433 0.572
## 0.430 0.409 0.551
## 0.491 0.466 0.525
## 0.246 0.231 0.515
## 0.816 0.776 0.786
## 0.251 0.238 0.609
## 0.241 0.227 0.602
## 0.721 0.682 0.684
## 0.391 0.369 0.592
## 1.108 0.225 0.225
## 0.843 0.200 0.200
## 1.109 0.902 0.902
## 1.509 0.166 0.166
## 0.871 0.216 0.216
## 0.830 0.418 0.418
## 0.906 1.000 1.000
lavTestScore(scalar2, release = 49:77) # X2 test for released constraints among the 34 intercepts
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 531.718 29 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p94. == .p228. 12.090 1 0.001
## 2 .p95. == .p229. 21.619 1 0.000
## 3 .p96. == .p230. 66.437 1 0.000
## 4 .p97. == .p231. 0.747 1 0.387
## 5 .p98. == .p232. 1.046 1 0.307
## 6 .p99. == .p233. 0.014 1 0.906
## 7 .p100. == .p234. 0.263 1 0.608
## 8 .p101. == .p235. 12.190 1 0.000
## 9 .p102. == .p236. 35.337 1 0.000
## 10 .p103. == .p237. 0.280 1 0.597
## 11 .p104. == .p238. 5.215 1 0.022
## 12 .p105. == .p239. 14.490 1 0.000
## 13 .p106. == .p240. 22.600 1 0.000
## 14 .p107. == .p241. 2.300 1 0.129
## 15 .p108. == .p242. 10.863 1 0.001
## 16 .p109. == .p243. 38.076 1 0.000
## 17 .p110. == .p244. 0.456 1 0.499
## 18 .p111. == .p245. 0.495 1 0.482
## 19 .p112. == .p246. 33.528 1 0.000
## 20 .p114. == .p248. 1.420 1 0.233
## 21 .p116. == .p250. 1.808 1 0.179
## 22 .p117. == .p251. 57.819 1 0.000
## 23 .p118. == .p252. 79.953 1 0.000
## 24 .p119. == .p253. 79.593 1 0.000
## 25 .p121. == .p255. 17.694 1 0.000
## 26 .p122. == .p256. 55.196 1 0.000
## 27 .p123. == .p257. 58.923 1 0.000
## 28 .p126. == .p260. 16.152 1 0.000
## 29 .p127. == .p261. 10.394 1 0.001
strict<-cfa(chc.hof.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("g=~science", "info=~Stest8aeronautics", "spatial=~Stest28mechanicalreasoning", "info=~Stest4socialstudies", "Stest10mechanics~1", "Stest8aeronautics~1", "Stest28mechanicalreasoning~1", "Stest4socialstudies~1", "Stest15theater~1"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov)
## does not appear to be positive definite! The smallest eigenvalue
## (= 1.049734e-14) is close to zero. This may be a symptom that the
## model is not identified.
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 7408.580 1115.000 0.000 0.944 0.043 0.051
## aic bic
## 464114.983 465075.026
Mc(strict)
## [1] 0.5961733
chc.hof<-cfa(chc.hof.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("g=~science", "info=~Stest8aeronautics", "spatial=~Stest28mechanicalreasoning", "info=~Stest4socialstudies", "Stest10mechanics~1", "Stest8aeronautics~1", "Stest28mechanicalreasoning~1", "Stest4socialstudies~1", "Stest15theater~1"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov)
## does not appear to be positive definite! The smallest eigenvalue
## (= 8.182673e-16) is close to zero. This may be a symptom that the
## model is not identified.
fitMeasures(chc.hof, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 7091.007 1088.000 0.000 0.946 0.043 0.057
## aic bic
## 463851.411 464992.720
Mc(chc.hof)
## [1] 0.6105813
summary(chc.hof, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 114 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 247
## Number of equality constraints 77
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 7091.007 6306.523
## Degrees of freedom 1088 1088
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.124
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 3325.404 2957.512
## 1 3765.603 3349.011
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.028 0.008 3.643 0.000 0.013
## Stst19d (.p2.) 0.160 0.010 15.585 0.000 0.140
## Stst20s (.p3.) 0.312 0.008 37.081 0.000 0.295
## Stst21c (.p4.) 0.343 0.008 41.056 0.000 0.326
## Stst22p (.p5.) 0.378 0.009 42.046 0.000 0.361
## Stst23n (.p6.) 0.387 0.010 38.636 0.000 0.367
## Stst24x (.p7.) 0.304 0.009 34.712 0.000 0.287
## Stst25w (.p8.) 0.095 0.009 10.984 0.000 0.078
## Stst26r (.p9.) 0.141 0.008 18.390 0.000 0.126
## Stst31b (.10.) 0.144 0.009 16.746 0.000 0.127
## Stst34r (.11.) 0.134 0.012 10.811 0.000 0.110
## math =~
## Stst5mt (.12.) 0.203 0.011 18.208 0.000 0.181
## Stst25w (.13.) 0.151 0.010 15.364 0.000 0.131
## Stst32r (.14.) 0.267 0.009 30.808 0.000 0.250
## Stst33h (.15.) 0.273 0.009 29.255 0.000 0.255
## Stst34r (.16.) 0.123 0.013 9.547 0.000 0.098
## speed =~
## Stst19d (.17.) 0.179 0.011 16.195 0.000 0.157
## Stst34r (.18.) 0.452 0.019 24.208 0.000 0.415
## Stst35t (.19.) 1.069 0.025 42.807 0.000 1.020
## Stst36c (.20.) 0.792 0.021 37.572 0.000 0.751
## Stst37b (.21.) 0.678 0.019 36.363 0.000 0.641
## info =~
## Stst1vc (.22.) 0.187 0.010 18.522 0.000 0.168
## Stst2lt (.23.) 0.292 0.008 34.571 0.000 0.275
## Stst3ms (.24.) 0.259 0.008 33.152 0.000 0.244
## Stst4sc 0.351 0.010 34.523 0.000 0.331
## Stst7bl (.26.) 0.099 0.009 11.581 0.000 0.082
## Stst8rn 0.221 0.008 26.335 0.000 0.205
## Stst11r (.28.) 0.276 0.008 33.069 0.000 0.259
## Stst12l (.29.) 0.208 0.007 30.964 0.000 0.195
## Stst13h (.30.) 0.302 0.009 34.649 0.000 0.285
## Stst14b (.31.) 0.220 0.007 31.904 0.000 0.207
## Stst15t (.32.) 0.224 0.007 31.409 0.000 0.210
## Stst16m (.33.) 0.252 0.008 33.195 0.000 0.237
## Stst19d (.34.) 0.099 0.008 12.527 0.000 0.084
## Stst26r (.35.) 0.238 0.008 30.707 0.000 0.223
## science =~
## Stst1vc (.36.) 0.127 0.007 17.813 0.000 0.113
## Stst5mt (.37.) 0.104 0.010 10.659 0.000 0.085
## Stst6ph (.38.) 0.232 0.009 25.864 0.000 0.215
## Stst7bl (.39.) 0.136 0.009 15.355 0.000 0.119
## Stst9lc (.40.) 0.228 0.010 22.701 0.000 0.208
## Stst10m (.41.) 0.194 0.008 24.744 0.000 0.179
## spatial =~
## Stst28m 0.464 0.013 36.525 0.000 0.439
## Sts292D (.43.) 0.396 0.012 33.027 0.000 0.373
## Sts303D (.44.) 0.354 0.010 34.427 0.000 0.334
## Stst31b (.45.) 0.373 0.013 28.629 0.000 0.348
## Stst37b (.46.) 0.098 0.012 8.464 0.000 0.075
## g =~
## english (.47.) 1.905 0.053 35.609 0.000 1.800
## math (.48.) 1.883 0.069 27.481 0.000 1.748
## speed (.49.) 0.342 0.021 16.239 0.000 0.300
## info (.50.) 2.453 0.080 30.733 0.000 2.296
## science 2.947 0.130 22.637 0.000 2.692
## spatial (.52.) 1.121 0.037 30.231 0.000 1.049
## ci.upper Std.lv Std.all
##
## 0.044 0.061 0.058
## 0.180 0.344 0.381
## 0.328 0.671 0.673
## 0.359 0.737 0.770
## 0.396 0.814 0.814
## 0.406 0.832 0.722
## 0.321 0.654 0.578
## 0.111 0.203 0.255
## 0.156 0.302 0.297
## 0.161 0.310 0.278
## 0.158 0.288 0.254
##
## 0.225 0.432 0.420
## 0.170 0.321 0.403
## 0.284 0.570 0.721
## 0.292 0.582 0.785
## 0.148 0.262 0.231
##
## 0.200 0.189 0.209
## 0.488 0.477 0.421
## 1.118 1.130 0.679
## 0.833 0.837 0.647
## 0.714 0.716 0.583
##
## 0.207 0.497 0.475
## 0.308 0.772 0.834
## 0.275 0.687 0.761
## 0.371 0.930 0.866
## 0.116 0.262 0.276
## 0.238 0.586 0.586
## 0.292 0.730 0.771
## 0.221 0.551 0.625
## 0.319 0.800 0.740
## 0.234 0.583 0.679
## 0.238 0.592 0.717
## 0.267 0.667 0.679
## 0.115 0.263 0.292
## 0.254 0.631 0.621
##
## 0.140 0.394 0.376
## 0.123 0.323 0.314
## 0.250 0.723 0.823
## 0.154 0.425 0.448
## 0.248 0.710 0.654
## 0.209 0.604 0.705
##
## 0.489 0.697 0.800
## 0.420 0.596 0.558
## 0.374 0.531 0.595
## 0.399 0.561 0.502
## 0.121 0.148 0.120
##
## 2.009 0.885 0.885
## 2.017 0.883 0.883
## 0.383 0.323 0.323
## 2.609 0.926 0.926
## 3.203 0.947 0.947
## 1.194 0.746 0.746
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.94.) -1.171 0.022 -52.773 0.000 -1.215
## .Stst19d (.95.) -1.031 0.016 -64.184 0.000 -1.062
## .Stst20s (.96.) -0.761 0.019 -40.448 0.000 -0.798
## .Stst21c (.97.) -1.174 0.018 -64.402 0.000 -1.210
## .Stst22p (.98.) -1.234 0.020 -61.554 0.000 -1.273
## .Stst23n (.99.) -1.061 0.022 -47.206 0.000 -1.105
## .Stst24x (.100) -0.958 0.020 -48.007 0.000 -0.997
## .Stst25w (.101) -0.841 0.014 -59.367 0.000 -0.869
## .Stst26r (.102) -1.330 0.021 -62.053 0.000 -1.372
## .Stst31b (.103) -1.066 0.023 -46.021 0.000 -1.111
## .Stst34r (.104) -1.175 0.022 -53.388 0.000 -1.218
## .Stst5mt (.105) -0.778 0.019 -39.965 0.000 -0.816
## .Stst32r (.106) -1.086 0.016 -67.831 0.000 -1.117
## .Stst33h (.107) -0.868 0.016 -55.458 0.000 -0.899
## .Stst35t (.108) -0.763 0.033 -23.181 0.000 -0.827
## .Stst36c (.109) 0.047 0.026 1.856 0.063 -0.003
## .Stst37b (.110) -0.309 0.023 -13.337 0.000 -0.355
## .Stst2lt (.111) -1.046 0.019 -54.466 0.000 -1.084
## .Stst3ms (.112) -0.872 0.018 -49.348 0.000 -0.907
## .Stst4sc -1.083 0.023 -46.133 0.000 -1.129
## .Stst7bl (.114) -0.626 0.019 -32.341 0.000 -0.664
## .Stst8rn -0.517 0.022 -23.664 0.000 -0.560
## .Stst11r (.116) -1.051 0.019 -56.712 0.000 -1.088
## .Stst12l (.117) -0.859 0.016 -53.938 0.000 -0.890
## .Stst13h (.118) -1.107 0.021 -51.978 0.000 -1.148
## .Stst14b (.119) -0.636 0.016 -38.868 0.000 -0.669
## .Stst15t -1.025 0.017 -59.426 0.000 -1.059
## .Stst16m (.121) -0.934 0.019 -50.185 0.000 -0.970
## .Stst6ph (.122) -0.697 0.019 -37.238 0.000 -0.734
## .Stst9lc (.123) -0.751 0.021 -35.141 0.000 -0.793
## .Stst10m -0.656 0.019 -33.970 0.000 -0.694
## .Stst28m -0.715 0.019 -36.895 0.000 -0.753
## .Sts292D (.126) -0.556 0.021 -26.632 0.000 -0.596
## .Sts303D (.127) -0.696 0.018 -38.433 0.000 -0.731
## ci.upper Std.lv Std.all
## -1.128 -1.171 -1.120
## -0.999 -1.031 -1.144
## -0.724 -0.761 -0.763
## -1.138 -1.174 -1.227
## -1.195 -1.234 -1.234
## -1.017 -1.061 -0.920
## -0.919 -0.958 -0.846
## -0.813 -0.841 -1.056
## -1.288 -1.330 -1.309
## -1.020 -1.066 -0.953
## -1.132 -1.175 -1.037
## -0.740 -0.778 -0.757
## -1.055 -1.086 -1.374
## -0.837 -0.868 -1.170
## -0.698 -0.763 -0.458
## 0.097 0.047 0.037
## -0.264 -0.309 -0.252
## -1.008 -1.046 -1.130
## -0.837 -0.872 -0.966
## -1.037 -1.083 -1.008
## -0.588 -0.626 -0.660
## -0.475 -0.517 -0.518
## -1.015 -1.051 -1.111
## -0.828 -0.859 -0.974
## -1.065 -1.107 -1.025
## -0.604 -0.636 -0.740
## -0.991 -1.025 -1.240
## -0.897 -0.934 -0.950
## -0.661 -0.697 -0.793
## -0.709 -0.751 -0.692
## -0.618 -0.656 -0.766
## -0.677 -0.715 -0.820
## -0.515 -0.556 -0.521
## -0.660 -0.696 -0.780
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.256 0.009 27.902 0.000 0.238
## .Stst19dsgsdwrd 0.374 0.014 27.189 0.000 0.347
## .Stest20spellng 0.543 0.017 31.098 0.000 0.509
## .Stest21cptlztn 0.372 0.015 24.499 0.000 0.342
## .Stest22puncttn 0.337 0.012 27.837 0.000 0.314
## .Stest23english 0.637 0.024 26.846 0.000 0.590
## .Stest24exprssn 0.853 0.025 33.467 0.000 0.803
## .Stst25wrdfnctn 0.387 0.012 32.709 0.000 0.364
## .Stst26rdngcmpr 0.230 0.009 25.464 0.000 0.212
## .Stst31bstrctrs 0.609 0.022 27.896 0.000 0.566
## .Stst34rthcmptt 0.636 0.030 20.979 0.000 0.576
## .Stest5math 0.533 0.020 26.734 0.000 0.494
## .Stst32rthrsnng 0.300 0.011 26.969 0.000 0.278
## .Stst33hghschlm 0.211 0.009 23.598 0.000 0.194
## .Stest35tblrdng 1.492 0.076 19.642 0.000 1.343
## .Stst36clrclchc 0.974 0.042 23.237 0.000 0.891
## .Stst37bjctnspc 0.921 0.034 26.976 0.000 0.854
## .Stest2literatr 0.260 0.009 29.705 0.000 0.243
## .Stest3music 0.344 0.012 28.970 0.000 0.321
## .Stest4soclstds 0.289 0.011 27.099 0.000 0.268
## .Stst7blgclscnc 0.455 0.014 32.592 0.000 0.428
## .Stest8aerontcs 0.657 0.018 37.075 0.000 0.622
## .Stest11art 0.363 0.012 29.834 0.000 0.339
## .Stest12law 0.474 0.015 32.626 0.000 0.445
## .Stest13health 0.527 0.016 32.159 0.000 0.495
## .Stest14bible 0.399 0.013 29.601 0.000 0.372
## .Stest15theater 0.333 0.011 30.662 0.000 0.311
## .Stest16mscllns 0.520 0.017 30.833 0.000 0.487
## .Stst6physclscn 0.250 0.010 24.448 0.000 0.230
## .Stest9elctrncs 0.675 0.027 25.020 0.000 0.622
## .Stest10mechncs 0.369 0.013 28.410 0.000 0.343
## .Stst28mchnclrs 0.274 0.015 17.973 0.000 0.244
## .Stst29vslztn2D 0.784 0.026 30.205 0.000 0.733
## .Stst30vslztn3D 0.514 0.017 30.506 0.000 0.481
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.274 0.256 0.234
## 0.401 0.374 0.461
## 0.577 0.543 0.547
## 0.402 0.372 0.406
## 0.361 0.337 0.337
## 0.683 0.637 0.479
## 0.903 0.853 0.666
## 0.411 0.387 0.611
## 0.247 0.230 0.223
## 0.651 0.609 0.487
## 0.695 0.636 0.496
## 0.572 0.533 0.504
## 0.322 0.300 0.480
## 0.229 0.211 0.384
## 1.641 1.492 0.539
## 1.056 0.974 0.581
## 0.988 0.921 0.611
## 0.278 0.260 0.304
## 0.367 0.344 0.422
## 0.310 0.289 0.250
## 0.483 0.455 0.506
## 0.692 0.657 0.657
## 0.387 0.363 0.405
## 0.502 0.474 0.609
## 0.559 0.527 0.452
## 0.425 0.399 0.540
## 0.354 0.333 0.487
## 0.553 0.520 0.539
## 0.270 0.250 0.323
## 0.728 0.675 0.573
## 0.394 0.369 0.503
## 0.303 0.274 0.360
## 0.835 0.784 0.689
## 0.547 0.514 0.646
## 1.000 0.216 0.216
## 1.000 0.220 0.220
## 1.000 0.895 0.895
## 1.000 0.143 0.143
## 1.000 0.103 0.103
## 1.000 0.443 0.443
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.028 0.008 3.643 0.000 0.013
## Stst19d (.p2.) 0.160 0.010 15.585 0.000 0.140
## Stst20s (.p3.) 0.312 0.008 37.081 0.000 0.295
## Stst21c (.p4.) 0.343 0.008 41.056 0.000 0.326
## Stst22p (.p5.) 0.378 0.009 42.046 0.000 0.361
## Stst23n (.p6.) 0.387 0.010 38.636 0.000 0.367
## Stst24x (.p7.) 0.304 0.009 34.712 0.000 0.287
## Stst25w (.p8.) 0.095 0.009 10.984 0.000 0.078
## Stst26r (.p9.) 0.141 0.008 18.390 0.000 0.126
## Stst31b (.10.) 0.144 0.009 16.746 0.000 0.127
## Stst34r (.11.) 0.134 0.012 10.811 0.000 0.110
## math =~
## Stst5mt (.12.) 0.203 0.011 18.208 0.000 0.181
## Stst25w (.13.) 0.151 0.010 15.364 0.000 0.131
## Stst32r (.14.) 0.267 0.009 30.808 0.000 0.250
## Stst33h (.15.) 0.273 0.009 29.255 0.000 0.255
## Stst34r (.16.) 0.123 0.013 9.547 0.000 0.098
## speed =~
## Stst19d (.17.) 0.179 0.011 16.195 0.000 0.157
## Stst34r (.18.) 0.452 0.019 24.208 0.000 0.415
## Stst35t (.19.) 1.069 0.025 42.807 0.000 1.020
## Stst36c (.20.) 0.792 0.021 37.572 0.000 0.751
## Stst37b (.21.) 0.678 0.019 36.363 0.000 0.641
## info =~
## Stst1vc (.22.) 0.187 0.010 18.522 0.000 0.168
## Stst2lt (.23.) 0.292 0.008 34.571 0.000 0.275
## Stst3ms (.24.) 0.259 0.008 33.152 0.000 0.244
## Stst4sc 0.287 0.008 34.067 0.000 0.270
## Stst7bl (.26.) 0.099 0.009 11.581 0.000 0.082
## Stst8rn 0.099 0.006 15.727 0.000 0.087
## Stst11r (.28.) 0.276 0.008 33.069 0.000 0.259
## Stst12l (.29.) 0.208 0.007 30.964 0.000 0.195
## Stst13h (.30.) 0.302 0.009 34.649 0.000 0.285
## Stst14b (.31.) 0.220 0.007 31.904 0.000 0.207
## Stst15t (.32.) 0.224 0.007 31.409 0.000 0.210
## Stst16m (.33.) 0.252 0.008 33.195 0.000 0.237
## Stst19d (.34.) 0.099 0.008 12.527 0.000 0.084
## Stst26r (.35.) 0.238 0.008 30.707 0.000 0.223
## science =~
## Stst1vc (.36.) 0.127 0.007 17.813 0.000 0.113
## Stst5mt (.37.) 0.104 0.010 10.659 0.000 0.085
## Stst6ph (.38.) 0.232 0.009 25.864 0.000 0.215
## Stst7bl (.39.) 0.136 0.009 15.355 0.000 0.119
## Stst9lc (.40.) 0.228 0.010 22.701 0.000 0.208
## Stst10m (.41.) 0.194 0.008 24.744 0.000 0.179
## spatial =~
## Stst28m 0.262 0.009 30.485 0.000 0.246
## Sts292D (.43.) 0.396 0.012 33.027 0.000 0.373
## Sts303D (.44.) 0.354 0.010 34.427 0.000 0.334
## Stst31b (.45.) 0.373 0.013 28.629 0.000 0.348
## Stst37b (.46.) 0.098 0.012 8.464 0.000 0.075
## g =~
## english (.47.) 1.905 0.053 35.609 0.000 1.800
## math (.48.) 1.883 0.069 27.481 0.000 1.748
## speed (.49.) 0.342 0.021 16.239 0.000 0.300
## info (.50.) 2.453 0.080 30.733 0.000 2.296
## science 1.828 0.087 21.096 0.000 1.658
## spatial (.52.) 1.121 0.037 30.231 0.000 1.049
## ci.upper Std.lv Std.all
##
## 0.044 0.061 0.066
## 0.180 0.344 0.376
## 0.328 0.671 0.683
## 0.359 0.737 0.738
## 0.396 0.814 0.827
## 0.406 0.832 0.747
## 0.321 0.654 0.593
## 0.111 0.203 0.258
## 0.156 0.302 0.300
## 0.161 0.310 0.280
## 0.158 0.288 0.248
##
## 0.225 0.432 0.437
## 0.170 0.321 0.408
## 0.284 0.570 0.735
## 0.292 0.582 0.805
## 0.148 0.262 0.226
##
## 0.200 0.189 0.207
## 0.488 0.477 0.412
## 1.118 1.130 0.697
## 0.833 0.837 0.647
## 0.714 0.716 0.622
##
## 0.207 0.497 0.535
## 0.308 0.772 0.842
## 0.275 0.687 0.759
## 0.303 0.759 0.834
## 0.116 0.262 0.305
## 0.111 0.262 0.315
## 0.292 0.730 0.756
## 0.221 0.551 0.646
## 0.319 0.800 0.717
## 0.234 0.583 0.663
## 0.238 0.592 0.679
## 0.267 0.667 0.699
## 0.115 0.263 0.287
## 0.254 0.631 0.627
##
## 0.140 0.264 0.284
## 0.123 0.216 0.219
## 0.250 0.484 0.711
## 0.154 0.284 0.331
## 0.248 0.475 0.476
## 0.209 0.404 0.639
##
## 0.279 0.394 0.635
## 0.420 0.596 0.587
## 0.374 0.531 0.662
## 0.399 0.561 0.506
## 0.121 0.148 0.128
##
## 2.009 0.885 0.885
## 2.017 0.883 0.883
## 0.383 0.323 0.323
## 2.609 0.926 0.926
## 1.998 0.877 0.877
## 1.194 0.746 0.746
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.94.) -1.171 0.022 -52.773 0.000 -1.215
## .Stst19d (.95.) -1.031 0.016 -64.184 0.000 -1.062
## .Stst20s (.96.) -0.761 0.019 -40.448 0.000 -0.798
## .Stst21c (.97.) -1.174 0.018 -64.402 0.000 -1.210
## .Stst22p (.98.) -1.234 0.020 -61.554 0.000 -1.273
## .Stst23n (.99.) -1.061 0.022 -47.206 0.000 -1.105
## .Stst24x (.100) -0.958 0.020 -48.007 0.000 -0.997
## .Stst25w (.101) -0.841 0.014 -59.367 0.000 -0.869
## .Stst26r (.102) -1.330 0.021 -62.053 0.000 -1.372
## .Stst31b (.103) -1.066 0.023 -46.021 0.000 -1.111
## .Stst34r (.104) -1.175 0.022 -53.388 0.000 -1.218
## .Stst5mt (.105) -0.778 0.019 -39.965 0.000 -0.816
## .Stst32r (.106) -1.086 0.016 -67.831 0.000 -1.117
## .Stst33h (.107) -0.868 0.016 -55.458 0.000 -0.899
## .Stst35t (.108) -0.763 0.033 -23.181 0.000 -0.827
## .Stst36c (.109) 0.047 0.026 1.856 0.063 -0.003
## .Stst37b (.110) -0.309 0.023 -13.337 0.000 -0.355
## .Stst2lt (.111) -1.046 0.019 -54.466 0.000 -1.084
## .Stst3ms (.112) -0.872 0.018 -49.348 0.000 -0.907
## .Stst4sc -1.287 0.020 -62.851 0.000 -1.327
## .Stst7bl (.114) -0.626 0.019 -32.341 0.000 -0.664
## .Stst8rn -0.947 0.015 -62.329 0.000 -0.977
## .Stst11r (.116) -1.051 0.019 -56.712 0.000 -1.088
## .Stst12l (.117) -0.859 0.016 -53.938 0.000 -0.890
## .Stst13h (.118) -1.107 0.021 -51.978 0.000 -1.148
## .Stst14b (.119) -0.636 0.016 -38.868 0.000 -0.669
## .Stst15t -0.867 0.018 -47.961 0.000 -0.902
## .Stst16m (.121) -0.934 0.019 -50.185 0.000 -0.970
## .Stst6ph (.122) -0.697 0.019 -37.238 0.000 -0.734
## .Stst9lc (.123) -0.751 0.021 -35.141 0.000 -0.793
## .Stst10m -1.084 0.019 -56.995 0.000 -1.121
## .Stst28m -1.102 0.018 -59.928 0.000 -1.138
## .Sts292D (.126) -0.556 0.021 -26.632 0.000 -0.596
## .Sts303D (.127) -0.696 0.018 -38.433 0.000 -0.731
## .english 1.092 0.041 26.628 0.000 1.011
## .math -0.019 0.039 -0.477 0.633 -0.095
## .speed 0.301 0.035 8.655 0.000 0.233
## .info 0.402 0.036 11.176 0.000 0.332
## .science -1.228 0.066 -18.728 0.000 -1.357
## .spatial -0.684 0.049 -14.034 0.000 -0.779
## g -0.143 0.031 -4.688 0.000 -0.203
## ci.upper Std.lv Std.all
## -1.128 -1.171 -1.262
## -0.999 -1.031 -1.128
## -0.724 -0.761 -0.774
## -1.138 -1.174 -1.176
## -1.195 -1.234 -1.254
## -1.017 -1.061 -0.952
## -0.919 -0.958 -0.869
## -0.813 -0.841 -1.069
## -1.288 -1.330 -1.322
## -1.020 -1.066 -0.962
## -1.132 -1.175 -1.014
## -0.740 -0.778 -0.786
## -1.055 -1.086 -1.401
## -0.837 -0.868 -1.199
## -0.698 -0.763 -0.470
## 0.097 0.047 0.037
## -0.264 -0.309 -0.269
## -1.008 -1.046 -1.140
## -0.837 -0.872 -0.964
## -1.247 -1.287 -1.414
## -0.588 -0.626 -0.729
## -0.917 -0.947 -1.136
## -1.015 -1.051 -1.089
## -0.828 -0.859 -1.006
## -1.065 -1.107 -0.992
## -0.604 -0.636 -0.724
## -0.832 -0.867 -0.994
## -0.897 -0.934 -0.978
## -0.661 -0.697 -1.024
## -0.709 -0.751 -0.752
## -1.047 -1.084 -1.715
## -1.066 -1.102 -1.775
## -0.515 -0.556 -0.548
## -0.660 -0.696 -0.867
## 1.172 0.507 0.507
## 0.058 -0.009 -0.009
## 0.369 0.285 0.285
## 0.473 0.152 0.152
## -1.100 -0.589 -0.589
## -0.588 -0.455 -0.455
## -0.083 -0.143 -0.143
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.254 0.007 35.003 0.000 0.240
## .Stst19dsgsdwrd 0.398 0.011 36.494 0.000 0.377
## .Stest20spellng 0.515 0.014 36.734 0.000 0.488
## .Stest21cptlztn 0.454 0.013 33.745 0.000 0.427
## .Stest22puncttn 0.306 0.010 29.631 0.000 0.286
## .Stest23english 0.550 0.017 32.837 0.000 0.517
## .Stest24exprssn 0.788 0.021 37.456 0.000 0.747
## .Stst25wrdfnctn 0.372 0.010 37.100 0.000 0.352
## .Stst26rdngcmpr 0.210 0.007 29.332 0.000 0.196
## .Stst31bstrctrs 0.587 0.017 34.293 0.000 0.554
## .Stst34rthcmptt 0.697 0.027 26.050 0.000 0.645
## .Stest5math 0.601 0.017 36.135 0.000 0.569
## .Stst32rthrsnng 0.276 0.008 32.625 0.000 0.259
## .Stst33hghschlm 0.185 0.007 26.922 0.000 0.171
## .Stest35tblrdng 1.354 0.068 19.960 0.000 1.221
## .Stst36clrclchc 0.971 0.034 28.850 0.000 0.905
## .Stst37bjctnspc 0.739 0.026 28.208 0.000 0.688
## .Stest2literatr 0.246 0.007 35.695 0.000 0.232
## .Stest3music 0.347 0.009 37.535 0.000 0.329
## .Stest4soclstds 0.252 0.007 34.631 0.000 0.238
## .Stst7blgclscnc 0.467 0.012 39.244 0.000 0.443
## .Stest8aerontcs 0.626 0.011 58.943 0.000 0.605
## .Stest11art 0.399 0.011 37.119 0.000 0.378
## .Stest12law 0.425 0.011 40.118 0.000 0.405
## .Stest13health 0.605 0.015 40.494 0.000 0.576
## .Stest14bible 0.433 0.013 33.918 0.000 0.408
## .Stest15theater 0.410 0.011 38.646 0.000 0.389
## .Stest16mscllns 0.467 0.012 37.924 0.000 0.442
## .Stst6physclscn 0.229 0.007 31.201 0.000 0.215
## .Stest9elctrncs 0.772 0.020 37.930 0.000 0.732
## .Stest10mechncs 0.236 0.006 36.921 0.000 0.224
## .Stst28mchnclrs 0.230 0.007 33.278 0.000 0.216
## .Stst29vslztn2D 0.674 0.019 34.876 0.000 0.636
## .Stst30vslztn3D 0.362 0.011 33.250 0.000 0.340
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.268 0.254 0.295
## 0.420 0.398 0.476
## 0.543 0.515 0.534
## 0.480 0.454 0.455
## 0.326 0.306 0.316
## 0.583 0.550 0.443
## 0.829 0.788 0.648
## 0.392 0.372 0.601
## 0.224 0.210 0.207
## 0.621 0.587 0.478
## 0.749 0.697 0.519
## 0.634 0.601 0.614
## 0.293 0.276 0.459
## 0.198 0.185 0.352
## 1.487 1.354 0.515
## 1.037 0.971 0.581
## 0.791 0.739 0.558
## 0.259 0.246 0.292
## 0.365 0.347 0.424
## 0.267 0.252 0.304
## 0.490 0.467 0.633
## 0.647 0.626 0.901
## 0.420 0.399 0.428
## 0.446 0.425 0.583
## 0.634 0.605 0.486
## 0.458 0.433 0.560
## 0.430 0.410 0.539
## 0.491 0.467 0.512
## 0.244 0.229 0.495
## 0.812 0.772 0.774
## 0.249 0.236 0.591
## 0.243 0.230 0.596
## 0.712 0.674 0.655
## 0.383 0.362 0.561
## 1.000 0.216 0.216
## 1.000 0.220 0.220
## 1.000 0.895 0.895
## 1.000 0.143 0.143
## 1.000 0.230 0.230
## 1.000 0.443 0.443
## 1.000 1.000 1.000
chc.weak<-cfa(chc.hof.weak.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("g=~science", "info=~Stest8aeronautics", "spatial=~Stest28mechanicalreasoning", "info=~Stest4socialstudies", "Stest10mechanics~1", "Stest8aeronautics~1", "Stest28mechanicalreasoning~1", "Stest4socialstudies~1", "Stest15theater~1"))
fitMeasures(chc.weak, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 7091.007 1089.000 0.000 0.946 0.043 0.057
## aic bic
## 463849.411 464984.006
Mc(chc.weak)
## [1] 0.6106315
summary(chc.weak, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 114 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 246
## Number of equality constraints 77
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 7091.007 6312.320
## Degrees of freedom 1089 1089
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.123
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 3325.404 2960.230
## 1 3765.603 3352.090
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.028 0.008 3.643 0.000 0.013
## Stst19d (.p2.) 0.160 0.010 15.585 0.000 0.140
## Stst20s (.p3.) 0.312 0.008 37.081 0.000 0.295
## Stst21c (.p4.) 0.343 0.008 41.056 0.000 0.326
## Stst22p (.p5.) 0.378 0.009 42.046 0.000 0.361
## Stst23n (.p6.) 0.387 0.010 38.636 0.000 0.367
## Stst24x (.p7.) 0.304 0.009 34.712 0.000 0.287
## Stst25w (.p8.) 0.095 0.009 10.984 0.000 0.078
## Stst26r (.p9.) 0.141 0.008 18.390 0.000 0.126
## Stst31b (.10.) 0.144 0.009 16.746 0.000 0.127
## Stst34r (.11.) 0.134 0.012 10.811 0.000 0.110
## math =~
## Stst5mt (.12.) 0.203 0.011 18.208 0.000 0.181
## Stst25w (.13.) 0.151 0.010 15.364 0.000 0.131
## Stst32r (.14.) 0.267 0.009 30.808 0.000 0.250
## Stst33h (.15.) 0.273 0.009 29.254 0.000 0.255
## Stst34r (.16.) 0.123 0.013 9.547 0.000 0.098
## speed =~
## Stst19d (.17.) 0.179 0.011 16.195 0.000 0.157
## Stst34r (.18.) 0.452 0.019 24.208 0.000 0.415
## Stst35t (.19.) 1.069 0.025 42.807 0.000 1.020
## Stst36c (.20.) 0.792 0.021 37.572 0.000 0.751
## Stst37b (.21.) 0.678 0.019 36.363 0.000 0.641
## info =~
## Stst1vc (.22.) 0.187 0.010 18.522 0.000 0.168
## Stst2lt (.23.) 0.292 0.008 34.571 0.000 0.275
## Stst3ms (.24.) 0.259 0.008 33.153 0.000 0.244
## Stst4sc 0.351 0.010 34.524 0.000 0.331
## Stst7bl (.26.) 0.099 0.009 11.581 0.000 0.082
## Stst8rn 0.221 0.008 26.335 0.000 0.205
## Stst11r (.28.) 0.276 0.008 33.069 0.000 0.259
## Stst12l (.29.) 0.208 0.007 30.965 0.000 0.195
## Stst13h (.30.) 0.302 0.009 34.650 0.000 0.285
## Stst14b (.31.) 0.220 0.007 31.904 0.000 0.207
## Stst15t (.32.) 0.224 0.007 31.409 0.000 0.210
## Stst16m (.33.) 0.252 0.008 33.196 0.000 0.237
## Stst19d (.34.) 0.099 0.008 12.527 0.000 0.084
## Stst26r (.35.) 0.238 0.008 30.707 0.000 0.223
## science =~
## Stst1vc (.36.) 0.127 0.007 17.813 0.000 0.113
## Stst5mt (.37.) 0.104 0.010 10.659 0.000 0.085
## Stst6ph (.38.) 0.232 0.009 25.863 0.000 0.215
## Stst7bl (.39.) 0.136 0.009 15.354 0.000 0.119
## Stst9lc (.40.) 0.228 0.010 22.700 0.000 0.208
## Stst10m (.41.) 0.194 0.008 24.743 0.000 0.179
## spatial =~
## Stst28m 0.464 0.013 36.525 0.000 0.439
## Sts292D (.43.) 0.396 0.012 33.027 0.000 0.373
## Sts303D (.44.) 0.354 0.010 34.427 0.000 0.334
## Stst31b (.45.) 0.373 0.013 28.629 0.000 0.348
## Stst37b (.46.) 0.098 0.012 8.464 0.000 0.075
## g =~
## english (.47.) 1.905 0.053 35.609 0.000 1.800
## math (.48.) 1.883 0.069 27.480 0.000 1.748
## speed (.49.) 0.342 0.021 16.238 0.000 0.300
## info (.50.) 2.453 0.080 30.733 0.000 2.296
## science 2.948 0.130 22.636 0.000 2.692
## spatial (.52.) 1.121 0.037 30.231 0.000 1.049
## ci.upper Std.lv Std.all
##
## 0.044 0.061 0.058
## 0.180 0.344 0.381
## 0.328 0.671 0.673
## 0.359 0.737 0.770
## 0.396 0.814 0.814
## 0.406 0.832 0.722
## 0.321 0.654 0.578
## 0.111 0.203 0.255
## 0.156 0.302 0.297
## 0.161 0.310 0.278
## 0.158 0.288 0.254
##
## 0.225 0.432 0.420
## 0.170 0.321 0.403
## 0.284 0.570 0.721
## 0.292 0.582 0.785
## 0.148 0.262 0.231
##
## 0.200 0.189 0.209
## 0.488 0.477 0.421
## 1.118 1.130 0.679
## 0.833 0.837 0.647
## 0.714 0.716 0.583
##
## 0.207 0.497 0.475
## 0.308 0.772 0.834
## 0.275 0.687 0.761
## 0.371 0.930 0.866
## 0.116 0.262 0.276
## 0.238 0.586 0.586
## 0.292 0.730 0.771
## 0.221 0.551 0.625
## 0.319 0.800 0.740
## 0.234 0.583 0.679
## 0.238 0.592 0.717
## 0.267 0.667 0.679
## 0.115 0.263 0.292
## 0.254 0.631 0.621
##
## 0.140 0.394 0.376
## 0.123 0.323 0.314
## 0.250 0.723 0.823
## 0.154 0.425 0.448
## 0.248 0.710 0.654
## 0.209 0.604 0.705
##
## 0.489 0.697 0.800
## 0.420 0.596 0.558
## 0.374 0.531 0.595
## 0.399 0.561 0.502
## 0.121 0.148 0.120
##
## 2.009 0.885 0.885
## 2.017 0.883 0.883
## 0.383 0.323 0.323
## 2.609 0.926 0.926
## 3.203 0.947 0.947
## 1.194 0.746 0.746
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .math 0.000 0.000
## .Stst1vc (.95.) -1.172 0.022 -52.773 0.000 -1.215
## .Stst19d (.96.) -1.031 0.016 -64.185 0.000 -1.062
## .Stst20s (.97.) -0.761 0.019 -40.448 0.000 -0.798
## .Stst21c (.98.) -1.174 0.018 -64.402 0.000 -1.210
## .Stst22p (.99.) -1.234 0.020 -61.554 0.000 -1.273
## .Stst23n (.100) -1.061 0.022 -47.206 0.000 -1.105
## .Stst24x (.101) -0.958 0.020 -48.007 0.000 -0.997
## .Stst25w (.102) -0.841 0.014 -59.368 0.000 -0.869
## .Stst26r (.103) -1.330 0.021 -62.053 0.000 -1.372
## .Stst31b (.104) -1.066 0.023 -46.021 0.000 -1.111
## .Stst34r (.105) -1.175 0.022 -53.388 0.000 -1.218
## .Stst5mt (.106) -0.778 0.019 -39.965 0.000 -0.816
## .Stst32r (.107) -1.086 0.016 -67.831 0.000 -1.117
## .Stst33h (.108) -0.868 0.016 -55.458 0.000 -0.899
## .Stst35t (.109) -0.763 0.033 -23.181 0.000 -0.827
## .Stst36c (.110) 0.047 0.026 1.856 0.063 -0.003
## .Stst37b (.111) -0.309 0.023 -13.337 0.000 -0.355
## .Stst2lt (.112) -1.046 0.019 -54.466 0.000 -1.084
## .Stst3ms (.113) -0.872 0.018 -49.348 0.000 -0.907
## .Stst4sc -1.083 0.023 -46.133 0.000 -1.129
## .Stst7bl (.115) -0.626 0.019 -32.342 0.000 -0.664
## .Stst8rn -0.517 0.022 -23.665 0.000 -0.560
## .Stst11r (.117) -1.051 0.019 -56.712 0.000 -1.088
## .Stst12l (.118) -0.859 0.016 -53.939 0.000 -0.890
## .Stst13h (.119) -1.107 0.021 -51.978 0.000 -1.148
## .Stst14b (.120) -0.636 0.016 -38.868 0.000 -0.669
## .Stst15t -1.025 0.017 -59.426 0.000 -1.059
## .Stst16m (.122) -0.934 0.019 -50.186 0.000 -0.970
## .Stst6ph (.123) -0.697 0.019 -37.238 0.000 -0.734
## .Stst9lc (.124) -0.751 0.021 -35.142 0.000 -0.793
## .Stst10m -0.656 0.019 -33.970 0.000 -0.694
## .Stst28m -0.715 0.019 -36.895 0.000 -0.753
## .Sts292D (.127) -0.556 0.021 -26.632 0.000 -0.596
## .Sts303D (.128) -0.696 0.018 -38.434 0.000 -0.731
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -1.128 -1.172 -1.120
## -0.999 -1.031 -1.144
## -0.724 -0.761 -0.763
## -1.138 -1.174 -1.227
## -1.195 -1.234 -1.234
## -1.017 -1.061 -0.920
## -0.919 -0.958 -0.846
## -0.813 -0.841 -1.056
## -1.288 -1.330 -1.309
## -1.020 -1.066 -0.953
## -1.132 -1.175 -1.037
## -0.740 -0.778 -0.757
## -1.055 -1.086 -1.374
## -0.837 -0.868 -1.170
## -0.698 -0.763 -0.458
## 0.097 0.047 0.037
## -0.264 -0.309 -0.252
## -1.008 -1.046 -1.130
## -0.837 -0.872 -0.966
## -1.037 -1.083 -1.008
## -0.588 -0.626 -0.660
## -0.475 -0.517 -0.518
## -1.015 -1.051 -1.111
## -0.828 -0.859 -0.974
## -1.065 -1.107 -1.025
## -0.604 -0.636 -0.740
## -0.991 -1.025 -1.240
## -0.897 -0.934 -0.950
## -0.661 -0.697 -0.793
## -0.709 -0.751 -0.692
## -0.618 -0.656 -0.766
## -0.677 -0.715 -0.820
## -0.515 -0.556 -0.521
## -0.660 -0.696 -0.780
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.256 0.009 27.902 0.000 0.238
## .Stst19dsgsdwrd 0.374 0.014 27.189 0.000 0.347
## .Stest20spellng 0.543 0.017 31.098 0.000 0.509
## .Stest21cptlztn 0.372 0.015 24.499 0.000 0.342
## .Stest22puncttn 0.337 0.012 27.837 0.000 0.314
## .Stest23english 0.637 0.024 26.846 0.000 0.590
## .Stest24exprssn 0.853 0.025 33.467 0.000 0.803
## .Stst25wrdfnctn 0.387 0.012 32.709 0.000 0.364
## .Stst26rdngcmpr 0.230 0.009 25.464 0.000 0.212
## .Stst31bstrctrs 0.609 0.022 27.896 0.000 0.566
## .Stst34rthcmptt 0.636 0.030 20.979 0.000 0.576
## .Stest5math 0.533 0.020 26.734 0.000 0.494
## .Stst32rthrsnng 0.300 0.011 26.969 0.000 0.278
## .Stst33hghschlm 0.211 0.009 23.598 0.000 0.194
## .Stest35tblrdng 1.492 0.076 19.642 0.000 1.343
## .Stst36clrclchc 0.974 0.042 23.237 0.000 0.891
## .Stst37bjctnspc 0.921 0.034 26.976 0.000 0.854
## .Stest2literatr 0.260 0.009 29.705 0.000 0.243
## .Stest3music 0.344 0.012 28.970 0.000 0.321
## .Stest4soclstds 0.289 0.011 27.099 0.000 0.268
## .Stst7blgclscnc 0.455 0.014 32.592 0.000 0.428
## .Stest8aerontcs 0.657 0.018 37.075 0.000 0.622
## .Stest11art 0.363 0.012 29.834 0.000 0.339
## .Stest12law 0.474 0.015 32.626 0.000 0.445
## .Stest13health 0.527 0.016 32.159 0.000 0.495
## .Stest14bible 0.399 0.013 29.601 0.000 0.372
## .Stest15theater 0.333 0.011 30.662 0.000 0.311
## .Stest16mscllns 0.520 0.017 30.833 0.000 0.487
## .Stst6physclscn 0.250 0.010 24.449 0.000 0.230
## .Stest9elctrncs 0.675 0.027 25.020 0.000 0.622
## .Stest10mechncs 0.369 0.013 28.410 0.000 0.343
## .Stst28mchnclrs 0.274 0.015 17.973 0.000 0.244
## .Stst29vslztn2D 0.784 0.026 30.205 0.000 0.733
## .Stst30vslztn3D 0.514 0.017 30.506 0.000 0.481
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.274 0.256 0.234
## 0.401 0.374 0.461
## 0.577 0.543 0.547
## 0.402 0.372 0.406
## 0.361 0.337 0.337
## 0.683 0.637 0.479
## 0.903 0.853 0.666
## 0.411 0.387 0.611
## 0.247 0.230 0.223
## 0.651 0.609 0.487
## 0.695 0.636 0.496
## 0.572 0.533 0.504
## 0.322 0.300 0.480
## 0.229 0.211 0.384
## 1.641 1.492 0.539
## 1.056 0.974 0.581
## 0.988 0.921 0.611
## 0.278 0.260 0.304
## 0.367 0.344 0.422
## 0.310 0.289 0.250
## 0.483 0.455 0.506
## 0.692 0.657 0.657
## 0.387 0.363 0.405
## 0.502 0.474 0.609
## 0.559 0.527 0.452
## 0.425 0.399 0.540
## 0.354 0.333 0.487
## 0.553 0.520 0.539
## 0.270 0.250 0.323
## 0.728 0.675 0.573
## 0.394 0.369 0.503
## 0.303 0.274 0.360
## 0.835 0.784 0.689
## 0.547 0.514 0.646
## 1.000 0.216 0.216
## 1.000 0.220 0.220
## 1.000 0.895 0.895
## 1.000 0.143 0.143
## 1.000 0.103 0.103
## 1.000 0.443 0.443
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.028 0.008 3.643 0.000 0.013
## Stst19d (.p2.) 0.160 0.010 15.585 0.000 0.140
## Stst20s (.p3.) 0.312 0.008 37.081 0.000 0.295
## Stst21c (.p4.) 0.343 0.008 41.056 0.000 0.326
## Stst22p (.p5.) 0.378 0.009 42.046 0.000 0.361
## Stst23n (.p6.) 0.387 0.010 38.636 0.000 0.367
## Stst24x (.p7.) 0.304 0.009 34.712 0.000 0.287
## Stst25w (.p8.) 0.095 0.009 10.984 0.000 0.078
## Stst26r (.p9.) 0.141 0.008 18.390 0.000 0.126
## Stst31b (.10.) 0.144 0.009 16.746 0.000 0.127
## Stst34r (.11.) 0.134 0.012 10.811 0.000 0.110
## math =~
## Stst5mt (.12.) 0.203 0.011 18.208 0.000 0.181
## Stst25w (.13.) 0.151 0.010 15.364 0.000 0.131
## Stst32r (.14.) 0.267 0.009 30.808 0.000 0.250
## Stst33h (.15.) 0.273 0.009 29.254 0.000 0.255
## Stst34r (.16.) 0.123 0.013 9.547 0.000 0.098
## speed =~
## Stst19d (.17.) 0.179 0.011 16.195 0.000 0.157
## Stst34r (.18.) 0.452 0.019 24.208 0.000 0.415
## Stst35t (.19.) 1.069 0.025 42.807 0.000 1.020
## Stst36c (.20.) 0.792 0.021 37.572 0.000 0.751
## Stst37b (.21.) 0.678 0.019 36.363 0.000 0.641
## info =~
## Stst1vc (.22.) 0.187 0.010 18.522 0.000 0.168
## Stst2lt (.23.) 0.292 0.008 34.571 0.000 0.275
## Stst3ms (.24.) 0.259 0.008 33.153 0.000 0.244
## Stst4sc 0.287 0.008 34.068 0.000 0.270
## Stst7bl (.26.) 0.099 0.009 11.581 0.000 0.082
## Stst8rn 0.099 0.006 15.727 0.000 0.087
## Stst11r (.28.) 0.276 0.008 33.069 0.000 0.259
## Stst12l (.29.) 0.208 0.007 30.965 0.000 0.195
## Stst13h (.30.) 0.302 0.009 34.650 0.000 0.285
## Stst14b (.31.) 0.220 0.007 31.904 0.000 0.207
## Stst15t (.32.) 0.224 0.007 31.409 0.000 0.210
## Stst16m (.33.) 0.252 0.008 33.196 0.000 0.237
## Stst19d (.34.) 0.099 0.008 12.527 0.000 0.084
## Stst26r (.35.) 0.238 0.008 30.707 0.000 0.223
## science =~
## Stst1vc (.36.) 0.127 0.007 17.813 0.000 0.113
## Stst5mt (.37.) 0.104 0.010 10.659 0.000 0.085
## Stst6ph (.38.) 0.232 0.009 25.863 0.000 0.215
## Stst7bl (.39.) 0.136 0.009 15.354 0.000 0.119
## Stst9lc (.40.) 0.228 0.010 22.700 0.000 0.208
## Stst10m (.41.) 0.194 0.008 24.743 0.000 0.179
## spatial =~
## Stst28m 0.262 0.009 30.485 0.000 0.246
## Sts292D (.43.) 0.396 0.012 33.027 0.000 0.373
## Sts303D (.44.) 0.354 0.010 34.427 0.000 0.334
## Stst31b (.45.) 0.373 0.013 28.629 0.000 0.348
## Stst37b (.46.) 0.098 0.012 8.464 0.000 0.075
## g =~
## english (.47.) 1.905 0.053 35.609 0.000 1.800
## math (.48.) 1.883 0.069 27.480 0.000 1.748
## speed (.49.) 0.342 0.021 16.238 0.000 0.300
## info (.50.) 2.453 0.080 30.733 0.000 2.296
## science 1.828 0.087 21.095 0.000 1.658
## spatial (.52.) 1.121 0.037 30.231 0.000 1.049
## ci.upper Std.lv Std.all
##
## 0.044 0.061 0.066
## 0.180 0.344 0.376
## 0.328 0.671 0.683
## 0.359 0.737 0.738
## 0.396 0.814 0.827
## 0.406 0.832 0.747
## 0.321 0.654 0.593
## 0.111 0.203 0.258
## 0.156 0.302 0.300
## 0.161 0.310 0.280
## 0.158 0.288 0.248
##
## 0.225 0.432 0.437
## 0.170 0.321 0.408
## 0.284 0.570 0.735
## 0.292 0.582 0.805
## 0.148 0.262 0.226
##
## 0.200 0.189 0.207
## 0.488 0.477 0.412
## 1.118 1.130 0.697
## 0.833 0.837 0.647
## 0.714 0.716 0.622
##
## 0.207 0.497 0.535
## 0.308 0.772 0.842
## 0.275 0.687 0.759
## 0.303 0.759 0.834
## 0.116 0.262 0.305
## 0.111 0.262 0.315
## 0.292 0.730 0.756
## 0.221 0.551 0.646
## 0.319 0.800 0.717
## 0.234 0.583 0.663
## 0.238 0.592 0.679
## 0.267 0.667 0.699
## 0.115 0.263 0.287
## 0.254 0.631 0.627
##
## 0.140 0.264 0.284
## 0.123 0.216 0.219
## 0.250 0.484 0.711
## 0.154 0.284 0.331
## 0.248 0.475 0.476
## 0.209 0.404 0.639
##
## 0.279 0.394 0.635
## 0.420 0.596 0.587
## 0.374 0.531 0.662
## 0.399 0.561 0.506
## 0.121 0.148 0.128
##
## 2.009 0.885 0.885
## 2.017 0.883 0.883
## 0.383 0.323 0.323
## 2.609 0.926 0.926
## 1.998 0.877 0.877
## 1.194 0.746 0.746
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .math 0.000 0.000
## .Stst1vc (.95.) -1.172 0.022 -52.773 0.000 -1.215
## .Stst19d (.96.) -1.031 0.016 -64.185 0.000 -1.062
## .Stst20s (.97.) -0.761 0.019 -40.448 0.000 -0.798
## .Stst21c (.98.) -1.174 0.018 -64.402 0.000 -1.210
## .Stst22p (.99.) -1.234 0.020 -61.554 0.000 -1.273
## .Stst23n (.100) -1.061 0.022 -47.206 0.000 -1.105
## .Stst24x (.101) -0.958 0.020 -48.007 0.000 -0.997
## .Stst25w (.102) -0.841 0.014 -59.368 0.000 -0.869
## .Stst26r (.103) -1.330 0.021 -62.053 0.000 -1.372
## .Stst31b (.104) -1.066 0.023 -46.021 0.000 -1.111
## .Stst34r (.105) -1.175 0.022 -53.388 0.000 -1.218
## .Stst5mt (.106) -0.778 0.019 -39.965 0.000 -0.816
## .Stst32r (.107) -1.086 0.016 -67.831 0.000 -1.117
## .Stst33h (.108) -0.868 0.016 -55.458 0.000 -0.899
## .Stst35t (.109) -0.763 0.033 -23.181 0.000 -0.827
## .Stst36c (.110) 0.047 0.026 1.856 0.063 -0.003
## .Stst37b (.111) -0.309 0.023 -13.337 0.000 -0.355
## .Stst2lt (.112) -1.046 0.019 -54.466 0.000 -1.084
## .Stst3ms (.113) -0.872 0.018 -49.348 0.000 -0.907
## .Stst4sc -1.287 0.020 -62.852 0.000 -1.327
## .Stst7bl (.115) -0.626 0.019 -32.342 0.000 -0.664
## .Stst8rn -0.947 0.015 -62.330 0.000 -0.977
## .Stst11r (.117) -1.051 0.019 -56.712 0.000 -1.088
## .Stst12l (.118) -0.859 0.016 -53.939 0.000 -0.890
## .Stst13h (.119) -1.107 0.021 -51.978 0.000 -1.148
## .Stst14b (.120) -0.636 0.016 -38.868 0.000 -0.669
## .Stst15t -0.867 0.018 -47.961 0.000 -0.902
## .Stst16m (.122) -0.934 0.019 -50.186 0.000 -0.970
## .Stst6ph (.123) -0.697 0.019 -37.238 0.000 -0.734
## .Stst9lc (.124) -0.751 0.021 -35.142 0.000 -0.793
## .Stst10m -1.084 0.019 -56.995 0.000 -1.121
## .Stst28m -1.102 0.018 -59.929 0.000 -1.138
## .Sts292D (.127) -0.556 0.021 -26.632 0.000 -0.596
## .Sts303D (.128) -0.696 0.018 -38.434 0.000 -0.731
## .english 1.110 0.061 18.215 0.000 0.991
## .speed 0.304 0.036 8.483 0.000 0.234
## .info 0.427 0.068 6.270 0.000 0.293
## .science -1.210 0.087 -13.959 0.000 -1.380
## .spatial -0.673 0.055 -12.326 0.000 -0.780
## g -0.153 0.036 -4.265 0.000 -0.224
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -1.128 -1.172 -1.262
## -0.999 -1.031 -1.128
## -0.724 -0.761 -0.774
## -1.138 -1.174 -1.176
## -1.195 -1.234 -1.254
## -1.017 -1.061 -0.952
## -0.919 -0.958 -0.869
## -0.813 -0.841 -1.069
## -1.288 -1.330 -1.322
## -1.020 -1.066 -0.962
## -1.132 -1.175 -1.014
## -0.740 -0.778 -0.786
## -1.055 -1.086 -1.401
## -0.837 -0.868 -1.199
## -0.698 -0.763 -0.470
## 0.097 0.047 0.037
## -0.264 -0.309 -0.269
## -1.008 -1.046 -1.140
## -0.837 -0.872 -0.964
## -1.247 -1.287 -1.414
## -0.588 -0.626 -0.729
## -0.917 -0.947 -1.136
## -1.015 -1.051 -1.089
## -0.828 -0.859 -1.006
## -1.065 -1.107 -0.992
## -0.604 -0.636 -0.724
## -0.832 -0.867 -0.994
## -0.897 -0.934 -0.978
## -0.661 -0.697 -1.024
## -0.709 -0.751 -0.752
## -1.047 -1.084 -1.715
## -1.066 -1.102 -1.775
## -0.515 -0.556 -0.548
## -0.660 -0.696 -0.867
## 1.230 0.516 0.516
## 0.375 0.288 0.288
## 0.560 0.161 0.161
## -1.040 -0.581 -0.581
## -0.566 -0.448 -0.448
## -0.083 -0.153 -0.153
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.254 0.007 35.003 0.000 0.240
## .Stst19dsgsdwrd 0.398 0.011 36.494 0.000 0.377
## .Stest20spellng 0.515 0.014 36.734 0.000 0.488
## .Stest21cptlztn 0.454 0.013 33.745 0.000 0.427
## .Stest22puncttn 0.306 0.010 29.631 0.000 0.286
## .Stest23english 0.550 0.017 32.837 0.000 0.517
## .Stest24exprssn 0.788 0.021 37.456 0.000 0.747
## .Stst25wrdfnctn 0.372 0.010 37.100 0.000 0.352
## .Stst26rdngcmpr 0.210 0.007 29.332 0.000 0.196
## .Stst31bstrctrs 0.587 0.017 34.293 0.000 0.554
## .Stst34rthcmptt 0.697 0.027 26.050 0.000 0.645
## .Stest5math 0.601 0.017 36.134 0.000 0.569
## .Stst32rthrsnng 0.276 0.008 32.625 0.000 0.259
## .Stst33hghschlm 0.185 0.007 26.922 0.000 0.171
## .Stest35tblrdng 1.354 0.068 19.960 0.000 1.221
## .Stst36clrclchc 0.971 0.034 28.850 0.000 0.905
## .Stst37bjctnspc 0.739 0.026 28.208 0.000 0.688
## .Stest2literatr 0.246 0.007 35.695 0.000 0.232
## .Stest3music 0.347 0.009 37.535 0.000 0.329
## .Stest4soclstds 0.252 0.007 34.631 0.000 0.238
## .Stst7blgclscnc 0.467 0.012 39.244 0.000 0.443
## .Stest8aerontcs 0.626 0.011 58.943 0.000 0.605
## .Stest11art 0.399 0.011 37.119 0.000 0.378
## .Stest12law 0.425 0.011 40.118 0.000 0.405
## .Stest13health 0.605 0.015 40.494 0.000 0.576
## .Stest14bible 0.433 0.013 33.918 0.000 0.408
## .Stest15theater 0.410 0.011 38.646 0.000 0.389
## .Stest16mscllns 0.467 0.012 37.924 0.000 0.442
## .Stst6physclscn 0.229 0.007 31.201 0.000 0.215
## .Stest9elctrncs 0.772 0.020 37.930 0.000 0.732
## .Stest10mechncs 0.236 0.006 36.921 0.000 0.224
## .Stst28mchnclrs 0.230 0.007 33.278 0.000 0.216
## .Stst29vslztn2D 0.674 0.019 34.876 0.000 0.636
## .Stst30vslztn3D 0.362 0.011 33.250 0.000 0.340
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.268 0.254 0.295
## 0.420 0.398 0.476
## 0.543 0.515 0.534
## 0.480 0.454 0.455
## 0.326 0.306 0.316
## 0.583 0.550 0.443
## 0.829 0.788 0.648
## 0.392 0.372 0.601
## 0.224 0.210 0.207
## 0.621 0.587 0.478
## 0.749 0.697 0.519
## 0.634 0.601 0.614
## 0.293 0.276 0.459
## 0.198 0.185 0.352
## 1.487 1.354 0.515
## 1.037 0.971 0.581
## 0.791 0.739 0.558
## 0.259 0.246 0.292
## 0.365 0.347 0.424
## 0.267 0.252 0.304
## 0.490 0.467 0.633
## 0.647 0.626 0.901
## 0.420 0.399 0.428
## 0.446 0.425 0.583
## 0.634 0.605 0.486
## 0.458 0.433 0.560
## 0.430 0.410 0.539
## 0.491 0.467 0.512
## 0.244 0.229 0.495
## 0.812 0.772 0.774
## 0.249 0.236 0.591
## 0.243 0.230 0.596
## 0.712 0.674 0.655
## 0.383 0.362 0.561
## 1.000 0.216 0.216
## 1.000 0.220 0.220
## 1.000 0.895 0.895
## 1.000 0.143 0.143
## 1.000 0.230 0.230
## 1.000 0.443 0.443
## 1.000 1.000 1.000
standardizedSolution(chc.weak) # get the correct SEs for standardized solution
## lhs op rhs group
## 1 english =~ Stest1vocab 1
## 2 english =~ Stest19disguisedwords 1
## 3 english =~ Stest20spelling 1
## 4 english =~ Stest21capitalization 1
## 5 english =~ Stest22punctuation 1
## 6 english =~ Stest23english 1
## 7 english =~ Stest24expression 1
## 8 english =~ Stest25wordfunctions 1
## 9 english =~ Stest26readingcomprehension 1
## 10 english =~ Stest31abstractreasoning 1
## 11 english =~ Stest34arithcomputation 1
## 12 math =~ Stest5math 1
## 13 math =~ Stest25wordfunctions 1
## 14 math =~ Stest32arithreasoning 1
## 15 math =~ Stest33highschoolmath 1
## 16 math =~ Stest34arithcomputation 1
## 17 speed =~ Stest19disguisedwords 1
## 18 speed =~ Stest34arithcomputation 1
## 19 speed =~ Stest35tablereading 1
## 20 speed =~ Stest36clericalchecking 1
## 21 speed =~ Stest37objectinspection 1
## 22 info =~ Stest1vocab 1
## 23 info =~ Stest2literature 1
## 24 info =~ Stest3music 1
## 25 info =~ Stest4socialstudies 1
## 26 info =~ Stest7biologicalscience 1
## 27 info =~ Stest8aeronautics 1
## 28 info =~ Stest11art 1
## 29 info =~ Stest12law 1
## 30 info =~ Stest13health 1
## 31 info =~ Stest14bible 1
## 32 info =~ Stest15theater 1
## 33 info =~ Stest16miscellaneous 1
## 34 info =~ Stest19disguisedwords 1
## 35 info =~ Stest26readingcomprehension 1
## 36 science =~ Stest1vocab 1
## 37 science =~ Stest5math 1
## 38 science =~ Stest6physicalscience 1
## 39 science =~ Stest7biologicalscience 1
## 40 science =~ Stest9electronics 1
## 41 science =~ Stest10mechanics 1
## 42 spatial =~ Stest28mechanicalreasoning 1
## 43 spatial =~ Stest29visualization2D 1
## 44 spatial =~ Stest30visualization3D 1
## 45 spatial =~ Stest31abstractreasoning 1
## 46 spatial =~ Stest37objectinspection 1
## 47 g =~ english 1
## 48 g =~ math 1
## 49 g =~ speed 1
## 50 g =~ info 1
## 51 g =~ science 1
## 52 g =~ spatial 1
## 53 math ~1 1
## 54 Stest1vocab ~~ Stest1vocab 1
## 55 Stest19disguisedwords ~~ Stest19disguisedwords 1
## 56 Stest20spelling ~~ Stest20spelling 1
## 57 Stest21capitalization ~~ Stest21capitalization 1
## 58 Stest22punctuation ~~ Stest22punctuation 1
## 59 Stest23english ~~ Stest23english 1
## 60 Stest24expression ~~ Stest24expression 1
## 61 Stest25wordfunctions ~~ Stest25wordfunctions 1
## 62 Stest26readingcomprehension ~~ Stest26readingcomprehension 1
## 63 Stest31abstractreasoning ~~ Stest31abstractreasoning 1
## 64 Stest34arithcomputation ~~ Stest34arithcomputation 1
## 65 Stest5math ~~ Stest5math 1
## 66 Stest32arithreasoning ~~ Stest32arithreasoning 1
## 67 Stest33highschoolmath ~~ Stest33highschoolmath 1
## 68 Stest35tablereading ~~ Stest35tablereading 1
## 69 Stest36clericalchecking ~~ Stest36clericalchecking 1
## 70 Stest37objectinspection ~~ Stest37objectinspection 1
## 71 Stest2literature ~~ Stest2literature 1
## 72 Stest3music ~~ Stest3music 1
## 73 Stest4socialstudies ~~ Stest4socialstudies 1
## 74 Stest7biologicalscience ~~ Stest7biologicalscience 1
## 75 Stest8aeronautics ~~ Stest8aeronautics 1
## 76 Stest11art ~~ Stest11art 1
## 77 Stest12law ~~ Stest12law 1
## 78 Stest13health ~~ Stest13health 1
## 79 Stest14bible ~~ Stest14bible 1
## 80 Stest15theater ~~ Stest15theater 1
## 81 Stest16miscellaneous ~~ Stest16miscellaneous 1
## 82 Stest6physicalscience ~~ Stest6physicalscience 1
## 83 Stest9electronics ~~ Stest9electronics 1
## 84 Stest10mechanics ~~ Stest10mechanics 1
## 85 Stest28mechanicalreasoning ~~ Stest28mechanicalreasoning 1
## 86 Stest29visualization2D ~~ Stest29visualization2D 1
## 87 Stest30visualization3D ~~ Stest30visualization3D 1
## 88 english ~~ english 1
## 89 math ~~ math 1
## 90 speed ~~ speed 1
## label est.std se z pvalue ci.lower ci.upper
## 1 .p1. 0.058 0.016 3.727 0 0.028 0.089
## 2 .p2. 0.381 0.022 17.173 0 0.338 0.425
## 3 .p3. 0.673 0.009 71.546 0 0.655 0.692
## 4 .p4. 0.770 0.008 96.881 0 0.755 0.786
## 5 .p5. 0.814 0.006 125.666 0 0.801 0.827
## 6 .p6. 0.722 0.009 84.804 0 0.705 0.738
## 7 .p7. 0.578 0.011 53.915 0 0.557 0.599
## 8 .p8. 0.255 0.022 11.562 0 0.212 0.299
## 9 .p9. 0.297 0.015 20.004 0 0.268 0.327
## 10 .p10. 0.278 0.015 18.380 0 0.248 0.307
## 11 .p11. 0.254 0.022 11.647 0 0.211 0.297
## 12 .p12. 0.420 0.022 19.084 0 0.377 0.463
## 13 .p13. 0.403 0.023 17.380 0 0.358 0.449
## 14 .p14. 0.721 0.011 68.320 0 0.700 0.742
## 15 .p15. 0.785 0.009 84.692 0 0.767 0.803
## 16 .p16. 0.231 0.022 10.368 0 0.187 0.275
## 17 .p17. 0.209 0.012 16.782 0 0.185 0.234
## 18 .p18. 0.421 0.015 27.612 0 0.391 0.451
## 19 .p19. 0.679 0.016 43.725 0 0.649 0.709
## 20 .p20. 0.647 0.015 42.832 0 0.617 0.677
## 21 .p21. 0.583 0.014 41.240 0 0.556 0.611
## 22 .p22. 0.475 0.021 22.536 0 0.433 0.516
## 23 .p23. 0.834 0.006 142.337 0 0.823 0.846
## 24 .p24. 0.761 0.008 100.608 0 0.746 0.775
## 25 0.866 0.006 156.873 0 0.855 0.877
## 26 .p26. 0.276 0.022 12.465 0 0.233 0.320
## 27 0.586 0.014 41.248 0 0.558 0.614
## 28 .p28. 0.771 0.007 109.614 0 0.758 0.785
## 29 .p29. 0.625 0.010 59.713 0 0.605 0.646
## 30 .p30. 0.740 0.008 98.104 0 0.726 0.755
## 31 .p31. 0.679 0.010 71.318 0 0.660 0.697
## 32 .p32. 0.717 0.009 81.585 0 0.699 0.734
## 33 .p33. 0.679 0.009 73.620 0 0.661 0.697
## 34 .p34. 0.292 0.022 13.533 0 0.249 0.334
## 35 .p35. 0.621 0.014 43.717 0 0.593 0.649
## 36 .p36. 0.376 0.017 22.571 0 0.344 0.409
## 37 .p37. 0.314 0.025 12.721 0 0.266 0.363
## 38 .p38. 0.823 0.008 103.561 0 0.807 0.838
## 39 .p39. 0.448 0.024 18.281 0 0.400 0.496
## 40 .p40. 0.654 0.013 50.405 0 0.628 0.679
## 41 .p41. 0.705 0.012 60.956 0 0.682 0.728
## 42 0.800 0.012 64.040 0 0.775 0.824
## 43 .p43. 0.558 0.013 44.241 0 0.533 0.583
## 44 .p44. 0.595 0.012 48.540 0 0.571 0.619
## 45 .p45. 0.502 0.016 31.444 0 0.470 0.533
## 46 .p46. 0.120 0.013 8.927 0 0.094 0.147
## 47 .p47. 0.885 0.005 164.774 0 0.875 0.896
## 48 .p48. 0.883 0.007 124.893 0 0.869 0.897
## 49 .p49. 0.323 0.018 18.134 0 0.288 0.358
## 50 .p50. 0.926 0.004 215.597 0 0.918 0.934
## 51 0.947 0.004 219.294 0 0.939 0.955
## 52 .p52. 0.746 0.011 68.250 0 0.725 0.768
## 53 0.000 0.000 NA NA 0.000 0.000
## 54 0.234 0.008 27.806 0 0.217 0.250
## 55 0.461 0.011 40.215 0 0.439 0.484
## 56 0.547 0.013 43.153 0 0.522 0.572
## 57 0.406 0.012 33.156 0 0.382 0.430
## 58 0.337 0.011 32.008 0 0.317 0.358
## 59 0.479 0.012 38.987 0 0.455 0.503
## 60 0.666 0.012 53.665 0 0.641 0.690
## 61 0.611 0.013 46.946 0 0.585 0.636
## 62 0.223 0.008 26.971 0 0.206 0.239
## 63 0.487 0.013 37.140 0 0.462 0.513
## 64 0.496 0.015 33.616 0 0.467 0.524
## 65 0.504 0.014 37.210 0 0.477 0.530
## 66 0.480 0.015 31.533 0 0.450 0.510
## 67 0.384 0.015 26.375 0 0.355 0.412
## 68 0.539 0.021 25.550 0 0.498 0.580
## 69 0.581 0.020 29.753 0 0.543 0.620
## 70 0.611 0.016 37.616 0 0.579 0.643
## 71 0.304 0.010 31.082 0 0.285 0.323
## 72 0.422 0.011 36.663 0 0.399 0.444
## 73 0.250 0.010 26.156 0 0.231 0.269
## 74 0.506 0.014 37.264 0 0.480 0.533
## 75 0.657 0.017 39.486 0 0.624 0.690
## 76 0.405 0.011 37.276 0 0.384 0.426
## 77 0.609 0.013 46.558 0 0.584 0.635
## 78 0.452 0.011 40.408 0 0.430 0.474
## 79 0.540 0.013 41.778 0 0.514 0.565
## 80 0.487 0.013 38.662 0 0.462 0.511
## 81 0.539 0.013 43.067 0 0.515 0.564
## 82 0.323 0.013 24.746 0 0.298 0.349
## 83 0.573 0.017 33.799 0 0.540 0.606
## 84 0.503 0.016 30.854 0 0.471 0.535
## 85 0.360 0.020 18.044 0 0.321 0.400
## 86 0.689 0.014 48.906 0 0.661 0.716
## 87 0.646 0.015 44.197 0 0.617 0.674
## 88 0.216 0.010 22.713 0 0.197 0.235
## 89 0.220 0.012 17.616 0 0.196 0.245
## 90 0.895 0.012 77.667 0 0.873 0.918
## [ reached 'max' / getOption("max.print") -- omitted 178 rows ]
# PAR.boot<- bootstrapLavaan(chc.weak, R=500, type="ordinary", FUN="coef") # bootstrap model parameters, unstandardized
# describeBy(PAR.boot) # check sd column for the standard errors, as sd is the variability of the parameter estimates across the bootstrap samples
tests<-lavTestLRT(configural, metric2, scalar2, chc.hof, chc.weak)
## Warning: lavaan->lav_test_diff_SatorraBentler2001():
## scaling factor is negative
Td=tests[2:5,"Chisq diff"]
Td
## [1] 387.26067 456.10132 48.70287 NA
dfd=tests[2:5,"Df diff"]
dfd
## [1] 41 22 7 1
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.05269456 0.08054532 0.04425782 NA
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04796616 0.05754724
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.07419175 0.08706141
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.03301546 0.05637746
RMSEA.CI(T=Td[4],df=dfd[4],N=N,G=2)
## [1] NA NA
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.829 0.006 0.000 0.000
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 1.000 0.565 0.000
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.230 0.015 0.000 0.000
round(pvals(T=Td[4],df=dfd[4],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## NA NA NA NA NA NA
tests<-lavTestLRT(configural, metric2, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 387.2607 1774.7199
dfd=tests[2:3,"Df diff"]
dfd
## [1] 41 27
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.05269456 0.14588483
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04796616 0.05754724
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.1401532 0.1516746
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.829 0.006 0.000 0.000
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 1 1 1 1
tests<-lavTestLRT(configural, metric2, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 387.2607 456.1013 322.0554
dfd=tests[2:4,"Df diff"]
dfd
## [1] 41 22 34
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.05269456 0.08054532 0.05277821
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04796616 0.05754724
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.07419175 0.08706141
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.04759447 0.05811349
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.829 0.006 0.000 0.000
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 1.000 0.565 0.000
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.815 0.013 0.000 0.000
tests<-lavTestLRT(configural, metric)
Td=tests[2,"Chisq diff"]
Td
## [1] 1065.819
dfd=tests[2,"Df diff"]
dfd
## [1] 45
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.0863623
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.08190212 0.09088893
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.00 1.00 1.00 1.00 0.99 0.00
hof.age <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest9electronics + Stest10mechanics
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g =~ english + math + speed + info + science + spatial
math ~ 0*1
g ~ age
'
hof.age2 <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest9electronics + Stest10mechanics
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g =~ english + math + speed + info + science + spatial
math ~ 0*1
g ~ age + age2
'
sem.age<-sem(hof.age, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("g=~science", "info=~Stest8aeronautics", "spatial=~Stest28mechanicalreasoning", "info=~Stest4socialstudies", "Stest10mechanics~1", "Stest8aeronautics~1", "Stest28mechanicalreasoning~1", "Stest4socialstudies~1", "Stest15theater~1"))
fitMeasures(sem.age, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 7581.130 1155.000 0.000 0.943 0.043 0.056
## ecvi aic bic
## 1.302 463849.562 464997.585
Mc(sem.age)
## [1] 0.5897142
summary(sem.age, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 117 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 248
## Number of equality constraints 77
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 7581.130 6758.025
## Degrees of freedom 1155 1155
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.122
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 3518.088 3136.119
## 1 4063.043 3621.906
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.028 0.008 3.643 0.000 0.013
## Stst19d (.p2.) 0.160 0.010 15.584 0.000 0.140
## Stst20s (.p3.) 0.312 0.008 37.080 0.000 0.295
## Stst21c (.p4.) 0.343 0.008 41.059 0.000 0.326
## Stst22p (.p5.) 0.378 0.009 42.031 0.000 0.361
## Stst23n (.p6.) 0.387 0.010 38.634 0.000 0.367
## Stst24x (.p7.) 0.304 0.009 34.710 0.000 0.287
## Stst25w (.p8.) 0.094 0.009 10.984 0.000 0.078
## Stst26r (.p9.) 0.141 0.008 18.386 0.000 0.126
## Stst31b (.10.) 0.144 0.009 16.746 0.000 0.127
## Stst34r (.11.) 0.134 0.012 10.811 0.000 0.110
## math =~
## Stst5mt (.12.) 0.203 0.011 18.208 0.000 0.181
## Stst25w (.13.) 0.151 0.010 15.361 0.000 0.132
## Stst32r (.14.) 0.267 0.009 30.794 0.000 0.250
## Stst33h (.15.) 0.273 0.009 29.253 0.000 0.255
## Stst34r (.16.) 0.123 0.013 9.550 0.000 0.098
## speed =~
## Stst19d (.17.) 0.179 0.011 16.195 0.000 0.157
## Stst34r (.18.) 0.452 0.019 24.208 0.000 0.415
## Stst35t (.19.) 1.069 0.025 42.808 0.000 1.020
## Stst36c (.20.) 0.792 0.021 37.573 0.000 0.751
## Stst37b (.21.) 0.678 0.019 36.361 0.000 0.641
## info =~
## Stst1vc (.22.) 0.187 0.010 18.503 0.000 0.168
## Stst2lt (.23.) 0.291 0.008 34.509 0.000 0.275
## Stst3ms (.24.) 0.259 0.008 33.078 0.000 0.244
## Stst4sc 0.351 0.010 34.447 0.000 0.331
## Stst7bl (.26.) 0.099 0.009 11.574 0.000 0.082
## Stst8rn 0.221 0.008 26.306 0.000 0.205
## Stst11r (.28.) 0.275 0.008 32.992 0.000 0.259
## Stst12l (.29.) 0.208 0.007 30.920 0.000 0.195
## Stst13h (.30.) 0.302 0.009 34.582 0.000 0.285
## Stst14b (.31.) 0.220 0.007 31.866 0.000 0.207
## Stst15t (.32.) 0.224 0.007 31.343 0.000 0.210
## Stst16m (.33.) 0.252 0.008 33.118 0.000 0.237
## Stst19d (.34.) 0.099 0.008 12.518 0.000 0.084
## Stst26r (.35.) 0.238 0.008 30.653 0.000 0.223
## science =~
## Stst1vc (.36.) 0.127 0.007 17.805 0.000 0.113
## Stst5mt (.37.) 0.104 0.010 10.659 0.000 0.085
## Stst6ph (.38.) 0.232 0.009 25.871 0.000 0.215
## Stst7bl (.39.) 0.136 0.009 15.348 0.000 0.119
## Stst9lc (.40.) 0.228 0.010 22.706 0.000 0.208
## Stst10m (.41.) 0.194 0.008 24.743 0.000 0.179
## spatial =~
## Stst28m 0.464 0.013 36.508 0.000 0.439
## Sts292D (.43.) 0.396 0.012 33.019 0.000 0.373
## Sts303D (.44.) 0.354 0.010 34.420 0.000 0.334
## Stst31b (.45.) 0.373 0.013 28.629 0.000 0.348
## Stst37b (.46.) 0.098 0.012 8.464 0.000 0.076
## g =~
## english (.47.) 1.904 0.054 35.581 0.000 1.799
## math (.48.) 1.881 0.069 27.455 0.000 1.747
## speed (.49.) 0.342 0.021 16.241 0.000 0.300
## info (.50.) 2.454 0.080 30.676 0.000 2.297
## science 2.946 0.130 22.627 0.000 2.690
## spatial (.52.) 1.121 0.037 30.178 0.000 1.048
## ci.upper Std.lv Std.all
##
## 0.044 0.061 0.058
## 0.180 0.344 0.381
## 0.328 0.671 0.673
## 0.359 0.737 0.771
## 0.396 0.814 0.814
## 0.406 0.832 0.722
## 0.321 0.655 0.578
## 0.111 0.203 0.255
## 0.155 0.302 0.297
## 0.161 0.310 0.278
## 0.158 0.288 0.254
##
## 0.225 0.432 0.420
## 0.170 0.321 0.404
## 0.284 0.570 0.721
## 0.292 0.583 0.785
## 0.148 0.262 0.231
##
## 0.200 0.189 0.209
## 0.488 0.477 0.421
## 1.118 1.130 0.679
## 0.833 0.837 0.647
## 0.714 0.716 0.583
##
## 0.207 0.497 0.475
## 0.308 0.772 0.834
## 0.274 0.687 0.761
## 0.371 0.931 0.866
## 0.116 0.262 0.276
## 0.237 0.586 0.586
## 0.292 0.730 0.772
## 0.221 0.551 0.625
## 0.319 0.800 0.741
## 0.234 0.584 0.679
## 0.237 0.593 0.717
## 0.266 0.667 0.679
## 0.115 0.263 0.292
## 0.253 0.632 0.621
##
## 0.140 0.394 0.376
## 0.123 0.323 0.314
## 0.250 0.723 0.823
## 0.154 0.425 0.448
## 0.248 0.710 0.654
## 0.209 0.604 0.705
##
## 0.489 0.697 0.800
## 0.420 0.596 0.558
## 0.374 0.532 0.595
## 0.399 0.561 0.502
## 0.121 0.148 0.120
##
## 2.009 0.885 0.885
## 2.015 0.883 0.883
## 0.383 0.323 0.323
## 2.611 0.926 0.926
## 3.201 0.947 0.947
## 1.193 0.746 0.746
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age -0.025 0.015 -1.698 0.090 -0.054
## ci.upper Std.lv Std.all
##
## 0.004 -0.025 -0.036
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .math 0.000 0.000
## .Stst1vc (.97.) -1.171 0.022 -52.763 0.000 -1.214
## .Stst19d (.98.) -1.030 0.016 -64.275 0.000 -1.062
## .Stst20s (.99.) -0.760 0.019 -40.448 0.000 -0.797
## .Stst21c (.100) -1.173 0.018 -64.437 0.000 -1.209
## .Stst22p (.101) -1.233 0.020 -61.574 0.000 -1.272
## .Stst23n (.102) -1.060 0.022 -47.200 0.000 -1.104
## .Stst24x (.103) -0.957 0.020 -48.008 0.000 -0.996
## .Stst25w (.104) -0.841 0.014 -59.347 0.000 -0.869
## .Stst26r (.105) -1.329 0.021 -62.079 0.000 -1.371
## .Stst31b (.106) -1.065 0.023 -46.080 0.000 -1.110
## .Stst34r (.107) -1.174 0.022 -53.447 0.000 -1.217
## .Stst5mt (.108) -0.777 0.019 -39.940 0.000 -0.816
## .Stst32r (.109) -1.085 0.016 -67.852 0.000 -1.117
## .Stst33h (.110) -0.867 0.016 -55.481 0.000 -0.898
## .Stst35t (.111) -0.762 0.033 -23.182 0.000 -0.827
## .Stst36c (.112) 0.048 0.026 1.869 0.062 -0.002
## .Stst37b (.113) -0.309 0.023 -13.329 0.000 -0.354
## .Stst2lt (.114) -1.045 0.019 -54.433 0.000 -1.083
## .Stst3ms (.115) -0.871 0.018 -49.332 0.000 -0.906
## .Stst4sc -1.082 0.023 -46.121 0.000 -1.128
## .Stst7bl (.117) -0.626 0.019 -32.309 0.000 -0.664
## .Stst8rn -0.517 0.022 -23.687 0.000 -0.560
## .Stst11r (.119) -1.051 0.019 -56.698 0.000 -1.087
## .Stst12l (.120) -0.858 0.016 -53.920 0.000 -0.890
## .Stst13h (.121) -1.106 0.021 -51.977 0.000 -1.147
## .Stst14b (.122) -0.636 0.016 -38.855 0.000 -0.668
## .Stst15t -1.025 0.017 -59.418 0.000 -1.058
## .Stst16m (.124) -0.933 0.019 -50.151 0.000 -0.969
## .Stst6ph (.125) -0.696 0.019 -37.316 0.000 -0.733
## .Stst9lc (.126) -0.750 0.021 -35.158 0.000 -0.792
## .Stst10m -0.655 0.019 -33.926 0.000 -0.693
## .Stst28m -0.714 0.019 -36.899 0.000 -0.752
## .Sts292D (.129) -0.555 0.021 -26.622 0.000 -0.596
## .Sts303D (.130) -0.695 0.018 -38.446 0.000 -0.731
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -1.127 -1.171 -1.118
## -0.999 -1.030 -1.143
## -0.723 -0.760 -0.763
## -1.138 -1.173 -1.226
## -1.194 -1.233 -1.233
## -1.016 -1.060 -0.919
## -0.918 -0.957 -0.846
## -0.813 -0.841 -1.056
## -1.287 -1.329 -1.308
## -1.020 -1.065 -0.953
## -1.131 -1.174 -1.037
## -0.739 -0.777 -0.756
## -1.054 -1.085 -1.373
## -0.837 -0.867 -1.169
## -0.698 -0.762 -0.458
## 0.098 0.048 0.037
## -0.263 -0.309 -0.252
## -1.007 -1.045 -1.129
## -0.837 -0.871 -0.965
## -1.036 -1.082 -1.006
## -0.588 -0.626 -0.660
## -0.474 -0.517 -0.517
## -1.014 -1.051 -1.110
## -0.827 -0.858 -0.973
## -1.064 -1.106 -1.024
## -0.604 -0.636 -0.739
## -0.991 -1.025 -1.239
## -0.896 -0.933 -0.950
## -0.660 -0.696 -0.793
## -0.708 -0.750 -0.691
## -0.618 -0.655 -0.765
## -0.676 -0.714 -0.820
## -0.514 -0.555 -0.520
## -0.660 -0.695 -0.779
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.256 0.009 27.902 0.000 0.238
## .Stst19dsgsdwrd 0.374 0.014 27.185 0.000 0.347
## .Stest20spellng 0.543 0.017 31.103 0.000 0.509
## .Stest21cptlztn 0.372 0.015 24.498 0.000 0.342
## .Stest22puncttn 0.337 0.012 27.839 0.000 0.314
## .Stest23english 0.637 0.024 26.846 0.000 0.590
## .Stest24exprssn 0.853 0.025 33.467 0.000 0.803
## .Stst25wrdfnctn 0.387 0.012 32.710 0.000 0.364
## .Stst26rdngcmpr 0.230 0.009 25.465 0.000 0.212
## .Stst31bstrctrs 0.609 0.022 27.890 0.000 0.566
## .Stst34rthcmptt 0.636 0.030 20.979 0.000 0.576
## .Stest5math 0.533 0.020 26.732 0.000 0.494
## .Stst32rthrsnng 0.300 0.011 26.970 0.000 0.278
## .Stst33hghschlm 0.211 0.009 23.590 0.000 0.194
## .Stest35tblrdng 1.492 0.076 19.642 0.000 1.343
## .Stst36clrclchc 0.974 0.042 23.238 0.000 0.892
## .Stst37bjctnspc 0.921 0.034 26.976 0.000 0.854
## .Stest2literatr 0.260 0.009 29.707 0.000 0.243
## .Stest3music 0.344 0.012 28.971 0.000 0.321
## .Stest4soclstds 0.289 0.011 27.098 0.000 0.268
## .Stst7blgclscnc 0.455 0.014 32.587 0.000 0.428
## .Stest8aerontcs 0.657 0.018 37.074 0.000 0.622
## .Stest11art 0.363 0.012 29.835 0.000 0.339
## .Stest12law 0.474 0.015 32.626 0.000 0.445
## .Stest13health 0.527 0.016 32.162 0.000 0.495
## .Stest14bible 0.399 0.013 29.600 0.000 0.372
## .Stest15theater 0.333 0.011 30.664 0.000 0.311
## .Stest16mscllns 0.520 0.017 30.833 0.000 0.487
## .Stst6physclscn 0.249 0.010 24.387 0.000 0.229
## .Stest9elctrncs 0.675 0.027 25.020 0.000 0.622
## .Stest10mechncs 0.369 0.013 28.407 0.000 0.344
## .Stst28mchnclrs 0.274 0.015 17.975 0.000 0.244
## .Stst29vslztn2D 0.784 0.026 30.203 0.000 0.733
## .Stst30vslztn3D 0.514 0.017 30.504 0.000 0.481
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.274 0.256 0.234
## 0.401 0.374 0.461
## 0.577 0.543 0.547
## 0.401 0.372 0.406
## 0.361 0.337 0.337
## 0.683 0.637 0.479
## 0.903 0.853 0.666
## 0.411 0.387 0.611
## 0.247 0.230 0.222
## 0.651 0.609 0.487
## 0.695 0.636 0.495
## 0.572 0.533 0.504
## 0.322 0.300 0.480
## 0.229 0.211 0.384
## 1.641 1.492 0.539
## 1.056 0.974 0.581
## 0.988 0.921 0.611
## 0.278 0.260 0.304
## 0.367 0.344 0.421
## 0.310 0.289 0.250
## 0.483 0.455 0.506
## 0.692 0.657 0.657
## 0.386 0.363 0.405
## 0.502 0.474 0.609
## 0.559 0.527 0.452
## 0.425 0.399 0.539
## 0.354 0.333 0.486
## 0.553 0.520 0.539
## 0.269 0.249 0.323
## 0.728 0.675 0.573
## 0.394 0.369 0.503
## 0.304 0.274 0.360
## 0.835 0.784 0.688
## 0.547 0.514 0.645
## 1.000 0.216 0.216
## 1.000 0.220 0.220
## 1.000 0.895 0.895
## 1.000 0.142 0.142
## 1.000 0.103 0.103
## 1.000 0.443 0.443
## 1.000 0.999 0.999
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.028 0.008 3.643 0.000 0.013
## Stst19d (.p2.) 0.160 0.010 15.584 0.000 0.140
## Stst20s (.p3.) 0.312 0.008 37.080 0.000 0.295
## Stst21c (.p4.) 0.343 0.008 41.059 0.000 0.326
## Stst22p (.p5.) 0.378 0.009 42.031 0.000 0.361
## Stst23n (.p6.) 0.387 0.010 38.634 0.000 0.367
## Stst24x (.p7.) 0.304 0.009 34.710 0.000 0.287
## Stst25w (.p8.) 0.094 0.009 10.984 0.000 0.078
## Stst26r (.p9.) 0.141 0.008 18.386 0.000 0.126
## Stst31b (.10.) 0.144 0.009 16.746 0.000 0.127
## Stst34r (.11.) 0.134 0.012 10.811 0.000 0.110
## math =~
## Stst5mt (.12.) 0.203 0.011 18.208 0.000 0.181
## Stst25w (.13.) 0.151 0.010 15.361 0.000 0.132
## Stst32r (.14.) 0.267 0.009 30.794 0.000 0.250
## Stst33h (.15.) 0.273 0.009 29.253 0.000 0.255
## Stst34r (.16.) 0.123 0.013 9.550 0.000 0.098
## speed =~
## Stst19d (.17.) 0.179 0.011 16.195 0.000 0.157
## Stst34r (.18.) 0.452 0.019 24.208 0.000 0.415
## Stst35t (.19.) 1.069 0.025 42.808 0.000 1.020
## Stst36c (.20.) 0.792 0.021 37.573 0.000 0.751
## Stst37b (.21.) 0.678 0.019 36.361 0.000 0.641
## info =~
## Stst1vc (.22.) 0.187 0.010 18.503 0.000 0.168
## Stst2lt (.23.) 0.291 0.008 34.509 0.000 0.275
## Stst3ms (.24.) 0.259 0.008 33.078 0.000 0.244
## Stst4sc 0.286 0.008 33.996 0.000 0.270
## Stst7bl (.26.) 0.099 0.009 11.574 0.000 0.082
## Stst8rn 0.099 0.006 15.722 0.000 0.087
## Stst11r (.28.) 0.275 0.008 32.992 0.000 0.259
## Stst12l (.29.) 0.208 0.007 30.920 0.000 0.195
## Stst13h (.30.) 0.302 0.009 34.582 0.000 0.285
## Stst14b (.31.) 0.220 0.007 31.866 0.000 0.207
## Stst15t (.32.) 0.224 0.007 31.343 0.000 0.210
## Stst16m (.33.) 0.252 0.008 33.118 0.000 0.237
## Stst19d (.34.) 0.099 0.008 12.518 0.000 0.084
## Stst26r (.35.) 0.238 0.008 30.653 0.000 0.223
## science =~
## Stst1vc (.36.) 0.127 0.007 17.805 0.000 0.113
## Stst5mt (.37.) 0.104 0.010 10.659 0.000 0.085
## Stst6ph (.38.) 0.232 0.009 25.871 0.000 0.215
## Stst7bl (.39.) 0.136 0.009 15.348 0.000 0.119
## Stst9lc (.40.) 0.228 0.010 22.706 0.000 0.208
## Stst10m (.41.) 0.194 0.008 24.743 0.000 0.179
## spatial =~
## Stst28m 0.263 0.009 30.476 0.000 0.246
## Sts292D (.43.) 0.396 0.012 33.019 0.000 0.373
## Sts303D (.44.) 0.354 0.010 34.420 0.000 0.334
## Stst31b (.45.) 0.373 0.013 28.629 0.000 0.348
## Stst37b (.46.) 0.098 0.012 8.464 0.000 0.076
## g =~
## english (.47.) 1.904 0.054 35.581 0.000 1.799
## math (.48.) 1.881 0.069 27.455 0.000 1.747
## speed (.49.) 0.342 0.021 16.241 0.000 0.300
## info (.50.) 2.454 0.080 30.676 0.000 2.297
## science 1.827 0.087 21.093 0.000 1.657
## spatial (.52.) 1.121 0.037 30.178 0.000 1.048
## ci.upper Std.lv Std.all
##
## 0.044 0.061 0.066
## 0.180 0.343 0.376
## 0.328 0.671 0.683
## 0.359 0.737 0.738
## 0.396 0.814 0.827
## 0.406 0.832 0.747
## 0.321 0.654 0.593
## 0.111 0.203 0.258
## 0.155 0.302 0.300
## 0.161 0.310 0.280
## 0.158 0.288 0.248
##
## 0.225 0.432 0.437
## 0.170 0.321 0.408
## 0.284 0.570 0.735
## 0.292 0.582 0.805
## 0.148 0.262 0.226
##
## 0.200 0.189 0.207
## 0.488 0.477 0.412
## 1.118 1.130 0.697
## 0.833 0.837 0.647
## 0.714 0.716 0.622
##
## 0.207 0.497 0.535
## 0.308 0.772 0.842
## 0.274 0.687 0.759
## 0.303 0.759 0.834
## 0.116 0.262 0.305
## 0.111 0.262 0.315
## 0.292 0.730 0.756
## 0.221 0.551 0.645
## 0.319 0.799 0.717
## 0.234 0.583 0.663
## 0.237 0.592 0.679
## 0.266 0.667 0.698
## 0.115 0.263 0.287
## 0.253 0.631 0.627
##
## 0.140 0.264 0.284
## 0.123 0.216 0.219
## 0.250 0.484 0.711
## 0.154 0.284 0.331
## 0.248 0.475 0.476
## 0.209 0.404 0.639
##
## 0.279 0.394 0.635
## 0.420 0.595 0.587
## 0.374 0.531 0.662
## 0.399 0.561 0.506
## 0.121 0.148 0.128
##
## 2.009 0.885 0.885
## 2.015 0.883 0.883
## 0.383 0.323 0.323
## 2.611 0.926 0.926
## 1.996 0.877 0.877
## 1.193 0.746 0.746
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.012 0.013 0.946 0.344 -0.013
## ci.upper Std.lv Std.all
##
## 0.037 0.012 0.016
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .math 0.000 0.000
## .Stst1vc (.97.) -1.171 0.022 -52.763 0.000 -1.214
## .Stst19d (.98.) -1.030 0.016 -64.275 0.000 -1.062
## .Stst20s (.99.) -0.760 0.019 -40.448 0.000 -0.797
## .Stst21c (.100) -1.173 0.018 -64.437 0.000 -1.209
## .Stst22p (.101) -1.233 0.020 -61.574 0.000 -1.272
## .Stst23n (.102) -1.060 0.022 -47.200 0.000 -1.104
## .Stst24x (.103) -0.957 0.020 -48.008 0.000 -0.996
## .Stst25w (.104) -0.841 0.014 -59.347 0.000 -0.869
## .Stst26r (.105) -1.329 0.021 -62.079 0.000 -1.371
## .Stst31b (.106) -1.065 0.023 -46.080 0.000 -1.110
## .Stst34r (.107) -1.174 0.022 -53.447 0.000 -1.217
## .Stst5mt (.108) -0.777 0.019 -39.940 0.000 -0.816
## .Stst32r (.109) -1.085 0.016 -67.852 0.000 -1.117
## .Stst33h (.110) -0.867 0.016 -55.481 0.000 -0.898
## .Stst35t (.111) -0.762 0.033 -23.182 0.000 -0.827
## .Stst36c (.112) 0.048 0.026 1.869 0.062 -0.002
## .Stst37b (.113) -0.309 0.023 -13.329 0.000 -0.354
## .Stst2lt (.114) -1.045 0.019 -54.433 0.000 -1.083
## .Stst3ms (.115) -0.871 0.018 -49.332 0.000 -0.906
## .Stst4sc -1.286 0.020 -62.836 0.000 -1.327
## .Stst7bl (.117) -0.626 0.019 -32.309 0.000 -0.664
## .Stst8rn -0.947 0.015 -62.318 0.000 -0.976
## .Stst11r (.119) -1.051 0.019 -56.698 0.000 -1.087
## .Stst12l (.120) -0.858 0.016 -53.920 0.000 -0.890
## .Stst13h (.121) -1.106 0.021 -51.977 0.000 -1.147
## .Stst14b (.122) -0.636 0.016 -38.855 0.000 -0.668
## .Stst15t -0.866 0.018 -47.940 0.000 -0.902
## .Stst16m (.124) -0.933 0.019 -50.151 0.000 -0.969
## .Stst6ph (.125) -0.696 0.019 -37.316 0.000 -0.733
## .Stst9lc (.126) -0.750 0.021 -35.158 0.000 -0.792
## .Stst10m -1.083 0.019 -57.064 0.000 -1.121
## .Stst28m -1.101 0.018 -59.926 0.000 -1.137
## .Sts292D (.129) -0.555 0.021 -26.622 0.000 -0.596
## .Sts303D (.130) -0.695 0.018 -38.446 0.000 -0.731
## .english 1.111 0.061 18.213 0.000 0.991
## .speed 0.304 0.036 8.483 0.000 0.234
## .info 0.427 0.068 6.269 0.000 0.293
## .science -1.211 0.087 -13.973 0.000 -1.381
## .spatial -0.672 0.055 -12.326 0.000 -0.779
## .g -0.152 0.036 -4.194 0.000 -0.222
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -1.127 -1.171 -1.261
## -0.999 -1.030 -1.127
## -0.723 -0.760 -0.774
## -1.138 -1.173 -1.175
## -1.194 -1.233 -1.253
## -1.016 -1.060 -0.951
## -0.918 -0.957 -0.868
## -0.813 -0.841 -1.069
## -1.287 -1.329 -1.321
## -1.020 -1.065 -0.961
## -1.131 -1.174 -1.013
## -0.739 -0.777 -0.785
## -1.054 -1.085 -1.400
## -0.837 -0.867 -1.198
## -0.698 -0.762 -0.470
## 0.098 0.048 0.037
## -0.263 -0.309 -0.268
## -1.007 -1.045 -1.139
## -0.837 -0.871 -0.963
## -1.246 -1.286 -1.413
## -0.588 -0.626 -0.729
## -0.917 -0.947 -1.136
## -1.014 -1.051 -1.088
## -0.827 -0.858 -1.005
## -1.064 -1.106 -0.991
## -0.604 -0.636 -0.723
## -0.831 -0.866 -0.994
## -0.896 -0.933 -0.977
## -0.660 -0.696 -1.023
## -0.708 -0.750 -0.751
## -1.046 -1.083 -1.714
## -1.065 -1.101 -1.774
## -0.514 -0.555 -0.547
## -0.660 -0.695 -0.867
## 1.230 0.516 0.516
## 0.375 0.288 0.288
## 0.560 0.161 0.161
## -1.041 -0.581 -0.581
## -0.566 -0.448 -0.448
## -0.081 -0.152 -0.152
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.254 0.007 34.998 0.000 0.240
## .Stst19dsgsdwrd 0.398 0.011 36.493 0.000 0.377
## .Stest20spellng 0.515 0.014 36.732 0.000 0.488
## .Stest21cptlztn 0.454 0.013 33.745 0.000 0.427
## .Stest22puncttn 0.306 0.010 29.632 0.000 0.286
## .Stest23english 0.550 0.017 32.833 0.000 0.517
## .Stest24exprssn 0.788 0.021 37.457 0.000 0.747
## .Stst25wrdfnctn 0.372 0.010 37.099 0.000 0.352
## .Stst26rdngcmpr 0.210 0.007 29.330 0.000 0.196
## .Stst31bstrctrs 0.587 0.017 34.291 0.000 0.554
## .Stst34rthcmptt 0.697 0.027 26.050 0.000 0.645
## .Stest5math 0.601 0.017 36.136 0.000 0.569
## .Stst32rthrsnng 0.276 0.008 32.624 0.000 0.259
## .Stst33hghschlm 0.185 0.007 26.907 0.000 0.171
## .Stest35tblrdng 1.354 0.068 19.959 0.000 1.221
## .Stst36clrclchc 0.971 0.034 28.851 0.000 0.905
## .Stst37bjctnspc 0.739 0.026 28.208 0.000 0.688
## .Stest2literatr 0.245 0.007 35.689 0.000 0.232
## .Stest3music 0.347 0.009 37.535 0.000 0.329
## .Stest4soclstds 0.252 0.007 34.632 0.000 0.238
## .Stst7blgclscnc 0.467 0.012 39.241 0.000 0.443
## .Stest8aerontcs 0.626 0.011 58.944 0.000 0.605
## .Stest11art 0.399 0.011 37.114 0.000 0.378
## .Stest12law 0.425 0.011 40.118 0.000 0.405
## .Stest13health 0.605 0.015 40.494 0.000 0.576
## .Stest14bible 0.433 0.013 33.919 0.000 0.408
## .Stest15theater 0.410 0.011 38.647 0.000 0.389
## .Stest16mscllns 0.467 0.012 37.925 0.000 0.442
## .Stst6physclscn 0.229 0.007 31.173 0.000 0.215
## .Stest9elctrncs 0.772 0.020 37.930 0.000 0.732
## .Stest10mechncs 0.236 0.006 36.915 0.000 0.224
## .Stst28mchnclrs 0.230 0.007 33.276 0.000 0.216
## .Stst29vslztn2D 0.674 0.019 34.873 0.000 0.636
## .Stst30vslztn3D 0.362 0.011 33.247 0.000 0.340
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.268 0.254 0.295
## 0.420 0.398 0.476
## 0.543 0.515 0.534
## 0.480 0.454 0.455
## 0.326 0.306 0.316
## 0.583 0.550 0.443
## 0.829 0.788 0.648
## 0.392 0.372 0.601
## 0.224 0.210 0.207
## 0.621 0.587 0.478
## 0.750 0.697 0.519
## 0.634 0.601 0.614
## 0.293 0.276 0.460
## 0.198 0.185 0.353
## 1.487 1.354 0.515
## 1.037 0.971 0.581
## 0.791 0.739 0.558
## 0.259 0.245 0.292
## 0.365 0.347 0.424
## 0.267 0.252 0.304
## 0.490 0.467 0.633
## 0.647 0.626 0.901
## 0.420 0.399 0.428
## 0.446 0.425 0.583
## 0.634 0.605 0.486
## 0.458 0.433 0.560
## 0.430 0.410 0.539
## 0.491 0.467 0.512
## 0.244 0.229 0.495
## 0.812 0.772 0.774
## 0.249 0.236 0.592
## 0.243 0.230 0.596
## 0.712 0.674 0.655
## 0.383 0.362 0.561
## 1.000 0.216 0.216
## 1.000 0.220 0.220
## 1.000 0.895 0.895
## 1.000 0.142 0.142
## 1.000 0.231 0.231
## 1.000 0.443 0.443
## 1.000 1.000 1.000
sem.age2<-sem(hof.age2, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("g=~science", "info=~Stest8aeronautics", "spatial=~Stest28mechanicalreasoning", "info=~Stest4socialstudies", "Stest10mechanics~1", "Stest8aeronautics~1", "Stest28mechanicalreasoning~1", "Stest4socialstudies~1", "Stest15theater~1"))
fitMeasures(sem.age2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 7741.367 1221.000 0.000 0.942 0.042 0.054
## ecvi aic bic
## 1.329 463799.878 464961.328
Mc(sem.age2)
## [1] 0.5851648
summary(sem.age2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 127 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 250
## Number of equality constraints 77
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 7741.367 6918.401
## Degrees of freedom 1221 1221
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.119
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 3578.444 3198.028
## 1 4162.923 3720.373
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.029 0.008 3.656 0.000 0.013
## Stst19d (.p2.) 0.160 0.010 15.588 0.000 0.140
## Stst20s (.p3.) 0.312 0.008 37.133 0.000 0.296
## Stst21c (.p4.) 0.343 0.008 41.130 0.000 0.326
## Stst22p (.p5.) 0.378 0.009 42.106 0.000 0.361
## Stst23n (.p6.) 0.387 0.010 38.677 0.000 0.367
## Stst24x (.p7.) 0.304 0.009 34.755 0.000 0.287
## Stst25w (.p8.) 0.095 0.009 10.987 0.000 0.078
## Stst26r (.p9.) 0.141 0.008 18.392 0.000 0.126
## Stst31b (.10.) 0.144 0.009 16.750 0.000 0.127
## Stst34r (.11.) 0.134 0.012 10.820 0.000 0.110
## math =~
## Stst5mt (.12.) 0.203 0.011 18.211 0.000 0.181
## Stst25w (.13.) 0.151 0.010 15.354 0.000 0.131
## Stst32r (.14.) 0.267 0.009 30.772 0.000 0.250
## Stst33h (.15.) 0.273 0.009 29.246 0.000 0.255
## Stst34r (.16.) 0.123 0.013 9.544 0.000 0.098
## speed =~
## Stst19d (.17.) 0.179 0.011 16.185 0.000 0.157
## Stst34r (.18.) 0.452 0.019 24.198 0.000 0.415
## Stst35t (.19.) 1.069 0.025 42.822 0.000 1.020
## Stst36c (.20.) 0.792 0.021 37.566 0.000 0.751
## Stst37b (.21.) 0.678 0.019 36.353 0.000 0.641
## info =~
## Stst1vc (.22.) 0.187 0.010 18.476 0.000 0.167
## Stst2lt (.23.) 0.291 0.008 34.462 0.000 0.275
## Stst3ms (.24.) 0.259 0.008 33.039 0.000 0.244
## Stst4sc 0.351 0.010 34.384 0.000 0.331
## Stst7bl (.26.) 0.099 0.009 11.569 0.000 0.082
## Stst8rn 0.221 0.008 26.270 0.000 0.204
## Stst11r (.28.) 0.275 0.008 32.950 0.000 0.259
## Stst12l (.29.) 0.208 0.007 30.862 0.000 0.195
## Stst13h (.30.) 0.302 0.009 34.535 0.000 0.284
## Stst14b (.31.) 0.220 0.007 31.824 0.000 0.206
## Stst15t (.32.) 0.223 0.007 31.310 0.000 0.209
## Stst16m (.33.) 0.251 0.008 33.074 0.000 0.237
## Stst19d (.34.) 0.099 0.008 12.514 0.000 0.084
## Stst26r (.35.) 0.238 0.008 30.630 0.000 0.223
## science =~
## Stst1vc (.36.) 0.127 0.007 17.826 0.000 0.113
## Stst5mt (.37.) 0.104 0.010 10.677 0.000 0.085
## Stst6ph (.38.) 0.233 0.009 25.950 0.000 0.215
## Stst7bl (.39.) 0.137 0.009 15.368 0.000 0.119
## Stst9lc (.40.) 0.228 0.010 22.764 0.000 0.209
## Stst10m (.41.) 0.194 0.008 24.803 0.000 0.179
## spatial =~
## Stst28m 0.464 0.013 36.522 0.000 0.439
## Sts292D (.43.) 0.396 0.012 33.014 0.000 0.373
## Sts303D (.44.) 0.354 0.010 34.407 0.000 0.333
## Stst31b (.45.) 0.373 0.013 28.625 0.000 0.347
## Stst37b (.46.) 0.098 0.012 8.459 0.000 0.075
## g =~
## english (.47.) 1.894 0.053 35.656 0.000 1.790
## math (.48.) 1.873 0.068 27.422 0.000 1.739
## speed (.49.) 0.340 0.021 16.274 0.000 0.299
## info (.50.) 2.444 0.080 30.626 0.000 2.287
## science 2.923 0.129 22.678 0.000 2.671
## spatial (.52.) 1.116 0.037 30.198 0.000 1.044
## ci.upper Std.lv Std.all
##
## 0.044 0.062 0.059
## 0.180 0.345 0.382
## 0.329 0.673 0.675
## 0.359 0.740 0.772
## 0.396 0.817 0.815
## 0.407 0.835 0.723
## 0.322 0.657 0.580
## 0.111 0.204 0.256
## 0.156 0.303 0.298
## 0.161 0.311 0.278
## 0.158 0.289 0.255
##
## 0.225 0.434 0.421
## 0.170 0.322 0.404
## 0.284 0.572 0.722
## 0.292 0.584 0.786
## 0.148 0.263 0.231
##
## 0.200 0.189 0.209
## 0.488 0.477 0.421
## 1.118 1.131 0.679
## 0.833 0.837 0.647
## 0.714 0.717 0.584
##
## 0.207 0.498 0.475
## 0.308 0.775 0.835
## 0.274 0.689 0.762
## 0.371 0.934 0.867
## 0.116 0.263 0.277
## 0.237 0.588 0.587
## 0.292 0.733 0.773
## 0.221 0.553 0.627
## 0.319 0.803 0.742
## 0.234 0.586 0.680
## 0.237 0.595 0.718
## 0.266 0.669 0.680
## 0.115 0.264 0.292
## 0.253 0.634 0.622
##
## 0.141 0.395 0.376
## 0.123 0.324 0.315
## 0.250 0.725 0.823
## 0.154 0.426 0.448
## 0.248 0.712 0.655
## 0.210 0.606 0.706
##
## 0.488 0.698 0.800
## 0.420 0.597 0.559
## 0.374 0.533 0.596
## 0.399 0.562 0.502
## 0.121 0.148 0.120
##
## 1.998 0.886 0.886
## 2.007 0.884 0.884
## 0.381 0.325 0.325
## 2.600 0.927 0.927
## 3.176 0.947 0.947
## 1.189 0.748 0.748
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.003 0.016 0.213 0.831 -0.028
## age2 -0.050 0.007 -6.736 0.000 -0.064
## ci.upper Std.lv Std.all
##
## 0.035 0.003 0.005
## -0.035 -0.049 -0.139
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .math 0.000 0.000
## .Stst1vc (.100) -1.080 0.027 -39.634 0.000 -1.134
## .Stst19d (.101) -0.968 0.020 -49.235 0.000 -1.007
## .Stst20s (.102) -0.700 0.021 -32.600 0.000 -0.742
## .Stst21c (.103) -1.107 0.022 -50.769 0.000 -1.150
## .Stst22p (.104) -1.160 0.024 -48.164 0.000 -1.207
## .Stst23n (.105) -0.985 0.026 -37.573 0.000 -1.036
## .Stst24x (.106) -0.898 0.022 -40.072 0.000 -0.942
## .Stst25w (.107) -0.793 0.017 -47.196 0.000 -0.826
## .Stst26r (.108) -1.242 0.027 -46.760 0.000 -1.294
## .Stst31b (.109) -0.994 0.026 -37.554 0.000 -1.046
## .Stst34r (.110) -1.109 0.025 -44.245 0.000 -1.158
## .Stst5mt (.111) -0.707 0.023 -30.189 0.000 -0.753
## .Stst32r (.112) -1.034 0.019 -54.151 0.000 -1.071
## .Stst33h (.113) -0.815 0.019 -43.105 0.000 -0.852
## .Stst35t (.114) -0.725 0.033 -21.811 0.000 -0.790
## .Stst36c (.115) 0.075 0.026 2.892 0.004 0.024
## .Stst37b (.116) -0.274 0.024 -11.337 0.000 -0.321
## .Stst2lt (.117) -0.972 0.023 -41.793 0.000 -1.018
## .Stst3ms (.118) -0.806 0.021 -37.817 0.000 -0.848
## .Stst4sc -0.994 0.028 -35.395 0.000 -1.049
## .Stst7bl (.120) -0.560 0.023 -24.324 0.000 -0.605
## .Stst8rn -0.462 0.024 -19.255 0.000 -0.509
## .Stst11r (.122) -0.982 0.022 -44.008 0.000 -1.025
## .Stst12l (.123) -0.806 0.019 -43.082 0.000 -0.843
## .Stst13h (.124) -1.030 0.025 -41.045 0.000 -1.079
## .Stst14b (.125) -0.581 0.019 -30.218 0.000 -0.618
## .Stst15t -0.969 0.020 -48.453 0.000 -1.008
## .Stst16m (.127) -0.870 0.022 -39.596 0.000 -0.913
## .Stst6ph (.128) -0.627 0.023 -27.501 0.000 -0.671
## .Stst9lc (.129) -0.682 0.025 -27.367 0.000 -0.731
## .Stst10m -0.597 0.022 -26.814 0.000 -0.641
## .Stst28m -0.661 0.022 -29.938 0.000 -0.705
## .Sts292D (.132) -0.510 0.023 -22.643 0.000 -0.554
## .Sts303D (.133) -0.655 0.020 -33.289 0.000 -0.694
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -1.027 -1.080 -1.029
## -0.930 -0.968 -1.072
## -0.658 -0.700 -0.701
## -1.064 -1.107 -1.155
## -1.113 -1.160 -1.157
## -0.934 -0.985 -0.853
## -0.854 -0.898 -0.793
## -0.761 -0.793 -0.995
## -1.190 -1.242 -1.219
## -0.942 -0.994 -0.888
## -1.060 -1.109 -0.978
## -0.661 -0.707 -0.686
## -0.997 -1.034 -1.306
## -0.778 -0.815 -1.096
## -0.660 -0.725 -0.436
## 0.126 0.075 0.058
## -0.227 -0.274 -0.223
## -0.927 -0.972 -1.048
## -0.765 -0.806 -0.891
## -0.939 -0.994 -0.922
## -0.515 -0.560 -0.589
## -0.415 -0.462 -0.461
## -0.938 -0.982 -1.035
## -0.770 -0.806 -0.913
## -0.981 -1.030 -0.952
## -0.543 -0.581 -0.674
## -0.930 -0.969 -1.169
## -0.827 -0.870 -0.884
## -0.582 -0.627 -0.712
## -0.633 -0.682 -0.627
## -0.554 -0.597 -0.696
## -0.618 -0.661 -0.758
## -0.466 -0.510 -0.477
## -0.616 -0.655 -0.733
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.256 0.009 27.906 0.000 0.238
## .Stst19dsgsdwrd 0.374 0.014 27.187 0.000 0.347
## .Stest20spellng 0.543 0.017 31.097 0.000 0.509
## .Stest21cptlztn 0.372 0.015 24.500 0.000 0.342
## .Stest22puncttn 0.337 0.012 27.839 0.000 0.314
## .Stest23english 0.637 0.024 26.849 0.000 0.590
## .Stest24exprssn 0.853 0.025 33.469 0.000 0.803
## .Stst25wrdfnctn 0.387 0.012 32.710 0.000 0.364
## .Stst26rdngcmpr 0.230 0.009 25.471 0.000 0.212
## .Stst31bstrctrs 0.609 0.022 27.897 0.000 0.566
## .Stst34rthcmptt 0.636 0.030 20.979 0.000 0.576
## .Stest5math 0.533 0.020 26.724 0.000 0.494
## .Stst32rthrsnng 0.300 0.011 26.947 0.000 0.278
## .Stst33hghschlm 0.211 0.009 23.600 0.000 0.194
## .Stest35tblrdng 1.492 0.076 19.640 0.000 1.343
## .Stst36clrclchc 0.974 0.042 23.243 0.000 0.892
## .Stst37bjctnspc 0.921 0.034 26.978 0.000 0.854
## .Stest2literatr 0.260 0.009 29.691 0.000 0.243
## .Stest3music 0.344 0.012 28.968 0.000 0.320
## .Stest4soclstds 0.289 0.011 27.091 0.000 0.268
## .Stst7blgclscnc 0.455 0.014 32.586 0.000 0.428
## .Stest8aerontcs 0.657 0.018 37.074 0.000 0.622
## .Stest11art 0.363 0.012 29.841 0.000 0.339
## .Stest12law 0.474 0.015 32.626 0.000 0.445
## .Stest13health 0.527 0.016 32.155 0.000 0.495
## .Stest14bible 0.399 0.013 29.598 0.000 0.373
## .Stest15theater 0.333 0.011 30.663 0.000 0.311
## .Stest16mscllns 0.520 0.017 30.837 0.000 0.487
## .Stst6physclscn 0.250 0.010 24.391 0.000 0.230
## .Stest9elctrncs 0.675 0.027 25.006 0.000 0.622
## .Stest10mechncs 0.369 0.013 28.405 0.000 0.343
## .Stst28mchnclrs 0.274 0.015 17.969 0.000 0.244
## .Stst29vslztn2D 0.784 0.026 30.208 0.000 0.733
## .Stst30vslztn3D 0.514 0.017 30.503 0.000 0.481
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.274 0.256 0.233
## 0.401 0.374 0.459
## 0.577 0.543 0.545
## 0.401 0.372 0.405
## 0.361 0.337 0.336
## 0.683 0.637 0.477
## 0.903 0.853 0.664
## 0.411 0.387 0.609
## 0.247 0.230 0.221
## 0.651 0.609 0.486
## 0.695 0.636 0.494
## 0.572 0.533 0.502
## 0.322 0.300 0.478
## 0.229 0.211 0.382
## 1.641 1.492 0.539
## 1.056 0.974 0.581
## 0.988 0.921 0.611
## 0.278 0.260 0.302
## 0.367 0.344 0.420
## 0.310 0.289 0.249
## 0.483 0.455 0.504
## 0.692 0.657 0.655
## 0.386 0.363 0.403
## 0.502 0.474 0.607
## 0.559 0.527 0.450
## 0.425 0.399 0.538
## 0.354 0.333 0.485
## 0.553 0.520 0.537
## 0.270 0.250 0.322
## 0.728 0.675 0.571
## 0.394 0.369 0.501
## 0.303 0.274 0.359
## 0.835 0.784 0.687
## 0.547 0.514 0.644
## 1.000 0.215 0.215
## 1.000 0.219 0.219
## 1.000 0.894 0.894
## 1.000 0.141 0.141
## 1.000 0.103 0.103
## 1.000 0.441 0.441
## 1.000 0.981 0.981
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.029 0.008 3.656 0.000 0.013
## Stst19d (.p2.) 0.160 0.010 15.588 0.000 0.140
## Stst20s (.p3.) 0.312 0.008 37.133 0.000 0.296
## Stst21c (.p4.) 0.343 0.008 41.130 0.000 0.326
## Stst22p (.p5.) 0.378 0.009 42.106 0.000 0.361
## Stst23n (.p6.) 0.387 0.010 38.677 0.000 0.367
## Stst24x (.p7.) 0.304 0.009 34.755 0.000 0.287
## Stst25w (.p8.) 0.095 0.009 10.987 0.000 0.078
## Stst26r (.p9.) 0.141 0.008 18.392 0.000 0.126
## Stst31b (.10.) 0.144 0.009 16.750 0.000 0.127
## Stst34r (.11.) 0.134 0.012 10.820 0.000 0.110
## math =~
## Stst5mt (.12.) 0.203 0.011 18.211 0.000 0.181
## Stst25w (.13.) 0.151 0.010 15.354 0.000 0.131
## Stst32r (.14.) 0.267 0.009 30.772 0.000 0.250
## Stst33h (.15.) 0.273 0.009 29.246 0.000 0.255
## Stst34r (.16.) 0.123 0.013 9.544 0.000 0.098
## speed =~
## Stst19d (.17.) 0.179 0.011 16.185 0.000 0.157
## Stst34r (.18.) 0.452 0.019 24.198 0.000 0.415
## Stst35t (.19.) 1.069 0.025 42.822 0.000 1.020
## Stst36c (.20.) 0.792 0.021 37.566 0.000 0.751
## Stst37b (.21.) 0.678 0.019 36.353 0.000 0.641
## info =~
## Stst1vc (.22.) 0.187 0.010 18.476 0.000 0.167
## Stst2lt (.23.) 0.291 0.008 34.462 0.000 0.275
## Stst3ms (.24.) 0.259 0.008 33.039 0.000 0.244
## Stst4sc 0.286 0.008 33.931 0.000 0.270
## Stst7bl (.26.) 0.099 0.009 11.569 0.000 0.082
## Stst8rn 0.099 0.006 15.722 0.000 0.087
## Stst11r (.28.) 0.275 0.008 32.950 0.000 0.259
## Stst12l (.29.) 0.208 0.007 30.862 0.000 0.195
## Stst13h (.30.) 0.302 0.009 34.535 0.000 0.284
## Stst14b (.31.) 0.220 0.007 31.824 0.000 0.206
## Stst15t (.32.) 0.223 0.007 31.310 0.000 0.209
## Stst16m (.33.) 0.251 0.008 33.074 0.000 0.237
## Stst19d (.34.) 0.099 0.008 12.514 0.000 0.084
## Stst26r (.35.) 0.238 0.008 30.630 0.000 0.223
## science =~
## Stst1vc (.36.) 0.127 0.007 17.826 0.000 0.113
## Stst5mt (.37.) 0.104 0.010 10.677 0.000 0.085
## Stst6ph (.38.) 0.233 0.009 25.950 0.000 0.215
## Stst7bl (.39.) 0.137 0.009 15.368 0.000 0.119
## Stst9lc (.40.) 0.228 0.010 22.764 0.000 0.209
## Stst10m (.41.) 0.194 0.008 24.803 0.000 0.179
## spatial =~
## Stst28m 0.262 0.009 30.462 0.000 0.246
## Sts292D (.43.) 0.396 0.012 33.014 0.000 0.373
## Sts303D (.44.) 0.354 0.010 34.407 0.000 0.333
## Stst31b (.45.) 0.373 0.013 28.625 0.000 0.347
## Stst37b (.46.) 0.098 0.012 8.459 0.000 0.075
## g =~
## english (.47.) 1.894 0.053 35.656 0.000 1.790
## math (.48.) 1.873 0.068 27.422 0.000 1.739
## speed (.49.) 0.340 0.021 16.274 0.000 0.299
## info (.50.) 2.444 0.080 30.626 0.000 2.287
## science 1.814 0.086 21.104 0.000 1.646
## spatial (.52.) 1.116 0.037 30.198 0.000 1.044
## ci.upper Std.lv Std.all
##
## 0.044 0.061 0.066
## 0.180 0.343 0.375
## 0.329 0.670 0.682
## 0.359 0.735 0.737
## 0.396 0.812 0.826
## 0.407 0.830 0.746
## 0.322 0.653 0.593
## 0.111 0.203 0.258
## 0.156 0.302 0.300
## 0.161 0.310 0.280
## 0.158 0.287 0.248
##
## 0.225 0.431 0.436
## 0.170 0.321 0.408
## 0.284 0.569 0.734
## 0.292 0.581 0.804
## 0.148 0.261 0.225
##
## 0.200 0.189 0.207
## 0.488 0.477 0.412
## 1.118 1.130 0.697
## 0.833 0.837 0.647
## 0.714 0.716 0.622
##
## 0.207 0.495 0.535
## 0.308 0.770 0.841
## 0.274 0.685 0.758
## 0.303 0.758 0.833
## 0.116 0.261 0.305
## 0.111 0.262 0.314
## 0.292 0.728 0.755
## 0.221 0.550 0.645
## 0.319 0.798 0.716
## 0.234 0.582 0.662
## 0.237 0.591 0.678
## 0.266 0.665 0.698
## 0.115 0.262 0.287
## 0.253 0.630 0.627
##
## 0.141 0.263 0.284
## 0.123 0.216 0.218
## 0.250 0.483 0.710
## 0.154 0.284 0.331
## 0.248 0.474 0.475
## 0.210 0.403 0.639
##
## 0.279 0.394 0.635
## 0.420 0.595 0.587
## 0.374 0.531 0.662
## 0.399 0.560 0.506
## 0.121 0.147 0.128
##
## 1.998 0.885 0.885
## 2.007 0.883 0.883
## 0.381 0.323 0.323
## 2.600 0.926 0.926
## 1.983 0.876 0.876
## 1.189 0.745 0.745
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.007 0.013 0.565 0.572 -0.018
## age2 -0.028 0.007 -4.009 0.000 -0.042
## ci.upper Std.lv Std.all
##
## 0.032 0.007 0.009
## -0.014 -0.028 -0.063
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .math 0.000 0.000
## .Stst1vc (.100) -1.080 0.027 -39.634 0.000 -1.134
## .Stst19d (.101) -0.968 0.020 -49.235 0.000 -1.007
## .Stst20s (.102) -0.700 0.021 -32.600 0.000 -0.742
## .Stst21c (.103) -1.107 0.022 -50.769 0.000 -1.150
## .Stst22p (.104) -1.160 0.024 -48.164 0.000 -1.207
## .Stst23n (.105) -0.985 0.026 -37.573 0.000 -1.036
## .Stst24x (.106) -0.898 0.022 -40.072 0.000 -0.942
## .Stst25w (.107) -0.793 0.017 -47.196 0.000 -0.826
## .Stst26r (.108) -1.242 0.027 -46.760 0.000 -1.294
## .Stst31b (.109) -0.994 0.026 -37.554 0.000 -1.046
## .Stst34r (.110) -1.109 0.025 -44.245 0.000 -1.158
## .Stst5mt (.111) -0.707 0.023 -30.189 0.000 -0.753
## .Stst32r (.112) -1.034 0.019 -54.151 0.000 -1.071
## .Stst33h (.113) -0.815 0.019 -43.105 0.000 -0.852
## .Stst35t (.114) -0.725 0.033 -21.811 0.000 -0.790
## .Stst36c (.115) 0.075 0.026 2.892 0.004 0.024
## .Stst37b (.116) -0.274 0.024 -11.337 0.000 -0.321
## .Stst2lt (.117) -0.972 0.023 -41.793 0.000 -1.018
## .Stst3ms (.118) -0.806 0.021 -37.817 0.000 -0.848
## .Stst4sc -1.215 0.024 -50.087 0.000 -1.262
## .Stst7bl (.120) -0.560 0.023 -24.324 0.000 -0.605
## .Stst8rn -0.922 0.016 -57.989 0.000 -0.953
## .Stst11r (.122) -0.982 0.022 -44.008 0.000 -1.025
## .Stst12l (.123) -0.806 0.019 -43.082 0.000 -0.843
## .Stst13h (.124) -1.030 0.025 -41.045 0.000 -1.079
## .Stst14b (.125) -0.581 0.019 -30.218 0.000 -0.618
## .Stst15t -0.810 0.021 -38.953 0.000 -0.851
## .Stst16m (.127) -0.870 0.022 -39.596 0.000 -0.913
## .Stst6ph (.128) -0.627 0.023 -27.501 0.000 -0.671
## .Stst9lc (.129) -0.682 0.025 -27.367 0.000 -0.731
## .Stst10m -1.025 0.022 -46.554 0.000 -1.068
## .Stst28m -1.071 0.020 -54.446 0.000 -1.110
## .Sts292D (.132) -0.510 0.023 -22.643 0.000 -0.554
## .Sts303D (.133) -0.655 0.020 -33.289 0.000 -0.694
## .english 1.110 0.061 18.218 0.000 0.991
## .speed 0.304 0.036 8.484 0.000 0.234
## .info 0.427 0.068 6.271 0.000 0.294
## .science -1.323 0.092 -14.404 0.000 -1.503
## .spatial -0.673 0.055 -12.327 0.000 -0.780
## .g -0.206 0.044 -4.705 0.000 -0.292
## ci.upper Std.lv Std.all
## 0.000 0.000 0.000
## -1.027 -1.080 -1.166
## -0.930 -0.968 -1.060
## -0.658 -0.700 -0.713
## -1.064 -1.107 -1.110
## -1.113 -1.160 -1.180
## -0.934 -0.985 -0.885
## -0.854 -0.898 -0.815
## -0.761 -0.793 -1.010
## -1.190 -1.242 -1.237
## -0.942 -0.994 -0.898
## -1.060 -1.109 -0.957
## -0.661 -0.707 -0.715
## -0.997 -1.034 -1.336
## -0.778 -0.815 -1.127
## -0.660 -0.725 -0.447
## 0.126 0.075 0.058
## -0.227 -0.274 -0.238
## -0.927 -0.972 -1.062
## -0.765 -0.806 -0.892
## -1.167 -1.215 -1.336
## -0.515 -0.560 -0.653
## -0.891 -0.922 -1.106
## -0.938 -0.982 -1.018
## -0.770 -0.806 -0.945
## -0.981 -1.030 -0.925
## -0.543 -0.581 -0.661
## -0.770 -0.810 -0.930
## -0.827 -0.870 -0.912
## -0.582 -0.627 -0.922
## -0.633 -0.682 -0.683
## -0.982 -1.025 -1.623
## -1.033 -1.071 -1.727
## -0.466 -0.510 -0.503
## -0.616 -0.655 -0.817
## 1.229 0.517 0.517
## 0.375 0.288 0.288
## 0.561 0.161 0.161
## -1.143 -0.637 -0.637
## -0.566 -0.448 -0.448
## -0.120 -0.206 -0.206
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.254 0.007 34.996 0.000 0.240
## .Stst19dsgsdwrd 0.398 0.011 36.497 0.000 0.377
## .Stest20spellng 0.515 0.014 36.730 0.000 0.488
## .Stest21cptlztn 0.454 0.013 33.742 0.000 0.427
## .Stest22puncttn 0.306 0.010 29.632 0.000 0.286
## .Stest23english 0.550 0.017 32.827 0.000 0.517
## .Stest24exprssn 0.788 0.021 37.455 0.000 0.747
## .Stst25wrdfnctn 0.372 0.010 37.097 0.000 0.352
## .Stst26rdngcmpr 0.210 0.007 29.337 0.000 0.196
## .Stst31bstrctrs 0.587 0.017 34.296 0.000 0.554
## .Stst34rthcmptt 0.697 0.027 26.051 0.000 0.645
## .Stest5math 0.601 0.017 36.136 0.000 0.569
## .Stst32rthrsnng 0.276 0.008 32.623 0.000 0.259
## .Stst33hghschlm 0.185 0.007 26.915 0.000 0.171
## .Stest35tblrdng 1.354 0.068 19.958 0.000 1.221
## .Stst36clrclchc 0.972 0.034 28.862 0.000 0.906
## .Stst37bjctnspc 0.739 0.026 28.211 0.000 0.688
## .Stest2literatr 0.245 0.007 35.679 0.000 0.232
## .Stest3music 0.347 0.009 37.537 0.000 0.329
## .Stest4soclstds 0.252 0.007 34.630 0.000 0.238
## .Stst7blgclscnc 0.467 0.012 39.230 0.000 0.443
## .Stest8aerontcs 0.626 0.011 58.945 0.000 0.605
## .Stest11art 0.399 0.011 37.114 0.000 0.378
## .Stest12law 0.425 0.011 40.116 0.000 0.405
## .Stest13health 0.605 0.015 40.486 0.000 0.576
## .Stest14bible 0.433 0.013 33.919 0.000 0.408
## .Stest15theater 0.410 0.011 38.646 0.000 0.389
## .Stest16mscllns 0.466 0.012 37.928 0.000 0.442
## .Stst6physclscn 0.229 0.007 31.161 0.000 0.215
## .Stest9elctrncs 0.772 0.020 37.926 0.000 0.732
## .Stest10mechncs 0.236 0.006 36.902 0.000 0.224
## .Stst28mchnclrs 0.230 0.007 33.272 0.000 0.216
## .Stst29vslztn2D 0.674 0.019 34.875 0.000 0.636
## .Stst30vslztn3D 0.362 0.011 33.243 0.000 0.340
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .info 1.000 1.000
## .science 1.000 1.000
## .spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.268 0.254 0.296
## 0.420 0.398 0.478
## 0.542 0.515 0.535
## 0.480 0.454 0.456
## 0.326 0.306 0.317
## 0.583 0.550 0.444
## 0.829 0.788 0.649
## 0.392 0.372 0.603
## 0.224 0.210 0.208
## 0.621 0.587 0.479
## 0.750 0.697 0.520
## 0.634 0.601 0.615
## 0.293 0.276 0.461
## 0.198 0.185 0.354
## 1.487 1.354 0.515
## 1.037 0.972 0.581
## 0.791 0.739 0.558
## 0.259 0.245 0.293
## 0.365 0.347 0.425
## 0.267 0.252 0.305
## 0.490 0.467 0.634
## 0.647 0.626 0.901
## 0.420 0.399 0.429
## 0.446 0.425 0.585
## 0.634 0.605 0.487
## 0.458 0.433 0.561
## 0.430 0.410 0.540
## 0.491 0.466 0.513
## 0.244 0.229 0.496
## 0.812 0.772 0.774
## 0.249 0.236 0.592
## 0.243 0.230 0.597
## 0.712 0.674 0.656
## 0.383 0.362 0.562
## 1.000 0.217 0.217
## 1.000 0.221 0.221
## 1.000 0.896 0.896
## 1.000 0.143 0.143
## 1.000 0.232 0.232
## 1.000 0.444 0.444
## 1.000 0.996 0.996
# CHC Bifactor models (most loadings in Science factors become zero after scalar invariance)
chc.bifactor.model <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest9electronics + Stest10mechanics
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g=~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
'
baseline<-cfa(chc.bifactor.model, data=dgroup, meanstructure=TRUE, sampling.weights="BY_WTA", orthogonal=T)
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 5831.383 481.000 0.000 0.953 0.043 0.034
## aic bic
## 468493.152 469486.762
Mc(baseline)
## [1] 0.6442236
configural<-cfa(chc.bifactor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T)
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 4786.652 962.000 0.000 0.966 0.036 0.025
## aic bic
## 461799.055 463786.276
Mc(configural)
## [1] 0.7302849
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 54 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 296
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 4786.652 4303.421
## Degrees of freedom 962 962
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.112
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 2226.862 2002.052
## 1 2559.790 2301.369
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stest1vocab 0.083 0.021 3.879 0.000 0.041
## Stst19dsgsdwrd 0.240 0.024 10.083 0.000 0.193
## Stest20spellng 0.373 0.025 15.072 0.000 0.325
## Stest21cptlztn 0.318 0.022 14.367 0.000 0.275
## Stest22puncttn 0.372 0.022 16.832 0.000 0.329
## Stest23english 0.410 0.028 14.405 0.000 0.354
## Stest24exprssn 0.325 0.030 10.871 0.000 0.266
## Stst25wrdfnctn 0.145 0.022 6.695 0.000 0.102
## Stst26rdngcmpr 0.165 0.018 9.178 0.000 0.130
## Stst31bstrctrs 0.160 0.027 5.908 0.000 0.107
## Stst34rthcmptt 0.212 0.029 7.280 0.000 0.155
## math =~
## Stest5math 0.216 0.024 9.105 0.000 0.170
## Stst25wrdfnctn 0.177 0.024 7.276 0.000 0.129
## Stst32rthrsnng 0.224 0.023 9.754 0.000 0.179
## Stst33hghschlm 0.363 0.027 13.391 0.000 0.310
## Stst34rthcmptt 0.217 0.027 8.168 0.000 0.165
## speed =~
## Stst19dsgsdwrd 0.163 0.016 10.068 0.000 0.131
## Stst34rthcmptt 0.444 0.029 15.489 0.000 0.388
## Stest35tblrdng 0.945 0.043 22.205 0.000 0.862
## Stst36clrclchc 0.892 0.029 31.222 0.000 0.836
## Stst37bjctnspc 0.733 0.029 25.266 0.000 0.676
## info =~
## Stest1vocab 0.194 0.027 7.089 0.000 0.140
## Stest2literatr 0.277 0.024 11.548 0.000 0.230
## Stest3music 0.280 0.022 12.563 0.000 0.236
## Stest4soclstds 0.197 0.031 6.324 0.000 0.136
## Stst7blgclscnc 0.078 0.032 2.466 0.014 0.016
## Stest8aerontcs 0.151 0.032 4.732 0.000 0.088
## Stest11art 0.345 0.022 15.800 0.000 0.302
## Stest12law 0.188 0.026 7.116 0.000 0.136
## Stest13health 0.224 0.031 7.285 0.000 0.164
## Stest14bible 0.192 0.024 7.872 0.000 0.144
## Stest15theater 0.316 0.021 14.846 0.000 0.275
## Stest16mscllns 0.283 0.029 9.888 0.000 0.227
## Stst19dsgsdwrd 0.159 0.026 6.029 0.000 0.107
## Stst26rdngcmpr 0.209 0.020 10.587 0.000 0.170
## science =~
## Stest1vocab 0.201 0.042 4.747 0.000 0.118
## Stest5math 0.132 0.029 4.591 0.000 0.075
## Stst6physclscn 0.146 0.033 4.393 0.000 0.081
## Stst7blgclscnc 0.129 0.034 3.799 0.000 0.062
## Stest9elctrncs 0.408 0.075 5.407 0.000 0.260
## Stest10mechncs 0.272 0.039 6.922 0.000 0.195
## spatial =~
## Stst28mchnclrs 0.381 0.019 19.689 0.000 0.343
## Stst29vslztn2D 0.487 0.028 17.242 0.000 0.432
## Stst30vslztn3D 0.506 0.023 22.019 0.000 0.461
## Stst31bstrctrs 0.447 0.023 19.275 0.000 0.401
## Stst37bjctnspc 0.313 0.028 11.367 0.000 0.259
## g =~
## Stest1vocab 0.898 0.019 48.142 0.000 0.862
## Stest2literatr 0.768 0.018 42.431 0.000 0.732
## Stest3music 0.629 0.018 35.607 0.000 0.594
## Stest4soclstds 0.946 0.017 54.492 0.000 0.912
## Stest5math 0.711 0.019 37.566 0.000 0.674
## Stst6physclscn 0.711 0.017 41.097 0.000 0.677
## Stst7blgclscnc 0.685 0.019 36.752 0.000 0.649
## Stest8aerontcs 0.591 0.021 28.331 0.000 0.550
## Stest9elctrncs 0.690 0.022 31.308 0.000 0.647
## Stest10mechncs 0.625 0.017 36.511 0.000 0.592
## Stest11art 0.668 0.017 39.352 0.000 0.634
## Stest12law 0.618 0.020 31.002 0.000 0.579
## Stest13health 0.789 0.019 40.954 0.000 0.751
## Stest14bible 0.560 0.019 29.900 0.000 0.523
## Stest15theater 0.514 0.017 29.404 0.000 0.480
## Stest16mscllns 0.713 0.020 35.642 0.000 0.674
## Stst19dsgsdwrd 0.546 0.019 28.994 0.000 0.509
## Stest20spellng 0.579 0.020 29.237 0.000 0.541
## Stest21cptlztn 0.636 0.017 37.810 0.000 0.603
## Stest22puncttn 0.712 0.019 36.892 0.000 0.674
## Stest23english 0.785 0.022 35.732 0.000 0.742
## Stest24exprssn 0.636 0.022 28.822 0.000 0.592
## Stst25wrdfnctn 0.412 0.018 22.384 0.000 0.376
## Stst26rdngcmpr 0.928 0.017 55.423 0.000 0.895
## Stst28mchnclrs 0.574 0.019 30.428 0.000 0.537
## Stst29vslztn2D 0.456 0.022 20.785 0.000 0.413
## Stst30vslztn3D 0.452 0.020 22.262 0.000 0.413
## Stst31bstrctrs 0.704 0.021 33.594 0.000 0.663
## Stst32rthrsnng 0.585 0.018 32.667 0.000 0.550
## Stst33hghschlm 0.563 0.018 31.023 0.000 0.527
## Stst34rthcmptt 0.631 0.022 28.373 0.000 0.587
## Stest35tblrdng 0.583 0.032 17.991 0.000 0.519
## Stst36clrclchc 0.158 0.027 5.776 0.000 0.104
## Stst37bjctnspc 0.246 0.026 9.385 0.000 0.195
## ci.upper Std.lv Std.all
##
## 0.125 0.083 0.078
## 0.286 0.240 0.275
## 0.422 0.373 0.374
## 0.362 0.318 0.337
## 0.416 0.372 0.373
## 0.465 0.410 0.345
## 0.383 0.325 0.279
## 0.187 0.145 0.186
## 0.200 0.165 0.154
## 0.213 0.160 0.140
## 0.269 0.212 0.186
##
## 0.263 0.216 0.206
## 0.225 0.177 0.228
## 0.269 0.224 0.266
## 0.416 0.363 0.462
## 0.269 0.217 0.190
##
## 0.194 0.163 0.186
## 0.500 0.444 0.389
## 1.028 0.945 0.566
## 0.948 0.892 0.688
## 0.790 0.733 0.596
##
## 0.248 0.194 0.182
## 0.324 0.277 0.288
## 0.323 0.280 0.311
## 0.258 0.197 0.178
## 0.141 0.078 0.081
## 0.213 0.151 0.149
## 0.387 0.345 0.362
## 0.239 0.188 0.201
## 0.285 0.224 0.205
## 0.240 0.192 0.223
## 0.358 0.316 0.387
## 0.339 0.283 0.270
## 0.211 0.159 0.182
## 0.248 0.209 0.195
##
## 0.285 0.201 0.189
## 0.188 0.132 0.125
## 0.211 0.146 0.164
## 0.195 0.129 0.132
## 0.556 0.408 0.367
## 0.348 0.272 0.303
##
## 0.419 0.381 0.423
## 0.542 0.487 0.446
## 0.551 0.506 0.534
## 0.492 0.447 0.392
## 0.367 0.313 0.255
##
## 0.935 0.898 0.843
## 0.803 0.768 0.797
## 0.663 0.629 0.700
## 0.981 0.946 0.855
## 0.748 0.711 0.678
## 0.745 0.711 0.799
## 0.722 0.685 0.704
## 0.631 0.591 0.582
## 0.734 0.690 0.621
## 0.659 0.625 0.697
## 0.701 0.668 0.702
## 0.657 0.618 0.660
## 0.827 0.789 0.722
## 0.597 0.560 0.649
## 0.548 0.514 0.629
## 0.753 0.713 0.682
## 0.583 0.546 0.626
## 0.618 0.579 0.581
## 0.669 0.636 0.674
## 0.750 0.712 0.714
## 0.828 0.785 0.660
## 0.679 0.636 0.546
## 0.448 0.412 0.530
## 0.961 0.928 0.863
## 0.611 0.574 0.639
## 0.499 0.456 0.418
## 0.492 0.452 0.477
## 0.745 0.704 0.618
## 0.621 0.585 0.697
## 0.598 0.563 0.717
## 0.674 0.631 0.553
## 0.646 0.583 0.349
## 0.212 0.158 0.122
## 0.298 0.246 0.200
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -1.155 0.023 -50.360 0.000 -1.200
## .Stst19dsgsdwrd -0.992 0.018 -53.776 0.000 -1.028
## .Stest20spellng -0.848 0.021 -39.900 0.000 -0.890
## .Stest21cptlztn -1.167 0.020 -58.007 0.000 -1.206
## .Stest22puncttn -1.226 0.021 -57.496 0.000 -1.268
## .Stest23english -1.062 0.026 -41.362 0.000 -1.113
## .Stest24exprssn -0.965 0.025 -38.928 0.000 -1.014
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.903
## .Stst26rdngcmpr -1.292 0.023 -56.802 0.000 -1.337
## .Stst31bstrctrs -1.070 0.024 -43.766 0.000 -1.118
## .Stst34rthcmptt -1.153 0.025 -46.702 0.000 -1.201
## .Stest5math -0.814 0.022 -36.442 0.000 -0.857
## .Stst32rthrsnng -1.052 0.018 -59.194 0.000 -1.087
## .Stst33hghschlm -0.875 0.016 -53.483 0.000 -0.907
## .Stest35tblrdng -0.712 0.037 -19.463 0.000 -0.784
## .Stst36clrclchc -0.032 0.028 -1.139 0.255 -0.086
## .Stst37bjctnspc -0.318 0.027 -11.957 0.000 -0.370
## .Stest2literatr -1.041 0.021 -50.624 0.000 -1.081
## .Stest3music -0.921 0.019 -48.386 0.000 -0.959
## .Stest4soclstds -1.083 0.023 -46.133 0.000 -1.129
## .Stst7blgclscnc -0.617 0.021 -29.442 0.000 -0.658
## .Stest8aerontcs -0.517 0.022 -23.664 0.000 -0.560
## .Stest11art -1.040 0.020 -51.542 0.000 -1.079
## .Stest12law -0.778 0.020 -39.122 0.000 -0.817
## .Stest13health -1.200 0.023 -51.595 0.000 -1.245
## .Stest14bible -0.720 0.018 -39.356 0.000 -0.756
## .Stest15theater -1.025 0.017 -59.426 0.000 -1.059
## .Stest16mscllns -0.887 0.022 -39.478 0.000 -0.931
## .Stst6physclscn -0.732 0.019 -38.793 0.000 -0.769
## .Stest9elctrncs -0.668 0.024 -27.887 0.000 -0.715
## .Stest10mechncs -0.656 0.019 -33.970 0.000 -0.694
## .Stst28mchnclrs -0.715 0.019 -36.895 0.000 -0.753
## .Stst29vslztn2D -0.512 0.023 -22.047 0.000 -0.557
## .Stst30vslztn3D -0.723 0.020 -35.874 0.000 -0.762
## ci.upper Std.lv Std.all
## -1.110 -1.155 -1.083
## -0.956 -0.992 -1.138
## -0.806 -0.848 -0.851
## -1.128 -1.167 -1.236
## -1.184 -1.226 -1.229
## -1.012 -1.062 -0.893
## -0.916 -0.965 -0.829
## -0.838 -0.871 -1.122
## -1.248 -1.292 -1.203
## -1.022 -1.070 -0.939
## -1.104 -1.153 -1.011
## -0.770 -0.814 -0.776
## -1.017 -1.052 -1.253
## -0.843 -0.875 -1.115
## -0.640 -0.712 -0.427
## 0.023 -0.032 -0.025
## -0.266 -0.318 -0.259
## -1.000 -1.041 -1.080
## -0.884 -0.921 -1.026
## -1.037 -1.083 -0.978
## -0.576 -0.617 -0.633
## -0.475 -0.517 -0.510
## -1.000 -1.040 -1.093
## -0.739 -0.778 -0.832
## -1.154 -1.200 -1.098
## -0.684 -0.720 -0.834
## -0.991 -1.025 -1.254
## -0.843 -0.887 -0.848
## -0.695 -0.732 -0.822
## -0.621 -0.668 -0.601
## -0.618 -0.656 -0.732
## -0.677 -0.715 -0.795
## -0.466 -0.512 -0.469
## -0.683 -0.723 -0.763
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.244 0.015 16.318 0.000 0.214
## .Stst19dsgsdwrd 0.353 0.015 24.085 0.000 0.324
## .Stest20spellng 0.519 0.019 27.921 0.000 0.482
## .Stest21cptlztn 0.385 0.015 24.952 0.000 0.355
## .Stest22puncttn 0.350 0.014 25.607 0.000 0.323
## .Stest23english 0.630 0.025 25.193 0.000 0.581
## .Stest24exprssn 0.846 0.027 31.803 0.000 0.794
## .Stst25wrdfnctn 0.380 0.013 29.261 0.000 0.355
## .Stst26rdngcmpr 0.223 0.009 25.274 0.000 0.206
## .Stst31bstrctrs 0.576 0.023 25.323 0.000 0.532
## .Stst34rthcmptt 0.613 0.028 22.071 0.000 0.559
## .Stest5math 0.530 0.020 26.100 0.000 0.490
## .Stst32rthrsnng 0.312 0.012 26.485 0.000 0.289
## .Stst33hghschlm 0.168 0.018 9.585 0.000 0.134
## .Stest35tblrdng 1.550 0.073 21.274 0.000 1.408
## .Stst36clrclchc 0.858 0.047 18.322 0.000 0.766
## .Stst37bjctnspc 0.817 0.038 21.698 0.000 0.743
## .Stest2literatr 0.261 0.009 28.017 0.000 0.243
## .Stest3music 0.333 0.012 27.019 0.000 0.309
## .Stest4soclstds 0.291 0.011 27.349 0.000 0.271
## .Stst7blgclscnc 0.456 0.014 32.100 0.000 0.428
## .Stest8aerontcs 0.657 0.018 37.266 0.000 0.622
## .Stest11art 0.340 0.013 26.233 0.000 0.314
## .Stest12law 0.458 0.014 33.101 0.000 0.431
## .Stest13health 0.522 0.016 31.801 0.000 0.490
## .Stest14bible 0.393 0.014 29.025 0.000 0.367
## .Stest15theater 0.304 0.012 24.453 0.000 0.280
## .Stest16mscllns 0.506 0.017 29.538 0.000 0.472
## .Stst6physclscn 0.265 0.011 24.907 0.000 0.245
## .Stest9elctrncs 0.592 0.059 10.064 0.000 0.477
## .Stest10mechncs 0.339 0.020 17.074 0.000 0.300
## .Stst28mchnclrs 0.334 0.015 22.387 0.000 0.305
## .Stst29vslztn2D 0.744 0.029 25.692 0.000 0.687
## .Stst30vslztn3D 0.438 0.020 21.494 0.000 0.398
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.273 0.244 0.215
## 0.381 0.353 0.464
## 0.555 0.519 0.522
## 0.415 0.385 0.432
## 0.377 0.350 0.351
## 0.679 0.630 0.445
## 0.898 0.846 0.624
## 0.406 0.380 0.632
## 0.240 0.223 0.193
## 0.621 0.576 0.444
## 0.668 0.613 0.472
## 0.570 0.530 0.482
## 0.335 0.312 0.443
## 0.203 0.168 0.273
## 1.693 1.550 0.557
## 0.950 0.858 0.511
## 0.891 0.817 0.540
## 0.280 0.261 0.282
## 0.358 0.333 0.413
## 0.312 0.291 0.238
## 0.484 0.456 0.481
## 0.691 0.657 0.639
## 0.365 0.340 0.376
## 0.485 0.458 0.524
## 0.554 0.522 0.437
## 0.420 0.393 0.529
## 0.328 0.304 0.455
## 0.539 0.506 0.462
## 0.286 0.265 0.335
## 0.707 0.592 0.479
## 0.378 0.339 0.422
## 0.363 0.334 0.413
## 0.801 0.744 0.626
## 0.478 0.438 0.487
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stest1vocab 0.105 0.020 5.133 0.000 0.065
## Stst19dsgsdwrd 0.254 0.024 10.778 0.000 0.207
## Stest20spellng 0.320 0.023 13.619 0.000 0.274
## Stest21cptlztn 0.297 0.021 14.233 0.000 0.256
## Stest22puncttn 0.343 0.020 16.816 0.000 0.303
## Stest23english 0.359 0.022 16.034 0.000 0.315
## Stest24exprssn 0.285 0.027 10.662 0.000 0.232
## Stst25wrdfnctn 0.080 0.021 3.831 0.000 0.039
## Stst26rdngcmpr 0.153 0.016 9.411 0.000 0.121
## Stst31bstrctrs 0.162 0.027 6.107 0.000 0.110
## Stst34rthcmptt 0.246 0.027 9.109 0.000 0.193
## math =~
## Stest5math 0.222 0.027 8.175 0.000 0.169
## Stst25wrdfnctn 0.160 0.036 4.494 0.000 0.090
## Stst32rthrsnng 0.143 0.027 5.231 0.000 0.089
## Stst33hghschlm 0.315 0.034 9.369 0.000 0.249
## Stst34rthcmptt 0.212 0.029 7.212 0.000 0.155
## speed =~
## Stst19dsgsdwrd 0.216 0.015 14.708 0.000 0.187
## Stst34rthcmptt 0.467 0.025 18.744 0.000 0.419
## Stest35tblrdng 0.947 0.034 27.914 0.000 0.880
## Stst36clrclchc 0.875 0.023 38.543 0.000 0.831
## Stst37bjctnspc 0.694 0.023 30.681 0.000 0.650
## info =~
## Stest1vocab 0.259 0.021 12.386 0.000 0.218
## Stest2literatr 0.334 0.019 17.980 0.000 0.298
## Stest3music 0.293 0.019 15.600 0.000 0.256
## Stest4soclstds 0.232 0.023 10.175 0.000 0.188
## Stst7blgclscnc 0.113 0.024 4.658 0.000 0.066
## Stest8aerontcs 0.143 0.021 6.908 0.000 0.103
## Stest11art 0.408 0.019 21.553 0.000 0.371
## Stest12law 0.200 0.019 10.584 0.000 0.163
## Stest13health 0.246 0.025 9.676 0.000 0.197
## Stest14bible 0.188 0.026 7.207 0.000 0.137
## Stest15theater 0.310 0.019 16.529 0.000 0.273
## Stest16mscllns 0.207 0.019 10.618 0.000 0.168
## Stst19dsgsdwrd 0.185 0.022 8.363 0.000 0.141
## Stst26rdngcmpr 0.229 0.018 12.946 0.000 0.194
## science =~
## Stest1vocab 0.160 0.024 6.665 0.000 0.113
## Stest5math 0.235 0.025 9.384 0.000 0.186
## Stst6physclscn 0.191 0.018 10.389 0.000 0.155
## Stst7blgclscnc 0.116 0.027 4.340 0.000 0.063
## Stest9elctrncs 0.368 0.037 9.950 0.000 0.296
## Stest10mechncs 0.154 0.018 8.595 0.000 0.118
## spatial =~
## Stst28mchnclrs 0.157 0.014 11.371 0.000 0.130
## Stst29vslztn2D 0.419 0.025 16.844 0.000 0.371
## Stst30vslztn3D 0.387 0.020 18.870 0.000 0.347
## Stst31bstrctrs 0.375 0.022 16.748 0.000 0.331
## Stst37bjctnspc 0.246 0.024 10.219 0.000 0.199
## g =~
## Stest1vocab 0.705 0.016 44.231 0.000 0.673
## Stest2literatr 0.666 0.015 43.529 0.000 0.636
## Stest3music 0.628 0.015 42.080 0.000 0.598
## Stest4soclstds 0.697 0.014 48.072 0.000 0.668
## Stest5math 0.553 0.017 32.404 0.000 0.519
## Stst6physclscn 0.459 0.013 34.295 0.000 0.433
## Stst7blgclscnc 0.464 0.016 28.186 0.000 0.432
## Stest8aerontcs 0.219 0.017 12.985 0.000 0.186
## Stest9elctrncs 0.296 0.018 16.024 0.000 0.260
## Stest10mechncs 0.324 0.011 28.467 0.000 0.301
## Stest11art 0.631 0.016 39.959 0.000 0.600
## Stest12law 0.448 0.015 29.758 0.000 0.419
## Stest13health 0.742 0.017 44.373 0.000 0.709
## Stest14bible 0.541 0.016 34.040 0.000 0.510
## Stest15theater 0.536 0.016 33.708 0.000 0.505
## Stest16mscllns 0.564 0.015 37.110 0.000 0.534
## Stst19dsgsdwrd 0.605 0.017 35.966 0.000 0.572
## Stest20spellng 0.566 0.016 35.299 0.000 0.535
## Stest21cptlztn 0.690 0.015 47.134 0.000 0.662
## Stest22puncttn 0.734 0.015 48.172 0.000 0.704
## Stest23english 0.709 0.017 42.221 0.000 0.676
## Stest24exprssn 0.542 0.017 31.096 0.000 0.507
## Stst25wrdfnctn 0.482 0.016 30.414 0.000 0.451
## Stst26rdngcmpr 0.809 0.014 58.807 0.000 0.782
## Stst28mchnclrs 0.323 0.012 26.285 0.000 0.299
## Stst29vslztn2D 0.384 0.018 21.758 0.000 0.349
## Stst30vslztn3D 0.333 0.015 22.550 0.000 0.304
## Stst31bstrctrs 0.669 0.017 39.504 0.000 0.636
## Stst32rthrsnng 0.473 0.015 31.213 0.000 0.443
## Stst33hghschlm 0.478 0.014 34.863 0.000 0.451
## Stst34rthcmptt 0.593 0.019 31.253 0.000 0.556
## Stest35tblrdng 0.597 0.027 22.218 0.000 0.545
## Stst36clrclchc 0.117 0.022 5.379 0.000 0.074
## Stst37bjctnspc 0.274 0.021 13.285 0.000 0.234
## ci.upper Std.lv Std.all
##
## 0.145 0.105 0.114
## 0.300 0.254 0.270
## 0.366 0.320 0.332
## 0.337 0.297 0.293
## 0.383 0.343 0.348
## 0.403 0.359 0.329
## 0.337 0.285 0.264
## 0.121 0.080 0.101
## 0.184 0.153 0.158
## 0.214 0.162 0.148
## 0.299 0.246 0.213
##
## 0.275 0.222 0.225
## 0.230 0.160 0.201
## 0.197 0.143 0.194
## 0.381 0.315 0.454
## 0.270 0.212 0.184
##
## 0.244 0.216 0.230
## 0.516 0.467 0.405
## 1.013 0.947 0.583
## 0.920 0.875 0.683
## 0.739 0.694 0.607
##
## 0.300 0.259 0.282
## 0.371 0.334 0.375
## 0.330 0.293 0.323
## 0.277 0.232 0.260
## 0.161 0.113 0.134
## 0.184 0.143 0.172
## 0.445 0.408 0.423
## 0.237 0.200 0.245
## 0.296 0.246 0.224
## 0.239 0.188 0.215
## 0.347 0.310 0.352
## 0.245 0.207 0.227
## 0.228 0.185 0.197
## 0.264 0.229 0.236
##
## 0.207 0.160 0.175
## 0.285 0.235 0.239
## 0.227 0.191 0.276
## 0.168 0.116 0.137
## 0.441 0.368 0.383
## 0.189 0.154 0.251
##
## 0.184 0.157 0.257
## 0.468 0.419 0.424
## 0.427 0.387 0.500
## 0.419 0.375 0.344
## 0.294 0.246 0.215
##
## 0.736 0.705 0.767
## 0.696 0.666 0.747
## 0.657 0.628 0.693
## 0.725 0.697 0.780
## 0.586 0.553 0.561
## 0.486 0.459 0.664
## 0.497 0.464 0.550
## 0.252 0.219 0.264
## 0.332 0.296 0.308
## 0.346 0.324 0.529
## 0.662 0.631 0.654
## 0.478 0.448 0.550
## 0.774 0.742 0.673
## 0.572 0.541 0.619
## 0.567 0.536 0.608
## 0.594 0.564 0.619
## 0.638 0.605 0.645
## 0.598 0.566 0.588
## 0.719 0.690 0.682
## 0.764 0.734 0.745
## 0.742 0.709 0.650
## 0.576 0.542 0.501
## 0.513 0.482 0.604
## 0.836 0.809 0.835
## 0.347 0.323 0.528
## 0.418 0.384 0.388
## 0.362 0.333 0.430
## 0.702 0.669 0.612
## 0.502 0.473 0.640
## 0.505 0.478 0.688
## 0.630 0.593 0.514
## 0.650 0.597 0.368
## 0.159 0.117 0.091
## 0.315 0.274 0.239
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -1.339 0.016 -83.554 0.000 -1.370
## .Stst19dsgsdwrd -0.878 0.016 -54.059 0.000 -0.910
## .Stest20spellng -0.450 0.017 -26.686 0.000 -0.483
## .Stest21cptlztn -0.899 0.017 -51.477 0.000 -0.934
## .Stest22puncttn -0.929 0.017 -53.286 0.000 -0.963
## .Stest23english -0.744 0.019 -38.449 0.000 -0.781
## .Stest24exprssn -0.704 0.019 -37.099 0.000 -0.742
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.816
## .Stst26rdngcmpr -1.226 0.017 -72.842 0.000 -1.259
## .Stst31bstrctrs -1.260 0.019 -65.843 0.000 -1.297
## .Stst34rthcmptt -1.004 0.021 -47.990 0.000 -1.045
## .Stest5math -0.965 0.017 -55.615 0.000 -0.999
## .Stst32rthrsnng -1.184 0.013 -92.849 0.000 -1.209
## .Stst33hghschlm -0.942 0.012 -78.389 0.000 -0.966
## .Stest35tblrdng -0.524 0.029 -17.830 0.000 -0.582
## .Stst36clrclchc 0.300 0.023 13.284 0.000 0.256
## .Stst37bjctnspc -0.217 0.021 -10.567 0.000 -0.257
## .Stest2literatr -1.034 0.016 -66.363 0.000 -1.065
## .Stest3music -0.825 0.016 -52.646 0.000 -0.856
## .Stest4soclstds -1.273 0.015 -82.694 0.000 -1.303
## .Stst7blgclscnc -0.831 0.015 -55.991 0.000 -0.860
## .Stest8aerontcs -0.942 0.014 -64.960 0.000 -0.970
## .Stest11art -1.046 0.017 -63.114 0.000 -1.078
## .Stest12law -0.897 0.014 -63.710 0.000 -0.925
## .Stest13health -1.020 0.019 -52.885 0.000 -1.057
## .Stest14bible -0.565 0.015 -36.958 0.000 -0.595
## .Stest15theater -0.856 0.015 -56.660 0.000 -0.885
## .Stest16mscllns -0.949 0.016 -60.013 0.000 -0.980
## .Stst6physclscn -1.022 0.012 -84.927 0.000 -1.046
## .Stest9elctrncs -1.154 0.017 -68.546 0.000 -1.187
## .Stest10mechncs -1.373 0.011 -128.778 0.000 -1.394
## .Stst28mchnclrs -1.323 0.011 -124.285 0.000 -1.344
## .Stst29vslztn2D -0.916 0.017 -52.801 0.000 -0.950
## .Stst30vslztn3D -0.982 0.014 -72.639 0.000 -1.008
## ci.upper Std.lv Std.all
## -1.307 -1.339 -1.458
## -0.846 -0.878 -0.937
## -0.417 -0.450 -0.467
## -0.865 -0.899 -0.889
## -0.895 -0.929 -0.942
## -0.706 -0.744 -0.682
## -0.667 -0.704 -0.652
## -0.761 -0.788 -0.989
## -1.193 -1.226 -1.265
## -1.222 -1.260 -1.153
## -0.963 -1.004 -0.869
## -0.931 -0.965 -0.978
## -1.159 -1.184 -1.604
## -0.919 -0.942 -1.356
## -0.466 -0.524 -0.323
## 0.344 0.300 0.234
## -0.176 -0.217 -0.189
## -1.004 -1.034 -1.160
## -0.795 -0.825 -0.911
## -1.243 -1.273 -1.425
## -0.802 -0.831 -0.985
## -0.913 -0.942 -1.133
## -1.013 -1.046 -1.085
## -0.870 -0.897 -1.101
## -0.982 -1.020 -0.926
## -0.535 -0.565 -0.647
## -0.826 -0.856 -0.970
## -0.918 -0.949 -1.042
## -0.998 -1.022 -1.477
## -1.121 -1.154 -1.202
## -1.352 -1.373 -2.245
## -1.303 -1.323 -2.162
## -0.882 -0.916 -0.926
## -0.955 -0.982 -1.270
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.243 0.010 24.502 0.000 0.224
## .Stst19dsgsdwrd 0.368 0.012 29.679 0.000 0.344
## .Stest20spellng 0.506 0.015 33.389 0.000 0.476
## .Stest21cptlztn 0.459 0.014 32.661 0.000 0.431
## .Stest22puncttn 0.315 0.011 27.718 0.000 0.293
## .Stest23english 0.559 0.017 31.953 0.000 0.524
## .Stest24exprssn 0.793 0.022 35.990 0.000 0.750
## .Stst25wrdfnctn 0.371 0.012 29.954 0.000 0.347
## .Stst26rdngcmpr 0.209 0.007 29.823 0.000 0.195
## .Stst31bstrctrs 0.579 0.019 31.293 0.000 0.543
## .Stst34rthcmptt 0.657 0.028 23.705 0.000 0.603
## .Stest5math 0.562 0.019 29.565 0.000 0.524
## .Stst32rthrsnng 0.301 0.009 32.980 0.000 0.283
## .Stst33hghschlm 0.155 0.021 7.293 0.000 0.113
## .Stest35tblrdng 1.383 0.059 23.501 0.000 1.268
## .Stst36clrclchc 0.862 0.036 23.667 0.000 0.791
## .Stst37bjctnspc 0.692 0.028 24.365 0.000 0.636
## .Stest2literatr 0.240 0.008 31.811 0.000 0.225
## .Stest3music 0.342 0.009 36.520 0.000 0.323
## .Stest4soclstds 0.258 0.007 35.266 0.000 0.243
## .Stst7blgclscnc 0.470 0.012 39.170 0.000 0.447
## .Stest8aerontcs 0.623 0.011 57.834 0.000 0.602
## .Stest11art 0.365 0.012 30.458 0.000 0.341
## .Stest12law 0.423 0.011 39.770 0.000 0.402
## .Stest13health 0.602 0.015 40.740 0.000 0.573
## .Stest14bible 0.434 0.013 34.641 0.000 0.410
## .Stest15theater 0.394 0.011 36.980 0.000 0.373
## .Stest16mscllns 0.468 0.012 38.363 0.000 0.444
## .Stst6physclscn 0.231 0.008 29.774 0.000 0.216
## .Stest9elctrncs 0.699 0.029 23.691 0.000 0.641
## .Stest10mechncs 0.246 0.007 34.061 0.000 0.231
## .Stst28mchnclrs 0.245 0.006 37.797 0.000 0.233
## .Stst29vslztn2D 0.654 0.022 29.180 0.000 0.610
## .Stst30vslztn3D 0.337 0.015 23.246 0.000 0.309
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.262 0.243 0.288
## 0.392 0.368 0.419
## 0.535 0.506 0.545
## 0.486 0.459 0.448
## 0.337 0.315 0.324
## 0.593 0.559 0.469
## 0.836 0.793 0.679
## 0.396 0.371 0.584
## 0.223 0.209 0.223
## 0.616 0.579 0.485
## 0.711 0.657 0.493
## 0.599 0.562 0.578
## 0.319 0.301 0.552
## 0.197 0.155 0.321
## 1.499 1.383 0.525
## 0.933 0.862 0.525
## 0.748 0.692 0.528
## 0.255 0.240 0.302
## 0.360 0.342 0.416
## 0.272 0.258 0.323
## 0.494 0.470 0.660
## 0.644 0.623 0.901
## 0.388 0.365 0.393
## 0.444 0.423 0.638
## 0.631 0.602 0.497
## 0.459 0.434 0.570
## 0.415 0.394 0.507
## 0.492 0.468 0.565
## 0.246 0.231 0.483
## 0.756 0.699 0.758
## 0.260 0.246 0.657
## 0.258 0.245 0.655
## 0.698 0.654 0.669
## 0.366 0.337 0.564
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
metric<-cfa(chc.bifactor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 5968.427 1035.000 0.000 0.956 0.040 0.061
## aic bic
## 462834.830 464331.959
Mc(metric)
## [1] 0.6666816
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 99 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 303
## Number of equality constraints 80
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 5968.427 5334.343
## Degrees of freedom 1035 1035
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.119
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 2824.718 2524.621
## 1 3143.709 2809.722
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.090 0.012 7.371 0.000 0.066
## Stst19d (.p2.) 0.253 0.015 16.514 0.000 0.223
## Stst20s (.p3.) 0.329 0.018 18.050 0.000 0.293
## Stst21c (.p4.) 0.321 0.016 20.541 0.000 0.291
## Stst22p (.p5.) 0.366 0.017 22.013 0.000 0.333
## Stst23n (.p6.) 0.369 0.020 18.649 0.000 0.330
## Stst24x (.p7.) 0.290 0.019 14.954 0.000 0.252
## Stst25w (.p8.) 0.125 0.013 9.341 0.000 0.099
## Stst26r (.p9.) 0.157 0.011 14.758 0.000 0.136
## Stst31b (.10.) 0.183 0.017 11.028 0.000 0.151
## Stst34r (.11.) 0.219 0.018 12.173 0.000 0.184
## math =~
## Stst5mt (.12.) 0.233 0.019 12.544 0.000 0.196
## Stst25w (.13.) 0.188 0.021 8.843 0.000 0.147
## Stst32r (.14.) 0.193 0.020 9.811 0.000 0.154
## Stst33h (.15.) 0.354 0.024 14.580 0.000 0.306
## Stst34r (.16.) 0.220 0.021 10.392 0.000 0.178
## speed =~
## Stst19d (.17.) 0.197 0.011 18.032 0.000 0.176
## Stst34r (.18.) 0.457 0.020 22.851 0.000 0.418
## Stst35t (.19.) 0.948 0.031 30.588 0.000 0.887
## Stst36c (.20.) 0.877 0.024 36.139 0.000 0.829
## Stst37b (.21.) 0.710 0.022 31.666 0.000 0.666
## info =~
## Stst1vc (.22.) 0.206 0.016 12.848 0.000 0.175
## Stst2lt (.23.) 0.277 0.017 15.888 0.000 0.243
## Stst3ms (.24.) 0.267 0.016 16.510 0.000 0.235
## Stst4sc (.25.) 0.176 0.019 9.462 0.000 0.140
## Stst7bl (.26.) 0.078 0.018 4.377 0.000 0.043
## Stst8rn (.27.) 0.101 0.019 5.431 0.000 0.065
## Stst11r (.28.) 0.359 0.017 21.558 0.000 0.326
## Stst12l (.29.) 0.162 0.016 10.143 0.000 0.130
## Stst13h (.30.) 0.224 0.019 11.617 0.000 0.186
## Stst14b (.31.) 0.165 0.018 9.447 0.000 0.131
## Stst15t (.32.) 0.296 0.016 18.565 0.000 0.265
## Stst16m (.33.) 0.202 0.018 10.949 0.000 0.166
## Stst19d (.34.) 0.178 0.015 11.981 0.000 0.149
## Stst26r (.35.) 0.200 0.013 14.902 0.000 0.174
## science =~
## Stst1vc (.36.) 0.220 0.024 8.970 0.000 0.172
## Stst5mt (.37.) 0.195 0.021 9.259 0.000 0.154
## Stst6ph (.38.) 0.215 0.018 12.133 0.000 0.180
## Stst7bl (.39.) 0.155 0.024 6.361 0.000 0.107
## Stst9lc (.40.) 0.505 0.037 13.593 0.000 0.432
## Stst10m (.41.) 0.279 0.025 11.288 0.000 0.230
## spatial =~
## Stst28m (.42.) 0.301 0.018 16.541 0.000 0.265
## Sts292D (.43.) 0.521 0.022 23.359 0.000 0.478
## Sts303D (.44.) 0.520 0.020 25.987 0.000 0.480
## Stst31b (.45.) 0.477 0.019 24.934 0.000 0.440
## Stst37b (.46.) 0.324 0.022 14.760 0.000 0.281
## g =~
## Stst1vc (.47.) 0.879 0.017 50.435 0.000 0.845
## Stst2lt (.48.) 0.801 0.016 50.860 0.000 0.770
## Stst3ms (.49.) 0.702 0.015 47.787 0.000 0.673
## Stst4sc (.50.) 0.913 0.018 52.015 0.000 0.879
## Stst5mt (.51.) 0.698 0.017 41.831 0.000 0.666
## Stst6ph (.52.) 0.636 0.016 40.364 0.000 0.605
## Stst7bl (.53.) 0.632 0.017 36.791 0.000 0.598
## Stst8rn (.54.) 0.435 0.019 23.476 0.000 0.399
## Stst9lc (.55.) 0.524 0.020 26.591 0.000 0.485
## Stst10m (.56.) 0.491 0.014 34.024 0.000 0.463
## Stst11r (.57.) 0.721 0.015 49.284 0.000 0.692
## Stst12l (.58.) 0.592 0.016 36.870 0.000 0.561
## Stst13h (.59.) 0.849 0.017 51.374 0.000 0.817
## Stst14b (.60.) 0.618 0.015 41.324 0.000 0.589
## Stst15t (.61.) 0.580 0.014 40.815 0.000 0.552
## Stst16m (.62.) 0.710 0.016 43.185 0.000 0.678
## Stst19d (.63.) 0.634 0.015 42.358 0.000 0.604
## Stst20s (.64.) 0.635 0.016 40.580 0.000 0.605
## Stst21c (.65.) 0.729 0.014 51.822 0.000 0.701
## Stst22p (.66.) 0.802 0.016 51.140 0.000 0.771
## Stst23n (.67.) 0.824 0.018 46.313 0.000 0.789
## Stst24x (.68.) 0.648 0.017 37.292 0.000 0.614
## Stst25w (.69.) 0.501 0.014 35.897 0.000 0.473
## Stst26r (.70.) 0.964 0.016 61.020 0.000 0.933
## Stst28m (.71.) 0.468 0.015 32.274 0.000 0.440
## Sts292D (.72.) 0.462 0.016 28.397 0.000 0.430
## Sts303D (.73.) 0.428 0.015 28.829 0.000 0.399
## Stst31b (.74.) 0.753 0.017 45.375 0.000 0.720
## Stst32r (.75.) 0.589 0.015 39.860 0.000 0.560
## Stst33h (.76.) 0.582 0.015 40.020 0.000 0.553
## Stst34r (.77.) 0.684 0.018 38.435 0.000 0.649
## Stst35t (.78.) 0.666 0.024 27.409 0.000 0.619
## Stst36c (.79.) 0.155 0.019 7.949 0.000 0.117
## Stst37b (.80.) 0.292 0.019 15.664 0.000 0.256
## ci.upper Std.lv Std.all
##
## 0.114 0.090 0.085
## 0.283 0.253 0.269
## 0.365 0.329 0.322
## 0.352 0.321 0.319
## 0.398 0.366 0.345
## 0.408 0.369 0.306
## 0.328 0.290 0.249
## 0.151 0.125 0.151
## 0.178 0.157 0.143
## 0.216 0.183 0.156
## 0.255 0.219 0.187
##
## 0.269 0.233 0.222
## 0.230 0.188 0.228
## 0.231 0.193 0.230
## 0.401 0.354 0.444
## 0.261 0.220 0.187
##
## 0.218 0.197 0.210
## 0.497 0.457 0.389
## 1.009 0.948 0.558
## 0.924 0.877 0.680
## 0.754 0.710 0.575
##
## 0.238 0.206 0.195
## 0.311 0.277 0.280
## 0.298 0.267 0.281
## 0.213 0.176 0.163
## 0.113 0.078 0.083
## 0.138 0.101 0.107
## 0.391 0.359 0.362
## 0.193 0.162 0.176
## 0.262 0.224 0.197
## 0.200 0.165 0.185
## 0.327 0.296 0.345
## 0.238 0.202 0.196
## 0.207 0.178 0.189
## 0.227 0.200 0.182
##
## 0.267 0.220 0.208
## 0.237 0.195 0.186
## 0.250 0.215 0.254
## 0.202 0.155 0.164
## 0.578 0.505 0.483
## 0.327 0.279 0.338
##
## 0.336 0.301 0.362
## 0.565 0.521 0.473
## 0.559 0.520 0.552
## 0.515 0.477 0.405
## 0.366 0.324 0.262
##
## 0.913 0.879 0.832
## 0.832 0.801 0.810
## 0.731 0.702 0.740
## 0.947 0.913 0.846
## 0.731 0.698 0.666
## 0.667 0.636 0.752
## 0.665 0.632 0.670
## 0.472 0.435 0.460
## 0.563 0.524 0.502
## 0.519 0.491 0.595
## 0.749 0.721 0.728
## 0.623 0.592 0.646
## 0.881 0.849 0.746
## 0.647 0.618 0.690
## 0.608 0.580 0.678
## 0.742 0.710 0.689
## 0.663 0.634 0.675
## 0.666 0.635 0.623
## 0.757 0.729 0.724
## 0.833 0.802 0.756
## 0.859 0.824 0.683
## 0.682 0.648 0.556
## 0.528 0.501 0.605
## 0.995 0.964 0.874
## 0.497 0.468 0.563
## 0.494 0.462 0.420
## 0.457 0.428 0.455
## 0.785 0.753 0.639
## 0.618 0.589 0.704
## 0.610 0.582 0.730
## 0.719 0.684 0.582
## 0.714 0.666 0.392
## 0.193 0.155 0.120
## 0.329 0.292 0.237
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -1.155 0.023 -50.360 0.000 -1.200
## .Stst19dsgsdwrd -0.992 0.018 -53.776 0.000 -1.028
## .Stest20spellng -0.848 0.021 -39.900 0.000 -0.890
## .Stest21cptlztn -1.167 0.020 -58.007 0.000 -1.206
## .Stest22puncttn -1.226 0.021 -57.496 0.000 -1.268
## .Stest23english -1.062 0.026 -41.362 0.000 -1.113
## .Stest24exprssn -0.965 0.025 -38.928 0.000 -1.014
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.903
## .Stst26rdngcmpr -1.292 0.023 -56.802 0.000 -1.337
## .Stst31bstrctrs -1.070 0.024 -43.766 0.000 -1.118
## .Stst34rthcmptt -1.153 0.025 -46.702 0.000 -1.201
## .Stest5math -0.814 0.022 -36.442 0.000 -0.857
## .Stst32rthrsnng -1.052 0.018 -59.194 0.000 -1.087
## .Stst33hghschlm -0.875 0.016 -53.483 0.000 -0.907
## .Stest35tblrdng -0.712 0.037 -19.463 0.000 -0.784
## .Stst36clrclchc -0.032 0.028 -1.139 0.255 -0.086
## .Stst37bjctnspc -0.318 0.027 -11.957 0.000 -0.370
## .Stest2literatr -1.041 0.021 -50.624 0.000 -1.081
## .Stest3music -0.921 0.019 -48.386 0.000 -0.959
## .Stest4soclstds -1.083 0.023 -46.133 0.000 -1.129
## .Stst7blgclscnc -0.617 0.021 -29.442 0.000 -0.658
## .Stest8aerontcs -0.517 0.022 -23.664 0.000 -0.560
## .Stest11art -1.040 0.020 -51.542 0.000 -1.079
## .Stest12law -0.778 0.020 -39.122 0.000 -0.817
## .Stest13health -1.200 0.023 -51.595 0.000 -1.245
## .Stest14bible -0.720 0.018 -39.356 0.000 -0.756
## .Stest15theater -1.025 0.017 -59.426 0.000 -1.059
## .Stest16mscllns -0.887 0.022 -39.478 0.000 -0.931
## .Stst6physclscn -0.732 0.019 -38.793 0.000 -0.769
## .Stest9elctrncs -0.668 0.024 -27.887 0.000 -0.715
## .Stest10mechncs -0.656 0.019 -33.970 0.000 -0.694
## .Stst28mchnclrs -0.715 0.019 -36.895 0.000 -0.753
## .Stst29vslztn2D -0.512 0.023 -22.047 0.000 -0.557
## .Stst30vslztn3D -0.723 0.020 -35.874 0.000 -0.762
## ci.upper Std.lv Std.all
## -1.110 -1.155 -1.093
## -0.956 -0.992 -1.056
## -0.806 -0.848 -0.831
## -1.128 -1.167 -1.158
## -1.184 -1.226 -1.156
## -1.012 -1.062 -0.880
## -0.916 -0.965 -0.829
## -0.838 -0.871 -1.053
## -1.248 -1.292 -1.172
## -1.022 -1.070 -0.909
## -1.104 -1.153 -0.981
## -0.770 -0.814 -0.776
## -1.017 -1.052 -1.257
## -0.843 -0.875 -1.099
## -0.640 -0.712 -0.419
## 0.023 -0.032 -0.025
## -0.266 -0.318 -0.258
## -1.000 -1.041 -1.052
## -0.884 -0.921 -0.972
## -1.037 -1.083 -1.003
## -0.576 -0.617 -0.654
## -0.475 -0.517 -0.547
## -1.000 -1.040 -1.050
## -0.739 -0.778 -0.849
## -1.154 -1.200 -1.055
## -0.684 -0.720 -0.803
## -0.991 -1.025 -1.197
## -0.843 -0.887 -0.860
## -0.695 -0.732 -0.866
## -0.621 -0.668 -0.640
## -0.618 -0.656 -0.796
## -0.677 -0.715 -0.860
## -0.466 -0.512 -0.464
## -0.683 -0.723 -0.769
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.246 0.011 22.728 0.000 0.224
## .Stst19dsgsdwrd 0.347 0.014 25.116 0.000 0.320
## .Stest20spellng 0.528 0.017 30.392 0.000 0.494
## .Stest21cptlztn 0.381 0.015 24.947 0.000 0.351
## .Stest22puncttn 0.348 0.013 27.543 0.000 0.323
## .Stest23english 0.642 0.024 26.552 0.000 0.594
## .Stest24exprssn 0.853 0.025 33.497 0.000 0.803
## .Stst25wrdfnctn 0.382 0.013 29.912 0.000 0.357
## .Stst26rdngcmpr 0.221 0.009 25.411 0.000 0.204
## .Stst31bstrctrs 0.558 0.022 25.262 0.000 0.515
## .Stst34rthcmptt 0.608 0.029 21.205 0.000 0.552
## .Stest5math 0.520 0.020 25.605 0.000 0.480
## .Stst32rthrsnng 0.316 0.011 28.456 0.000 0.294
## .Stst33hghschlm 0.171 0.015 11.049 0.000 0.141
## .Stest35tblrdng 1.540 0.068 22.539 0.000 1.406
## .Stst36clrclchc 0.869 0.040 21.545 0.000 0.790
## .Stst37bjctnspc 0.829 0.034 24.418 0.000 0.763
## .Stest2literatr 0.260 0.009 29.012 0.000 0.242
## .Stest3music 0.335 0.012 27.854 0.000 0.312
## .Stest4soclstds 0.300 0.011 27.555 0.000 0.278
## .Stst7blgclscnc 0.459 0.014 32.499 0.000 0.432
## .Stest8aerontcs 0.696 0.018 39.018 0.000 0.661
## .Stest11art 0.333 0.012 27.092 0.000 0.309
## .Stest12law 0.463 0.014 33.395 0.000 0.436
## .Stest13health 0.523 0.017 31.616 0.000 0.490
## .Stest14bible 0.394 0.013 29.166 0.000 0.367
## .Stest15theater 0.309 0.011 27.947 0.000 0.287
## .Stest16mscllns 0.518 0.016 31.442 0.000 0.485
## .Stst6physclscn 0.264 0.010 25.662 0.000 0.243
## .Stest9elctrncs 0.561 0.040 13.876 0.000 0.482
## .Stest10mechncs 0.361 0.015 24.363 0.000 0.332
## .Stst28mchnclrs 0.382 0.015 24.635 0.000 0.351
## .Stst29vslztn2D 0.728 0.028 26.396 0.000 0.674
## .Stst30vslztn3D 0.431 0.019 22.119 0.000 0.393
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.267 0.246 0.220
## 0.374 0.347 0.393
## 0.562 0.528 0.508
## 0.411 0.381 0.375
## 0.372 0.348 0.309
## 0.689 0.642 0.441
## 0.903 0.853 0.629
## 0.407 0.382 0.559
## 0.238 0.221 0.182
## 0.602 0.558 0.403
## 0.664 0.608 0.440
## 0.560 0.520 0.473
## 0.338 0.316 0.451
## 0.201 0.171 0.270
## 1.674 1.540 0.534
## 0.948 0.869 0.523
## 0.896 0.829 0.544
## 0.278 0.260 0.266
## 0.359 0.335 0.373
## 0.321 0.300 0.257
## 0.487 0.459 0.517
## 0.731 0.696 0.777
## 0.357 0.333 0.339
## 0.490 0.463 0.551
## 0.555 0.523 0.404
## 0.420 0.394 0.490
## 0.331 0.309 0.421
## 0.550 0.518 0.487
## 0.284 0.264 0.369
## 0.641 0.561 0.515
## 0.390 0.361 0.531
## 0.412 0.382 0.552
## 0.782 0.728 0.600
## 0.469 0.431 0.487
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.090 0.012 7.371 0.000 0.066
## Stst19d (.p2.) 0.253 0.015 16.514 0.000 0.223
## Stst20s (.p3.) 0.329 0.018 18.050 0.000 0.293
## Stst21c (.p4.) 0.321 0.016 20.541 0.000 0.291
## Stst22p (.p5.) 0.366 0.017 22.013 0.000 0.333
## Stst23n (.p6.) 0.369 0.020 18.649 0.000 0.330
## Stst24x (.p7.) 0.290 0.019 14.954 0.000 0.252
## Stst25w (.p8.) 0.125 0.013 9.341 0.000 0.099
## Stst26r (.p9.) 0.157 0.011 14.758 0.000 0.136
## Stst31b (.10.) 0.183 0.017 11.028 0.000 0.151
## Stst34r (.11.) 0.219 0.018 12.173 0.000 0.184
## math =~
## Stst5mt (.12.) 0.233 0.019 12.544 0.000 0.196
## Stst25w (.13.) 0.188 0.021 8.843 0.000 0.147
## Stst32r (.14.) 0.193 0.020 9.811 0.000 0.154
## Stst33h (.15.) 0.354 0.024 14.580 0.000 0.306
## Stst34r (.16.) 0.220 0.021 10.392 0.000 0.178
## speed =~
## Stst19d (.17.) 0.197 0.011 18.032 0.000 0.176
## Stst34r (.18.) 0.457 0.020 22.851 0.000 0.418
## Stst35t (.19.) 0.948 0.031 30.588 0.000 0.887
## Stst36c (.20.) 0.877 0.024 36.139 0.000 0.829
## Stst37b (.21.) 0.710 0.022 31.666 0.000 0.666
## info =~
## Stst1vc (.22.) 0.206 0.016 12.848 0.000 0.175
## Stst2lt (.23.) 0.277 0.017 15.888 0.000 0.243
## Stst3ms (.24.) 0.267 0.016 16.510 0.000 0.235
## Stst4sc (.25.) 0.176 0.019 9.462 0.000 0.140
## Stst7bl (.26.) 0.078 0.018 4.377 0.000 0.043
## Stst8rn (.27.) 0.101 0.019 5.431 0.000 0.065
## Stst11r (.28.) 0.359 0.017 21.558 0.000 0.326
## Stst12l (.29.) 0.162 0.016 10.143 0.000 0.130
## Stst13h (.30.) 0.224 0.019 11.617 0.000 0.186
## Stst14b (.31.) 0.165 0.018 9.447 0.000 0.131
## Stst15t (.32.) 0.296 0.016 18.565 0.000 0.265
## Stst16m (.33.) 0.202 0.018 10.949 0.000 0.166
## Stst19d (.34.) 0.178 0.015 11.981 0.000 0.149
## Stst26r (.35.) 0.200 0.013 14.902 0.000 0.174
## science =~
## Stst1vc (.36.) 0.220 0.024 8.970 0.000 0.172
## Stst5mt (.37.) 0.195 0.021 9.259 0.000 0.154
## Stst6ph (.38.) 0.215 0.018 12.133 0.000 0.180
## Stst7bl (.39.) 0.155 0.024 6.361 0.000 0.107
## Stst9lc (.40.) 0.505 0.037 13.593 0.000 0.432
## Stst10m (.41.) 0.279 0.025 11.288 0.000 0.230
## spatial =~
## Stst28m (.42.) 0.301 0.018 16.541 0.000 0.265
## Sts292D (.43.) 0.521 0.022 23.359 0.000 0.478
## Sts303D (.44.) 0.520 0.020 25.987 0.000 0.480
## Stst31b (.45.) 0.477 0.019 24.934 0.000 0.440
## Stst37b (.46.) 0.324 0.022 14.760 0.000 0.281
## g =~
## Stst1vc (.47.) 0.879 0.017 50.435 0.000 0.845
## Stst2lt (.48.) 0.801 0.016 50.860 0.000 0.770
## Stst3ms (.49.) 0.702 0.015 47.787 0.000 0.673
## Stst4sc (.50.) 0.913 0.018 52.015 0.000 0.879
## Stst5mt (.51.) 0.698 0.017 41.831 0.000 0.666
## Stst6ph (.52.) 0.636 0.016 40.364 0.000 0.605
## Stst7bl (.53.) 0.632 0.017 36.791 0.000 0.598
## Stst8rn (.54.) 0.435 0.019 23.476 0.000 0.399
## Stst9lc (.55.) 0.524 0.020 26.591 0.000 0.485
## Stst10m (.56.) 0.491 0.014 34.024 0.000 0.463
## Stst11r (.57.) 0.721 0.015 49.284 0.000 0.692
## Stst12l (.58.) 0.592 0.016 36.870 0.000 0.561
## Stst13h (.59.) 0.849 0.017 51.374 0.000 0.817
## Stst14b (.60.) 0.618 0.015 41.324 0.000 0.589
## Stst15t (.61.) 0.580 0.014 40.815 0.000 0.552
## Stst16m (.62.) 0.710 0.016 43.185 0.000 0.678
## Stst19d (.63.) 0.634 0.015 42.358 0.000 0.604
## Stst20s (.64.) 0.635 0.016 40.580 0.000 0.605
## Stst21c (.65.) 0.729 0.014 51.822 0.000 0.701
## Stst22p (.66.) 0.802 0.016 51.140 0.000 0.771
## Stst23n (.67.) 0.824 0.018 46.313 0.000 0.789
## Stst24x (.68.) 0.648 0.017 37.292 0.000 0.614
## Stst25w (.69.) 0.501 0.014 35.897 0.000 0.473
## Stst26r (.70.) 0.964 0.016 61.020 0.000 0.933
## Stst28m (.71.) 0.468 0.015 32.274 0.000 0.440
## Sts292D (.72.) 0.462 0.016 28.397 0.000 0.430
## Sts303D (.73.) 0.428 0.015 28.829 0.000 0.399
## Stst31b (.74.) 0.753 0.017 45.375 0.000 0.720
## Stst32r (.75.) 0.589 0.015 39.860 0.000 0.560
## Stst33h (.76.) 0.582 0.015 40.020 0.000 0.553
## Stst34r (.77.) 0.684 0.018 38.435 0.000 0.649
## Stst35t (.78.) 0.666 0.024 27.409 0.000 0.619
## Stst36c (.79.) 0.155 0.019 7.949 0.000 0.117
## Stst37b (.80.) 0.292 0.019 15.664 0.000 0.256
## ci.upper Std.lv Std.all
##
## 0.114 0.098 0.108
## 0.283 0.276 0.313
## 0.365 0.359 0.380
## 0.352 0.351 0.365
## 0.398 0.399 0.425
## 0.408 0.403 0.375
## 0.328 0.317 0.294
## 0.151 0.136 0.179
## 0.178 0.172 0.183
## 0.216 0.200 0.189
## 0.255 0.239 0.212
##
## 0.269 0.208 0.212
## 0.230 0.168 0.221
## 0.231 0.172 0.232
## 0.401 0.316 0.459
## 0.261 0.196 0.174
##
## 0.218 0.197 0.223
## 0.497 0.458 0.406
## 1.009 0.950 0.592
## 0.924 0.878 0.683
## 0.754 0.711 0.623
##
## 0.238 0.240 0.264
## 0.311 0.323 0.372
## 0.298 0.310 0.358
## 0.213 0.205 0.226
## 0.113 0.091 0.105
## 0.138 0.118 0.134
## 0.391 0.418 0.449
## 0.193 0.188 0.228
## 0.262 0.261 0.245
## 0.200 0.193 0.228
## 0.327 0.345 0.406
## 0.238 0.236 0.257
## 0.207 0.207 0.234
## 0.227 0.233 0.248
##
## 0.267 0.147 0.162
## 0.237 0.131 0.134
## 0.250 0.144 0.201
## 0.202 0.104 0.121
## 0.578 0.339 0.339
## 0.327 0.187 0.288
##
## 0.336 0.220 0.338
## 0.565 0.382 0.390
## 0.559 0.380 0.490
## 0.515 0.350 0.331
## 0.366 0.237 0.208
##
## 0.913 0.700 0.770
## 0.832 0.638 0.735
## 0.731 0.559 0.645
## 0.947 0.727 0.801
## 0.731 0.556 0.569
## 0.667 0.506 0.707
## 0.665 0.503 0.585
## 0.472 0.347 0.395
## 0.563 0.418 0.417
## 0.519 0.391 0.602
## 0.749 0.574 0.617
## 0.623 0.472 0.571
## 0.881 0.676 0.636
## 0.647 0.492 0.582
## 0.608 0.462 0.544
## 0.742 0.566 0.616
## 0.663 0.505 0.572
## 0.666 0.506 0.536
## 0.757 0.581 0.605
## 0.833 0.639 0.681
## 0.859 0.656 0.612
## 0.682 0.516 0.479
## 0.528 0.399 0.524
## 0.995 0.768 0.817
## 0.497 0.373 0.574
## 0.494 0.368 0.376
## 0.457 0.341 0.440
## 0.785 0.600 0.567
## 0.618 0.469 0.634
## 0.610 0.464 0.674
## 0.719 0.545 0.483
## 0.714 0.531 0.331
## 0.193 0.123 0.096
## 0.329 0.233 0.204
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -1.339 0.016 -83.554 0.000 -1.370
## .Stst19dsgsdwrd -0.878 0.016 -54.059 0.000 -0.910
## .Stest20spellng -0.450 0.017 -26.686 0.000 -0.483
## .Stest21cptlztn -0.899 0.017 -51.477 0.000 -0.934
## .Stest22puncttn -0.929 0.017 -53.286 0.000 -0.963
## .Stest23english -0.744 0.019 -38.449 0.000 -0.781
## .Stest24exprssn -0.704 0.019 -37.099 0.000 -0.742
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.816
## .Stst26rdngcmpr -1.226 0.017 -72.842 0.000 -1.259
## .Stst31bstrctrs -1.260 0.019 -65.843 0.000 -1.297
## .Stst34rthcmptt -1.004 0.021 -47.990 0.000 -1.045
## .Stest5math -0.965 0.017 -55.615 0.000 -0.999
## .Stst32rthrsnng -1.184 0.013 -92.849 0.000 -1.209
## .Stst33hghschlm -0.942 0.012 -78.389 0.000 -0.966
## .Stest35tblrdng -0.524 0.029 -17.830 0.000 -0.582
## .Stst36clrclchc 0.300 0.023 13.284 0.000 0.256
## .Stst37bjctnspc -0.217 0.021 -10.567 0.000 -0.257
## .Stest2literatr -1.034 0.016 -66.363 0.000 -1.065
## .Stest3music -0.825 0.016 -52.646 0.000 -0.856
## .Stest4soclstds -1.273 0.015 -82.694 0.000 -1.303
## .Stst7blgclscnc -0.831 0.015 -55.991 0.000 -0.860
## .Stest8aerontcs -0.942 0.014 -64.960 0.000 -0.970
## .Stest11art -1.046 0.017 -63.114 0.000 -1.078
## .Stest12law -0.897 0.014 -63.710 0.000 -0.925
## .Stest13health -1.020 0.019 -52.885 0.000 -1.057
## .Stest14bible -0.565 0.015 -36.958 0.000 -0.595
## .Stest15theater -0.856 0.015 -56.660 0.000 -0.885
## .Stest16mscllns -0.949 0.016 -60.013 0.000 -0.980
## .Stst6physclscn -1.022 0.012 -84.927 0.000 -1.046
## .Stest9elctrncs -1.154 0.017 -68.546 0.000 -1.187
## .Stest10mechncs -1.373 0.011 -128.778 0.000 -1.394
## .Stst28mchnclrs -1.323 0.011 -124.285 0.000 -1.344
## .Stst29vslztn2D -0.916 0.017 -52.801 0.000 -0.950
## .Stst30vslztn3D -0.982 0.014 -72.639 0.000 -1.008
## ci.upper Std.lv Std.all
## -1.307 -1.339 -1.473
## -0.846 -0.878 -0.995
## -0.417 -0.450 -0.477
## -0.865 -0.899 -0.936
## -0.895 -0.929 -0.990
## -0.706 -0.744 -0.693
## -0.667 -0.704 -0.654
## -0.761 -0.788 -1.036
## -1.193 -1.226 -1.305
## -1.222 -1.260 -1.191
## -0.963 -1.004 -0.890
## -0.931 -0.965 -0.986
## -1.159 -1.184 -1.598
## -0.919 -0.942 -1.371
## -0.466 -0.524 -0.327
## 0.344 0.300 0.233
## -0.176 -0.217 -0.190
## -1.004 -1.034 -1.191
## -0.795 -0.825 -0.952
## -1.243 -1.273 -1.402
## -0.802 -0.831 -0.965
## -0.913 -0.942 -1.073
## -1.013 -1.046 -1.124
## -0.870 -0.897 -1.087
## -0.982 -1.020 -0.958
## -0.535 -0.565 -0.668
## -0.826 -0.856 -1.007
## -0.918 -0.949 -1.034
## -0.998 -1.022 -1.427
## -1.121 -1.154 -1.154
## -1.352 -1.373 -2.113
## -1.303 -1.323 -2.035
## -0.882 -0.916 -0.935
## -0.955 -0.982 -1.264
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.246 0.008 30.062 0.000 0.230
## .Stst19dsgsdwrd 0.367 0.012 31.596 0.000 0.344
## .Stest20spellng 0.506 0.014 35.361 0.000 0.478
## .Stest21cptlztn 0.462 0.014 33.195 0.000 0.435
## .Stest22puncttn 0.313 0.011 28.269 0.000 0.291
## .Stest23english 0.557 0.017 32.558 0.000 0.524
## .Stest24exprssn 0.792 0.021 36.908 0.000 0.750
## .Stst25wrdfnctn 0.374 0.011 33.907 0.000 0.352
## .Stst26rdngcmpr 0.209 0.007 29.786 0.000 0.196
## .Stst31bstrctrs 0.596 0.017 34.416 0.000 0.562
## .Stst34rthcmptt 0.668 0.027 24.880 0.000 0.616
## .Stest5math 0.588 0.017 34.757 0.000 0.555
## .Stst32rthrsnng 0.299 0.009 34.039 0.000 0.281
## .Stst33hghschlm 0.158 0.013 12.451 0.000 0.133
## .Stest35tblrdng 1.390 0.057 24.301 0.000 1.278
## .Stst36clrclchc 0.866 0.033 26.289 0.000 0.802
## .Stst37bjctnspc 0.686 0.027 25.856 0.000 0.634
## .Stest2literatr 0.242 0.007 33.907 0.000 0.228
## .Stest3music 0.343 0.009 36.517 0.000 0.325
## .Stest4soclstds 0.252 0.007 35.003 0.000 0.238
## .Stst7blgclscnc 0.469 0.012 38.966 0.000 0.445
## .Stest8aerontcs 0.636 0.011 55.992 0.000 0.614
## .Stest11art 0.362 0.012 31.409 0.000 0.340
## .Stest12law 0.423 0.011 40.091 0.000 0.403
## .Stest13health 0.607 0.015 41.563 0.000 0.579
## .Stest14bible 0.436 0.013 34.785 0.000 0.411
## .Stest15theater 0.389 0.011 36.349 0.000 0.368
## .Stest16mscllns 0.467 0.012 38.102 0.000 0.443
## .Stst6physclscn 0.236 0.007 33.450 0.000 0.222
## .Stest9elctrncs 0.711 0.026 27.460 0.000 0.660
## .Stest10mechncs 0.234 0.007 32.418 0.000 0.220
## .Stst28mchnclrs 0.235 0.007 35.488 0.000 0.222
## .Stst29vslztn2D 0.678 0.020 34.153 0.000 0.639
## .Stst30vslztn3D 0.342 0.012 28.069 0.000 0.318
## english 1.192 0.102 11.660 0.000 0.992
## math 0.797 0.091 8.738 0.000 0.618
## speed 1.003 0.060 16.722 0.000 0.886
## info 1.357 0.136 9.979 0.000 1.090
## science 0.451 0.058 7.726 0.000 0.336
## spatial 0.536 0.043 12.412 0.000 0.451
## g 0.635 0.030 21.176 0.000 0.576
## ci.upper Std.lv Std.all
## 0.263 0.246 0.298
## 0.389 0.367 0.470
## 0.534 0.506 0.568
## 0.489 0.462 0.501
## 0.335 0.313 0.355
## 0.591 0.557 0.485
## 0.834 0.792 0.684
## 0.395 0.374 0.645
## 0.223 0.209 0.237
## 0.630 0.596 0.533
## 0.721 0.668 0.526
## 0.621 0.588 0.614
## 0.316 0.299 0.544
## 0.183 0.158 0.334
## 1.502 1.390 0.540
## 0.931 0.866 0.524
## 0.738 0.686 0.527
## 0.256 0.242 0.321
## 0.362 0.343 0.456
## 0.267 0.252 0.306
## 0.492 0.469 0.633
## 0.659 0.636 0.826
## 0.385 0.362 0.418
## 0.444 0.423 0.621
## 0.636 0.607 0.536
## 0.461 0.436 0.609
## 0.410 0.389 0.539
## 0.491 0.467 0.554
## 0.250 0.236 0.460
## 0.762 0.711 0.711
## 0.248 0.234 0.555
## 0.248 0.235 0.556
## 0.716 0.678 0.707
## 0.366 0.342 0.567
## 1.393 1.000 1.000
## 0.976 1.000 1.000
## 1.121 1.000 1.000
## 1.623 1.000 1.000
## 0.565 1.000 1.000
## 0.621 1.000 1.000
## 0.694 1.000 1.000
lavTestScore(metric, release = 1:80)
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 1108.421 80 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p184. 0.154 1 0.695
## 2 .p2. == .p185. 0.867 1 0.352
## 3 .p3. == .p186. 4.895 1 0.027
## 4 .p4. == .p187. 0.859 1 0.354
## 5 .p5. == .p188. 0.125 1 0.724
## 6 .p6. == .p189. 2.286 1 0.131
## 7 .p7. == .p190. 0.649 1 0.420
## 8 .p8. == .p191. 1.339 1 0.247
## 9 .p9. == .p192. 0.874 1 0.350
## 10 .p10. == .p193. 4.312 1 0.038
## 11 .p11. == .p194. 1.013 1 0.314
## 12 .p12. == .p195. 0.326 1 0.568
## 13 .p13. == .p196. 3.204 1 0.073
## 14 .p14. == .p197. 5.173 1 0.023
## 15 .p15. == .p198. 0.065 1 0.799
## 16 .p16. == .p199. 0.169 1 0.681
## 17 .p17. == .p200. 8.183 1 0.004
## 18 .p18. == .p201. 0.952 1 0.329
## 19 .p19. == .p202. 0.027 1 0.869
## 20 .p20. == .p203. 1.082 1 0.298
## 21 .p21. == .p204. 1.806 1 0.179
## 22 .p22. == .p205. 1.352 1 0.245
## 23 .p23. == .p206. 0.405 1 0.524
## 24 .p24. == .p207. 0.071 1 0.790
## 25 .p25. == .p208. 0.406 1 0.524
## 26 .p26. == .p209. 0.133 1 0.715
## 27 .p27. == .p210. 19.217 1 0.000
## 28 .p28. == .p211. 2.515 1 0.113
## 29 .p29. == .p212. 0.351 1 0.554
## 30 .p30. == .p213. 0.775 1 0.379
## 31 .p31. == .p214. 0.094 1 0.759
## 32 .p32. == .p215. 0.025 1 0.875
## 33 .p33. == .p216. 15.775 1 0.000
## 34 .p34. == .p217. 0.814 1 0.367
## 35 .p35. == .p218. 0.012 1 0.915
## 36 .p36. == .p219. 0.308 1 0.579
## 37 .p37. == .p220. 13.797 1 0.000
## 38 .p38. == .p221. 0.212 1 0.646
## 39 .p39. == .p222. 1.146 1 0.284
## 40 .p40. == .p223. 0.800 1 0.371
## 41 .p41. == .p224. 12.605 1 0.000
## 42 .p42. == .p225. 64.415 1 0.000
## 43 .p43. == .p226. 8.011 1 0.005
## 44 .p44. == .p227. 1.500 1 0.221
## 45 .p45. == .p228. 8.668 1 0.003
## 46 .p46. == .p229. 0.714 1 0.398
## 47 .p47. == .p230. 0.641 1 0.423
## 48 .p48. == .p231. 2.773 1 0.096
## 49 .p49. == .p232. 38.285 1 0.000
## 50 .p50. == .p233. 39.991 1 0.000
## 51 .p51. == .p234. 2.573 1 0.109
## 52 .p52. == .p235. 20.396 1 0.000
## 53 .p53. == .p236. 9.859 1 0.002
## 54 .p54. == .p237. 171.420 1 0.000
## 55 .p55. == .p238. 54.913 1 0.000
## 56 .p56. == .p239. 83.494 1 0.000
## 57 .p57. == .p240. 11.098 1 0.001
## 58 .p58. == .p241. 18.787 1 0.000
## 59 .p59. == .p242. 19.464 1 0.000
## 60 .p60. == .p243. 20.234 1 0.000
## 61 .p61. == .p244. 27.009 1 0.000
## 62 .p62. == .p245. 8.235 1 0.004
## 63 .p63. == .p246. 21.453 1 0.000
## 64 .p64. == .p247. 0.556 1 0.456
## 65 .p65. == .p248. 37.466 1 0.000
## 66 .p66. == .p249. 25.086 1 0.000
## 67 .p67. == .p250. 1.168 1 0.280
## 68 .p68. == .p251. 5.492 1 0.019
## 69 .p69. == .p252. 50.278 1 0.000
## 70 .p70. == .p253. 0.295 1 0.587
## 71 .p71. == .p254. 100.338 1 0.000
## 72 .p72. == .p255. 2.792 1 0.095
## 73 .p73. == .p256. 1.116 1 0.291
## 74 .p74. == .p257. 14.732 1 0.000
## 75 .p75. == .p258. 0.996 1 0.318
## 76 .p76. == .p259. 0.431 1 0.511
## 77 .p77. == .p260. 0.038 1 0.846
## 78 .p78. == .p261. 7.025 1 0.008
## 79 .p79. == .p262. 9.524 1 0.002
## 80 .p80. == .p263. 5.471 1 0.019
metric2<-cfa(chc.bifactor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings"), group.partial=c("g=~Stest8aeronautics", "g=~Stest28mechanicalreasoning", "g=~Stest10mechanics", "g=~Stest9electronics", "g=~Stest6physicalscience", "g=~Stest4socialstudies"))
fitMeasures(metric2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 5341.198 1029.000 0.000 0.961 0.037 0.041
## aic bic
## 462219.601 463757.011
Mc(metric2)
## [1] 0.7016024
summary(metric2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 104 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 303
## Number of equality constraints 74
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 5341.198 4775.101
## Degrees of freedom 1029 1029
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.119
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 2513.340 2246.959
## 1 2827.858 2528.142
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.085 0.014 5.857 0.000 0.056
## Stst19d (.p2.) 0.256 0.016 15.576 0.000 0.224
## Stst20s (.p3.) 0.342 0.019 17.776 0.000 0.304
## Stst21c (.p4.) 0.321 0.016 19.739 0.000 0.290
## Stst22p (.p5.) 0.368 0.017 21.657 0.000 0.335
## Stst23n (.p6.) 0.380 0.021 18.408 0.000 0.339
## Stst24x (.p7.) 0.299 0.021 14.395 0.000 0.259
## Stst25w (.p8.) 0.121 0.015 8.337 0.000 0.093
## Stst26r (.p9.) 0.155 0.012 13.210 0.000 0.132
## Stst31b (.10.) 0.173 0.018 9.512 0.000 0.137
## Stst34r (.11.) 0.229 0.020 11.722 0.000 0.191
## math =~
## Stst5mt (.12.) 0.240 0.019 12.726 0.000 0.203
## Stst25w (.13.) 0.187 0.021 8.891 0.000 0.146
## Stst32r (.14.) 0.197 0.020 9.963 0.000 0.158
## Stst33h (.15.) 0.362 0.024 15.247 0.000 0.315
## Stst34r (.16.) 0.227 0.021 10.670 0.000 0.185
## speed =~
## Stst19d (.17.) 0.195 0.011 17.879 0.000 0.174
## Stst34r (.18.) 0.457 0.020 22.827 0.000 0.418
## Stst35t (.19.) 0.948 0.031 30.549 0.000 0.887
## Stst36c (.20.) 0.878 0.024 36.204 0.000 0.831
## Stst37b (.21.) 0.710 0.022 31.666 0.000 0.666
## info =~
## Stst1vc (.22.) 0.207 0.017 12.194 0.000 0.174
## Stst2lt (.23.) 0.288 0.017 16.792 0.000 0.255
## Stst3ms (.24.) 0.270 0.016 16.949 0.000 0.239
## Stst4sc (.25.) 0.195 0.019 10.019 0.000 0.157
## Stst7bl (.26.) 0.081 0.019 4.252 0.000 0.044
## Stst8rn (.27.) 0.135 0.018 7.587 0.000 0.100
## Stst11r (.28.) 0.363 0.016 23.019 0.000 0.332
## Stst12l (.29.) 0.171 0.016 10.497 0.000 0.139
## Stst13h (.30.) 0.223 0.020 11.282 0.000 0.184
## Stst14b (.31.) 0.168 0.018 9.193 0.000 0.132
## Stst15t (.32.) 0.299 0.016 18.874 0.000 0.268
## Stst16m (.33.) 0.211 0.019 11.300 0.000 0.175
## Stst19d (.34.) 0.173 0.016 10.960 0.000 0.142
## Stst26r (.35.) 0.203 0.014 14.664 0.000 0.176
## science =~
## Stst1vc (.36.) 0.199 0.029 6.801 0.000 0.142
## Stst5mt (.37.) 0.204 0.021 9.797 0.000 0.163
## Stst6ph (.38.) 0.191 0.017 11.244 0.000 0.158
## Stst7bl (.39.) 0.137 0.026 5.213 0.000 0.086
## Stst9lc (.40.) 0.449 0.039 11.525 0.000 0.373
## Stst10m (.41.) 0.227 0.025 8.926 0.000 0.177
## spatial =~
## Stst28m (.42.) 0.300 0.018 16.785 0.000 0.265
## Sts292D (.43.) 0.520 0.022 23.230 0.000 0.477
## Sts303D (.44.) 0.517 0.020 25.927 0.000 0.478
## Stst31b (.45.) 0.475 0.019 24.698 0.000 0.438
## Stst37b (.46.) 0.324 0.022 14.719 0.000 0.281
## g =~
## Stst1vc (.47.) 0.854 0.018 48.439 0.000 0.820
## Stst2lt (.48.) 0.769 0.016 48.934 0.000 0.738
## Stst3ms (.49.) 0.677 0.015 46.693 0.000 0.649
## Stst4sc 0.950 0.017 56.278 0.000 0.917
## Stst5mt (.51.) 0.673 0.016 41.629 0.000 0.641
## Stst6ph 0.695 0.017 39.868 0.000 0.660
## Stst7bl (.53.) 0.609 0.017 36.055 0.000 0.576
## Stst8rn 0.593 0.020 29.534 0.000 0.553
## Stst9lc 0.657 0.021 30.601 0.000 0.615
## Stst10m 0.611 0.018 34.849 0.000 0.577
## Stst11r (.57.) 0.697 0.014 48.132 0.000 0.669
## Stst12l (.58.) 0.565 0.016 36.297 0.000 0.535
## Stst13h (.59.) 0.821 0.017 49.448 0.000 0.788
## Stst14b (.60.) 0.596 0.015 40.261 0.000 0.567
## Stst15t (.61.) 0.562 0.014 40.241 0.000 0.535
## Stst16m (.62.) 0.679 0.016 42.276 0.000 0.647
## Stst19d (.63.) 0.620 0.015 42.593 0.000 0.591
## Stst20s (.64.) 0.616 0.015 40.150 0.000 0.586
## Stst21c (.65.) 0.710 0.014 51.189 0.000 0.683
## Stst22p (.66.) 0.780 0.015 50.922 0.000 0.750
## Stst23n (.67.) 0.798 0.018 45.549 0.000 0.763
## Stst24x (.68.) 0.626 0.017 36.730 0.000 0.593
## Stst25w (.69.) 0.484 0.013 36.074 0.000 0.458
## Stst26r (.70.) 0.930 0.016 58.040 0.000 0.899
## Stst28m 0.571 0.018 31.780 0.000 0.536
## Sts292D (.72.) 0.446 0.016 28.630 0.000 0.416
## Sts303D (.73.) 0.410 0.014 28.973 0.000 0.382
## Stst31b (.74.) 0.733 0.016 45.176 0.000 0.701
## Stst32r (.75.) 0.562 0.014 39.607 0.000 0.535
## Stst33h (.76.) 0.555 0.014 40.266 0.000 0.528
## Stst34r (.77.) 0.658 0.017 37.989 0.000 0.624
## Stst35t (.78.) 0.639 0.023 27.311 0.000 0.594
## Stst36c (.79.) 0.146 0.019 7.839 0.000 0.109
## Stst37b (.80.) 0.283 0.018 15.874 0.000 0.248
## ci.upper Std.lv Std.all
##
## 0.113 0.085 0.082
## 0.289 0.256 0.275
## 0.380 0.342 0.338
## 0.353 0.321 0.323
## 0.402 0.368 0.353
## 0.420 0.380 0.319
## 0.340 0.299 0.259
## 0.150 0.121 0.148
## 0.178 0.155 0.145
## 0.208 0.173 0.148
## 0.267 0.229 0.197
##
## 0.277 0.240 0.232
## 0.228 0.187 0.229
## 0.235 0.197 0.240
## 0.408 0.362 0.464
## 0.268 0.227 0.195
##
## 0.217 0.195 0.210
## 0.497 0.457 0.393
## 1.009 0.948 0.561
## 0.926 0.878 0.682
## 0.754 0.710 0.576
##
## 0.240 0.207 0.200
## 0.322 0.288 0.298
## 0.302 0.270 0.290
## 0.233 0.195 0.175
## 0.119 0.081 0.088
## 0.170 0.135 0.133
## 0.394 0.363 0.372
## 0.202 0.171 0.189
## 0.262 0.223 0.200
## 0.204 0.168 0.190
## 0.330 0.299 0.353
## 0.248 0.211 0.209
## 0.204 0.173 0.186
## 0.230 0.203 0.189
##
## 0.257 0.199 0.193
## 0.244 0.204 0.197
## 0.224 0.191 0.217
## 0.189 0.137 0.148
## 0.526 0.449 0.410
## 0.276 0.227 0.256
##
## 0.335 0.300 0.340
## 0.564 0.520 0.476
## 0.556 0.517 0.554
## 0.513 0.475 0.409
## 0.367 0.324 0.263
##
## 0.889 0.854 0.826
## 0.799 0.769 0.796
## 0.706 0.677 0.728
## 0.983 0.950 0.855
## 0.704 0.673 0.650
## 0.729 0.695 0.787
## 0.642 0.609 0.656
## 0.632 0.593 0.584
## 0.699 0.657 0.599
## 0.646 0.611 0.691
## 0.725 0.697 0.715
## 0.596 0.565 0.627
## 0.853 0.821 0.735
## 0.625 0.596 0.675
## 0.590 0.562 0.665
## 0.710 0.679 0.671
## 0.648 0.620 0.666
## 0.646 0.616 0.610
## 0.738 0.710 0.714
## 0.810 0.780 0.747
## 0.832 0.798 0.669
## 0.660 0.626 0.542
## 0.511 0.484 0.593
## 0.961 0.930 0.866
## 0.606 0.571 0.647
## 0.477 0.446 0.408
## 0.437 0.410 0.439
## 0.765 0.733 0.630
## 0.590 0.562 0.686
## 0.582 0.555 0.712
## 0.692 0.658 0.566
## 0.685 0.639 0.379
## 0.182 0.146 0.113
## 0.318 0.283 0.230
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -1.155 0.023 -50.360 0.000 -1.200
## .Stst19dsgsdwrd -0.992 0.018 -53.776 0.000 -1.028
## .Stest20spellng -0.848 0.021 -39.900 0.000 -0.890
## .Stest21cptlztn -1.167 0.020 -58.007 0.000 -1.206
## .Stest22puncttn -1.226 0.021 -57.496 0.000 -1.268
## .Stest23english -1.062 0.026 -41.362 0.000 -1.113
## .Stest24exprssn -0.965 0.025 -38.928 0.000 -1.014
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.903
## .Stst26rdngcmpr -1.292 0.023 -56.802 0.000 -1.337
## .Stst31bstrctrs -1.070 0.024 -43.766 0.000 -1.118
## .Stst34rthcmptt -1.153 0.025 -46.702 0.000 -1.201
## .Stest5math -0.814 0.022 -36.442 0.000 -0.857
## .Stst32rthrsnng -1.052 0.018 -59.194 0.000 -1.087
## .Stst33hghschlm -0.875 0.016 -53.483 0.000 -0.907
## .Stest35tblrdng -0.712 0.037 -19.463 0.000 -0.784
## .Stst36clrclchc -0.032 0.028 -1.139 0.255 -0.086
## .Stst37bjctnspc -0.318 0.027 -11.957 0.000 -0.370
## .Stest2literatr -1.041 0.021 -50.624 0.000 -1.081
## .Stest3music -0.921 0.019 -48.386 0.000 -0.959
## .Stest4soclstds -1.083 0.023 -46.133 0.000 -1.129
## .Stst7blgclscnc -0.617 0.021 -29.442 0.000 -0.658
## .Stest8aerontcs -0.517 0.022 -23.664 0.000 -0.560
## .Stest11art -1.040 0.020 -51.542 0.000 -1.079
## .Stest12law -0.778 0.020 -39.122 0.000 -0.817
## .Stest13health -1.200 0.023 -51.595 0.000 -1.245
## .Stest14bible -0.720 0.018 -39.356 0.000 -0.756
## .Stest15theater -1.025 0.017 -59.426 0.000 -1.059
## .Stest16mscllns -0.887 0.022 -39.478 0.000 -0.931
## .Stst6physclscn -0.732 0.019 -38.793 0.000 -0.769
## .Stest9elctrncs -0.668 0.024 -27.887 0.000 -0.715
## .Stest10mechncs -0.656 0.019 -33.970 0.000 -0.694
## .Stst28mchnclrs -0.715 0.019 -36.895 0.000 -0.753
## .Stst29vslztn2D -0.512 0.023 -22.047 0.000 -0.557
## .Stst30vslztn3D -0.723 0.020 -35.874 0.000 -0.762
## ci.upper Std.lv Std.all
## -1.110 -1.155 -1.117
## -0.956 -0.992 -1.065
## -0.806 -0.848 -0.839
## -1.128 -1.167 -1.173
## -1.184 -1.226 -1.174
## -1.012 -1.062 -0.891
## -0.916 -0.965 -0.835
## -0.838 -0.871 -1.065
## -1.248 -1.292 -1.203
## -1.022 -1.070 -0.920
## -1.104 -1.153 -0.991
## -0.770 -0.814 -0.787
## -1.017 -1.052 -1.282
## -0.843 -0.875 -1.123
## -0.640 -0.712 -0.422
## 0.023 -0.032 -0.025
## -0.266 -0.318 -0.258
## -1.000 -1.041 -1.077
## -0.884 -0.921 -0.990
## -1.037 -1.083 -0.974
## -0.576 -0.617 -0.665
## -0.475 -0.517 -0.510
## -1.000 -1.040 -1.066
## -0.739 -0.778 -0.863
## -1.154 -1.200 -1.075
## -0.684 -0.720 -0.816
## -0.991 -1.025 -1.213
## -0.843 -0.887 -0.876
## -0.695 -0.732 -0.829
## -0.621 -0.668 -0.609
## -0.618 -0.656 -0.742
## -0.677 -0.715 -0.810
## -0.466 -0.512 -0.468
## -0.683 -0.723 -0.775
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.250 0.012 21.564 0.000 0.227
## .Stst19dsgsdwrd 0.349 0.014 25.137 0.000 0.321
## .Stest20spellng 0.525 0.018 29.896 0.000 0.491
## .Stest21cptlztn 0.382 0.015 24.999 0.000 0.352
## .Stest22puncttn 0.348 0.013 27.348 0.000 0.323
## .Stest23english 0.640 0.024 26.364 0.000 0.592
## .Stest24exprssn 0.853 0.026 33.334 0.000 0.803
## .Stst25wrdfnctn 0.384 0.013 30.151 0.000 0.359
## .Stst26rdngcmpr 0.224 0.009 25.529 0.000 0.207
## .Stst31bstrctrs 0.560 0.022 25.439 0.000 0.517
## .Stst34rthcmptt 0.606 0.029 21.256 0.000 0.550
## .Stest5math 0.518 0.021 25.235 0.000 0.478
## .Stst32rthrsnng 0.318 0.011 28.414 0.000 0.296
## .Stst33hghschlm 0.169 0.015 10.906 0.000 0.138
## .Stest35tblrdng 1.543 0.068 22.543 0.000 1.409
## .Stst36clrclchc 0.867 0.040 21.485 0.000 0.788
## .Stst37bjctnspc 0.829 0.034 24.417 0.000 0.762
## .Stest2literatr 0.259 0.009 28.918 0.000 0.242
## .Stest3music 0.335 0.012 27.900 0.000 0.312
## .Stest4soclstds 0.294 0.011 27.557 0.000 0.273
## .Stst7blgclscnc 0.465 0.014 32.690 0.000 0.437
## .Stest8aerontcs 0.659 0.018 37.365 0.000 0.624
## .Stest11art 0.334 0.012 27.057 0.000 0.310
## .Stest12law 0.465 0.014 33.478 0.000 0.437
## .Stest13health 0.523 0.016 31.814 0.000 0.490
## .Stest14bible 0.395 0.014 29.207 0.000 0.368
## .Stest15theater 0.310 0.011 27.726 0.000 0.288
## .Stest16mscllns 0.519 0.017 31.363 0.000 0.487
## .Stst6physclscn 0.260 0.010 25.597 0.000 0.240
## .Stest9elctrncs 0.570 0.040 14.202 0.000 0.491
## .Stest10mechncs 0.358 0.014 25.424 0.000 0.330
## .Stst28mchnclrs 0.362 0.015 24.560 0.000 0.334
## .Stst29vslztn2D 0.727 0.027 26.522 0.000 0.674
## .Stst30vslztn3D 0.435 0.019 22.463 0.000 0.397
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.273 0.250 0.234
## 0.376 0.349 0.402
## 0.560 0.525 0.514
## 0.412 0.382 0.386
## 0.373 0.348 0.318
## 0.687 0.640 0.450
## 0.903 0.853 0.639
## 0.408 0.384 0.574
## 0.241 0.224 0.194
## 0.603 0.560 0.414
## 0.662 0.606 0.448
## 0.558 0.518 0.484
## 0.340 0.318 0.472
## 0.199 0.169 0.278
## 1.677 1.543 0.541
## 0.947 0.867 0.523
## 0.895 0.829 0.546
## 0.277 0.259 0.278
## 0.359 0.335 0.386
## 0.315 0.294 0.239
## 0.493 0.465 0.540
## 0.694 0.659 0.641
## 0.358 0.334 0.351
## 0.492 0.465 0.571
## 0.555 0.523 0.420
## 0.421 0.395 0.508
## 0.331 0.310 0.433
## 0.552 0.519 0.507
## 0.280 0.260 0.334
## 0.648 0.570 0.473
## 0.385 0.358 0.457
## 0.391 0.362 0.465
## 0.781 0.727 0.607
## 0.473 0.435 0.500
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.085 0.014 5.857 0.000 0.056
## Stst19d (.p2.) 0.256 0.016 15.576 0.000 0.224
## Stst20s (.p3.) 0.342 0.019 17.776 0.000 0.304
## Stst21c (.p4.) 0.321 0.016 19.739 0.000 0.290
## Stst22p (.p5.) 0.368 0.017 21.657 0.000 0.335
## Stst23n (.p6.) 0.380 0.021 18.408 0.000 0.339
## Stst24x (.p7.) 0.299 0.021 14.395 0.000 0.259
## Stst25w (.p8.) 0.121 0.015 8.337 0.000 0.093
## Stst26r (.p9.) 0.155 0.012 13.210 0.000 0.132
## Stst31b (.10.) 0.173 0.018 9.512 0.000 0.137
## Stst34r (.11.) 0.229 0.020 11.722 0.000 0.191
## math =~
## Stst5mt (.12.) 0.240 0.019 12.726 0.000 0.203
## Stst25w (.13.) 0.187 0.021 8.891 0.000 0.146
## Stst32r (.14.) 0.197 0.020 9.963 0.000 0.158
## Stst33h (.15.) 0.362 0.024 15.247 0.000 0.315
## Stst34r (.16.) 0.227 0.021 10.670 0.000 0.185
## speed =~
## Stst19d (.17.) 0.195 0.011 17.879 0.000 0.174
## Stst34r (.18.) 0.457 0.020 22.827 0.000 0.418
## Stst35t (.19.) 0.948 0.031 30.549 0.000 0.887
## Stst36c (.20.) 0.878 0.024 36.204 0.000 0.831
## Stst37b (.21.) 0.710 0.022 31.666 0.000 0.666
## info =~
## Stst1vc (.22.) 0.207 0.017 12.194 0.000 0.174
## Stst2lt (.23.) 0.288 0.017 16.792 0.000 0.255
## Stst3ms (.24.) 0.270 0.016 16.949 0.000 0.239
## Stst4sc (.25.) 0.195 0.019 10.019 0.000 0.157
## Stst7bl (.26.) 0.081 0.019 4.252 0.000 0.044
## Stst8rn (.27.) 0.135 0.018 7.587 0.000 0.100
## Stst11r (.28.) 0.363 0.016 23.019 0.000 0.332
## Stst12l (.29.) 0.171 0.016 10.497 0.000 0.139
## Stst13h (.30.) 0.223 0.020 11.282 0.000 0.184
## Stst14b (.31.) 0.168 0.018 9.193 0.000 0.132
## Stst15t (.32.) 0.299 0.016 18.874 0.000 0.268
## Stst16m (.33.) 0.211 0.019 11.300 0.000 0.175
## Stst19d (.34.) 0.173 0.016 10.960 0.000 0.142
## Stst26r (.35.) 0.203 0.014 14.664 0.000 0.176
## science =~
## Stst1vc (.36.) 0.199 0.029 6.801 0.000 0.142
## Stst5mt (.37.) 0.204 0.021 9.797 0.000 0.163
## Stst6ph (.38.) 0.191 0.017 11.244 0.000 0.158
## Stst7bl (.39.) 0.137 0.026 5.213 0.000 0.086
## Stst9lc (.40.) 0.449 0.039 11.525 0.000 0.373
## Stst10m (.41.) 0.227 0.025 8.926 0.000 0.177
## spatial =~
## Stst28m (.42.) 0.300 0.018 16.785 0.000 0.265
## Sts292D (.43.) 0.520 0.022 23.230 0.000 0.477
## Sts303D (.44.) 0.517 0.020 25.927 0.000 0.478
## Stst31b (.45.) 0.475 0.019 24.698 0.000 0.438
## Stst37b (.46.) 0.324 0.022 14.719 0.000 0.281
## g =~
## Stst1vc (.47.) 0.854 0.018 48.439 0.000 0.820
## Stst2lt (.48.) 0.769 0.016 48.934 0.000 0.738
## Stst3ms (.49.) 0.677 0.015 46.693 0.000 0.649
## Stst4sc 0.805 0.019 42.686 0.000 0.768
## Stst5mt (.51.) 0.673 0.016 41.629 0.000 0.641
## Stst6ph 0.541 0.015 35.464 0.000 0.511
## Stst7bl (.53.) 0.609 0.017 36.055 0.000 0.576
## Stst8rn 0.251 0.019 13.368 0.000 0.214
## Stst9lc 0.363 0.021 17.363 0.000 0.322
## Stst10m 0.382 0.013 28.510 0.000 0.356
## Stst11r (.57.) 0.697 0.014 48.132 0.000 0.669
## Stst12l (.58.) 0.565 0.016 36.297 0.000 0.535
## Stst13h (.59.) 0.821 0.017 49.448 0.000 0.788
## Stst14b (.60.) 0.596 0.015 40.261 0.000 0.567
## Stst15t (.61.) 0.562 0.014 40.241 0.000 0.535
## Stst16m (.62.) 0.679 0.016 42.276 0.000 0.647
## Stst19d (.63.) 0.620 0.015 42.593 0.000 0.591
## Stst20s (.64.) 0.616 0.015 40.150 0.000 0.586
## Stst21c (.65.) 0.710 0.014 51.189 0.000 0.683
## Stst22p (.66.) 0.780 0.015 50.922 0.000 0.750
## Stst23n (.67.) 0.798 0.018 45.549 0.000 0.763
## Stst24x (.68.) 0.626 0.017 36.730 0.000 0.593
## Stst25w (.69.) 0.484 0.013 36.074 0.000 0.458
## Stst26r (.70.) 0.930 0.016 58.040 0.000 0.899
## Stst28m 0.370 0.014 27.111 0.000 0.343
## Sts292D (.72.) 0.446 0.016 28.630 0.000 0.416
## Sts303D (.73.) 0.410 0.014 28.973 0.000 0.382
## Stst31b (.74.) 0.733 0.016 45.176 0.000 0.701
## Stst32r (.75.) 0.562 0.014 39.607 0.000 0.535
## Stst33h (.76.) 0.555 0.014 40.266 0.000 0.528
## Stst34r (.77.) 0.658 0.017 37.989 0.000 0.624
## Stst35t (.78.) 0.639 0.023 27.311 0.000 0.594
## Stst36c (.79.) 0.146 0.019 7.839 0.000 0.109
## Stst37b (.80.) 0.283 0.018 15.874 0.000 0.248
## ci.upper Std.lv Std.all
##
## 0.113 0.085 0.091
## 0.289 0.258 0.288
## 0.380 0.344 0.361
## 0.353 0.324 0.332
## 0.402 0.371 0.389
## 0.420 0.382 0.351
## 0.340 0.301 0.278
## 0.150 0.122 0.159
## 0.178 0.156 0.162
## 0.208 0.174 0.162
## 0.267 0.230 0.202
##
## 0.277 0.207 0.207
## 0.228 0.161 0.209
## 0.235 0.169 0.225
## 0.408 0.312 0.446
## 0.268 0.195 0.172
##
## 0.217 0.196 0.218
## 0.497 0.458 0.402
## 1.009 0.949 0.589
## 0.926 0.879 0.684
## 0.754 0.710 0.621
##
## 0.240 0.230 0.245
## 0.322 0.320 0.360
## 0.302 0.300 0.340
## 0.233 0.216 0.243
## 0.119 0.090 0.103
## 0.170 0.150 0.180
## 0.394 0.404 0.427
## 0.202 0.190 0.226
## 0.262 0.248 0.229
## 0.204 0.187 0.217
## 0.330 0.332 0.386
## 0.248 0.235 0.252
## 0.204 0.192 0.215
## 0.230 0.225 0.233
##
## 0.257 0.159 0.169
## 0.244 0.163 0.163
## 0.224 0.153 0.220
## 0.189 0.109 0.125
## 0.526 0.359 0.372
## 0.276 0.181 0.293
##
## 0.335 0.219 0.352
## 0.564 0.380 0.386
## 0.556 0.377 0.482
## 0.513 0.347 0.324
## 0.367 0.236 0.207
##
## 0.889 0.742 0.790
## 0.799 0.667 0.751
## 0.706 0.588 0.666
## 0.842 0.699 0.786
## 0.704 0.584 0.587
## 0.571 0.470 0.677
## 0.642 0.528 0.603
## 0.287 0.218 0.262
## 0.404 0.315 0.327
## 0.408 0.332 0.538
## 0.725 0.605 0.640
## 0.596 0.491 0.586
## 0.853 0.712 0.658
## 0.625 0.517 0.602
## 0.590 0.488 0.568
## 0.710 0.589 0.632
## 0.648 0.538 0.601
## 0.646 0.535 0.561
## 0.738 0.617 0.634
## 0.810 0.677 0.710
## 0.832 0.693 0.637
## 0.660 0.544 0.501
## 0.511 0.421 0.547
## 0.961 0.807 0.834
## 0.397 0.321 0.516
## 0.477 0.387 0.393
## 0.437 0.356 0.455
## 0.765 0.636 0.593
## 0.590 0.488 0.650
## 0.582 0.482 0.690
## 0.692 0.571 0.502
## 0.685 0.555 0.345
## 0.182 0.127 0.099
## 0.318 0.246 0.215
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -1.339 0.016 -83.554 0.000 -1.370
## .Stst19dsgsdwrd -0.878 0.016 -54.059 0.000 -0.910
## .Stest20spellng -0.450 0.017 -26.686 0.000 -0.483
## .Stest21cptlztn -0.899 0.017 -51.477 0.000 -0.934
## .Stest22puncttn -0.929 0.017 -53.286 0.000 -0.963
## .Stest23english -0.744 0.019 -38.449 0.000 -0.781
## .Stest24exprssn -0.704 0.019 -37.099 0.000 -0.742
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.816
## .Stst26rdngcmpr -1.226 0.017 -72.842 0.000 -1.259
## .Stst31bstrctrs -1.260 0.019 -65.843 0.000 -1.297
## .Stst34rthcmptt -1.004 0.021 -47.990 0.000 -1.045
## .Stest5math -0.965 0.017 -55.615 0.000 -0.999
## .Stst32rthrsnng -1.184 0.013 -92.849 0.000 -1.209
## .Stst33hghschlm -0.942 0.012 -78.389 0.000 -0.966
## .Stest35tblrdng -0.524 0.029 -17.830 0.000 -0.582
## .Stst36clrclchc 0.300 0.023 13.284 0.000 0.256
## .Stst37bjctnspc -0.217 0.021 -10.567 0.000 -0.257
## .Stest2literatr -1.034 0.016 -66.363 0.000 -1.065
## .Stest3music -0.825 0.016 -52.646 0.000 -0.856
## .Stest4soclstds -1.273 0.015 -82.694 0.000 -1.303
## .Stst7blgclscnc -0.831 0.015 -55.991 0.000 -0.860
## .Stest8aerontcs -0.942 0.014 -64.960 0.000 -0.970
## .Stest11art -1.046 0.017 -63.114 0.000 -1.078
## .Stest12law -0.897 0.014 -63.710 0.000 -0.925
## .Stest13health -1.020 0.019 -52.885 0.000 -1.057
## .Stest14bible -0.565 0.015 -36.958 0.000 -0.595
## .Stest15theater -0.856 0.015 -56.660 0.000 -0.885
## .Stest16mscllns -0.949 0.016 -60.013 0.000 -0.980
## .Stst6physclscn -1.022 0.012 -84.927 0.000 -1.046
## .Stest9elctrncs -1.154 0.017 -68.546 0.000 -1.187
## .Stest10mechncs -1.373 0.011 -128.778 0.000 -1.394
## .Stst28mchnclrs -1.323 0.011 -124.285 0.000 -1.344
## .Stst29vslztn2D -0.916 0.017 -52.801 0.000 -0.950
## .Stst30vslztn3D -0.982 0.014 -72.639 0.000 -1.008
## ci.upper Std.lv Std.all
## -1.307 -1.339 -1.426
## -0.846 -0.878 -0.981
## -0.417 -0.450 -0.472
## -0.865 -0.899 -0.924
## -0.895 -0.929 -0.974
## -0.706 -0.744 -0.684
## -0.667 -0.704 -0.649
## -0.761 -0.788 -1.025
## -1.193 -1.226 -1.267
## -1.222 -1.260 -1.175
## -0.963 -1.004 -0.882
## -0.931 -0.965 -0.969
## -1.159 -1.184 -1.575
## -0.919 -0.942 -1.349
## -0.466 -0.524 -0.325
## 0.344 0.300 0.233
## -0.176 -0.217 -0.190
## -1.004 -1.034 -1.164
## -0.795 -0.825 -0.935
## -1.243 -1.273 -1.431
## -0.802 -0.831 -0.948
## -0.913 -0.942 -1.132
## -1.013 -1.046 -1.106
## -0.870 -0.897 -1.072
## -0.982 -1.020 -0.941
## -0.535 -0.565 -0.658
## -0.826 -0.856 -0.996
## -0.918 -0.949 -1.017
## -0.998 -1.022 -1.472
## -1.121 -1.154 -1.198
## -1.352 -1.373 -2.226
## -1.303 -1.323 -2.128
## -0.882 -0.916 -0.929
## -0.955 -0.982 -1.255
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.246 0.009 28.226 0.000 0.229
## .Stst19dsgsdwrd 0.370 0.012 31.463 0.000 0.347
## .Stest20spellng 0.504 0.014 35.139 0.000 0.476
## .Stest21cptlztn 0.462 0.014 33.452 0.000 0.435
## .Stest22puncttn 0.314 0.011 28.471 0.000 0.293
## .Stest23english 0.556 0.017 32.461 0.000 0.523
## .Stest24exprssn 0.792 0.021 36.898 0.000 0.750
## .Stst25wrdfnctn 0.374 0.011 34.669 0.000 0.353
## .Stst26rdngcmpr 0.209 0.007 29.772 0.000 0.195
## .Stst31bstrctrs 0.594 0.017 34.503 0.000 0.560
## .Stst34rthcmptt 0.668 0.027 24.833 0.000 0.615
## .Stest5math 0.581 0.017 34.098 0.000 0.548
## .Stst32rthrsnng 0.298 0.009 34.270 0.000 0.281
## .Stst33hghschlm 0.158 0.012 12.921 0.000 0.134
## .Stest35tblrdng 1.386 0.057 24.351 0.000 1.275
## .Stst36clrclchc 0.865 0.033 26.232 0.000 0.800
## .Stst37bjctnspc 0.686 0.026 25.891 0.000 0.634
## .Stest2literatr 0.242 0.007 33.597 0.000 0.228
## .Stest3music 0.343 0.009 36.668 0.000 0.324
## .Stest4soclstds 0.256 0.007 35.395 0.000 0.242
## .Stst7blgclscnc 0.470 0.012 38.598 0.000 0.446
## .Stest8aerontcs 0.622 0.011 58.295 0.000 0.601
## .Stest11art 0.365 0.012 31.611 0.000 0.342
## .Stest12law 0.424 0.011 39.937 0.000 0.403
## .Stest13health 0.605 0.015 41.374 0.000 0.576
## .Stest14bible 0.434 0.012 34.802 0.000 0.410
## .Stest15theater 0.390 0.011 36.497 0.000 0.369
## .Stest16mscllns 0.467 0.012 38.021 0.000 0.443
## .Stst6physclscn 0.238 0.007 32.592 0.000 0.224
## .Stest9elctrncs 0.700 0.030 23.324 0.000 0.641
## .Stest10mechncs 0.238 0.007 32.218 0.000 0.223
## .Stst28mchnclrs 0.236 0.007 35.909 0.000 0.223
## .Stst29vslztn2D 0.676 0.020 34.070 0.000 0.637
## .Stst30vslztn3D 0.343 0.012 28.234 0.000 0.319
## english 1.013 0.088 11.517 0.000 0.841
## math 0.742 0.084 8.801 0.000 0.577
## speed 1.002 0.060 16.731 0.000 0.884
## info 1.235 0.117 10.562 0.000 1.006
## science 0.637 0.086 7.386 0.000 0.468
## spatial 0.534 0.043 12.462 0.000 0.450
## g 0.754 0.033 22.533 0.000 0.688
## ci.upper Std.lv Std.all
## 0.263 0.246 0.279
## 0.394 0.370 0.462
## 0.532 0.504 0.555
## 0.490 0.462 0.488
## 0.336 0.314 0.345
## 0.590 0.556 0.471
## 0.834 0.792 0.672
## 0.395 0.374 0.632
## 0.223 0.209 0.223
## 0.628 0.594 0.517
## 0.720 0.668 0.516
## 0.615 0.581 0.586
## 0.315 0.298 0.527
## 0.182 0.158 0.325
## 1.498 1.386 0.534
## 0.929 0.865 0.523
## 0.738 0.686 0.525
## 0.256 0.242 0.306
## 0.361 0.343 0.440
## 0.270 0.256 0.323
## 0.494 0.470 0.611
## 0.643 0.622 0.899
## 0.387 0.365 0.408
## 0.445 0.424 0.605
## 0.633 0.605 0.515
## 0.459 0.434 0.590
## 0.411 0.390 0.528
## 0.491 0.467 0.537
## 0.253 0.238 0.494
## 0.759 0.700 0.754
## 0.252 0.238 0.625
## 0.248 0.236 0.609
## 0.715 0.676 0.696
## 0.367 0.343 0.560
## 1.186 1.000 1.000
## 0.908 1.000 1.000
## 1.119 1.000 1.000
## 1.464 1.000 1.000
## 0.806 1.000 1.000
## 0.617 1.000 1.000
## 0.819 1.000 1.000
lavTestScore(metric2, release = 1:74)
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 541.021 74 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p184. 0.008 1 0.928
## 2 .p2. == .p185. 3.266 1 0.071
## 3 .p3. == .p186. 3.745 1 0.053
## 4 .p4. == .p187. 0.611 1 0.434
## 5 .p5. == .p188. 0.256 1 0.613
## 6 .p6. == .p189. 1.636 1 0.201
## 7 .p7. == .p190. 0.791 1 0.374
## 8 .p8. == .p191. 2.177 1 0.140
## 9 .p9. == .p192. 0.001 1 0.972
## 10 .p10. == .p193. 1.751 1 0.186
## 11 .p11. == .p194. 1.704 1 0.192
## 12 .p12. == .p195. 0.181 1 0.670
## 13 .p13. == .p196. 3.480 1 0.062
## 14 .p14. == .p197. 6.827 1 0.009
## 15 .p15. == .p198. 0.000 1 0.990
## 16 .p16. == .p199. 0.437 1 0.509
## 17 .p17. == .p200. 8.393 1 0.004
## 18 .p18. == .p201. 0.945 1 0.331
## 19 .p19. == .p202. 0.015 1 0.902
## 20 .p20. == .p203. 1.006 1 0.316
## 21 .p21. == .p204. 1.807 1 0.179
## 22 .p22. == .p205. 0.421 1 0.516
## 23 .p23. == .p206. 0.594 1 0.441
## 24 .p24. == .p207. 0.067 1 0.795
## 25 .p25. == .p208. 0.002 1 0.965
## 26 .p26. == .p209. 0.905 1 0.341
## 27 .p27. == .p210. 1.991 1 0.158
## 28 .p28. == .p211. 4.454 1 0.035
## 29 .p29. == .p212. 0.571 1 0.450
## 30 .p30. == .p213. 0.239 1 0.625
## 31 .p31. == .p214. 0.858 1 0.354
## 32 .p32. == .p215. 0.002 1 0.966
## 33 .p33. == .p216. 17.096 1 0.000
## 34 .p34. == .p217. 1.844 1 0.174
## 35 .p35. == .p218. 0.504 1 0.478
## 36 .p36. == .p219. 1.383 1 0.240
## 37 .p37. == .p220. 10.545 1 0.001
## 38 .p38. == .p221. 2.064 1 0.151
## 39 .p39. == .p222. 1.268 1 0.260
## 40 .p40. == .p223. 0.367 1 0.545
## 41 .p41. == .p224. 7.097 1 0.008
## 42 .p42. == .p225. 54.861 1 0.000
## 43 .p43. == .p226. 7.236 1 0.007
## 44 .p44. == .p227. 1.269 1 0.260
## 45 .p45. == .p228. 7.073 1 0.008
## 46 .p46. == .p229. 0.641 1 0.424
## 47 .p47. == .p230. 37.803 1 0.000
## 48 .p48. == .p231. 0.495 1 0.482
## 49 .p49. == .p232. 23.653 1 0.000
## 50 .p51. == .p234. 3.217 1 0.073
## 51 .p53. == .p236. 46.986 1 0.000
## 52 .p57. == .p240. 7.099 1 0.008
## 53 .p58. == .p241. 34.573 1 0.000
## 54 .p59. == .p242. 6.743 1 0.009
## 55 .p60. == .p243. 9.450 1 0.002
## 56 .p61. == .p244. 23.710 1 0.000
## 57 .p62. == .p245. 20.537 1 0.000
## 58 .p63. == .p246. 28.932 1 0.000
## 59 .p64. == .p247. 0.188 1 0.664
## 60 .p65. == .p248. 29.644 1 0.000
## 61 .p66. == .p249. 17.075 1 0.000
## 62 .p67. == .p250. 3.521 1 0.061
## 63 .p68. == .p251. 7.350 1 0.007
## 64 .p69. == .p252. 45.525 1 0.000
## 65 .p70. == .p253. 7.857 1 0.005
## 66 .p72. == .p255. 0.087 1 0.768
## 67 .p73. == .p256. 14.812 1 0.000
## 68 .p74. == .p257. 4.345 1 0.037
## 69 .p75. == .p258. 9.121 1 0.003
## 70 .p76. == .p259. 1.492 1 0.222
## 71 .p77. == .p260. 0.009 1 0.924
## 72 .p78. == .p261. 2.958 1 0.085
## 73 .p79. == .p262. 8.556 1 0.003
## 74 .p80. == .p263. 3.006 1 0.083
scalar<-cfa(chc.bifactor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("g=~Stest8aeronautics", "g=~Stest28mechanicalreasoning", "g=~Stest10mechanics", "g=~Stest9electronics", "g=~Stest6physicalscience", "g=~Stest4socialstudies"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 6508.662 1056.000 0.000 0.951 0.041 0.046
## aic bic
## 463333.066 464689.209
Mc(scalar)
## [1] 0.6388313
summary(scalar, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 144 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 310
## Number of equality constraints 108
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 6508.662 5815.793
## Degrees of freedom 1056 1056
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.119
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 3026.345 2704.181
## 1 3482.317 3111.612
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.065 0.009 6.963 0.000 0.047
## Stst19d (.p2.) 0.174 0.011 15.305 0.000 0.152
## Stst20s (.p3.) 0.376 0.014 27.016 0.000 0.349
## Stst21c (.p4.) 0.357 0.012 29.543 0.000 0.334
## Stst22p (.p5.) 0.400 0.014 29.463 0.000 0.373
## Stst23n (.p6.) 0.412 0.016 26.541 0.000 0.382
## Stst24x (.p7.) 0.331 0.014 22.952 0.000 0.303
## Stst25w (.p8.) 0.112 0.011 10.408 0.000 0.091
## Stst26r (.p9.) 0.157 0.009 17.841 0.000 0.139
## Stst31b (.10.) 0.210 0.013 16.609 0.000 0.185
## Stst34r (.11.) 0.150 0.013 11.276 0.000 0.124
## math =~
## Stst5mt (.12.) 0.285 0.020 14.038 0.000 0.245
## Stst25w (.13.) 0.202 0.015 13.667 0.000 0.173
## Stst32r (.14.) 0.236 0.015 15.704 0.000 0.206
## Stst33h (.15.) 0.330 0.021 15.493 0.000 0.289
## Stst34r (.16.) 0.170 0.024 7.039 0.000 0.123
## speed =~
## Stst19d (.17.) 0.185 0.011 16.818 0.000 0.164
## Stst34r (.18.) 0.445 0.020 22.151 0.000 0.406
## Stst35t (.19.) 0.975 0.030 32.078 0.000 0.916
## Stst36c (.20.) 0.873 0.024 36.449 0.000 0.826
## Stst37b (.21.) 0.716 0.022 32.636 0.000 0.673
## info =~
## Stst1vc (.22.) 0.189 0.012 15.183 0.000 0.164
## Stst2lt (.23.) 0.261 0.013 19.836 0.000 0.235
## Stst3ms (.24.) 0.263 0.013 20.600 0.000 0.238
## Stst4sc (.25.) 0.189 0.012 15.620 0.000 0.165
## Stst7bl (.26.) 0.120 0.013 9.079 0.000 0.094
## Stst8rn (.27.) -0.024 0.010 -2.281 0.023 -0.044
## Stst11r (.28.) 0.264 0.014 18.741 0.000 0.236
## Stst12l (.29.) 0.144 0.011 13.427 0.000 0.123
## Stst13h (.30.) 0.308 0.014 21.552 0.000 0.280
## Stst14b (.31.) 0.238 0.012 20.424 0.000 0.215
## Stst15t (.32.) 0.266 0.013 19.715 0.000 0.239
## Stst16m (.33.) 0.199 0.013 15.405 0.000 0.174
## Stst19d (.34.) 0.077 0.011 7.175 0.000 0.056
## Stst26r (.35.) 0.186 0.011 16.727 0.000 0.164
## science =~
## Stst1vc (.36.) 0.141 0.023 6.093 0.000 0.096
## Stst5mt (.37.) 0.047 0.026 1.805 0.071 -0.004
## Stst6ph (.38.) -0.005 0.017 -0.301 0.764 -0.038
## Stst7bl (.39.) 0.083 0.023 3.517 0.000 0.037
## Stst9lc (.40.) 0.231 0.026 8.812 0.000 0.179
## Stst10m (.41.) 0.471 0.034 13.921 0.000 0.405
## spatial =~
## Stst28m (.42.) 0.327 0.027 11.974 0.000 0.274
## Sts292D (.43.) 0.521 0.023 23.161 0.000 0.477
## Sts303D (.44.) 0.485 0.022 21.716 0.000 0.441
## Stst31b (.45.) 0.489 0.019 25.329 0.000 0.452
## Stst37b (.46.) 0.327 0.022 14.990 0.000 0.284
## g =~
## Stst1vc (.47.) 0.868 0.016 53.989 0.000 0.836
## Stst2lt (.48.) 0.779 0.015 52.378 0.000 0.750
## Stst3ms (.49.) 0.682 0.014 48.638 0.000 0.654
## Stst4sc 0.951 0.016 58.843 0.000 0.919
## Stst5mt (.51.) 0.667 0.016 42.834 0.000 0.636
## Stst6ph 0.718 0.017 42.113 0.000 0.685
## Stst7bl (.53.) 0.600 0.016 38.585 0.000 0.570
## Stst8rn 0.620 0.020 31.078 0.000 0.581
## Stst9lc 0.701 0.022 32.352 0.000 0.659
## Stst10m 0.612 0.018 34.305 0.000 0.577
## Stst11r (.57.) 0.731 0.014 51.752 0.000 0.703
## Stst12l (.58.) 0.575 0.015 38.840 0.000 0.546
## Stst13h (.59.) 0.793 0.015 51.918 0.000 0.763
## Stst14b (.60.) 0.574 0.014 41.725 0.000 0.547
## Stst15t (.61.) 0.574 0.014 42.132 0.000 0.548
## Stst16m (.62.) 0.685 0.015 45.630 0.000 0.655
## Stst19d (.63.) 0.655 0.014 46.502 0.000 0.628
## Stst20s (.64.) 0.603 0.015 41.121 0.000 0.574
## Stst21c (.65.) 0.699 0.014 51.196 0.000 0.672
## Stst22p (.66.) 0.767 0.015 50.925 0.000 0.738
## Stst23n (.67.) 0.785 0.017 46.025 0.000 0.752
## Stst24x (.68.) 0.613 0.016 37.314 0.000 0.581
## Stst25w (.69.) 0.485 0.013 37.058 0.000 0.460
## Stst26r (.70.) 0.932 0.015 60.411 0.000 0.902
## Stst28m 0.574 0.019 29.943 0.000 0.536
## Sts292D (.72.) 0.433 0.015 28.918 0.000 0.403
## Sts303D (.73.) 0.377 0.014 27.507 0.000 0.350
## Stst31b (.74.) 0.716 0.016 45.506 0.000 0.686
## Stst32r (.75.) 0.551 0.014 39.128 0.000 0.524
## Stst33h (.76.) 0.554 0.014 40.118 0.000 0.527
## Stst34r (.77.) 0.677 0.017 40.358 0.000 0.644
## Stst35t (.78.) 0.604 0.023 26.032 0.000 0.559
## Stst36c (.79.) 0.154 0.018 8.449 0.000 0.119
## Stst37b (.80.) 0.276 0.018 15.653 0.000 0.242
## ci.upper Std.lv Std.all
##
## 0.083 0.065 0.063
## 0.197 0.174 0.187
## 0.403 0.376 0.371
## 0.381 0.357 0.359
## 0.426 0.400 0.383
## 0.443 0.412 0.345
## 0.359 0.331 0.286
## 0.133 0.112 0.136
## 0.174 0.157 0.146
## 0.235 0.210 0.181
## 0.176 0.150 0.129
##
## 0.324 0.285 0.277
## 0.231 0.202 0.246
## 0.265 0.236 0.287
## 0.372 0.330 0.424
## 0.217 0.170 0.147
##
## 0.207 0.185 0.198
## 0.485 0.445 0.384
## 1.035 0.975 0.577
## 0.920 0.873 0.677
## 0.760 0.716 0.581
##
## 0.213 0.189 0.182
## 0.286 0.261 0.269
## 0.288 0.263 0.282
## 0.213 0.189 0.170
## 0.146 0.120 0.130
## -0.003 -0.024 -0.023
## 0.291 0.264 0.269
## 0.165 0.144 0.159
## 0.336 0.308 0.276
## 0.261 0.238 0.271
## 0.292 0.266 0.313
## 0.224 0.199 0.196
## 0.098 0.077 0.082
## 0.208 0.186 0.173
##
## 0.187 0.141 0.137
## 0.097 0.047 0.045
## 0.028 -0.005 -0.006
## 0.129 0.083 0.089
## 0.282 0.231 0.208
## 0.537 0.471 0.532
##
## 0.381 0.327 0.363
## 0.565 0.521 0.479
## 0.529 0.485 0.527
## 0.527 0.489 0.422
## 0.370 0.327 0.265
##
## 0.899 0.868 0.838
## 0.809 0.779 0.805
## 0.709 0.682 0.731
## 0.983 0.951 0.856
## 0.697 0.667 0.649
## 0.752 0.718 0.807
## 0.631 0.600 0.649
## 0.659 0.620 0.607
## 0.744 0.701 0.633
## 0.647 0.612 0.691
## 0.759 0.731 0.745
## 0.604 0.575 0.636
## 0.823 0.793 0.713
## 0.601 0.574 0.653
## 0.601 0.574 0.677
## 0.714 0.685 0.676
## 0.683 0.655 0.701
## 0.632 0.603 0.595
## 0.725 0.699 0.701
## 0.797 0.767 0.734
## 0.818 0.785 0.658
## 0.645 0.613 0.530
## 0.511 0.485 0.593
## 0.963 0.932 0.867
## 0.611 0.574 0.636
## 0.462 0.433 0.397
## 0.404 0.377 0.410
## 0.747 0.716 0.617
## 0.579 0.551 0.672
## 0.581 0.554 0.710
## 0.710 0.677 0.583
## 0.650 0.604 0.357
## 0.190 0.154 0.120
## 0.311 0.276 0.224
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.143) -1.192 0.029 -41.299 0.000 -1.249
## .Stst19d (.144) -1.055 0.024 -44.527 0.000 -1.101
## .Stst20s (.145) -0.859 0.023 -36.887 0.000 -0.904
## .Stst21c (.146) -1.196 0.024 -49.433 0.000 -1.243
## .Stst22p (.147) -1.265 0.027 -47.334 0.000 -1.317
## .Stst23n (.148) -1.096 0.029 -37.313 0.000 -1.154
## .Stst24x (.149) -0.996 0.027 -37.249 0.000 -1.049
## .Stst25w (.150) -0.905 0.018 -50.690 0.000 -0.940
## .Stst26r (.151) -1.343 0.030 -44.529 0.000 -1.402
## .Stst31b (.152) -1.101 0.027 -41.218 0.000 -1.154
## .Stst34r (.153) -1.239 0.029 -43.207 0.000 -1.295
## .Stst5mt (.154) -0.805 0.024 -33.439 0.000 -0.853
## .Stst32r (.155) -1.068 0.020 -53.204 0.000 -1.107
## .Stst33h (.156) -0.912 0.019 -48.393 0.000 -0.949
## .Stst35t (.157) -0.668 0.038 -17.401 0.000 -0.743
## .Stst36c (.158) -0.045 0.026 -1.775 0.076 -0.095
## .Stst37b (.159) -0.323 0.025 -12.886 0.000 -0.372
## .Stst2lt (.160) -1.085 0.026 -41.363 0.000 -1.137
## .Stst3ms (.161) -0.953 0.023 -41.299 0.000 -0.998
## .Stst4sc (.162) -1.141 0.031 -36.485 0.000 -1.202
## .Stst7bl (.163) -0.632 0.024 -26.392 0.000 -0.679
## .Stst8rn (.164) -0.618 0.030 -20.671 0.000 -0.677
## .Stst11r (.165) -1.113 0.026 -42.193 0.000 -1.165
## .Stst12l (.166) -0.821 0.024 -34.572 0.000 -0.868
## .Stst13h (.167) -1.200 0.027 -45.081 0.000 -1.252
## .Stst14b (.168) -0.725 0.020 -35.860 0.000 -0.764
## .Stst15t (.169) -1.057 0.020 -51.765 0.000 -1.097
## .Stst16m (.170) -0.927 0.027 -34.490 0.000 -0.980
## .Stst6ph (.171) -0.715 0.029 -25.022 0.000 -0.771
## .Stst9lc (.172) -0.701 0.030 -23.523 0.000 -0.760
## .Stst10m (.173) -0.692 0.023 -29.818 0.000 -0.737
## .Stst28m (.174) -0.887 0.023 -37.992 0.000 -0.933
## .Sts292D (.175) -0.506 0.022 -23.314 0.000 -0.549
## .Sts303D (.176) -0.650 0.019 -33.867 0.000 -0.687
## ci.upper Std.lv Std.all
## -1.136 -1.192 -1.151
## -1.008 -1.055 -1.129
## -0.813 -0.859 -0.847
## -1.148 -1.196 -1.200
## -1.212 -1.265 -1.211
## -1.039 -1.096 -0.919
## -0.944 -0.996 -0.862
## -0.870 -0.905 -1.106
## -1.284 -1.343 -1.249
## -1.049 -1.101 -0.949
## -1.182 -1.239 -1.067
## -0.758 -0.805 -0.784
## -1.029 -1.068 -1.302
## -0.875 -0.912 -1.169
## -0.593 -0.668 -0.395
## 0.005 -0.045 -0.035
## -0.274 -0.323 -0.262
## -1.034 -1.085 -1.122
## -0.908 -0.953 -1.021
## -1.079 -1.141 -1.027
## -0.585 -0.632 -0.684
## -0.559 -0.618 -0.606
## -1.061 -1.113 -1.135
## -0.775 -0.821 -0.908
## -1.148 -1.200 -1.079
## -0.685 -0.725 -0.825
## -1.017 -1.057 -1.246
## -0.874 -0.927 -0.915
## -0.659 -0.715 -0.803
## -0.643 -0.701 -0.634
## -0.646 -0.692 -0.781
## -0.842 -0.887 -0.984
## -0.464 -0.506 -0.465
## -0.612 -0.650 -0.706
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.260 0.010 27.189 0.000 0.241
## .Stst19dsgsdwrd 0.373 0.014 27.382 0.000 0.347
## .Stest20spellng 0.523 0.017 30.194 0.000 0.489
## .Stest21cptlztn 0.377 0.015 24.360 0.000 0.346
## .Stest22puncttn 0.343 0.012 27.942 0.000 0.319
## .Stest23english 0.637 0.024 26.961 0.000 0.591
## .Stest24exprssn 0.852 0.025 33.520 0.000 0.802
## .Stst25wrdfnctn 0.381 0.012 32.039 0.000 0.358
## .Stst26rdngcmpr 0.227 0.009 25.518 0.000 0.209
## .Stst31bstrctrs 0.551 0.022 24.560 0.000 0.507
## .Stst34rthcmptt 0.638 0.031 20.527 0.000 0.578
## .Stest5math 0.529 0.020 26.069 0.000 0.489
## .Stst32rthrsnng 0.314 0.011 27.762 0.000 0.292
## .Stst33hghschlm 0.192 0.012 16.110 0.000 0.169
## .Stest35tblrdng 1.543 0.069 22.241 0.000 1.407
## .Stst36clrclchc 0.874 0.041 21.420 0.000 0.794
## .Stst37bjctnspc 0.823 0.034 24.226 0.000 0.757
## .Stest2literatr 0.261 0.009 29.507 0.000 0.244
## .Stest3music 0.337 0.012 27.955 0.000 0.313
## .Stest4soclstds 0.294 0.011 27.939 0.000 0.273
## .Stst7blgclscnc 0.474 0.014 33.643 0.000 0.446
## .Stest8aerontcs 0.656 0.019 34.893 0.000 0.619
## .Stest11art 0.358 0.012 29.046 0.000 0.334
## .Stest12law 0.466 0.014 33.433 0.000 0.439
## .Stest13health 0.515 0.017 30.949 0.000 0.482
## .Stest14bible 0.387 0.014 28.405 0.000 0.360
## .Stest15theater 0.319 0.011 28.450 0.000 0.297
## .Stest16mscllns 0.519 0.017 31.205 0.000 0.486
## .Stst6physclscn 0.277 0.011 26.054 0.000 0.256
## .Stest9elctrncs 0.681 0.029 23.547 0.000 0.624
## .Stest10mechncs 0.188 0.035 5.383 0.000 0.120
## .Stst28mchnclrs 0.377 0.018 20.922 0.000 0.341
## .Stst29vslztn2D 0.727 0.027 26.515 0.000 0.673
## .Stst30vslztn3D 0.468 0.021 22.687 0.000 0.428
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.279 0.260 0.242
## 0.400 0.373 0.427
## 0.557 0.523 0.509
## 0.407 0.377 0.380
## 0.367 0.343 0.314
## 0.684 0.637 0.448
## 0.901 0.852 0.637
## 0.404 0.381 0.569
## 0.244 0.227 0.196
## 0.595 0.551 0.409
## 0.699 0.638 0.474
## 0.569 0.529 0.501
## 0.336 0.314 0.466
## 0.215 0.192 0.316
## 1.679 1.543 0.540
## 0.954 0.874 0.527
## 0.890 0.823 0.542
## 0.278 0.261 0.279
## 0.360 0.337 0.387
## 0.314 0.294 0.238
## 0.501 0.474 0.554
## 0.693 0.656 0.631
## 0.383 0.358 0.372
## 0.493 0.466 0.570
## 0.547 0.515 0.416
## 0.413 0.387 0.500
## 0.341 0.319 0.444
## 0.551 0.519 0.505
## 0.298 0.277 0.349
## 0.738 0.681 0.556
## 0.257 0.188 0.240
## 0.412 0.377 0.463
## 0.780 0.727 0.613
## 0.509 0.468 0.554
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.065 0.009 6.963 0.000 0.047
## Stst19d (.p2.) 0.174 0.011 15.305 0.000 0.152
## Stst20s (.p3.) 0.376 0.014 27.016 0.000 0.349
## Stst21c (.p4.) 0.357 0.012 29.543 0.000 0.334
## Stst22p (.p5.) 0.400 0.014 29.463 0.000 0.373
## Stst23n (.p6.) 0.412 0.016 26.541 0.000 0.382
## Stst24x (.p7.) 0.331 0.014 22.952 0.000 0.303
## Stst25w (.p8.) 0.112 0.011 10.408 0.000 0.091
## Stst26r (.p9.) 0.157 0.009 17.841 0.000 0.139
## Stst31b (.10.) 0.210 0.013 16.609 0.000 0.185
## Stst34r (.11.) 0.150 0.013 11.276 0.000 0.124
## math =~
## Stst5mt (.12.) 0.285 0.020 14.038 0.000 0.245
## Stst25w (.13.) 0.202 0.015 13.667 0.000 0.173
## Stst32r (.14.) 0.236 0.015 15.704 0.000 0.206
## Stst33h (.15.) 0.330 0.021 15.493 0.000 0.289
## Stst34r (.16.) 0.170 0.024 7.039 0.000 0.123
## speed =~
## Stst19d (.17.) 0.185 0.011 16.818 0.000 0.164
## Stst34r (.18.) 0.445 0.020 22.151 0.000 0.406
## Stst35t (.19.) 0.975 0.030 32.078 0.000 0.916
## Stst36c (.20.) 0.873 0.024 36.449 0.000 0.826
## Stst37b (.21.) 0.716 0.022 32.636 0.000 0.673
## info =~
## Stst1vc (.22.) 0.189 0.012 15.183 0.000 0.164
## Stst2lt (.23.) 0.261 0.013 19.836 0.000 0.235
## Stst3ms (.24.) 0.263 0.013 20.600 0.000 0.238
## Stst4sc (.25.) 0.189 0.012 15.620 0.000 0.165
## Stst7bl (.26.) 0.120 0.013 9.079 0.000 0.094
## Stst8rn (.27.) -0.024 0.010 -2.281 0.023 -0.044
## Stst11r (.28.) 0.264 0.014 18.741 0.000 0.236
## Stst12l (.29.) 0.144 0.011 13.427 0.000 0.123
## Stst13h (.30.) 0.308 0.014 21.552 0.000 0.280
## Stst14b (.31.) 0.238 0.012 20.424 0.000 0.215
## Stst15t (.32.) 0.266 0.013 19.715 0.000 0.239
## Stst16m (.33.) 0.199 0.013 15.405 0.000 0.174
## Stst19d (.34.) 0.077 0.011 7.175 0.000 0.056
## Stst26r (.35.) 0.186 0.011 16.727 0.000 0.164
## science =~
## Stst1vc (.36.) 0.141 0.023 6.093 0.000 0.096
## Stst5mt (.37.) 0.047 0.026 1.805 0.071 -0.004
## Stst6ph (.38.) -0.005 0.017 -0.301 0.764 -0.038
## Stst7bl (.39.) 0.083 0.023 3.517 0.000 0.037
## Stst9lc (.40.) 0.231 0.026 8.812 0.000 0.179
## Stst10m (.41.) 0.471 0.034 13.921 0.000 0.405
## spatial =~
## Stst28m (.42.) 0.327 0.027 11.974 0.000 0.274
## Sts292D (.43.) 0.521 0.023 23.161 0.000 0.477
## Sts303D (.44.) 0.485 0.022 21.716 0.000 0.441
## Stst31b (.45.) 0.489 0.019 25.329 0.000 0.452
## Stst37b (.46.) 0.327 0.022 14.990 0.000 0.284
## g =~
## Stst1vc (.47.) 0.868 0.016 53.989 0.000 0.836
## Stst2lt (.48.) 0.779 0.015 52.378 0.000 0.750
## Stst3ms (.49.) 0.682 0.014 48.638 0.000 0.654
## Stst4sc 0.811 0.017 48.301 0.000 0.778
## Stst5mt (.51.) 0.667 0.016 42.834 0.000 0.636
## Stst6ph 0.511 0.020 26.009 0.000 0.472
## Stst7bl (.53.) 0.600 0.016 38.585 0.000 0.570
## Stst8rn 0.336 0.018 18.950 0.000 0.301
## Stst9lc 0.375 0.022 17.023 0.000 0.332
## Stst10m 0.395 0.013 29.412 0.000 0.369
## Stst11r (.57.) 0.731 0.014 51.752 0.000 0.703
## Stst12l (.58.) 0.575 0.015 38.840 0.000 0.546
## Stst13h (.59.) 0.793 0.015 51.918 0.000 0.763
## Stst14b (.60.) 0.574 0.014 41.725 0.000 0.547
## Stst15t (.61.) 0.574 0.014 42.132 0.000 0.548
## Stst16m (.62.) 0.685 0.015 45.630 0.000 0.655
## Stst19d (.63.) 0.655 0.014 46.502 0.000 0.628
## Stst20s (.64.) 0.603 0.015 41.121 0.000 0.574
## Stst21c (.65.) 0.699 0.014 51.196 0.000 0.672
## Stst22p (.66.) 0.767 0.015 50.925 0.000 0.738
## Stst23n (.67.) 0.785 0.017 46.025 0.000 0.752
## Stst24x (.68.) 0.613 0.016 37.314 0.000 0.581
## Stst25w (.69.) 0.485 0.013 37.058 0.000 0.460
## Stst26r (.70.) 0.932 0.015 60.411 0.000 0.902
## Stst28m 0.432 0.017 25.633 0.000 0.399
## Sts292D (.72.) 0.433 0.015 28.918 0.000 0.403
## Sts303D (.73.) 0.377 0.014 27.507 0.000 0.350
## Stst31b (.74.) 0.716 0.016 45.506 0.000 0.686
## Stst32r (.75.) 0.551 0.014 39.128 0.000 0.524
## Stst33h (.76.) 0.554 0.014 40.118 0.000 0.527
## Stst34r (.77.) 0.677 0.017 40.358 0.000 0.644
## Stst35t (.78.) 0.604 0.023 26.032 0.000 0.559
## Stst36c (.79.) 0.154 0.018 8.449 0.000 0.119
## Stst37b (.80.) 0.276 0.018 15.653 0.000 0.242
## ci.upper Std.lv Std.all
##
## 0.083 0.064 0.068
## 0.197 0.172 0.193
## 0.403 0.371 0.388
## 0.381 0.353 0.362
## 0.426 0.395 0.413
## 0.443 0.407 0.374
## 0.359 0.327 0.301
## 0.133 0.110 0.144
## 0.174 0.155 0.160
## 0.235 0.207 0.194
## 0.176 0.148 0.130
##
## 0.324 0.242 0.243
## 0.231 0.172 0.224
## 0.265 0.201 0.267
## 0.372 0.281 0.403
## 0.217 0.145 0.128
##
## 0.207 0.184 0.207
## 0.485 0.443 0.391
## 1.035 0.971 0.602
## 0.920 0.869 0.676
## 0.760 0.714 0.625
##
## 0.213 0.209 0.222
## 0.286 0.288 0.325
## 0.288 0.291 0.330
## 0.213 0.209 0.235
## 0.146 0.133 0.152
## -0.003 -0.026 -0.031
## 0.291 0.292 0.310
## 0.165 0.159 0.190
## 0.336 0.340 0.312
## 0.261 0.263 0.305
## 0.292 0.294 0.343
## 0.224 0.220 0.236
## 0.098 0.085 0.096
## 0.208 0.206 0.213
##
## 0.187 0.096 0.102
## 0.097 0.032 0.032
## 0.028 -0.003 -0.005
## 0.129 0.056 0.064
## 0.282 0.156 0.163
## 0.537 0.319 0.518
##
## 0.381 0.236 0.360
## 0.565 0.377 0.384
## 0.529 0.351 0.456
## 0.527 0.354 0.330
## 0.370 0.236 0.207
##
## 0.899 0.754 0.804
## 0.809 0.677 0.763
## 0.709 0.593 0.672
## 0.843 0.705 0.790
## 0.697 0.580 0.582
## 0.549 0.444 0.657
## 0.631 0.522 0.594
## 0.370 0.292 0.345
## 0.418 0.326 0.340
## 0.421 0.343 0.557
## 0.759 0.636 0.675
## 0.604 0.500 0.597
## 0.823 0.689 0.632
## 0.601 0.499 0.578
## 0.601 0.499 0.582
## 0.714 0.595 0.638
## 0.683 0.570 0.640
## 0.632 0.524 0.547
## 0.725 0.607 0.623
## 0.797 0.667 0.698
## 0.818 0.682 0.627
## 0.645 0.533 0.491
## 0.511 0.422 0.549
## 0.963 0.811 0.839
## 0.465 0.376 0.572
## 0.462 0.376 0.384
## 0.404 0.328 0.426
## 0.747 0.623 0.581
## 0.579 0.479 0.639
## 0.581 0.482 0.689
## 0.710 0.589 0.519
## 0.650 0.525 0.326
## 0.190 0.134 0.104
## 0.311 0.240 0.210
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.143) -1.192 0.029 -41.299 0.000 -1.249
## .Stst19d (.144) -1.055 0.024 -44.527 0.000 -1.101
## .Stst20s (.145) -0.859 0.023 -36.887 0.000 -0.904
## .Stst21c (.146) -1.196 0.024 -49.433 0.000 -1.243
## .Stst22p (.147) -1.265 0.027 -47.334 0.000 -1.317
## .Stst23n (.148) -1.096 0.029 -37.313 0.000 -1.154
## .Stst24x (.149) -0.996 0.027 -37.249 0.000 -1.049
## .Stst25w (.150) -0.905 0.018 -50.690 0.000 -0.940
## .Stst26r (.151) -1.343 0.030 -44.529 0.000 -1.402
## .Stst31b (.152) -1.101 0.027 -41.218 0.000 -1.154
## .Stst34r (.153) -1.239 0.029 -43.207 0.000 -1.295
## .Stst5mt (.154) -0.805 0.024 -33.439 0.000 -0.853
## .Stst32r (.155) -1.068 0.020 -53.204 0.000 -1.107
## .Stst33h (.156) -0.912 0.019 -48.393 0.000 -0.949
## .Stst35t (.157) -0.668 0.038 -17.401 0.000 -0.743
## .Stst36c (.158) -0.045 0.026 -1.775 0.076 -0.095
## .Stst37b (.159) -0.323 0.025 -12.886 0.000 -0.372
## .Stst2lt (.160) -1.085 0.026 -41.363 0.000 -1.137
## .Stst3ms (.161) -0.953 0.023 -41.299 0.000 -0.998
## .Stst4sc (.162) -1.141 0.031 -36.485 0.000 -1.202
## .Stst7bl (.163) -0.632 0.024 -26.392 0.000 -0.679
## .Stst8rn (.164) -0.618 0.030 -20.671 0.000 -0.677
## .Stst11r (.165) -1.113 0.026 -42.193 0.000 -1.165
## .Stst12l (.166) -0.821 0.024 -34.572 0.000 -0.868
## .Stst13h (.167) -1.200 0.027 -45.081 0.000 -1.252
## .Stst14b (.168) -0.725 0.020 -35.860 0.000 -0.764
## .Stst15t (.169) -1.057 0.020 -51.765 0.000 -1.097
## .Stst16m (.170) -0.927 0.027 -34.490 0.000 -0.980
## .Stst6ph (.171) -0.715 0.029 -25.022 0.000 -0.771
## .Stst9lc (.172) -0.701 0.030 -23.523 0.000 -0.760
## .Stst10m (.173) -0.692 0.023 -29.818 0.000 -0.737
## .Stst28m (.174) -0.887 0.023 -37.992 0.000 -0.933
## .Sts292D (.175) -0.506 0.022 -23.314 0.000 -0.549
## .Sts303D (.176) -0.650 0.019 -33.867 0.000 -0.687
## english 2.132 0.141 15.077 0.000 1.855
## math 1.053 0.152 6.924 0.000 0.755
## speed 0.519 0.044 11.830 0.000 0.433
## info 2.225 0.181 12.262 0.000 1.869
## science -0.876 0.064 -13.586 0.000 -1.002
## spatial -0.258 0.084 -3.088 0.002 -0.423
## g -0.675 0.083 -8.125 0.000 -0.838
## ci.upper Std.lv Std.all
## -1.136 -1.192 -1.270
## -1.008 -1.055 -1.184
## -0.813 -0.859 -0.897
## -1.148 -1.196 -1.227
## -1.212 -1.265 -1.323
## -1.039 -1.096 -1.007
## -0.944 -0.996 -0.918
## -0.870 -0.905 -1.179
## -1.284 -1.343 -1.390
## -1.049 -1.101 -1.028
## -1.182 -1.239 -1.092
## -0.758 -0.805 -0.809
## -1.029 -1.068 -1.423
## -0.875 -0.912 -1.304
## -0.593 -0.668 -0.414
## 0.005 -0.045 -0.035
## -0.274 -0.323 -0.283
## -1.034 -1.085 -1.222
## -0.908 -0.953 -1.080
## -1.079 -1.141 -1.279
## -0.585 -0.632 -0.720
## -0.559 -0.618 -0.730
## -1.061 -1.113 -1.183
## -0.775 -0.821 -0.981
## -1.148 -1.200 -1.100
## -0.685 -0.725 -0.839
## -1.017 -1.057 -1.233
## -0.874 -0.927 -0.994
## -0.659 -0.715 -1.058
## -0.643 -0.701 -0.731
## -0.646 -0.692 -1.121
## -0.842 -0.887 -1.350
## -0.464 -0.506 -0.516
## -0.612 -0.650 -0.845
## 2.410 2.159 2.159
## 1.351 1.236 1.236
## 0.605 0.521 0.521
## 2.581 2.010 2.010
## -0.749 -1.292 -1.292
## -0.094 -0.358 -0.358
## -0.512 -0.776 -0.776
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.255 0.008 33.996 0.000 0.241
## .Stst19dsgsdwrd 0.397 0.011 36.271 0.000 0.376
## .Stest20spellng 0.504 0.014 35.845 0.000 0.477
## .Stest21cptlztn 0.457 0.013 34.248 0.000 0.431
## .Stest22puncttn 0.312 0.011 29.591 0.000 0.292
## .Stest23english 0.553 0.017 32.456 0.000 0.520
## .Stest24exprssn 0.787 0.021 36.888 0.000 0.745
## .Stst25wrdfnctn 0.370 0.010 35.491 0.000 0.349
## .Stst26rdngcmpr 0.211 0.007 29.495 0.000 0.197
## .Stst31bstrctrs 0.592 0.017 33.872 0.000 0.558
## .Stst34rthcmptt 0.700 0.026 26.545 0.000 0.648
## .Stest5math 0.597 0.018 34.073 0.000 0.562
## .Stst32rthrsnng 0.293 0.008 34.621 0.000 0.277
## .Stst33hghschlm 0.177 0.009 20.046 0.000 0.160
## .Stest35tblrdng 1.381 0.058 23.932 0.000 1.268
## .Stst36clrclchc 0.878 0.032 27.799 0.000 0.816
## .Stst37bjctnspc 0.682 0.026 25.842 0.000 0.630
## .Stest2literatr 0.247 0.007 35.665 0.000 0.233
## .Stest3music 0.342 0.009 37.380 0.000 0.324
## .Stest4soclstds 0.255 0.007 35.583 0.000 0.241
## .Stst7blgclscnc 0.477 0.012 38.732 0.000 0.453
## .Stest8aerontcs 0.630 0.011 56.907 0.000 0.609
## .Stest11art 0.396 0.011 36.889 0.000 0.375
## .Stest12law 0.426 0.010 40.662 0.000 0.405
## .Stest13health 0.599 0.015 40.475 0.000 0.570
## .Stest14bible 0.427 0.012 34.305 0.000 0.403
## .Stest15theater 0.399 0.010 38.073 0.000 0.379
## .Stest16mscllns 0.467 0.012 38.218 0.000 0.443
## .Stst6physclscn 0.260 0.008 33.829 0.000 0.245
## .Stest9elctrncs 0.789 0.019 40.676 0.000 0.751
## .Stest10mechncs 0.160 0.017 9.186 0.000 0.126
## .Stst28mchnclrs 0.235 0.008 30.588 0.000 0.220
## .Stst29vslztn2D 0.678 0.020 33.212 0.000 0.638
## .Stst30vslztn3D 0.361 0.014 25.810 0.000 0.333
## english 0.975 0.079 12.391 0.000 0.821
## math 0.725 0.085 8.487 0.000 0.558
## speed 0.992 0.059 16.723 0.000 0.876
## info 1.225 0.124 9.905 0.000 0.982
## science 0.459 0.071 6.484 0.000 0.321
## spatial 0.522 0.046 11.428 0.000 0.433
## g 0.756 0.033 22.858 0.000 0.691
## ci.upper Std.lv Std.all
## 0.270 0.255 0.290
## 0.419 0.397 0.501
## 0.532 0.504 0.550
## 0.483 0.457 0.481
## 0.333 0.312 0.342
## 0.586 0.553 0.467
## 0.829 0.787 0.668
## 0.390 0.370 0.627
## 0.225 0.211 0.226
## 0.626 0.592 0.516
## 0.752 0.700 0.544
## 0.631 0.597 0.601
## 0.310 0.293 0.521
## 0.195 0.177 0.363
## 1.494 1.381 0.531
## 0.940 0.878 0.532
## 0.734 0.682 0.523
## 0.260 0.247 0.313
## 0.360 0.342 0.440
## 0.269 0.255 0.320
## 0.502 0.477 0.620
## 0.652 0.630 0.880
## 0.417 0.396 0.447
## 0.446 0.426 0.608
## 0.628 0.599 0.503
## 0.452 0.427 0.573
## 0.420 0.399 0.543
## 0.491 0.467 0.537
## 0.275 0.260 0.569
## 0.827 0.789 0.858
## 0.195 0.160 0.422
## 0.250 0.235 0.544
## 0.718 0.678 0.705
## 0.388 0.361 0.610
## 1.130 1.000 1.000
## 0.893 1.000 1.000
## 1.108 1.000 1.000
## 1.467 1.000 1.000
## 0.598 1.000 1.000
## 0.612 1.000 1.000
## 0.821 1.000 1.000
lavTestScore(scalar, release = 75:108) # X2 test for released constraints among the 34 intercepts
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 1003.94 34 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p143. == .p326. 8.260 1 0.004
## 2 .p144. == .p327. 93.657 1 0.000
## 3 .p145. == .p328. 14.567 1 0.000
## 4 .p146. == .p329. 2.708 1 0.100
## 5 .p147. == .p330. 0.085 1 0.770
## 6 .p148. == .p331. 1.086 1 0.297
## 7 .p149. == .p332. 0.000 1 0.994
## 8 .p150. == .p333. 5.550 1 0.018
## 9 .p151. == .p334. 1.296 1 0.255
## 10 .p152. == .p335. 0.937 1 0.333
## 11 .p153. == .p336. 102.774 1 0.000
## 12 .p154. == .p337. 47.071 1 0.000
## 13 .p155. == .p338. 6.101 1 0.014
## 14 .p156. == .p339. 10.719 1 0.001
## 15 .p157. == .p340. 29.060 1 0.000
## 16 .p158. == .p341. 0.316 1 0.574
## 17 .p159. == .p342. 0.861 1 0.354
## 18 .p160. == .p343. 1.604 1 0.205
## 19 .p161. == .p344. 0.783 1 0.376
## 20 .p162. == .p345. 5.506 1 0.019
## 21 .p163. == .p346. 9.282 1 0.002
## 22 .p164. == .p347. 134.134 1 0.000
## 23 .p165. == .p348. 73.501 1 0.000
## 24 .p166. == .p349. 6.453 1 0.011
## 25 .p167. == .p350. 65.808 1 0.000
## 26 .p168. == .p351. 30.752 1 0.000
## 27 .p169. == .p352. 0.441 1 0.507
## 28 .p170. == .p353. 0.728 1 0.393
## 29 .p171. == .p354. 175.602 1 0.000
## 30 .p172. == .p355. 0.249 1 0.618
## 31 .p173. == .p356. 28.684 1 0.000
## 32 .p174. == .p357. 329.484 1 0.000
## 33 .p175. == .p358. 6.681 1 0.010
## 34 .p176. == .p359. 129.732 1 0.000
scalar2<-cfa(chc.bifactor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("g=~Stest8aeronautics", "g=~Stest28mechanicalreasoning", "g=~Stest10mechanics", "g=~Stest9electronics", "g=~Stest6physicalscience", "g=~Stest4socialstudies", "Stest28mechanicalreasoning~1", "Stest8aeronautics~1", "Stest19disguisedwords~1", "Stest13health~1"))
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 5801.985 1052.000 0.000 0.957 0.039 0.042
## aic bic
## 462634.389 464017.386
Mc(scalar2)
## [1] 0.6768085
summary(scalar2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 123 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 310
## Number of equality constraints 104
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 5801.985 5178.899
## Degrees of freedom 1052 1052
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.120
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 2669.172 2382.524
## 1 3132.813 2796.374
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.076 0.010 7.645 0.000 0.056
## Stst19d (.p2.) 0.258 0.015 17.200 0.000 0.229
## Stst20s (.p3.) 0.375 0.015 25.715 0.000 0.346
## Stst21c (.p4.) 0.339 0.013 26.953 0.000 0.314
## Stst22p (.p5.) 0.381 0.014 27.336 0.000 0.353
## Stst23n (.p6.) 0.396 0.016 24.544 0.000 0.365
## Stst24x (.p7.) 0.315 0.015 20.422 0.000 0.285
## Stst25w (.p8.) 0.122 0.010 11.725 0.000 0.102
## Stst26r (.p9.) 0.150 0.009 17.555 0.000 0.133
## Stst31b (.10.) 0.165 0.012 13.619 0.000 0.141
## Stst34r (.11.) 0.153 0.014 11.120 0.000 0.126
## math =~
## Stst5mt (.12.) 0.243 0.021 11.524 0.000 0.201
## Stst25w (.13.) 0.194 0.018 10.482 0.000 0.158
## Stst32r (.14.) 0.207 0.017 11.900 0.000 0.173
## Stst33h (.15.) 0.358 0.025 14.333 0.000 0.309
## Stst34r (.16.) 0.189 0.023 8.151 0.000 0.143
## speed =~
## Stst19d (.17.) 0.198 0.011 18.174 0.000 0.176
## Stst34r (.18.) 0.444 0.020 22.237 0.000 0.405
## Stst35t (.19.) 0.957 0.030 31.431 0.000 0.898
## Stst36c (.20.) 0.882 0.024 36.967 0.000 0.835
## Stst37b (.21.) 0.710 0.022 32.555 0.000 0.667
## info =~
## Stst1vc (.22.) 0.204 0.013 15.774 0.000 0.179
## Stst2lt (.23.) 0.280 0.014 19.899 0.000 0.252
## Stst3ms (.24.) 0.290 0.014 21.423 0.000 0.264
## Stst4sc (.25.) 0.169 0.014 12.513 0.000 0.143
## Stst7bl (.26.) 0.095 0.016 5.879 0.000 0.063
## Stst8rn (.27.) 0.127 0.017 7.369 0.000 0.094
## Stst11r (.28.) 0.307 0.015 19.909 0.000 0.277
## Stst12l (.29.) 0.145 0.012 11.744 0.000 0.121
## Stst13h (.30.) 0.221 0.018 12.510 0.000 0.187
## Stst14b (.31.) 0.236 0.014 16.644 0.000 0.208
## Stst15t (.32.) 0.313 0.014 21.706 0.000 0.284
## Stst16m (.33.) 0.201 0.015 13.817 0.000 0.173
## Stst19d (.34.) 0.175 0.015 11.656 0.000 0.145
## Stst26r (.35.) 0.194 0.011 17.472 0.000 0.172
## science =~
## Stst1vc (.36.) 0.164 0.019 8.744 0.000 0.127
## Stst5mt (.37.) 0.044 0.018 2.392 0.017 0.008
## Stst6ph (.38.) 0.060 0.015 3.962 0.000 0.030
## Stst7bl (.39.) 0.080 0.018 4.321 0.000 0.044
## Stst9lc (.40.) 0.276 0.020 13.573 0.000 0.236
## Stst10m (.41.) 0.431 0.021 20.427 0.000 0.389
## spatial =~
## Stst28m (.42.) 0.301 0.018 17.012 0.000 0.266
## Sts292D (.43.) 0.535 0.022 23.834 0.000 0.491
## Sts303D (.44.) 0.503 0.020 25.423 0.000 0.464
## Stst31b (.45.) 0.482 0.019 25.172 0.000 0.444
## Stst37b (.46.) 0.322 0.022 14.905 0.000 0.279
## g =~
## Stst1vc (.47.) 0.863 0.016 53.635 0.000 0.832
## Stst2lt (.48.) 0.775 0.015 51.623 0.000 0.745
## Stst3ms (.49.) 0.674 0.014 47.926 0.000 0.646
## Stst4sc 0.955 0.016 58.661 0.000 0.923
## Stst5mt (.51.) 0.678 0.016 42.613 0.000 0.647
## Stst6ph 0.713 0.017 42.326 0.000 0.680
## Stst7bl (.53.) 0.610 0.016 38.092 0.000 0.579
## Stst8rn 0.598 0.020 30.233 0.000 0.559
## Stst9lc 0.690 0.021 32.372 0.000 0.648
## Stst10m 0.606 0.017 34.786 0.000 0.572
## Stst11r (.57.) 0.719 0.014 50.294 0.000 0.691
## Stst12l (.58.) 0.577 0.015 38.205 0.000 0.548
## Stst13h (.59.) 0.824 0.016 51.579 0.000 0.793
## Stst14b (.60.) 0.572 0.014 40.915 0.000 0.545
## Stst15t (.61.) 0.559 0.014 40.868 0.000 0.532
## Stst16m (.62.) 0.685 0.015 44.764 0.000 0.655
## Stst19d (.63.) 0.620 0.014 43.167 0.000 0.591
## Stst20s (.64.) 0.608 0.015 41.064 0.000 0.579
## Stst21c (.65.) 0.707 0.014 51.335 0.000 0.680
## Stst22p (.66.) 0.777 0.015 51.378 0.000 0.747
## Stst23n (.67.) 0.794 0.017 46.240 0.000 0.761
## Stst24x (.68.) 0.621 0.017 37.474 0.000 0.589
## Stst25w (.69.) 0.484 0.013 37.065 0.000 0.459
## Stst26r (.70.) 0.935 0.016 60.299 0.000 0.905
## Stst28m 0.571 0.018 31.914 0.000 0.536
## Sts292D (.72.) 0.454 0.015 29.527 0.000 0.424
## Sts303D (.73.) 0.404 0.014 29.071 0.000 0.377
## Stst31b (.74.) 0.735 0.016 46.360 0.000 0.704
## Stst32r (.75.) 0.560 0.014 39.825 0.000 0.533
## Stst33h (.76.) 0.557 0.014 40.460 0.000 0.530
## Stst34r (.77.) 0.679 0.017 39.913 0.000 0.646
## Stst35t (.78.) 0.631 0.023 27.333 0.000 0.585
## Stst36c (.79.) 0.144 0.019 7.758 0.000 0.107
## Stst37b (.80.) 0.281 0.018 15.907 0.000 0.246
## ci.upper Std.lv Std.all
##
## 0.095 0.076 0.073
## 0.288 0.258 0.278
## 0.404 0.375 0.369
## 0.364 0.339 0.340
## 0.408 0.381 0.364
## 0.428 0.396 0.332
## 0.346 0.315 0.273
## 0.143 0.122 0.150
## 0.167 0.150 0.139
## 0.189 0.165 0.142
## 0.180 0.153 0.132
##
## 0.284 0.243 0.236
## 0.230 0.194 0.237
## 0.241 0.207 0.252
## 0.407 0.358 0.458
## 0.234 0.189 0.163
##
## 0.219 0.198 0.212
## 0.483 0.444 0.382
## 1.017 0.957 0.566
## 0.928 0.882 0.684
## 0.753 0.710 0.577
##
## 0.229 0.204 0.197
## 0.307 0.280 0.289
## 0.317 0.290 0.311
## 0.195 0.169 0.152
## 0.126 0.095 0.102
## 0.161 0.127 0.125
## 0.337 0.307 0.313
## 0.169 0.145 0.160
## 0.256 0.221 0.198
## 0.264 0.236 0.268
## 0.341 0.313 0.369
## 0.230 0.201 0.198
## 0.204 0.175 0.188
## 0.216 0.194 0.180
##
## 0.200 0.164 0.158
## 0.080 0.044 0.043
## 0.090 0.060 0.068
## 0.116 0.080 0.086
## 0.316 0.276 0.250
## 0.472 0.431 0.485
##
## 0.335 0.301 0.341
## 0.579 0.535 0.486
## 0.542 0.503 0.542
## 0.519 0.482 0.413
## 0.364 0.322 0.261
##
## 0.895 0.863 0.833
## 0.804 0.775 0.800
## 0.701 0.674 0.723
## 0.987 0.955 0.860
## 0.710 0.678 0.659
## 0.746 0.713 0.803
## 0.642 0.610 0.659
## 0.637 0.598 0.589
## 0.732 0.690 0.625
## 0.640 0.606 0.683
## 0.747 0.719 0.733
## 0.607 0.577 0.637
## 0.855 0.824 0.737
## 0.600 0.572 0.649
## 0.586 0.559 0.661
## 0.715 0.685 0.675
## 0.648 0.620 0.666
## 0.637 0.608 0.599
## 0.734 0.707 0.709
## 0.806 0.777 0.742
## 0.828 0.794 0.665
## 0.654 0.621 0.537
## 0.510 0.484 0.592
## 0.966 0.935 0.868
## 0.606 0.571 0.647
## 0.484 0.454 0.412
## 0.431 0.404 0.435
## 0.766 0.735 0.631
## 0.588 0.560 0.682
## 0.583 0.557 0.712
## 0.713 0.679 0.585
## 0.676 0.631 0.373
## 0.180 0.144 0.111
## 0.316 0.281 0.228
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.143) -1.153 0.023 -49.991 0.000 -1.198
## .Stst19d -0.996 0.019 -53.392 0.000 -1.033
## .Stst20s (.145) -0.830 0.021 -40.343 0.000 -0.871
## .Stst21c (.146) -1.167 0.020 -59.399 0.000 -1.206
## .Stst22p (.147) -1.232 0.021 -57.957 0.000 -1.274
## .Stst23n (.148) -1.066 0.025 -42.863 0.000 -1.115
## .Stst24x (.149) -0.967 0.023 -41.652 0.000 -1.012
## .Stst25w (.150) -0.879 0.016 -56.067 0.000 -0.910
## .Stst26r (.151) -1.310 0.023 -57.021 0.000 -1.355
## .Stst31b (.152) -1.086 0.024 -45.618 0.000 -1.132
## .Stst34r (.153) -1.211 0.023 -52.269 0.000 -1.257
## .Stst5mt (.154) -0.774 0.021 -36.938 0.000 -0.816
## .Stst32r (.155) -1.051 0.017 -62.004 0.000 -1.084
## .Stst33h (.156) -0.882 0.016 -54.307 0.000 -0.913
## .Stst35t (.157) -0.681 0.033 -20.677 0.000 -0.746
## .Stst36c (.158) -0.021 0.026 -0.815 0.415 -0.072
## .Stst37b (.159) -0.315 0.024 -13.040 0.000 -0.363
## .Stst2lt (.160) -1.049 0.020 -51.640 0.000 -1.089
## .Stst3ms (.161) -0.909 0.019 -48.304 0.000 -0.946
## .Stst4sc (.162) -1.114 0.024 -46.696 0.000 -1.161
## .Stst7bl (.163) -0.602 0.020 -29.428 0.000 -0.642
## .Stst8rn -0.522 0.022 -23.618 0.000 -0.565
## .Stst11r (.165) -1.088 0.020 -55.070 0.000 -1.127
## .Stst12l (.166) -0.812 0.019 -42.735 0.000 -0.849
## .Stst13h -1.206 0.024 -50.923 0.000 -1.252
## .Stst14b (.168) -0.660 0.019 -35.394 0.000 -0.697
## .Stst15t (.169) -1.016 0.017 -59.930 0.000 -1.049
## .Stst16m (.170) -0.900 0.022 -41.863 0.000 -0.943
## .Stst6ph (.171) -0.723 0.020 -36.714 0.000 -0.762
## .Stst9lc (.172) -0.664 0.024 -28.080 0.000 -0.710
## .Stst10m (.173) -0.671 0.020 -32.947 0.000 -0.711
## .Stst28m -0.719 0.020 -36.669 0.000 -0.757
## .Sts292D (.175) -0.555 0.021 -26.358 0.000 -0.596
## .Sts303D (.176) -0.693 0.018 -37.632 0.000 -0.729
## ci.upper Std.lv Std.all
## -1.108 -1.153 -1.112
## -0.960 -0.996 -1.070
## -0.790 -0.830 -0.818
## -1.129 -1.167 -1.170
## -1.190 -1.232 -1.177
## -1.017 -1.066 -0.893
## -0.921 -0.967 -0.835
## -0.848 -0.879 -1.074
## -1.265 -1.310 -1.216
## -1.039 -1.086 -0.932
## -1.166 -1.211 -1.043
## -0.733 -0.774 -0.753
## -1.018 -1.051 -1.278
## -0.850 -0.882 -1.129
## -0.617 -0.681 -0.403
## 0.030 -0.021 -0.016
## -0.268 -0.315 -0.256
## -1.009 -1.049 -1.083
## -0.872 -0.909 -0.976
## -1.068 -1.114 -1.003
## -0.562 -0.602 -0.650
## -0.479 -0.522 -0.514
## -1.049 -1.088 -1.110
## -0.775 -0.812 -0.896
## -1.159 -1.206 -1.079
## -0.623 -0.660 -0.749
## -0.983 -1.016 -1.200
## -0.858 -0.900 -0.887
## -0.685 -0.723 -0.815
## -0.617 -0.664 -0.601
## -0.631 -0.671 -0.755
## -0.681 -0.719 -0.814
## -0.514 -0.555 -0.504
## -0.657 -0.693 -0.747
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.255 0.009 27.418 0.000 0.237
## .Stst19dsgsdwrd 0.346 0.014 25.346 0.000 0.319
## .Stest20spellng 0.519 0.017 29.939 0.000 0.485
## .Stest21cptlztn 0.380 0.016 24.494 0.000 0.350
## .Stest22puncttn 0.348 0.012 28.194 0.000 0.324
## .Stest23english 0.638 0.024 26.938 0.000 0.591
## .Stest24exprssn 0.854 0.025 33.662 0.000 0.804
## .Stst25wrdfnctn 0.383 0.012 31.271 0.000 0.359
## .Stst26rdngcmpr 0.226 0.009 25.586 0.000 0.209
## .Stst31bstrctrs 0.559 0.022 25.335 0.000 0.516
## .Stst34rthcmptt 0.632 0.031 20.564 0.000 0.572
## .Stest5math 0.538 0.020 26.501 0.000 0.498
## .Stst32rthrsnng 0.319 0.011 27.969 0.000 0.297
## .Stst33hghschlm 0.172 0.015 11.163 0.000 0.142
## .Stest35tblrdng 1.542 0.068 22.569 0.000 1.408
## .Stst36clrclchc 0.866 0.041 21.161 0.000 0.786
## .Stst37bjctnspc 0.830 0.034 24.483 0.000 0.763
## .Stest2literatr 0.259 0.009 29.235 0.000 0.242
## .Stest3music 0.331 0.012 27.448 0.000 0.307
## .Stest4soclstds 0.293 0.011 27.600 0.000 0.272
## .Stst7blgclscnc 0.471 0.014 33.552 0.000 0.443
## .Stest8aerontcs 0.657 0.018 37.359 0.000 0.622
## .Stest11art 0.350 0.012 28.330 0.000 0.326
## .Stest12law 0.466 0.014 33.296 0.000 0.439
## .Stest13health 0.522 0.016 31.999 0.000 0.490
## .Stest14bible 0.394 0.014 28.329 0.000 0.367
## .Stest15theater 0.306 0.011 27.289 0.000 0.284
## .Stest16mscllns 0.520 0.017 31.198 0.000 0.487
## .Stst6physclscn 0.276 0.010 27.459 0.000 0.256
## .Stest9elctrncs 0.665 0.029 23.145 0.000 0.609
## .Stest10mechncs 0.236 0.020 11.791 0.000 0.197
## .Stst28mchnclrs 0.363 0.015 24.560 0.000 0.334
## .Stst29vslztn2D 0.722 0.028 26.050 0.000 0.667
## .Stst30vslztn3D 0.446 0.019 23.361 0.000 0.408
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.274 0.255 0.237
## 0.373 0.346 0.399
## 0.553 0.519 0.504
## 0.410 0.380 0.382
## 0.372 0.348 0.318
## 0.684 0.638 0.447
## 0.903 0.854 0.637
## 0.407 0.383 0.571
## 0.244 0.226 0.195
## 0.602 0.559 0.412
## 0.692 0.632 0.468
## 0.578 0.538 0.508
## 0.341 0.319 0.472
## 0.203 0.172 0.283
## 1.676 1.542 0.540
## 0.946 0.866 0.520
## 0.896 0.830 0.547
## 0.276 0.259 0.276
## 0.355 0.331 0.381
## 0.314 0.293 0.237
## 0.498 0.471 0.548
## 0.691 0.657 0.637
## 0.374 0.350 0.364
## 0.494 0.466 0.568
## 0.554 0.522 0.418
## 0.421 0.394 0.507
## 0.328 0.306 0.427
## 0.553 0.520 0.505
## 0.296 0.276 0.350
## 0.722 0.665 0.546
## 0.275 0.236 0.299
## 0.392 0.363 0.465
## 0.776 0.722 0.594
## 0.483 0.446 0.517
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.076 0.010 7.645 0.000 0.056
## Stst19d (.p2.) 0.258 0.015 17.200 0.000 0.229
## Stst20s (.p3.) 0.375 0.015 25.715 0.000 0.346
## Stst21c (.p4.) 0.339 0.013 26.953 0.000 0.314
## Stst22p (.p5.) 0.381 0.014 27.336 0.000 0.353
## Stst23n (.p6.) 0.396 0.016 24.544 0.000 0.365
## Stst24x (.p7.) 0.315 0.015 20.422 0.000 0.285
## Stst25w (.p8.) 0.122 0.010 11.725 0.000 0.102
## Stst26r (.p9.) 0.150 0.009 17.555 0.000 0.133
## Stst31b (.10.) 0.165 0.012 13.619 0.000 0.141
## Stst34r (.11.) 0.153 0.014 11.120 0.000 0.126
## math =~
## Stst5mt (.12.) 0.243 0.021 11.524 0.000 0.201
## Stst25w (.13.) 0.194 0.018 10.482 0.000 0.158
## Stst32r (.14.) 0.207 0.017 11.900 0.000 0.173
## Stst33h (.15.) 0.358 0.025 14.333 0.000 0.309
## Stst34r (.16.) 0.189 0.023 8.151 0.000 0.143
## speed =~
## Stst19d (.17.) 0.198 0.011 18.174 0.000 0.176
## Stst34r (.18.) 0.444 0.020 22.237 0.000 0.405
## Stst35t (.19.) 0.957 0.030 31.431 0.000 0.898
## Stst36c (.20.) 0.882 0.024 36.967 0.000 0.835
## Stst37b (.21.) 0.710 0.022 32.555 0.000 0.667
## info =~
## Stst1vc (.22.) 0.204 0.013 15.774 0.000 0.179
## Stst2lt (.23.) 0.280 0.014 19.899 0.000 0.252
## Stst3ms (.24.) 0.290 0.014 21.423 0.000 0.264
## Stst4sc (.25.) 0.169 0.014 12.513 0.000 0.143
## Stst7bl (.26.) 0.095 0.016 5.879 0.000 0.063
## Stst8rn (.27.) 0.127 0.017 7.369 0.000 0.094
## Stst11r (.28.) 0.307 0.015 19.909 0.000 0.277
## Stst12l (.29.) 0.145 0.012 11.744 0.000 0.121
## Stst13h (.30.) 0.221 0.018 12.510 0.000 0.187
## Stst14b (.31.) 0.236 0.014 16.644 0.000 0.208
## Stst15t (.32.) 0.313 0.014 21.706 0.000 0.284
## Stst16m (.33.) 0.201 0.015 13.817 0.000 0.173
## Stst19d (.34.) 0.175 0.015 11.656 0.000 0.145
## Stst26r (.35.) 0.194 0.011 17.472 0.000 0.172
## science =~
## Stst1vc (.36.) 0.164 0.019 8.744 0.000 0.127
## Stst5mt (.37.) 0.044 0.018 2.392 0.017 0.008
## Stst6ph (.38.) 0.060 0.015 3.962 0.000 0.030
## Stst7bl (.39.) 0.080 0.018 4.321 0.000 0.044
## Stst9lc (.40.) 0.276 0.020 13.573 0.000 0.236
## Stst10m (.41.) 0.431 0.021 20.427 0.000 0.389
## spatial =~
## Stst28m (.42.) 0.301 0.018 17.012 0.000 0.266
## Sts292D (.43.) 0.535 0.022 23.834 0.000 0.491
## Sts303D (.44.) 0.503 0.020 25.423 0.000 0.464
## Stst31b (.45.) 0.482 0.019 25.172 0.000 0.444
## Stst37b (.46.) 0.322 0.022 14.905 0.000 0.279
## g =~
## Stst1vc (.47.) 0.863 0.016 53.635 0.000 0.832
## Stst2lt (.48.) 0.775 0.015 51.623 0.000 0.745
## Stst3ms (.49.) 0.674 0.014 47.926 0.000 0.646
## Stst4sc 0.826 0.018 47.152 0.000 0.792
## Stst5mt (.51.) 0.678 0.016 42.613 0.000 0.647
## Stst6ph 0.543 0.016 34.453 0.000 0.512
## Stst7bl (.53.) 0.610 0.016 38.092 0.000 0.579
## Stst8rn 0.256 0.019 13.551 0.000 0.219
## Stst9lc 0.371 0.021 17.580 0.000 0.330
## Stst10m 0.393 0.013 29.327 0.000 0.367
## Stst11r (.57.) 0.719 0.014 50.294 0.000 0.691
## Stst12l (.58.) 0.577 0.015 38.205 0.000 0.548
## Stst13h (.59.) 0.824 0.016 51.579 0.000 0.793
## Stst14b (.60.) 0.572 0.014 40.915 0.000 0.545
## Stst15t (.61.) 0.559 0.014 40.868 0.000 0.532
## Stst16m (.62.) 0.685 0.015 44.764 0.000 0.655
## Stst19d (.63.) 0.620 0.014 43.167 0.000 0.591
## Stst20s (.64.) 0.608 0.015 41.064 0.000 0.579
## Stst21c (.65.) 0.707 0.014 51.335 0.000 0.680
## Stst22p (.66.) 0.777 0.015 51.378 0.000 0.747
## Stst23n (.67.) 0.794 0.017 46.240 0.000 0.761
## Stst24x (.68.) 0.621 0.017 37.474 0.000 0.589
## Stst25w (.69.) 0.484 0.013 37.065 0.000 0.459
## Stst26r (.70.) 0.935 0.016 60.299 0.000 0.905
## Stst28m 0.371 0.014 27.307 0.000 0.345
## Sts292D (.72.) 0.454 0.015 29.527 0.000 0.424
## Sts303D (.73.) 0.404 0.014 29.071 0.000 0.377
## Stst31b (.74.) 0.735 0.016 46.360 0.000 0.704
## Stst32r (.75.) 0.560 0.014 39.825 0.000 0.533
## Stst33h (.76.) 0.557 0.014 40.460 0.000 0.530
## Stst34r (.77.) 0.679 0.017 39.913 0.000 0.646
## Stst35t (.78.) 0.631 0.023 27.333 0.000 0.585
## Stst36c (.79.) 0.144 0.019 7.758 0.000 0.107
## Stst37b (.80.) 0.281 0.018 15.907 0.000 0.246
## ci.upper Std.lv Std.all
##
## 0.095 0.076 0.081
## 0.288 0.258 0.289
## 0.404 0.374 0.391
## 0.364 0.339 0.348
## 0.408 0.380 0.399
## 0.428 0.396 0.364
## 0.346 0.315 0.290
## 0.143 0.122 0.159
## 0.167 0.150 0.155
## 0.189 0.165 0.154
## 0.180 0.153 0.135
##
## 0.284 0.208 0.209
## 0.230 0.166 0.217
## 0.241 0.178 0.237
## 0.407 0.307 0.440
## 0.234 0.162 0.143
##
## 0.219 0.198 0.221
## 0.483 0.444 0.392
## 1.017 0.958 0.594
## 0.928 0.882 0.685
## 0.753 0.710 0.622
##
## 0.229 0.226 0.241
## 0.307 0.310 0.350
## 0.317 0.321 0.364
## 0.195 0.187 0.210
## 0.126 0.105 0.120
## 0.161 0.141 0.170
## 0.337 0.340 0.362
## 0.169 0.161 0.192
## 0.256 0.245 0.227
## 0.264 0.261 0.303
## 0.341 0.346 0.402
## 0.230 0.223 0.240
## 0.204 0.194 0.217
## 0.216 0.215 0.223
##
## 0.200 0.114 0.122
## 0.080 0.031 0.031
## 0.090 0.042 0.061
## 0.116 0.056 0.064
## 0.316 0.193 0.201
## 0.472 0.301 0.486
##
## 0.335 0.221 0.355
## 0.579 0.393 0.398
## 0.542 0.370 0.475
## 0.519 0.354 0.330
## 0.364 0.236 0.207
##
## 0.895 0.744 0.795
## 0.804 0.668 0.753
## 0.701 0.581 0.658
## 0.860 0.712 0.798
## 0.710 0.585 0.588
## 0.574 0.468 0.679
## 0.642 0.526 0.601
## 0.293 0.220 0.265
## 0.412 0.320 0.334
## 0.420 0.339 0.548
## 0.747 0.619 0.659
## 0.607 0.497 0.595
## 0.855 0.710 0.657
## 0.600 0.493 0.571
## 0.586 0.482 0.560
## 0.715 0.591 0.634
## 0.648 0.534 0.598
## 0.637 0.524 0.548
## 0.734 0.609 0.626
## 0.806 0.670 0.703
## 0.828 0.685 0.630
## 0.654 0.535 0.494
## 0.510 0.417 0.544
## 0.966 0.806 0.836
## 0.398 0.320 0.515
## 0.484 0.391 0.395
## 0.431 0.348 0.447
## 0.766 0.633 0.591
## 0.588 0.483 0.644
## 0.583 0.480 0.687
## 0.713 0.585 0.517
## 0.676 0.544 0.337
## 0.180 0.124 0.096
## 0.316 0.242 0.212
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.143) -1.153 0.023 -49.991 0.000 -1.198
## .Stst19d -1.346 0.039 -34.083 0.000 -1.423
## .Stst20s (.145) -0.830 0.021 -40.343 0.000 -0.871
## .Stst21c (.146) -1.167 0.020 -59.399 0.000 -1.206
## .Stst22p (.147) -1.232 0.021 -57.957 0.000 -1.274
## .Stst23n (.148) -1.066 0.025 -42.863 0.000 -1.115
## .Stst24x (.149) -0.967 0.023 -41.652 0.000 -1.012
## .Stst25w (.150) -0.879 0.016 -56.067 0.000 -0.910
## .Stst26r (.151) -1.310 0.023 -57.021 0.000 -1.355
## .Stst31b (.152) -1.086 0.024 -45.618 0.000 -1.132
## .Stst34r (.153) -1.211 0.023 -52.269 0.000 -1.257
## .Stst5mt (.154) -0.774 0.021 -36.938 0.000 -0.816
## .Stst32r (.155) -1.051 0.017 -62.004 0.000 -1.084
## .Stst33h (.156) -0.882 0.016 -54.307 0.000 -0.913
## .Stst35t (.157) -0.681 0.033 -20.677 0.000 -0.746
## .Stst36c (.158) -0.021 0.026 -0.815 0.415 -0.072
## .Stst37b (.159) -0.315 0.024 -13.040 0.000 -0.363
## .Stst2lt (.160) -1.049 0.020 -51.640 0.000 -1.089
## .Stst3ms (.161) -0.909 0.019 -48.304 0.000 -0.946
## .Stst4sc (.162) -1.114 0.024 -46.696 0.000 -1.161
## .Stst7bl (.163) -0.602 0.020 -29.428 0.000 -0.642
## .Stst8rn -0.991 0.029 -34.678 0.000 -1.047
## .Stst11r (.165) -1.088 0.020 -55.070 0.000 -1.127
## .Stst12l (.166) -0.812 0.019 -42.735 0.000 -0.849
## .Stst13h -0.942 0.033 -28.299 0.000 -1.007
## .Stst14b (.168) -0.660 0.019 -35.394 0.000 -0.697
## .Stst15t (.169) -1.016 0.017 -59.930 0.000 -1.049
## .Stst16m (.170) -0.900 0.022 -41.863 0.000 -0.943
## .Stst6ph (.171) -0.723 0.020 -36.714 0.000 -0.762
## .Stst9lc (.172) -0.664 0.024 -28.080 0.000 -0.710
## .Stst10m (.173) -0.671 0.020 -32.947 0.000 -0.711
## .Stst28m -1.085 0.018 -58.734 0.000 -1.121
## .Sts292D (.175) -0.555 0.021 -26.358 0.000 -0.596
## .Sts303D (.176) -0.693 0.018 -37.632 0.000 -0.729
## english 1.671 0.104 16.142 0.000 1.468
## math 0.501 0.093 5.392 0.000 0.319
## speed 0.425 0.040 10.630 0.000 0.346
## info 1.245 0.111 11.210 0.000 1.027
## science -1.227 0.075 -16.427 0.000 -1.373
## spatial -0.264 0.047 -5.623 0.000 -0.355
## g -0.429 0.047 -9.042 0.000 -0.522
## ci.upper Std.lv Std.all
## -1.108 -1.153 -1.232
## -1.268 -1.346 -1.507
## -0.790 -0.830 -0.868
## -1.129 -1.167 -1.199
## -1.190 -1.232 -1.293
## -1.017 -1.066 -0.981
## -0.921 -0.967 -0.891
## -0.848 -0.879 -1.145
## -1.265 -1.310 -1.359
## -1.039 -1.086 -1.013
## -1.166 -1.211 -1.070
## -0.733 -0.774 -0.779
## -1.018 -1.051 -1.401
## -0.850 -0.882 -1.264
## -0.617 -0.681 -0.423
## 0.030 -0.021 -0.016
## -0.268 -0.315 -0.276
## -1.009 -1.049 -1.183
## -0.872 -0.909 -1.030
## -1.068 -1.114 -1.249
## -0.562 -0.602 -0.688
## -0.935 -0.991 -1.192
## -1.049 -1.088 -1.157
## -0.775 -0.812 -0.971
## -0.877 -0.942 -0.871
## -0.623 -0.660 -0.764
## -0.983 -1.016 -1.181
## -0.858 -0.900 -0.967
## -0.685 -0.723 -1.050
## -0.617 -0.664 -0.693
## -0.631 -0.671 -1.085
## -1.049 -1.085 -1.745
## -0.514 -0.555 -0.561
## -0.657 -0.693 -0.890
## 1.874 1.673 1.673
## 0.683 0.583 0.583
## 0.503 0.425 0.425
## 1.462 1.123 1.123
## -1.081 -1.758 -1.758
## -0.172 -0.359 -0.359
## -0.336 -0.498 -0.498
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.253 0.008 33.263 0.000 0.238
## .Stst19dsgsdwrd 0.369 0.011 32.244 0.000 0.347
## .Stest20spellng 0.500 0.014 35.608 0.000 0.473
## .Stest21cptlztn 0.461 0.013 34.491 0.000 0.435
## .Stest22puncttn 0.315 0.011 29.825 0.000 0.294
## .Stest23english 0.555 0.017 32.458 0.000 0.521
## .Stest24exprssn 0.790 0.021 36.930 0.000 0.748
## .Stst25wrdfnctn 0.373 0.011 34.644 0.000 0.352
## .Stst26rdngcmpr 0.211 0.007 29.668 0.000 0.197
## .Stst31bstrctrs 0.594 0.017 34.296 0.000 0.560
## .Stst34rthcmptt 0.693 0.026 26.307 0.000 0.642
## .Stest5math 0.603 0.017 35.770 0.000 0.570
## .Stst32rthrsnng 0.297 0.009 34.540 0.000 0.281
## .Stst33hghschlm 0.162 0.012 13.819 0.000 0.139
## .Stest35tblrdng 1.385 0.057 24.179 0.000 1.272
## .Stst36clrclchc 0.863 0.032 26.988 0.000 0.800
## .Stst37bjctnspc 0.687 0.026 26.072 0.000 0.635
## .Stest2literatr 0.244 0.007 34.958 0.000 0.230
## .Stest3music 0.339 0.009 36.702 0.000 0.321
## .Stest4soclstds 0.254 0.007 35.492 0.000 0.240
## .Stst7blgclscnc 0.475 0.012 38.312 0.000 0.451
## .Stest8aerontcs 0.622 0.011 58.394 0.000 0.602
## .Stest11art 0.385 0.011 35.567 0.000 0.364
## .Stest12law 0.426 0.010 40.664 0.000 0.406
## .Stest13health 0.606 0.015 41.417 0.000 0.577
## .Stest14bible 0.434 0.013 34.017 0.000 0.409
## .Stest15theater 0.388 0.010 37.088 0.000 0.368
## .Stest16mscllns 0.468 0.012 38.328 0.000 0.444
## .Stst6physclscn 0.254 0.007 35.603 0.000 0.240
## .Stest9elctrncs 0.779 0.019 40.307 0.000 0.741
## .Stest10mechncs 0.177 0.011 15.968 0.000 0.155
## .Stst28mchnclrs 0.235 0.007 35.841 0.000 0.222
## .Stst29vslztn2D 0.671 0.020 33.259 0.000 0.631
## .Stst30vslztn3D 0.348 0.012 28.962 0.000 0.325
## english 0.997 0.082 12.139 0.000 0.836
## math 0.737 0.086 8.533 0.000 0.568
## speed 1.001 0.059 16.851 0.000 0.884
## info 1.227 0.115 10.682 0.000 1.002
## science 0.487 0.067 7.305 0.000 0.357
## spatial 0.540 0.043 12.499 0.000 0.455
## g 0.743 0.032 22.972 0.000 0.680
## ci.upper Std.lv Std.all
## 0.268 0.253 0.288
## 0.391 0.369 0.463
## 0.528 0.500 0.546
## 0.487 0.461 0.487
## 0.336 0.315 0.347
## 0.588 0.555 0.470
## 0.832 0.790 0.672
## 0.394 0.373 0.632
## 0.225 0.211 0.227
## 0.628 0.594 0.518
## 0.745 0.693 0.540
## 0.636 0.603 0.609
## 0.314 0.297 0.529
## 0.185 0.162 0.333
## 1.497 1.385 0.533
## 0.926 0.863 0.521
## 0.738 0.687 0.526
## 0.258 0.244 0.310
## 0.357 0.339 0.435
## 0.268 0.254 0.319
## 0.500 0.475 0.620
## 0.643 0.622 0.901
## 0.406 0.385 0.435
## 0.447 0.426 0.609
## 0.634 0.606 0.518
## 0.459 0.434 0.582
## 0.409 0.388 0.524
## 0.492 0.468 0.540
## 0.268 0.254 0.535
## 0.817 0.779 0.848
## 0.199 0.177 0.463
## 0.248 0.235 0.609
## 0.710 0.671 0.686
## 0.372 0.348 0.574
## 1.159 1.000 1.000
## 0.906 1.000 1.000
## 1.117 1.000 1.000
## 1.453 1.000 1.000
## 0.618 1.000 1.000
## 0.624 1.000 1.000
## 0.806 1.000 1.000
lavTestScore(scalar2, release = 75:104)
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to
## ordinary score test
## $test
##
## total score test:
##
## test X2 df p.value
## 1 score 402.333 30 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p143. == .p326. 6.002 1 0.014
## 2 .p145. == .p328. 12.410 1 0.000
## 3 .p146. == .p329. 0.966 1 0.326
## 4 .p147. == .p330. 0.000 1 0.999
## 5 .p148. == .p331. 0.077 1 0.781
## 6 .p149. == .p332. 0.088 1 0.767
## 7 .p150. == .p333. 0.848 1 0.357
## 8 .p151. == .p334. 9.781 1 0.002
## 9 .p152. == .p335. 2.661 1 0.103
## 10 .p153. == .p336. 67.892 1 0.000
## 11 .p154. == .p337. 42.494 1 0.000
## 12 .p155. == .p338. 0.625 1 0.429
## 13 .p156. == .p339. 0.808 1 0.369
## 14 .p157. == .p340. 5.631 1 0.018
## 15 .p158. == .p341. 1.295 1 0.255
## 16 .p159. == .p342. 0.185 1 0.667
## 17 .p160. == .p343. 0.208 1 0.648
## 18 .p161. == .p344. 8.506 1 0.004
## 19 .p162. == .p345. 22.527 1 0.000
## 20 .p163. == .p346. 9.877 1 0.002
## 21 .p165. == .p348. 53.485 1 0.000
## 22 .p166. == .p349. 14.880 1 0.000
## 23 .p168. == .p351. 91.979 1 0.000
## 24 .p169. == .p352. 7.267 1 0.007
## 25 .p170. == .p353. 1.061 1 0.303
## 26 .p171. == .p354. 9.207 1 0.002
## 27 .p172. == .p355. 3.074 1 0.080
## 28 .p173. == .p356. 87.610 1 0.000
## 29 .p175. == .p358. 14.300 1 0.000
## 30 .p176. == .p359. 19.357 1 0.000
strict<-cfa(chc.bifactor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("g=~Stest8aeronautics", "g=~Stest28mechanicalreasoning", "g=~Stest10mechanics", "g=~Stest9electronics", "g=~Stest6physicalscience", "g=~Stest4socialstudies", "Stest28mechanicalreasoning~1", "Stest8aeronautics~1", "Stest19disguisedwords~1", "Stest13health~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 6138.901 1086.000 0.000 0.955 0.039 0.044
## aic bic
## 462903.304 464058.040
Mc(strict)
## [1] 0.6601677
chc.bifactor<-cfa(chc.bifactor.model, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("g=~Stest8aeronautics", "g=~Stest28mechanicalreasoning", "g=~Stest10mechanics", "g=~Stest9electronics", "g=~Stest6physicalscience", "g=~Stest4socialstudies", "Stest28mechanicalreasoning~1", "Stest8aeronautics~1", "Stest19disguisedwords~1", "Stest13health~1"))
fitMeasures(chc.bifactor, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 5976.010 1059.000 0.000 0.956 0.039 0.058
## aic bic
## 462794.414 464130.416
Mc(chc.bifactor)
## [1] 0.6675817
summary(chc.bifactor, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 90 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 303
## Number of equality constraints 104
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 5976.010 5330.532
## Degrees of freedom 1059 1059
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.121
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 2792.548 2490.921
## 1 3183.462 2839.612
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.073 0.010 7.339 0.000 0.053
## Stst19d (.p2.) 0.255 0.014 17.805 0.000 0.227
## Stst20s (.p3.) 0.372 0.011 34.305 0.000 0.351
## Stst21c (.p4.) 0.337 0.010 33.153 0.000 0.317
## Stst22p (.p5.) 0.378 0.011 35.850 0.000 0.358
## Stst23n (.p6.) 0.394 0.012 31.926 0.000 0.370
## Stst24x (.p7.) 0.314 0.013 24.284 0.000 0.289
## Stst25w (.p8.) 0.121 0.010 11.991 0.000 0.101
## Stst26r (.p9.) 0.149 0.008 19.251 0.000 0.134
## Stst31b (.10.) 0.165 0.012 14.104 0.000 0.142
## Stst34r (.11.) 0.151 0.013 11.466 0.000 0.125
## math =~
## Stst5mt (.12.) 0.230 0.019 11.826 0.000 0.192
## Stst25w (.13.) 0.181 0.017 10.699 0.000 0.148
## Stst32r (.14.) 0.191 0.014 13.408 0.000 0.163
## Stst33h (.15.) 0.326 0.021 15.792 0.000 0.286
## Stst34r (.16.) 0.174 0.021 8.108 0.000 0.132
## speed =~
## Stst19d (.17.) 0.197 0.011 18.266 0.000 0.176
## Stst34r (.18.) 0.444 0.019 23.764 0.000 0.408
## Stst35t (.19.) 0.959 0.026 37.406 0.000 0.908
## Stst36c (.20.) 0.881 0.017 51.503 0.000 0.848
## Stst37b (.21.) 0.710 0.017 40.828 0.000 0.676
## info =~
## Stst1vc (.22.) 0.212 0.012 17.006 0.000 0.188
## Stst2lt (.23.) 0.298 0.012 25.202 0.000 0.274
## Stst3ms (.24.) 0.307 0.011 27.940 0.000 0.286
## Stst4sc (.25.) 0.181 0.013 13.700 0.000 0.155
## Stst7bl (.26.) 0.098 0.017 5.711 0.000 0.064
## Stst8rn (.27.) 0.139 0.018 7.840 0.000 0.104
## Stst11r (.28.) 0.323 0.014 23.395 0.000 0.296
## Stst12l (.29.) 0.156 0.012 12.982 0.000 0.133
## Stst13h (.30.) 0.231 0.018 12.978 0.000 0.196
## Stst14b (.31.) 0.252 0.012 20.437 0.000 0.228
## Stst15t (.32.) 0.330 0.012 27.545 0.000 0.307
## Stst16m (.33.) 0.217 0.013 17.061 0.000 0.192
## Stst19d (.34.) 0.181 0.016 11.674 0.000 0.151
## Stst26r (.35.) 0.206 0.010 20.176 0.000 0.186
## science =~
## Stst1vc (.36.) 0.124 0.015 8.308 0.000 0.095
## Stst5mt (.37.) 0.036 0.016 2.316 0.021 0.006
## Stst6ph (.38.) 0.047 0.013 3.745 0.000 0.022
## Stst7bl (.39.) 0.056 0.015 3.715 0.000 0.026
## Stst9lc (.40.) 0.224 0.017 13.539 0.000 0.191
## Stst10m (.41.) 0.350 0.015 23.445 0.000 0.321
## spatial =~
## Stst28m (.42.) 0.234 0.012 20.213 0.000 0.211
## Sts292D (.43.) 0.460 0.019 24.830 0.000 0.423
## Sts303D (.44.) 0.421 0.015 27.622 0.000 0.391
## Stst31b (.45.) 0.416 0.016 25.972 0.000 0.385
## Stst37b (.46.) 0.272 0.018 15.230 0.000 0.237
## g =~
## Stst1vc (.47.) 0.798 0.011 71.462 0.000 0.776
## Stst2lt (.48.) 0.714 0.011 63.490 0.000 0.692
## Stst3ms (.49.) 0.621 0.011 55.862 0.000 0.599
## Stst4sc 0.885 0.013 68.121 0.000 0.860
## Stst5mt (.51.) 0.623 0.013 49.694 0.000 0.598
## Stst6ph 0.668 0.014 49.176 0.000 0.641
## Stst7bl (.53.) 0.563 0.012 45.912 0.000 0.539
## Stst8rn 0.556 0.017 32.245 0.000 0.522
## Stst9lc 0.654 0.018 35.376 0.000 0.618
## Stst10m 0.578 0.015 38.788 0.000 0.549
## Stst11r (.57.) 0.663 0.011 58.991 0.000 0.641
## Stst12l (.58.) 0.531 0.012 45.051 0.000 0.507
## Stst13h (.59.) 0.761 0.012 62.709 0.000 0.737
## Stst14b (.60.) 0.527 0.012 45.106 0.000 0.504
## Stst15t (.61.) 0.516 0.012 44.706 0.000 0.494
## Stst16m (.62.) 0.630 0.012 54.220 0.000 0.607
## Stst19d (.63.) 0.573 0.012 47.146 0.000 0.549
## Stst20s (.64.) 0.561 0.012 46.436 0.000 0.537
## Stst21c (.65.) 0.652 0.011 60.206 0.000 0.631
## Stst22p (.66.) 0.715 0.012 61.083 0.000 0.692
## Stst23n (.67.) 0.731 0.013 55.033 0.000 0.705
## Stst24x (.68.) 0.572 0.013 43.024 0.000 0.546
## Stst25w (.69.) 0.446 0.011 39.297 0.000 0.423
## Stst26r (.70.) 0.861 0.010 85.874 0.000 0.841
## Stst28m 0.538 0.015 34.731 0.000 0.508
## Sts292D (.72.) 0.418 0.013 31.097 0.000 0.392
## Sts303D (.73.) 0.371 0.012 31.485 0.000 0.348
## Stst31b (.74.) 0.678 0.013 54.187 0.000 0.654
## Stst32r (.75.) 0.514 0.011 45.391 0.000 0.492
## Stst33h (.76.) 0.510 0.011 46.320 0.000 0.489
## Stst34r (.77.) 0.625 0.014 44.706 0.000 0.598
## Stst35t (.78.) 0.580 0.020 28.426 0.000 0.540
## Stst36c (.79.) 0.132 0.017 7.800 0.000 0.099
## Stst37b (.80.) 0.260 0.016 16.162 0.000 0.229
## ci.upper Std.lv Std.all
##
## 0.092 0.073 0.074
## 0.283 0.255 0.283
## 0.394 0.372 0.377
## 0.357 0.337 0.352
## 0.399 0.378 0.378
## 0.418 0.394 0.342
## 0.340 0.314 0.278
## 0.140 0.121 0.152
## 0.165 0.149 0.147
## 0.187 0.165 0.149
## 0.177 0.151 0.134
##
## 0.268 0.230 0.233
## 0.214 0.181 0.229
## 0.219 0.191 0.242
## 0.367 0.326 0.439
## 0.216 0.174 0.154
##
## 0.218 0.197 0.219
## 0.481 0.444 0.394
## 1.009 0.959 0.574
## 0.915 0.881 0.684
## 0.744 0.710 0.583
##
## 0.237 0.212 0.216
## 0.321 0.298 0.322
## 0.329 0.307 0.341
## 0.207 0.181 0.172
## 0.131 0.098 0.109
## 0.173 0.139 0.140
## 0.350 0.323 0.342
## 0.180 0.156 0.178
## 0.266 0.231 0.215
## 0.276 0.252 0.294
## 0.354 0.330 0.401
## 0.242 0.217 0.221
## 0.212 0.181 0.201
## 0.226 0.206 0.203
##
## 0.154 0.124 0.127
## 0.067 0.036 0.036
## 0.071 0.047 0.055
## 0.085 0.056 0.062
## 0.256 0.224 0.209
## 0.379 0.350 0.410
##
## 0.256 0.234 0.275
## 0.496 0.460 0.435
## 0.451 0.421 0.475
## 0.448 0.416 0.376
## 0.307 0.272 0.224
##
## 0.820 0.798 0.813
## 0.736 0.714 0.771
## 0.643 0.621 0.690
## 0.911 0.885 0.839
## 0.648 0.623 0.629
## 0.694 0.668 0.785
## 0.588 0.563 0.629
## 0.590 0.556 0.561
## 0.690 0.654 0.611
## 0.607 0.578 0.676
## 0.685 0.663 0.702
## 0.554 0.531 0.604
## 0.784 0.761 0.708
## 0.550 0.527 0.615
## 0.539 0.516 0.626
## 0.653 0.630 0.641
## 0.597 0.573 0.636
## 0.584 0.561 0.568
## 0.673 0.652 0.680
## 0.738 0.715 0.714
## 0.757 0.731 0.635
## 0.598 0.572 0.505
## 0.468 0.446 0.562
## 0.880 0.861 0.847
## 0.568 0.538 0.634
## 0.445 0.418 0.396
## 0.394 0.371 0.419
## 0.703 0.678 0.612
## 0.536 0.514 0.652
## 0.532 0.510 0.687
## 0.653 0.625 0.554
## 0.620 0.580 0.347
## 0.165 0.132 0.102
## 0.292 0.260 0.214
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.143) -1.152 0.023 -50.087 0.000 -1.198
## .Stst19d -0.996 0.019 -53.471 0.000 -1.032
## .Stst20s (.145) -0.830 0.021 -40.338 0.000 -0.871
## .Stst21c (.146) -1.166 0.020 -59.488 0.000 -1.204
## .Stst22p (.147) -1.231 0.021 -58.005 0.000 -1.273
## .Stst23n (.148) -1.065 0.025 -42.898 0.000 -1.114
## .Stst24x (.149) -0.967 0.023 -41.656 0.000 -1.013
## .Stst25w (.150) -0.880 0.016 -55.988 0.000 -0.910
## .Stst26r (.151) -1.309 0.023 -57.170 0.000 -1.354
## .Stst31b (.152) -1.083 0.024 -45.479 0.000 -1.130
## .Stst34r (.153) -1.211 0.023 -52.254 0.000 -1.256
## .Stst5mt (.154) -0.774 0.021 -36.990 0.000 -0.815
## .Stst32r (.155) -1.049 0.017 -61.779 0.000 -1.083
## .Stst33h (.156) -0.881 0.016 -54.418 0.000 -0.913
## .Stst35t (.157) -0.679 0.033 -20.577 0.000 -0.743
## .Stst36c (.158) -0.022 0.026 -0.841 0.400 -0.072
## .Stst37b (.159) -0.316 0.024 -13.031 0.000 -0.363
## .Stst2lt (.160) -1.048 0.020 -51.795 0.000 -1.087
## .Stst3ms (.161) -0.908 0.019 -48.322 0.000 -0.945
## .Stst4sc (.162) -1.113 0.024 -46.960 0.000 -1.160
## .Stst7bl (.163) -0.604 0.021 -29.481 0.000 -0.645
## .Stst8rn -0.521 0.022 -23.638 0.000 -0.564
## .Stst11r (.165) -1.085 0.020 -55.088 0.000 -1.124
## .Stst12l (.166) -0.812 0.019 -42.733 0.000 -0.849
## .Stst13h -1.205 0.024 -51.059 0.000 -1.251
## .Stst14b (.168) -0.661 0.019 -35.425 0.000 -0.697
## .Stst15t (.169) -1.016 0.017 -60.081 0.000 -1.049
## .Stst16m (.170) -0.901 0.022 -41.853 0.000 -0.943
## .Stst6ph (.171) -0.723 0.020 -36.943 0.000 -0.762
## .Stst9lc (.172) -0.663 0.024 -27.862 0.000 -0.710
## .Stst10m (.173) -0.671 0.020 -32.987 0.000 -0.711
## .Stst28m -0.719 0.020 -36.693 0.000 -0.757
## .Sts292D (.175) -0.553 0.021 -26.188 0.000 -0.594
## .Sts303D (.176) -0.693 0.018 -37.795 0.000 -0.728
## ci.upper Std.lv Std.all
## -1.107 -1.152 -1.174
## -0.959 -0.996 -1.105
## -0.790 -0.830 -0.841
## -1.127 -1.166 -1.216
## -1.189 -1.231 -1.230
## -1.017 -1.065 -0.925
## -0.922 -0.967 -0.855
## -0.849 -0.880 -1.109
## -1.264 -1.309 -1.288
## -1.037 -1.083 -0.978
## -1.165 -1.211 -1.072
## -0.733 -0.774 -0.782
## -1.016 -1.049 -1.331
## -0.850 -0.881 -1.186
## -0.614 -0.679 -0.406
## 0.029 -0.022 -0.017
## -0.268 -0.316 -0.260
## -1.008 -1.048 -1.132
## -0.871 -0.908 -1.009
## -1.067 -1.113 -1.055
## -0.564 -0.604 -0.674
## -0.478 -0.521 -0.525
## -1.047 -1.085 -1.148
## -0.774 -0.812 -0.923
## -1.159 -1.205 -1.121
## -0.624 -0.661 -0.770
## -0.983 -1.016 -1.232
## -0.859 -0.901 -0.918
## -0.685 -0.723 -0.850
## -0.617 -0.663 -0.619
## -0.631 -0.671 -0.785
## -0.680 -0.719 -0.847
## -0.512 -0.553 -0.523
## -0.657 -0.693 -0.782
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.260 0.009 27.866 0.000 0.242
## .Stst19dsgsdwrd 0.347 0.014 25.353 0.000 0.320
## .Stest20spellng 0.521 0.017 30.019 0.000 0.487
## .Stest21cptlztn 0.380 0.016 24.463 0.000 0.350
## .Stest22puncttn 0.347 0.012 28.293 0.000 0.323
## .Stest23english 0.638 0.024 26.955 0.000 0.591
## .Stest24exprssn 0.854 0.025 33.741 0.000 0.805
## .Stst25wrdfnctn 0.383 0.012 31.520 0.000 0.359
## .Stst26rdngcmpr 0.228 0.009 25.713 0.000 0.210
## .Stst31bstrctrs 0.566 0.022 25.749 0.000 0.523
## .Stst34rthcmptt 0.633 0.031 20.458 0.000 0.572
## .Stest5math 0.538 0.020 26.422 0.000 0.498
## .Stst32rthrsnng 0.321 0.011 28.128 0.000 0.299
## .Stst33hghschlm 0.185 0.014 13.281 0.000 0.158
## .Stest35tblrdng 1.538 0.068 22.506 0.000 1.404
## .Stst36clrclchc 0.867 0.040 21.733 0.000 0.789
## .Stst37bjctnspc 0.836 0.034 24.871 0.000 0.770
## .Stest2literatr 0.259 0.009 29.129 0.000 0.241
## .Stest3music 0.330 0.012 27.364 0.000 0.307
## .Stest4soclstds 0.296 0.011 27.776 0.000 0.275
## .Stst7blgclscnc 0.474 0.014 33.568 0.000 0.446
## .Stest8aerontcs 0.656 0.018 37.384 0.000 0.621
## .Stest11art 0.349 0.012 28.290 0.000 0.325
## .Stest12law 0.467 0.014 33.300 0.000 0.439
## .Stest13health 0.522 0.016 32.012 0.000 0.490
## .Stest14bible 0.394 0.014 28.249 0.000 0.367
## .Stest15theater 0.305 0.011 27.064 0.000 0.283
## .Stest16mscllns 0.520 0.017 31.066 0.000 0.487
## .Stst6physclscn 0.275 0.010 27.369 0.000 0.255
## .Stest9elctrncs 0.670 0.028 23.759 0.000 0.614
## .Stest10mechncs 0.274 0.016 16.919 0.000 0.242
## .Stst28mchnclrs 0.376 0.015 25.856 0.000 0.348
## .Stst29vslztn2D 0.732 0.027 27.237 0.000 0.679
## .Stst30vslztn3D 0.470 0.018 25.455 0.000 0.434
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.279 0.260 0.270
## 0.373 0.347 0.427
## 0.555 0.521 0.535
## 0.411 0.380 0.414
## 0.371 0.347 0.347
## 0.684 0.638 0.480
## 0.904 0.854 0.667
## 0.406 0.383 0.609
## 0.245 0.228 0.220
## 0.609 0.566 0.462
## 0.694 0.633 0.497
## 0.578 0.538 0.549
## 0.343 0.321 0.517
## 0.212 0.185 0.335
## 1.672 1.538 0.551
## 0.945 0.867 0.522
## 0.901 0.836 0.564
## 0.276 0.259 0.302
## 0.354 0.330 0.408
## 0.317 0.296 0.266
## 0.501 0.474 0.589
## 0.690 0.656 0.666
## 0.373 0.349 0.391
## 0.494 0.467 0.604
## 0.554 0.522 0.453
## 0.421 0.394 0.536
## 0.327 0.305 0.448
## 0.553 0.520 0.540
## 0.295 0.275 0.380
## 0.725 0.670 0.584
## 0.305 0.274 0.375
## 0.405 0.376 0.522
## 0.784 0.732 0.654
## 0.506 0.470 0.598
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.073 0.010 7.339 0.000 0.053
## Stst19d (.p2.) 0.255 0.014 17.805 0.000 0.227
## Stst20s (.p3.) 0.372 0.011 34.305 0.000 0.351
## Stst21c (.p4.) 0.337 0.010 33.153 0.000 0.317
## Stst22p (.p5.) 0.378 0.011 35.850 0.000 0.358
## Stst23n (.p6.) 0.394 0.012 31.926 0.000 0.370
## Stst24x (.p7.) 0.314 0.013 24.284 0.000 0.289
## Stst25w (.p8.) 0.121 0.010 11.991 0.000 0.101
## Stst26r (.p9.) 0.149 0.008 19.251 0.000 0.134
## Stst31b (.10.) 0.165 0.012 14.104 0.000 0.142
## Stst34r (.11.) 0.151 0.013 11.466 0.000 0.125
## math =~
## Stst5mt (.12.) 0.230 0.019 11.826 0.000 0.192
## Stst25w (.13.) 0.181 0.017 10.699 0.000 0.148
## Stst32r (.14.) 0.191 0.014 13.408 0.000 0.163
## Stst33h (.15.) 0.326 0.021 15.792 0.000 0.286
## Stst34r (.16.) 0.174 0.021 8.108 0.000 0.132
## speed =~
## Stst19d (.17.) 0.197 0.011 18.266 0.000 0.176
## Stst34r (.18.) 0.444 0.019 23.764 0.000 0.408
## Stst35t (.19.) 0.959 0.026 37.406 0.000 0.908
## Stst36c (.20.) 0.881 0.017 51.503 0.000 0.848
## Stst37b (.21.) 0.710 0.017 40.828 0.000 0.676
## info =~
## Stst1vc (.22.) 0.212 0.012 17.006 0.000 0.188
## Stst2lt (.23.) 0.298 0.012 25.202 0.000 0.274
## Stst3ms (.24.) 0.307 0.011 27.940 0.000 0.286
## Stst4sc (.25.) 0.181 0.013 13.700 0.000 0.155
## Stst7bl (.26.) 0.098 0.017 5.711 0.000 0.064
## Stst8rn (.27.) 0.139 0.018 7.840 0.000 0.104
## Stst11r (.28.) 0.323 0.014 23.395 0.000 0.296
## Stst12l (.29.) 0.156 0.012 12.982 0.000 0.133
## Stst13h (.30.) 0.231 0.018 12.978 0.000 0.196
## Stst14b (.31.) 0.252 0.012 20.437 0.000 0.228
## Stst15t (.32.) 0.330 0.012 27.545 0.000 0.307
## Stst16m (.33.) 0.217 0.013 17.061 0.000 0.192
## Stst19d (.34.) 0.181 0.016 11.674 0.000 0.151
## Stst26r (.35.) 0.206 0.010 20.176 0.000 0.186
## science =~
## Stst1vc (.36.) 0.124 0.015 8.308 0.000 0.095
## Stst5mt (.37.) 0.036 0.016 2.316 0.021 0.006
## Stst6ph (.38.) 0.047 0.013 3.745 0.000 0.022
## Stst7bl (.39.) 0.056 0.015 3.715 0.000 0.026
## Stst9lc (.40.) 0.224 0.017 13.539 0.000 0.191
## Stst10m (.41.) 0.350 0.015 23.445 0.000 0.321
## spatial =~
## Stst28m (.42.) 0.234 0.012 20.213 0.000 0.211
## Sts292D (.43.) 0.460 0.019 24.830 0.000 0.423
## Sts303D (.44.) 0.421 0.015 27.622 0.000 0.391
## Stst31b (.45.) 0.416 0.016 25.972 0.000 0.385
## Stst37b (.46.) 0.272 0.018 15.230 0.000 0.237
## g =~
## Stst1vc (.47.) 0.798 0.011 71.462 0.000 0.776
## Stst2lt (.48.) 0.714 0.011 63.490 0.000 0.692
## Stst3ms (.49.) 0.621 0.011 55.862 0.000 0.599
## Stst4sc 0.755 0.012 63.828 0.000 0.732
## Stst5mt (.51.) 0.623 0.013 49.694 0.000 0.598
## Stst6ph 0.492 0.013 37.569 0.000 0.466
## Stst7bl (.53.) 0.563 0.012 45.912 0.000 0.539
## Stst8rn 0.235 0.017 13.811 0.000 0.201
## Stst9lc 0.335 0.019 18.044 0.000 0.299
## Stst10m 0.357 0.011 31.921 0.000 0.335
## Stst11r (.57.) 0.663 0.011 58.991 0.000 0.641
## Stst12l (.58.) 0.531 0.012 45.051 0.000 0.507
## Stst13h (.59.) 0.761 0.012 62.709 0.000 0.737
## Stst14b (.60.) 0.527 0.012 45.106 0.000 0.504
## Stst15t (.61.) 0.516 0.012 44.706 0.000 0.494
## Stst16m (.62.) 0.630 0.012 54.220 0.000 0.607
## Stst19d (.63.) 0.573 0.012 47.146 0.000 0.549
## Stst20s (.64.) 0.561 0.012 46.436 0.000 0.537
## Stst21c (.65.) 0.652 0.011 60.206 0.000 0.631
## Stst22p (.66.) 0.715 0.012 61.083 0.000 0.692
## Stst23n (.67.) 0.731 0.013 55.033 0.000 0.705
## Stst24x (.68.) 0.572 0.013 43.024 0.000 0.546
## Stst25w (.69.) 0.446 0.011 39.297 0.000 0.423
## Stst26r (.70.) 0.861 0.010 85.874 0.000 0.841
## Stst28m 0.338 0.012 28.476 0.000 0.315
## Sts292D (.72.) 0.418 0.013 31.097 0.000 0.392
## Sts303D (.73.) 0.371 0.012 31.485 0.000 0.348
## Stst31b (.74.) 0.678 0.013 54.187 0.000 0.654
## Stst32r (.75.) 0.514 0.011 45.391 0.000 0.492
## Stst33h (.76.) 0.510 0.011 46.320 0.000 0.489
## Stst34r (.77.) 0.625 0.014 44.706 0.000 0.598
## Stst35t (.78.) 0.580 0.020 28.426 0.000 0.540
## Stst36c (.79.) 0.132 0.017 7.800 0.000 0.099
## Stst37b (.80.) 0.260 0.016 16.162 0.000 0.229
## ci.upper Std.lv Std.all
##
## 0.092 0.073 0.074
## 0.283 0.255 0.279
## 0.394 0.372 0.382
## 0.357 0.337 0.337
## 0.399 0.378 0.384
## 0.418 0.394 0.353
## 0.340 0.314 0.285
## 0.140 0.121 0.154
## 0.165 0.149 0.148
## 0.187 0.165 0.148
## 0.177 0.151 0.131
##
## 0.268 0.230 0.225
## 0.214 0.181 0.231
## 0.219 0.191 0.247
## 0.367 0.326 0.451
## 0.216 0.174 0.150
##
## 0.218 0.197 0.216
## 0.481 0.444 0.385
## 1.009 0.959 0.590
## 0.915 0.881 0.685
## 0.744 0.710 0.616
##
## 0.237 0.212 0.217
## 0.321 0.298 0.324
## 0.329 0.307 0.340
## 0.207 0.181 0.196
## 0.131 0.098 0.109
## 0.173 0.139 0.166
## 0.350 0.323 0.335
## 0.180 0.156 0.182
## 0.266 0.231 0.208
## 0.276 0.252 0.286
## 0.354 0.330 0.378
## 0.242 0.217 0.227
## 0.212 0.181 0.198
## 0.226 0.206 0.205
##
## 0.154 0.124 0.127
## 0.067 0.036 0.035
## 0.071 0.047 0.066
## 0.085 0.056 0.062
## 0.256 0.224 0.231
## 0.379 0.350 0.551
##
## 0.256 0.234 0.366
## 0.496 0.460 0.451
## 0.451 0.421 0.522
## 0.448 0.416 0.374
## 0.307 0.272 0.236
##
## 0.820 0.798 0.816
## 0.736 0.714 0.778
## 0.643 0.621 0.686
## 0.779 0.755 0.816
## 0.648 0.623 0.610
## 0.517 0.492 0.696
## 0.588 0.563 0.628
## 0.268 0.235 0.281
## 0.372 0.335 0.346
## 0.379 0.357 0.562
## 0.685 0.663 0.687
## 0.554 0.531 0.620
## 0.784 0.761 0.684
## 0.550 0.527 0.599
## 0.539 0.516 0.590
## 0.653 0.630 0.660
## 0.597 0.573 0.626
## 0.584 0.561 0.575
## 0.673 0.652 0.652
## 0.738 0.715 0.726
## 0.757 0.731 0.655
## 0.598 0.572 0.518
## 0.468 0.446 0.567
## 0.880 0.861 0.854
## 0.362 0.338 0.530
## 0.445 0.418 0.410
## 0.394 0.371 0.460
## 0.703 0.678 0.609
## 0.536 0.514 0.664
## 0.532 0.510 0.705
## 0.653 0.625 0.541
## 0.620 0.580 0.357
## 0.165 0.132 0.102
## 0.292 0.260 0.226
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## science ~~
## spatial 0.000 0.000
## g 0.000 0.000
## spatial ~~
## g 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.143) -1.152 0.023 -50.087 0.000 -1.198
## .Stst19d -1.341 0.040 -33.165 0.000 -1.420
## .Stst20s (.145) -0.830 0.021 -40.338 0.000 -0.871
## .Stst21c (.146) -1.166 0.020 -59.488 0.000 -1.204
## .Stst22p (.147) -1.231 0.021 -58.005 0.000 -1.273
## .Stst23n (.148) -1.065 0.025 -42.898 0.000 -1.114
## .Stst24x (.149) -0.967 0.023 -41.656 0.000 -1.013
## .Stst25w (.150) -0.880 0.016 -55.988 0.000 -0.910
## .Stst26r (.151) -1.309 0.023 -57.170 0.000 -1.354
## .Stst31b (.152) -1.083 0.024 -45.479 0.000 -1.130
## .Stst34r (.153) -1.211 0.023 -52.254 0.000 -1.256
## .Stst5mt (.154) -0.774 0.021 -36.990 0.000 -0.815
## .Stst32r (.155) -1.049 0.017 -61.779 0.000 -1.083
## .Stst33h (.156) -0.881 0.016 -54.418 0.000 -0.913
## .Stst35t (.157) -0.679 0.033 -20.577 0.000 -0.743
## .Stst36c (.158) -0.022 0.026 -0.841 0.400 -0.072
## .Stst37b (.159) -0.316 0.024 -13.031 0.000 -0.363
## .Stst2lt (.160) -1.048 0.020 -51.795 0.000 -1.087
## .Stst3ms (.161) -0.908 0.019 -48.322 0.000 -0.945
## .Stst4sc (.162) -1.113 0.024 -46.960 0.000 -1.160
## .Stst7bl (.163) -0.604 0.021 -29.481 0.000 -0.645
## .Stst8rn -0.996 0.029 -34.115 0.000 -1.053
## .Stst11r (.165) -1.085 0.020 -55.088 0.000 -1.124
## .Stst12l (.166) -0.812 0.019 -42.733 0.000 -0.849
## .Stst13h -0.932 0.034 -27.669 0.000 -0.998
## .Stst14b (.168) -0.661 0.019 -35.425 0.000 -0.697
## .Stst15t (.169) -1.016 0.017 -60.081 0.000 -1.049
## .Stst16m (.170) -0.901 0.022 -41.853 0.000 -0.943
## .Stst6ph (.171) -0.723 0.020 -36.943 0.000 -0.762
## .Stst9lc (.172) -0.663 0.024 -27.862 0.000 -0.710
## .Stst10m (.173) -0.671 0.020 -32.987 0.000 -0.711
## .Stst28m -1.091 0.018 -60.046 0.000 -1.126
## .Sts292D (.175) -0.553 0.021 -26.188 0.000 -0.594
## .Sts303D (.176) -0.693 0.018 -37.795 0.000 -0.728
## english 1.707 0.098 17.492 0.000 1.515
## math 0.569 0.104 5.486 0.000 0.366
## speed 0.428 0.038 11.363 0.000 0.354
## info 1.203 0.103 11.694 0.000 1.001
## science -1.505 0.085 -17.783 0.000 -1.670
## spatial -0.301 0.056 -5.339 0.000 -0.411
## g -0.481 0.054 -8.966 0.000 -0.586
## ci.upper Std.lv Std.all
## -1.107 -1.152 -1.178
## -1.262 -1.341 -1.467
## -0.790 -0.830 -0.851
## -1.127 -1.166 -1.167
## -1.189 -1.231 -1.250
## -1.017 -1.065 -0.955
## -0.922 -0.967 -0.877
## -0.849 -0.880 -1.120
## -1.264 -1.309 -1.298
## -1.037 -1.083 -0.973
## -1.165 -1.211 -1.048
## -0.733 -0.774 -0.758
## -1.016 -1.049 -1.357
## -0.850 -0.881 -1.217
## -0.614 -0.679 -0.418
## 0.029 -0.022 -0.017
## -0.268 -0.316 -0.274
## -1.008 -1.048 -1.142
## -0.871 -0.908 -1.003
## -1.067 -1.113 -1.202
## -0.564 -0.604 -0.673
## -0.938 -0.996 -1.193
## -1.047 -1.085 -1.125
## -0.774 -0.812 -0.949
## -0.866 -0.932 -0.838
## -0.624 -0.661 -0.750
## -0.983 -1.016 -1.161
## -0.859 -0.901 -0.944
## -0.685 -0.723 -1.024
## -0.617 -0.663 -0.684
## -0.631 -0.671 -1.056
## -1.055 -1.091 -1.710
## -0.512 -0.553 -0.542
## -0.657 -0.693 -0.858
## 1.898 1.707 1.707
## 0.773 0.569 0.569
## 0.502 0.428 0.428
## 1.404 1.203 1.203
## -1.339 -1.505 -1.505
## -0.190 -0.301 -0.301
## -0.376 -0.481 -0.481
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.254 0.008 33.431 0.000 0.239
## .Stst19dsgsdwrd 0.371 0.011 32.432 0.000 0.349
## .Stest20spellng 0.499 0.014 35.667 0.000 0.472
## .Stest21cptlztn 0.460 0.013 34.549 0.000 0.434
## .Stest22puncttn 0.316 0.011 30.026 0.000 0.295
## .Stest23english 0.555 0.017 32.475 0.000 0.521
## .Stest24exprssn 0.790 0.021 36.970 0.000 0.748
## .Stst25wrdfnctn 0.371 0.011 33.980 0.000 0.350
## .Stst26rdngcmpr 0.210 0.007 29.611 0.000 0.196
## .Stst31bstrctrs 0.581 0.017 33.550 0.000 0.547
## .Stst34rthcmptt 0.693 0.026 26.210 0.000 0.641
## .Stest5math 0.601 0.017 35.531 0.000 0.568
## .Stst32rthrsnng 0.298 0.009 34.081 0.000 0.281
## .Stst33hghschlm 0.158 0.013 12.555 0.000 0.133
## .Stest35tblrdng 1.385 0.057 24.187 0.000 1.273
## .Stst36clrclchc 0.863 0.032 27.325 0.000 0.801
## .Stst37bjctnspc 0.683 0.026 25.961 0.000 0.631
## .Stest2literatr 0.244 0.007 35.077 0.000 0.231
## .Stest3music 0.339 0.009 36.817 0.000 0.321
## .Stest4soclstds 0.254 0.007 35.454 0.000 0.240
## .Stst7blgclscnc 0.476 0.012 38.180 0.000 0.451
## .Stest8aerontcs 0.622 0.011 58.386 0.000 0.602
## .Stest11art 0.387 0.011 35.939 0.000 0.366
## .Stest12law 0.426 0.010 40.631 0.000 0.405
## .Stest13health 0.605 0.015 41.383 0.000 0.576
## .Stest14bible 0.434 0.013 34.050 0.000 0.409
## .Stest15theater 0.390 0.010 37.277 0.000 0.369
## .Stest16mscllns 0.468 0.012 38.292 0.000 0.444
## .Stst6physclscn 0.255 0.007 35.769 0.000 0.241
## .Stest9elctrncs 0.777 0.019 40.208 0.000 0.739
## .Stest10mechncs 0.153 0.012 12.911 0.000 0.130
## .Stst28mchnclrs 0.238 0.007 36.552 0.000 0.225
## .Stst29vslztn2D 0.655 0.020 32.090 0.000 0.615
## .Stst30vslztn3D 0.337 0.012 27.468 0.000 0.313
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.269 0.254 0.265
## 0.393 0.371 0.444
## 0.527 0.499 0.524
## 0.486 0.460 0.461
## 0.337 0.316 0.326
## 0.588 0.555 0.446
## 0.832 0.790 0.650
## 0.393 0.371 0.602
## 0.224 0.210 0.207
## 0.615 0.581 0.468
## 0.744 0.693 0.519
## 0.634 0.601 0.576
## 0.315 0.298 0.498
## 0.182 0.158 0.300
## 1.497 1.385 0.525
## 0.925 0.863 0.521
## 0.734 0.683 0.514
## 0.258 0.244 0.290
## 0.357 0.339 0.414
## 0.268 0.254 0.296
## 0.500 0.476 0.590
## 0.643 0.622 0.893
## 0.408 0.387 0.415
## 0.447 0.426 0.582
## 0.633 0.605 0.489
## 0.459 0.434 0.559
## 0.410 0.390 0.509
## 0.492 0.468 0.513
## 0.269 0.255 0.511
## 0.815 0.777 0.827
## 0.176 0.153 0.380
## 0.251 0.238 0.584
## 0.695 0.655 0.629
## 0.361 0.337 0.517
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
standardizedSolution(chc.bifactor) # get the correct SEs for standardized solution
## lhs op rhs group
## 1 english =~ Stest1vocab 1
## 2 english =~ Stest19disguisedwords 1
## 3 english =~ Stest20spelling 1
## 4 english =~ Stest21capitalization 1
## 5 english =~ Stest22punctuation 1
## 6 english =~ Stest23english 1
## 7 english =~ Stest24expression 1
## 8 english =~ Stest25wordfunctions 1
## 9 english =~ Stest26readingcomprehension 1
## 10 english =~ Stest31abstractreasoning 1
## 11 english =~ Stest34arithcomputation 1
## 12 math =~ Stest5math 1
## 13 math =~ Stest25wordfunctions 1
## 14 math =~ Stest32arithreasoning 1
## 15 math =~ Stest33highschoolmath 1
## 16 math =~ Stest34arithcomputation 1
## 17 speed =~ Stest19disguisedwords 1
## 18 speed =~ Stest34arithcomputation 1
## 19 speed =~ Stest35tablereading 1
## 20 speed =~ Stest36clericalchecking 1
## 21 speed =~ Stest37objectinspection 1
## 22 info =~ Stest1vocab 1
## 23 info =~ Stest2literature 1
## 24 info =~ Stest3music 1
## 25 info =~ Stest4socialstudies 1
## 26 info =~ Stest7biologicalscience 1
## 27 info =~ Stest8aeronautics 1
## 28 info =~ Stest11art 1
## 29 info =~ Stest12law 1
## 30 info =~ Stest13health 1
## 31 info =~ Stest14bible 1
## 32 info =~ Stest15theater 1
## 33 info =~ Stest16miscellaneous 1
## 34 info =~ Stest19disguisedwords 1
## 35 info =~ Stest26readingcomprehension 1
## 36 science =~ Stest1vocab 1
## 37 science =~ Stest5math 1
## 38 science =~ Stest6physicalscience 1
## 39 science =~ Stest7biologicalscience 1
## 40 science =~ Stest9electronics 1
## 41 science =~ Stest10mechanics 1
## 42 spatial =~ Stest28mechanicalreasoning 1
## 43 spatial =~ Stest29visualization2D 1
## 44 spatial =~ Stest30visualization3D 1
## 45 spatial =~ Stest31abstractreasoning 1
## 46 spatial =~ Stest37objectinspection 1
## 47 g =~ Stest1vocab 1
## 48 g =~ Stest2literature 1
## 49 g =~ Stest3music 1
## 50 g =~ Stest4socialstudies 1
## 51 g =~ Stest5math 1
## 52 g =~ Stest6physicalscience 1
## 53 g =~ Stest7biologicalscience 1
## 54 g =~ Stest8aeronautics 1
## 55 g =~ Stest9electronics 1
## 56 g =~ Stest10mechanics 1
## 57 g =~ Stest11art 1
## 58 g =~ Stest12law 1
## 59 g =~ Stest13health 1
## 60 g =~ Stest14bible 1
## 61 g =~ Stest15theater 1
## 62 g =~ Stest16miscellaneous 1
## 63 g =~ Stest19disguisedwords 1
## 64 g =~ Stest20spelling 1
## 65 g =~ Stest21capitalization 1
## 66 g =~ Stest22punctuation 1
## 67 g =~ Stest23english 1
## 68 g =~ Stest24expression 1
## 69 g =~ Stest25wordfunctions 1
## 70 g =~ Stest26readingcomprehension 1
## 71 g =~ Stest28mechanicalreasoning 1
## 72 g =~ Stest29visualization2D 1
## 73 g =~ Stest30visualization3D 1
## 74 g =~ Stest31abstractreasoning 1
## 75 g =~ Stest32arithreasoning 1
## 76 g =~ Stest33highschoolmath 1
## 77 g =~ Stest34arithcomputation 1
## 78 g =~ Stest35tablereading 1
## 79 g =~ Stest36clericalchecking 1
## 80 g =~ Stest37objectinspection 1
## 81 Stest1vocab ~~ Stest1vocab 1
## 82 Stest19disguisedwords ~~ Stest19disguisedwords 1
## 83 Stest20spelling ~~ Stest20spelling 1
## 84 Stest21capitalization ~~ Stest21capitalization 1
## 85 Stest22punctuation ~~ Stest22punctuation 1
## 86 Stest23english ~~ Stest23english 1
## 87 Stest24expression ~~ Stest24expression 1
## 88 Stest25wordfunctions ~~ Stest25wordfunctions 1
## 89 Stest26readingcomprehension ~~ Stest26readingcomprehension 1
## 90 Stest31abstractreasoning ~~ Stest31abstractreasoning 1
## label est.std se z pvalue ci.lower ci.upper
## 1 .p1. 0.074 0.010 7.340 0.000 0.054 0.094
## 2 .p2. 0.283 0.016 17.986 0.000 0.252 0.314
## 3 .p3. 0.377 0.011 34.247 0.000 0.356 0.399
## 4 .p4. 0.352 0.011 32.446 0.000 0.330 0.373
## 5 .p5. 0.378 0.010 36.030 0.000 0.357 0.399
## 6 .p6. 0.342 0.010 32.798 0.000 0.322 0.362
## 7 .p7. 0.278 0.011 24.739 0.000 0.256 0.300
## 8 .p8. 0.152 0.013 12.019 0.000 0.127 0.177
## 9 .p9. 0.147 0.008 19.216 0.000 0.132 0.162
## 10 .p10. 0.149 0.011 14.122 0.000 0.128 0.169
## 11 .p11. 0.134 0.012 11.285 0.000 0.111 0.157
## 12 .p12. 0.233 0.020 11.886 0.000 0.194 0.271
## 13 .p13. 0.229 0.021 10.865 0.000 0.187 0.270
## 14 .p14. 0.242 0.018 13.720 0.000 0.207 0.277
## 15 .p15. 0.439 0.028 15.864 0.000 0.385 0.494
## 16 .p16. 0.154 0.019 7.964 0.000 0.116 0.192
## 17 .p17. 0.219 0.012 18.676 0.000 0.196 0.242
## 18 .p18. 0.394 0.015 26.785 0.000 0.365 0.422
## 19 .p19. 0.574 0.014 41.660 0.000 0.547 0.601
## 20 .p20. 0.684 0.013 50.865 0.000 0.657 0.710
## 21 .p21. 0.583 0.013 43.583 0.000 0.557 0.609
## 22 .p22. 0.216 0.013 16.966 0.000 0.191 0.241
## 23 .p23. 0.322 0.013 25.305 0.000 0.297 0.346
## 24 .p24. 0.341 0.012 27.980 0.000 0.317 0.365
## 25 .p25. 0.172 0.013 13.533 0.000 0.147 0.197
## 26 .p26. 0.109 0.019 5.714 0.000 0.071 0.146
## 27 .p27. 0.140 0.018 7.868 0.000 0.105 0.174
## 28 .p28. 0.342 0.014 23.806 0.000 0.314 0.370
## 29 .p29. 0.178 0.014 13.007 0.000 0.151 0.204
## 30 .p30. 0.215 0.017 12.916 0.000 0.183 0.248
## 31 .p31. 0.294 0.015 20.032 0.000 0.265 0.323
## 32 .p32. 0.401 0.014 27.973 0.000 0.372 0.429
## 33 .p33. 0.221 0.013 16.704 0.000 0.195 0.247
## 34 .p34. 0.201 0.017 11.712 0.000 0.168 0.235
## 35 .p35. 0.203 0.010 20.020 0.000 0.183 0.223
## 36 .p36. 0.127 0.015 8.280 0.000 0.097 0.157
## 37 .p37. 0.036 0.016 2.306 0.021 0.005 0.067
## 38 .p38. 0.055 0.015 3.745 0.000 0.026 0.084
## 39 .p39. 0.062 0.017 3.707 0.000 0.029 0.095
## 40 .p40. 0.209 0.017 12.585 0.000 0.176 0.241
## 41 .p41. 0.410 0.018 22.705 0.000 0.374 0.445
## 42 .p42. 0.275 0.014 19.303 0.000 0.247 0.303
## 43 .p43. 0.435 0.018 24.711 0.000 0.400 0.469
## 44 .p44. 0.475 0.017 27.889 0.000 0.442 0.509
## 45 .p45. 0.376 0.015 25.600 0.000 0.347 0.405
## 46 .p46. 0.224 0.015 15.105 0.000 0.195 0.253
## 47 .p47. 0.813 0.007 116.898 0.000 0.800 0.827
## 48 .p48. 0.771 0.007 105.517 0.000 0.757 0.786
## 49 .p49. 0.690 0.009 81.032 0.000 0.673 0.707
## 50 0.839 0.006 129.174 0.000 0.827 0.852
## 51 .p51. 0.629 0.011 56.893 0.000 0.607 0.651
## 52 0.785 0.009 85.822 0.000 0.767 0.803
## 53 .p53. 0.629 0.012 54.090 0.000 0.606 0.651
## 54 0.561 0.015 37.777 0.000 0.532 0.590
## 55 0.611 0.013 45.933 0.000 0.584 0.637
## 56 0.676 0.013 53.761 0.000 0.652 0.701
## 57 .p57. 0.702 0.009 82.524 0.000 0.685 0.718
## 58 .p58. 0.604 0.011 56.699 0.000 0.583 0.624
## 59 .p59. 0.708 0.009 80.922 0.000 0.691 0.725
## 60 .p60. 0.615 0.010 59.776 0.000 0.595 0.635
## 61 .p61. 0.626 0.010 60.787 0.000 0.606 0.646
## 62 .p62. 0.641 0.009 68.478 0.000 0.623 0.660
## 63 .p63. 0.636 0.010 62.056 0.000 0.616 0.656
## 64 .p64. 0.568 0.010 55.531 0.000 0.548 0.588
## 65 .p65. 0.680 0.009 78.561 0.000 0.663 0.697
## 66 .p66. 0.714 0.008 91.244 0.000 0.699 0.730
## 67 .p67. 0.635 0.009 69.208 0.000 0.617 0.653
## 68 .p68. 0.505 0.011 46.127 0.000 0.484 0.527
## 69 .p69. 0.562 0.011 51.803 0.000 0.541 0.583
## 70 .p70. 0.847 0.005 160.233 0.000 0.836 0.857
## 71 0.634 0.013 47.900 0.000 0.608 0.660
## 72 .p72. 0.396 0.013 31.249 0.000 0.371 0.420
## 73 .p73. 0.419 0.013 33.463 0.000 0.394 0.443
## 74 .p74. 0.612 0.010 61.862 0.000 0.593 0.632
## 75 .p75. 0.652 0.010 62.948 0.000 0.632 0.672
## 76 .p76. 0.687 0.010 71.996 0.000 0.668 0.706
## 77 .p77. 0.554 0.012 46.404 0.000 0.530 0.577
## 78 .p78. 0.347 0.011 30.539 0.000 0.325 0.369
## 79 .p79. 0.102 0.013 7.823 0.000 0.077 0.128
## 80 .p80. 0.214 0.013 16.512 0.000 0.188 0.239
## 81 0.270 0.010 28.319 0.000 0.252 0.289
## 82 0.427 0.013 34.080 0.000 0.403 0.452
## 83 0.535 0.013 41.504 0.000 0.509 0.560
## 84 0.414 0.012 33.809 0.000 0.390 0.438
## 85 0.347 0.011 32.943 0.000 0.326 0.367
## 86 0.480 0.012 39.345 0.000 0.456 0.504
## 87 0.667 0.012 54.197 0.000 0.643 0.692
## 88 0.609 0.014 42.430 0.000 0.581 0.637
## 89 0.220 0.008 27.360 0.000 0.205 0.236
## 90 0.462 0.014 32.827 0.000 0.434 0.489
## [ reached 'max' / getOption("max.print") -- omitted 276 rows ]
# PAR.boot<- bootstrapLavaan(chc.bifactor, R=500, type="ordinary", FUN="coef") # bootstrap model parameters, unstandardized
# describeBy(PAR.boot) # check sd column for the standard errors, as sd is the variability of the parameter estimates across the bootstrap samples
tests<-lavTestLRT(configural, metric2, scalar2, chc.bifactor)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 458.8868 384.2813 140.5664
dfd=tests[2:4,"Df diff"]
dfd
## [1] 67 23 7
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04385297 0.07186459 0.07920555
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04010082 0.04768912
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.06563885 0.07826420
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.06808186 0.09087927
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.004 0.000 0.000 0.000
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 0.999 0.018 0.000
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 0.998 0.471 0.002
tests<-lavTestLRT(configural, metric2, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 458.8868 1022.8414
dfd=tests[2:3,"Df diff"]
dfd
## [1] 67 27
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04385297 0.11012078
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04010082 0.04768912
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.1043887 0.1159422
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.004 0.000 0.000 0.000
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 1.000 1.000 0.998
tests<-lavTestLRT(configural, metric2, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 458.8868 384.2813 284.2203
dfd=tests[2:4,"Df diff"]
dfd
## [1] 67 23 34
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04385297 0.07186459 0.04919012
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04010082 0.04768912
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.06563885 0.07826420
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.04398894 0.05455132
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.004 0.000 0.000 0.000
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 0.999 0.018 0.000
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.412 0.000 0.000 0.000
tests<-lavTestLRT(configural, metric)
Td=tests[2,"Chisq diff"]
Td
## [1] 980.2731
dfd=tests[2,"Df diff"]
dfd
## [1] 73
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.06392396
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.06039177 0.06751004
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 0.966 0.000 0.000
bf.age <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest9electronics + Stest10mechanics
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g=~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
g ~ age
'
bf.age2 <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
info =~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest7biologicalscience + Stest8aeronautics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest26readingcomprehension
science =~ Stest1vocab + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest9electronics + Stest10mechanics
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g=~ Stest1vocab + Stest2literature + Stest3music + Stest4socialstudies + Stest5math + Stest6physicalscience + Stest7biologicalscience + Stest8aeronautics + Stest9electronics + Stest10mechanics + Stest11art + Stest12law + Stest13health + Stest14bible + Stest15theater + Stest16miscellaneous + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
g ~ age + age2
'
sem.age<-sem(bf.age, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("g=~Stest8aeronautics", "g=~Stest28mechanicalreasoning", "g=~Stest10mechanics", "g=~Stest9electronics", "g=~Stest6physicalscience", "g=~Stest4socialstudies", "Stest28mechanicalreasoning~1", "Stest8aeronautics~1", "Stest19disguisedwords~1", "Stest13health~1"))
fitMeasures(sem.age, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 6465.648 1125.000 0.000 0.952 0.040 0.057
## ecvi aic bic
## 1.129 462794.079 464143.509
Mc(sem.age)
## [1] 0.6447393
summary(sem.age, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 87 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 305
## Number of equality constraints 104
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 6465.648 5775.031
## Degrees of freedom 1125 1125
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.120
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 2985.167 2666.312
## 1 3480.481 3108.719
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.073 0.010 7.346 0.000 0.053
## Stst19d (.p2.) 0.255 0.014 17.793 0.000 0.227
## Stst20s (.p3.) 0.372 0.011 34.299 0.000 0.351
## Stst21c (.p4.) 0.337 0.010 33.154 0.000 0.317
## Stst22p (.p5.) 0.378 0.011 35.840 0.000 0.358
## Stst23n (.p6.) 0.394 0.012 31.919 0.000 0.370
## Stst24x (.p7.) 0.314 0.013 24.278 0.000 0.289
## Stst25w (.p8.) 0.121 0.010 11.989 0.000 0.101
## Stst26r (.p9.) 0.149 0.008 19.252 0.000 0.134
## Stst31b (.10.) 0.165 0.012 14.097 0.000 0.142
## Stst34r (.11.) 0.151 0.013 11.463 0.000 0.125
## math =~
## Stst5mt (.12.) 0.231 0.019 11.834 0.000 0.192
## Stst25w (.13.) 0.181 0.017 10.706 0.000 0.148
## Stst32r (.14.) 0.191 0.014 13.415 0.000 0.163
## Stst33h (.15.) 0.327 0.021 15.794 0.000 0.286
## Stst34r (.16.) 0.174 0.021 8.115 0.000 0.132
## speed =~
## Stst19d (.17.) 0.197 0.011 18.264 0.000 0.176
## Stst34r (.18.) 0.444 0.019 23.763 0.000 0.408
## Stst35t (.19.) 0.958 0.026 37.405 0.000 0.908
## Stst36c (.20.) 0.881 0.017 51.502 0.000 0.848
## Stst37b (.21.) 0.710 0.017 40.827 0.000 0.676
## info =~
## Stst1vc (.22.) 0.212 0.012 16.977 0.000 0.188
## Stst2lt (.23.) 0.297 0.012 25.144 0.000 0.274
## Stst3ms (.24.) 0.307 0.011 27.911 0.000 0.286
## Stst4sc (.25.) 0.181 0.013 13.636 0.000 0.155
## Stst7bl (.26.) 0.097 0.017 5.693 0.000 0.064
## Stst8rn (.27.) 0.138 0.018 7.828 0.000 0.104
## Stst11r (.28.) 0.323 0.014 23.366 0.000 0.296
## Stst12l (.29.) 0.156 0.012 12.967 0.000 0.132
## Stst13h (.30.) 0.231 0.018 12.941 0.000 0.196
## Stst14b (.31.) 0.252 0.012 20.404 0.000 0.228
## Stst15t (.32.) 0.330 0.012 27.517 0.000 0.307
## Stst16m (.33.) 0.217 0.013 17.045 0.000 0.192
## Stst19d (.34.) 0.181 0.016 11.649 0.000 0.151
## Stst26r (.35.) 0.206 0.010 20.133 0.000 0.186
## science =~
## Stst1vc (.36.) 0.124 0.015 8.310 0.000 0.095
## Stst5mt (.37.) 0.036 0.016 2.324 0.020 0.006
## Stst6ph (.38.) 0.047 0.013 3.759 0.000 0.023
## Stst7bl (.39.) 0.056 0.015 3.717 0.000 0.026
## Stst9lc (.40.) 0.224 0.017 13.555 0.000 0.191
## Stst10m (.41.) 0.350 0.015 23.478 0.000 0.321
## spatial =~
## Stst28m (.42.) 0.234 0.012 20.215 0.000 0.211
## Sts292D (.43.) 0.460 0.019 24.830 0.000 0.424
## Sts303D (.44.) 0.421 0.015 27.628 0.000 0.391
## Stst31b (.45.) 0.416 0.016 25.968 0.000 0.385
## Stst37b (.46.) 0.272 0.018 15.231 0.000 0.237
## g =~
## Stst1vc (.47.) 0.798 0.011 71.296 0.000 0.776
## Stst2lt (.48.) 0.714 0.011 63.375 0.000 0.692
## Stst3ms (.49.) 0.621 0.011 55.832 0.000 0.599
## Stst4sc 0.885 0.013 68.040 0.000 0.859
## Stst5mt (.51.) 0.623 0.013 49.581 0.000 0.598
## Stst6ph 0.668 0.014 49.228 0.000 0.641
## Stst7bl (.53.) 0.563 0.012 45.815 0.000 0.539
## Stst8rn 0.556 0.017 32.277 0.000 0.522
## Stst9lc 0.654 0.018 35.354 0.000 0.617
## Stst10m 0.578 0.015 38.660 0.000 0.548
## Stst11r (.57.) 0.663 0.011 58.986 0.000 0.641
## Stst12l (.58.) 0.530 0.012 44.998 0.000 0.507
## Stst13h (.59.) 0.760 0.012 62.707 0.000 0.737
## Stst14b (.60.) 0.527 0.012 45.140 0.000 0.504
## Stst15t (.61.) 0.516 0.012 44.698 0.000 0.493
## Stst16m (.62.) 0.630 0.012 54.178 0.000 0.607
## Stst19d (.63.) 0.573 0.012 47.156 0.000 0.549
## Stst20s (.64.) 0.561 0.012 46.411 0.000 0.537
## Stst21c (.65.) 0.652 0.011 60.228 0.000 0.630
## Stst22p (.66.) 0.715 0.012 61.014 0.000 0.692
## Stst23n (.67.) 0.731 0.013 54.976 0.000 0.705
## Stst24x (.68.) 0.571 0.013 42.982 0.000 0.545
## Stst25w (.69.) 0.445 0.011 39.296 0.000 0.423
## Stst26r (.70.) 0.860 0.010 85.780 0.000 0.841
## Stst28m 0.538 0.015 34.703 0.000 0.507
## Sts292D (.72.) 0.418 0.013 31.040 0.000 0.392
## Sts303D (.73.) 0.371 0.012 31.446 0.000 0.348
## Stst31b (.74.) 0.678 0.013 54.113 0.000 0.653
## Stst32r (.75.) 0.514 0.011 45.349 0.000 0.491
## Stst33h (.76.) 0.510 0.011 46.235 0.000 0.489
## Stst34r (.77.) 0.625 0.014 44.675 0.000 0.598
## Stst35t (.78.) 0.580 0.020 28.430 0.000 0.540
## Stst36c (.79.) 0.132 0.017 7.803 0.000 0.099
## Stst37b (.80.) 0.260 0.016 16.159 0.000 0.229
## ci.upper Std.lv Std.all
##
## 0.092 0.073 0.074
## 0.283 0.255 0.283
## 0.394 0.372 0.377
## 0.357 0.337 0.352
## 0.399 0.378 0.378
## 0.418 0.394 0.342
## 0.340 0.314 0.278
## 0.140 0.121 0.152
## 0.165 0.149 0.147
## 0.187 0.165 0.149
## 0.177 0.151 0.134
##
## 0.269 0.231 0.233
## 0.214 0.181 0.229
## 0.219 0.191 0.242
## 0.367 0.327 0.439
## 0.216 0.174 0.154
##
## 0.218 0.197 0.219
## 0.481 0.444 0.394
## 1.009 0.958 0.574
## 0.915 0.881 0.684
## 0.744 0.710 0.583
##
## 0.237 0.212 0.216
## 0.321 0.297 0.321
## 0.329 0.307 0.341
## 0.207 0.181 0.171
## 0.131 0.097 0.109
## 0.173 0.138 0.139
## 0.350 0.323 0.342
## 0.180 0.156 0.177
## 0.266 0.231 0.215
## 0.276 0.252 0.294
## 0.354 0.330 0.400
## 0.242 0.217 0.221
## 0.212 0.181 0.201
## 0.226 0.206 0.203
##
## 0.154 0.124 0.127
## 0.067 0.036 0.037
## 0.072 0.047 0.055
## 0.086 0.056 0.062
## 0.256 0.224 0.209
## 0.379 0.350 0.410
##
## 0.256 0.234 0.275
## 0.496 0.460 0.435
## 0.451 0.421 0.475
## 0.448 0.416 0.376
## 0.307 0.272 0.224
##
## 0.820 0.798 0.813
## 0.736 0.714 0.771
## 0.643 0.621 0.690
## 0.910 0.886 0.839
## 0.647 0.623 0.629
## 0.694 0.668 0.786
## 0.587 0.564 0.629
## 0.590 0.557 0.561
## 0.690 0.654 0.611
## 0.607 0.578 0.676
## 0.685 0.664 0.702
## 0.553 0.531 0.604
## 0.784 0.761 0.708
## 0.550 0.528 0.615
## 0.539 0.516 0.626
## 0.652 0.630 0.642
## 0.596 0.573 0.636
## 0.584 0.561 0.568
## 0.673 0.652 0.680
## 0.738 0.715 0.715
## 0.757 0.731 0.635
## 0.597 0.572 0.505
## 0.468 0.446 0.562
## 0.880 0.861 0.847
## 0.568 0.538 0.634
## 0.444 0.418 0.396
## 0.394 0.371 0.419
## 0.702 0.678 0.612
## 0.536 0.514 0.652
## 0.532 0.511 0.687
## 0.652 0.625 0.554
## 0.619 0.580 0.347
## 0.165 0.132 0.102
## 0.292 0.260 0.214
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age -0.026 0.015 -1.696 0.090 -0.056
## ci.upper Std.lv Std.all
##
## 0.004 -0.026 -0.038
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## science ~~
## spatial 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.139) -1.152 0.023 -50.045 0.000 -1.197
## .Stst19d -0.995 0.019 -53.535 0.000 -1.031
## .Stst20s (.141) -0.830 0.021 -40.314 0.000 -0.870
## .Stst21c (.142) -1.165 0.020 -59.480 0.000 -1.203
## .Stst22p (.143) -1.230 0.021 -58.004 0.000 -1.272
## .Stst23n (.144) -1.065 0.025 -42.875 0.000 -1.113
## .Stst24x (.145) -0.966 0.023 -41.647 0.000 -1.012
## .Stst25w (.146) -0.879 0.016 -55.949 0.000 -0.910
## .Stst26r (.147) -1.308 0.023 -57.173 0.000 -1.353
## .Stst31b (.148) -1.083 0.024 -45.516 0.000 -1.129
## .Stst34r (.149) -1.210 0.023 -52.285 0.000 -1.255
## .Stst5mt (.150) -0.774 0.021 -36.935 0.000 -0.815
## .Stst32r (.151) -1.049 0.017 -61.793 0.000 -1.082
## .Stst33h (.152) -0.881 0.016 -54.450 0.000 -0.913
## .Stst35t (.153) -0.678 0.033 -20.568 0.000 -0.743
## .Stst36c (.154) -0.022 0.026 -0.835 0.404 -0.072
## .Stst37b (.155) -0.316 0.024 -13.024 0.000 -0.363
## .Stst2lt (.156) -1.047 0.020 -51.732 0.000 -1.087
## .Stst3ms (.157) -0.908 0.019 -48.296 0.000 -0.945
## .Stst4sc (.158) -1.112 0.024 -46.918 0.000 -1.159
## .Stst7bl (.159) -0.604 0.021 -29.432 0.000 -0.644
## .Stst8rn -0.521 0.022 -23.655 0.000 -0.564
## .Stst11r (.161) -1.085 0.020 -55.033 0.000 -1.123
## .Stst12l (.162) -0.811 0.019 -42.705 0.000 -0.848
## .Stst13h -1.204 0.024 -51.047 0.000 -1.250
## .Stst14b (.164) -0.660 0.019 -35.384 0.000 -0.696
## .Stst15t (.165) -1.015 0.017 -60.066 0.000 -1.048
## .Stst16m (.166) -0.900 0.022 -41.792 0.000 -0.943
## .Stst6ph (.167) -0.723 0.020 -37.011 0.000 -0.761
## .Stst9lc (.168) -0.663 0.024 -27.847 0.000 -0.709
## .Stst10m (.169) -0.670 0.020 -32.934 0.000 -0.710
## .Stst28m -0.718 0.020 -36.686 0.000 -0.756
## .Sts292D (.171) -0.553 0.021 -26.175 0.000 -0.594
## .Sts303D (.172) -0.692 0.018 -37.801 0.000 -0.728
## ci.upper Std.lv Std.all
## -1.106 -1.152 -1.173
## -0.959 -0.995 -1.104
## -0.789 -0.830 -0.841
## -1.127 -1.165 -1.215
## -1.189 -1.230 -1.229
## -1.016 -1.065 -0.924
## -0.921 -0.966 -0.854
## -0.848 -0.879 -1.109
## -1.263 -1.308 -1.286
## -1.036 -1.083 -0.977
## -1.165 -1.210 -1.072
## -0.733 -0.774 -0.781
## -1.016 -1.049 -1.330
## -0.849 -0.881 -1.185
## -0.613 -0.678 -0.406
## 0.029 -0.022 -0.017
## -0.268 -0.316 -0.259
## -1.007 -1.047 -1.131
## -0.871 -0.908 -1.008
## -1.066 -1.112 -1.054
## -0.563 -0.604 -0.673
## -0.477 -0.521 -0.525
## -1.046 -1.085 -1.147
## -0.774 -0.811 -0.922
## -1.158 -1.204 -1.120
## -0.623 -0.660 -0.769
## -0.982 -1.015 -1.231
## -0.858 -0.900 -0.917
## -0.684 -0.723 -0.850
## -0.616 -0.663 -0.619
## -0.630 -0.670 -0.784
## -0.680 -0.718 -0.846
## -0.511 -0.553 -0.523
## -0.656 -0.692 -0.781
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.260 0.009 27.857 0.000 0.242
## .Stst19dsgsdwrd 0.347 0.014 25.361 0.000 0.320
## .Stest20spellng 0.521 0.017 30.020 0.000 0.487
## .Stest21cptlztn 0.380 0.016 24.464 0.000 0.350
## .Stest22puncttn 0.347 0.012 28.294 0.000 0.323
## .Stest23english 0.638 0.024 26.955 0.000 0.591
## .Stest24exprssn 0.854 0.025 33.741 0.000 0.805
## .Stst25wrdfnctn 0.383 0.012 31.523 0.000 0.359
## .Stst26rdngcmpr 0.228 0.009 25.713 0.000 0.210
## .Stst31bstrctrs 0.566 0.022 25.749 0.000 0.523
## .Stst34rthcmptt 0.633 0.031 20.458 0.000 0.572
## .Stest5math 0.538 0.020 26.416 0.000 0.499
## .Stst32rthrsnng 0.321 0.011 28.131 0.000 0.299
## .Stst33hghschlm 0.185 0.014 13.277 0.000 0.158
## .Stest35tblrdng 1.538 0.068 22.506 0.000 1.404
## .Stst36clrclchc 0.867 0.040 21.733 0.000 0.789
## .Stst37bjctnspc 0.836 0.034 24.871 0.000 0.770
## .Stest2literatr 0.259 0.009 29.130 0.000 0.241
## .Stest3music 0.330 0.012 27.364 0.000 0.307
## .Stest4soclstds 0.296 0.011 27.771 0.000 0.275
## .Stst7blgclscnc 0.474 0.014 33.563 0.000 0.446
## .Stest8aerontcs 0.655 0.018 37.380 0.000 0.621
## .Stest11art 0.349 0.012 28.292 0.000 0.325
## .Stest12law 0.467 0.014 33.300 0.000 0.439
## .Stest13health 0.522 0.016 32.017 0.000 0.490
## .Stest14bible 0.394 0.014 28.248 0.000 0.367
## .Stest15theater 0.305 0.011 27.057 0.000 0.283
## .Stest16mscllns 0.520 0.017 31.065 0.000 0.487
## .Stst6physclscn 0.275 0.010 27.302 0.000 0.255
## .Stest9elctrncs 0.669 0.028 23.753 0.000 0.614
## .Stest10mechncs 0.274 0.016 16.939 0.000 0.242
## .Stst28mchnclrs 0.376 0.015 25.850 0.000 0.348
## .Stst29vslztn2D 0.732 0.027 27.235 0.000 0.679
## .Stst30vslztn3D 0.470 0.018 25.456 0.000 0.434
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.279 0.260 0.270
## 0.373 0.347 0.427
## 0.555 0.521 0.535
## 0.411 0.380 0.414
## 0.371 0.347 0.346
## 0.684 0.638 0.480
## 0.904 0.854 0.667
## 0.406 0.383 0.609
## 0.245 0.228 0.220
## 0.609 0.566 0.462
## 0.694 0.633 0.497
## 0.578 0.538 0.549
## 0.343 0.321 0.516
## 0.212 0.185 0.335
## 1.672 1.538 0.551
## 0.945 0.867 0.522
## 0.901 0.836 0.564
## 0.276 0.259 0.302
## 0.354 0.330 0.407
## 0.317 0.296 0.266
## 0.501 0.474 0.589
## 0.690 0.655 0.666
## 0.373 0.349 0.390
## 0.494 0.467 0.604
## 0.554 0.522 0.452
## 0.421 0.394 0.536
## 0.327 0.305 0.448
## 0.553 0.520 0.539
## 0.294 0.275 0.380
## 0.725 0.669 0.583
## 0.306 0.274 0.375
## 0.405 0.376 0.522
## 0.784 0.732 0.654
## 0.506 0.470 0.598
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 0.999 0.999
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.073 0.010 7.346 0.000 0.053
## Stst19d (.p2.) 0.255 0.014 17.793 0.000 0.227
## Stst20s (.p3.) 0.372 0.011 34.299 0.000 0.351
## Stst21c (.p4.) 0.337 0.010 33.154 0.000 0.317
## Stst22p (.p5.) 0.378 0.011 35.840 0.000 0.358
## Stst23n (.p6.) 0.394 0.012 31.919 0.000 0.370
## Stst24x (.p7.) 0.314 0.013 24.278 0.000 0.289
## Stst25w (.p8.) 0.121 0.010 11.989 0.000 0.101
## Stst26r (.p9.) 0.149 0.008 19.252 0.000 0.134
## Stst31b (.10.) 0.165 0.012 14.097 0.000 0.142
## Stst34r (.11.) 0.151 0.013 11.463 0.000 0.125
## math =~
## Stst5mt (.12.) 0.231 0.019 11.834 0.000 0.192
## Stst25w (.13.) 0.181 0.017 10.706 0.000 0.148
## Stst32r (.14.) 0.191 0.014 13.415 0.000 0.163
## Stst33h (.15.) 0.327 0.021 15.794 0.000 0.286
## Stst34r (.16.) 0.174 0.021 8.115 0.000 0.132
## speed =~
## Stst19d (.17.) 0.197 0.011 18.264 0.000 0.176
## Stst34r (.18.) 0.444 0.019 23.763 0.000 0.408
## Stst35t (.19.) 0.958 0.026 37.405 0.000 0.908
## Stst36c (.20.) 0.881 0.017 51.502 0.000 0.848
## Stst37b (.21.) 0.710 0.017 40.827 0.000 0.676
## info =~
## Stst1vc (.22.) 0.212 0.012 16.977 0.000 0.188
## Stst2lt (.23.) 0.297 0.012 25.144 0.000 0.274
## Stst3ms (.24.) 0.307 0.011 27.911 0.000 0.286
## Stst4sc (.25.) 0.181 0.013 13.636 0.000 0.155
## Stst7bl (.26.) 0.097 0.017 5.693 0.000 0.064
## Stst8rn (.27.) 0.138 0.018 7.828 0.000 0.104
## Stst11r (.28.) 0.323 0.014 23.366 0.000 0.296
## Stst12l (.29.) 0.156 0.012 12.967 0.000 0.132
## Stst13h (.30.) 0.231 0.018 12.941 0.000 0.196
## Stst14b (.31.) 0.252 0.012 20.404 0.000 0.228
## Stst15t (.32.) 0.330 0.012 27.517 0.000 0.307
## Stst16m (.33.) 0.217 0.013 17.045 0.000 0.192
## Stst19d (.34.) 0.181 0.016 11.649 0.000 0.151
## Stst26r (.35.) 0.206 0.010 20.133 0.000 0.186
## science =~
## Stst1vc (.36.) 0.124 0.015 8.310 0.000 0.095
## Stst5mt (.37.) 0.036 0.016 2.324 0.020 0.006
## Stst6ph (.38.) 0.047 0.013 3.759 0.000 0.023
## Stst7bl (.39.) 0.056 0.015 3.717 0.000 0.026
## Stst9lc (.40.) 0.224 0.017 13.555 0.000 0.191
## Stst10m (.41.) 0.350 0.015 23.478 0.000 0.321
## spatial =~
## Stst28m (.42.) 0.234 0.012 20.215 0.000 0.211
## Sts292D (.43.) 0.460 0.019 24.830 0.000 0.424
## Sts303D (.44.) 0.421 0.015 27.628 0.000 0.391
## Stst31b (.45.) 0.416 0.016 25.968 0.000 0.385
## Stst37b (.46.) 0.272 0.018 15.231 0.000 0.237
## g =~
## Stst1vc (.47.) 0.798 0.011 71.296 0.000 0.776
## Stst2lt (.48.) 0.714 0.011 63.375 0.000 0.692
## Stst3ms (.49.) 0.621 0.011 55.832 0.000 0.599
## Stst4sc 0.755 0.012 63.776 0.000 0.732
## Stst5mt (.51.) 0.623 0.013 49.581 0.000 0.598
## Stst6ph 0.491 0.013 37.495 0.000 0.466
## Stst7bl (.53.) 0.563 0.012 45.815 0.000 0.539
## Stst8rn 0.235 0.017 13.812 0.000 0.201
## Stst9lc 0.335 0.019 18.029 0.000 0.299
## Stst10m 0.357 0.011 31.929 0.000 0.335
## Stst11r (.57.) 0.663 0.011 58.986 0.000 0.641
## Stst12l (.58.) 0.530 0.012 44.998 0.000 0.507
## Stst13h (.59.) 0.760 0.012 62.707 0.000 0.737
## Stst14b (.60.) 0.527 0.012 45.140 0.000 0.504
## Stst15t (.61.) 0.516 0.012 44.698 0.000 0.493
## Stst16m (.62.) 0.630 0.012 54.178 0.000 0.607
## Stst19d (.63.) 0.573 0.012 47.156 0.000 0.549
## Stst20s (.64.) 0.561 0.012 46.411 0.000 0.537
## Stst21c (.65.) 0.652 0.011 60.228 0.000 0.630
## Stst22p (.66.) 0.715 0.012 61.014 0.000 0.692
## Stst23n (.67.) 0.731 0.013 54.976 0.000 0.705
## Stst24x (.68.) 0.571 0.013 42.982 0.000 0.545
## Stst25w (.69.) 0.445 0.011 39.296 0.000 0.423
## Stst26r (.70.) 0.860 0.010 85.780 0.000 0.841
## Stst28m 0.338 0.012 28.460 0.000 0.315
## Sts292D (.72.) 0.418 0.013 31.040 0.000 0.392
## Sts303D (.73.) 0.371 0.012 31.446 0.000 0.348
## Stst31b (.74.) 0.678 0.013 54.113 0.000 0.653
## Stst32r (.75.) 0.514 0.011 45.349 0.000 0.491
## Stst33h (.76.) 0.510 0.011 46.235 0.000 0.489
## Stst34r (.77.) 0.625 0.014 44.675 0.000 0.598
## Stst35t (.78.) 0.580 0.020 28.430 0.000 0.540
## Stst36c (.79.) 0.132 0.017 7.803 0.000 0.099
## Stst37b (.80.) 0.260 0.016 16.159 0.000 0.229
## ci.upper Std.lv Std.all
##
## 0.092 0.073 0.075
## 0.283 0.255 0.279
## 0.394 0.372 0.382
## 0.357 0.337 0.337
## 0.399 0.378 0.384
## 0.418 0.394 0.353
## 0.340 0.314 0.285
## 0.140 0.121 0.154
## 0.165 0.149 0.148
## 0.187 0.165 0.148
## 0.177 0.151 0.131
##
## 0.269 0.231 0.226
## 0.214 0.181 0.231
## 0.219 0.191 0.247
## 0.367 0.327 0.451
## 0.216 0.174 0.151
##
## 0.218 0.197 0.216
## 0.481 0.444 0.385
## 1.009 0.958 0.590
## 0.915 0.881 0.685
## 0.744 0.710 0.616
##
## 0.237 0.212 0.217
## 0.321 0.297 0.324
## 0.329 0.307 0.339
## 0.207 0.181 0.195
## 0.131 0.097 0.109
## 0.173 0.138 0.166
## 0.350 0.323 0.335
## 0.180 0.156 0.182
## 0.266 0.231 0.208
## 0.276 0.252 0.286
## 0.354 0.330 0.378
## 0.242 0.217 0.227
## 0.212 0.181 0.198
## 0.226 0.206 0.204
##
## 0.154 0.124 0.127
## 0.067 0.036 0.035
## 0.072 0.047 0.067
## 0.086 0.056 0.062
## 0.256 0.224 0.231
## 0.379 0.350 0.551
##
## 0.256 0.234 0.366
## 0.496 0.460 0.451
## 0.451 0.421 0.522
## 0.448 0.416 0.374
## 0.307 0.272 0.236
##
## 0.820 0.798 0.816
## 0.736 0.714 0.778
## 0.643 0.621 0.686
## 0.779 0.755 0.816
## 0.647 0.623 0.610
## 0.517 0.491 0.696
## 0.587 0.563 0.628
## 0.268 0.235 0.281
## 0.372 0.335 0.346
## 0.379 0.357 0.562
## 0.685 0.663 0.687
## 0.553 0.530 0.620
## 0.784 0.760 0.684
## 0.550 0.527 0.599
## 0.539 0.516 0.590
## 0.652 0.630 0.660
## 0.596 0.573 0.626
## 0.584 0.561 0.574
## 0.673 0.652 0.652
## 0.738 0.715 0.726
## 0.757 0.731 0.655
## 0.597 0.571 0.518
## 0.468 0.445 0.567
## 0.880 0.861 0.854
## 0.361 0.338 0.530
## 0.444 0.418 0.410
## 0.394 0.371 0.459
## 0.702 0.678 0.609
## 0.536 0.514 0.664
## 0.532 0.510 0.704
## 0.652 0.625 0.541
## 0.619 0.580 0.357
## 0.165 0.132 0.102
## 0.292 0.260 0.226
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.014 0.013 1.113 0.266 -0.011
## ci.upper Std.lv Std.all
##
## 0.039 0.014 0.018
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## science ~~
## spatial 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.139) -1.152 0.023 -50.045 0.000 -1.197
## .Stst19d -1.340 0.041 -33.090 0.000 -1.420
## .Stst20s (.141) -0.830 0.021 -40.314 0.000 -0.870
## .Stst21c (.142) -1.165 0.020 -59.480 0.000 -1.203
## .Stst22p (.143) -1.230 0.021 -58.004 0.000 -1.272
## .Stst23n (.144) -1.065 0.025 -42.875 0.000 -1.113
## .Stst24x (.145) -0.966 0.023 -41.647 0.000 -1.012
## .Stst25w (.146) -0.879 0.016 -55.949 0.000 -0.910
## .Stst26r (.147) -1.308 0.023 -57.173 0.000 -1.353
## .Stst31b (.148) -1.083 0.024 -45.516 0.000 -1.129
## .Stst34r (.149) -1.210 0.023 -52.285 0.000 -1.255
## .Stst5mt (.150) -0.774 0.021 -36.935 0.000 -0.815
## .Stst32r (.151) -1.049 0.017 -61.793 0.000 -1.082
## .Stst33h (.152) -0.881 0.016 -54.450 0.000 -0.913
## .Stst35t (.153) -0.678 0.033 -20.568 0.000 -0.743
## .Stst36c (.154) -0.022 0.026 -0.835 0.404 -0.072
## .Stst37b (.155) -0.316 0.024 -13.024 0.000 -0.363
## .Stst2lt (.156) -1.047 0.020 -51.732 0.000 -1.087
## .Stst3ms (.157) -0.908 0.019 -48.296 0.000 -0.945
## .Stst4sc (.158) -1.112 0.024 -46.918 0.000 -1.159
## .Stst7bl (.159) -0.604 0.021 -29.432 0.000 -0.644
## .Stst8rn -0.995 0.029 -34.078 0.000 -1.052
## .Stst11r (.161) -1.085 0.020 -55.033 0.000 -1.123
## .Stst12l (.162) -0.811 0.019 -42.705 0.000 -0.848
## .Stst13h -0.931 0.034 -27.619 0.000 -0.997
## .Stst14b (.164) -0.660 0.019 -35.384 0.000 -0.696
## .Stst15t (.165) -1.015 0.017 -60.066 0.000 -1.048
## .Stst16m (.166) -0.900 0.022 -41.792 0.000 -0.943
## .Stst6ph (.167) -0.723 0.020 -37.011 0.000 -0.761
## .Stst9lc (.168) -0.663 0.024 -27.847 0.000 -0.709
## .Stst10m (.169) -0.670 0.020 -32.934 0.000 -0.710
## .Stst28m -1.090 0.018 -60.035 0.000 -1.126
## .Sts292D (.171) -0.553 0.021 -26.175 0.000 -0.594
## .Sts303D (.172) -0.692 0.018 -37.801 0.000 -0.728
## english 1.707 0.098 17.466 0.000 1.515
## math 0.569 0.104 5.475 0.000 0.365
## speed 0.428 0.038 11.360 0.000 0.354
## info 1.203 0.103 11.685 0.000 1.001
## science -1.505 0.085 -17.787 0.000 -1.671
## spatial -0.301 0.056 -5.336 0.000 -0.411
## .g -0.479 0.054 -8.877 0.000 -0.584
## ci.upper Std.lv Std.all
## -1.106 -1.152 -1.178
## -1.261 -1.340 -1.466
## -0.789 -0.830 -0.850
## -1.127 -1.165 -1.166
## -1.189 -1.230 -1.249
## -1.016 -1.065 -0.954
## -0.921 -0.966 -0.877
## -0.848 -0.879 -1.119
## -1.263 -1.308 -1.298
## -1.036 -1.083 -0.972
## -1.165 -1.210 -1.048
## -0.733 -0.774 -0.757
## -1.016 -1.049 -1.356
## -0.849 -0.881 -1.216
## -0.613 -0.678 -0.417
## 0.029 -0.022 -0.017
## -0.268 -0.316 -0.274
## -1.007 -1.047 -1.141
## -0.871 -0.908 -1.003
## -1.066 -1.112 -1.201
## -0.563 -0.604 -0.673
## -0.938 -0.995 -1.192
## -1.046 -1.085 -1.124
## -0.774 -0.811 -0.948
## -0.865 -0.931 -0.837
## -0.623 -0.660 -0.750
## -0.982 -1.015 -1.161
## -0.858 -0.900 -0.943
## -0.684 -0.723 -1.023
## -0.616 -0.663 -0.684
## -0.630 -0.670 -1.055
## -1.055 -1.090 -1.709
## -0.511 -0.553 -0.541
## -0.656 -0.692 -0.857
## 1.898 1.707 1.707
## 0.772 0.569 0.569
## 0.502 0.428 0.428
## 1.405 1.203 1.203
## -1.339 -1.505 -1.505
## -0.190 -0.301 -0.301
## -0.373 -0.479 -0.479
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.254 0.008 33.426 0.000 0.239
## .Stst19dsgsdwrd 0.371 0.011 32.419 0.000 0.349
## .Stest20spellng 0.499 0.014 35.667 0.000 0.472
## .Stest21cptlztn 0.460 0.013 34.550 0.000 0.434
## .Stest22puncttn 0.316 0.011 30.025 0.000 0.295
## .Stest23english 0.555 0.017 32.474 0.000 0.521
## .Stest24exprssn 0.790 0.021 36.970 0.000 0.748
## .Stst25wrdfnctn 0.371 0.011 33.984 0.000 0.350
## .Stst26rdngcmpr 0.210 0.007 29.607 0.000 0.196
## .Stst31bstrctrs 0.581 0.017 33.551 0.000 0.547
## .Stst34rthcmptt 0.693 0.026 26.209 0.000 0.641
## .Stest5math 0.601 0.017 35.528 0.000 0.568
## .Stst32rthrsnng 0.298 0.009 34.080 0.000 0.281
## .Stst33hghschlm 0.158 0.013 12.556 0.000 0.133
## .Stest35tblrdng 1.385 0.057 24.187 0.000 1.273
## .Stst36clrclchc 0.863 0.032 27.325 0.000 0.801
## .Stst37bjctnspc 0.683 0.026 25.962 0.000 0.631
## .Stest2literatr 0.244 0.007 35.077 0.000 0.230
## .Stest3music 0.339 0.009 36.816 0.000 0.321
## .Stest4soclstds 0.254 0.007 35.451 0.000 0.240
## .Stst7blgclscnc 0.475 0.012 38.172 0.000 0.451
## .Stest8aerontcs 0.622 0.011 58.386 0.000 0.602
## .Stest11art 0.387 0.011 35.939 0.000 0.366
## .Stest12law 0.426 0.010 40.630 0.000 0.405
## .Stest13health 0.605 0.015 41.382 0.000 0.576
## .Stest14bible 0.434 0.013 34.051 0.000 0.409
## .Stest15theater 0.390 0.010 37.265 0.000 0.369
## .Stest16mscllns 0.468 0.012 38.292 0.000 0.444
## .Stst6physclscn 0.255 0.007 35.719 0.000 0.241
## .Stest9elctrncs 0.777 0.019 40.205 0.000 0.739
## .Stest10mechncs 0.153 0.012 12.932 0.000 0.130
## .Stst28mchnclrs 0.238 0.007 36.550 0.000 0.225
## .Stst29vslztn2D 0.655 0.020 32.088 0.000 0.615
## .Stst30vslztn3D 0.337 0.012 27.469 0.000 0.313
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.269 0.254 0.265
## 0.393 0.371 0.444
## 0.527 0.499 0.524
## 0.486 0.460 0.461
## 0.337 0.316 0.326
## 0.588 0.555 0.446
## 0.832 0.790 0.650
## 0.393 0.371 0.602
## 0.224 0.210 0.207
## 0.615 0.581 0.468
## 0.744 0.693 0.519
## 0.634 0.601 0.576
## 0.315 0.298 0.498
## 0.182 0.158 0.300
## 1.497 1.385 0.525
## 0.925 0.863 0.521
## 0.734 0.683 0.514
## 0.258 0.244 0.290
## 0.357 0.339 0.414
## 0.268 0.254 0.296
## 0.500 0.475 0.590
## 0.643 0.622 0.893
## 0.408 0.387 0.415
## 0.447 0.426 0.582
## 0.633 0.605 0.489
## 0.459 0.434 0.560
## 0.410 0.390 0.509
## 0.492 0.468 0.513
## 0.269 0.255 0.512
## 0.815 0.777 0.827
## 0.176 0.153 0.380
## 0.251 0.238 0.585
## 0.695 0.655 0.629
## 0.361 0.337 0.517
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
sem.age2<-sem(bf.age2, data=dgroup, group="sex", meanstructure=TRUE, sampling.weights="BY_WTA", std.lv=T, orthogonal=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("g=~Stest8aeronautics", "g=~Stest28mechanicalreasoning", "g=~Stest10mechanics", "g=~Stest9electronics", "g=~Stest6physicalscience", "g=~Stest4socialstudies", "Stest28mechanicalreasoning~1", "Stest8aeronautics~1", "Stest19disguisedwords~1", "Stest13health~1"))
fitMeasures(sem.age2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 6630.171 1191.000 0.000 0.951 0.039 0.054
## ecvi aic bic
## 1.156 462748.682 464111.540
Mc(sem.age2)
## [1] 0.63954
summary(sem.age2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 94 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 307
## Number of equality constraints 104
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 6630.171 5937.070
## Degrees of freedom 1191 1191
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.117
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 3049.383 2730.608
## 1 3580.788 3206.462
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.075 0.010 7.640 0.000 0.056
## Stst19d (.p2.) 0.256 0.014 17.843 0.000 0.228
## Stst20s (.p3.) 0.372 0.011 34.357 0.000 0.350
## Stst21c (.p4.) 0.337 0.010 33.402 0.000 0.317
## Stst22p (.p5.) 0.378 0.011 35.964 0.000 0.358
## Stst23n (.p6.) 0.394 0.012 32.110 0.000 0.370
## Stst24x (.p7.) 0.314 0.013 24.461 0.000 0.289
## Stst25w (.p8.) 0.120 0.010 11.713 0.000 0.100
## Stst26r (.p9.) 0.150 0.008 19.393 0.000 0.135
## Stst31b (.10.) 0.164 0.012 14.245 0.000 0.142
## Stst34r (.11.) 0.150 0.013 11.445 0.000 0.124
## math =~
## Stst5mt (.12.) 0.233 0.020 11.635 0.000 0.194
## Stst25w (.13.) 0.182 0.017 10.967 0.000 0.149
## Stst32r (.14.) 0.192 0.014 13.752 0.000 0.165
## Stst33h (.15.) 0.324 0.021 15.547 0.000 0.283
## Stst34r (.16.) 0.171 0.022 7.841 0.000 0.129
## speed =~
## Stst19d (.17.) 0.197 0.011 18.274 0.000 0.176
## Stst34r (.18.) 0.444 0.019 23.762 0.000 0.408
## Stst35t (.19.) 0.959 0.026 37.452 0.000 0.909
## Stst36c (.20.) 0.881 0.017 51.474 0.000 0.847
## Stst37b (.21.) 0.709 0.017 40.786 0.000 0.675
## info =~
## Stst1vc (.22.) 0.215 0.013 17.158 0.000 0.190
## Stst2lt (.23.) 0.297 0.012 25.256 0.000 0.274
## Stst3ms (.24.) 0.307 0.011 28.002 0.000 0.285
## Stst4sc (.25.) 0.179 0.013 13.379 0.000 0.153
## Stst7bl (.26.) 0.100 0.017 5.740 0.000 0.066
## Stst8rn (.27.) 0.139 0.018 7.864 0.000 0.104
## Stst11r (.28.) 0.321 0.014 23.383 0.000 0.294
## Stst12l (.29.) 0.156 0.012 13.124 0.000 0.133
## Stst13h (.30.) 0.231 0.018 12.914 0.000 0.196
## Stst14b (.31.) 0.253 0.012 20.848 0.000 0.229
## Stst15t (.32.) 0.328 0.012 27.348 0.000 0.305
## Stst16m (.33.) 0.217 0.013 17.214 0.000 0.193
## Stst19d (.34.) 0.182 0.016 11.682 0.000 0.152
## Stst26r (.35.) 0.206 0.010 20.214 0.000 0.186
## science =~
## Stst1vc (.36.) 0.124 0.015 8.230 0.000 0.095
## Stst5mt (.37.) 0.035 0.016 2.177 0.030 0.003
## Stst6ph (.38.) 0.050 0.012 4.026 0.000 0.026
## Stst7bl (.39.) 0.054 0.015 3.577 0.000 0.024
## Stst9lc (.40.) 0.230 0.016 13.997 0.000 0.198
## Stst10m (.41.) 0.347 0.014 24.092 0.000 0.319
## spatial =~
## Stst28m (.42.) 0.234 0.012 20.208 0.000 0.211
## Sts292D (.43.) 0.459 0.019 24.692 0.000 0.423
## Sts303D (.44.) 0.422 0.015 27.592 0.000 0.392
## Stst31b (.45.) 0.416 0.016 25.896 0.000 0.384
## Stst37b (.46.) 0.273 0.018 15.213 0.000 0.238
## g =~
## Stst1vc (.47.) 0.793 0.011 71.310 0.000 0.771
## Stst2lt (.48.) 0.710 0.011 63.473 0.000 0.689
## Stst3ms (.49.) 0.618 0.011 55.993 0.000 0.597
## Stst4sc 0.878 0.013 67.468 0.000 0.852
## Stst5mt (.51.) 0.619 0.012 49.601 0.000 0.595
## Stst6ph 0.665 0.013 49.682 0.000 0.638
## Stst7bl (.53.) 0.560 0.012 45.653 0.000 0.536
## Stst8rn 0.553 0.017 32.249 0.000 0.519
## Stst9lc 0.650 0.018 35.539 0.000 0.614
## Stst10m 0.573 0.015 38.258 0.000 0.544
## Stst11r (.57.) 0.661 0.011 59.250 0.000 0.639
## Stst12l (.58.) 0.528 0.012 45.112 0.000 0.505
## Stst13h (.59.) 0.757 0.012 62.859 0.000 0.733
## Stst14b (.60.) 0.524 0.012 45.089 0.000 0.501
## Stst15t (.61.) 0.514 0.011 44.836 0.000 0.492
## Stst16m (.62.) 0.627 0.012 54.433 0.000 0.604
## Stst19d (.63.) 0.570 0.012 47.142 0.000 0.546
## Stst20s (.64.) 0.558 0.012 46.618 0.000 0.535
## Stst21c (.65.) 0.649 0.011 60.114 0.000 0.627
## Stst22p (.66.) 0.711 0.012 61.113 0.000 0.689
## Stst23n (.67.) 0.727 0.013 54.954 0.000 0.702
## Stst24x (.68.) 0.569 0.013 43.083 0.000 0.543
## Stst25w (.69.) 0.444 0.011 39.350 0.000 0.421
## Stst26r (.70.) 0.856 0.010 86.066 0.000 0.837
## Stst28m 0.535 0.015 34.875 0.000 0.505
## Sts292D (.72.) 0.417 0.013 31.085 0.000 0.390
## Sts303D (.73.) 0.369 0.012 31.455 0.000 0.346
## Stst31b (.74.) 0.675 0.012 54.242 0.000 0.651
## Stst32r (.75.) 0.511 0.011 45.459 0.000 0.489
## Stst33h (.76.) 0.508 0.011 46.383 0.000 0.487
## Stst34r (.77.) 0.623 0.014 44.768 0.000 0.596
## Stst35t (.78.) 0.576 0.020 28.405 0.000 0.537
## Stst36c (.79.) 0.132 0.017 7.832 0.000 0.099
## Stst37b (.80.) 0.260 0.016 16.203 0.000 0.228
## ci.upper Std.lv Std.all
##
## 0.095 0.075 0.077
## 0.284 0.256 0.284
## 0.393 0.372 0.376
## 0.357 0.337 0.351
## 0.399 0.378 0.377
## 0.418 0.394 0.341
## 0.339 0.314 0.277
## 0.140 0.120 0.151
## 0.165 0.150 0.147
## 0.187 0.164 0.148
## 0.176 0.150 0.133
##
## 0.272 0.233 0.235
## 0.215 0.182 0.229
## 0.220 0.192 0.243
## 0.365 0.324 0.435
## 0.214 0.171 0.152
##
## 0.219 0.197 0.219
## 0.481 0.444 0.393
## 1.010 0.959 0.574
## 0.914 0.881 0.683
## 0.743 0.709 0.583
##
## 0.239 0.215 0.218
## 0.320 0.297 0.320
## 0.328 0.307 0.340
## 0.205 0.179 0.169
## 0.134 0.100 0.111
## 0.174 0.139 0.140
## 0.348 0.321 0.339
## 0.180 0.156 0.177
## 0.266 0.231 0.214
## 0.277 0.253 0.295
## 0.352 0.328 0.398
## 0.242 0.217 0.221
## 0.213 0.182 0.202
## 0.226 0.206 0.202
##
## 0.154 0.124 0.126
## 0.066 0.035 0.035
## 0.074 0.050 0.059
## 0.084 0.054 0.060
## 0.262 0.230 0.215
## 0.375 0.347 0.406
##
## 0.256 0.234 0.275
## 0.495 0.459 0.434
## 0.452 0.422 0.476
## 0.447 0.416 0.375
## 0.308 0.273 0.224
##
## 0.815 0.800 0.813
## 0.732 0.717 0.773
## 0.640 0.624 0.692
## 0.903 0.886 0.840
## 0.644 0.625 0.630
## 0.691 0.671 0.786
## 0.584 0.565 0.629
## 0.587 0.558 0.562
## 0.686 0.656 0.612
## 0.603 0.579 0.676
## 0.683 0.667 0.704
## 0.551 0.533 0.605
## 0.781 0.764 0.710
## 0.547 0.529 0.616
## 0.537 0.519 0.628
## 0.649 0.632 0.643
## 0.593 0.575 0.637
## 0.582 0.563 0.570
## 0.670 0.654 0.682
## 0.734 0.718 0.716
## 0.753 0.734 0.636
## 0.595 0.574 0.507
## 0.466 0.448 0.564
## 0.876 0.864 0.848
## 0.565 0.540 0.635
## 0.443 0.420 0.397
## 0.392 0.372 0.420
## 0.699 0.681 0.614
## 0.533 0.516 0.653
## 0.530 0.513 0.689
## 0.650 0.628 0.556
## 0.616 0.581 0.348
## 0.165 0.133 0.103
## 0.291 0.262 0.215
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.002 0.017 0.101 0.919 -0.031
## age2 -0.048 0.008 -6.301 0.000 -0.063
## ci.upper Std.lv Std.all
##
## 0.034 0.002 0.002
## -0.033 -0.048 -0.135
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## science ~~
## spatial 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.142) -1.073 0.028 -38.718 0.000 -1.127
## .Stst19d -0.939 0.022 -43.371 0.000 -0.982
## .Stst20s (.144) -0.776 0.023 -33.497 0.000 -0.821
## .Stst21c (.145) -1.101 0.023 -47.436 0.000 -1.147
## .Stst22p (.146) -1.160 0.026 -45.284 0.000 -1.211
## .Stst23n (.147) -0.994 0.029 -34.431 0.000 -1.050
## .Stst24x (.148) -0.911 0.026 -35.261 0.000 -0.961
## .Stst25w (.149) -0.836 0.018 -46.017 0.000 -0.872
## .Stst26r (.150) -1.223 0.028 -43.097 0.000 -1.279
## .Stst31b (.151) -1.016 0.027 -37.096 0.000 -1.070
## .Stst34r (.152) -1.148 0.027 -43.103 0.000 -1.201
## .Stst5mt (.153) -0.712 0.024 -29.296 0.000 -0.760
## .Stst32r (.154) -0.998 0.020 -49.265 0.000 -1.037
## .Stst33h (.155) -0.832 0.020 -42.592 0.000 -0.870
## .Stst35t (.156) -0.618 0.035 -17.797 0.000 -0.686
## .Stst36c (.157) -0.010 0.026 -0.375 0.708 -0.060
## .Stst37b (.158) -0.292 0.025 -11.800 0.000 -0.340
## .Stst2lt (.159) -0.977 0.025 -39.857 0.000 -1.025
## .Stst3ms (.160) -0.848 0.023 -37.626 0.000 -0.892
## .Stst4sc (.161) -1.027 0.029 -35.331 0.000 -1.084
## .Stst7bl (.162) -0.547 0.024 -23.252 0.000 -0.593
## .Stst8rn -0.466 0.025 -19.029 0.000 -0.514
## .Stst11r (.164) -1.019 0.024 -43.017 0.000 -1.066
## .Stst12l (.165) -0.758 0.022 -34.153 0.000 -0.801
## .Stst13h -1.130 0.028 -40.757 0.000 -1.184
## .Stst14b (.167) -0.610 0.021 -28.781 0.000 -0.652
## .Stst15t (.168) -0.966 0.020 -49.324 0.000 -1.005
## .Stst16m (.169) -0.838 0.025 -33.100 0.000 -0.887
## .Stst6ph (.170) -0.658 0.024 -27.670 0.000 -0.705
## .Stst9lc (.171) -0.601 0.027 -22.499 0.000 -0.653
## .Stst10m (.172) -0.614 0.023 -26.173 0.000 -0.660
## .Stst28m -0.665 0.023 -29.398 0.000 -0.710
## .Sts292D (.174) -0.511 0.023 -22.547 0.000 -0.556
## .Sts303D (.175) -0.656 0.020 -32.897 0.000 -0.695
## ci.upper Std.lv Std.all
## -1.018 -1.073 -1.090
## -0.897 -0.939 -1.041
## -0.730 -0.776 -0.785
## -1.056 -1.101 -1.147
## -1.110 -1.160 -1.157
## -0.937 -0.994 -0.861
## -0.860 -0.911 -0.804
## -0.801 -0.836 -1.054
## -1.168 -1.223 -1.200
## -0.962 -1.016 -0.916
## -1.096 -1.148 -1.016
## -0.665 -0.712 -0.718
## -0.958 -0.998 -1.264
## -0.793 -0.832 -1.117
## -0.550 -0.618 -0.370
## 0.041 -0.010 -0.008
## -0.243 -0.292 -0.240
## -0.929 -0.977 -1.053
## -0.804 -0.848 -0.940
## -0.970 -1.027 -0.974
## -0.501 -0.547 -0.609
## -0.418 -0.466 -0.470
## -0.973 -1.019 -1.076
## -0.714 -0.758 -0.861
## -1.075 -1.130 -1.050
## -0.569 -0.610 -0.711
## -0.928 -0.966 -1.170
## -0.788 -0.838 -0.852
## -0.611 -0.658 -0.772
## -0.548 -0.601 -0.560
## -0.568 -0.614 -0.718
## -0.621 -0.665 -0.783
## -0.467 -0.511 -0.483
## -0.617 -0.656 -0.740
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.260 0.009 27.773 0.000 0.242
## .Stst19dsgsdwrd 0.346 0.014 25.321 0.000 0.320
## .Stest20spellng 0.521 0.017 30.051 0.000 0.487
## .Stest21cptlztn 0.380 0.016 24.466 0.000 0.350
## .Stest22puncttn 0.347 0.012 28.300 0.000 0.323
## .Stest23english 0.638 0.024 26.958 0.000 0.591
## .Stest24exprssn 0.854 0.025 33.746 0.000 0.805
## .Stst25wrdfnctn 0.382 0.012 31.582 0.000 0.359
## .Stst26rdngcmpr 0.228 0.009 25.716 0.000 0.210
## .Stst31bstrctrs 0.566 0.022 25.758 0.000 0.523
## .Stst34rthcmptt 0.634 0.031 20.456 0.000 0.573
## .Stest5math 0.538 0.020 26.347 0.000 0.498
## .Stst32rthrsnng 0.321 0.011 28.085 0.000 0.298
## .Stst33hghschlm 0.186 0.014 13.468 0.000 0.159
## .Stest35tblrdng 1.537 0.068 22.478 0.000 1.403
## .Stst36clrclchc 0.868 0.040 21.745 0.000 0.789
## .Stst37bjctnspc 0.836 0.034 24.879 0.000 0.770
## .Stest2literatr 0.259 0.009 29.123 0.000 0.241
## .Stest3music 0.331 0.012 27.382 0.000 0.307
## .Stest4soclstds 0.296 0.011 27.741 0.000 0.275
## .Stst7blgclscnc 0.474 0.014 33.574 0.000 0.446
## .Stest8aerontcs 0.656 0.018 37.385 0.000 0.621
## .Stest11art 0.350 0.012 28.332 0.000 0.325
## .Stest12law 0.467 0.014 33.312 0.000 0.439
## .Stest13health 0.522 0.016 32.002 0.000 0.490
## .Stest14bible 0.394 0.014 28.221 0.000 0.366
## .Stest15theater 0.305 0.011 27.112 0.000 0.283
## .Stest16mscllns 0.520 0.017 31.074 0.000 0.487
## .Stst6physclscn 0.275 0.010 27.312 0.000 0.255
## .Stest9elctrncs 0.667 0.028 23.624 0.000 0.612
## .Stest10mechncs 0.276 0.016 17.426 0.000 0.245
## .Stst28mchnclrs 0.376 0.015 25.832 0.000 0.348
## .Stst29vslztn2D 0.732 0.027 27.249 0.000 0.679
## .Stst30vslztn3D 0.469 0.018 25.389 0.000 0.433
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.279 0.260 0.269
## 0.373 0.346 0.425
## 0.555 0.521 0.534
## 0.411 0.380 0.412
## 0.371 0.347 0.345
## 0.684 0.638 0.479
## 0.904 0.854 0.666
## 0.406 0.382 0.607
## 0.245 0.228 0.219
## 0.610 0.566 0.460
## 0.694 0.634 0.496
## 0.578 0.538 0.547
## 0.343 0.321 0.514
## 0.213 0.186 0.336
## 1.671 1.537 0.550
## 0.946 0.868 0.522
## 0.902 0.836 0.564
## 0.276 0.259 0.300
## 0.354 0.331 0.406
## 0.317 0.296 0.266
## 0.502 0.474 0.588
## 0.690 0.656 0.665
## 0.374 0.350 0.390
## 0.494 0.467 0.602
## 0.554 0.522 0.451
## 0.421 0.394 0.534
## 0.327 0.305 0.447
## 0.553 0.520 0.538
## 0.295 0.275 0.378
## 0.722 0.667 0.580
## 0.307 0.276 0.378
## 0.405 0.376 0.521
## 0.785 0.732 0.654
## 0.506 0.469 0.597
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 0.982 0.982
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.075 0.010 7.640 0.000 0.056
## Stst19d (.p2.) 0.256 0.014 17.843 0.000 0.228
## Stst20s (.p3.) 0.372 0.011 34.357 0.000 0.350
## Stst21c (.p4.) 0.337 0.010 33.402 0.000 0.317
## Stst22p (.p5.) 0.378 0.011 35.964 0.000 0.358
## Stst23n (.p6.) 0.394 0.012 32.110 0.000 0.370
## Stst24x (.p7.) 0.314 0.013 24.461 0.000 0.289
## Stst25w (.p8.) 0.120 0.010 11.713 0.000 0.100
## Stst26r (.p9.) 0.150 0.008 19.393 0.000 0.135
## Stst31b (.10.) 0.164 0.012 14.245 0.000 0.142
## Stst34r (.11.) 0.150 0.013 11.445 0.000 0.124
## math =~
## Stst5mt (.12.) 0.233 0.020 11.635 0.000 0.194
## Stst25w (.13.) 0.182 0.017 10.967 0.000 0.149
## Stst32r (.14.) 0.192 0.014 13.752 0.000 0.165
## Stst33h (.15.) 0.324 0.021 15.547 0.000 0.283
## Stst34r (.16.) 0.171 0.022 7.841 0.000 0.129
## speed =~
## Stst19d (.17.) 0.197 0.011 18.274 0.000 0.176
## Stst34r (.18.) 0.444 0.019 23.762 0.000 0.408
## Stst35t (.19.) 0.959 0.026 37.452 0.000 0.909
## Stst36c (.20.) 0.881 0.017 51.474 0.000 0.847
## Stst37b (.21.) 0.709 0.017 40.786 0.000 0.675
## info =~
## Stst1vc (.22.) 0.215 0.013 17.158 0.000 0.190
## Stst2lt (.23.) 0.297 0.012 25.256 0.000 0.274
## Stst3ms (.24.) 0.307 0.011 28.002 0.000 0.285
## Stst4sc (.25.) 0.179 0.013 13.379 0.000 0.153
## Stst7bl (.26.) 0.100 0.017 5.740 0.000 0.066
## Stst8rn (.27.) 0.139 0.018 7.864 0.000 0.104
## Stst11r (.28.) 0.321 0.014 23.383 0.000 0.294
## Stst12l (.29.) 0.156 0.012 13.124 0.000 0.133
## Stst13h (.30.) 0.231 0.018 12.914 0.000 0.196
## Stst14b (.31.) 0.253 0.012 20.848 0.000 0.229
## Stst15t (.32.) 0.328 0.012 27.348 0.000 0.305
## Stst16m (.33.) 0.217 0.013 17.214 0.000 0.193
## Stst19d (.34.) 0.182 0.016 11.682 0.000 0.152
## Stst26r (.35.) 0.206 0.010 20.214 0.000 0.186
## science =~
## Stst1vc (.36.) 0.124 0.015 8.230 0.000 0.095
## Stst5mt (.37.) 0.035 0.016 2.177 0.030 0.003
## Stst6ph (.38.) 0.050 0.012 4.026 0.000 0.026
## Stst7bl (.39.) 0.054 0.015 3.577 0.000 0.024
## Stst9lc (.40.) 0.230 0.016 13.997 0.000 0.198
## Stst10m (.41.) 0.347 0.014 24.092 0.000 0.319
## spatial =~
## Stst28m (.42.) 0.234 0.012 20.208 0.000 0.211
## Sts292D (.43.) 0.459 0.019 24.692 0.000 0.423
## Sts303D (.44.) 0.422 0.015 27.592 0.000 0.392
## Stst31b (.45.) 0.416 0.016 25.896 0.000 0.384
## Stst37b (.46.) 0.273 0.018 15.213 0.000 0.238
## g =~
## Stst1vc (.47.) 0.793 0.011 71.310 0.000 0.771
## Stst2lt (.48.) 0.710 0.011 63.473 0.000 0.689
## Stst3ms (.49.) 0.618 0.011 55.993 0.000 0.597
## Stst4sc 0.755 0.012 64.611 0.000 0.732
## Stst5mt (.51.) 0.619 0.012 49.601 0.000 0.595
## Stst6ph 0.488 0.013 37.184 0.000 0.462
## Stst7bl (.53.) 0.560 0.012 45.653 0.000 0.536
## Stst8rn 0.234 0.017 13.798 0.000 0.200
## Stst9lc 0.334 0.019 17.963 0.000 0.297
## Stst10m 0.356 0.011 31.912 0.000 0.334
## Stst11r (.57.) 0.661 0.011 59.250 0.000 0.639
## Stst12l (.58.) 0.528 0.012 45.112 0.000 0.505
## Stst13h (.59.) 0.757 0.012 62.859 0.000 0.733
## Stst14b (.60.) 0.524 0.012 45.089 0.000 0.501
## Stst15t (.61.) 0.514 0.011 44.836 0.000 0.492
## Stst16m (.62.) 0.627 0.012 54.433 0.000 0.604
## Stst19d (.63.) 0.570 0.012 47.142 0.000 0.546
## Stst20s (.64.) 0.558 0.012 46.618 0.000 0.535
## Stst21c (.65.) 0.649 0.011 60.114 0.000 0.627
## Stst22p (.66.) 0.711 0.012 61.113 0.000 0.689
## Stst23n (.67.) 0.727 0.013 54.954 0.000 0.702
## Stst24x (.68.) 0.569 0.013 43.083 0.000 0.543
## Stst25w (.69.) 0.444 0.011 39.350 0.000 0.421
## Stst26r (.70.) 0.856 0.010 86.066 0.000 0.837
## Stst28m 0.337 0.012 28.439 0.000 0.313
## Sts292D (.72.) 0.417 0.013 31.085 0.000 0.390
## Sts303D (.73.) 0.369 0.012 31.455 0.000 0.346
## Stst31b (.74.) 0.675 0.012 54.242 0.000 0.651
## Stst32r (.75.) 0.511 0.011 45.459 0.000 0.489
## Stst33h (.76.) 0.508 0.011 46.383 0.000 0.487
## Stst34r (.77.) 0.623 0.014 44.768 0.000 0.596
## Stst35t (.78.) 0.576 0.020 28.405 0.000 0.537
## Stst36c (.79.) 0.132 0.017 7.832 0.000 0.099
## Stst37b (.80.) 0.260 0.016 16.203 0.000 0.228
## ci.upper Std.lv Std.all
##
## 0.095 0.075 0.077
## 0.284 0.256 0.280
## 0.393 0.372 0.381
## 0.357 0.337 0.338
## 0.399 0.378 0.385
## 0.418 0.394 0.354
## 0.339 0.314 0.285
## 0.140 0.120 0.152
## 0.165 0.150 0.149
## 0.187 0.164 0.148
## 0.176 0.150 0.130
##
## 0.272 0.233 0.228
## 0.215 0.182 0.232
## 0.220 0.192 0.249
## 0.365 0.324 0.448
## 0.214 0.171 0.149
##
## 0.219 0.197 0.216
## 0.481 0.444 0.385
## 1.010 0.959 0.591
## 0.914 0.881 0.684
## 0.743 0.709 0.615
##
## 0.239 0.215 0.220
## 0.320 0.297 0.324
## 0.328 0.307 0.339
## 0.205 0.179 0.193
## 0.134 0.100 0.112
## 0.174 0.139 0.167
## 0.348 0.321 0.333
## 0.180 0.156 0.183
## 0.266 0.231 0.208
## 0.277 0.253 0.288
## 0.352 0.328 0.376
## 0.242 0.217 0.228
## 0.213 0.182 0.200
## 0.226 0.206 0.205
##
## 0.154 0.124 0.128
## 0.066 0.035 0.034
## 0.074 0.050 0.071
## 0.084 0.054 0.060
## 0.262 0.230 0.237
## 0.375 0.347 0.547
##
## 0.256 0.234 0.367
## 0.495 0.459 0.450
## 0.452 0.422 0.523
## 0.447 0.416 0.374
## 0.308 0.273 0.237
##
## 0.815 0.795 0.814
## 0.732 0.712 0.777
## 0.640 0.619 0.685
## 0.778 0.756 0.817
## 0.644 0.620 0.608
## 0.514 0.489 0.694
## 0.584 0.561 0.626
## 0.267 0.234 0.280
## 0.370 0.334 0.345
## 0.378 0.357 0.562
## 0.683 0.662 0.687
## 0.551 0.529 0.619
## 0.781 0.758 0.683
## 0.547 0.525 0.597
## 0.537 0.515 0.590
## 0.649 0.628 0.658
## 0.593 0.571 0.625
## 0.582 0.559 0.574
## 0.670 0.650 0.651
## 0.734 0.713 0.725
## 0.753 0.729 0.654
## 0.595 0.570 0.517
## 0.466 0.444 0.566
## 0.876 0.858 0.853
## 0.360 0.337 0.529
## 0.443 0.417 0.409
## 0.392 0.370 0.458
## 0.699 0.676 0.608
## 0.533 0.512 0.663
## 0.530 0.509 0.704
## 0.650 0.624 0.541
## 0.616 0.577 0.355
## 0.165 0.132 0.102
## 0.291 0.260 0.226
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.009 0.012 0.767 0.443 -0.015
## age2 -0.026 0.007 -3.766 0.000 -0.039
## ci.upper Std.lv Std.all
##
## 0.034 0.009 0.012
## -0.012 -0.026 -0.058
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## math ~~
## speed 0.000 0.000
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## speed ~~
## info 0.000 0.000
## science 0.000 0.000
## spatial 0.000 0.000
## info ~~
## science 0.000 0.000
## spatial 0.000 0.000
## science ~~
## spatial 0.000 0.000
## ci.upper Std.lv Std.all
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
## 0.000 0.000 0.000
##
## 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.142) -1.073 0.028 -38.718 0.000 -1.127
## .Stst19d -1.295 0.043 -30.221 0.000 -1.379
## .Stst20s (.144) -0.776 0.023 -33.497 0.000 -0.821
## .Stst21c (.145) -1.101 0.023 -47.436 0.000 -1.147
## .Stst22p (.146) -1.160 0.026 -45.284 0.000 -1.211
## .Stst23n (.147) -0.994 0.029 -34.431 0.000 -1.050
## .Stst24x (.148) -0.911 0.026 -35.261 0.000 -0.961
## .Stst25w (.149) -0.836 0.018 -46.017 0.000 -0.872
## .Stst26r (.150) -1.223 0.028 -43.097 0.000 -1.279
## .Stst31b (.151) -1.016 0.027 -37.096 0.000 -1.070
## .Stst34r (.152) -1.148 0.027 -43.103 0.000 -1.201
## .Stst5mt (.153) -0.712 0.024 -29.296 0.000 -0.760
## .Stst32r (.154) -0.998 0.020 -49.265 0.000 -1.037
## .Stst33h (.155) -0.832 0.020 -42.592 0.000 -0.870
## .Stst35t (.156) -0.618 0.035 -17.797 0.000 -0.686
## .Stst36c (.157) -0.010 0.026 -0.375 0.708 -0.060
## .Stst37b (.158) -0.292 0.025 -11.800 0.000 -0.340
## .Stst2lt (.159) -0.977 0.025 -39.857 0.000 -1.025
## .Stst3ms (.160) -0.848 0.023 -37.626 0.000 -0.892
## .Stst4sc (.161) -1.027 0.029 -35.331 0.000 -1.084
## .Stst7bl (.162) -0.547 0.024 -23.252 0.000 -0.593
## .Stst8rn -0.975 0.031 -31.279 0.000 -1.036
## .Stst11r (.164) -1.019 0.024 -43.017 0.000 -1.066
## .Stst12l (.165) -0.758 0.022 -34.153 0.000 -0.801
## .Stst13h -0.852 0.038 -22.574 0.000 -0.926
## .Stst14b (.167) -0.610 0.021 -28.781 0.000 -0.652
## .Stst15t (.168) -0.966 0.020 -49.324 0.000 -1.005
## .Stst16m (.169) -0.838 0.025 -33.100 0.000 -0.887
## .Stst6ph (.170) -0.658 0.024 -27.670 0.000 -0.705
## .Stst9lc (.171) -0.601 0.027 -22.499 0.000 -0.653
## .Stst10m (.172) -0.614 0.023 -26.173 0.000 -0.660
## .Stst28m -1.054 0.020 -52.616 0.000 -1.094
## .Sts292D (.174) -0.511 0.023 -22.547 0.000 -0.556
## .Sts303D (.175) -0.656 0.020 -32.897 0.000 -0.695
## english 1.743 0.102 17.018 0.000 1.542
## math 0.608 0.111 5.452 0.000 0.389
## speed 0.434 0.038 11.413 0.000 0.359
## info 1.249 0.108 11.620 0.000 1.039
## science -1.558 0.089 -17.501 0.000 -1.732
## spatial -0.284 0.058 -4.910 0.000 -0.398
## .g -0.554 0.063 -8.856 0.000 -0.676
## ci.upper Std.lv Std.all
## -1.018 -1.073 -1.099
## -1.211 -1.295 -1.418
## -0.730 -0.776 -0.796
## -1.056 -1.101 -1.104
## -1.110 -1.160 -1.180
## -0.937 -0.994 -0.892
## -0.860 -0.911 -0.827
## -0.801 -0.836 -1.066
## -1.168 -1.223 -1.216
## -0.962 -1.016 -0.913
## -1.096 -1.148 -0.995
## -0.665 -0.712 -0.698
## -0.958 -0.998 -1.292
## -0.793 -0.832 -1.150
## -0.550 -0.618 -0.381
## 0.041 -0.010 -0.008
## -0.243 -0.292 -0.253
## -0.929 -0.977 -1.067
## -0.804 -0.848 -0.938
## -0.970 -1.027 -1.109
## -0.501 -0.547 -0.611
## -0.914 -0.975 -1.169
## -0.973 -1.019 -1.058
## -0.714 -0.758 -0.887
## -0.778 -0.852 -0.768
## -0.569 -0.610 -0.694
## -0.928 -0.966 -1.106
## -0.788 -0.838 -0.879
## -0.611 -0.658 -0.933
## -0.548 -0.601 -0.619
## -0.568 -0.614 -0.967
## -1.015 -1.054 -1.654
## -0.467 -0.511 -0.501
## -0.617 -0.656 -0.813
## 1.944 1.743 1.743
## 0.826 0.608 0.608
## 0.508 0.434 0.434
## 1.460 1.249 1.249
## -1.383 -1.558 -1.558
## -0.171 -0.284 -0.284
## -0.431 -0.553 -0.553
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.254 0.008 33.362 0.000 0.239
## .Stst19dsgsdwrd 0.371 0.011 32.344 0.000 0.348
## .Stest20spellng 0.499 0.014 35.702 0.000 0.472
## .Stest21cptlztn 0.460 0.013 34.537 0.000 0.434
## .Stest22puncttn 0.316 0.011 30.050 0.000 0.295
## .Stest23english 0.555 0.017 32.479 0.000 0.521
## .Stest24exprssn 0.790 0.021 36.979 0.000 0.748
## .Stst25wrdfnctn 0.371 0.011 34.037 0.000 0.349
## .Stst26rdngcmpr 0.210 0.007 29.614 0.000 0.196
## .Stst31bstrctrs 0.581 0.017 33.567 0.000 0.547
## .Stst34rthcmptt 0.693 0.026 26.222 0.000 0.641
## .Stest5math 0.601 0.017 35.368 0.000 0.567
## .Stst32rthrsnng 0.297 0.009 34.065 0.000 0.280
## .Stst33hghschlm 0.159 0.012 12.823 0.000 0.135
## .Stest35tblrdng 1.384 0.057 24.168 0.000 1.272
## .Stst36clrclchc 0.864 0.032 27.352 0.000 0.802
## .Stst37bjctnspc 0.683 0.026 25.977 0.000 0.631
## .Stest2literatr 0.244 0.007 35.104 0.000 0.230
## .Stest3music 0.339 0.009 36.842 0.000 0.321
## .Stest4soclstds 0.254 0.007 35.422 0.000 0.240
## .Stst7blgclscnc 0.476 0.012 38.158 0.000 0.451
## .Stest8aerontcs 0.622 0.011 58.352 0.000 0.601
## .Stest11art 0.387 0.011 36.023 0.000 0.366
## .Stest12law 0.426 0.010 40.625 0.000 0.405
## .Stest13health 0.605 0.015 41.373 0.000 0.576
## .Stest14bible 0.433 0.013 34.057 0.000 0.408
## .Stest15theater 0.390 0.010 37.308 0.000 0.370
## .Stest16mscllns 0.468 0.012 38.290 0.000 0.444
## .Stst6physclscn 0.256 0.007 35.700 0.000 0.242
## .Stest9elctrncs 0.775 0.019 40.072 0.000 0.737
## .Stest10mechncs 0.155 0.011 13.737 0.000 0.133
## .Stst28mchnclrs 0.238 0.007 36.548 0.000 0.225
## .Stst29vslztn2D 0.655 0.020 32.123 0.000 0.615
## .Stst30vslztn3D 0.337 0.012 27.385 0.000 0.313
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## info 1.000 1.000
## science 1.000 1.000
## spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.268 0.254 0.266
## 0.393 0.371 0.444
## 0.527 0.499 0.526
## 0.486 0.460 0.462
## 0.337 0.316 0.327
## 0.588 0.555 0.447
## 0.832 0.790 0.651
## 0.392 0.371 0.602
## 0.224 0.210 0.208
## 0.615 0.581 0.469
## 0.745 0.693 0.520
## 0.634 0.601 0.577
## 0.314 0.297 0.499
## 0.184 0.159 0.304
## 1.496 1.384 0.525
## 0.925 0.864 0.521
## 0.734 0.683 0.514
## 0.258 0.244 0.291
## 0.358 0.339 0.415
## 0.268 0.254 0.296
## 0.500 0.476 0.592
## 0.643 0.622 0.894
## 0.408 0.387 0.417
## 0.446 0.426 0.583
## 0.633 0.605 0.490
## 0.458 0.433 0.560
## 0.411 0.390 0.511
## 0.492 0.468 0.515
## 0.270 0.256 0.514
## 0.813 0.775 0.825
## 0.177 0.155 0.385
## 0.251 0.238 0.586
## 0.695 0.655 0.630
## 0.361 0.337 0.517
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 0.996 0.996
# CROSS VALIDATION (rerun the above models using data=dhalf1 and then data=dhalf2 instead of data=dgroup)
# MGCFA FOR WHITES
dmale<- subset(dw, sex==0)
dfemale<- subset(dw, sex==1)
datamale<- select(dmale, starts_with("Stest"), -Stest17memsentences, -Stest18memwords, -Stest27creativity)
datafemale<- select(dfemale, starts_with("Stest"), -Stest17memsentences, -Stest18memwords, -Stest27creativity)
datagroup<- select(dw, starts_with("Stest"), -Stest17memsentences, -Stest18memwords, -Stest27creativity)
dgroup<- select(dw, starts_with("Stest"), wb, age, age2, sex, BY_WTA, -Stest17memsentences, -Stest18memwords, -Stest27creativity)
set.seed(123) # For reproducibility, set seed if needed
split_indices <- sample(1:nrow(dgroup), size = nrow(dgroup) / 2)
dhalf1 <- dgroup[split_indices, ]
dhalf2 <- dgroup[-split_indices, ]
split_indices <- sample(1:nrow(datamale), size = nrow(datamale) / 2)
dmale1 <- datamale[split_indices, ]
dmale2 <- datamale[-split_indices, ]
split_indices <- sample(1:nrow(datafemale), size = nrow(datafemale) / 2)
dfemale1 <- datafemale[split_indices, ]
dfemale2 <- datafemale[-split_indices, ]
# MGCFA FOR BLACKS
dmale<- subset(db, sex==0)
dfemale<- subset(db, sex==1)
datamale<- select(dmale, starts_with("Stest"), -Stest17memsentences, -Stest18memwords, -Stest27creativity)
datafemale<- select(dfemale, starts_with("Stest"), -Stest17memsentences, -Stest18memwords, -Stest27creativity)
datagroup<- select(db, starts_with("Stest"), -Stest17memsentences, -Stest18memwords, -Stest27creativity)
dgroup<- select(db, starts_with("Stest"), wb, age, age2, sex, BY_WTA, -Stest17memsentences, -Stest18memwords, -Stest27creativity)
set.seed(123) # For reproducibility, set seed if needed
split_indices <- sample(1:nrow(dgroup), size = nrow(dgroup) / 2)
dhalf1 <- dgroup[split_indices, ]
dhalf2 <- dgroup[-split_indices, ]
split_indices <- sample(1:nrow(datamale), size = nrow(datamale) / 2)
dmale1 <- datamale[split_indices, ]
dmale2 <- datamale[-split_indices, ]
split_indices <- sample(1:nrow(datafemale), size = nrow(datafemale) / 2)
dfemale1 <- datafemale[split_indices, ]
dfemale2 <- datafemale[-split_indices, ]