SUPPLEMENTARY ANALYSIS FOR PROJECT TALENT - REMOVING ALL KNOWLEDGE
ITEMS
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"), -Stest2literature, -Stest3music, -Stest4socialstudies, -Stest6physicalscience, -Stest7biologicalscience, -Stest8aeronautics, -Stest9electronics, -Stest10mechanics, -Stest11art, -Stest12law, -Stest13health, -Stest14bible, -Stest15theater, -Stest16miscellaneous, -Stest17memsentences, -Stest18memwords, -Stest27creativity)
datafemale<- select(dfemale, starts_with("Stest"), -Stest2literature, -Stest3music, -Stest4socialstudies, -Stest6physicalscience, -Stest7biologicalscience, -Stest8aeronautics, -Stest9electronics, -Stest10mechanics, -Stest11art, -Stest12law, -Stest13health, -Stest14bible, -Stest15theater, -Stest16miscellaneous, -Stest17memsentences, -Stest18memwords, -Stest27creativity)
datagroup<- select(dw, starts_with("Stest"), -Stest2literature, -Stest3music, -Stest4socialstudies, -Stest6physicalscience, -Stest7biologicalscience, -Stest8aeronautics, -Stest9electronics, -Stest10mechanics, -Stest11art, -Stest12law, -Stest13health, -Stest14bible, -Stest15theater, -Stest16miscellaneous, -Stest17memsentences, -Stest18memwords, -Stest27creativity)
dgroup<- select(dw, starts_with("Stest"), wb, age, age2, sex, BY_WTA, -Stest2literature, -Stest3music, -Stest4socialstudies, -Stest6physicalscience, -Stest7biologicalscience, -Stest8aeronautics, -Stest9electronics, -Stest10mechanics, -Stest11art, -Stest12law, -Stest13health, -Stest14bible, -Stest15theater, -Stest16miscellaneous, -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
## Stest5math 2 70776 0.22 0.94 0.33 0.30 0.90
## Stest19disguisedwords 3 70776 -0.09 0.98 -0.15 -0.12 1.08
## Stest20spelling 4 70776 -0.24 1.00 -0.26 -0.24 1.00
## Stest21capitalization 5 70776 -0.20 0.98 -0.34 -0.18 0.83
## Stest22punctuation 6 70776 -0.20 0.99 -0.14 -0.18 1.01
## Stest23english 7 70776 -0.13 1.02 -0.07 -0.09 0.95
## Stest24expression 8 70776 -0.11 1.04 0.02 -0.01 0.68
## Stest25wordfunctions 9 70776 -0.13 0.97 -0.10 -0.13 1.22
## Stest26readingcomprehension 10 70776 -0.01 1.02 0.15 0.07 1.04
## Stest28mechanicalreasoning 11 70776 0.53 0.89 0.66 0.58 1.05
## Stest29visualization2D 12 70776 0.22 0.97 0.28 0.28 1.08
## Stest30visualization3D 13 70776 0.20 1.02 0.29 0.23 0.93
## Stest31abstractreasoning 14 70776 0.07 0.98 0.18 0.13 1.06
## Stest32arithreasoning 15 70776 0.13 0.99 0.25 0.15 1.27
## Stest33highschoolmath 16 70776 0.14 1.04 0.09 0.10 1.20
## Stest34arithcomputation 17 70776 -0.07 0.99 -0.06 -0.07 0.91
## Stest35tablereading 18 70776 -0.05 1.03 0.08 -0.03 0.84
## Stest36clericalchecking 19 70776 -0.13 1.01 -0.41 -0.27 0.75
## Stest37objectinspection 20 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
## Stest5math -3.10 1.58 4.68 -0.88 0.70 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
## Stest5math 2 71381 -0.14 0.99 0.00 -0.06 1.04
## Stest19disguisedwords 3 71381 0.17 0.97 0.14 0.18 1.08
## Stest20spelling 4 71381 0.29 0.91 0.41 0.32 1.00
## Stest21capitalization 5 71381 0.28 0.92 0.22 0.31 1.04
## Stest22punctuation 6 71381 0.28 0.90 0.32 0.33 1.01
## Stest23english 7 71381 0.20 0.91 0.25 0.23 0.95
## Stest24expression 8 71381 0.17 0.89 0.48 0.25 0.68
## Stest25wordfunctions 9 71381 0.20 0.99 0.25 0.24 1.13
## Stest26readingcomprehension 10 71381 0.12 0.91 0.25 0.18 1.04
## Stest28mechanicalreasoning 11 71381 -0.43 0.82 -0.52 -0.46 0.70
## Stest29visualization2D 12 71381 -0.15 0.96 -0.09 -0.13 1.08
## Stest30visualization3D 13 71381 -0.12 0.93 -0.02 -0.13 0.93
## Stest31abstractreasoning 14 71381 0.03 0.95 0.18 0.09 1.06
## Stest32arithreasoning 15 71381 -0.04 0.97 -0.04 -0.03 1.27
## Stest33highschoolmath 16 71381 -0.06 0.93 -0.12 -0.11 0.90
## Stest34arithcomputation 17 71381 0.16 0.93 0.14 0.18 0.91
## Stest35tablereading 18 71381 0.10 0.87 0.08 0.12 0.65
## Stest36clericalchecking 19 71381 0.11 0.94 -0.05 0.01 0.75
## Stest37objectinspection 20 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
## Stest5math -3.10 1.58 4.68 -0.73 0.37 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)
## eigen() decomposition
## $values
## [1] 8.5396339 1.9845448 1.5383661 0.8133725 0.6539512 0.6373901
## [7] 0.5960808 0.5427751 0.5064525 0.4969972 0.4858162 0.4643757
## [13] 0.4456274 0.4054590 0.3885191 0.3739552 0.3482104 0.3216457
## [19] 0.2311029 0.2257241
##
## $vectors
## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.27098000 -1.093056e-01 0.006286144 -0.135527901 -0.168620247
## [2,] -0.27274201 -6.885167e-02 0.002832519 0.250188427 -0.128450035
## [3,] -0.23293037 1.354194e-01 0.177630984 -0.361325249 0.238327776
## [4,] -0.21756609 -5.458943e-03 0.346390987 -0.090345519 0.366776182
## [5,] -0.22619723 -6.289444e-02 0.159556921 -0.006620043 0.176205431
## [6,] -0.27167503 -9.881283e-02 0.120404748 0.033723082 0.132590808
## [7,] -0.23490503 -1.033638e-01 0.117589740 -0.353053839 -0.004933944
## [8,] -0.21283303 -1.152906e-01 0.071768663 -0.400643270 -0.397305332
## [9,] -0.25718694 -8.591291e-02 0.075043221 0.139104098 0.083410799
## [10,] -0.28288611 -1.201889e-01 0.068783597 -0.145719282 -0.162281607
## [11,] -0.21024694 -3.769939e-02 -0.445840736 -0.113197434 -0.036607466
## [12,] -0.15562812 2.069733e-01 -0.407928365 -0.092212886 0.539987714
## [13,] -0.18962320 4.200204e-06 -0.490723994 0.024373328 0.083871309
## [14,] -0.22819625 -3.585847e-02 -0.264279575 0.085402863 -0.036098937
## [15,] -0.26572438 -1.034584e-01 -0.050334933 0.231140212 -0.151303389
## [16,] -0.27976537 -7.072512e-02 0.004302615 0.372164023 -0.050647477
## [17,] -0.20837378 2.239348e-01 0.215897579 0.448195241 0.028017138
## [18,] -0.13209276 4.867586e-01 0.054137184 0.068448133 -0.327392572
## [19,] -0.07822059 5.419773e-01 0.168946510 -0.033119394 0.123579723
## [20,] -0.08155087 5.131770e-01 -0.150484628 -0.159984565 -0.271993790
## [,6] [,7] [,8] [,9] [,10]
## [1,] -0.39103753 0.019282340 0.23200616 0.09544724 -0.15946453
## [2,] -0.26761518 -0.023227279 0.11607108 -0.07540119 -0.08983110
## [3,] -0.33767816 0.012158912 -0.10015134 0.12633752 -0.11815103
## [4,] -0.03893303 0.044700787 -0.31908354 0.05943108 -0.20965719
## [5,] 0.46767004 0.458729229 0.48975994 0.34424732 -0.10173741
## [6,] 0.17923721 0.141000808 -0.02228076 -0.15619432 0.12088628
## [7,] 0.07554269 -0.009045989 0.08896613 -0.35513232 0.60230626
## [8,] 0.42090130 -0.456384359 -0.19071384 0.05343221 -0.21516740
## [9,] 0.04859948 0.116090288 -0.15847386 -0.38106411 0.19831333
## [10,] -0.15648952 -0.031671698 0.11120853 0.09580640 -0.10864795
## [11,] -0.19389177 0.070607618 0.11334058 0.18109718 0.07538826
## [12,] 0.14554029 -0.481922677 0.29352695 -0.11005754 -0.07952436
## [13,] 0.03993348 0.163091506 -0.25566652 0.08365681 0.13520231
## [14,] 0.22412477 0.190280246 -0.52318518 0.21837396 -0.08556917
## [15,] -0.07802379 -0.113111955 0.02904112 0.01894068 0.01213942
## [16,] -0.08409047 -0.055238854 0.00548858 -0.15067139 -0.01656663
## [17,] 0.16695452 -0.310696876 0.03583327 -0.01930687 -0.13860884
## [18,] 0.08605143 -0.072922114 0.10145493 0.35173132 0.42711507
## [19,] -0.17850136 0.020887910 -0.20375246 0.13566450 0.15331950
## [20,] 0.09203156 0.354412104 0.08166282 -0.52373470 -0.40030188
## [,11] [,12] [,13] [,14] [,15]
## [1,] 5.407706e-02 -0.0277901327 -0.04530118 0.169846113 -0.108584213
## [2,] -1.511061e-02 -0.0777537425 0.04678720 0.351249409 -0.269058762
## [3,] 2.458054e-03 -0.1423554997 -0.10006928 -0.527710431 -0.268749571
## [4,] 3.641461e-01 0.4395288708 0.03901941 0.305857639 0.278108602
## [5,] -1.635575e-01 -0.0662296724 0.09838300 0.018377001 -0.057170156
## [6,] -8.278547e-02 0.0912837966 -0.09704420 -0.033052950 0.139128590
## [7,] 3.097402e-01 -0.2667605316 0.30791046 0.083404263 -0.003999085
## [8,] -2.798660e-01 0.1078992066 0.10338492 0.025119859 -0.032993093
## [9,] -3.773982e-01 0.1783958256 -0.46071775 -0.223543513 -0.066822341
## [10,] -7.985040e-06 0.0009451502 -0.15852082 0.059877460 -0.073047558
## [11,] 1.247268e-02 0.1114963680 0.15632370 -0.322394930 0.485311544
## [12,] 6.218592e-03 -0.0842798624 -0.24010532 0.200682352 -0.004515200
## [13,] -6.340294e-02 0.4257973182 0.37391240 0.018357940 -0.440822506
## [14,] 2.433767e-01 -0.5664293942 -0.23377954 0.083987245 0.012453926
## [15,] -1.156392e-01 -0.0202485985 0.03840833 -0.057729763 0.505398654
## [16,] -5.819908e-02 -0.0506038571 0.07218769 0.097468143 -0.057223506
## [17,] 2.528072e-01 -0.0633085924 0.34195619 -0.426630159 -0.111126437
## [18,] 2.438814e-01 0.2675950897 -0.38103677 0.047390410 -0.060112026
## [19,] -5.421620e-01 -0.2249563811 0.27672040 0.253909026 0.146420466
## [20,] 1.280852e-01 0.0388776679 0.01743801 -0.003159859 0.081142709
## [,16] [,17] [,18] [,19] [,20]
## [1,] 0.03670990 -0.364959226 0.223924911 -0.242767874 0.579763203
## [2,] -0.33899397 0.283296431 -0.153886968 -0.386360854 -0.412338744
## [3,] 0.08898063 0.397137527 -0.084762031 -0.014758057 0.018517308
## [4,] -0.04145095 -0.050292847 -0.186144004 -0.003640335 0.005543828
## [5,] 0.03610886 0.006105459 -0.208552971 -0.022670848 0.026210680
## [6,] -0.19701377 0.272033095 0.795341697 -0.032910529 -0.013382349
## [7,] 0.06231000 -0.048669261 -0.133207027 -0.011591682 -0.005529726
## [8,] -0.14900782 0.087439412 -0.080277324 -0.046651183 0.077971235
## [9,] -0.06006522 -0.346867946 -0.286140496 -0.147328890 0.024177525
## [10,] 0.23525779 -0.338714451 0.171525827 0.494519170 -0.562398240
## [11,] -0.48751753 -0.096092833 -0.117195200 0.059409676 -0.082950853
## [12,] 0.05686738 -0.002789169 0.004773671 -0.002148022 0.008058075
## [13,] 0.26376199 -0.010974506 0.081297678 -0.025597645 -0.004108626
## [14,] -0.02514166 -0.086591259 0.002172608 -0.044919402 0.030671729
## [15,] 0.64641157 0.245824004 -0.070820075 -0.247586446 -0.031515301
## [16,] -0.10307734 0.284638577 -0.176681395 0.664386818 0.392819094
## [17,] -0.05455175 -0.325584401 0.105708814 -0.103739782 -0.052431270
## [18,] -0.01921824 0.124159358 -0.026173129 0.002180911 0.055223788
## [19,] -0.03849675 -0.158375312 0.063968935 0.038034085 -0.019319933
## [20,] 0.06731805 0.048884379 -0.015449570 0.016306956 -0.015805705
eigen(femalecor)
## eigen() decomposition
## $values
## [1] 8.0369714 1.9508864 1.4432300 0.9030562 0.7021201 0.6774020
## [7] 0.6340137 0.5748603 0.5467003 0.5249176 0.5026568 0.4954461
## [13] 0.4693188 0.4606989 0.4355252 0.4132046 0.3726155 0.3432385
## [19] 0.2798137 0.2333240
##
## $vectors
## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.27697963 -0.121071551 -0.028932353 -0.07117637 0.31220781
## [2,] -0.25576652 -0.104551197 0.009938376 0.37833177 0.28940945
## [3,] -0.23605751 0.162013222 -0.205448381 -0.26437763 0.13885603
## [4,] -0.21903300 0.011034418 -0.365498682 -0.08053695 -0.16952428
## [5,] -0.21372758 -0.056813964 -0.167363428 -0.07039273 -0.65089474
## [6,] -0.27869045 -0.095223937 -0.113004272 -0.02195230 -0.16799753
## [7,] -0.23067858 -0.093155440 -0.159187897 -0.28717460 0.05269258
## [8,] -0.20117477 -0.100928170 -0.096943802 -0.46462916 0.13373606
## [9,] -0.27120052 -0.096208454 -0.054171959 0.11447566 -0.01209509
## [10,] -0.28927576 -0.126155238 -0.058605282 -0.12939345 0.17163724
## [11,] -0.21008735 -0.021629861 0.441096016 -0.09732313 0.11727469
## [12,] -0.15802022 0.199854474 0.411640313 -0.08797744 -0.31334620
## [13,] -0.19705365 0.004898562 0.477128658 -0.05176858 -0.11427510
## [14,] -0.23526849 -0.023479685 0.249575235 -0.05691795 -0.15750915
## [15,] -0.26595883 -0.116885168 0.057698204 0.17453112 0.04973001
## [16,] -0.26607563 -0.101244186 0.038159921 0.43614613 0.13180747
## [17,] -0.20713278 0.203865958 -0.188409742 0.42400482 -0.23158538
## [18,] -0.12459148 0.492582263 -0.074283445 0.05993902 0.01089409
## [19,] -0.08531216 0.538602787 -0.145241121 0.02270050 0.16284008
## [20,] -0.09685675 0.502514239 0.143275158 -0.11865608 0.13665136
## [,6] [,7] [,8] [,9] [,10]
## [1,] 0.068808993 0.13360283 0.15894691 0.146144917 0.10144041
## [2,] 0.043470777 0.04110537 0.26540797 0.080028328 -0.12068754
## [3,] 0.378835198 0.05857916 -0.12670163 0.162012794 0.04032020
## [4,] 0.319126340 0.01110599 -0.38874439 -0.003427988 -0.15224967
## [5,] -0.188933513 0.38350060 0.38581531 0.300373428 0.08727126
## [6,] 0.002124482 0.05903030 -0.03991343 -0.107677554 -0.06529660
## [7,] 0.118792433 0.02281642 0.22460056 -0.762848729 0.05796628
## [8,] -0.443511995 -0.57836918 0.03877278 0.269634075 -0.08738214
## [9,] -0.041046078 0.05194881 -0.07251732 -0.036959686 -0.10423793
## [10,] -0.054431523 0.07734028 0.04878054 0.102964187 0.09607588
## [11,] 0.101841691 0.15290717 -0.01934297 0.068058298 0.27273859
## [12,] 0.441400977 -0.45265239 0.37490559 0.022198523 -0.08859067
## [13,] 0.007265906 0.09684215 -0.33853558 -0.031745659 0.13605133
## [14,] -0.231921989 0.08061416 -0.44352802 -0.060191788 -0.22673260
## [15,] -0.109088274 -0.06745781 -0.08597722 0.029708994 0.09490045
## [16,] -0.016578639 -0.05904816 0.11624914 0.003561801 -0.09700386
## [17,] -0.067247706 -0.38863881 -0.13283881 -0.119620382 -0.03134980
## [18,] -0.329157614 -0.03523809 0.01625973 -0.193369348 0.61544000
## [19,] 0.189617100 0.07238718 -0.07041724 0.306297165 0.02658601
## [20,] -0.277148886 0.27004807 0.17623439 -0.146221313 -0.59694453
## [,11] [,12] [,13] [,14] [,15]
## [1,] -0.28006235 -0.1065939382 -0.00603337 0.019695330 0.293259999
## [2,] 0.09061784 -0.0008005108 -0.11227072 -0.458366884 -0.025191501
## [3,] -0.05939183 -0.1048034395 0.28012250 -0.019283116 -0.025818762
## [4,] -0.33726548 0.1525709877 -0.26671197 -0.271398503 -0.071348117
## [5,] 0.08936519 0.0973271379 0.09783867 -0.082280804 0.094580406
## [6,] 0.05763033 -0.0077797696 -0.14759559 0.168109927 -0.307257715
## [7,] 0.32274838 0.1061899003 0.11595967 -0.036070287 0.152256197
## [8,] 0.12713301 0.2086447481 -0.03250368 -0.130357314 -0.088155557
## [9,] 0.13876600 -0.0885896549 -0.28067218 0.368119421 -0.512026772
## [10,] -0.19606799 -0.1853527281 -0.04712368 0.147676387 0.218361207
## [11,] -0.11246844 0.2927711877 0.46697266 -0.007340183 -0.459059262
## [12,] -0.07964151 -0.2695806969 -0.16199957 0.028527275 0.005106173
## [13,] 0.10495734 0.4502953658 -0.37551198 -0.092174523 0.332688926
## [14,] 0.20138832 -0.5806476382 0.26572344 -0.262553863 0.081426958
## [15,] -0.03217749 -0.0673975417 -0.02617714 0.564015206 0.274312586
## [16,] 0.13765191 0.0619890187 -0.00844360 -0.190236340 -0.055465575
## [17,] -0.16958130 0.2527502432 0.44787353 0.092621090 0.160805331
## [18,] -0.18047601 -0.2259877608 -0.22992049 -0.192043457 -0.147541341
## [19,] 0.60896993 0.0625915193 -0.02178826 0.127077296 0.097056023
## [20,] -0.28986251 0.1492226708 -0.01692806 0.103092881 0.001846721
## [,16] [,17] [,18] [,19] [,20]
## [1,] -0.07229264 -0.39794274 0.043849114 -0.086035127 0.613691881
## [2,] -0.03664166 0.07720971 0.034650106 0.587536803 -0.128118702
## [3,] -0.44779055 0.54840415 0.009809835 -0.007481705 0.018283874
## [4,] 0.43823540 -0.05277908 -0.158113876 -0.003000514 -0.007493957
## [5,] 0.01540246 0.07019562 -0.126412162 0.006717569 0.032619833
## [6,] -0.05890731 -0.07440295 0.832658148 0.017640969 0.019431117
## [7,] 0.08513191 -0.02107956 -0.125405092 0.016867053 0.008473672
## [8,] 0.04161732 0.04698808 -0.018496898 0.009407914 0.056888826
## [9,] -0.31549337 -0.14690503 -0.490987186 0.054662815 0.101965378
## [10,] -0.07545642 -0.26705409 -0.024151618 -0.154124545 -0.757465285
## [11,] 0.27952188 -0.11192656 -0.038082427 0.042826489 -0.057433232
## [12,] 0.05303169 -0.03819505 -0.023717540 -0.009390686 -0.008228244
## [13,] -0.31258741 0.04854736 0.012361868 0.002522213 -0.001963826
## [14,] 0.06501716 -0.08355653 -0.027106997 0.026832198 0.071973185
## [15,] 0.43366053 0.44489689 -0.019682401 0.231157519 0.078545358
## [16,] 0.09099293 0.24273095 -0.003677225 -0.744063680 0.015235335
## [17,] -0.24389142 -0.24702928 -0.010539343 0.097480307 -0.018330464
## [18,] 0.01469004 0.09746964 -0.001247739 -0.012805410 0.039560822
## [19,] 0.20864089 -0.25950730 0.036648166 -0.012493675 -0.025381511
## [20,] 0.02222771 0.08993726 0.001854358 -0.018057903 -0.013416533
mpa<- fa.parallel(malecor, n.obs=70776, n.iter=1000)
## Parallel analysis suggests that the number of factors = 6 and the number of components = 3
fpa<- fa.parallel(femalecor, n.obs=71381, n.iter=1000)
## Parallel analysis suggests that the number of factors = 6 and the number of components = 3
mqqnorm(datafemale, main = "Multi-normal Q-Q Plot") # serious departure
## 135135 72667
## 64359 1891
mqqnorm(datamale, main = "Multi-normal Q-Q Plot") # serious departure
## [1] 51628 6849
mqqnorm(datagroup, main = "Multi-normal Q-Q Plot") # serious departure
## [1] 51628 6849
#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=4, 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 = 4, 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 h2 u2 com
## Stest1vocab 0.78 -0.14 -0.01 0.13 0.64 0.36 1.1
## Stest5math 0.78 -0.09 -0.01 -0.17 0.65 0.35 1.1
## Stest19disguisedwords 0.66 0.18 -0.18 0.24 0.56 0.44 1.6
## Stest20spelling 0.61 0.01 -0.35 0.07 0.51 0.49 1.6
## Stest21capitalization 0.64 -0.06 -0.16 0.02 0.43 0.57 1.1
## Stest22punctuation 0.78 -0.12 -0.14 -0.01 0.64 0.36 1.1
## Stest23english 0.66 -0.12 -0.12 0.18 0.50 0.50 1.3
## Stest24expression 0.60 -0.12 -0.07 0.15 0.40 0.60 1.3
## Stest25wordfunctions 0.73 -0.09 -0.09 -0.07 0.55 0.45 1.1
## Stest26readingcomprehension 0.82 -0.16 -0.09 0.16 0.73 0.27 1.2
## Stest28mechanicalreasoning 0.60 -0.06 0.50 0.10 0.63 0.37 2.0
## Stest29visualization2D 0.43 0.22 0.38 0.04 0.38 0.62 2.5
## Stest30visualization3D 0.54 -0.01 0.52 0.00 0.56 0.44 2.0
## Stest31abstractreasoning 0.64 -0.05 0.26 -0.03 0.49 0.51 1.3
## Stest32arithreasoning 0.76 -0.13 0.05 -0.14 0.62 0.38 1.1
## Stest33highschoolmath 0.82 -0.10 -0.01 -0.36 0.81 0.19 1.4
## Stest34arithcomputation 0.59 0.30 -0.21 -0.25 0.54 0.46 2.2
## Stest35tablereading 0.38 0.59 -0.03 -0.03 0.49 0.51 1.7
## Stest36clericalchecking 0.22 0.68 -0.14 0.02 0.53 0.47 1.3
## Stest37objectinspection 0.23 0.60 0.17 0.06 0.44 0.56 1.5
##
## PA1 PA2 PA3 PA4
## SS loadings 8.15 1.47 1.07 0.42
## Proportion Var 0.41 0.07 0.05 0.02
## Cumulative Var 0.41 0.48 0.53 0.55
## Proportion Explained 0.73 0.13 0.10 0.04
## Cumulative Proportion 0.73 0.87 0.96 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 190 with the objective function = 10.6 0.1 with Chi Square = 750359.4
## df of the model are 116 and the objective function was 0.29
## 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 7197.46 with prob < 0
## 0.1The total n.obs was 70776 with Likelihood Chi Square = 20266.68 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.956
## RMSEA index = 0.05 and the 90 % confidence intervals are 0.049 0.05 0.1
## BIC = 18971.28
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA2 PA3 PA4
## Correlation of (regression) scores with factors 0.98 0.87 0.84 0.76
## Multiple R square of scores with factors 0.96 0.75 0.70 0.57
## Minimum correlation of possible factor scores 0.91 0.50 0.41 0.14
FAfemale<-fa(r=datafemale, nfactors=4, 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 = 4, 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 h2 u2 com
## Stest1vocab 0.77 -0.15 -0.04 0.09 0.63 0.37 1.1
## Stest5math 0.71 -0.13 0.01 -0.27 0.59 0.41 1.4
## Stest19disguisedwords 0.65 0.21 -0.20 0.19 0.54 0.46 1.6
## Stest20spelling 0.60 0.03 -0.35 0.07 0.49 0.51 1.7
## Stest21capitalization 0.58 -0.05 -0.14 0.05 0.36 0.64 1.2
## Stest22punctuation 0.78 -0.11 -0.13 0.04 0.63 0.37 1.1
## Stest23english 0.63 -0.10 -0.15 0.16 0.45 0.55 1.3
## Stest24expression 0.54 -0.10 -0.08 0.19 0.35 0.65 1.4
## Stest25wordfunctions 0.75 -0.11 -0.07 -0.05 0.58 0.42 1.1
## Stest26readingcomprehension 0.81 -0.17 -0.08 0.15 0.72 0.28 1.2
## Stest28mechanicalreasoning 0.58 -0.03 0.45 0.09 0.55 0.45 2.0
## Stest29visualization2D 0.42 0.22 0.35 0.05 0.35 0.65 2.5
## Stest30visualization3D 0.54 0.00 0.48 0.06 0.53 0.47 2.0
## Stest31abstractreasoning 0.64 -0.03 0.24 0.06 0.47 0.53 1.3
## Stest32arithreasoning 0.74 -0.14 0.06 -0.09 0.57 0.43 1.1
## Stest33highschoolmath 0.75 -0.14 0.05 -0.43 0.78 0.22 1.7
## Stest34arithcomputation 0.56 0.25 -0.17 -0.23 0.46 0.54 2.0
## Stest35tablereading 0.35 0.58 -0.04 -0.04 0.46 0.54 1.7
## Stest36clericalchecking 0.24 0.66 -0.12 -0.04 0.50 0.50 1.3
## Stest37objectinspection 0.26 0.58 0.15 0.04 0.43 0.57 1.6
##
## PA1 PA2 PA3 PA4
## SS loadings 7.61 1.42 0.93 0.48
## Proportion Var 0.38 0.07 0.05 0.02
## Cumulative Var 0.38 0.45 0.50 0.52
## Proportion Explained 0.73 0.14 0.09 0.05
## Cumulative Proportion 0.73 0.86 0.95 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 190 with the objective function = 9.4 0.1 with Chi Square = 670968.9
## df of the model are 116 and the objective function was 0.26
## 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 7319.94 with prob < 0
## 0.1The total n.obs was 71381 with Likelihood Chi Square = 18380.34 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.955
## RMSEA index = 0.047 and the 90 % confidence intervals are 0.046 0.048 0.1
## BIC = 17083.95
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA2 PA3 PA4
## Correlation of (regression) scores with factors 0.97 0.86 0.81 0.77
## Multiple R square of scores with factors 0.95 0.74 0.65 0.59
## Minimum correlation of possible factor scores 0.90 0.47 0.31 0.18
FA<-fa(r=datagroup, nfactors=4, 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 = 4, 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 h2 u2 com
## Stest1vocab 0.76 -0.19 -0.04 0.03 0.61 0.39 1.1
## Stest5math 0.72 -0.21 0.03 -0.26 0.64 0.36 1.4
## Stest19disguisedwords 0.65 0.27 -0.02 0.14 0.52 0.48 1.4
## Stest20spelling 0.60 0.31 -0.29 0.03 0.54 0.46 2.0
## Stest21capitalization 0.60 0.15 -0.22 0.06 0.44 0.56 1.4
## Stest22punctuation 0.77 0.10 -0.25 0.06 0.66 0.34 1.3
## Stest23english 0.65 0.07 -0.22 0.17 0.50 0.50 1.4
## Stest24expression 0.57 0.03 -0.18 0.18 0.39 0.61 1.4
## Stest25wordfunctions 0.74 0.03 -0.16 -0.03 0.57 0.43 1.1
## Stest26readingcomprehension 0.82 -0.06 -0.17 0.12 0.72 0.28 1.1
## Stest28mechanicalreasoning 0.49 -0.49 0.41 0.08 0.65 0.35 3.0
## Stest29visualization2D 0.40 -0.13 0.44 0.10 0.39 0.61 2.3
## Stest30visualization3D 0.52 -0.33 0.35 0.14 0.52 0.48 2.7
## Stest31abstractreasoning 0.64 -0.17 0.14 0.10 0.46 0.54 1.3
## Stest32arithreasoning 0.74 -0.19 -0.01 -0.10 0.60 0.40 1.2
## Stest33highschoolmath 0.78 -0.19 0.01 -0.38 0.79 0.21 1.6
## Stest34arithcomputation 0.58 0.32 0.05 -0.25 0.51 0.49 2.0
## Stest35tablereading 0.37 0.46 0.37 -0.05 0.48 0.52 2.9
## Stest36clericalchecking 0.24 0.58 0.35 -0.05 0.52 0.48 2.0
## Stest37objectinspection 0.25 0.37 0.47 0.09 0.43 0.57 2.5
##
## PA1 PA2 PA3 PA4
## SS loadings 7.61 1.54 1.32 0.45
## Proportion Var 0.38 0.08 0.07 0.02
## Cumulative Var 0.38 0.46 0.52 0.55
## Proportion Explained 0.70 0.14 0.12 0.04
## Cumulative Proportion 0.70 0.84 0.96 1.00
##
## Mean item complexity = 1.8
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 190 with the objective function = 10.11 0.1 with Chi Square = 1436471
## df of the model are 116 and the objective function was 0.35
## 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 142157 with the empirical chi square 20145.9 with prob < 0
## 0.1The total n.obs was 142157 with Likelihood Chi Square = 50400.21 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.943
## RMSEA index = 0.055 and the 90 % confidence intervals are 0.055 0.056 0.1
## BIC = 49023.91
## 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 0.86 0.76
## Multiple R square of scores with factors 0.95 0.77 0.73 0.57
## Minimum correlation of possible factor scores 0.90 0.55 0.47 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.
male3<-fa(datamale, nfactors=3, rotate="promax", fm="minres", weight=dmale$BY_WTA)
print(male3, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datamale, nfactors = 3, rotate = "promax", fm = "minres",
## weight = dmale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## Stest1vocab 0.71 0.17 -0.07 0.63 0.37 1.1
## Stest5math 0.68 0.17 -0.02 0.62 0.38 1.1
## Stest19disguisedwords 0.61 -0.05 0.25 0.49 0.51 1.3
## Stest20spelling 0.80 -0.28 0.09 0.50 0.50 1.3
## Stest21capitalization 0.68 -0.04 0.01 0.44 0.56 1.0
## Stest22punctuation 0.81 0.01 -0.04 0.65 0.35 1.0
## Stest23english 0.69 0.01 -0.05 0.46 0.54 1.0
## Stest24expression 0.60 0.06 -0.07 0.37 0.63 1.0
## Stest25wordfunctions 0.71 0.07 -0.03 0.55 0.45 1.0
## Stest26readingcomprehension 0.81 0.08 -0.09 0.71 0.29 1.0
## Stest28mechanicalreasoning 0.10 0.73 -0.05 0.61 0.39 1.1
## Stest29visualization2D -0.06 0.55 0.24 0.38 0.62 1.4
## Stest30visualization3D 0.00 0.76 -0.01 0.57 0.43 1.0
## Stest31abstractreasoning 0.32 0.47 -0.02 0.49 0.51 1.8
## Stest32arithreasoning 0.63 0.24 -0.07 0.60 0.40 1.3
## Stest33highschoolmath 0.70 0.18 -0.02 0.65 0.35 1.1
## Stest34arithcomputation 0.53 -0.11 0.36 0.46 0.54 1.9
## Stest35tablereading 0.08 0.05 0.65 0.49 0.51 1.0
## Stest36clericalchecking 0.02 -0.14 0.75 0.54 0.46 1.1
## Stest37objectinspection -0.21 0.25 0.63 0.43 0.57 1.5
##
## MR1 MR3 MR2
## SS loadings 6.71 2.24 1.69
## Proportion Var 0.34 0.11 0.08
## Cumulative Var 0.34 0.45 0.53
## Proportion Explained 0.63 0.21 0.16
## Cumulative Proportion 0.63 0.84 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.57 0.32
## MR3 0.57 1.00 0.24
## MR2 0.32 0.24 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 190 with the objective function = 10.6 0.1 with Chi Square = 750359.4
## df of the model are 133 and the objective function was 0.59
## 0.1
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.03
## 0.1
## The harmonic n.obs is 70776 with the empirical chi square 17359.93 with prob < 0
## 0.1The total n.obs was 70776 with Likelihood Chi Square = 42001.3 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.92
## RMSEA index = 0.067 and the 90 % confidence intervals are 0.066 0.067 0.1
## BIC = 40516.05
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.97 0.91 0.88
## Multiple R square of scores with factors 0.94 0.83 0.77
## Minimum correlation of possible factor scores 0.88 0.66 0.55
male4<-fa(datamale, nfactors=4, rotate="promax", fm="minres", weight=dmale$BY_WTA)
print(male4, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datamale, nfactors = 4, rotate = "promax", fm = "minres",
## weight = dmale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR4 MR2 h2 u2 com
## Stest1vocab 0.71 0.19 -0.01 -0.07 0.64 0.36 1.2
## Stest5math 0.38 0.15 0.40 -0.04 0.65 0.35 2.3
## Stest19disguisedwords 0.75 -0.02 -0.17 0.27 0.56 0.44 1.4
## Stest20spelling 0.75 -0.26 0.07 0.09 0.51 0.49 1.3
## Stest21capitalization 0.59 -0.03 0.12 0.01 0.43 0.57 1.1
## Stest22punctuation 0.66 0.01 0.19 -0.04 0.64 0.36 1.2
## Stest23english 0.76 0.04 -0.10 -0.04 0.50 0.50 1.0
## Stest24expression 0.65 0.08 -0.08 -0.06 0.40 0.60 1.1
## Stest25wordfunctions 0.52 0.06 0.26 -0.03 0.55 0.45 1.5
## Stest26readingcomprehension 0.83 0.11 -0.03 -0.08 0.73 0.27 1.1
## Stest28mechanicalreasoning 0.14 0.75 -0.07 -0.04 0.63 0.37 1.1
## Stest29visualization2D -0.05 0.55 -0.01 0.24 0.38 0.62 1.4
## Stest30visualization3D -0.04 0.75 0.05 -0.01 0.56 0.44 1.0
## Stest31abstractreasoning 0.21 0.46 0.15 -0.02 0.49 0.51 1.6
## Stest32arithreasoning 0.37 0.22 0.34 -0.08 0.62 0.38 2.7
## Stest33highschoolmath 0.22 0.12 0.67 -0.06 0.81 0.19 1.3
## Stest34arithcomputation 0.20 -0.16 0.49 0.35 0.54 0.46 2.5
## Stest35tablereading 0.03 0.04 0.11 0.64 0.49 0.51 1.1
## Stest36clericalchecking 0.03 -0.13 0.03 0.73 0.53 0.47 1.1
## Stest37objectinspection -0.13 0.26 -0.07 0.62 0.44 0.56 1.5
##
## MR1 MR3 MR4 MR2
## SS loadings 5.47 2.24 1.73 1.66
## Proportion Var 0.27 0.11 0.09 0.08
## Cumulative Var 0.27 0.39 0.47 0.55
## Proportion Explained 0.49 0.20 0.16 0.15
## Cumulative Proportion 0.49 0.69 0.85 1.00
##
## With factor correlations of
## MR1 MR3 MR4 MR2
## MR1 1.00 0.56 0.69 0.26
## MR3 0.56 1.00 0.50 0.21
## MR4 0.69 0.50 1.00 0.23
## MR2 0.26 0.21 0.23 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 190 with the objective function = 10.6 0.1 with Chi Square = 750359.4
## df of the model are 116 and the objective function was 0.29
## 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 7197.14 with prob < 0
## 0.1The total n.obs was 70776 with Likelihood Chi Square = 20254.15 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.956
## RMSEA index = 0.05 and the 90 % confidence intervals are 0.049 0.05 0.1
## BIC = 18958.75
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR4 MR2
## Correlation of (regression) scores with factors 0.96 0.91 0.91 0.88
## Multiple R square of scores with factors 0.93 0.83 0.83 0.77
## Minimum correlation of possible factor scores 0.86 0.66 0.67 0.54
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 MR3 MR4 MR2 MR5 h2 u2 com
## Stest1vocab 0.40 0.01 0.14 0.02 0.52 0.78 0.22 2.0
## Stest5math 0.18 0.05 0.54 0.01 0.23 0.68 0.32 1.6
## Stest19disguisedwords 0.67 -0.03 -0.16 0.28 0.15 0.55 0.45 1.6
## Stest20spelling 0.77 -0.21 0.02 0.07 -0.02 0.51 0.49 1.2
## Stest21capitalization 0.64 0.03 0.06 -0.02 -0.06 0.45 0.55 1.0
## Stest22punctuation 0.78 0.10 0.10 -0.10 -0.14 0.69 0.31 1.2
## Stest23english 0.74 0.07 -0.12 -0.06 0.05 0.50 0.50 1.1
## Stest24expression 0.62 0.10 -0.08 -0.07 0.07 0.40 0.60 1.1
## Stest25wordfunctions 0.55 0.10 0.23 -0.06 -0.05 0.57 0.43 1.5
## Stest26readingcomprehension 0.63 0.02 0.06 -0.04 0.32 0.76 0.24 1.5
## Stest28mechanicalreasoning 0.04 0.70 -0.01 -0.03 0.15 0.62 0.38 1.1
## Stest29visualization2D -0.01 0.58 -0.04 0.22 -0.05 0.39 0.61 1.3
## Stest30visualization3D -0.01 0.78 0.03 -0.03 -0.05 0.58 0.42 1.0
## Stest31abstractreasoning 0.24 0.50 0.12 -0.04 -0.05 0.50 0.50 1.6
## Stest32arithreasoning 0.29 0.18 0.40 -0.07 0.10 0.62 0.38 2.5
## Stest33highschoolmath 0.14 0.09 0.74 -0.04 0.05 0.81 0.19 1.1
## Stest34arithcomputation 0.22 -0.14 0.47 0.35 -0.07 0.54 0.46 2.6
## Stest35tablereading 0.01 0.02 0.12 0.65 0.03 0.49 0.51 1.1
## Stest36clericalchecking 0.04 -0.13 0.01 0.74 -0.01 0.53 0.47 1.1
## Stest37objectinspection -0.13 0.24 -0.07 0.63 0.01 0.44 0.56 1.4
##
## MR1 MR3 MR4 MR2 MR5
## SS loadings 4.86 2.13 1.96 1.67 0.81
## Proportion Var 0.24 0.11 0.10 0.08 0.04
## Cumulative Var 0.24 0.35 0.45 0.53 0.57
## Proportion Explained 0.43 0.19 0.17 0.15 0.07
## Cumulative Proportion 0.43 0.61 0.78 0.93 1.00
##
## With factor correlations of
## MR1 MR3 MR4 MR2 MR5
## MR1 1.00 0.53 0.73 0.30 0.43
## MR3 0.53 1.00 0.53 0.24 0.46
## MR4 0.73 0.53 1.00 0.25 0.30
## MR2 0.30 0.24 0.25 1.00 0.01
## MR5 0.43 0.46 0.30 0.01 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 5 factors are sufficient.
##
## df null model = 190 with the objective function = 10.6 0.1 with Chi Square = 750359.4
## df of the model are 100 and the objective function was 0.12
## 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 70776 with the empirical chi square 3185.6 with prob < 0
## 0.1The total n.obs was 70776 with Likelihood Chi Square = 8390.97 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.979
## RMSEA index = 0.034 and the 90 % confidence intervals are 0.034 0.035 0.1
## BIC = 7274.24
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR4 MR2
## Correlation of (regression) scores with factors 0.96 0.91 0.93 0.88
## Multiple R square of scores with factors 0.92 0.83 0.86 0.77
## Minimum correlation of possible factor scores 0.84 0.66 0.72 0.54
## MR5
## Correlation of (regression) scores with factors 0.83
## Multiple R square of scores with factors 0.69
## Minimum correlation of possible factor scores 0.37
female3<-fa(datafemale, nfactors=3, rotate="promax", fm="minres", weight=dfemale$BY_WTA)
print(female3, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datafemale, nfactors = 3, rotate = "promax", fm = "minres",
## weight = dfemale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## Stest1vocab 0.72 0.14 -0.09 0.62 0.38 1.1
## Stest5math 0.61 0.17 -0.07 0.50 0.50 1.2
## Stest19disguisedwords 0.60 -0.08 0.29 0.50 0.50 1.5
## Stest20spelling 0.77 -0.28 0.12 0.49 0.51 1.3
## Stest21capitalization 0.61 -0.04 0.02 0.36 0.64 1.0
## Stest22punctuation 0.79 0.03 -0.03 0.64 0.36 1.0
## Stest23english 0.68 -0.03 -0.03 0.42 0.58 1.0
## Stest24expression 0.55 0.03 -0.05 0.31 0.69 1.0
## Stest25wordfunctions 0.71 0.10 -0.04 0.58 0.42 1.0
## Stest26readingcomprehension 0.79 0.11 -0.09 0.70 0.30 1.1
## Stest28mechanicalreasoning 0.09 0.69 -0.03 0.54 0.46 1.0
## Stest29visualization2D -0.06 0.53 0.23 0.35 0.65 1.4
## Stest30visualization3D 0.01 0.72 0.00 0.53 0.47 1.0
## Stest31abstractreasoning 0.32 0.45 0.01 0.47 0.53 1.8
## Stest32arithreasoning 0.61 0.24 -0.09 0.57 0.43 1.4
## Stest33highschoolmath 0.61 0.22 -0.07 0.55 0.45 1.3
## Stest34arithcomputation 0.48 -0.06 0.33 0.40 0.60 1.8
## Stest35tablereading 0.05 0.03 0.65 0.46 0.54 1.0
## Stest36clericalchecking 0.00 -0.09 0.73 0.51 0.49 1.0
## Stest37objectinspection -0.18 0.25 0.61 0.42 0.58 1.5
##
## MR1 MR3 MR2
## SS loadings 6.15 2.11 1.65
## Proportion Var 0.31 0.11 0.08
## Cumulative Var 0.31 0.41 0.50
## Proportion Explained 0.62 0.21 0.17
## Cumulative Proportion 0.62 0.83 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.58 0.33
## MR3 0.58 1.00 0.25
## MR2 0.33 0.25 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 190 with the objective function = 9.4 0.1 with Chi Square = 670968.9
## df of the model are 133 and the objective function was 0.55
## 0.1
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.03
## 0.1
## The harmonic n.obs is 71381 with the empirical chi square 19950.35 with prob < 0
## 0.1The total n.obs was 71381 with Likelihood Chi Square = 39548.86 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.916
## RMSEA index = 0.064 and the 90 % confidence intervals are 0.064 0.065 0.1
## BIC = 38062.48
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.97 0.90 0.87
## Multiple R square of scores with factors 0.93 0.81 0.76
## Minimum correlation of possible factor scores 0.86 0.61 0.52
female4<-fa(datafemale, nfactors=4, rotate="promax", fm="minres", weight=dfemale$BY_WTA)
print(female4, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datafemale, nfactors = 4, rotate = "promax", fm = "minres",
## weight = dfemale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR4 MR2 h2 u2 com
## Stest1vocab 0.66 0.16 0.08 -0.09 0.63 0.37 1.2
## Stest5math 0.17 0.08 0.60 -0.05 0.59 0.41 1.2
## Stest19disguisedwords 0.72 -0.03 -0.16 0.29 0.54 0.46 1.4
## Stest20spelling 0.74 -0.26 0.04 0.12 0.49 0.51 1.3
## Stest21capitalization 0.55 -0.02 0.07 0.01 0.36 0.64 1.0
## Stest22punctuation 0.68 0.03 0.14 -0.03 0.63 0.37 1.1
## Stest23english 0.73 0.01 -0.07 -0.04 0.45 0.55 1.0
## Stest24expression 0.65 0.09 -0.14 -0.06 0.34 0.66 1.2
## Stest25wordfunctions 0.50 0.08 0.28 -0.03 0.58 0.42 1.6
## Stest26readingcomprehension 0.79 0.14 -0.01 -0.10 0.72 0.28 1.1
## Stest28mechanicalreasoning 0.07 0.70 0.01 -0.04 0.55 0.45 1.0
## Stest29visualization2D -0.06 0.53 0.00 0.22 0.35 0.65 1.4
## Stest30visualization3D -0.02 0.71 0.04 0.00 0.53 0.47 1.0
## Stest31abstractreasoning 0.26 0.45 0.07 0.00 0.47 0.53 1.7
## Stest32arithreasoning 0.35 0.20 0.33 -0.08 0.57 0.43 2.7
## Stest33highschoolmath -0.02 0.08 0.87 -0.05 0.78 0.22 1.0
## Stest34arithcomputation 0.16 -0.14 0.44 0.35 0.46 0.54 2.4
## Stest35tablereading 0.03 0.02 0.05 0.65 0.46 0.54 1.0
## Stest36clericalchecking 0.00 -0.09 0.00 0.73 0.51 0.49 1.0
## Stest37objectinspection -0.10 0.27 -0.10 0.61 0.43 0.57 1.5
##
## MR1 MR3 MR4 MR2
## SS loadings 4.81 2.03 1.96 1.64
## Proportion Var 0.24 0.10 0.10 0.08
## Cumulative Var 0.24 0.34 0.44 0.52
## Proportion Explained 0.46 0.19 0.19 0.16
## Cumulative Proportion 0.46 0.65 0.84 1.00
##
## With factor correlations of
## MR1 MR3 MR4 MR2
## MR1 1.00 0.56 0.74 0.32
## MR3 0.56 1.00 0.54 0.25
## MR4 0.74 0.54 1.00 0.26
## MR2 0.32 0.25 0.26 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 190 with the objective function = 9.4 0.1 with Chi Square = 670968.9
## df of the model are 116 and the objective function was 0.26
## 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 7319.28 with prob < 0
## 0.1The total n.obs was 71381 with Likelihood Chi Square = 18371.41 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.955
## RMSEA index = 0.047 and the 90 % confidence intervals are 0.046 0.048 0.1
## BIC = 17075.02
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR4 MR2
## Correlation of (regression) scores with factors 0.96 0.90 0.93 0.87
## Multiple R square of scores with factors 0.92 0.80 0.87 0.76
## Minimum correlation of possible factor scores 0.84 0.61 0.74 0.53
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 MR2 MR5 h2 u2 com
## Stest1vocab 0.50 0.24 0.00 0.04 0.46 0.76 0.24 2.5
## Stest5math 0.06 0.72 0.00 0.01 0.19 0.62 0.38 1.2
## Stest19disguisedwords 0.68 -0.12 -0.06 0.31 0.14 0.55 0.45 1.6
## Stest20spelling 0.78 -0.01 -0.22 0.08 -0.02 0.50 0.50 1.2
## Stest21capitalization 0.61 0.00 0.04 -0.04 -0.08 0.38 0.62 1.0
## Stest22punctuation 0.75 0.05 0.11 -0.10 -0.09 0.67 0.33 1.1
## Stest23english 0.71 -0.07 0.02 -0.05 0.07 0.45 0.55 1.0
## Stest24expression 0.63 -0.14 0.09 -0.06 0.08 0.34 0.66 1.2
## Stest25wordfunctions 0.51 0.25 0.10 -0.06 0.00 0.59 0.41 1.6
## Stest26readingcomprehension 0.70 0.08 0.06 -0.03 0.29 0.75 0.25 1.4
## Stest28mechanicalreasoning 0.02 0.06 0.66 -0.01 0.12 0.55 0.45 1.1
## Stest29visualization2D -0.05 -0.02 0.55 0.20 -0.04 0.35 0.65 1.3
## Stest30visualization3D -0.01 0.01 0.75 -0.04 -0.04 0.54 0.46 1.0
## Stest31abstractreasoning 0.29 0.03 0.50 -0.04 -0.05 0.49 0.51 1.6
## Stest32arithreasoning 0.34 0.33 0.21 -0.09 0.04 0.57 0.43 2.8
## Stest33highschoolmath -0.05 0.88 0.07 -0.04 0.05 0.77 0.23 1.0
## Stest34arithcomputation 0.21 0.38 -0.09 0.30 -0.13 0.48 0.52 2.9
## Stest35tablereading 0.04 0.03 0.02 0.64 -0.03 0.46 0.54 1.0
## Stest36clericalchecking -0.01 0.02 -0.12 0.75 0.03 0.52 0.48 1.1
## Stest37objectinspection -0.11 -0.08 0.24 0.62 0.03 0.43 0.57 1.4
##
## MR1 MR4 MR3 MR2 MR5
## SS loadings 4.59 2.08 1.98 1.64 0.46
## Proportion Var 0.23 0.10 0.10 0.08 0.02
## Cumulative Var 0.23 0.33 0.43 0.51 0.54
## Proportion Explained 0.43 0.19 0.18 0.15 0.04
## Cumulative Proportion 0.43 0.62 0.80 0.96 1.00
##
## With factor correlations of
## MR1 MR4 MR3 MR2 MR5
## MR1 1.00 0.76 0.56 0.35 0.08
## MR4 0.76 1.00 0.56 0.27 -0.01
## MR3 0.56 0.56 1.00 0.29 0.24
## MR2 0.35 0.27 0.29 1.00 -0.19
## MR5 0.08 -0.01 0.24 -0.19 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 5 factors are sufficient.
##
## df null model = 190 with the objective function = 9.4 0.1 with Chi Square = 670968.9
## df of the model are 100 and the objective function was 0.11
## 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 71381 with the empirical chi square 3369.98 with prob < 0
## 0.1The total n.obs was 71381 with Likelihood Chi Square = 7920.46 with prob < 0
## 0.1
## Tucker Lewis Index of factoring reliability = 0.978
## RMSEA index = 0.033 and the 90 % confidence intervals are 0.032 0.034 0.1
## BIC = 6802.88
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR4 MR3 MR2
## Correlation of (regression) scores with factors 0.96 0.93 0.90 0.88
## Multiple R square of scores with factors 0.91 0.87 0.81 0.77
## Minimum correlation of possible factor scores 0.83 0.74 0.62 0.53
## MR5
## Correlation of (regression) scores with factors 0.74
## Multiple R square of scores with factors 0.55
## Minimum correlation of possible factor scores 0.09
CHC common factor model
chc.factor.model <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
'
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
## 125267.631 157.000 0.000 0.913 0.075 0.051
## aic bic
## 6635984.941 6636705.063
Mc(baseline)
## [1] 0.6440062
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
## 82009.186 314.000 0.000 0.943 0.061 0.041
## aic bic
## 6488872.722 6490312.967
Mc(configural)
## [1] 0.750254
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 39 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 146
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 82009.186 69636.869
## Degrees of freedom 314 314
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.178
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 46113.207 39156.337
## 1 35895.979 30480.532
##
## 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 0.751 0.003 236.610 0.000 0.744
## Stst19dsgsdwrd 0.575 0.003 176.852 0.000 0.568
## Stest20spellng 0.639 0.004 178.362 0.000 0.632
## Stest21cptlztn 0.643 0.003 190.651 0.000 0.636
## Stest22puncttn 0.785 0.003 244.705 0.000 0.779
## Stest23english 0.706 0.004 175.390 0.000 0.698
## Stest24exprssn 0.655 0.004 162.702 0.000 0.647
## Stst25wrdfnctn 0.442 0.008 56.793 0.000 0.427
## Stst26rdngcmpr 0.873 0.003 295.671 0.000 0.867
## Stst31bstrctrs 0.293 0.005 61.856 0.000 0.284
## Stst32rthrsnng 0.259 0.009 30.356 0.000 0.243
## math =~
## Stest5math 0.785 0.003 278.143 0.000 0.779
## Stst25wrdfnctn 0.304 0.008 38.742 0.000 0.289
## Stst32rthrsnng 0.534 0.009 62.477 0.000 0.517
## Stst33hghschlm 0.921 0.003 319.850 0.000 0.915
## Stst34rthcmptt 0.491 0.004 131.645 0.000 0.484
## speed =~
## Stst19dsgsdwrd 0.273 0.004 73.324 0.000 0.266
## Stst29vslztn2D 0.225 0.004 55.111 0.000 0.217
## Stst34rthcmptt 0.376 0.004 91.724 0.000 0.368
## Stest35tblrdng 0.730 0.006 131.869 0.000 0.719
## Stst36clrclchc 0.712 0.005 146.945 0.000 0.703
## Stst37bjctnspc 0.587 0.005 122.687 0.000 0.578
## spatial =~
## Stst28mchnclrs 0.696 0.003 213.440 0.000 0.689
## Stst29vslztn2D 0.511 0.004 128.199 0.000 0.503
## Stst30vslztn3D 0.771 0.004 217.726 0.000 0.764
## Stst31bstrctrs 0.469 0.005 93.081 0.000 0.459
## Stst37bjctnspc 0.142 0.005 31.346 0.000 0.133
## ci.upper Std.lv Std.all
##
## 0.757 0.751 0.803
## 0.581 0.575 0.588
## 0.646 0.639 0.639
## 0.649 0.643 0.657
## 0.791 0.785 0.793
## 0.714 0.706 0.691
## 0.663 0.655 0.625
## 0.458 0.442 0.455
## 0.879 0.873 0.856
## 0.303 0.293 0.299
## 0.276 0.259 0.263
##
## 0.790 0.785 0.834
## 0.320 0.304 0.313
## 0.550 0.534 0.540
## 0.926 0.921 0.885
## 0.499 0.491 0.496
##
## 0.280 0.273 0.279
## 0.233 0.225 0.231
## 0.384 0.376 0.379
## 0.741 0.730 0.706
## 0.722 0.712 0.713
## 0.597 0.587 0.572
##
## 0.702 0.696 0.785
## 0.519 0.511 0.525
## 0.778 0.771 0.756
## 0.478 0.469 0.477
## 0.151 0.142 0.138
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.866 0.002 485.567 0.000 0.863
## speed 0.238 0.006 41.909 0.000 0.227
## spatial 0.609 0.004 165.416 0.000 0.602
## math ~~
## speed 0.231 0.005 42.022 0.000 0.220
## spatial 0.652 0.004 185.143 0.000 0.646
## speed ~~
## spatial 0.160 0.006 25.989 0.000 0.148
## ci.upper Std.lv Std.all
##
## 0.870 0.866 0.866
## 0.249 0.238 0.238
## 0.616 0.609 0.609
##
## 0.241 0.231 0.231
## 0.659 0.652 0.652
##
## 0.172 0.160 0.160
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.167 0.004 44.518 0.000 0.160
## .Stst19dsgsdwrd -0.119 0.004 -30.513 0.000 -0.126
## .Stest20spellng -0.258 0.004 -64.136 0.000 -0.265
## .Stest21cptlztn -0.212 0.004 -54.084 0.000 -0.220
## .Stest22puncttn -0.208 0.004 -52.316 0.000 -0.216
## .Stest23english -0.144 0.004 -35.041 0.000 -0.152
## .Stest24exprssn -0.118 0.004 -28.047 0.000 -0.126
## .Stst25wrdfnctn -0.139 0.004 -35.813 0.000 -0.147
## .Stst26rdngcmpr -0.032 0.004 -7.896 0.000 -0.041
## .Stst31bstrctrs 0.055 0.004 13.853 0.000 0.047
## .Stst32rthrsnng 0.121 0.004 30.651 0.000 0.114
## .Stest5math 0.193 0.004 51.128 0.000 0.186
## .Stst33hghschlm 0.117 0.004 28.152 0.000 0.109
## .Stst34rthcmptt -0.078 0.004 -19.713 0.000 -0.086
## .Stst29vslztn2D 0.212 0.004 54.436 0.000 0.204
## .Stest35tblrdng -0.068 0.004 -16.347 0.000 -0.076
## .Stst36clrclchc -0.147 0.004 -37.322 0.000 -0.155
## .Stst37bjctnspc -0.095 0.004 -23.187 0.000 -0.103
## .Stst28mchnclrs 0.536 0.004 151.033 0.000 0.529
## .Stst30vslztn3D 0.190 0.004 46.616 0.000 0.182
## ci.upper Std.lv Std.all
## 0.175 0.167 0.179
## -0.111 -0.119 -0.122
## -0.250 -0.258 -0.257
## -0.204 -0.212 -0.217
## -0.200 -0.208 -0.210
## -0.136 -0.144 -0.141
## -0.110 -0.118 -0.113
## -0.132 -0.139 -0.143
## -0.024 -0.032 -0.032
## 0.063 0.055 0.056
## 0.129 0.121 0.123
## 0.201 0.193 0.205
## 0.125 0.117 0.113
## -0.070 -0.078 -0.079
## 0.219 0.212 0.217
## -0.060 -0.068 -0.066
## -0.140 -0.147 -0.148
## -0.087 -0.095 -0.092
## 0.543 0.536 0.605
## 0.198 0.190 0.186
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.311 0.002 140.394 0.000 0.307
## .Stst19dsgsdwrd 0.475 0.003 156.570 0.000 0.469
## .Stest20spellng 0.593 0.004 168.091 0.000 0.586
## .Stest21cptlztn 0.543 0.003 168.866 0.000 0.537
## .Stest22puncttn 0.363 0.003 139.914 0.000 0.358
## .Stest23english 0.544 0.004 143.444 0.000 0.537
## .Stest24exprssn 0.667 0.004 154.214 0.000 0.659
## .Stst25wrdfnctn 0.424 0.003 157.664 0.000 0.419
## .Stst26rdngcmpr 0.277 0.002 119.890 0.000 0.273
## .Stst31bstrctrs 0.493 0.003 150.266 0.000 0.486
## .Stst32rthrsnng 0.383 0.003 153.304 0.000 0.378
## .Stest5math 0.269 0.003 90.742 0.000 0.263
## .Stst33hghschlm 0.234 0.002 98.470 0.000 0.229
## .Stst34rthcmptt 0.514 0.004 139.231 0.000 0.507
## .Stst29vslztn2D 0.599 0.004 139.839 0.000 0.591
## .Stest35tblrdng 0.536 0.008 64.704 0.000 0.520
## .Stst36clrclchc 0.490 0.006 80.917 0.000 0.478
## .Stst37bjctnspc 0.663 0.005 128.638 0.000 0.653
## .Stst28mchnclrs 0.301 0.003 101.432 0.000 0.295
## .Stst30vslztn3D 0.445 0.004 112.426 0.000 0.437
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.316 0.311 0.356
## 0.481 0.475 0.498
## 0.600 0.593 0.592
## 0.550 0.543 0.568
## 0.369 0.363 0.371
## 0.552 0.544 0.522
## 0.676 0.667 0.609
## 0.429 0.424 0.448
## 0.282 0.277 0.266
## 0.499 0.493 0.510
## 0.388 0.383 0.393
## 0.275 0.269 0.304
## 0.238 0.234 0.216
## 0.521 0.514 0.523
## 0.608 0.599 0.632
## 0.552 0.536 0.501
## 0.502 0.490 0.491
## 0.673 0.663 0.629
## 0.307 0.301 0.384
## 0.453 0.445 0.428
## 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 0.784 0.003 265.362 0.000 0.778
## Stst19dsgsdwrd 0.547 0.003 163.871 0.000 0.540
## Stest20spellng 0.561 0.003 169.562 0.000 0.554
## Stest21cptlztn 0.548 0.004 154.897 0.000 0.541
## Stest22puncttn 0.713 0.003 239.954 0.000 0.707
## Stest23english 0.593 0.004 169.021 0.000 0.587
## Stest24exprssn 0.511 0.004 143.687 0.000 0.504
## Stst25wrdfnctn 0.509 0.006 82.379 0.000 0.497
## Stst26rdngcmpr 0.776 0.003 283.956 0.000 0.771
## Stst31bstrctrs 0.301 0.005 62.945 0.000 0.291
## Stst32rthrsnng 0.395 0.006 60.998 0.000 0.383
## math =~
## Stest5math 0.787 0.003 261.466 0.000 0.781
## Stst25wrdfnctn 0.278 0.006 44.726 0.000 0.266
## Stst32rthrsnng 0.366 0.007 55.168 0.000 0.353
## Stst33hghschlm 0.793 0.003 269.073 0.000 0.787
## Stst34rthcmptt 0.440 0.004 123.544 0.000 0.433
## speed =~
## Stst19dsgsdwrd 0.303 0.004 82.798 0.000 0.295
## Stst29vslztn2D 0.202 0.004 48.407 0.000 0.194
## Stst34rthcmptt 0.346 0.004 86.139 0.000 0.338
## Stest35tblrdng 0.596 0.005 127.673 0.000 0.587
## Stst36clrclchc 0.656 0.004 149.494 0.000 0.647
## Stst37bjctnspc 0.527 0.004 122.518 0.000 0.518
## spatial =~
## Stst28mchnclrs 0.615 0.003 202.814 0.000 0.609
## Stst29vslztn2D 0.479 0.004 124.703 0.000 0.472
## Stst30vslztn3D 0.682 0.003 202.231 0.000 0.675
## Stst31bstrctrs 0.425 0.005 86.338 0.000 0.415
## Stst37bjctnspc 0.142 0.004 36.133 0.000 0.134
## ci.upper Std.lv Std.all
##
## 0.790 0.784 0.803
## 0.553 0.547 0.563
## 0.567 0.561 0.616
## 0.555 0.548 0.594
## 0.719 0.713 0.789
## 0.600 0.593 0.654
## 0.518 0.511 0.570
## 0.521 0.509 0.516
## 0.781 0.776 0.854
## 0.310 0.301 0.316
## 0.408 0.395 0.410
##
## 0.793 0.787 0.795
## 0.291 0.278 0.282
## 0.379 0.366 0.380
## 0.799 0.793 0.860
## 0.447 0.440 0.473
##
## 0.310 0.303 0.312
## 0.210 0.202 0.211
## 0.353 0.346 0.372
## 0.605 0.596 0.691
## 0.664 0.656 0.703
## 0.535 0.527 0.567
##
## 0.620 0.615 0.748
## 0.487 0.479 0.501
## 0.688 0.682 0.733
## 0.434 0.425 0.446
## 0.150 0.142 0.153
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.802 0.002 359.409 0.000 0.798
## speed 0.247 0.006 44.077 0.000 0.236
## spatial 0.624 0.003 179.833 0.000 0.617
## math ~~
## speed 0.182 0.005 34.458 0.000 0.172
## spatial 0.633 0.004 168.817 0.000 0.625
## speed ~~
## spatial 0.195 0.006 33.518 0.000 0.183
## ci.upper Std.lv Std.all
##
## 0.807 0.802 0.802
## 0.258 0.247 0.247
## 0.631 0.624 0.624
##
## 0.192 0.182 0.182
## 0.640 0.633 0.633
##
## 0.206 0.195 0.195
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -0.095 0.004 -24.615 0.000 -0.103
## .Stst19dsgsdwrd 0.150 0.004 38.967 0.000 0.142
## .Stest20spellng 0.280 0.004 77.302 0.000 0.273
## .Stest21cptlztn 0.276 0.004 74.784 0.000 0.268
## .Stest22puncttn 0.278 0.004 76.957 0.000 0.271
## .Stest23english 0.190 0.004 52.481 0.000 0.183
## .Stest24exprssn 0.165 0.004 46.240 0.000 0.158
## .Stst25wrdfnctn 0.196 0.004 50.126 0.000 0.189
## .Stst26rdngcmpr 0.105 0.004 29.044 0.000 0.098
## .Stst31bstrctrs 0.026 0.004 6.799 0.000 0.018
## .Stst32rthrsnng -0.040 0.004 -10.549 0.000 -0.048
## .Stest5math -0.155 0.004 -39.596 0.000 -0.163
## .Stst33hghschlm -0.072 0.004 -19.964 0.000 -0.080
## .Stst34rthcmptt 0.165 0.004 44.491 0.000 0.158
## .Stst29vslztn2D -0.150 0.004 -39.724 0.000 -0.157
## .Stest35tblrdng 0.085 0.003 24.796 0.000 0.078
## .Stst36clrclchc 0.094 0.004 25.710 0.000 0.087
## .Stst37bjctnspc 0.084 0.004 22.827 0.000 0.076
## .Stst28mchnclrs -0.428 0.003 -131.000 0.000 -0.434
## .Stst30vslztn3D -0.115 0.004 -31.342 0.000 -0.122
## ci.upper Std.lv Std.all
## -0.088 -0.095 -0.097
## 0.158 0.150 0.155
## 0.287 0.280 0.308
## 0.283 0.276 0.299
## 0.285 0.278 0.307
## 0.197 0.190 0.209
## 0.172 0.165 0.184
## 0.204 0.196 0.199
## 0.112 0.105 0.116
## 0.033 0.026 0.027
## -0.033 -0.040 -0.042
## -0.147 -0.155 -0.157
## -0.065 -0.072 -0.079
## 0.172 0.165 0.177
## -0.143 -0.150 -0.157
## 0.091 0.085 0.098
## 0.101 0.094 0.100
## 0.091 0.084 0.090
## -0.422 -0.428 -0.521
## -0.108 -0.115 -0.124
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.340 0.002 144.791 0.000 0.335
## .Stst19dsgsdwrd 0.470 0.003 153.982 0.000 0.464
## .Stest20spellng 0.515 0.003 171.911 0.000 0.509
## .Stest21cptlztn 0.552 0.003 170.231 0.000 0.545
## .Stest22puncttn 0.309 0.002 138.966 0.000 0.304
## .Stest23english 0.472 0.003 146.391 0.000 0.466
## .Stest24exprssn 0.542 0.004 151.515 0.000 0.535
## .Stst25wrdfnctn 0.408 0.003 149.003 0.000 0.403
## .Stst26rdngcmpr 0.223 0.002 117.452 0.000 0.220
## .Stst31bstrctrs 0.478 0.003 154.488 0.000 0.472
## .Stst32rthrsnng 0.409 0.002 163.664 0.000 0.404
## .Stest5math 0.360 0.004 100.754 0.000 0.353
## .Stst33hghschlm 0.221 0.002 95.135 0.000 0.217
## .Stst34rthcmptt 0.496 0.004 133.887 0.000 0.489
## .Stst29vslztn2D 0.609 0.004 156.840 0.000 0.601
## .Stest35tblrdng 0.388 0.005 71.943 0.000 0.377
## .Stst36clrclchc 0.439 0.005 87.985 0.000 0.429
## .Stst37bjctnspc 0.538 0.004 133.041 0.000 0.530
## .Stst28mchnclrs 0.298 0.003 115.211 0.000 0.293
## .Stst30vslztn3D 0.400 0.003 118.855 0.000 0.393
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.344 0.340 0.356
## 0.476 0.470 0.498
## 0.521 0.515 0.621
## 0.558 0.552 0.647
## 0.313 0.309 0.378
## 0.479 0.472 0.573
## 0.549 0.542 0.675
## 0.413 0.408 0.420
## 0.227 0.223 0.270
## 0.484 0.478 0.526
## 0.414 0.409 0.439
## 0.367 0.360 0.368
## 0.226 0.221 0.260
## 0.503 0.496 0.574
## 0.616 0.609 0.664
## 0.398 0.388 0.522
## 0.449 0.439 0.505
## 0.546 0.538 0.622
## 0.303 0.298 0.441
## 0.406 0.400 0.462
## 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
## 466 Stest1vocab ~~ Stest26readingcomprehension 2 2
## 223 Stest1vocab ~~ Stest26readingcomprehension 1 1
## 182 math =~ Stest35tablereading 1 1
## 203 spatial =~ Stest20spelling 1 1
## 214 spatial =~ Stest35tablereading 1 1
## 167 english =~ Stest35tablereading 1 1
## 226 Stest1vocab ~~ Stest5math 1 1
## 184 math =~ Stest37objectinspection 1 1
## 446 spatial =~ Stest20spelling 2 2
## 169 english =~ Stest37objectinspection 1 1
## 213 spatial =~ Stest34arithcomputation 1 1
## 219 Stest1vocab ~~ Stest22punctuation 1 1
## 289 Stest22punctuation ~~ Stest26readingcomprehension 1 1
## 233 Stest1vocab ~~ Stest28mechanicalreasoning 1 1
## 478 Stest19disguisedwords ~~ Stest20spelling 2 2
## 469 Stest1vocab ~~ Stest5math 2 2
## 425 math =~ Stest35tablereading 2 2
## 170 english =~ Stest28mechanicalreasoning 1 1
## 506 Stest20spelling ~~ Stest34arithcomputation 2 2
## 263 Stest20spelling ~~ Stest34arithcomputation 1 1
## 462 Stest1vocab ~~ Stest22punctuation 2 2
## 431 speed =~ Stest20spelling 2 2
## 235 Stest19disguisedwords ~~ Stest20spelling 1 1
## 410 english =~ Stest35tablereading 2 2
## 532 Stest22punctuation ~~ Stest26readingcomprehension 2 2
## 457 spatial =~ Stest35tablereading 2 2
## 412 english =~ Stest37objectinspection 2 2
## 288 Stest22punctuation ~~ Stest25wordfunctions 1 1
## 427 math =~ Stest37objectinspection 2 2
## 164 english =~ Stest33highschoolmath 1 1
## level mi epc sepc.lv sepc.all sepc.nox
## 466 1 5114.694 0.099 0.099 0.360 0.360
## 223 1 4983.954 0.101 0.101 0.345 0.345
## 182 1 4295.231 0.267 0.267 0.259 0.259
## 203 1 3837.075 -0.285 -0.285 -0.285 -0.285
## 214 1 3818.138 0.263 0.263 0.255 0.255
## 167 1 3607.096 0.240 0.240 0.233 0.233
## 226 1 3031.351 0.072 0.072 0.250 0.250
## 184 1 2905.976 -0.291 -0.291 -0.283 -0.283
## 446 1 2856.374 -0.241 -0.241 -0.265 -0.265
## 169 1 2795.607 -0.264 -0.264 -0.257 -0.257
## 213 1 2708.566 -0.251 -0.251 -0.253 -0.253
## 219 1 2435.393 -0.075 -0.075 -0.222 -0.222
## 289 1 2376.516 -0.075 -0.075 -0.235 -0.235
## 233 1 2376.186 0.071 0.071 0.233 0.233
## 478 1 2195.566 0.094 0.094 0.191 0.191
## 469 1 2136.186 0.074 0.074 0.212 0.212
## 425 1 2024.141 0.155 0.155 0.180 0.180
## 170 1 1851.075 0.208 0.208 0.235 0.235
## 506 1 1840.673 0.088 0.088 0.174 0.174
## 263 1 1806.266 0.095 0.095 0.173 0.173
## 462 1 1802.311 -0.063 -0.063 -0.195 -0.195
## 431 1 1794.126 0.143 0.143 0.157 0.157
## 235 1 1791.161 0.091 0.091 0.171 0.171
## 410 1 1756.921 0.143 0.143 0.166 0.166
## 532 1 1721.842 -0.054 -0.054 -0.206 -0.206
## 457 1 1683.270 0.153 0.153 0.177 0.177
## 412 1 1644.252 -0.191 -0.191 -0.205 -0.205
## 288 1 1619.565 0.068 0.068 0.172 0.172
## 427 1 1597.304 -0.195 -0.195 -0.209 -0.209
## 164 1 1543.050 -0.403 -0.403 -0.387 -0.387
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
## 86406.629 337.000 0.000 0.939 0.060 0.046
## aic bic
## 6493224.165 6494437.522
Mc(metric)
## [1] 0.7387989
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 54 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 150
## Number of equality constraints 27
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 86406.629 73397.341
## Degrees of freedom 337 337
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.177
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 48172.831 40919.982
## 1 38233.798 32477.359
##
## 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.) 0.791 0.003 289.927 0.000 0.785
## Stst19d (.p2.) 0.583 0.003 219.676 0.000 0.578
## Stst20s (.p3.) 0.622 0.003 216.015 0.000 0.616
## Stst21c (.p4.) 0.619 0.003 217.387 0.000 0.614
## Stst22p (.p5.) 0.777 0.003 278.223 0.000 0.772
## Stst23n (.p6.) 0.673 0.003 210.744 0.000 0.667
## Stst24x (.p7.) 0.601 0.003 190.323 0.000 0.595
## Stst25w (.p8.) 0.502 0.005 97.725 0.000 0.492
## Stst26r (.p9.) 0.854 0.003 307.379 0.000 0.848
## Stst31b (.10.) 0.309 0.004 87.848 0.000 0.302
## Stst32r (.11.) 0.354 0.006 63.773 0.000 0.343
## math =~
## Stst5mt (.12.) 0.810 0.003 320.529 0.000 0.805
## Stst25w (.13.) 0.292 0.005 56.284 0.000 0.282
## Stst32r (.14.) 0.453 0.006 79.661 0.000 0.441
## Stst33h (.15.) 0.892 0.003 318.703 0.000 0.886
## Stst34r (.16.) 0.486 0.003 169.476 0.000 0.480
## speed =~
## Stst19d (.17.) 0.302 0.003 107.312 0.000 0.296
## Sts292D (.18.) 0.227 0.003 72.368 0.000 0.220
## Stst34r (.19.) 0.381 0.003 118.283 0.000 0.375
## Stst35t (.20.) 0.697 0.005 153.882 0.000 0.688
## Stst36c (.21.) 0.724 0.004 181.328 0.000 0.716
## Stst37b (.22.) 0.589 0.004 153.560 0.000 0.582
## spatial =~
## Stst28m (.23.) 0.691 0.003 241.879 0.000 0.686
## Sts292D (.24.) 0.522 0.003 165.439 0.000 0.516
## Sts303D (.25.) 0.766 0.003 246.463 0.000 0.760
## Stst31b (.26.) 0.469 0.004 122.056 0.000 0.462
## Stst37b (.27.) 0.151 0.003 47.835 0.000 0.145
## ci.upper Std.lv Std.all
##
## 0.796 0.791 0.819
## 0.588 0.583 0.588
## 0.628 0.622 0.627
## 0.625 0.619 0.642
## 0.783 0.777 0.789
## 0.679 0.673 0.672
## 0.607 0.601 0.590
## 0.512 0.502 0.498
## 0.859 0.854 0.850
## 0.316 0.309 0.312
## 0.365 0.354 0.355
##
## 0.815 0.810 0.847
## 0.302 0.292 0.290
## 0.464 0.453 0.454
## 0.897 0.892 0.876
## 0.492 0.486 0.492
##
## 0.307 0.302 0.305
## 0.233 0.227 0.232
## 0.387 0.381 0.385
## 0.706 0.697 0.681
## 0.732 0.724 0.724
## 0.597 0.589 0.573
##
## 0.697 0.691 0.783
## 0.528 0.522 0.534
## 0.772 0.766 0.754
## 0.477 0.469 0.473
## 0.158 0.151 0.147
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.866 0.002 507.060 0.000 0.862
## speed 0.226 0.005 42.444 0.000 0.216
## spatial 0.610 0.004 170.802 0.000 0.603
## math ~~
## speed 0.221 0.005 42.706 0.000 0.211
## spatial 0.648 0.003 190.220 0.000 0.641
## speed ~~
## spatial 0.148 0.006 25.945 0.000 0.137
## ci.upper Std.lv Std.all
##
## 0.869 0.866 0.866
## 0.237 0.226 0.226
## 0.617 0.610 0.610
##
## 0.231 0.221 0.221
## 0.654 0.648 0.648
##
## 0.159 0.148 0.148
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.167 0.004 44.518 0.000 0.160
## .Stst19dsgsdwrd -0.119 0.004 -30.513 0.000 -0.126
## .Stest20spellng -0.258 0.004 -64.136 0.000 -0.265
## .Stest21cptlztn -0.212 0.004 -54.084 0.000 -0.220
## .Stest22puncttn -0.208 0.004 -52.316 0.000 -0.216
## .Stest23english -0.144 0.004 -35.041 0.000 -0.152
## .Stest24exprssn -0.118 0.004 -28.047 0.000 -0.126
## .Stst25wrdfnctn -0.139 0.004 -35.813 0.000 -0.147
## .Stst26rdngcmpr -0.032 0.004 -7.896 0.000 -0.041
## .Stst31bstrctrs 0.055 0.004 13.853 0.000 0.047
## .Stst32rthrsnng 0.121 0.004 30.651 0.000 0.114
## .Stest5math 0.193 0.004 51.128 0.000 0.186
## .Stst33hghschlm 0.117 0.004 28.152 0.000 0.109
## .Stst34rthcmptt -0.078 0.004 -19.713 0.000 -0.086
## .Stst29vslztn2D 0.212 0.004 54.436 0.000 0.204
## .Stest35tblrdng -0.068 0.004 -16.347 0.000 -0.076
## .Stst36clrclchc -0.147 0.004 -37.322 0.000 -0.155
## .Stst37bjctnspc -0.095 0.004 -23.187 0.000 -0.103
## .Stst28mchnclrs 0.536 0.004 151.033 0.000 0.529
## .Stst30vslztn3D 0.190 0.004 46.616 0.000 0.182
## ci.upper Std.lv Std.all
## 0.175 0.167 0.173
## -0.111 -0.119 -0.120
## -0.250 -0.258 -0.260
## -0.204 -0.212 -0.220
## -0.200 -0.208 -0.211
## -0.136 -0.144 -0.144
## -0.110 -0.118 -0.116
## -0.132 -0.139 -0.138
## -0.024 -0.032 -0.032
## 0.063 0.055 0.055
## 0.129 0.121 0.122
## 0.201 0.193 0.202
## 0.125 0.117 0.115
## -0.070 -0.078 -0.079
## 0.219 0.212 0.217
## -0.060 -0.068 -0.066
## -0.140 -0.147 -0.147
## -0.087 -0.095 -0.092
## 0.543 0.536 0.607
## 0.198 0.190 0.187
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.307 0.002 141.258 0.000 0.303
## .Stst19dsgsdwrd 0.471 0.003 158.377 0.000 0.465
## .Stest20spellng 0.597 0.003 170.861 0.000 0.590
## .Stest21cptlztn 0.547 0.003 171.968 0.000 0.541
## .Stest22puncttn 0.365 0.003 142.323 0.000 0.360
## .Stest23english 0.551 0.004 143.205 0.000 0.543
## .Stest24exprssn 0.676 0.004 154.647 0.000 0.668
## .Stst25wrdfnctn 0.424 0.003 156.727 0.000 0.418
## .Stst26rdngcmpr 0.279 0.002 123.133 0.000 0.275
## .Stst31bstrctrs 0.492 0.003 152.614 0.000 0.486
## .Stst32rthrsnng 0.388 0.002 157.581 0.000 0.383
## .Stest5math 0.259 0.003 87.212 0.000 0.253
## .Stst33hghschlm 0.242 0.002 108.616 0.000 0.238
## .Stst34rthcmptt 0.514 0.004 141.079 0.000 0.507
## .Stst29vslztn2D 0.596 0.004 141.971 0.000 0.588
## .Stest35tblrdng 0.561 0.008 69.447 0.000 0.545
## .Stst36clrclchc 0.475 0.006 86.314 0.000 0.464
## .Stst37bjctnspc 0.663 0.005 134.667 0.000 0.653
## .Stst28mchnclrs 0.302 0.003 109.943 0.000 0.297
## .Stst30vslztn3D 0.446 0.004 121.123 0.000 0.439
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.311 0.307 0.329
## 0.477 0.471 0.480
## 0.604 0.597 0.607
## 0.554 0.547 0.588
## 0.370 0.365 0.377
## 0.558 0.551 0.549
## 0.685 0.676 0.652
## 0.429 0.424 0.418
## 0.283 0.279 0.277
## 0.498 0.492 0.499
## 0.393 0.388 0.389
## 0.265 0.259 0.283
## 0.246 0.242 0.233
## 0.521 0.514 0.526
## 0.604 0.596 0.625
## 0.577 0.561 0.536
## 0.486 0.475 0.475
## 0.672 0.663 0.626
## 0.308 0.302 0.388
## 0.453 0.446 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
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.791 0.003 289.927 0.000 0.785
## Stst19d (.p2.) 0.583 0.003 219.676 0.000 0.578
## Stst20s (.p3.) 0.622 0.003 216.015 0.000 0.616
## Stst21c (.p4.) 0.619 0.003 217.387 0.000 0.614
## Stst22p (.p5.) 0.777 0.003 278.223 0.000 0.772
## Stst23n (.p6.) 0.673 0.003 210.744 0.000 0.667
## Stst24x (.p7.) 0.601 0.003 190.323 0.000 0.595
## Stst25w (.p8.) 0.502 0.005 97.725 0.000 0.492
## Stst26r (.p9.) 0.854 0.003 307.379 0.000 0.848
## Stst31b (.10.) 0.309 0.004 87.848 0.000 0.302
## Stst32r (.11.) 0.354 0.006 63.773 0.000 0.343
## math =~
## Stst5mt (.12.) 0.810 0.003 320.529 0.000 0.805
## Stst25w (.13.) 0.292 0.005 56.284 0.000 0.282
## Stst32r (.14.) 0.453 0.006 79.661 0.000 0.441
## Stst33h (.15.) 0.892 0.003 318.703 0.000 0.886
## Stst34r (.16.) 0.486 0.003 169.476 0.000 0.480
## speed =~
## Stst19d (.17.) 0.302 0.003 107.312 0.000 0.296
## Sts292D (.18.) 0.227 0.003 72.368 0.000 0.220
## Stst34r (.19.) 0.381 0.003 118.283 0.000 0.375
## Stst35t (.20.) 0.697 0.005 153.882 0.000 0.688
## Stst36c (.21.) 0.724 0.004 181.328 0.000 0.716
## Stst37b (.22.) 0.589 0.004 153.560 0.000 0.582
## spatial =~
## Stst28m (.23.) 0.691 0.003 241.879 0.000 0.686
## Sts292D (.24.) 0.522 0.003 165.439 0.000 0.516
## Sts303D (.25.) 0.766 0.003 246.463 0.000 0.760
## Stst31b (.26.) 0.469 0.004 122.056 0.000 0.462
## Stst37b (.27.) 0.151 0.003 47.835 0.000 0.145
## ci.upper Std.lv Std.all
##
## 0.796 0.733 0.778
## 0.588 0.540 0.565
## 0.628 0.577 0.628
## 0.625 0.574 0.613
## 0.783 0.721 0.793
## 0.679 0.624 0.674
## 0.607 0.557 0.605
## 0.512 0.465 0.489
## 0.859 0.792 0.859
## 0.316 0.287 0.304
## 0.365 0.328 0.344
##
## 0.815 0.746 0.772
## 0.302 0.269 0.283
## 0.464 0.417 0.437
## 0.897 0.822 0.872
## 0.492 0.448 0.481
##
## 0.307 0.269 0.281
## 0.233 0.202 0.212
## 0.387 0.339 0.364
## 0.706 0.621 0.714
## 0.732 0.645 0.693
## 0.597 0.525 0.566
##
## 0.697 0.620 0.751
## 0.528 0.468 0.491
## 0.772 0.687 0.736
## 0.477 0.421 0.446
## 0.158 0.136 0.146
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.687 0.005 130.782 0.000 0.676
## speed 0.212 0.005 44.811 0.000 0.203
## spatial 0.519 0.005 104.982 0.000 0.509
## math ~~
## speed 0.155 0.004 36.035 0.000 0.147
## spatial 0.527 0.005 104.806 0.000 0.517
## speed ~~
## spatial 0.162 0.005 35.197 0.000 0.153
## ci.upper Std.lv Std.all
##
## 0.697 0.804 0.804
## 0.221 0.256 0.256
## 0.529 0.624 0.624
##
## 0.164 0.189 0.189
## 0.537 0.638 0.638
##
## 0.171 0.203 0.203
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -0.095 0.004 -24.615 0.000 -0.103
## .Stst19dsgsdwrd 0.150 0.004 38.967 0.000 0.142
## .Stest20spellng 0.280 0.004 77.302 0.000 0.273
## .Stest21cptlztn 0.276 0.004 74.784 0.000 0.268
## .Stest22puncttn 0.278 0.004 76.957 0.000 0.271
## .Stest23english 0.190 0.004 52.481 0.000 0.183
## .Stest24exprssn 0.165 0.004 46.240 0.000 0.158
## .Stst25wrdfnctn 0.196 0.004 50.126 0.000 0.189
## .Stst26rdngcmpr 0.105 0.004 29.044 0.000 0.098
## .Stst31bstrctrs 0.026 0.004 6.799 0.000 0.018
## .Stst32rthrsnng -0.040 0.004 -10.549 0.000 -0.048
## .Stest5math -0.155 0.004 -39.596 0.000 -0.163
## .Stst33hghschlm -0.072 0.004 -19.964 0.000 -0.080
## .Stst34rthcmptt 0.165 0.004 44.491 0.000 0.158
## .Stst29vslztn2D -0.150 0.004 -39.724 0.000 -0.157
## .Stest35tblrdng 0.085 0.003 24.796 0.000 0.078
## .Stst36clrclchc 0.094 0.004 25.710 0.000 0.087
## .Stst37bjctnspc 0.084 0.004 22.827 0.000 0.076
## .Stst28mchnclrs -0.428 0.003 -131.000 0.000 -0.434
## .Stst30vslztn3D -0.115 0.004 -31.342 0.000 -0.122
## ci.upper Std.lv Std.all
## -0.088 -0.095 -0.101
## 0.158 0.150 0.157
## 0.287 0.280 0.305
## 0.283 0.276 0.294
## 0.285 0.278 0.306
## 0.197 0.190 0.205
## 0.172 0.165 0.179
## 0.204 0.196 0.206
## 0.112 0.105 0.114
## 0.033 0.026 0.027
## -0.033 -0.040 -0.042
## -0.147 -0.155 -0.160
## -0.065 -0.072 -0.077
## 0.172 0.165 0.177
## -0.143 -0.150 -0.157
## 0.091 0.085 0.097
## 0.101 0.094 0.101
## 0.091 0.084 0.090
## -0.422 -0.428 -0.519
## -0.108 -0.115 -0.124
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.350 0.002 152.078 0.000 0.346
## .Stst19dsgsdwrd 0.477 0.003 161.748 0.000 0.471
## .Stest20spellng 0.512 0.003 172.959 0.000 0.506
## .Stest21cptlztn 0.548 0.003 170.549 0.000 0.542
## .Stest22puncttn 0.306 0.002 140.102 0.000 0.302
## .Stest23english 0.469 0.003 146.051 0.000 0.462
## .Stest24exprssn 0.539 0.004 150.849 0.000 0.532
## .Stst25wrdfnctn 0.415 0.003 151.637 0.000 0.410
## .Stst26rdngcmpr 0.224 0.002 119.141 0.000 0.220
## .Stst31bstrctrs 0.480 0.003 157.218 0.000 0.474
## .Stst32rthrsnng 0.408 0.002 165.560 0.000 0.404
## .Stest5math 0.377 0.004 102.161 0.000 0.369
## .Stst33hghschlm 0.213 0.002 94.398 0.000 0.208
## .Stst34rthcmptt 0.495 0.004 135.960 0.000 0.488
## .Stst29vslztn2D 0.612 0.004 162.117 0.000 0.605
## .Stest35tblrdng 0.371 0.005 69.489 0.000 0.361
## .Stst36clrclchc 0.451 0.005 96.478 0.000 0.442
## .Stst37bjctnspc 0.538 0.004 139.154 0.000 0.531
## .Stst28mchnclrs 0.296 0.002 123.238 0.000 0.292
## .Stst30vslztn3D 0.399 0.003 126.953 0.000 0.392
## english 0.860 0.007 122.035 0.000 0.846
## math 0.849 0.007 127.740 0.000 0.836
## speed 0.794 0.010 80.682 0.000 0.774
## spatial 0.804 0.008 106.150 0.000 0.790
## ci.upper Std.lv Std.all
## 0.355 0.350 0.395
## 0.482 0.477 0.521
## 0.518 0.512 0.606
## 0.555 0.548 0.625
## 0.311 0.306 0.371
## 0.475 0.469 0.546
## 0.546 0.539 0.634
## 0.420 0.415 0.459
## 0.227 0.224 0.263
## 0.486 0.480 0.539
## 0.413 0.408 0.449
## 0.384 0.377 0.403
## 0.217 0.213 0.240
## 0.503 0.495 0.570
## 0.619 0.612 0.672
## 0.382 0.371 0.490
## 0.460 0.451 0.520
## 0.546 0.538 0.625
## 0.301 0.296 0.435
## 0.405 0.399 0.458
## 0.874 1.000 1.000
## 0.863 1.000 1.000
## 0.813 1.000 1.000
## 0.819 1.000 1.000
lavTestScore(metric, release = 1:27)
## 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 4340.637 27 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p82. 962.202 1 0.000
## 2 .p2. == .p83. 62.158 1 0.000
## 3 .p3. == .p84. 54.552 1 0.000
## 4 .p4. == .p85. 141.224 1 0.000
## 5 .p5. == .p86. 21.873 1 0.000
## 6 .p6. == .p87. 262.985 1 0.000
## 7 .p7. == .p88. 557.393 1 0.000
## 8 .p8. == .p89. 850.152 1 0.000
## 9 .p9. == .p90. 254.357 1 0.000
## 10 .p10. == .p91. 76.289 1 0.000
## 11 .p11. == .p92. 164.434 1 0.000
## 12 .p12. == .p93. 489.658 1 0.000
## 13 .p13. == .p94. 729.790 1 0.000
## 14 .p14. == .p95. 35.128 1 0.000
## 15 .p15. == .p96. 997.064 1 0.000
## 16 .p16. == .p97. 18.325 1 0.000
## 17 .p17. == .p98. 205.498 1 0.000
## 18 .p18. == .p99. 0.361 1 0.548
## 19 .p19. == .p100. 3.187 1 0.074
## 20 .p20. == .p101. 151.159 1 0.000
## 21 .p21. == .p102. 1.572 1 0.210
## 22 .p22. == .p103. 3.552 1 0.059
## 23 .p23. == .p104. 18.697 1 0.000
## 24 .p24. == .p105. 15.274 1 0.000
## 25 .p25. == .p106. 16.716 1 0.000
## 26 .p26. == .p107. 56.852 1 0.000
## 27 .p27. == .p108. 1.005 1 0.316
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 srmr
## 163169.161 353.000 0.000 0.885 0.081 0.061
## aic bic
## 6569954.696 6571010.218
Mc(scalar)
## [1] 0.5640191
summary(scalar, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 63 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 154
## Number of equality constraints 47
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 163169.161 138849.214
## Degrees of freedom 353 353
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.175
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 84815.830 72174.247
## 1 78353.330 66674.967
##
## 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.) 0.717 0.003 251.333 0.000 0.711
## Stst19d (.p2.) 0.573 0.003 215.858 0.000 0.568
## Stst20s (.p3.) 0.657 0.003 225.661 0.000 0.651
## Stst21c (.p4.) 0.651 0.003 227.562 0.000 0.645
## Stst22p (.p5.) 0.807 0.003 288.657 0.000 0.802
## Stst23n (.p6.) 0.684 0.003 214.665 0.000 0.678
## Stst24x (.p7.) 0.608 0.003 192.721 0.000 0.602
## Stst25w (.p8.) 0.666 0.004 156.562 0.000 0.657
## Stst26r (.p9.) 0.826 0.003 295.591 0.000 0.821
## Stst31b (.10.) 0.435 0.003 146.916 0.000 0.429
## Stst32r (.11.) 0.240 0.005 49.429 0.000 0.230
## math =~
## Stst5mt (.12.) 0.818 0.002 329.665 0.000 0.813
## Stst25w (.13.) 0.128 0.004 28.979 0.000 0.119
## Stst32r (.14.) 0.566 0.005 113.663 0.000 0.557
## Stst33h (.15.) 0.882 0.003 310.826 0.000 0.876
## Stst34r (.16.) 0.451 0.003 155.542 0.000 0.445
## speed =~
## Stst19d (.17.) 0.289 0.003 103.748 0.000 0.284
## Sts292D (.18.) 0.252 0.003 84.096 0.000 0.246
## Stst34r (.19.) 0.420 0.003 133.476 0.000 0.413
## Stst35t (.20.) 0.681 0.004 155.397 0.000 0.672
## Stst36c (.21.) 0.712 0.004 185.373 0.000 0.704
## Stst37b (.22.) 0.608 0.004 165.450 0.000 0.601
## spatial =~
## Stst28m (.23.) 0.791 0.003 303.811 0.000 0.786
## Sts292D (.24.) 0.483 0.003 164.700 0.000 0.478
## Sts303D (.25.) 0.600 0.003 174.652 0.000 0.593
## Stst31b (.26.) 0.307 0.003 102.522 0.000 0.301
## Stst37b (.27.) 0.112 0.003 42.921 0.000 0.107
## ci.upper Std.lv Std.all
##
## 0.723 0.717 0.754
## 0.578 0.573 0.581
## 0.663 0.657 0.642
## 0.656 0.651 0.658
## 0.813 0.807 0.802
## 0.691 0.684 0.678
## 0.614 0.608 0.594
## 0.674 0.666 0.656
## 0.832 0.826 0.829
## 0.441 0.435 0.440
## 0.249 0.240 0.240
##
## 0.823 0.818 0.847
## 0.136 0.128 0.126
## 0.576 0.566 0.566
## 0.887 0.882 0.868
## 0.457 0.451 0.453
##
## 0.295 0.289 0.293
## 0.258 0.252 0.260
## 0.426 0.420 0.421
## 0.689 0.681 0.670
## 0.719 0.712 0.714
## 0.615 0.608 0.589
##
## 0.796 0.791 0.860
## 0.489 0.483 0.497
## 0.606 0.600 0.615
## 0.313 0.307 0.310
## 0.117 0.112 0.108
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.880 0.002 522.492 0.000 0.877
## speed 0.251 0.005 47.702 0.000 0.241
## spatial 0.604 0.004 171.557 0.000 0.597
## math ~~
## speed 0.235 0.005 45.615 0.000 0.225
## spatial 0.636 0.003 181.852 0.000 0.629
## speed ~~
## spatial 0.148 0.006 26.523 0.000 0.137
## ci.upper Std.lv Std.all
##
## 0.883 0.880 0.880
## 0.262 0.251 0.251
## 0.611 0.604 0.604
##
## 0.245 0.235 0.235
## 0.643 0.636 0.636
##
## 0.159 0.148 0.148
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.58.) -0.072 0.004 -17.547 0.000 -0.080
## .Stst19d (.59.) -0.148 0.003 -42.474 0.000 -0.155
## .Stst20s (.60.) -0.101 0.004 -27.187 0.000 -0.109
## .Stst21c (.61.) -0.091 0.004 -24.815 0.000 -0.099
## .Stst22p (.62.) -0.109 0.004 -27.778 0.000 -0.117
## .Stst23n (.63.) -0.103 0.004 -27.732 0.000 -0.110
## .Stst24x (.64.) -0.088 0.004 -24.080 0.000 -0.095
## .Stst25w (.65.) -0.078 0.004 -20.891 0.000 -0.086
## .Stst26r (.66.) -0.128 0.004 -31.965 0.000 -0.136
## .Stst31b (.67.) 0.120 0.004 32.917 0.000 0.113
## .Stst32r (.68.) 0.077 0.004 19.566 0.000 0.069
## .Stst5mt (.69.) 0.145 0.004 38.100 0.000 0.138
## .Stst33h (.70.) 0.148 0.004 36.255 0.000 0.140
## .Stst34r (.71.) 0.027 0.004 7.275 0.000 0.020
## .Sts292D (.72.) 0.235 0.003 69.759 0.000 0.228
## .Stst35t (.73.) -0.135 0.004 -35.057 0.000 -0.142
## .Stst36c (.74.) -0.165 0.004 -46.088 0.000 -0.172
## .Stst37b (.75.) -0.062 0.004 -16.567 0.000 -0.069
## .Stst28m (.76.) 0.470 0.004 111.840 0.000 0.462
## .Sts303D (.77.) 0.363 0.003 104.860 0.000 0.356
## ci.upper Std.lv Std.all
## -0.064 -0.072 -0.075
## -0.141 -0.148 -0.150
## -0.094 -0.101 -0.099
## -0.084 -0.091 -0.092
## -0.101 -0.109 -0.108
## -0.096 -0.103 -0.102
## -0.081 -0.088 -0.086
## -0.071 -0.078 -0.077
## -0.121 -0.128 -0.129
## 0.127 0.120 0.122
## 0.084 0.077 0.077
## 0.153 0.145 0.150
## 0.156 0.148 0.145
## 0.034 0.027 0.027
## 0.241 0.235 0.242
## -0.127 -0.135 -0.133
## -0.158 -0.165 -0.166
## -0.054 -0.062 -0.060
## 0.479 0.470 0.512
## 0.369 0.363 0.372
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.391 0.003 132.151 0.000 0.385
## .Stst19dsgsdwrd 0.478 0.003 160.405 0.000 0.472
## .Stest20spellng 0.617 0.004 163.070 0.000 0.610
## .Stest21cptlztn 0.555 0.003 167.218 0.000 0.549
## .Stest22puncttn 0.362 0.003 136.182 0.000 0.356
## .Stest23english 0.550 0.004 142.713 0.000 0.543
## .Stest24exprssn 0.678 0.004 154.263 0.000 0.669
## .Stst25wrdfnctn 0.421 0.003 150.746 0.000 0.416
## .Stst26rdngcmpr 0.310 0.002 127.342 0.000 0.306
## .Stst31bstrctrs 0.533 0.003 157.993 0.000 0.527
## .Stst32rthrsnng 0.383 0.003 152.251 0.000 0.378
## .Stest5math 0.263 0.003 87.616 0.000 0.257
## .Stst33hghschlm 0.253 0.002 111.745 0.000 0.249
## .Stst34rthcmptt 0.525 0.004 136.548 0.000 0.518
## .Stst29vslztn2D 0.611 0.004 141.259 0.000 0.603
## .Stest35tblrdng 0.569 0.008 74.405 0.000 0.554
## .Stst36clrclchc 0.488 0.006 86.828 0.000 0.477
## .Stst37bjctnspc 0.662 0.005 132.987 0.000 0.653
## .Stst28mchnclrs 0.219 0.004 61.283 0.000 0.212
## .Stst30vslztn3D 0.591 0.004 138.670 0.000 0.583
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.397 0.391 0.432
## 0.484 0.478 0.491
## 0.625 0.617 0.588
## 0.562 0.555 0.567
## 0.367 0.362 0.357
## 0.558 0.550 0.540
## 0.686 0.678 0.647
## 0.427 0.421 0.409
## 0.315 0.310 0.313
## 0.540 0.533 0.545
## 0.388 0.383 0.383
## 0.269 0.263 0.282
## 0.258 0.253 0.246
## 0.533 0.525 0.528
## 0.620 0.611 0.647
## 0.584 0.569 0.551
## 0.499 0.488 0.490
## 0.672 0.662 0.622
## 0.226 0.219 0.260
## 0.600 0.591 0.622
## 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.) 0.717 0.003 251.333 0.000 0.711
## Stst19d (.p2.) 0.573 0.003 215.858 0.000 0.568
## Stst20s (.p3.) 0.657 0.003 225.661 0.000 0.651
## Stst21c (.p4.) 0.651 0.003 227.562 0.000 0.645
## Stst22p (.p5.) 0.807 0.003 288.657 0.000 0.802
## Stst23n (.p6.) 0.684 0.003 214.665 0.000 0.678
## Stst24x (.p7.) 0.608 0.003 192.721 0.000 0.602
## Stst25w (.p8.) 0.666 0.004 156.562 0.000 0.657
## Stst26r (.p9.) 0.826 0.003 295.591 0.000 0.821
## Stst31b (.10.) 0.435 0.003 146.916 0.000 0.429
## Stst32r (.11.) 0.240 0.005 49.429 0.000 0.230
## math =~
## Stst5mt (.12.) 0.818 0.002 329.665 0.000 0.813
## Stst25w (.13.) 0.128 0.004 28.979 0.000 0.119
## Stst32r (.14.) 0.566 0.005 113.663 0.000 0.557
## Stst33h (.15.) 0.882 0.003 310.826 0.000 0.876
## Stst34r (.16.) 0.451 0.003 155.542 0.000 0.445
## speed =~
## Stst19d (.17.) 0.289 0.003 103.748 0.000 0.284
## Sts292D (.18.) 0.252 0.003 84.096 0.000 0.246
## Stst34r (.19.) 0.420 0.003 133.476 0.000 0.413
## Stst35t (.20.) 0.681 0.004 155.397 0.000 0.672
## Stst36c (.21.) 0.712 0.004 185.373 0.000 0.704
## Stst37b (.22.) 0.608 0.004 165.450 0.000 0.601
## spatial =~
## Stst28m (.23.) 0.791 0.003 303.811 0.000 0.786
## Sts292D (.24.) 0.483 0.003 164.700 0.000 0.478
## Sts303D (.25.) 0.600 0.003 174.652 0.000 0.593
## Stst31b (.26.) 0.307 0.003 102.522 0.000 0.301
## Stst37b (.27.) 0.112 0.003 42.921 0.000 0.107
## ci.upper Std.lv Std.all
##
## 0.723 0.661 0.691
## 0.578 0.528 0.555
## 0.663 0.606 0.641
## 0.656 0.600 0.626
## 0.813 0.744 0.804
## 0.691 0.631 0.678
## 0.614 0.560 0.606
## 0.674 0.613 0.639
## 0.832 0.761 0.836
## 0.441 0.401 0.426
## 0.249 0.221 0.231
##
## 0.823 0.752 0.772
## 0.136 0.117 0.122
## 0.576 0.521 0.544
## 0.887 0.811 0.863
## 0.457 0.415 0.442
##
## 0.295 0.259 0.272
## 0.258 0.225 0.237
## 0.426 0.375 0.399
## 0.689 0.608 0.703
## 0.719 0.636 0.685
## 0.615 0.543 0.584
##
## 0.796 0.710 0.827
## 0.489 0.434 0.457
## 0.606 0.539 0.602
## 0.313 0.276 0.293
## 0.117 0.100 0.108
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.696 0.005 129.618 0.000 0.686
## speed 0.232 0.005 48.870 0.000 0.223
## spatial 0.507 0.005 103.551 0.000 0.498
## math ~~
## speed 0.167 0.004 38.169 0.000 0.158
## spatial 0.521 0.005 103.010 0.000 0.511
## speed ~~
## spatial 0.162 0.005 35.345 0.000 0.153
## ci.upper Std.lv Std.all
##
## 0.707 0.822 0.822
## 0.242 0.282 0.282
## 0.517 0.613 0.613
##
## 0.175 0.203 0.203
## 0.530 0.630 0.630
##
## 0.171 0.201 0.201
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.58.) -0.072 0.004 -17.547 0.000 -0.080
## .Stst19d (.59.) -0.148 0.003 -42.474 0.000 -0.155
## .Stst20s (.60.) -0.101 0.004 -27.187 0.000 -0.109
## .Stst21c (.61.) -0.091 0.004 -24.815 0.000 -0.099
## .Stst22p (.62.) -0.109 0.004 -27.778 0.000 -0.117
## .Stst23n (.63.) -0.103 0.004 -27.732 0.000 -0.110
## .Stst24x (.64.) -0.088 0.004 -24.080 0.000 -0.095
## .Stst25w (.65.) -0.078 0.004 -20.891 0.000 -0.086
## .Stst26r (.66.) -0.128 0.004 -31.965 0.000 -0.136
## .Stst31b (.67.) 0.120 0.004 32.917 0.000 0.113
## .Stst32r (.68.) 0.077 0.004 19.566 0.000 0.069
## .Stst5mt (.69.) 0.145 0.004 38.100 0.000 0.138
## .Stst33h (.70.) 0.148 0.004 36.255 0.000 0.140
## .Stst34r (.71.) 0.027 0.004 7.275 0.000 0.020
## .Sts292D (.72.) 0.235 0.003 69.759 0.000 0.228
## .Stst35t (.73.) -0.135 0.004 -35.057 0.000 -0.142
## .Stst36c (.74.) -0.165 0.004 -46.088 0.000 -0.172
## .Stst37b (.75.) -0.062 0.004 -16.567 0.000 -0.069
## .Stst28m (.76.) 0.470 0.004 111.840 0.000 0.462
## .Sts303D (.77.) 0.363 0.003 104.860 0.000 0.356
## english 0.376 0.006 62.029 0.000 0.364
## math -0.281 0.006 -46.570 0.000 -0.293
## speed 0.388 0.007 55.007 0.000 0.374
## spatial -1.048 0.008 -123.536 0.000 -1.064
## ci.upper Std.lv Std.all
## -0.064 -0.072 -0.075
## -0.141 -0.148 -0.156
## -0.094 -0.101 -0.107
## -0.084 -0.091 -0.095
## -0.101 -0.109 -0.118
## -0.096 -0.103 -0.111
## -0.081 -0.088 -0.095
## -0.071 -0.078 -0.082
## -0.121 -0.128 -0.141
## 0.127 0.120 0.128
## 0.084 0.077 0.080
## 0.153 0.145 0.149
## 0.156 0.148 0.157
## 0.034 0.027 0.029
## 0.241 0.235 0.247
## -0.127 -0.135 -0.156
## -0.158 -0.165 -0.178
## -0.054 -0.062 -0.066
## 0.479 0.470 0.547
## 0.369 0.363 0.405
## 0.388 0.408 0.408
## -0.269 -0.305 -0.305
## 0.401 0.434 0.434
## -1.031 -1.166 -1.166
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.478 0.004 131.723 0.000 0.470
## .Stst19dsgsdwrd 0.483 0.003 163.278 0.000 0.477
## .Stest20spellng 0.527 0.003 168.469 0.000 0.521
## .Stest21cptlztn 0.559 0.003 166.243 0.000 0.553
## .Stest22puncttn 0.302 0.002 135.931 0.000 0.298
## .Stest23english 0.468 0.003 146.271 0.000 0.462
## .Stest24exprssn 0.541 0.004 151.532 0.000 0.534
## .Stst25wrdfnctn 0.413 0.003 147.777 0.000 0.408
## .Stst26rdngcmpr 0.249 0.002 120.348 0.000 0.245
## .Stst31bstrctrs 0.512 0.003 163.928 0.000 0.506
## .Stst32rthrsnng 0.408 0.003 158.324 0.000 0.403
## .Stest5math 0.384 0.004 100.043 0.000 0.376
## .Stst33hghschlm 0.225 0.002 98.930 0.000 0.221
## .Stst34rthcmptt 0.505 0.004 133.870 0.000 0.498
## .Stst29vslztn2D 0.623 0.004 163.615 0.000 0.616
## .Stest35tblrdng 0.378 0.005 70.060 0.000 0.367
## .Stst36clrclchc 0.459 0.004 104.092 0.000 0.450
## .Stst37bjctnspc 0.538 0.004 137.870 0.000 0.530
## .Stst28mchnclrs 0.234 0.003 75.563 0.000 0.228
## .Stst30vslztn3D 0.511 0.003 149.046 0.000 0.505
## english 0.849 0.007 121.469 0.000 0.835
## math 0.845 0.007 127.156 0.000 0.832
## speed 0.799 0.010 81.222 0.000 0.780
## spatial 0.808 0.008 105.469 0.000 0.792
## ci.upper Std.lv Std.all
## 0.485 0.478 0.522
## 0.489 0.483 0.533
## 0.533 0.527 0.590
## 0.566 0.559 0.609
## 0.307 0.302 0.353
## 0.475 0.468 0.541
## 0.548 0.541 0.633
## 0.419 0.413 0.448
## 0.253 0.249 0.300
## 0.519 0.512 0.579
## 0.413 0.408 0.445
## 0.391 0.384 0.404
## 0.230 0.225 0.255
## 0.513 0.505 0.574
## 0.631 0.623 0.691
## 0.388 0.378 0.505
## 0.467 0.459 0.531
## 0.545 0.538 0.622
## 0.240 0.234 0.316
## 0.518 0.511 0.638
## 0.863 1.000 1.000
## 0.858 1.000 1.000
## 0.818 1.000 1.000
## 0.823 1.000 1.000
lavTestScore(scalar, release = 28:47)
## 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 71731.63 20 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p58. == .p139. 27364.523 1 0
## 2 .p59. == .p140. 316.148 1 0
## 3 .p60. == .p141. 5908.498 1 0
## 4 .p61. == .p142. 4234.861 1 0
## 5 .p62. == .p143. 4608.171 1 0
## 6 .p63. == .p144. 466.978 1 0
## 7 .p64. == .p145. 191.731 1 0
## 8 .p65. == .p146. 2481.586 1 0
## 9 .p66. == .p147. 5256.827 1 0
## 10 .p67. == .p148. 2750.767 1 0
## 11 .p68. == .p149. 1678.587 1 0
## 12 .p69. == .p150. 2395.331 1 0
## 13 .p70. == .p151. 1115.089 1 0
## 14 .p71. == .p152. 3927.351 1 0
## 15 .p72. == .p153. 227.174 1 0
## 16 .p73. == .p154. 1499.977 1 0
## 17 .p74. == .p155. 154.363 1 0
## 18 .p75. == .p156. 405.333 1 0
## 19 .p76. == .p157. 16769.018 1 0
## 20 .p77. == .p158. 12013.381 1 0
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("Stest1vocab~1", "Stest28mechanicalreasoning~1", "Stest26readingcomprehension~1", "Stest34arithcomputation~1", "Stest33highschoolmath~1", "Stest19disguisedwords~1", "Stest29visualization2D~1"))
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 91276.094 346.000 0.000 0.936 0.061 0.047
## aic bic
## 6498075.629 6499200.204
Mc(scalar2)
## [1] 0.7262761
summary(scalar2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 66 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 154
## Number of equality constraints 40
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 91276.094 77577.303
## Degrees of freedom 346 346
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.177
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 50517.102 42935.454
## 1 40758.991 34641.849
##
## 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.) 0.789 0.003 290.400 0.000 0.784
## Stst19d (.p2.) 0.583 0.003 220.647 0.000 0.578
## Stst20s (.p3.) 0.645 0.003 234.504 0.000 0.640
## Stst21c (.p4.) 0.634 0.003 230.780 0.000 0.628
## Stst22p (.p5.) 0.775 0.003 283.415 0.000 0.770
## Stst23n (.p6.) 0.655 0.003 210.630 0.000 0.649
## Stst24x (.p7.) 0.581 0.003 189.548 0.000 0.575
## Stst25w (.p8.) 0.585 0.003 184.056 0.000 0.579
## Stst26r (.p9.) 0.852 0.003 307.957 0.000 0.847
## Stst31b (.10.) 0.293 0.003 100.164 0.000 0.288
## Stst32r (.11.) 0.236 0.004 65.252 0.000 0.229
## math =~
## Stst5mt (.12.) 0.806 0.003 322.093 0.000 0.801
## Stst25w (.13.) 0.207 0.003 63.724 0.000 0.201
## Stst32r (.14.) 0.571 0.004 148.183 0.000 0.563
## Stst33h (.15.) 0.889 0.003 322.502 0.000 0.884
## Stst34r (.16.) 0.487 0.003 170.070 0.000 0.482
## speed =~
## Stst19d (.17.) 0.301 0.003 107.869 0.000 0.296
## Sts292D (.18.) 0.227 0.003 72.568 0.000 0.221
## Stst34r (.19.) 0.379 0.003 118.064 0.000 0.373
## Stst35t (.20.) 0.687 0.004 152.932 0.000 0.678
## Stst36c (.21.) 0.728 0.004 187.917 0.000 0.720
## Stst37b (.22.) 0.598 0.004 159.975 0.000 0.591
## spatial =~
## Stst28m (.23.) 0.690 0.003 241.994 0.000 0.685
## Sts292D (.24.) 0.521 0.003 165.147 0.000 0.514
## Sts303D (.25.) 0.764 0.003 246.115 0.000 0.758
## Stst31b (.26.) 0.486 0.003 149.822 0.000 0.479
## Stst37b (.27.) 0.141 0.003 45.998 0.000 0.135
## ci.upper Std.lv Std.all
##
## 0.795 0.789 0.818
## 0.588 0.583 0.589
## 0.651 0.645 0.641
## 0.639 0.634 0.651
## 0.780 0.775 0.789
## 0.661 0.655 0.660
## 0.587 0.581 0.575
## 0.591 0.585 0.579
## 0.857 0.852 0.849
## 0.299 0.293 0.296
## 0.243 0.236 0.236
##
## 0.811 0.806 0.844
## 0.214 0.207 0.205
## 0.578 0.571 0.572
## 0.895 0.889 0.873
## 0.493 0.487 0.493
##
## 0.307 0.301 0.304
## 0.233 0.227 0.232
## 0.385 0.379 0.383
## 0.696 0.687 0.673
## 0.735 0.728 0.727
## 0.605 0.598 0.580
##
## 0.696 0.690 0.782
## 0.527 0.521 0.533
## 0.770 0.764 0.752
## 0.492 0.486 0.489
## 0.147 0.141 0.136
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.872 0.002 521.134 0.000 0.869
## speed 0.227 0.005 42.832 0.000 0.216
## spatial 0.610 0.004 172.849 0.000 0.603
## math ~~
## speed 0.219 0.005 42.406 0.000 0.209
## spatial 0.656 0.003 197.593 0.000 0.649
## speed ~~
## spatial 0.149 0.006 26.278 0.000 0.138
## ci.upper Std.lv Std.all
##
## 0.876 0.872 0.872
## 0.237 0.227 0.227
## 0.617 0.610 0.610
##
## 0.229 0.219 0.219
## 0.662 0.656 0.656
##
## 0.160 0.149 0.149
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc 0.167 0.004 44.518 0.000 0.160
## .Stst19d -0.119 0.004 -30.513 0.000 -0.126
## .Stst20s (.60.) -0.194 0.004 -53.312 0.000 -0.201
## .Stst21c (.61.) -0.174 0.004 -48.436 0.000 -0.182
## .Stst22p (.62.) -0.218 0.004 -57.107 0.000 -0.225
## .Stst23n (.63.) -0.194 0.004 -51.825 0.000 -0.201
## .Stst24x (.64.) -0.171 0.004 -45.736 0.000 -0.178
## .Stst25w (.65.) -0.114 0.004 -30.347 0.000 -0.121
## .Stst26r -0.032 0.004 -7.897 0.000 -0.041
## .Stst31b (.67.) 0.044 0.004 11.574 0.000 0.036
## .Stst32r (.68.) 0.095 0.004 24.316 0.000 0.088
## .Stst5mt (.69.) 0.202 0.004 54.641 0.000 0.195
## .Stst33h 0.117 0.004 28.152 0.000 0.109
## .Stst34r -0.078 0.004 -19.713 0.000 -0.086
## .Sts292D 0.212 0.004 54.436 0.000 0.204
## .Stst35t (.73.) -0.102 0.004 -27.125 0.000 -0.110
## .Stst36c (.74.) -0.138 0.004 -37.187 0.000 -0.145
## .Stst37b (.75.) -0.065 0.004 -18.249 0.000 -0.072
## .Stst28m 0.536 0.004 151.033 0.000 0.529
## .Sts303D (.77.) 0.193 0.004 48.466 0.000 0.185
## ci.upper Std.lv Std.all
## 0.175 0.167 0.173
## -0.111 -0.119 -0.120
## -0.187 -0.194 -0.193
## -0.167 -0.174 -0.179
## -0.210 -0.218 -0.222
## -0.187 -0.194 -0.195
## -0.164 -0.171 -0.169
## -0.107 -0.114 -0.113
## -0.024 -0.032 -0.032
## 0.051 0.044 0.044
## 0.103 0.095 0.096
## 0.209 0.202 0.211
## 0.125 0.117 0.115
## -0.070 -0.078 -0.079
## 0.219 0.212 0.217
## -0.095 -0.102 -0.100
## -0.130 -0.138 -0.138
## -0.058 -0.065 -0.063
## 0.543 0.536 0.607
## 0.201 0.193 0.190
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.309 0.002 141.702 0.000 0.305
## .Stst19dsgsdwrd 0.470 0.003 158.327 0.000 0.464
## .Stest20spellng 0.597 0.004 168.511 0.000 0.590
## .Stest21cptlztn 0.546 0.003 170.953 0.000 0.540
## .Stest22puncttn 0.364 0.003 142.881 0.000 0.359
## .Stest23english 0.557 0.004 144.401 0.000 0.549
## .Stest24exprssn 0.685 0.004 158.391 0.000 0.676
## .Stst25wrdfnctn 0.424 0.003 155.175 0.000 0.419
## .Stst26rdngcmpr 0.281 0.002 124.152 0.000 0.277
## .Stst31bstrctrs 0.489 0.003 151.526 0.000 0.483
## .Stst32rthrsnng 0.381 0.002 153.986 0.000 0.376
## .Stest5math 0.262 0.003 87.937 0.000 0.256
## .Stst33hghschlm 0.248 0.002 112.573 0.000 0.243
## .Stst34rthcmptt 0.516 0.004 141.536 0.000 0.509
## .Stst29vslztn2D 0.597 0.004 142.137 0.000 0.589
## .Stest35tblrdng 0.569 0.008 72.091 0.000 0.554
## .Stst36clrclchc 0.472 0.006 84.180 0.000 0.461
## .Stst37bjctnspc 0.661 0.005 133.550 0.000 0.651
## .Stst28mchnclrs 0.304 0.003 111.159 0.000 0.298
## .Stst30vslztn3D 0.448 0.004 121.985 0.000 0.440
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.313 0.309 0.331
## 0.476 0.470 0.479
## 0.604 0.597 0.589
## 0.553 0.546 0.576
## 0.369 0.364 0.377
## 0.564 0.557 0.565
## 0.693 0.685 0.669
## 0.429 0.424 0.415
## 0.286 0.281 0.279
## 0.496 0.489 0.497
## 0.386 0.381 0.382
## 0.268 0.262 0.287
## 0.252 0.248 0.238
## 0.523 0.516 0.527
## 0.605 0.597 0.625
## 0.585 0.569 0.547
## 0.483 0.472 0.471
## 0.671 0.661 0.621
## 0.309 0.304 0.389
## 0.455 0.448 0.434
## 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.) 0.789 0.003 290.400 0.000 0.784
## Stst19d (.p2.) 0.583 0.003 220.647 0.000 0.578
## Stst20s (.p3.) 0.645 0.003 234.504 0.000 0.640
## Stst21c (.p4.) 0.634 0.003 230.780 0.000 0.628
## Stst22p (.p5.) 0.775 0.003 283.415 0.000 0.770
## Stst23n (.p6.) 0.655 0.003 210.630 0.000 0.649
## Stst24x (.p7.) 0.581 0.003 189.548 0.000 0.575
## Stst25w (.p8.) 0.585 0.003 184.056 0.000 0.579
## Stst26r (.p9.) 0.852 0.003 307.957 0.000 0.847
## Stst31b (.10.) 0.293 0.003 100.164 0.000 0.288
## Stst32r (.11.) 0.236 0.004 65.252 0.000 0.229
## math =~
## Stst5mt (.12.) 0.806 0.003 322.093 0.000 0.801
## Stst25w (.13.) 0.207 0.003 63.724 0.000 0.201
## Stst32r (.14.) 0.571 0.004 148.183 0.000 0.563
## Stst33h (.15.) 0.889 0.003 322.502 0.000 0.884
## Stst34r (.16.) 0.487 0.003 170.070 0.000 0.482
## speed =~
## Stst19d (.17.) 0.301 0.003 107.869 0.000 0.296
## Sts292D (.18.) 0.227 0.003 72.568 0.000 0.221
## Stst34r (.19.) 0.379 0.003 118.064 0.000 0.373
## Stst35t (.20.) 0.687 0.004 152.932 0.000 0.678
## Stst36c (.21.) 0.728 0.004 187.917 0.000 0.720
## Stst37b (.22.) 0.598 0.004 159.975 0.000 0.591
## spatial =~
## Stst28m (.23.) 0.690 0.003 241.994 0.000 0.685
## Sts292D (.24.) 0.521 0.003 165.147 0.000 0.514
## Sts303D (.25.) 0.764 0.003 246.115 0.000 0.758
## Stst31b (.26.) 0.486 0.003 149.822 0.000 0.479
## Stst37b (.27.) 0.141 0.003 45.998 0.000 0.135
## ci.upper Std.lv Std.all
##
## 0.795 0.733 0.777
## 0.588 0.541 0.565
## 0.651 0.599 0.641
## 0.639 0.588 0.622
## 0.780 0.719 0.793
## 0.661 0.608 0.663
## 0.587 0.540 0.591
## 0.591 0.543 0.568
## 0.857 0.791 0.857
## 0.299 0.272 0.289
## 0.243 0.219 0.229
##
## 0.811 0.740 0.767
## 0.214 0.190 0.199
## 0.578 0.524 0.548
## 0.895 0.816 0.865
## 0.493 0.447 0.480
##
## 0.307 0.269 0.281
## 0.233 0.202 0.212
## 0.385 0.338 0.363
## 0.696 0.613 0.707
## 0.735 0.649 0.697
## 0.605 0.534 0.574
##
## 0.696 0.619 0.750
## 0.527 0.467 0.490
## 0.770 0.686 0.735
## 0.492 0.436 0.462
## 0.147 0.126 0.136
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.696 0.005 131.716 0.000 0.685
## speed 0.213 0.005 45.130 0.000 0.204
## spatial 0.521 0.005 104.625 0.000 0.511
## math ~~
## speed 0.156 0.004 36.191 0.000 0.148
## spatial 0.533 0.005 106.164 0.000 0.523
## speed ~~
## spatial 0.164 0.005 35.443 0.000 0.155
## ci.upper Std.lv Std.all
##
## 0.706 0.817 0.817
## 0.222 0.257 0.257
## 0.530 0.625 0.625
##
## 0.165 0.191 0.191
## 0.543 0.648 0.648
##
## 0.173 0.205 0.205
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -0.609 0.005 -120.226 0.000 -0.618
## .Stst19d -0.321 0.005 -69.676 0.000 -0.330
## .Stst20s (.60.) -0.194 0.004 -53.312 0.000 -0.201
## .Stst21c (.61.) -0.174 0.004 -48.436 0.000 -0.182
## .Stst22p (.62.) -0.218 0.004 -57.107 0.000 -0.225
## .Stst23n (.63.) -0.194 0.004 -51.825 0.000 -0.201
## .Stst24x (.64.) -0.171 0.004 -45.736 0.000 -0.178
## .Stst25w (.65.) -0.114 0.004 -30.347 0.000 -0.121
## .Stst26r -0.449 0.005 -87.332 0.000 -0.459
## .Stst31b (.67.) 0.044 0.004 11.574 0.000 0.036
## .Stst32r (.68.) 0.095 0.004 24.316 0.000 0.088
## .Stst5mt (.69.) 0.202 0.004 54.641 0.000 0.195
## .Stst33h 0.335 0.005 60.988 0.000 0.324
## .Stst34r 0.272 0.005 55.913 0.000 0.263
## .Sts292D -0.008 0.005 -1.581 0.114 -0.017
## .Stst35t (.73.) -0.102 0.004 -27.125 0.000 -0.110
## .Stst36c (.74.) -0.138 0.004 -37.187 0.000 -0.145
## .Stst37b (.75.) -0.065 0.004 -18.249 0.000 -0.072
## .Stst28m -0.147 0.005 -30.471 0.000 -0.157
## .Sts303D (.77.) 0.193 0.004 48.466 0.000 0.185
## english 0.650 0.006 103.439 0.000 0.638
## math -0.458 0.007 -65.929 0.000 -0.472
## speed 0.305 0.007 44.745 0.000 0.292
## spatial -0.407 0.007 -56.099 0.000 -0.421
## ci.upper Std.lv Std.all
## -0.599 -0.609 -0.646
## -0.312 -0.321 -0.336
## -0.187 -0.194 -0.208
## -0.167 -0.174 -0.184
## -0.210 -0.218 -0.240
## -0.187 -0.194 -0.212
## -0.164 -0.171 -0.187
## -0.107 -0.114 -0.119
## -0.439 -0.449 -0.487
## 0.051 0.044 0.046
## 0.103 0.095 0.100
## 0.209 0.202 0.209
## 0.346 0.335 0.355
## 0.282 0.272 0.292
## 0.002 -0.008 -0.008
## -0.095 -0.102 -0.118
## -0.130 -0.138 -0.148
## -0.058 -0.065 -0.070
## -0.138 -0.147 -0.179
## 0.201 0.193 0.207
## 0.663 0.701 0.701
## -0.445 -0.499 -0.499
## 0.318 0.342 0.342
## -0.393 -0.453 -0.453
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.352 0.002 152.194 0.000 0.347
## .Stst19dsgsdwrd 0.476 0.003 161.915 0.000 0.470
## .Stest20spellng 0.513 0.003 171.616 0.000 0.507
## .Stest21cptlztn 0.549 0.003 169.621 0.000 0.543
## .Stest22puncttn 0.305 0.002 139.799 0.000 0.301
## .Stest23english 0.472 0.003 145.233 0.000 0.465
## .Stest24exprssn 0.542 0.004 149.220 0.000 0.535
## .Stst25wrdfnctn 0.415 0.003 150.590 0.000 0.409
## .Stst26rdngcmpr 0.226 0.002 120.010 0.000 0.222
## .Stst31bstrctrs 0.478 0.003 157.695 0.000 0.472
## .Stst32rthrsnng 0.405 0.003 160.525 0.000 0.400
## .Stest5math 0.382 0.004 104.018 0.000 0.375
## .Stst33hghschlm 0.224 0.002 101.162 0.000 0.219
## .Stst34rthcmptt 0.496 0.004 136.194 0.000 0.489
## .Stst29vslztn2D 0.612 0.004 162.277 0.000 0.605
## .Stest35tblrdng 0.377 0.005 69.453 0.000 0.366
## .Stst36clrclchc 0.448 0.005 98.704 0.000 0.439
## .Stst37bjctnspc 0.536 0.004 138.443 0.000 0.529
## .Stst28mchnclrs 0.297 0.002 124.221 0.000 0.293
## .Stst30vslztn3D 0.400 0.003 128.198 0.000 0.394
## english 0.861 0.007 122.908 0.000 0.848
## math 0.842 0.007 128.335 0.000 0.829
## speed 0.796 0.010 80.779 0.000 0.777
## spatial 0.805 0.008 106.004 0.000 0.790
## ci.upper Std.lv Std.all
## 0.356 0.352 0.396
## 0.482 0.476 0.520
## 0.519 0.513 0.589
## 0.555 0.549 0.613
## 0.309 0.305 0.371
## 0.478 0.472 0.561
## 0.549 0.542 0.651
## 0.420 0.415 0.454
## 0.230 0.226 0.265
## 0.484 0.478 0.537
## 0.410 0.405 0.443
## 0.389 0.382 0.411
## 0.228 0.224 0.252
## 0.503 0.496 0.572
## 0.620 0.612 0.673
## 0.388 0.377 0.501
## 0.456 0.448 0.515
## 0.544 0.536 0.620
## 0.302 0.297 0.437
## 0.406 0.400 0.460
## 0.875 1.000 1.000
## 0.854 1.000 1.000
## 0.815 1.000 1.000
## 0.820 1.000 1.000
lavTestScore(scalar2, release = 28:40)
## 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 4827.481 13 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p60. == .p141. 1182.761 1 0
## 2 .p61. == .p142. 486.611 1 0
## 3 .p62. == .p143. 60.294 1 0
## 4 .p63. == .p144. 787.315 1 0
## 5 .p64. == .p145. 658.106 1 0
## 6 .p65. == .p146. 730.939 1 0
## 7 .p67. == .p148. 77.641 1 0
## 8 .p68. == .p149. 1050.482 1 0
## 9 .p69. == .p150. 466.131 1 0
## 10 .p73. == .p154. 408.909 1 0
## 11 .p74. == .p155. 51.648 1 0
## 12 .p75. == .p156. 242.578 1 0
## 13 .p77. == .p158. 14.313 1 0
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("Stest1vocab~1", "Stest28mechanicalreasoning~1", "Stest26readingcomprehension~1", "Stest34arithcomputation~1", "Stest33highschoolmath~1", "Stest19disguisedwords~1", "Stest29visualization2D~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 98543.621 366.000 0.000 0.931 0.061 0.050
## aic bic
## 6505303.157 6506230.437
Mc(strict)
## [1] 0.7079962
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("Stest1vocab~1", "Stest28mechanicalreasoning~1", "Stest26readingcomprehension~1", "Stest34arithcomputation~1", "Stest33highschoolmath~1", "Stest19disguisedwords~1", "Stest29visualization2D~1"))
fitMeasures(chc.cov, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 92146.630 352.000 0.000 0.935 0.061 0.058
## aic bic
## 6498934.165 6499999.552
Mc(chc.cov)
## [1] 0.724071
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("Stest1vocab~1", "Stest28mechanicalreasoning~1", "Stest26readingcomprehension~1", "Stest34arithcomputation~1", "Stest33highschoolmath~1", "Stest19disguisedwords~1", "Stest29visualization2D~1"))
fitMeasures(chc.vcov, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 93205.386 356.000 0.000 0.935 0.061 0.059
## aic bic
## 6499984.922 6501010.849
Mc(chc.vcov)
## [1] 0.7213898
summary(chc.vcov, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 43 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 150
## Number of equality constraints 46
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 93205.386 79252.605
## Degrees of freedom 356 356
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.176
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 51512.873 43801.432
## 1 41692.513 35451.173
##
## 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.) 0.762 0.002 347.165 0.000 0.758
## Stst19d (.p2.) 0.562 0.002 242.063 0.000 0.558
## Stst20s (.p3.) 0.622 0.002 271.272 0.000 0.618
## Stst21c (.p4.) 0.611 0.002 264.837 0.000 0.607
## Stst22p (.p5.) 0.747 0.002 348.075 0.000 0.743
## Stst23n (.p6.) 0.632 0.003 239.770 0.000 0.627
## Stst24x (.p7.) 0.561 0.003 212.541 0.000 0.555
## Stst25w (.p8.) 0.563 0.003 184.383 0.000 0.557
## Stst26r (.p9.) 0.822 0.002 404.656 0.000 0.818
## Stst31b (.10.) 0.282 0.003 101.860 0.000 0.277
## Stst32r (.11.) 0.224 0.003 64.726 0.000 0.217
## math =~
## Stst5mt (.12.) 0.775 0.002 371.989 0.000 0.770
## Stst25w (.13.) 0.201 0.003 64.707 0.000 0.195
## Stst32r (.14.) 0.552 0.003 157.978 0.000 0.545
## Stst33h (.15.) 0.852 0.002 408.518 0.000 0.848
## Stst34r (.16.) 0.468 0.003 181.348 0.000 0.463
## speed =~
## Stst19d (.17.) 0.287 0.003 110.588 0.000 0.282
## Sts292D (.18.) 0.215 0.003 73.742 0.000 0.209
## Stst34r (.19.) 0.358 0.003 125.271 0.000 0.352
## Stst35t (.20.) 0.646 0.004 180.101 0.000 0.639
## Stst36c (.21.) 0.689 0.003 217.750 0.000 0.683
## Stst37b (.22.) 0.565 0.003 181.221 0.000 0.559
## spatial =~
## Stst28m (.23.) 0.655 0.002 294.134 0.000 0.651
## Sts292D (.24.) 0.495 0.003 178.619 0.000 0.489
## Sts303D (.25.) 0.725 0.002 297.363 0.000 0.720
## Stst31b (.26.) 0.462 0.003 155.701 0.000 0.456
## Stst37b (.27.) 0.134 0.003 46.434 0.000 0.128
## ci.upper Std.lv Std.all
##
## 0.766 0.762 0.808
## 0.567 0.562 0.578
## 0.627 0.622 0.627
## 0.616 0.611 0.637
## 0.752 0.747 0.778
## 0.637 0.632 0.646
## 0.566 0.561 0.561
## 0.569 0.563 0.570
## 0.826 0.822 0.840
## 0.288 0.282 0.291
## 0.231 0.224 0.231
##
## 0.779 0.775 0.834
## 0.207 0.201 0.204
## 0.559 0.552 0.568
## 0.856 0.852 0.865
## 0.473 0.468 0.484
##
## 0.292 0.287 0.295
## 0.221 0.215 0.223
## 0.364 0.358 0.370
## 0.653 0.646 0.648
## 0.695 0.689 0.705
## 0.571 0.565 0.557
##
## 0.660 0.655 0.763
## 0.500 0.495 0.514
## 0.729 0.725 0.732
## 0.467 0.462 0.475
## 0.139 0.134 0.132
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math (.52.) 0.848 0.001 602.720 0.000 0.845
## speed (.53.) 0.241 0.004 60.753 0.000 0.233
## spatial (.54.) 0.618 0.003 245.848 0.000 0.613
## math ~~
## speed (.55.) 0.207 0.004 54.069 0.000 0.199
## spatial (.56.) 0.653 0.002 262.876 0.000 0.649
## speed ~~
## spatial (.57.) 0.175 0.004 41.354 0.000 0.167
## ci.upper Std.lv Std.all
##
## 0.851 0.848 0.848
## 0.249 0.241 0.241
## 0.623 0.618 0.618
##
## 0.214 0.207 0.207
## 0.658 0.653 0.653
##
## 0.183 0.175 0.175
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc 0.167 0.004 44.519 0.000 0.160
## .Stst19d -0.119 0.004 -30.513 0.000 -0.126
## .Stst20s (.60.) -0.194 0.004 -53.434 0.000 -0.202
## .Stst21c (.61.) -0.175 0.004 -48.528 0.000 -0.182
## .Stst22p (.62.) -0.218 0.004 -57.230 0.000 -0.226
## .Stst23n (.63.) -0.194 0.004 -51.933 0.000 -0.202
## .Stst24x (.64.) -0.171 0.004 -45.825 0.000 -0.179
## .Stst25w (.65.) -0.113 0.004 -30.162 0.000 -0.121
## .Stst26r -0.032 0.004 -7.896 0.000 -0.041
## .Stst31b (.67.) 0.044 0.004 11.626 0.000 0.036
## .Stst32r (.68.) 0.097 0.004 24.590 0.000 0.089
## .Stst5mt (.69.) 0.201 0.004 54.512 0.000 0.194
## .Stst33h 0.117 0.004 28.153 0.000 0.109
## .Stst34r -0.078 0.004 -19.713 0.000 -0.086
## .Sts292D 0.212 0.004 54.436 0.000 0.204
## .Stst35t (.73.) -0.102 0.004 -27.151 0.000 -0.109
## .Stst36c (.74.) -0.138 0.004 -37.226 0.000 -0.145
## .Stst37b (.75.) -0.065 0.004 -18.236 0.000 -0.073
## .Stst28m 0.536 0.004 151.033 0.000 0.529
## .Sts303D (.77.) 0.193 0.004 48.456 0.000 0.185
## ci.upper Std.lv Std.all
## 0.175 0.167 0.177
## -0.111 -0.119 -0.122
## -0.187 -0.194 -0.196
## -0.168 -0.175 -0.182
## -0.211 -0.218 -0.227
## -0.187 -0.194 -0.199
## -0.164 -0.171 -0.171
## -0.106 -0.113 -0.115
## -0.024 -0.032 -0.033
## 0.051 0.044 0.045
## 0.104 0.097 0.100
## 0.208 0.201 0.217
## 0.125 0.117 0.119
## -0.070 -0.078 -0.081
## 0.219 0.212 0.220
## -0.095 -0.102 -0.102
## -0.131 -0.138 -0.141
## -0.058 -0.065 -0.065
## 0.543 0.536 0.624
## 0.201 0.193 0.195
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.308 0.002 141.564 0.000 0.304
## .Stst19dsgsdwrd 0.468 0.003 158.398 0.000 0.462
## .Stest20spellng 0.597 0.004 168.703 0.000 0.590
## .Stest21cptlztn 0.546 0.003 171.031 0.000 0.540
## .Stest22puncttn 0.365 0.003 142.852 0.000 0.360
## .Stest23english 0.556 0.004 144.179 0.000 0.549
## .Stest24exprssn 0.684 0.004 158.243 0.000 0.676
## .Stst25wrdfnctn 0.424 0.003 155.380 0.000 0.419
## .Stst26rdngcmpr 0.281 0.002 124.386 0.000 0.276
## .Stst31bstrctrs 0.490 0.003 151.602 0.000 0.484
## .Stst32rthrsnng 0.381 0.002 153.943 0.000 0.376
## .Stest5math 0.262 0.003 87.021 0.000 0.256
## .Stst33hghschlm 0.245 0.002 114.185 0.000 0.240
## .Stst34rthcmptt 0.518 0.004 142.075 0.000 0.511
## .Stst29vslztn2D 0.600 0.004 143.156 0.000 0.591
## .Stest35tblrdng 0.576 0.008 72.649 0.000 0.560
## .Stst36clrclchc 0.480 0.006 85.608 0.000 0.469
## .Stst37bjctnspc 0.664 0.005 134.722 0.000 0.655
## .Stst28mchnclrs 0.308 0.003 114.977 0.000 0.302
## .Stst30vslztn3D 0.456 0.004 126.376 0.000 0.449
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.313 0.308 0.347
## 0.474 0.468 0.496
## 0.604 0.597 0.607
## 0.553 0.546 0.594
## 0.370 0.365 0.395
## 0.564 0.556 0.582
## 0.693 0.684 0.685
## 0.429 0.424 0.436
## 0.285 0.281 0.294
## 0.497 0.490 0.519
## 0.385 0.381 0.403
## 0.267 0.262 0.304
## 0.249 0.245 0.252
## 0.525 0.518 0.554
## 0.608 0.600 0.646
## 0.591 0.576 0.580
## 0.491 0.480 0.503
## 0.674 0.664 0.646
## 0.313 0.308 0.417
## 0.463 0.456 0.465
## 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.) 0.762 0.002 347.165 0.000 0.758
## Stst19d (.p2.) 0.562 0.002 242.063 0.000 0.558
## Stst20s (.p3.) 0.622 0.002 271.272 0.000 0.618
## Stst21c (.p4.) 0.611 0.002 264.837 0.000 0.607
## Stst22p (.p5.) 0.747 0.002 348.075 0.000 0.743
## Stst23n (.p6.) 0.632 0.003 239.770 0.000 0.627
## Stst24x (.p7.) 0.561 0.003 212.541 0.000 0.555
## Stst25w (.p8.) 0.563 0.003 184.383 0.000 0.557
## Stst26r (.p9.) 0.822 0.002 404.656 0.000 0.818
## Stst31b (.10.) 0.282 0.003 101.860 0.000 0.277
## Stst32r (.11.) 0.224 0.003 64.726 0.000 0.217
## math =~
## Stst5mt (.12.) 0.775 0.002 371.989 0.000 0.770
## Stst25w (.13.) 0.201 0.003 64.707 0.000 0.195
## Stst32r (.14.) 0.552 0.003 157.978 0.000 0.545
## Stst33h (.15.) 0.852 0.002 408.518 0.000 0.848
## Stst34r (.16.) 0.468 0.003 181.348 0.000 0.463
## speed =~
## Stst19d (.17.) 0.287 0.003 110.588 0.000 0.282
## Sts292D (.18.) 0.215 0.003 73.742 0.000 0.209
## Stst34r (.19.) 0.358 0.003 125.271 0.000 0.352
## Stst35t (.20.) 0.646 0.004 180.101 0.000 0.639
## Stst36c (.21.) 0.689 0.003 217.750 0.000 0.683
## Stst37b (.22.) 0.565 0.003 181.221 0.000 0.559
## spatial =~
## Stst28m (.23.) 0.655 0.002 294.134 0.000 0.651
## Sts292D (.24.) 0.495 0.003 178.619 0.000 0.489
## Sts303D (.25.) 0.725 0.002 297.363 0.000 0.720
## Stst31b (.26.) 0.462 0.003 155.701 0.000 0.456
## Stst37b (.27.) 0.134 0.003 46.434 0.000 0.128
## ci.upper Std.lv Std.all
##
## 0.766 0.762 0.789
## 0.567 0.562 0.576
## 0.627 0.622 0.656
## 0.616 0.611 0.636
## 0.752 0.747 0.804
## 0.637 0.632 0.677
## 0.566 0.561 0.606
## 0.569 0.563 0.573
## 0.826 0.822 0.866
## 0.288 0.282 0.293
## 0.231 0.224 0.228
##
## 0.779 0.775 0.782
## 0.207 0.201 0.205
## 0.559 0.552 0.561
## 0.856 0.852 0.870
## 0.473 0.468 0.490
##
## 0.292 0.287 0.294
## 0.221 0.215 0.222
## 0.364 0.358 0.375
## 0.653 0.646 0.725
## 0.695 0.689 0.721
## 0.571 0.565 0.596
##
## 0.660 0.655 0.771
## 0.500 0.495 0.511
## 0.729 0.725 0.756
## 0.467 0.462 0.478
## 0.139 0.134 0.141
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math (.52.) 0.848 0.001 602.720 0.000 0.845
## speed (.53.) 0.241 0.004 60.753 0.000 0.233
## spatial (.54.) 0.618 0.003 245.848 0.000 0.613
## math ~~
## speed (.55.) 0.207 0.004 54.069 0.000 0.199
## spatial (.56.) 0.653 0.002 262.876 0.000 0.649
## speed ~~
## spatial (.57.) 0.175 0.004 41.354 0.000 0.167
## ci.upper Std.lv Std.all
##
## 0.851 0.848 0.848
## 0.249 0.241 0.241
## 0.623 0.618 0.618
##
## 0.214 0.207 0.207
## 0.658 0.653 0.653
##
## 0.183 0.175 0.175
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -0.610 0.005 -120.213 0.000 -0.620
## .Stst19d -0.322 0.005 -69.819 0.000 -0.331
## .Stst20s (.60.) -0.194 0.004 -53.434 0.000 -0.202
## .Stst21c (.61.) -0.175 0.004 -48.528 0.000 -0.182
## .Stst22p (.62.) -0.218 0.004 -57.230 0.000 -0.226
## .Stst23n (.63.) -0.194 0.004 -51.933 0.000 -0.202
## .Stst24x (.64.) -0.171 0.004 -45.825 0.000 -0.179
## .Stst25w (.65.) -0.113 0.004 -30.162 0.000 -0.121
## .Stst26r -0.450 0.005 -87.585 0.000 -0.460
## .Stst31b (.67.) 0.044 0.004 11.626 0.000 0.036
## .Stst32r (.68.) 0.097 0.004 24.590 0.000 0.089
## .Stst5mt (.69.) 0.201 0.004 54.512 0.000 0.194
## .Stst33h 0.332 0.005 60.984 0.000 0.321
## .Stst34r 0.271 0.005 55.865 0.000 0.262
## .Sts292D -0.008 0.005 -1.581 0.114 -0.017
## .Stst35t (.73.) -0.102 0.004 -27.151 0.000 -0.109
## .Stst36c (.74.) -0.138 0.004 -37.226 0.000 -0.145
## .Stst37b (.75.) -0.065 0.004 -18.236 0.000 -0.073
## .Stst28m -0.147 0.005 -30.377 0.000 -0.157
## .Sts303D (.77.) 0.193 0.004 48.456 0.000 0.185
## english 0.675 0.007 100.943 0.000 0.662
## math -0.475 0.007 -66.581 0.000 -0.489
## speed 0.324 0.007 46.947 0.000 0.310
## spatial -0.429 0.008 -56.991 0.000 -0.444
## ci.upper Std.lv Std.all
## -0.600 -0.610 -0.632
## -0.313 -0.322 -0.330
## -0.187 -0.194 -0.205
## -0.168 -0.175 -0.182
## -0.211 -0.218 -0.235
## -0.187 -0.194 -0.208
## -0.164 -0.171 -0.185
## -0.106 -0.113 -0.116
## -0.440 -0.450 -0.474
## 0.051 0.044 0.045
## 0.104 0.097 0.098
## 0.208 0.201 0.203
## 0.343 0.332 0.339
## 0.281 0.271 0.284
## 0.002 -0.008 -0.008
## -0.095 -0.102 -0.114
## -0.131 -0.138 -0.144
## -0.058 -0.065 -0.069
## -0.138 -0.147 -0.173
## 0.201 0.193 0.201
## 0.688 0.675 0.675
## -0.461 -0.475 -0.475
## 0.337 0.324 0.324
## -0.414 -0.429 -0.429
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.351 0.002 152.766 0.000 0.347
## .Stst19dsgsdwrd 0.476 0.003 162.284 0.000 0.470
## .Stest20spellng 0.513 0.003 171.951 0.000 0.508
## .Stest21cptlztn 0.549 0.003 169.744 0.000 0.543
## .Stest22puncttn 0.305 0.002 139.942 0.000 0.301
## .Stest23english 0.472 0.003 145.295 0.000 0.466
## .Stest24exprssn 0.543 0.004 149.323 0.000 0.536
## .Stst25wrdfnctn 0.414 0.003 150.608 0.000 0.409
## .Stst26rdngcmpr 0.226 0.002 120.584 0.000 0.223
## .Stst31bstrctrs 0.477 0.003 157.513 0.000 0.471
## .Stst32rthrsnng 0.404 0.003 160.874 0.000 0.399
## .Stest5math 0.382 0.004 104.566 0.000 0.375
## .Stst33hghschlm 0.232 0.002 109.190 0.000 0.228
## .Stst34rthcmptt 0.494 0.004 136.040 0.000 0.487
## .Stst29vslztn2D 0.609 0.004 162.013 0.000 0.602
## .Stest35tblrdng 0.377 0.005 69.487 0.000 0.366
## .Stst36clrclchc 0.439 0.004 97.667 0.000 0.430
## .Stst37bjctnspc 0.534 0.004 138.188 0.000 0.526
## .Stst28mchnclrs 0.294 0.002 121.552 0.000 0.289
## .Stst30vslztn3D 0.394 0.003 126.210 0.000 0.388
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.356 0.351 0.377
## 0.482 0.476 0.500
## 0.519 0.513 0.570
## 0.556 0.549 0.595
## 0.309 0.305 0.353
## 0.478 0.472 0.542
## 0.550 0.543 0.633
## 0.419 0.414 0.430
## 0.230 0.226 0.251
## 0.483 0.477 0.513
## 0.409 0.404 0.417
## 0.389 0.382 0.389
## 0.236 0.232 0.242
## 0.502 0.494 0.543
## 0.617 0.609 0.650
## 0.387 0.377 0.475
## 0.448 0.439 0.480
## 0.541 0.534 0.595
## 0.298 0.294 0.406
## 0.400 0.394 0.429
## 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, metric, scalar2, chc.cov, chc.vcov)
Td=tests[2:5,"Chisq diff"]
Td
## [1] 3753.8426 4227.7525 790.9207 851.4462
dfd=tests[2:5,"Df diff"]
dfd
## [1] 23 9 6 4
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04777201 0.08120910 0.04290137 0.05459590
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04648984 0.04906655
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.07916090 0.08327594
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.04040560 0.04545111
RMSEA.CI(T=Td[4],df=dfd[4],N=N,G=2)
## [1] 0.05154023 0.05771534
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 0.002 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 0.835 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 0 0 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
## 1.000 1.000 0.993 0.002 0.000 0.000
tests<-lavTestLRT(configural, metric, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 3753.843 67864.707
dfd=tests[2:3,"Df diff"]
dfd
## [1] 23 16
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04777201 0.24425571
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04648984 0.04906655
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.2427142 0.2457991
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 0.002 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] 3753.843 4227.753 5010.892
dfd=tests[2:4,"Df diff"]
dfd
## [1] 23 9 20
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04777201 0.08120910 0.05925268
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04648984 0.04906655
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.07916090 0.08327594
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.05787750 0.06063927
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 0.002 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 0.835 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 0.189 0.000 0.000
CHC higher order models
chc.hof.model <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g =~ english + math + speed + spatial
'
baseline<-cfa(chc.hof.model, data=dgroup, meanstructure=TRUE, sampling.weights="BY_WTA")
## Warning: lavaan->lav_object_post_check():
## some estimated lv variances are negative
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 129206.654 159.000 0.000 0.910 0.076 0.056
## aic bic
## 6639919.964 6640620.357
Mc(baseline)
## [1] 0.6351497
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
## 82423.073 318.000 0.000 0.942 0.060 0.041
## aic bic
## 6489278.609 6490679.394
Mc(configural)
## [1] 0.7491732
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 91 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 142
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 82423.073 69998.907
## Degrees of freedom 318 318
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.177
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 46168.817 39209.491
## 1 36254.256 30789.416
##
## 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 0.323 0.004 89.166 0.000 0.315
## Stst19dsgsdwrd 0.247 0.003 78.899 0.000 0.241
## Stest20spellng 0.274 0.003 79.644 0.000 0.267
## Stest21cptlztn 0.276 0.003 83.901 0.000 0.270
## Stest22puncttn 0.337 0.004 87.771 0.000 0.330
## Stest23english 0.303 0.004 81.741 0.000 0.296
## Stest24exprssn 0.281 0.003 80.453 0.000 0.275
## Stst25wrdfnctn 0.190 0.004 49.182 0.000 0.182
## Stst26rdngcmpr 0.375 0.004 88.557 0.000 0.367
## Stst31bstrctrs 0.126 0.002 55.366 0.000 0.121
## Stst32rthrsnng 0.113 0.003 32.631 0.000 0.106
## math =~
## Stest5math 0.221 0.007 32.777 0.000 0.208
## Stst25wrdfnctn 0.086 0.003 26.402 0.000 0.080
## Stst32rthrsnng 0.149 0.004 37.564 0.000 0.142
## Stst33hghschlm 0.259 0.008 32.213 0.000 0.244
## Stst34rthcmptt 0.139 0.004 31.342 0.000 0.130
## speed =~
## Stst19dsgsdwrd 0.266 0.004 71.527 0.000 0.258
## Stst29vslztn2D 0.217 0.004 53.904 0.000 0.209
## Stst34rthcmptt 0.361 0.004 92.773 0.000 0.353
## Stest35tblrdng 0.707 0.005 140.549 0.000 0.698
## Stst36clrclchc 0.690 0.005 134.847 0.000 0.680
## Stst37bjctnspc 0.569 0.005 117.637 0.000 0.560
## spatial =~
## Stst28mchnclrs 0.512 0.003 178.857 0.000 0.506
## Stst29vslztn2D 0.375 0.003 109.179 0.000 0.369
## Stst30vslztn3D 0.567 0.004 160.081 0.000 0.560
## Stst31bstrctrs 0.345 0.004 96.600 0.000 0.338
## Stst37bjctnspc 0.103 0.003 30.367 0.000 0.096
## g =~
## english 2.102 0.029 72.622 0.000 2.046
## math 3.407 0.113 30.210 0.000 3.186
## speed 0.258 0.006 40.991 0.000 0.245
## spatial 0.922 0.009 106.989 0.000 0.905
## ci.upper Std.lv Std.all
##
## 0.330 0.751 0.803
## 0.253 0.575 0.589
## 0.281 0.638 0.638
## 0.282 0.643 0.657
## 0.345 0.785 0.793
## 0.311 0.706 0.691
## 0.288 0.655 0.626
## 0.197 0.441 0.454
## 0.384 0.874 0.857
## 0.130 0.293 0.298
## 0.119 0.262 0.266
##
## 0.234 0.785 0.834
## 0.092 0.305 0.314
## 0.157 0.530 0.537
## 0.275 0.921 0.885
## 0.147 0.492 0.496
##
## 0.273 0.274 0.281
## 0.225 0.224 0.230
## 0.368 0.372 0.376
## 0.717 0.731 0.707
## 0.700 0.712 0.713
## 0.579 0.588 0.572
##
## 0.517 0.696 0.785
## 0.382 0.511 0.524
## 0.574 0.771 0.756
## 0.352 0.469 0.477
## 0.110 0.140 0.136
##
## 2.159 0.903 0.903
## 3.628 0.960 0.960
## 0.270 0.249 0.249
## 0.939 0.678 0.678
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.167 0.004 44.518 0.000 0.160
## .Stst19dsgsdwrd -0.119 0.004 -30.513 0.000 -0.126
## .Stest20spellng -0.258 0.004 -64.136 0.000 -0.265
## .Stest21cptlztn -0.212 0.004 -54.084 0.000 -0.220
## .Stest22puncttn -0.208 0.004 -52.316 0.000 -0.216
## .Stest23english -0.144 0.004 -35.041 0.000 -0.152
## .Stest24exprssn -0.118 0.004 -28.047 0.000 -0.126
## .Stst25wrdfnctn -0.139 0.004 -35.813 0.000 -0.147
## .Stst26rdngcmpr -0.032 0.004 -7.896 0.000 -0.041
## .Stst31bstrctrs 0.055 0.004 13.853 0.000 0.047
## .Stst32rthrsnng 0.121 0.004 30.651 0.000 0.114
## .Stest5math 0.193 0.004 51.128 0.000 0.186
## .Stst33hghschlm 0.117 0.004 28.152 0.000 0.109
## .Stst34rthcmptt -0.078 0.004 -19.713 0.000 -0.086
## .Stst29vslztn2D 0.212 0.004 54.436 0.000 0.204
## .Stest35tblrdng -0.068 0.004 -16.347 0.000 -0.076
## .Stst36clrclchc -0.147 0.004 -37.322 0.000 -0.155
## .Stst37bjctnspc -0.095 0.004 -23.187 0.000 -0.103
## .Stst28mchnclrs 0.536 0.004 151.033 0.000 0.529
## .Stst30vslztn3D 0.190 0.004 46.616 0.000 0.182
## ci.upper Std.lv Std.all
## 0.175 0.167 0.179
## -0.111 -0.119 -0.122
## -0.250 -0.258 -0.257
## -0.204 -0.212 -0.217
## -0.200 -0.208 -0.210
## -0.136 -0.144 -0.141
## -0.110 -0.118 -0.113
## -0.132 -0.139 -0.143
## -0.024 -0.032 -0.032
## 0.063 0.055 0.056
## 0.129 0.121 0.123
## 0.201 0.193 0.205
## 0.125 0.117 0.113
## -0.070 -0.078 -0.079
## 0.219 0.212 0.217
## -0.060 -0.068 -0.066
## -0.140 -0.147 -0.148
## -0.087 -0.095 -0.092
## 0.543 0.536 0.605
## 0.198 0.190 0.186
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.311 0.002 140.617 0.000 0.306
## .Stst19dsgsdwrd 0.476 0.003 157.154 0.000 0.470
## .Stest20spellng 0.594 0.004 168.491 0.000 0.587
## .Stest21cptlztn 0.544 0.003 168.949 0.000 0.537
## .Stest22puncttn 0.364 0.003 139.880 0.000 0.359
## .Stest23english 0.544 0.004 143.400 0.000 0.537
## .Stest24exprssn 0.667 0.004 154.217 0.000 0.659
## .Stst25wrdfnctn 0.424 0.003 157.668 0.000 0.419
## .Stst26rdngcmpr 0.277 0.002 119.891 0.000 0.272
## .Stst31bstrctrs 0.493 0.003 150.235 0.000 0.487
## .Stst32rthrsnng 0.384 0.002 153.768 0.000 0.379
## .Stest5math 0.269 0.003 90.745 0.000 0.263
## .Stst33hghschlm 0.234 0.002 98.807 0.000 0.229
## .Stst34rthcmptt 0.514 0.004 140.040 0.000 0.507
## .Stst29vslztn2D 0.599 0.004 139.890 0.000 0.591
## .Stest35tblrdng 0.535 0.008 64.815 0.000 0.519
## .Stst36clrclchc 0.490 0.006 82.042 0.000 0.479
## .Stst37bjctnspc 0.662 0.005 129.669 0.000 0.652
## .Stst28mchnclrs 0.301 0.003 101.840 0.000 0.295
## .Stst30vslztn3D 0.446 0.004 112.713 0.000 0.438
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.315 0.311 0.355
## 0.482 0.476 0.500
## 0.601 0.594 0.593
## 0.550 0.544 0.568
## 0.369 0.364 0.371
## 0.552 0.544 0.522
## 0.676 0.667 0.609
## 0.429 0.424 0.448
## 0.281 0.277 0.266
## 0.499 0.493 0.510
## 0.389 0.384 0.394
## 0.275 0.269 0.304
## 0.238 0.234 0.216
## 0.521 0.514 0.523
## 0.608 0.599 0.632
## 0.551 0.535 0.501
## 0.502 0.490 0.492
## 0.672 0.662 0.627
## 0.307 0.301 0.383
## 0.453 0.446 0.429
## 1.000 0.184 0.184
## 1.000 0.079 0.079
## 1.000 0.938 0.938
## 1.000 0.541 0.541
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stest1vocab 0.342 0.004 80.107 0.000 0.333
## Stst19dsgsdwrd 0.238 0.003 71.225 0.000 0.232
## Stest20spellng 0.243 0.003 73.326 0.000 0.237
## Stest21cptlztn 0.238 0.003 74.382 0.000 0.232
## Stest22puncttn 0.310 0.004 79.903 0.000 0.303
## Stest23english 0.258 0.003 74.080 0.000 0.251
## Stest24exprssn 0.222 0.003 71.249 0.000 0.216
## Stst25wrdfnctn 0.220 0.004 62.515 0.000 0.213
## Stst26rdngcmpr 0.338 0.004 79.648 0.000 0.330
## Stst31bstrctrs 0.131 0.002 53.906 0.000 0.126
## Stst32rthrsnng 0.174 0.003 58.536 0.000 0.168
## math =~
## Stest5math 0.356 0.005 78.781 0.000 0.347
## Stst25wrdfnctn 0.127 0.003 43.056 0.000 0.122
## Stst32rthrsnng 0.164 0.003 58.117 0.000 0.159
## Stst33hghschlm 0.358 0.005 75.839 0.000 0.349
## Stst34rthcmptt 0.199 0.003 69.473 0.000 0.194
## speed =~
## Stst19dsgsdwrd 0.296 0.004 81.443 0.000 0.289
## Stst29vslztn2D 0.199 0.004 49.012 0.000 0.191
## Stst34rthcmptt 0.327 0.004 86.413 0.000 0.319
## Stest35tblrdng 0.576 0.004 131.620 0.000 0.568
## Stst36clrclchc 0.638 0.005 138.661 0.000 0.629
## Stst37bjctnspc 0.510 0.004 118.372 0.000 0.501
## spatial =~
## Stst28mchnclrs 0.439 0.003 160.764 0.000 0.433
## Stst29vslztn2D 0.342 0.003 104.388 0.000 0.335
## Stst30vslztn3D 0.486 0.003 148.098 0.000 0.480
## Stst31bstrctrs 0.303 0.004 85.580 0.000 0.296
## Stst37bjctnspc 0.103 0.003 35.490 0.000 0.098
## g =~
## english 2.068 0.031 65.813 0.000 2.007
## math 1.971 0.031 63.943 0.000 1.910
## speed 0.255 0.006 40.495 0.000 0.243
## spatial 0.983 0.010 103.075 0.000 0.964
## ci.upper Std.lv Std.all
##
## 0.350 0.785 0.803
## 0.245 0.548 0.565
## 0.250 0.559 0.614
## 0.245 0.548 0.593
## 0.318 0.713 0.789
## 0.265 0.593 0.653
## 0.229 0.511 0.570
## 0.227 0.506 0.513
## 0.346 0.777 0.855
## 0.135 0.300 0.315
## 0.179 0.399 0.413
##
## 0.365 0.787 0.795
## 0.133 0.281 0.285
## 0.170 0.363 0.376
## 0.368 0.792 0.859
## 0.205 0.441 0.473
##
## 0.303 0.305 0.315
## 0.207 0.206 0.215
## 0.334 0.337 0.362
## 0.585 0.595 0.690
## 0.647 0.659 0.707
## 0.518 0.526 0.566
##
## 0.444 0.615 0.748
## 0.348 0.479 0.501
## 0.493 0.682 0.733
## 0.309 0.424 0.445
## 0.109 0.145 0.156
##
## 2.130 0.900 0.900
## 2.031 0.892 0.892
## 0.267 0.247 0.247
## 1.002 0.701 0.701
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -0.095 0.004 -24.615 0.000 -0.103
## .Stst19dsgsdwrd 0.150 0.004 38.967 0.000 0.142
## .Stest20spellng 0.280 0.004 77.302 0.000 0.273
## .Stest21cptlztn 0.276 0.004 74.784 0.000 0.268
## .Stest22puncttn 0.278 0.004 76.957 0.000 0.271
## .Stest23english 0.190 0.004 52.481 0.000 0.183
## .Stest24exprssn 0.165 0.004 46.240 0.000 0.158
## .Stst25wrdfnctn 0.196 0.004 50.126 0.000 0.189
## .Stst26rdngcmpr 0.105 0.004 29.044 0.000 0.098
## .Stst31bstrctrs 0.026 0.004 6.799 0.000 0.018
## .Stst32rthrsnng -0.040 0.004 -10.549 0.000 -0.048
## .Stest5math -0.155 0.004 -39.596 0.000 -0.163
## .Stst33hghschlm -0.072 0.004 -19.964 0.000 -0.080
## .Stst34rthcmptt 0.165 0.004 44.491 0.000 0.158
## .Stst29vslztn2D -0.150 0.004 -39.724 0.000 -0.157
## .Stest35tblrdng 0.085 0.003 24.796 0.000 0.078
## .Stst36clrclchc 0.094 0.004 25.710 0.000 0.087
## .Stst37bjctnspc 0.084 0.004 22.827 0.000 0.076
## .Stst28mchnclrs -0.428 0.003 -131.000 0.000 -0.434
## .Stst30vslztn3D -0.115 0.004 -31.342 0.000 -0.122
## ci.upper Std.lv Std.all
## -0.088 -0.095 -0.097
## 0.158 0.150 0.155
## 0.287 0.280 0.308
## 0.283 0.276 0.299
## 0.285 0.278 0.307
## 0.197 0.190 0.209
## 0.172 0.165 0.184
## 0.204 0.196 0.199
## 0.112 0.105 0.116
## 0.033 0.026 0.027
## -0.033 -0.040 -0.042
## -0.147 -0.155 -0.157
## -0.065 -0.072 -0.079
## 0.172 0.165 0.177
## -0.143 -0.150 -0.157
## 0.091 0.085 0.098
## 0.101 0.094 0.100
## 0.091 0.084 0.090
## -0.422 -0.428 -0.521
## -0.108 -0.115 -0.124
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.339 0.002 144.902 0.000 0.334
## .Stst19dsgsdwrd 0.471 0.003 154.753 0.000 0.465
## .Stest20spellng 0.517 0.003 172.374 0.000 0.511
## .Stest21cptlztn 0.552 0.003 170.315 0.000 0.546
## .Stest22puncttn 0.309 0.002 138.893 0.000 0.305
## .Stest23english 0.472 0.003 146.394 0.000 0.466
## .Stest24exprssn 0.541 0.004 151.502 0.000 0.534
## .Stst25wrdfnctn 0.408 0.003 149.065 0.000 0.403
## .Stst26rdngcmpr 0.222 0.002 117.245 0.000 0.218
## .Stst31bstrctrs 0.478 0.003 154.372 0.000 0.472
## .Stst32rthrsnng 0.409 0.002 163.932 0.000 0.404
## .Stest5math 0.360 0.004 100.819 0.000 0.353
## .Stst33hghschlm 0.223 0.002 95.780 0.000 0.218
## .Stst34rthcmptt 0.495 0.004 133.958 0.000 0.488
## .Stst29vslztn2D 0.609 0.004 156.963 0.000 0.602
## .Stest35tblrdng 0.389 0.005 71.602 0.000 0.378
## .Stst36clrclchc 0.435 0.005 87.297 0.000 0.425
## .Stst37bjctnspc 0.539 0.004 134.283 0.000 0.531
## .Stst28mchnclrs 0.297 0.003 114.914 0.000 0.292
## .Stst30vslztn3D 0.400 0.003 118.681 0.000 0.393
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.343 0.339 0.355
## 0.477 0.471 0.502
## 0.523 0.517 0.623
## 0.559 0.552 0.648
## 0.314 0.309 0.378
## 0.479 0.472 0.573
## 0.548 0.541 0.675
## 0.413 0.408 0.420
## 0.226 0.222 0.269
## 0.484 0.478 0.526
## 0.414 0.409 0.439
## 0.367 0.360 0.368
## 0.227 0.223 0.262
## 0.502 0.495 0.570
## 0.617 0.609 0.666
## 0.399 0.389 0.524
## 0.445 0.435 0.501
## 0.547 0.539 0.624
## 0.302 0.297 0.440
## 0.406 0.400 0.462
## 1.000 0.189 0.189
## 1.000 0.205 0.205
## 1.000 0.939 0.939
## 1.000 0.509 0.509
## 1.000 1.000 1.000
modificationIndices(configural, sort=T, maximum.number=30)
## lhs op rhs block group
## 516 Stest1vocab ~~ Stest26readingcomprehension 2 2
## 243 Stest1vocab ~~ Stest26readingcomprehension 1 1
## 231 g =~ Stest35tablereading 1 1
## 182 math =~ Stest35tablereading 1 1
## 203 spatial =~ Stest20spelling 1 1
## 167 english =~ Stest35tablereading 1 1
## 214 spatial =~ Stest35tablereading 1 1
## 246 Stest1vocab ~~ Stest5math 1 1
## 233 g =~ Stest37objectinspection 1 1
## 476 spatial =~ Stest20spelling 2 2
## 184 math =~ Stest37objectinspection 1 1
## 213 spatial =~ Stest34arithcomputation 1 1
## 169 english =~ Stest37objectinspection 1 1
## 239 Stest1vocab ~~ Stest22punctuation 1 1
## 309 Stest22punctuation ~~ Stest26readingcomprehension 1 1
## 253 Stest1vocab ~~ Stest28mechanicalreasoning 1 1
## 528 Stest19disguisedwords ~~ Stest20spelling 2 2
## 519 Stest1vocab ~~ Stest5math 2 2
## 504 g =~ Stest35tablereading 2 2
## 461 speed =~ Stest20spelling 2 2
## 506 g =~ Stest37objectinspection 2 2
## 455 math =~ Stest35tablereading 2 2
## 440 english =~ Stest35tablereading 2 2
## 556 Stest20spelling ~~ Stest34arithcomputation 2 2
## 512 Stest1vocab ~~ Stest22punctuation 2 2
## 283 Stest20spelling ~~ Stest34arithcomputation 1 1
## 255 Stest19disguisedwords ~~ Stest20spelling 1 1
## 170 english =~ Stest28mechanicalreasoning 1 1
## 582 Stest22punctuation ~~ Stest26readingcomprehension 2 2
## 457 math =~ Stest37objectinspection 2 2
## level mi epc sepc.lv sepc.all sepc.nox
## 516 1 4980.882 0.098 0.098 0.357 0.357
## 243 1 4930.099 0.101 0.101 0.343 0.343
## 231 1 4392.812 0.276 0.276 0.267 0.267
## 182 1 4238.437 0.075 0.266 0.257 0.257
## 203 1 3821.040 -0.210 -0.285 -0.285 -0.285
## 167 1 3625.388 0.102 0.238 0.230 0.230
## 214 1 3383.515 0.174 0.237 0.229 0.229
## 246 1 3054.402 0.073 0.073 0.251 0.251
## 233 1 2945.660 -0.307 -0.307 -0.299 -0.299
## 476 1 2942.278 -0.176 -0.247 -0.271 -0.271
## 184 1 2802.219 -0.079 -0.280 -0.273 -0.273
## 213 1 2619.678 -0.178 -0.243 -0.245 -0.245
## 169 1 2608.765 -0.108 -0.250 -0.244 -0.244
## 239 1 2454.672 -0.075 -0.075 -0.223 -0.223
## 309 1 2397.709 -0.075 -0.075 -0.237 -0.237
## 253 1 2363.009 0.071 0.071 0.233 0.233
## 528 1 2227.170 0.095 0.095 0.192 0.192
## 519 1 2191.064 0.075 0.075 0.215 0.215
## 504 1 2185.706 0.169 0.169 0.196 0.196
## 461 1 1926.621 0.142 0.147 0.161 0.161
## 506 1 1890.746 -0.247 -0.247 -0.266 -0.266
## 455 1 1883.979 0.068 0.150 0.174 0.174
## 440 1 1881.398 0.064 0.146 0.169 0.169
## 556 1 1840.209 0.088 0.088 0.174 0.174
## 512 1 1829.308 -0.064 -0.064 -0.197 -0.197
## 283 1 1826.700 0.096 0.096 0.173 0.173
## 255 1 1820.337 0.092 0.092 0.173 0.173
## 170 1 1778.686 0.088 0.204 0.231 0.231
## 582 1 1763.746 -0.055 -0.055 -0.208 -0.208
## 457 1 1721.969 -0.090 -0.199 -0.214 -0.214
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
## 86982.717 344.000 0.000 0.939 0.060 0.047
## aic bic
## 6493786.253 6494930.557
Mc(metric)
## [1] 0.7373216
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 85 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 147
## Number of equality constraints 31
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 86982.717 73915.505
## Degrees of freedom 344 344
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.177
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 48305.405 41048.596
## 1 38677.312 32866.910
##
## 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.) 0.322 0.004 88.816 0.000 0.315
## Stst19d (.p2.) 0.237 0.003 82.544 0.000 0.232
## Stst20s (.p3.) 0.253 0.003 82.846 0.000 0.247
## Stst21c (.p4.) 0.252 0.003 85.218 0.000 0.246
## Stst22p (.p5.) 0.316 0.004 88.011 0.000 0.309
## Stst23n (.p6.) 0.274 0.003 83.462 0.000 0.268
## Stst24x (.p7.) 0.245 0.003 82.226 0.000 0.239
## Stst25w (.p8.) 0.202 0.003 72.573 0.000 0.197
## Stst26r (.p9.) 0.348 0.004 87.880 0.000 0.340
## Stst31b (.10.) 0.126 0.002 69.223 0.000 0.122
## Stst32r (.11.) 0.145 0.002 64.321 0.000 0.140
## math =~
## Stst5mt (.12.) 0.259 0.005 51.609 0.000 0.249
## Stst25w (.13.) 0.095 0.002 41.453 0.000 0.090
## Stst32r (.14.) 0.144 0.003 52.033 0.000 0.139
## Stst33h (.15.) 0.285 0.006 50.428 0.000 0.274
## Stst34r (.16.) 0.156 0.003 48.909 0.000 0.149
## speed =~
## Stst19d (.17.) 0.295 0.003 104.880 0.000 0.290
## Sts292D (.18.) 0.221 0.003 71.609 0.000 0.215
## Stst34r (.19.) 0.364 0.003 117.565 0.000 0.358
## Stst35t (.20.) 0.677 0.004 156.985 0.000 0.668
## Stst36c (.21.) 0.704 0.004 168.538 0.000 0.696
## Stst37b (.22.) 0.572 0.004 147.412 0.000 0.564
## spatial =~
## Stst28m (.23.) 0.508 0.003 193.624 0.000 0.503
## Sts292D (.24.) 0.383 0.003 137.128 0.000 0.378
## Sts303D (.25.) 0.563 0.003 181.625 0.000 0.556
## Stst31b (.26.) 0.344 0.003 121.094 0.000 0.339
## Stst37b (.27.) 0.112 0.002 46.383 0.000 0.107
## g =~
## english (.28.) 2.251 0.029 76.962 0.000 2.193
## math (.29.) 2.943 0.063 46.682 0.000 2.819
## speed (.30.) 0.253 0.004 56.521 0.000 0.244
## spatial (.31.) 0.939 0.007 132.253 0.000 0.925
## ci.upper Std.lv Std.all
##
## 0.329 0.793 0.820
## 0.243 0.585 0.589
## 0.259 0.623 0.627
## 0.258 0.621 0.642
## 0.324 0.779 0.790
## 0.281 0.675 0.673
## 0.251 0.603 0.591
## 0.208 0.498 0.495
## 0.356 0.857 0.852
## 0.129 0.310 0.311
## 0.149 0.357 0.358
##
## 0.269 0.806 0.846
## 0.099 0.295 0.293
## 0.150 0.448 0.450
## 0.296 0.886 0.874
## 0.162 0.484 0.490
##
## 0.301 0.304 0.307
## 0.227 0.228 0.232
## 0.370 0.375 0.380
## 0.685 0.698 0.682
## 0.712 0.726 0.725
## 0.580 0.590 0.572
##
## 0.514 0.697 0.786
## 0.389 0.526 0.535
## 0.569 0.772 0.756
## 0.350 0.472 0.474
## 0.116 0.153 0.148
##
## 2.308 0.914 0.914
## 3.067 0.947 0.947
## 0.262 0.245 0.245
## 0.953 0.685 0.685
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.167 0.004 44.518 0.000 0.160
## .Stst19dsgsdwrd -0.119 0.004 -30.513 0.000 -0.126
## .Stest20spellng -0.258 0.004 -64.136 0.000 -0.265
## .Stest21cptlztn -0.212 0.004 -54.084 0.000 -0.220
## .Stest22puncttn -0.208 0.004 -52.316 0.000 -0.216
## .Stest23english -0.144 0.004 -35.041 0.000 -0.152
## .Stest24exprssn -0.118 0.004 -28.047 0.000 -0.126
## .Stst25wrdfnctn -0.139 0.004 -35.813 0.000 -0.147
## .Stst26rdngcmpr -0.032 0.004 -7.896 0.000 -0.041
## .Stst31bstrctrs 0.055 0.004 13.853 0.000 0.047
## .Stst32rthrsnng 0.121 0.004 30.651 0.000 0.114
## .Stest5math 0.193 0.004 51.128 0.000 0.186
## .Stst33hghschlm 0.117 0.004 28.152 0.000 0.109
## .Stst34rthcmptt -0.078 0.004 -19.713 0.000 -0.086
## .Stst29vslztn2D 0.212 0.004 54.436 0.000 0.204
## .Stest35tblrdng -0.068 0.004 -16.347 0.000 -0.076
## .Stst36clrclchc -0.147 0.004 -37.322 0.000 -0.155
## .Stst37bjctnspc -0.095 0.004 -23.187 0.000 -0.103
## .Stst28mchnclrs 0.536 0.004 151.033 0.000 0.529
## .Stst30vslztn3D 0.190 0.004 46.616 0.000 0.182
## ci.upper Std.lv Std.all
## 0.175 0.167 0.173
## -0.111 -0.119 -0.120
## -0.250 -0.258 -0.259
## -0.204 -0.212 -0.220
## -0.200 -0.208 -0.211
## -0.136 -0.144 -0.144
## -0.110 -0.118 -0.116
## -0.132 -0.139 -0.138
## -0.024 -0.032 -0.032
## 0.063 0.055 0.055
## 0.129 0.121 0.122
## 0.201 0.193 0.203
## 0.125 0.117 0.115
## -0.070 -0.078 -0.079
## 0.219 0.212 0.216
## -0.060 -0.068 -0.066
## -0.140 -0.147 -0.147
## -0.087 -0.095 -0.092
## 0.543 0.536 0.604
## 0.198 0.190 0.186
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.306 0.002 141.423 0.000 0.302
## .Stst19dsgsdwrd 0.471 0.003 158.819 0.000 0.465
## .Stest20spellng 0.598 0.003 171.246 0.000 0.591
## .Stest21cptlztn 0.548 0.003 172.038 0.000 0.542
## .Stest22puncttn 0.366 0.003 142.328 0.000 0.361
## .Stest23english 0.551 0.004 143.194 0.000 0.543
## .Stest24exprssn 0.676 0.004 154.639 0.000 0.667
## .Stst25wrdfnctn 0.424 0.003 156.791 0.000 0.418
## .Stst26rdngcmpr 0.278 0.002 123.125 0.000 0.274
## .Stst31bstrctrs 0.492 0.003 152.626 0.000 0.486
## .Stst32rthrsnng 0.388 0.002 157.798 0.000 0.383
## .Stest5math 0.259 0.003 86.976 0.000 0.253
## .Stst33hghschlm 0.243 0.002 109.082 0.000 0.239
## .Stst34rthcmptt 0.515 0.004 141.780 0.000 0.508
## .Stst29vslztn2D 0.596 0.004 142.099 0.000 0.588
## .Stest35tblrdng 0.561 0.008 69.590 0.000 0.545
## .Stst36clrclchc 0.475 0.005 86.770 0.000 0.464
## .Stst37bjctnspc 0.662 0.005 135.532 0.000 0.652
## .Stst28mchnclrs 0.301 0.003 110.435 0.000 0.296
## .Stst30vslztn3D 0.447 0.004 121.608 0.000 0.440
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.311 0.306 0.327
## 0.477 0.471 0.478
## 0.605 0.598 0.607
## 0.554 0.548 0.587
## 0.371 0.366 0.376
## 0.558 0.551 0.547
## 0.685 0.676 0.650
## 0.429 0.424 0.418
## 0.283 0.278 0.275
## 0.499 0.492 0.495
## 0.393 0.388 0.391
## 0.265 0.259 0.285
## 0.247 0.243 0.237
## 0.522 0.515 0.528
## 0.604 0.596 0.618
## 0.576 0.561 0.535
## 0.486 0.475 0.474
## 0.671 0.662 0.622
## 0.307 0.301 0.382
## 0.454 0.447 0.429
## 1.000 0.165 0.165
## 1.000 0.104 0.104
## 1.000 0.940 0.940
## 1.000 0.531 0.531
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.322 0.004 88.816 0.000 0.315
## Stst19d (.p2.) 0.237 0.003 82.544 0.000 0.232
## Stst20s (.p3.) 0.253 0.003 82.846 0.000 0.247
## Stst21c (.p4.) 0.252 0.003 85.218 0.000 0.246
## Stst22p (.p5.) 0.316 0.004 88.011 0.000 0.309
## Stst23n (.p6.) 0.274 0.003 83.462 0.000 0.268
## Stst24x (.p7.) 0.245 0.003 82.226 0.000 0.239
## Stst25w (.p8.) 0.202 0.003 72.573 0.000 0.197
## Stst26r (.p9.) 0.348 0.004 87.880 0.000 0.340
## Stst31b (.10.) 0.126 0.002 69.223 0.000 0.122
## Stst32r (.11.) 0.145 0.002 64.321 0.000 0.140
## math =~
## Stst5mt (.12.) 0.259 0.005 51.609 0.000 0.249
## Stst25w (.13.) 0.095 0.002 41.453 0.000 0.090
## Stst32r (.14.) 0.144 0.003 52.033 0.000 0.139
## Stst33h (.15.) 0.285 0.006 50.428 0.000 0.274
## Stst34r (.16.) 0.156 0.003 48.909 0.000 0.149
## speed =~
## Stst19d (.17.) 0.295 0.003 104.880 0.000 0.290
## Sts292D (.18.) 0.221 0.003 71.609 0.000 0.215
## Stst34r (.19.) 0.364 0.003 117.565 0.000 0.358
## Stst35t (.20.) 0.677 0.004 156.985 0.000 0.668
## Stst36c (.21.) 0.704 0.004 168.538 0.000 0.696
## Stst37b (.22.) 0.572 0.004 147.412 0.000 0.564
## spatial =~
## Stst28m (.23.) 0.508 0.003 193.624 0.000 0.503
## Sts292D (.24.) 0.383 0.003 137.128 0.000 0.378
## Sts303D (.25.) 0.563 0.003 181.625 0.000 0.556
## Stst31b (.26.) 0.344 0.003 121.094 0.000 0.339
## Stst37b (.27.) 0.112 0.002 46.383 0.000 0.107
## g =~
## english (.28.) 2.251 0.029 76.962 0.000 2.193
## math (.29.) 2.943 0.063 46.682 0.000 2.819
## speed (.30.) 0.253 0.004 56.521 0.000 0.244
## spatial (.31.) 0.939 0.007 132.253 0.000 0.925
## ci.upper Std.lv Std.all
##
## 0.329 0.731 0.778
## 0.243 0.539 0.566
## 0.259 0.574 0.625
## 0.258 0.572 0.611
## 0.324 0.718 0.792
## 0.281 0.622 0.673
## 0.251 0.556 0.604
## 0.208 0.459 0.483
## 0.356 0.790 0.859
## 0.129 0.285 0.304
## 0.149 0.329 0.344
##
## 0.269 0.753 0.776
## 0.099 0.276 0.290
## 0.150 0.419 0.438
## 0.296 0.828 0.872
## 0.162 0.452 0.483
##
## 0.301 0.270 0.284
## 0.227 0.202 0.213
## 0.370 0.333 0.356
## 0.685 0.620 0.713
## 0.712 0.645 0.694
## 0.580 0.524 0.566
##
## 0.514 0.616 0.749
## 0.389 0.464 0.489
## 0.569 0.681 0.734
## 0.350 0.417 0.444
## 0.116 0.135 0.146
##
## 2.308 0.889 0.889
## 3.067 0.908 0.908
## 0.262 0.247 0.247
## 0.953 0.695 0.695
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab -0.095 0.004 -24.615 0.000 -0.103
## .Stst19dsgsdwrd 0.150 0.004 38.967 0.000 0.142
## .Stest20spellng 0.280 0.004 77.302 0.000 0.273
## .Stest21cptlztn 0.276 0.004 74.784 0.000 0.268
## .Stest22puncttn 0.278 0.004 76.957 0.000 0.271
## .Stest23english 0.190 0.004 52.481 0.000 0.183
## .Stest24exprssn 0.165 0.004 46.240 0.000 0.158
## .Stst25wrdfnctn 0.196 0.004 50.126 0.000 0.189
## .Stst26rdngcmpr 0.105 0.004 29.044 0.000 0.098
## .Stst31bstrctrs 0.026 0.004 6.799 0.000 0.018
## .Stst32rthrsnng -0.040 0.004 -10.549 0.000 -0.048
## .Stest5math -0.155 0.004 -39.596 0.000 -0.163
## .Stst33hghschlm -0.072 0.004 -19.964 0.000 -0.080
## .Stst34rthcmptt 0.165 0.004 44.491 0.000 0.158
## .Stst29vslztn2D -0.150 0.004 -39.724 0.000 -0.157
## .Stest35tblrdng 0.085 0.003 24.796 0.000 0.078
## .Stst36clrclchc 0.094 0.004 25.710 0.000 0.087
## .Stst37bjctnspc 0.084 0.004 22.827 0.000 0.076
## .Stst28mchnclrs -0.428 0.003 -131.000 0.000 -0.434
## .Stst30vslztn3D -0.115 0.004 -31.342 0.000 -0.122
## ci.upper Std.lv Std.all
## -0.088 -0.095 -0.101
## 0.158 0.150 0.158
## 0.287 0.280 0.305
## 0.283 0.276 0.294
## 0.285 0.278 0.306
## 0.197 0.190 0.205
## 0.172 0.165 0.179
## 0.204 0.196 0.206
## 0.112 0.105 0.114
## 0.033 0.026 0.027
## -0.033 -0.040 -0.042
## -0.147 -0.155 -0.160
## -0.065 -0.072 -0.076
## 0.172 0.165 0.176
## -0.143 -0.150 -0.158
## 0.091 0.085 0.097
## 0.101 0.094 0.101
## 0.091 0.084 0.090
## -0.422 -0.428 -0.521
## -0.108 -0.115 -0.124
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.350 0.002 152.257 0.000 0.345
## .Stst19dsgsdwrd 0.478 0.003 162.707 0.000 0.473
## .Stest20spellng 0.513 0.003 173.410 0.000 0.508
## .Stest21cptlztn 0.549 0.003 170.631 0.000 0.543
## .Stest22puncttn 0.307 0.002 139.994 0.000 0.302
## .Stest23english 0.469 0.003 146.080 0.000 0.462
## .Stest24exprssn 0.539 0.004 150.854 0.000 0.532
## .Stst25wrdfnctn 0.415 0.003 151.682 0.000 0.410
## .Stst26rdngcmpr 0.222 0.002 118.864 0.000 0.219
## .Stst31bstrctrs 0.480 0.003 157.168 0.000 0.474
## .Stst32rthrsnng 0.409 0.002 165.708 0.000 0.404
## .Stest5math 0.376 0.004 102.412 0.000 0.369
## .Stst33hghschlm 0.215 0.002 96.113 0.000 0.211
## .Stst34rthcmptt 0.494 0.004 135.979 0.000 0.487
## .Stst29vslztn2D 0.612 0.004 162.490 0.000 0.605
## .Stest35tblrdng 0.372 0.005 69.049 0.000 0.361
## .Stst36clrclchc 0.448 0.005 96.116 0.000 0.439
## .Stst37bjctnspc 0.539 0.004 139.952 0.000 0.532
## .Stst28mchnclrs 0.296 0.002 122.880 0.000 0.291
## .Stst30vslztn3D 0.398 0.003 126.596 0.000 0.392
## .english 1.084 0.026 41.717 0.000 1.033
## .math 1.484 0.055 26.949 0.000 1.376
## .speed 0.789 0.010 75.861 0.000 0.768
## .spatial 0.759 0.010 74.433 0.000 0.739
## g 0.803 0.006 125.385 0.000 0.790
## ci.upper Std.lv Std.all
## 0.354 0.350 0.395
## 0.484 0.478 0.528
## 0.519 0.513 0.609
## 0.555 0.549 0.627
## 0.311 0.307 0.373
## 0.475 0.469 0.548
## 0.546 0.539 0.636
## 0.420 0.415 0.458
## 0.226 0.222 0.263
## 0.486 0.480 0.544
## 0.413 0.409 0.447
## 0.383 0.376 0.399
## 0.220 0.215 0.239
## 0.501 0.494 0.563
## 0.620 0.612 0.680
## 0.382 0.372 0.491
## 0.457 0.448 0.518
## 0.547 0.539 0.629
## 0.300 0.296 0.438
## 0.405 0.398 0.462
## 1.135 0.210 0.210
## 1.592 0.176 0.176
## 0.809 0.939 0.939
## 0.779 0.517 0.517
## 0.815 1.000 1.000
lavTestScore(metric, release = 1:31)
## 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 4481.753 31 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p82. 993.106 1 0.000
## 2 .p2. == .p83. 74.925 1 0.000
## 3 .p3. == .p84. 49.907 1 0.000
## 4 .p4. == .p85. 132.830 1 0.000
## 5 .p5. == .p86. 16.297 1 0.000
## 6 .p6. == .p87. 248.162 1 0.000
## 7 .p7. == .p88. 539.406 1 0.000
## 8 .p8. == .p89. 820.232 1 0.000
## 9 .p9. == .p90. 216.989 1 0.000
## 10 .p10. == .p91. 99.002 1 0.000
## 11 .p11. == .p92. 135.475 1 0.000
## 12 .p12. == .p93. 360.526 1 0.000
## 13 .p13. == .p94. 711.081 1 0.000
## 14 .p14. == .p95. 25.954 1 0.000
## 15 .p15. == .p96. 1112.729 1 0.000
## 16 .p16. == .p97. 29.807 1 0.000
## 17 .p17. == .p98. 225.155 1 0.000
## 18 .p18. == .p99. 5.635 1 0.018
## 19 .p19. == .p100. 0.076 1 0.782
## 20 .p20. == .p101. 156.405 1 0.000
## 21 .p21. == .p102. 5.257 1 0.022
## 22 .p22. == .p103. 4.422 1 0.035
## 23 .p23. == .p104. 6.778 1 0.009
## 24 .p24. == .p105. 27.340 1 0.000
## 25 .p25. == .p106. 4.285 1 0.038
## 26 .p26. == .p107. 73.206 1 0.000
## 27 .p27. == .p108. 8.270 1 0.004
## 28 .p28. == .p109. 26.019 1 0.000
## 29 .p29. == .p110. 113.863 1 0.000
## 30 .p30. == .p111. 5.816 1 0.016
## 31 .p31. == .p112. 37.688 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
## (= 2.665942e-15) 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
## 163931.663 359.000 0.000 0.885 0.080 0.062
## aic bic
## 6570705.198 6571701.532
Mc(scalar)
## [1] 0.5625203
summary(scalar, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 104 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 152
## Number of equality constraints 51
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 163931.663 139166.850
## Degrees of freedom 359 359
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.178
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 85015.943 72172.763
## 1 78915.719 66994.087
##
## 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.) 0.272 0.003 79.120 0.000 0.266
## Stst19d (.p2.) 0.217 0.003 73.384 0.000 0.212
## Stst20s (.p3.) 0.249 0.003 73.447 0.000 0.242
## Stst21c (.p4.) 0.247 0.003 74.988 0.000 0.240
## Stst22p (.p5.) 0.306 0.004 76.726 0.000 0.298
## Stst23n (.p6.) 0.260 0.004 74.032 0.000 0.253
## Stst24x (.p7.) 0.231 0.003 73.218 0.000 0.225
## Stst25w (.p8.) 0.252 0.003 76.303 0.000 0.246
## Stst26r (.p9.) 0.314 0.004 77.873 0.000 0.306
## Stst31b (.10.) 0.165 0.002 77.297 0.000 0.161
## Stst32r (.11.) 0.092 0.002 47.316 0.000 0.088
## math =~
## Stst5mt (.12.) 0.254 0.005 48.474 0.000 0.244
## Stst25w (.13.) 0.040 0.002 24.602 0.000 0.037
## Stst32r (.14.) 0.175 0.003 51.808 0.000 0.168
## Stst33h (.15.) 0.274 0.006 47.522 0.000 0.262
## Stst34r (.16.) 0.140 0.003 45.809 0.000 0.134
## speed =~
## Stst19d (.17.) 0.282 0.003 101.940 0.000 0.277
## Sts292D (.18.) 0.244 0.003 82.908 0.000 0.238
## Stst34r (.19.) 0.399 0.003 133.535 0.000 0.393
## Stst35t (.20.) 0.658 0.004 157.306 0.000 0.650
## Stst36c (.21.) 0.688 0.004 170.789 0.000 0.680
## Stst37b (.22.) 0.588 0.004 157.145 0.000 0.580
## spatial =~
## Stst28m (.23.) 0.592 0.003 209.794 0.000 0.587
## Sts292D (.24.) 0.361 0.002 147.309 0.000 0.356
## Sts303D (.25.) 0.448 0.003 165.695 0.000 0.443
## Stst31b (.26.) 0.228 0.002 98.742 0.000 0.224
## Stst37b (.27.) 0.083 0.002 41.712 0.000 0.079
## g =~
## english (.28.) 2.444 0.036 68.652 0.000 2.375
## math (.29.) 3.045 0.069 44.245 0.000 2.910
## speed (.30.) 0.275 0.005 60.678 0.000 0.266
## spatial (.31.) 0.900 0.007 132.924 0.000 0.886
## ci.upper Std.lv Std.all
##
## 0.279 0.719 0.755
## 0.223 0.574 0.581
## 0.255 0.657 0.641
## 0.253 0.652 0.658
## 0.314 0.809 0.802
## 0.267 0.686 0.679
## 0.237 0.609 0.595
## 0.258 0.666 0.655
## 0.322 0.829 0.830
## 0.169 0.436 0.440
## 0.096 0.242 0.243
##
## 0.265 0.815 0.847
## 0.043 0.128 0.126
## 0.182 0.561 0.562
## 0.285 0.877 0.867
## 0.146 0.449 0.451
##
## 0.288 0.293 0.296
## 0.249 0.253 0.259
## 0.404 0.413 0.415
## 0.667 0.683 0.672
## 0.696 0.714 0.714
## 0.595 0.610 0.590
##
## 0.598 0.797 0.862
## 0.366 0.486 0.497
## 0.454 0.603 0.617
## 0.233 0.307 0.310
## 0.087 0.111 0.108
##
## 2.514 0.926 0.926
## 3.180 0.950 0.950
## 0.284 0.265 0.265
## 0.913 0.669 0.669
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.57.) -0.071 0.004 -17.474 0.000 -0.079
## .Stst19d (.58.) -0.148 0.003 -42.420 0.000 -0.155
## .Stst20s (.59.) -0.101 0.004 -27.031 0.000 -0.108
## .Stst21c (.60.) -0.091 0.004 -24.696 0.000 -0.098
## .Stst22p (.61.) -0.109 0.004 -27.641 0.000 -0.116
## .Stst23n (.62.) -0.103 0.004 -27.636 0.000 -0.110
## .Stst24x (.63.) -0.088 0.004 -24.005 0.000 -0.095
## .Stst25w (.64.) -0.078 0.004 -20.655 0.000 -0.085
## .Stst26r (.65.) -0.128 0.004 -31.912 0.000 -0.136
## .Stst31b (.66.) 0.120 0.004 32.778 0.000 0.113
## .Stst32r (.67.) 0.076 0.004 19.393 0.000 0.068
## .Stst5mt (.68.) 0.145 0.004 38.060 0.000 0.138
## .Stst33h (.69.) 0.148 0.004 36.204 0.000 0.140
## .Stst34r (.70.) 0.029 0.004 7.802 0.000 0.022
## .Sts292D (.71.) 0.235 0.003 69.756 0.000 0.228
## .Stst35t (.72.) -0.134 0.004 -34.949 0.000 -0.142
## .Stst36c (.73.) -0.165 0.004 -46.073 0.000 -0.172
## .Stst37b (.74.) -0.062 0.004 -16.624 0.000 -0.069
## .Stst28m (.75.) 0.471 0.004 112.406 0.000 0.463
## .Sts303D (.76.) 0.363 0.003 104.943 0.000 0.356
## ci.upper Std.lv Std.all
## -0.063 -0.071 -0.075
## -0.141 -0.148 -0.150
## -0.093 -0.101 -0.098
## -0.084 -0.091 -0.092
## -0.101 -0.109 -0.108
## -0.095 -0.103 -0.102
## -0.081 -0.088 -0.086
## -0.070 -0.078 -0.076
## -0.120 -0.128 -0.128
## 0.127 0.120 0.121
## 0.084 0.076 0.076
## 0.153 0.145 0.151
## 0.155 0.148 0.146
## 0.036 0.029 0.029
## 0.241 0.235 0.240
## -0.127 -0.134 -0.132
## -0.158 -0.165 -0.165
## -0.055 -0.062 -0.060
## 0.479 0.471 0.509
## 0.369 0.363 0.371
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.390 0.003 132.453 0.000 0.384
## .Stst19dsgsdwrd 0.479 0.003 160.900 0.000 0.473
## .Stest20spellng 0.619 0.004 163.439 0.000 0.612
## .Stest21cptlztn 0.556 0.003 167.267 0.000 0.550
## .Stest22puncttn 0.362 0.003 136.094 0.000 0.357
## .Stest23english 0.550 0.004 142.661 0.000 0.543
## .Stest24exprssn 0.677 0.004 154.243 0.000 0.668
## .Stst25wrdfnctn 0.422 0.003 150.747 0.000 0.416
## .Stst26rdngcmpr 0.309 0.002 127.388 0.000 0.305
## .Stst31bstrctrs 0.534 0.003 158.002 0.000 0.527
## .Stst32rthrsnng 0.383 0.003 152.713 0.000 0.378
## .Stest5math 0.263 0.003 87.375 0.000 0.257
## .Stst33hghschlm 0.254 0.002 111.970 0.000 0.249
## .Stst34rthcmptt 0.527 0.004 137.679 0.000 0.519
## .Stst29vslztn2D 0.611 0.004 141.430 0.000 0.603
## .Stest35tblrdng 0.568 0.008 74.449 0.000 0.553
## .Stst36clrclchc 0.489 0.006 87.289 0.000 0.478
## .Stst37bjctnspc 0.661 0.005 133.844 0.000 0.651
## .Stst28mchnclrs 0.219 0.004 62.039 0.000 0.212
## .Stst30vslztn3D 0.591 0.004 139.456 0.000 0.583
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.396 0.390 0.430
## 0.485 0.479 0.490
## 0.627 0.619 0.590
## 0.563 0.556 0.567
## 0.367 0.362 0.356
## 0.558 0.550 0.539
## 0.686 0.677 0.646
## 0.427 0.422 0.409
## 0.314 0.309 0.311
## 0.540 0.534 0.542
## 0.388 0.383 0.385
## 0.268 0.263 0.283
## 0.258 0.254 0.248
## 0.534 0.527 0.531
## 0.619 0.611 0.640
## 0.582 0.568 0.549
## 0.499 0.489 0.490
## 0.670 0.661 0.618
## 0.226 0.219 0.257
## 0.600 0.591 0.619
## 1.000 0.143 0.143
## 1.000 0.097 0.097
## 1.000 0.930 0.930
## 1.000 0.553 0.553
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.272 0.003 79.120 0.000 0.266
## Stst19d (.p2.) 0.217 0.003 73.384 0.000 0.212
## Stst20s (.p3.) 0.249 0.003 73.447 0.000 0.242
## Stst21c (.p4.) 0.247 0.003 74.988 0.000 0.240
## Stst22p (.p5.) 0.306 0.004 76.726 0.000 0.298
## Stst23n (.p6.) 0.260 0.004 74.032 0.000 0.253
## Stst24x (.p7.) 0.231 0.003 73.218 0.000 0.225
## Stst25w (.p8.) 0.252 0.003 76.303 0.000 0.246
## Stst26r (.p9.) 0.314 0.004 77.873 0.000 0.306
## Stst31b (.10.) 0.165 0.002 77.297 0.000 0.161
## Stst32r (.11.) 0.092 0.002 47.316 0.000 0.088
## math =~
## Stst5mt (.12.) 0.254 0.005 48.474 0.000 0.244
## Stst25w (.13.) 0.040 0.002 24.602 0.000 0.037
## Stst32r (.14.) 0.175 0.003 51.808 0.000 0.168
## Stst33h (.15.) 0.274 0.006 47.522 0.000 0.262
## Stst34r (.16.) 0.140 0.003 45.809 0.000 0.134
## speed =~
## Stst19d (.17.) 0.282 0.003 101.940 0.000 0.277
## Sts292D (.18.) 0.244 0.003 82.908 0.000 0.238
## Stst34r (.19.) 0.399 0.003 133.535 0.000 0.393
## Stst35t (.20.) 0.658 0.004 157.306 0.000 0.650
## Stst36c (.21.) 0.688 0.004 170.789 0.000 0.680
## Stst37b (.22.) 0.588 0.004 157.145 0.000 0.580
## spatial =~
## Stst28m (.23.) 0.592 0.003 209.794 0.000 0.587
## Sts292D (.24.) 0.361 0.002 147.309 0.000 0.356
## Sts303D (.25.) 0.448 0.003 165.695 0.000 0.443
## Stst31b (.26.) 0.228 0.002 98.742 0.000 0.224
## Stst37b (.27.) 0.083 0.002 41.712 0.000 0.079
## g =~
## english (.28.) 2.444 0.036 68.652 0.000 2.375
## math (.29.) 3.045 0.069 44.245 0.000 2.910
## speed (.30.) 0.275 0.005 60.678 0.000 0.266
## spatial (.31.) 0.900 0.007 132.924 0.000 0.886
## ci.upper Std.lv Std.all
##
## 0.279 0.660 0.691
## 0.223 0.527 0.556
## 0.255 0.603 0.638
## 0.253 0.598 0.624
## 0.314 0.742 0.803
## 0.267 0.629 0.677
## 0.237 0.559 0.605
## 0.258 0.611 0.636
## 0.322 0.760 0.837
## 0.169 0.400 0.427
## 0.096 0.222 0.232
##
## 0.265 0.758 0.774
## 0.043 0.119 0.124
## 0.182 0.522 0.544
## 0.285 0.816 0.864
## 0.146 0.417 0.443
##
## 0.288 0.261 0.275
## 0.249 0.225 0.238
## 0.404 0.368 0.390
## 0.667 0.608 0.703
## 0.696 0.635 0.685
## 0.595 0.543 0.585
##
## 0.598 0.706 0.826
## 0.366 0.430 0.455
## 0.454 0.534 0.598
## 0.233 0.272 0.290
## 0.087 0.099 0.106
##
## 2.514 0.902 0.902
## 3.180 0.914 0.914
## 0.284 0.266 0.266
## 0.913 0.675 0.675
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.57.) -0.071 0.004 -17.474 0.000 -0.079
## .Stst19d (.58.) -0.148 0.003 -42.420 0.000 -0.155
## .Stst20s (.59.) -0.101 0.004 -27.031 0.000 -0.108
## .Stst21c (.60.) -0.091 0.004 -24.696 0.000 -0.098
## .Stst22p (.61.) -0.109 0.004 -27.641 0.000 -0.116
## .Stst23n (.62.) -0.103 0.004 -27.636 0.000 -0.110
## .Stst24x (.63.) -0.088 0.004 -24.005 0.000 -0.095
## .Stst25w (.64.) -0.078 0.004 -20.655 0.000 -0.085
## .Stst26r (.65.) -0.128 0.004 -31.912 0.000 -0.136
## .Stst31b (.66.) 0.120 0.004 32.778 0.000 0.113
## .Stst32r (.67.) 0.076 0.004 19.393 0.000 0.068
## .Stst5mt (.68.) 0.145 0.004 38.060 0.000 0.138
## .Stst33h (.69.) 0.148 0.004 36.204 0.000 0.140
## .Stst34r (.70.) 0.029 0.004 7.802 0.000 0.022
## .Sts292D (.71.) 0.235 0.003 69.756 0.000 0.228
## .Stst35t (.72.) -0.134 0.004 -34.949 0.000 -0.142
## .Stst36c (.73.) -0.165 0.004 -46.073 0.000 -0.172
## .Stst37b (.74.) -0.062 0.004 -16.624 0.000 -0.069
## .Stst28m (.75.) 0.471 0.004 112.406 0.000 0.463
## .Sts303D (.76.) 0.363 0.003 104.943 0.000 0.356
## .english 1.267 0.011 114.717 0.000 1.245
## .math -0.557 0.009 -65.058 0.000 -0.574
## .speed 0.431 0.007 58.673 0.000 0.417
## .spatial -1.299 0.011 -122.107 0.000 -1.319
## g -0.114 0.007 -17.449 0.000 -0.127
## ci.upper Std.lv Std.all
## -0.063 -0.071 -0.075
## -0.141 -0.148 -0.156
## -0.093 -0.101 -0.106
## -0.084 -0.091 -0.095
## -0.101 -0.109 -0.118
## -0.095 -0.103 -0.111
## -0.081 -0.088 -0.095
## -0.070 -0.078 -0.081
## -0.120 -0.128 -0.141
## 0.127 0.120 0.128
## 0.084 0.076 0.079
## 0.153 0.145 0.148
## 0.155 0.148 0.156
## 0.036 0.029 0.031
## 0.241 0.235 0.248
## -0.127 -0.134 -0.155
## -0.158 -0.165 -0.178
## -0.055 -0.062 -0.067
## 0.479 0.471 0.551
## 0.369 0.363 0.406
## 1.289 0.523 0.523
## -0.541 -0.187 -0.187
## 0.446 0.467 0.467
## -1.278 -1.090 -1.090
## -0.101 -0.127 -0.127
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.476 0.004 131.886 0.000 0.469
## .Stst19dsgsdwrd 0.485 0.003 164.438 0.000 0.479
## .Stest20spellng 0.529 0.003 169.055 0.000 0.523
## .Stest21cptlztn 0.560 0.003 166.314 0.000 0.553
## .Stest22puncttn 0.303 0.002 135.735 0.000 0.298
## .Stest23english 0.468 0.003 146.298 0.000 0.462
## .Stest24exprssn 0.540 0.004 151.537 0.000 0.533
## .Stst25wrdfnctn 0.414 0.003 147.773 0.000 0.408
## .Stst26rdngcmpr 0.247 0.002 119.996 0.000 0.243
## .Stst31bstrctrs 0.513 0.003 163.971 0.000 0.507
## .Stst32rthrsnng 0.408 0.003 158.893 0.000 0.403
## .Stest5math 0.383 0.004 100.203 0.000 0.376
## .Stst33hghschlm 0.227 0.002 99.964 0.000 0.222
## .Stst34rthcmptt 0.504 0.004 133.956 0.000 0.497
## .Stst29vslztn2D 0.624 0.004 164.217 0.000 0.617
## .Stest35tblrdng 0.377 0.005 69.612 0.000 0.367
## .Stst36clrclchc 0.457 0.004 103.744 0.000 0.448
## .Stst37bjctnspc 0.538 0.004 138.659 0.000 0.530
## .Stst28mchnclrs 0.231 0.003 75.363 0.000 0.225
## .Stst30vslztn3D 0.513 0.003 149.852 0.000 0.506
## .english 1.092 0.029 37.657 0.000 1.035
## .math 1.462 0.057 25.821 0.000 1.351
## .speed 0.792 0.010 75.996 0.000 0.772
## .spatial 0.772 0.010 74.620 0.000 0.752
## g 0.800 0.006 125.357 0.000 0.788
## ci.upper Std.lv Std.all
## 0.483 0.476 0.522
## 0.491 0.485 0.541
## 0.535 0.529 0.593
## 0.567 0.560 0.610
## 0.307 0.303 0.355
## 0.474 0.468 0.542
## 0.547 0.540 0.633
## 0.419 0.414 0.449
## 0.251 0.247 0.300
## 0.519 0.513 0.583
## 0.413 0.408 0.443
## 0.391 0.383 0.400
## 0.231 0.227 0.254
## 0.512 0.504 0.567
## 0.631 0.624 0.698
## 0.388 0.377 0.505
## 0.465 0.457 0.531
## 0.546 0.538 0.624
## 0.237 0.231 0.317
## 0.520 0.513 0.643
## 1.149 0.186 0.186
## 1.573 0.165 0.165
## 0.813 0.929 0.929
## 0.792 0.544 0.544
## 0.813 1.000 1.000
lavTestScore(scalar, release = 32:51)
## 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 71964.22 20 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p57. == .p138. 27396.393 1 0
## 2 .p58. == .p139. 315.460 1 0
## 3 .p59. == .p140. 5937.040 1 0
## 4 .p60. == .p141. 4260.986 1 0
## 5 .p61. == .p142. 4650.352 1 0
## 6 .p62. == .p143. 476.147 1 0
## 7 .p63. == .p144. 195.650 1 0
## 8 .p64. == .p145. 2558.878 1 0
## 9 .p65. == .p146. 5253.180 1 0
## 10 .p66. == .p147. 2729.921 1 0
## 11 .p67. == .p148. 1728.967 1 0
## 12 .p68. == .p149. 2400.227 1 0
## 13 .p69. == .p150. 1096.133 1 0
## 14 .p70. == .p151. 4040.069 1 0
## 15 .p71. == .p152. 226.634 1 0
## 16 .p72. == .p153. 1494.041 1 0
## 17 .p73. == .p154. 148.684 1 0
## 18 .p74. == .p155. 397.726 1 0
## 19 .p75. == .p156. 16668.585 1 0
## 20 .p76. == .p157. 11991.572 1 0
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("Stest1vocab~1", "Stest28mechanicalreasoning~1", "Stest26readingcomprehension~1", "Stest34arithcomputation~1", "Stest33highschoolmath~1", "Stest19disguisedwords~1", "Stest29visualization2D~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
## (= 9.738754e-16) 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
## 91930.232 352.000 0.000 0.936 0.061 0.048
## aic bic
## 6498717.768 6499783.154
Mc(scalar2)
## [1] 0.7246223
summary(scalar2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 108 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 152
## Number of equality constraints 44
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 91930.232 77947.545
## Degrees of freedom 352 352
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.179
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 50671.669 42964.453
## 1 41258.563 34983.091
##
## 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.) 0.323 0.003 95.184 0.000 0.317
## Stst19d (.p2.) 0.239 0.003 88.060 0.000 0.234
## Stst20s (.p3.) 0.264 0.003 89.611 0.000 0.258
## Stst21c (.p4.) 0.259 0.003 91.692 0.000 0.254
## Stst22p (.p5.) 0.317 0.003 94.543 0.000 0.311
## Stst23n (.p6.) 0.268 0.003 89.543 0.000 0.262
## Stst24x (.p7.) 0.238 0.003 87.891 0.000 0.233
## Stst25w (.p8.) 0.239 0.003 91.619 0.000 0.234
## Stst26r (.p9.) 0.349 0.004 94.147 0.000 0.342
## Stst31b (.10.) 0.120 0.002 74.741 0.000 0.117
## Stst32r (.11.) 0.097 0.002 58.586 0.000 0.093
## math =~
## Stst5mt (.12.) 0.238 0.005 45.844 0.000 0.227
## Stst25w (.13.) 0.061 0.002 38.320 0.000 0.058
## Stst32r (.14.) 0.168 0.004 47.195 0.000 0.161
## Stst33h (.15.) 0.261 0.006 44.773 0.000 0.250
## Stst34r (.16.) 0.144 0.003 43.569 0.000 0.137
## speed =~
## Stst19d (.17.) 0.295 0.003 105.628 0.000 0.289
## Sts292D (.18.) 0.222 0.003 71.966 0.000 0.216
## Stst34r (.19.) 0.362 0.003 116.909 0.000 0.356
## Stst35t (.20.) 0.667 0.004 155.688 0.000 0.659
## Stst36c (.21.) 0.708 0.004 174.983 0.000 0.700
## Stst37b (.22.) 0.581 0.004 153.774 0.000 0.574
## spatial =~
## Stst28m (.23.) 0.507 0.003 194.693 0.000 0.501
## Sts292D (.24.) 0.381 0.003 137.697 0.000 0.376
## Sts303D (.25.) 0.560 0.003 184.018 0.000 0.554
## Stst31b (.26.) 0.355 0.003 140.960 0.000 0.350
## Stst37b (.27.) 0.104 0.002 44.980 0.000 0.099
## g =~
## english (.28.) 2.238 0.027 82.466 0.000 2.184
## math (.29.) 3.227 0.077 41.903 0.000 3.076
## speed (.30.) 0.251 0.004 56.486 0.000 0.242
## spatial (.31.) 0.943 0.007 134.391 0.000 0.929
## ci.upper Std.lv Std.all
##
## 0.330 0.793 0.819
## 0.244 0.585 0.590
## 0.269 0.646 0.641
## 0.265 0.635 0.652
## 0.324 0.777 0.790
## 0.274 0.657 0.661
## 0.243 0.584 0.577
## 0.244 0.585 0.579
## 0.356 0.856 0.850
## 0.123 0.294 0.295
## 0.100 0.237 0.238
##
## 0.248 0.802 0.843
## 0.065 0.208 0.205
## 0.175 0.567 0.569
## 0.273 0.883 0.871
## 0.150 0.486 0.492
##
## 0.300 0.304 0.306
## 0.228 0.228 0.233
## 0.368 0.373 0.377
## 0.676 0.688 0.674
## 0.716 0.730 0.728
## 0.588 0.599 0.580
##
## 0.512 0.696 0.785
## 0.387 0.524 0.534
## 0.566 0.769 0.754
## 0.360 0.488 0.490
## 0.108 0.143 0.138
##
## 2.291 0.913 0.913
## 3.378 0.955 0.955
## 0.259 0.243 0.243
## 0.956 0.686 0.686
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc 0.167 0.004 44.518 0.000 0.160
## .Stst19d -0.119 0.004 -30.513 0.000 -0.126
## .Stst20s (.59.) -0.194 0.004 -53.260 0.000 -0.201
## .Stst21c (.60.) -0.174 0.004 -48.438 0.000 -0.182
## .Stst22p (.61.) -0.218 0.004 -57.136 0.000 -0.226
## .Stst23n (.62.) -0.194 0.004 -51.868 0.000 -0.202
## .Stst24x (.63.) -0.171 0.004 -45.798 0.000 -0.179
## .Stst25w (.64.) -0.113 0.004 -30.153 0.000 -0.121
## .Stst26r -0.032 0.004 -7.896 0.000 -0.041
## .Stst31b (.66.) 0.044 0.004 11.578 0.000 0.036
## .Stst32r (.67.) 0.095 0.004 24.212 0.000 0.087
## .Stst5mt (.68.) 0.202 0.004 54.660 0.000 0.195
## .Stst33h 0.117 0.004 28.152 0.000 0.109
## .Stst34r -0.078 0.004 -19.713 0.000 -0.086
## .Sts292D 0.212 0.004 54.436 0.000 0.204
## .Stst35t (.72.) -0.102 0.004 -27.126 0.000 -0.109
## .Stst36c (.73.) -0.138 0.004 -37.260 0.000 -0.145
## .Stst37b (.74.) -0.065 0.004 -18.186 0.000 -0.072
## .Stst28m 0.536 0.004 151.033 0.000 0.529
## .Sts303D (.76.) 0.193 0.004 48.430 0.000 0.185
## ci.upper Std.lv Std.all
## 0.175 0.167 0.173
## -0.111 -0.119 -0.120
## -0.187 -0.194 -0.192
## -0.167 -0.174 -0.179
## -0.211 -0.218 -0.222
## -0.187 -0.194 -0.195
## -0.164 -0.171 -0.169
## -0.106 -0.113 -0.112
## -0.024 -0.032 -0.032
## 0.051 0.044 0.044
## 0.103 0.095 0.095
## 0.209 0.202 0.212
## 0.125 0.117 0.115
## -0.070 -0.078 -0.079
## 0.219 0.212 0.216
## -0.095 -0.102 -0.100
## -0.131 -0.138 -0.138
## -0.058 -0.065 -0.063
## 0.543 0.536 0.604
## 0.201 0.193 0.189
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.308 0.002 141.871 0.000 0.304
## .Stst19dsgsdwrd 0.471 0.003 158.801 0.000 0.465
## .Stest20spellng 0.599 0.004 168.872 0.000 0.592
## .Stest21cptlztn 0.547 0.003 171.015 0.000 0.541
## .Stest22puncttn 0.364 0.003 142.857 0.000 0.359
## .Stest23english 0.557 0.004 144.376 0.000 0.549
## .Stest24exprssn 0.684 0.004 158.377 0.000 0.676
## .Stst25wrdfnctn 0.424 0.003 155.190 0.000 0.419
## .Stst26rdngcmpr 0.281 0.002 124.164 0.000 0.276
## .Stst31bstrctrs 0.490 0.003 151.529 0.000 0.484
## .Stst32rthrsnng 0.382 0.002 154.249 0.000 0.377
## .Stest5math 0.262 0.003 87.717 0.000 0.256
## .Stst33hghschlm 0.248 0.002 112.935 0.000 0.244
## .Stst34rthcmptt 0.516 0.004 142.214 0.000 0.509
## .Stst29vslztn2D 0.597 0.004 142.263 0.000 0.589
## .Stest35tblrdng 0.569 0.008 72.247 0.000 0.553
## .Stst36clrclchc 0.472 0.006 84.626 0.000 0.461
## .Stst37bjctnspc 0.660 0.005 134.535 0.000 0.650
## .Stst28mchnclrs 0.302 0.003 111.568 0.000 0.297
## .Stst30vslztn3D 0.449 0.004 122.432 0.000 0.442
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.312 0.308 0.329
## 0.477 0.471 0.478
## 0.606 0.599 0.589
## 0.553 0.547 0.575
## 0.369 0.364 0.376
## 0.564 0.557 0.563
## 0.693 0.684 0.668
## 0.429 0.424 0.415
## 0.285 0.281 0.277
## 0.496 0.490 0.493
## 0.386 0.382 0.384
## 0.268 0.262 0.289
## 0.253 0.248 0.242
## 0.523 0.516 0.529
## 0.605 0.597 0.619
## 0.584 0.569 0.546
## 0.483 0.472 0.470
## 0.670 0.660 0.618
## 0.308 0.302 0.384
## 0.456 0.449 0.431
## 1.000 0.166 0.166
## 1.000 0.088 0.088
## 1.000 0.941 0.941
## 1.000 0.529 0.529
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.323 0.003 95.184 0.000 0.317
## Stst19d (.p2.) 0.239 0.003 88.060 0.000 0.234
## Stst20s (.p3.) 0.264 0.003 89.611 0.000 0.258
## Stst21c (.p4.) 0.259 0.003 91.692 0.000 0.254
## Stst22p (.p5.) 0.317 0.003 94.543 0.000 0.311
## Stst23n (.p6.) 0.268 0.003 89.543 0.000 0.262
## Stst24x (.p7.) 0.238 0.003 87.891 0.000 0.233
## Stst25w (.p8.) 0.239 0.003 91.619 0.000 0.234
## Stst26r (.p9.) 0.349 0.004 94.147 0.000 0.342
## Stst31b (.10.) 0.120 0.002 74.741 0.000 0.117
## Stst32r (.11.) 0.097 0.002 58.586 0.000 0.093
## math =~
## Stst5mt (.12.) 0.238 0.005 45.844 0.000 0.227
## Stst25w (.13.) 0.061 0.002 38.320 0.000 0.058
## Stst32r (.14.) 0.168 0.004 47.195 0.000 0.161
## Stst33h (.15.) 0.261 0.006 44.773 0.000 0.250
## Stst34r (.16.) 0.144 0.003 43.569 0.000 0.137
## speed =~
## Stst19d (.17.) 0.295 0.003 105.628 0.000 0.289
## Sts292D (.18.) 0.222 0.003 71.966 0.000 0.216
## Stst34r (.19.) 0.362 0.003 116.909 0.000 0.356
## Stst35t (.20.) 0.667 0.004 155.688 0.000 0.659
## Stst36c (.21.) 0.708 0.004 174.983 0.000 0.700
## Stst37b (.22.) 0.581 0.004 153.774 0.000 0.574
## spatial =~
## Stst28m (.23.) 0.507 0.003 194.693 0.000 0.501
## Sts292D (.24.) 0.381 0.003 137.697 0.000 0.376
## Sts303D (.25.) 0.560 0.003 184.018 0.000 0.554
## Stst31b (.26.) 0.355 0.003 140.960 0.000 0.350
## Stst37b (.27.) 0.104 0.002 44.980 0.000 0.099
## g =~
## english (.28.) 2.238 0.027 82.466 0.000 2.184
## math (.29.) 3.227 0.077 41.903 0.000 3.076
## speed (.30.) 0.251 0.004 56.486 0.000 0.242
## spatial (.31.) 0.943 0.007 134.391 0.000 0.929
## ci.upper Std.lv Std.all
##
## 0.330 0.730 0.777
## 0.244 0.539 0.567
## 0.269 0.595 0.639
## 0.265 0.585 0.620
## 0.324 0.716 0.792
## 0.274 0.605 0.661
## 0.243 0.538 0.590
## 0.244 0.539 0.564
## 0.356 0.788 0.857
## 0.123 0.271 0.288
## 0.100 0.218 0.228
##
## 0.248 0.746 0.770
## 0.065 0.193 0.202
## 0.175 0.527 0.550
## 0.273 0.821 0.865
## 0.150 0.452 0.482
##
## 0.300 0.271 0.284
## 0.228 0.203 0.214
## 0.368 0.332 0.354
## 0.676 0.612 0.706
## 0.716 0.650 0.698
## 0.588 0.533 0.575
##
## 0.512 0.615 0.749
## 0.387 0.463 0.488
## 0.566 0.680 0.733
## 0.360 0.432 0.460
## 0.108 0.126 0.136
##
## 2.291 0.889 0.889
## 3.378 0.921 0.921
## 0.259 0.245 0.245
## 0.956 0.696 0.696
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -0.609 0.005 -120.248 0.000 -0.619
## .Stst19d -0.322 0.005 -69.811 0.000 -0.331
## .Stst20s (.59.) -0.194 0.004 -53.260 0.000 -0.201
## .Stst21c (.60.) -0.174 0.004 -48.438 0.000 -0.182
## .Stst22p (.61.) -0.218 0.004 -57.136 0.000 -0.226
## .Stst23n (.62.) -0.194 0.004 -51.868 0.000 -0.202
## .Stst24x (.63.) -0.171 0.004 -45.798 0.000 -0.179
## .Stst25w (.64.) -0.113 0.004 -30.153 0.000 -0.121
## .Stst26r -0.450 0.005 -87.432 0.000 -0.460
## .Stst31b (.66.) 0.044 0.004 11.578 0.000 0.036
## .Stst32r (.67.) 0.095 0.004 24.212 0.000 0.087
## .Stst5mt (.68.) 0.202 0.004 54.660 0.000 0.195
## .Stst33h 0.334 0.005 61.175 0.000 0.323
## .Stst34r 0.275 0.005 56.798 0.000 0.265
## .Sts292D -0.008 0.005 -1.682 0.093 -0.017
## .Stst35t (.72.) -0.102 0.004 -27.126 0.000 -0.109
## .Stst36c (.73.) -0.138 0.004 -37.260 0.000 -0.145
## .Stst37b (.74.) -0.065 0.004 -18.186 0.000 -0.072
## .Stst28m -0.147 0.005 -30.328 0.000 -0.156
## .Sts303D (.76.) 0.193 0.004 48.430 0.000 0.185
## .english 1.743 0.014 121.675 0.000 1.715
## .math -1.333 0.012 -114.203 0.000 -1.356
## .speed 0.331 0.007 46.160 0.000 0.317
## .spatial -0.490 0.011 -45.218 0.000 -0.512
## g -0.069 0.009 -7.869 0.000 -0.086
## ci.upper Std.lv Std.all
## -0.599 -0.609 -0.648
## -0.313 -0.322 -0.339
## -0.187 -0.194 -0.208
## -0.167 -0.174 -0.185
## -0.211 -0.218 -0.241
## -0.187 -0.194 -0.212
## -0.164 -0.171 -0.188
## -0.106 -0.113 -0.119
## -0.440 -0.450 -0.489
## 0.051 0.044 0.046
## 0.103 0.095 0.099
## 0.209 0.202 0.208
## 0.345 0.334 0.352
## 0.284 0.275 0.294
## 0.001 -0.008 -0.008
## -0.095 -0.102 -0.118
## -0.131 -0.138 -0.148
## -0.058 -0.065 -0.070
## -0.137 -0.147 -0.179
## 0.201 0.193 0.208
## 1.771 0.772 0.772
## -1.311 -0.424 -0.424
## 0.345 0.361 0.361
## -0.469 -0.404 -0.404
## -0.052 -0.077 -0.077
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.351 0.002 152.378 0.000 0.346
## .Stst19dsgsdwrd 0.478 0.003 162.898 0.000 0.472
## .Stest20spellng 0.515 0.003 172.089 0.000 0.509
## .Stest21cptlztn 0.549 0.003 169.698 0.000 0.543
## .Stest22puncttn 0.305 0.002 139.663 0.000 0.301
## .Stest23english 0.472 0.003 145.240 0.000 0.465
## .Stest24exprssn 0.542 0.004 149.194 0.000 0.535
## .Stst25wrdfnctn 0.415 0.003 150.642 0.000 0.409
## .Stst26rdngcmpr 0.225 0.002 119.700 0.000 0.221
## .Stst31bstrctrs 0.479 0.003 157.650 0.000 0.473
## .Stst32rthrsnng 0.405 0.003 160.858 0.000 0.401
## .Stest5math 0.381 0.004 104.293 0.000 0.374
## .Stst33hghschlm 0.226 0.002 102.492 0.000 0.222
## .Stst34rthcmptt 0.495 0.004 136.193 0.000 0.487
## .Stst29vslztn2D 0.613 0.004 162.669 0.000 0.605
## .Stest35tblrdng 0.377 0.005 69.003 0.000 0.367
## .Stst36clrclchc 0.445 0.005 98.344 0.000 0.436
## .Stst37bjctnspc 0.537 0.004 139.336 0.000 0.530
## .Stst28mchnclrs 0.297 0.002 123.818 0.000 0.292
## .Stst30vslztn3D 0.400 0.003 127.849 0.000 0.393
## .english 1.068 0.025 43.590 0.000 1.020
## .math 1.489 0.063 23.622 0.000 1.366
## .speed 0.791 0.010 76.015 0.000 0.771
## .spatial 0.761 0.010 74.526 0.000 0.741
## g 0.805 0.006 126.329 0.000 0.792
## ci.upper Std.lv Std.all
## 0.355 0.351 0.397
## 0.484 0.478 0.528
## 0.521 0.515 0.592
## 0.556 0.549 0.616
## 0.310 0.305 0.373
## 0.478 0.472 0.563
## 0.549 0.542 0.652
## 0.420 0.415 0.454
## 0.228 0.225 0.265
## 0.484 0.479 0.542
## 0.410 0.405 0.441
## 0.389 0.381 0.406
## 0.230 0.226 0.251
## 0.502 0.495 0.564
## 0.620 0.613 0.680
## 0.388 0.377 0.502
## 0.454 0.445 0.513
## 0.545 0.537 0.625
## 0.301 0.297 0.439
## 0.406 0.400 0.463
## 1.117 0.210 0.210
## 1.613 0.151 0.151
## 0.811 0.940 0.940
## 0.781 0.516 0.516
## 0.817 1.000 1.000
lavTestScore(scalar2, release = 32:44)
## 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 4915.808 13 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p59. == .p140. 1190.147 1 0
## 2 .p60. == .p141. 486.696 1 0
## 3 .p61. == .p142. 61.348 1 0
## 4 .p62. == .p143. 792.679 1 0
## 5 .p63. == .p144. 665.003 1 0
## 6 .p64. == .p145. 776.825 1 0
## 7 .p66. == .p147. 78.169 1 0
## 8 .p67. == .p148. 1084.094 1 0
## 9 .p68. == .p149. 470.245 1 0
## 10 .p72. == .p153. 407.627 1 0
## 11 .p73. == .p154. 49.995 1 0
## 12 .p74. == .p155. 245.356 1 0
## 13 .p76. == .p157. 13.836 1 0
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("Stest1vocab~1", "Stest28mechanicalreasoning~1", "Stest26readingcomprehension~1", "Stest34arithcomputation~1", "Stest33highschoolmath~1", "Stest19disguisedwords~1", "Stest29visualization2D~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
## (= 5.401808e-15) 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
## 99208.213 372.000 0.000 0.930 0.061 0.050
## aic bic
## 6505955.749 6506823.842
Mc(strict)
## [1] 0.7063581
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("Stest1vocab~1", "Stest28mechanicalreasoning~1", "Stest26readingcomprehension~1", "Stest34arithcomputation~1", "Stest33highschoolmath~1", "Stest19disguisedwords~1", "Stest29visualization2D~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
## (= 1.518892e-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
## 93589.101 357.000 0.000 0.934 0.061 0.060
## aic bic
## 6500366.636 6501382.699
Mc(chc.hof)
## [1] 0.7204194
summary(chc.hof, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 72 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 147
## Number of equality constraints 44
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 93589.101 79368.082
## Degrees of freedom 357 357
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.179
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 51534.698 43703.915
## 1 42054.403 35664.167
##
## 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.) 0.328 0.003 125.191 0.000 0.323
## Stst19d (.p2.) 0.242 0.002 110.659 0.000 0.238
## Stst20s (.p3.) 0.267 0.002 115.362 0.000 0.263
## Stst21c (.p4.) 0.263 0.002 118.777 0.000 0.259
## Stst22p (.p5.) 0.321 0.003 124.649 0.000 0.316
## Stst23n (.p6.) 0.272 0.002 115.430 0.000 0.267
## Stst24x (.p7.) 0.241 0.002 111.911 0.000 0.237
## Stst25w (.p8.) 0.242 0.002 111.672 0.000 0.238
## Stst26r (.p9.) 0.354 0.003 124.633 0.000 0.348
## Stst31b (.10.) 0.121 0.001 84.402 0.000 0.118
## Stst32r (.11.) 0.097 0.002 61.098 0.000 0.094
## math =~
## Stst5mt (.12.) 0.264 0.004 69.759 0.000 0.257
## Stst25w (.13.) 0.069 0.001 48.449 0.000 0.066
## Stst32r (.14.) 0.188 0.002 75.489 0.000 0.183
## Stst33h (.15.) 0.291 0.004 67.640 0.000 0.282
## Stst34r (.16.) 0.160 0.002 64.589 0.000 0.155
## speed =~
## Stst19d (.17.) 0.281 0.003 108.632 0.000 0.276
## Sts292D (.18.) 0.210 0.003 73.262 0.000 0.204
## Stst34r (.19.) 0.342 0.003 125.694 0.000 0.336
## Stst35t (.20.) 0.626 0.003 187.862 0.000 0.619
## Stst36c (.21.) 0.670 0.003 201.597 0.000 0.663
## Stst37b (.22.) 0.548 0.003 174.834 0.000 0.542
## spatial =~
## Stst28m (.23.) 0.475 0.002 241.475 0.000 0.471
## Sts292D (.24.) 0.358 0.002 151.817 0.000 0.353
## Sts303D (.25.) 0.524 0.002 221.691 0.000 0.519
## Stst31b (.26.) 0.334 0.002 153.538 0.000 0.329
## Stst37b (.27.) 0.097 0.002 45.612 0.000 0.093
## g =~
## english (.28.) 2.098 0.020 102.800 0.000 2.058
## math (.29.) 2.753 0.045 61.558 0.000 2.665
## speed (.30.) 0.250 0.004 56.694 0.000 0.242
## spatial (.31.) 0.955 0.006 151.405 0.000 0.942
## ci.upper Std.lv Std.all
##
## 0.333 0.763 0.809
## 0.246 0.563 0.580
## 0.272 0.621 0.626
## 0.267 0.611 0.637
## 0.327 0.747 0.778
## 0.276 0.632 0.646
## 0.246 0.561 0.561
## 0.246 0.562 0.570
## 0.359 0.823 0.841
## 0.124 0.282 0.290
## 0.100 0.226 0.232
##
## 0.272 0.774 0.835
## 0.072 0.201 0.204
## 0.193 0.550 0.566
## 0.299 0.852 0.865
## 0.165 0.469 0.485
##
## 0.286 0.289 0.298
## 0.215 0.216 0.224
## 0.347 0.352 0.364
## 0.633 0.645 0.648
## 0.676 0.691 0.707
## 0.554 0.565 0.557
##
## 0.478 0.656 0.764
## 0.362 0.495 0.514
## 0.529 0.724 0.731
## 0.338 0.461 0.475
## 0.102 0.135 0.133
##
## 2.138 0.903 0.903
## 2.841 0.940 0.940
## 0.259 0.243 0.243
## 0.967 0.690 0.690
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc 0.167 0.004 44.519 0.000 0.160
## .Stst19d -0.119 0.004 -30.513 0.000 -0.126
## .Stst20s (.59.) -0.194 0.004 -53.349 0.000 -0.201
## .Stst21c (.60.) -0.175 0.004 -48.504 0.000 -0.182
## .Stst22p (.61.) -0.218 0.004 -57.222 0.000 -0.226
## .Stst23n (.62.) -0.194 0.004 -51.935 0.000 -0.202
## .Stst24x (.63.) -0.171 0.004 -45.848 0.000 -0.179
## .Stst25w (.64.) -0.113 0.004 -30.068 0.000 -0.120
## .Stst26r -0.032 0.004 -7.896 0.000 -0.041
## .Stst31b (.66.) 0.044 0.004 11.657 0.000 0.037
## .Stst32r (.67.) 0.096 0.004 24.423 0.000 0.088
## .Stst5mt (.68.) 0.201 0.004 54.589 0.000 0.194
## .Stst33h 0.117 0.004 28.152 0.000 0.109
## .Stst34r -0.078 0.004 -19.713 0.000 -0.086
## .Sts292D 0.212 0.004 54.436 0.000 0.204
## .Stst35t (.72.) -0.102 0.004 -27.155 0.000 -0.109
## .Stst36c (.73.) -0.138 0.004 -37.329 0.000 -0.146
## .Stst37b (.74.) -0.065 0.004 -18.173 0.000 -0.072
## .Stst28m 0.536 0.004 151.033 0.000 0.529
## .Sts303D (.76.) 0.193 0.004 48.414 0.000 0.185
## ci.upper Std.lv Std.all
## 0.175 0.167 0.177
## -0.111 -0.119 -0.122
## -0.187 -0.194 -0.196
## -0.168 -0.175 -0.182
## -0.211 -0.218 -0.227
## -0.187 -0.194 -0.199
## -0.164 -0.171 -0.171
## -0.106 -0.113 -0.115
## -0.024 -0.032 -0.033
## 0.051 0.044 0.045
## 0.104 0.096 0.099
## 0.209 0.201 0.217
## 0.125 0.117 0.119
## -0.070 -0.078 -0.081
## 0.219 0.212 0.220
## -0.095 -0.102 -0.102
## -0.131 -0.138 -0.142
## -0.058 -0.065 -0.064
## 0.543 0.536 0.624
## 0.201 0.193 0.195
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.307 0.002 141.550 0.000 0.303
## .Stst19dsgsdwrd 0.469 0.003 158.870 0.000 0.464
## .Stest20spellng 0.599 0.004 168.990 0.000 0.592
## .Stest21cptlztn 0.547 0.003 171.106 0.000 0.541
## .Stest22puncttn 0.365 0.003 142.769 0.000 0.360
## .Stest23english 0.556 0.004 144.116 0.000 0.549
## .Stest24exprssn 0.684 0.004 158.238 0.000 0.675
## .Stst25wrdfnctn 0.424 0.003 155.360 0.000 0.419
## .Stst26rdngcmpr 0.280 0.002 124.195 0.000 0.276
## .Stst31bstrctrs 0.491 0.003 151.535 0.000 0.484
## .Stst32rthrsnng 0.381 0.002 154.277 0.000 0.376
## .Stest5math 0.261 0.003 87.055 0.000 0.256
## .Stst33hghschlm 0.245 0.002 114.509 0.000 0.241
## .Stst34rthcmptt 0.517 0.004 142.242 0.000 0.510
## .Stst29vslztn2D 0.600 0.004 143.260 0.000 0.592
## .Stest35tblrdng 0.576 0.008 72.527 0.000 0.560
## .Stst36clrclchc 0.478 0.006 85.747 0.000 0.467
## .Stst37bjctnspc 0.665 0.005 135.642 0.000 0.655
## .Stst28mchnclrs 0.307 0.003 114.882 0.000 0.301
## .Stst30vslztn3D 0.456 0.004 126.529 0.000 0.449
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.312 0.307 0.346
## 0.475 0.469 0.499
## 0.606 0.599 0.608
## 0.553 0.547 0.594
## 0.370 0.365 0.395
## 0.564 0.556 0.582
## 0.692 0.684 0.685
## 0.430 0.424 0.436
## 0.284 0.280 0.293
## 0.497 0.491 0.519
## 0.386 0.381 0.403
## 0.267 0.261 0.304
## 0.249 0.245 0.252
## 0.524 0.517 0.552
## 0.608 0.600 0.647
## 0.591 0.576 0.580
## 0.489 0.478 0.501
## 0.674 0.665 0.647
## 0.312 0.307 0.416
## 0.464 0.456 0.465
## 1.000 0.185 0.185
## 1.000 0.117 0.117
## 1.000 0.941 0.941
## 1.000 0.523 0.523
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.328 0.003 125.191 0.000 0.323
## Stst19d (.p2.) 0.242 0.002 110.659 0.000 0.238
## Stst20s (.p3.) 0.267 0.002 115.362 0.000 0.263
## Stst21c (.p4.) 0.263 0.002 118.777 0.000 0.259
## Stst22p (.p5.) 0.321 0.003 124.649 0.000 0.316
## Stst23n (.p6.) 0.272 0.002 115.430 0.000 0.267
## Stst24x (.p7.) 0.241 0.002 111.911 0.000 0.237
## Stst25w (.p8.) 0.242 0.002 111.672 0.000 0.238
## Stst26r (.p9.) 0.354 0.003 124.633 0.000 0.348
## Stst31b (.10.) 0.121 0.001 84.402 0.000 0.118
## Stst32r (.11.) 0.097 0.002 61.098 0.000 0.094
## math =~
## Stst5mt (.12.) 0.264 0.004 69.759 0.000 0.257
## Stst25w (.13.) 0.069 0.001 48.449 0.000 0.066
## Stst32r (.14.) 0.188 0.002 75.489 0.000 0.183
## Stst33h (.15.) 0.291 0.004 67.640 0.000 0.282
## Stst34r (.16.) 0.160 0.002 64.589 0.000 0.155
## speed =~
## Stst19d (.17.) 0.281 0.003 108.632 0.000 0.276
## Sts292D (.18.) 0.210 0.003 73.262 0.000 0.204
## Stst34r (.19.) 0.342 0.003 125.694 0.000 0.336
## Stst35t (.20.) 0.626 0.003 187.862 0.000 0.619
## Stst36c (.21.) 0.670 0.003 201.597 0.000 0.663
## Stst37b (.22.) 0.548 0.003 174.834 0.000 0.542
## spatial =~
## Stst28m (.23.) 0.475 0.002 241.475 0.000 0.471
## Sts292D (.24.) 0.358 0.002 151.817 0.000 0.353
## Sts303D (.25.) 0.524 0.002 221.691 0.000 0.519
## Stst31b (.26.) 0.334 0.002 153.538 0.000 0.329
## Stst37b (.27.) 0.097 0.002 45.612 0.000 0.093
## g =~
## english (.28.) 2.098 0.020 102.800 0.000 2.058
## math (.29.) 2.753 0.045 61.558 0.000 2.665
## speed (.30.) 0.250 0.004 56.694 0.000 0.242
## spatial (.31.) 0.955 0.006 151.405 0.000 0.942
## ci.upper Std.lv Std.all
##
## 0.333 0.763 0.790
## 0.246 0.563 0.578
## 0.272 0.621 0.654
## 0.267 0.611 0.636
## 0.327 0.747 0.804
## 0.276 0.632 0.677
## 0.246 0.561 0.606
## 0.246 0.562 0.573
## 0.359 0.823 0.866
## 0.124 0.282 0.292
## 0.100 0.226 0.229
##
## 0.272 0.774 0.781
## 0.072 0.201 0.205
## 0.193 0.550 0.559
## 0.299 0.852 0.870
## 0.165 0.469 0.491
##
## 0.286 0.289 0.297
## 0.215 0.216 0.223
## 0.347 0.352 0.368
## 0.633 0.645 0.724
## 0.676 0.691 0.722
## 0.554 0.565 0.597
##
## 0.478 0.656 0.771
## 0.362 0.495 0.511
## 0.529 0.724 0.756
## 0.338 0.461 0.478
## 0.102 0.135 0.142
##
## 2.138 0.903 0.903
## 2.841 0.940 0.940
## 0.259 0.243 0.243
## 0.967 0.690 0.690
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -0.610 0.005 -120.199 0.000 -0.620
## .Stst19d -0.324 0.005 -69.953 0.000 -0.333
## .Stst20s (.59.) -0.194 0.004 -53.349 0.000 -0.201
## .Stst21c (.60.) -0.175 0.004 -48.504 0.000 -0.182
## .Stst22p (.61.) -0.218 0.004 -57.222 0.000 -0.226
## .Stst23n (.62.) -0.194 0.004 -51.935 0.000 -0.202
## .Stst24x (.63.) -0.171 0.004 -45.848 0.000 -0.179
## .Stst25w (.64.) -0.113 0.004 -30.068 0.000 -0.120
## .Stst26r -0.450 0.005 -87.594 0.000 -0.460
## .Stst31b (.66.) 0.044 0.004 11.657 0.000 0.037
## .Stst32r (.67.) 0.096 0.004 24.423 0.000 0.088
## .Stst5mt (.68.) 0.201 0.004 54.589 0.000 0.194
## .Stst33h 0.333 0.005 61.123 0.000 0.322
## .Stst34r 0.274 0.005 56.722 0.000 0.265
## .Sts292D -0.008 0.005 -1.682 0.093 -0.017
## .Stst35t (.72.) -0.102 0.004 -27.155 0.000 -0.109
## .Stst36c (.73.) -0.138 0.004 -37.329 0.000 -0.146
## .Stst37b (.74.) -0.065 0.004 -18.173 0.000 -0.072
## .Stst28m -0.147 0.005 -30.302 0.000 -0.156
## .Sts303D (.76.) 0.193 0.004 48.414 0.000 0.185
## .english 1.675 0.011 153.280 0.000 1.653
## .math -1.255 0.009 -137.898 0.000 -1.272
## .speed 0.346 0.007 49.480 0.000 0.333
## .spatial -0.545 0.010 -54.549 0.000 -0.564
## g -0.050 0.008 -6.554 0.000 -0.065
## ci.upper Std.lv Std.all
## -0.600 -0.610 -0.632
## -0.315 -0.324 -0.332
## -0.187 -0.194 -0.204
## -0.168 -0.175 -0.182
## -0.211 -0.218 -0.235
## -0.187 -0.194 -0.208
## -0.164 -0.171 -0.185
## -0.106 -0.113 -0.115
## -0.440 -0.450 -0.474
## 0.051 0.044 0.046
## 0.104 0.096 0.098
## 0.209 0.201 0.203
## 0.343 0.333 0.340
## 0.283 0.274 0.287
## 0.001 -0.008 -0.008
## -0.095 -0.102 -0.114
## -0.131 -0.138 -0.145
## -0.058 -0.065 -0.069
## -0.137 -0.147 -0.173
## 0.201 0.193 0.201
## 1.696 0.721 0.721
## -1.237 -0.428 -0.428
## 0.360 0.336 0.336
## -0.525 -0.394 -0.394
## -0.035 -0.050 -0.050
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.350 0.002 152.770 0.000 0.346
## .Stst19dsgsdwrd 0.477 0.003 162.773 0.000 0.471
## .Stest20spellng 0.515 0.003 172.189 0.000 0.509
## .Stest21cptlztn 0.550 0.003 169.793 0.000 0.543
## .Stest22puncttn 0.305 0.002 139.870 0.000 0.301
## .Stest23english 0.472 0.003 145.294 0.000 0.466
## .Stest24exprssn 0.543 0.004 149.308 0.000 0.536
## .Stst25wrdfnctn 0.414 0.003 150.622 0.000 0.409
## .Stst26rdngcmpr 0.225 0.002 120.327 0.000 0.222
## .Stst31bstrctrs 0.477 0.003 157.466 0.000 0.471
## .Stst32rthrsnng 0.404 0.003 161.123 0.000 0.399
## .Stest5math 0.382 0.004 104.604 0.000 0.375
## .Stst33hghschlm 0.233 0.002 109.601 0.000 0.229
## .Stst34rthcmptt 0.494 0.004 136.077 0.000 0.487
## .Stst29vslztn2D 0.609 0.004 162.053 0.000 0.602
## .Stest35tblrdng 0.377 0.005 69.336 0.000 0.367
## .Stst36clrclchc 0.437 0.004 97.603 0.000 0.429
## .Stst37bjctnspc 0.534 0.004 138.815 0.000 0.527
## .Stst28mchnclrs 0.293 0.002 121.446 0.000 0.288
## .Stst30vslztn3D 0.394 0.003 126.284 0.000 0.388
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.355 0.350 0.376
## 0.483 0.477 0.503
## 0.521 0.515 0.572
## 0.556 0.550 0.596
## 0.309 0.305 0.353
## 0.478 0.472 0.542
## 0.550 0.543 0.633
## 0.420 0.414 0.430
## 0.229 0.225 0.250
## 0.483 0.477 0.512
## 0.409 0.404 0.417
## 0.390 0.382 0.389
## 0.237 0.233 0.243
## 0.501 0.494 0.541
## 0.617 0.609 0.651
## 0.388 0.377 0.475
## 0.446 0.437 0.478
## 0.542 0.534 0.595
## 0.298 0.293 0.405
## 0.400 0.394 0.429
## 1.000 0.185 0.185
## 1.000 0.117 0.117
## 1.000 0.941 0.941
## 1.000 0.523 0.523
## 1.000 1.000 1.000
standardizedSolution(chc.hof) # 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 =~ Stest32arithreasoning 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 =~ Stest29visualization2D 1
## 19 speed =~ Stest34arithcomputation 1
## 20 speed =~ Stest35tablereading 1
## 21 speed =~ Stest36clericalchecking 1
## 22 speed =~ Stest37objectinspection 1
## 23 spatial =~ Stest28mechanicalreasoning 1
## 24 spatial =~ Stest29visualization2D 1
## 25 spatial =~ Stest30visualization3D 1
## 26 spatial =~ Stest31abstractreasoning 1
## 27 spatial =~ Stest37objectinspection 1
## 28 g =~ english 1
## 29 g =~ math 1
## 30 g =~ speed 1
## 31 g =~ spatial 1
## 32 Stest1vocab ~~ Stest1vocab 1
## 33 Stest19disguisedwords ~~ Stest19disguisedwords 1
## 34 Stest20spelling ~~ Stest20spelling 1
## 35 Stest21capitalization ~~ Stest21capitalization 1
## 36 Stest22punctuation ~~ Stest22punctuation 1
## 37 Stest23english ~~ Stest23english 1
## 38 Stest24expression ~~ Stest24expression 1
## 39 Stest25wordfunctions ~~ Stest25wordfunctions 1
## 40 Stest26readingcomprehension ~~ Stest26readingcomprehension 1
## 41 Stest31abstractreasoning ~~ Stest31abstractreasoning 1
## 42 Stest32arithreasoning ~~ Stest32arithreasoning 1
## 43 Stest5math ~~ Stest5math 1
## 44 Stest33highschoolmath ~~ Stest33highschoolmath 1
## 45 Stest34arithcomputation ~~ Stest34arithcomputation 1
## 46 Stest29visualization2D ~~ Stest29visualization2D 1
## 47 Stest35tablereading ~~ Stest35tablereading 1
## 48 Stest36clericalchecking ~~ Stest36clericalchecking 1
## 49 Stest37objectinspection ~~ Stest37objectinspection 1
## 50 Stest28mechanicalreasoning ~~ Stest28mechanicalreasoning 1
## 51 Stest30visualization3D ~~ Stest30visualization3D 1
## 52 english ~~ english 1
## 53 math ~~ math 1
## 54 speed ~~ speed 1
## 55 spatial ~~ spatial 1
## 56 g ~~ g 1
## 57 Stest1vocab ~1 1
## 58 Stest19disguisedwords ~1 1
## 59 Stest20spelling ~1 1
## 60 Stest21capitalization ~1 1
## 61 Stest22punctuation ~1 1
## 62 Stest23english ~1 1
## 63 Stest24expression ~1 1
## 64 Stest25wordfunctions ~1 1
## 65 Stest26readingcomprehension ~1 1
## 66 Stest31abstractreasoning ~1 1
## 67 Stest32arithreasoning ~1 1
## 68 Stest5math ~1 1
## 69 Stest33highschoolmath ~1 1
## 70 Stest34arithcomputation ~1 1
## 71 Stest29visualization2D ~1 1
## 72 Stest35tablereading ~1 1
## 73 Stest36clericalchecking ~1 1
## 74 Stest37objectinspection ~1 1
## 75 Stest28mechanicalreasoning ~1 1
## 76 Stest30visualization3D ~1 1
## 77 english ~1 1
## 78 math ~1 1
## 79 speed ~1 1
## 80 spatial ~1 1
## 81 g ~1 1
## 82 english =~ Stest1vocab 2
## 83 english =~ Stest19disguisedwords 2
## 84 english =~ Stest20spelling 2
## 85 english =~ Stest21capitalization 2
## 86 english =~ Stest22punctuation 2
## 87 english =~ Stest23english 2
## 88 english =~ Stest24expression 2
## 89 english =~ Stest25wordfunctions 2
## 90 english =~ Stest26readingcomprehension 2
## label est.std se z pvalue ci.lower ci.upper
## 1 .p1. 0.809 0.001 608.981 0 0.806 0.811
## 2 .p2. 0.580 0.002 272.763 0 0.576 0.584
## 3 .p3. 0.626 0.002 319.703 0 0.622 0.630
## 4 .p4. 0.637 0.002 314.222 0 0.633 0.641
## 5 .p5. 0.778 0.001 523.622 0 0.775 0.781
## 6 .p6. 0.646 0.002 317.832 0 0.642 0.650
## 7 .p7. 0.561 0.002 254.987 0 0.557 0.566
## 8 .p8. 0.570 0.003 195.364 0 0.564 0.575
## 9 .p9. 0.841 0.001 665.016 0 0.839 0.844
## 10 .p10. 0.290 0.003 106.875 0 0.284 0.295
## 11 .p11. 0.232 0.003 66.552 0 0.225 0.239
## 12 .p12. 0.835 0.001 577.183 0 0.832 0.837
## 13 .p13. 0.204 0.003 65.158 0 0.198 0.210
## 14 .p14. 0.566 0.003 162.885 0 0.559 0.573
## 15 .p15. 0.865 0.001 688.781 0 0.862 0.867
## 16 .p16. 0.485 0.002 198.155 0 0.480 0.490
## 17 .p17. 0.298 0.003 112.084 0 0.293 0.304
## 18 .p18. 0.224 0.003 72.996 0 0.218 0.230
## 19 .p19. 0.364 0.003 130.393 0 0.358 0.369
## 20 .p20. 0.648 0.004 180.849 0 0.641 0.655
## 21 .p21. 0.707 0.003 227.070 0 0.701 0.713
## 22 .p22. 0.557 0.003 192.411 0 0.552 0.563
## 23 .p23. 0.764 0.002 370.108 0 0.760 0.768
## 24 .p24. 0.514 0.003 194.152 0 0.509 0.519
## 25 .p25. 0.731 0.002 348.448 0 0.727 0.735
## 26 .p26. 0.475 0.003 163.490 0 0.469 0.480
## 27 .p27. 0.133 0.003 48.192 0 0.127 0.138
## 28 .p28. 0.903 0.002 555.320 0 0.900 0.906
## 29 .p29. 0.940 0.002 528.132 0 0.936 0.943
## 30 .p30. 0.243 0.004 60.248 0 0.235 0.251
## 31 .p31. 0.690 0.002 289.350 0 0.686 0.695
## 32 0.346 0.002 161.000 0 0.342 0.350
## 33 0.499 0.002 200.377 0 0.494 0.504
## 34 0.608 0.002 248.215 0 0.603 0.613
## 35 0.594 0.003 230.195 0 0.589 0.599
## 36 0.395 0.002 171.113 0 0.391 0.400
## 37 0.582 0.003 221.381 0 0.577 0.587
## 38 0.685 0.002 277.107 0 0.680 0.690
## 39 0.436 0.002 204.189 0 0.432 0.440
## 40 0.293 0.002 137.550 0 0.288 0.297
## 41 0.519 0.003 197.390 0 0.514 0.525
## 42 0.403 0.002 179.378 0 0.399 0.408
## 43 0.304 0.002 125.801 0 0.299 0.308
## 44 0.252 0.002 116.173 0 0.248 0.256
## 45 0.552 0.003 192.979 0 0.546 0.558
## 46 0.647 0.003 224.105 0 0.641 0.653
## 47 0.580 0.005 125.024 0 0.571 0.589
## 48 0.501 0.004 113.789 0 0.492 0.509
## 49 0.647 0.003 201.885 0 0.641 0.653
## 50 0.416 0.003 131.857 0 0.410 0.422
## 51 0.465 0.003 151.616 0 0.459 0.471
## 52 0.185 0.003 63.076 0 0.179 0.191
## 53 0.117 0.003 34.840 0 0.110 0.123
## 54 0.941 0.002 480.652 0 0.937 0.945
## 55 0.523 0.003 158.793 0 0.517 0.530
## 56 1.000 0.000 NA NA 1.000 1.000
## 57 0.177 0.004 43.066 0 0.169 0.186
## 58 -0.122 0.004 -30.252 0 -0.130 -0.114
## 59 .p59. -0.196 0.004 -53.593 0 -0.203 -0.188
## 60 .p60. -0.182 0.004 -48.656 0 -0.189 -0.175
## 61 .p61. -0.227 0.004 -58.266 0 -0.235 -0.220
## 62 .p62. -0.199 0.004 -54.209 0 -0.206 -0.192
## 63 .p63. -0.171 0.004 -48.501 0 -0.178 -0.165
## 64 .p64. -0.115 0.004 -30.197 0 -0.122 -0.107
## 65 -0.033 0.004 -7.941 0 -0.041 -0.025
## 66 .p66. 0.045 0.004 11.540 0 0.038 0.053
## 67 .p67. 0.099 0.004 24.276 0 0.091 0.107
## 68 .p68. 0.217 0.004 50.150 0 0.208 0.225
## 69 0.119 0.004 28.348 0 0.111 0.127
## 70 -0.081 0.004 -19.687 0 -0.089 -0.073
## 71 0.220 0.004 51.704 0 0.212 0.228
## 72 .p72. -0.102 0.004 -27.813 0 -0.109 -0.095
## 73 .p73. -0.142 0.004 -35.156 0 -0.149 -0.134
## 74 .p74. -0.064 0.004 -17.947 0 -0.071 -0.057
## 75 0.624 0.005 133.172 0 0.615 0.633
## 76 .p76. 0.195 0.004 47.374 0 0.187 0.203
## 77 0.000 0.000 NA NA 0.000 0.000
## 78 0.000 0.000 NA NA 0.000 0.000
## 79 0.000 0.000 NA NA 0.000 0.000
## 80 0.000 0.000 NA NA 0.000 0.000
## 81 0.000 0.000 NA NA 0.000 0.000
## 82 .p1. 0.790 0.001 540.405 0 0.787 0.793
## 83 .p2. 0.578 0.002 274.011 0 0.573 0.582
## 84 .p3. 0.654 0.002 347.288 0 0.651 0.658
## 85 .p4. 0.636 0.002 329.508 0 0.632 0.640
## 86 .p5. 0.804 0.001 586.756 0 0.801 0.807
## 87 .p6. 0.677 0.002 341.193 0 0.673 0.681
## 88 .p7. 0.606 0.002 273.947 0 0.601 0.610
## 89 .p8. 0.573 0.003 181.348 0 0.567 0.579
## 90 .p9. 0.866 0.001 784.239 0 0.864 0.868
## [ reached 'max' / getOption("max.print") -- omitted 72 rows ]
tests<-lavTestLRT(configural, metric, scalar2, chc.hof)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 3903.262 3831.752 1424.473
dfd=tests[2:4,"Df diff"]
dfd
## [1] 26 8 5
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04580468 0.08200377 0.06319934
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04459847 0.04702230
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.07983189 0.08419648
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.06046022 0.06598240
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
## 1.000 1.000 1.000 1.000 0.936 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 0.973 0.000 0.000
tests<-lavTestLRT(configural, metric, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 3903.262 63876.000
dfd=tests[2:3,"Df diff"]
dfd
## [1] 26 15
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04580468 0.24474068
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04459847 0.04702230
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.2431486 0.2463348
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] 3903.262 3831.752 5015.075
dfd=tests[2:4,"Df diff"]
dfd
## [1] 26 8 20
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04580468 0.08200377 0.05927751
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04459847 0.04702230
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.07983189 0.08419648
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.05790233 0.06066409
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
## 1.000 1.000 1.000 1.000 0.936 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 0.197 0.000 0.000
hof.age <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g =~ english + math + speed + spatial
g ~ age
'
hof.age2 <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning + Stest32arithreasoning
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g =~ english + math + speed + spatial
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("Stest1vocab~1", "Stest28mechanicalreasoning~1", "Stest26readingcomprehension~1", "Stest34arithcomputation~1", "Stest33highschoolmath~1", "Stest19disguisedwords~1", "Stest29visualization2D~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
## (= 1.135167e-16) is close to zero. This may be a symptom that the
## model is not identified.
fitMeasures(sem.age, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 102456.575 395.000 0.000 0.929 0.060 0.058
## ecvi aic bic
## 0.722 6498832.490 6499868.283
Mc(sem.age)
## [1] 0.6983902
summary(sem.age, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 71 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 149
## Number of equality constraints 44
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 102456.575 87031.306
## Degrees of freedom 395 395
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.177
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 54711.648 46474.579
## 1 47744.927 40556.727
##
## 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.) 0.319 0.003 115.706 0.000 0.314
## Stst19d (.p2.) 0.235 0.002 103.298 0.000 0.231
## Stst20s (.p3.) 0.260 0.002 107.936 0.000 0.255
## Stst21c (.p4.) 0.256 0.002 110.334 0.000 0.251
## Stst22p (.p5.) 0.313 0.003 115.042 0.000 0.308
## Stst23n (.p6.) 0.265 0.002 107.687 0.000 0.260
## Stst24x (.p7.) 0.235 0.002 104.979 0.000 0.231
## Stst25w (.p8.) 0.235 0.002 105.031 0.000 0.231
## Stst26r (.p9.) 0.345 0.003 114.997 0.000 0.339
## Stst31b (.10.) 0.118 0.001 81.625 0.000 0.115
## Stst32r (.11.) 0.095 0.002 60.550 0.000 0.092
## math =~
## Stst5mt (.12.) 0.276 0.004 74.421 0.000 0.269
## Stst25w (.13.) 0.072 0.001 49.730 0.000 0.069
## Stst32r (.14.) 0.196 0.002 80.488 0.000 0.191
## Stst33h (.15.) 0.304 0.004 72.151 0.000 0.296
## Stst34r (.16.) 0.167 0.002 68.418 0.000 0.163
## speed =~
## Stst19d (.17.) 0.280 0.003 108.270 0.000 0.275
## Sts292D (.18.) 0.209 0.003 73.104 0.000 0.204
## Stst34r (.19.) 0.341 0.003 125.657 0.000 0.336
## Stst35t (.20.) 0.626 0.003 187.990 0.000 0.619
## Stst36c (.21.) 0.669 0.003 201.018 0.000 0.663
## Stst37b (.22.) 0.548 0.003 174.568 0.000 0.541
## spatial =~
## Stst28m (.23.) 0.475 0.002 240.863 0.000 0.471
## Sts292D (.24.) 0.357 0.002 151.551 0.000 0.353
## Sts303D (.25.) 0.524 0.002 221.793 0.000 0.519
## Stst31b (.26.) 0.333 0.002 153.282 0.000 0.329
## Stst37b (.27.) 0.097 0.002 45.487 0.000 0.093
## g =~
## english (.28.) 2.154 0.022 96.465 0.000 2.111
## math (.29.) 2.603 0.040 64.624 0.000 2.524
## speed (.30.) 0.252 0.004 57.348 0.000 0.243
## spatial (.31.) 0.949 0.006 151.187 0.000 0.937
## ci.upper Std.lv Std.all
##
## 0.325 0.764 0.809
## 0.240 0.563 0.580
## 0.265 0.622 0.626
## 0.260 0.611 0.637
## 0.318 0.748 0.778
## 0.269 0.633 0.647
## 0.239 0.562 0.562
## 0.240 0.563 0.570
## 0.350 0.824 0.841
## 0.121 0.282 0.290
## 0.098 0.226 0.233
##
## 0.283 0.775 0.835
## 0.075 0.201 0.204
## 0.201 0.550 0.565
## 0.312 0.853 0.865
## 0.172 0.470 0.486
##
## 0.285 0.289 0.298
## 0.215 0.216 0.224
## 0.347 0.352 0.364
## 0.632 0.646 0.648
## 0.676 0.690 0.706
## 0.554 0.565 0.557
##
## 0.479 0.657 0.765
## 0.362 0.495 0.513
## 0.528 0.725 0.731
## 0.338 0.461 0.474
## 0.101 0.134 0.133
##
## 2.198 0.908 0.908
## 2.682 0.934 0.934
## 0.261 0.246 0.246
## 0.961 0.691 0.691
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.099 0.004 26.726 0.000 0.092
## ci.upper Std.lv Std.all
##
## 0.106 0.098 0.123
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc 0.175 0.004 46.467 0.000 0.168
## .Stst19d -0.112 0.004 -28.639 0.000 -0.120
## .Stst20s (.61.) -0.188 0.004 -51.556 0.000 -0.195
## .Stst21c (.62.) -0.168 0.004 -46.646 0.000 -0.175
## .Stst22p (.63.) -0.211 0.004 -54.857 0.000 -0.218
## .Stst23n (.64.) -0.188 0.004 -50.110 0.000 -0.195
## .Stst24x (.65.) -0.166 0.004 -44.436 0.000 -0.173
## .Stst25w (.66.) -0.105 0.004 -27.802 0.000 -0.113
## .Stst26r -0.024 0.004 -5.853 0.000 -0.032
## .Stst31b (.68.) 0.050 0.004 13.309 0.000 0.043
## .Stst32r (.69.) 0.104 0.004 26.245 0.000 0.096
## .Stst5mt (.70.) 0.210 0.004 56.454 0.000 0.202
## .Stst33h 0.126 0.004 29.909 0.000 0.118
## .Stst34r -0.072 0.004 -18.199 0.000 -0.080
## .Sts292D 0.216 0.004 55.515 0.000 0.209
## .Stst35t (.74.) -0.100 0.004 -26.789 0.000 -0.107
## .Stst36c (.75.) -0.136 0.004 -36.877 0.000 -0.144
## .Stst37b (.76.) -0.063 0.004 -17.502 0.000 -0.070
## .Stst28m 0.541 0.004 152.544 0.000 0.534
## .Sts303D (.78.) 0.198 0.004 49.818 0.000 0.191
## ci.upper Std.lv Std.all
## 0.182 0.175 0.186
## -0.105 -0.112 -0.116
## -0.180 -0.188 -0.189
## -0.161 -0.168 -0.175
## -0.203 -0.211 -0.219
## -0.181 -0.188 -0.192
## -0.158 -0.166 -0.166
## -0.098 -0.105 -0.107
## -0.016 -0.024 -0.025
## 0.058 0.050 0.052
## 0.112 0.104 0.107
## 0.217 0.210 0.226
## 0.134 0.126 0.128
## -0.065 -0.072 -0.075
## 0.224 0.216 0.224
## -0.093 -0.100 -0.100
## -0.129 -0.136 -0.139
## -0.056 -0.063 -0.062
## 0.548 0.541 0.630
## 0.206 0.198 0.200
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.307 0.002 141.533 0.000 0.303
## .Stst19dsgsdwrd 0.470 0.003 158.958 0.000 0.464
## .Stest20spellng 0.599 0.004 169.014 0.000 0.592
## .Stest21cptlztn 0.547 0.003 171.152 0.000 0.541
## .Stest22puncttn 0.365 0.003 142.849 0.000 0.360
## .Stest23english 0.556 0.004 144.078 0.000 0.549
## .Stest24exprssn 0.683 0.004 158.211 0.000 0.675
## .Stst25wrdfnctn 0.424 0.003 155.459 0.000 0.419
## .Stst26rdngcmpr 0.280 0.002 124.216 0.000 0.275
## .Stst31bstrctrs 0.491 0.003 151.532 0.000 0.485
## .Stst32rthrsnng 0.381 0.002 154.218 0.000 0.376
## .Stest5math 0.261 0.003 86.834 0.000 0.255
## .Stst33hghschlm 0.245 0.002 114.317 0.000 0.241
## .Stst34rthcmptt 0.516 0.004 142.182 0.000 0.509
## .Stst29vslztn2D 0.600 0.004 143.313 0.000 0.592
## .Stest35tblrdng 0.575 0.008 72.495 0.000 0.560
## .Stst36clrclchc 0.478 0.006 85.780 0.000 0.468
## .Stst37bjctnspc 0.665 0.005 135.658 0.000 0.655
## .Stst28mchnclrs 0.306 0.003 114.670 0.000 0.301
## .Stst30vslztn3D 0.457 0.004 126.532 0.000 0.450
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.311 0.307 0.345
## 0.476 0.470 0.498
## 0.606 0.599 0.608
## 0.553 0.547 0.594
## 0.370 0.365 0.395
## 0.564 0.556 0.582
## 0.692 0.683 0.684
## 0.430 0.424 0.436
## 0.284 0.280 0.292
## 0.498 0.491 0.519
## 0.386 0.381 0.403
## 0.267 0.261 0.303
## 0.249 0.245 0.252
## 0.524 0.516 0.551
## 0.608 0.600 0.647
## 0.591 0.575 0.580
## 0.489 0.478 0.501
## 0.674 0.665 0.647
## 0.311 0.306 0.415
## 0.464 0.457 0.465
## 1.000 0.175 0.175
## 1.000 0.127 0.127
## 1.000 0.939 0.939
## 1.000 0.522 0.522
## 1.000 0.985 0.985
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.319 0.003 115.706 0.000 0.314
## Stst19d (.p2.) 0.235 0.002 103.298 0.000 0.231
## Stst20s (.p3.) 0.260 0.002 107.936 0.000 0.255
## Stst21c (.p4.) 0.256 0.002 110.334 0.000 0.251
## Stst22p (.p5.) 0.313 0.003 115.042 0.000 0.308
## Stst23n (.p6.) 0.265 0.002 107.687 0.000 0.260
## Stst24x (.p7.) 0.235 0.002 104.979 0.000 0.231
## Stst25w (.p8.) 0.235 0.002 105.031 0.000 0.231
## Stst26r (.p9.) 0.345 0.003 114.997 0.000 0.339
## Stst31b (.10.) 0.118 0.001 81.625 0.000 0.115
## Stst32r (.11.) 0.095 0.002 60.550 0.000 0.092
## math =~
## Stst5mt (.12.) 0.276 0.004 74.421 0.000 0.269
## Stst25w (.13.) 0.072 0.001 49.730 0.000 0.069
## Stst32r (.14.) 0.196 0.002 80.488 0.000 0.191
## Stst33h (.15.) 0.304 0.004 72.151 0.000 0.296
## Stst34r (.16.) 0.167 0.002 68.418 0.000 0.163
## speed =~
## Stst19d (.17.) 0.280 0.003 108.270 0.000 0.275
## Sts292D (.18.) 0.209 0.003 73.104 0.000 0.204
## Stst34r (.19.) 0.341 0.003 125.657 0.000 0.336
## Stst35t (.20.) 0.626 0.003 187.990 0.000 0.619
## Stst36c (.21.) 0.669 0.003 201.018 0.000 0.663
## Stst37b (.22.) 0.548 0.003 174.568 0.000 0.541
## spatial =~
## Stst28m (.23.) 0.475 0.002 240.863 0.000 0.471
## Sts292D (.24.) 0.357 0.002 151.551 0.000 0.353
## Sts303D (.25.) 0.524 0.002 221.793 0.000 0.519
## Stst31b (.26.) 0.333 0.002 153.282 0.000 0.329
## Stst37b (.27.) 0.097 0.002 45.487 0.000 0.093
## g =~
## english (.28.) 2.154 0.022 96.465 0.000 2.111
## math (.29.) 2.603 0.040 64.624 0.000 2.524
## speed (.30.) 0.252 0.004 57.348 0.000 0.243
## spatial (.31.) 0.949 0.006 151.187 0.000 0.937
## ci.upper Std.lv Std.all
##
## 0.325 0.762 0.790
## 0.240 0.562 0.577
## 0.265 0.620 0.654
## 0.260 0.610 0.635
## 0.318 0.746 0.804
## 0.269 0.631 0.677
## 0.239 0.561 0.606
## 0.240 0.562 0.573
## 0.350 0.822 0.866
## 0.121 0.281 0.291
## 0.098 0.226 0.230
##
## 0.283 0.774 0.781
## 0.075 0.201 0.205
## 0.201 0.549 0.558
## 0.312 0.851 0.869
## 0.172 0.469 0.491
##
## 0.285 0.289 0.297
## 0.215 0.216 0.223
## 0.347 0.352 0.368
## 0.632 0.646 0.725
## 0.676 0.690 0.722
## 0.554 0.565 0.596
##
## 0.479 0.656 0.771
## 0.362 0.494 0.510
## 0.528 0.724 0.755
## 0.338 0.460 0.477
## 0.101 0.134 0.142
##
## 2.198 0.908 0.908
## 2.682 0.934 0.934
## 0.261 0.246 0.246
## 0.961 0.690 0.690
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.084 0.004 22.890 0.000 0.076
## ci.upper Std.lv Std.all
##
## 0.091 0.083 0.099
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -0.602 0.005 -118.473 0.000 -0.612
## .Stst19d -0.317 0.005 -68.365 0.000 -0.326
## .Stst20s (.61.) -0.188 0.004 -51.556 0.000 -0.195
## .Stst21c (.62.) -0.168 0.004 -46.646 0.000 -0.175
## .Stst22p (.63.) -0.211 0.004 -54.857 0.000 -0.218
## .Stst23n (.64.) -0.188 0.004 -50.110 0.000 -0.195
## .Stst24x (.65.) -0.166 0.004 -44.436 0.000 -0.173
## .Stst25w (.66.) -0.105 0.004 -27.802 0.000 -0.113
## .Stst26r -0.442 0.005 -85.792 0.000 -0.452
## .Stst31b (.68.) 0.050 0.004 13.309 0.000 0.043
## .Stst32r (.69.) 0.104 0.004 26.245 0.000 0.096
## .Stst5mt (.70.) 0.210 0.004 56.454 0.000 0.202
## .Stst33h 0.342 0.005 62.502 0.000 0.331
## .Stst34r 0.280 0.005 57.928 0.000 0.271
## .Sts292D -0.004 0.005 -0.767 0.443 -0.013
## .Stst35t (.74.) -0.100 0.004 -26.789 0.000 -0.107
## .Stst36c (.75.) -0.136 0.004 -36.877 0.000 -0.144
## .Stst37b (.76.) -0.063 0.004 -17.502 0.000 -0.070
## .Stst28m -0.142 0.005 -29.183 0.000 -0.151
## .Sts303D (.78.) 0.198 0.004 49.818 0.000 0.191
## .english 1.685 0.011 155.819 0.000 1.663
## .math -1.247 0.009 -133.768 0.000 -1.265
## .speed 0.342 0.007 48.907 0.000 0.329
## .spatial -0.561 0.010 -56.315 0.000 -0.580
## .g -0.027 0.008 -3.427 0.001 -0.043
## ci.upper Std.lv Std.all
## -0.592 -0.602 -0.624
## -0.307 -0.317 -0.325
## -0.180 -0.188 -0.198
## -0.161 -0.168 -0.175
## -0.203 -0.211 -0.227
## -0.181 -0.188 -0.201
## -0.158 -0.166 -0.179
## -0.098 -0.105 -0.107
## -0.432 -0.442 -0.466
## 0.058 0.050 0.052
## 0.112 0.104 0.106
## 0.217 0.210 0.212
## 0.353 0.342 0.349
## 0.290 0.280 0.293
## 0.006 -0.004 -0.004
## -0.093 -0.100 -0.112
## -0.129 -0.136 -0.143
## -0.056 -0.063 -0.066
## -0.132 -0.142 -0.167
## 0.206 0.198 0.207
## 1.706 0.706 0.706
## -1.228 -0.445 -0.445
## 0.356 0.332 0.332
## -0.541 -0.406 -0.406
## -0.012 -0.027 -0.027
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.350 0.002 152.778 0.000 0.345
## .Stst19dsgsdwrd 0.478 0.003 162.862 0.000 0.472
## .Stest20spellng 0.515 0.003 172.208 0.000 0.509
## .Stest21cptlztn 0.550 0.003 169.817 0.000 0.543
## .Stest22puncttn 0.305 0.002 139.922 0.000 0.301
## .Stest23english 0.472 0.003 145.275 0.000 0.466
## .Stest24exprssn 0.542 0.004 149.299 0.000 0.535
## .Stst25wrdfnctn 0.414 0.003 150.664 0.000 0.409
## .Stst26rdngcmpr 0.225 0.002 120.442 0.000 0.222
## .Stst31bstrctrs 0.478 0.003 157.472 0.000 0.472
## .Stst32rthrsnng 0.404 0.003 161.088 0.000 0.399
## .Stest5math 0.383 0.004 104.517 0.000 0.375
## .Stst33hghschlm 0.234 0.002 109.517 0.000 0.230
## .Stst34rthcmptt 0.493 0.004 135.974 0.000 0.486
## .Stst29vslztn2D 0.610 0.004 162.098 0.000 0.602
## .Stest35tblrdng 0.377 0.005 69.314 0.000 0.366
## .Stst36clrclchc 0.438 0.004 97.635 0.000 0.429
## .Stst37bjctnspc 0.534 0.004 138.832 0.000 0.527
## .Stst28mchnclrs 0.293 0.002 121.399 0.000 0.288
## .Stst30vslztn3D 0.394 0.003 126.250 0.000 0.388
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.354 0.350 0.376
## 0.483 0.478 0.503
## 0.521 0.515 0.572
## 0.556 0.550 0.596
## 0.310 0.305 0.354
## 0.478 0.472 0.542
## 0.550 0.542 0.633
## 0.420 0.414 0.431
## 0.229 0.225 0.250
## 0.483 0.478 0.513
## 0.409 0.404 0.418
## 0.390 0.383 0.390
## 0.238 0.234 0.244
## 0.500 0.493 0.540
## 0.617 0.610 0.651
## 0.388 0.377 0.475
## 0.447 0.438 0.479
## 0.542 0.534 0.596
## 0.298 0.293 0.405
## 0.400 0.394 0.429
## 1.000 0.176 0.176
## 1.000 0.128 0.128
## 1.000 0.940 0.940
## 1.000 0.524 0.524
## 1.000 0.990 0.990
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("Stest1vocab~1", "Stest28mechanicalreasoning~1", "Stest26readingcomprehension~1", "Stest34arithcomputation~1", "Stest33highschoolmath~1", "Stest19disguisedwords~1", "Stest29visualization2D~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
## (= 1.648325e-16) is close to zero. This may be a symptom that the
## model is not identified.
fitMeasures(sem.age2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 103058.049 433.000 0.000 0.928 0.058 0.056
## ecvi aic bic
## 0.726 6497569.242 6498624.764
Mc(sem.age2)
## [1] 0.6970074
summary(sem.age2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 74 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 151
## Number of equality constraints 44
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 103058.049 87543.461
## Degrees of freedom 433 433
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.177
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 54986.160 46708.421
## 1 48071.890 40835.040
##
## 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.) 0.320 0.003 116.906 0.000 0.314
## Stst19d (.p2.) 0.236 0.002 104.190 0.000 0.231
## Stst20s (.p3.) 0.260 0.002 108.945 0.000 0.255
## Stst21c (.p4.) 0.256 0.002 111.411 0.000 0.251
## Stst22p (.p5.) 0.313 0.003 116.214 0.000 0.308
## Stst23n (.p6.) 0.265 0.002 108.664 0.000 0.260
## Stst24x (.p7.) 0.235 0.002 105.908 0.000 0.231
## Stst25w (.p8.) 0.235 0.002 105.847 0.000 0.231
## Stst26r (.p9.) 0.345 0.003 116.201 0.000 0.339
## Stst31b (.10.) 0.118 0.001 81.952 0.000 0.115
## Stst32r (.11.) 0.095 0.002 60.594 0.000 0.092
## math =~
## Stst5mt (.12.) 0.276 0.004 75.242 0.000 0.269
## Stst25w (.13.) 0.072 0.001 49.947 0.000 0.069
## Stst32r (.14.) 0.196 0.002 81.166 0.000 0.191
## Stst33h (.15.) 0.304 0.004 72.923 0.000 0.296
## Stst34r (.16.) 0.168 0.002 69.070 0.000 0.163
## speed =~
## Stst19d (.17.) 0.280 0.003 108.189 0.000 0.275
## Sts292D (.18.) 0.209 0.003 73.058 0.000 0.203
## Stst34r (.19.) 0.341 0.003 125.565 0.000 0.336
## Stst35t (.20.) 0.626 0.003 188.026 0.000 0.619
## Stst36c (.21.) 0.669 0.003 200.879 0.000 0.662
## Stst37b (.22.) 0.547 0.003 174.516 0.000 0.541
## spatial =~
## Stst28m (.23.) 0.475 0.002 240.969 0.000 0.471
## Sts292D (.24.) 0.357 0.002 151.566 0.000 0.353
## Sts303D (.25.) 0.524 0.002 221.777 0.000 0.519
## Stst31b (.26.) 0.333 0.002 153.264 0.000 0.329
## Stst37b (.27.) 0.097 0.002 45.466 0.000 0.093
## g =~
## english (.28.) 2.143 0.022 97.481 0.000 2.100
## math (.29.) 2.589 0.040 65.316 0.000 2.511
## speed (.30.) 0.252 0.004 57.550 0.000 0.243
## spatial (.31.) 0.944 0.006 151.151 0.000 0.932
## ci.upper Std.lv Std.all
##
## 0.325 0.765 0.810
## 0.240 0.564 0.580
## 0.265 0.623 0.627
## 0.260 0.612 0.638
## 0.318 0.749 0.778
## 0.269 0.634 0.647
## 0.239 0.563 0.563
## 0.240 0.564 0.571
## 0.350 0.825 0.842
## 0.121 0.282 0.290
## 0.098 0.227 0.233
##
## 0.284 0.777 0.836
## 0.075 0.202 0.204
## 0.201 0.551 0.566
## 0.312 0.854 0.865
## 0.172 0.471 0.486
##
## 0.285 0.289 0.297
## 0.215 0.216 0.224
## 0.346 0.352 0.363
## 0.632 0.646 0.648
## 0.675 0.690 0.706
## 0.554 0.565 0.557
##
## 0.479 0.657 0.765
## 0.362 0.495 0.514
## 0.528 0.725 0.732
## 0.337 0.461 0.474
## 0.101 0.134 0.133
##
## 2.186 0.909 0.909
## 2.666 0.935 0.935
## 0.260 0.248 0.248
## 0.956 0.692 0.692
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.090 0.004 25.062 0.000 0.083
## age2 -0.065 0.002 -26.497 0.000 -0.070
## ci.upper Std.lv Std.all
##
## 0.097 0.089 0.111
## -0.060 -0.064 -0.119
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc 0.244 0.005 53.658 0.000 0.235
## .Stst19d -0.054 0.005 -12.035 0.000 -0.063
## .Stst20s (.64.) -0.131 0.004 -31.429 0.000 -0.140
## .Stst21c (.65.) -0.113 0.004 -27.419 0.000 -0.121
## .Stst22p (.66.) -0.143 0.005 -31.148 0.000 -0.152
## .Stst23n (.67.) -0.131 0.004 -30.603 0.000 -0.139
## .Stst24x (.68.) -0.115 0.004 -27.889 0.000 -0.123
## .Stst25w (.69.) -0.036 0.005 -7.688 0.000 -0.045
## .Stst26r 0.050 0.005 10.165 0.000 0.041
## .Stst31b (.71.) 0.108 0.004 25.036 0.000 0.099
## .Stst32r (.72.) 0.175 0.005 36.552 0.000 0.166
## .Stst5mt (.73.) 0.282 0.005 61.618 0.000 0.273
## .Stst33h 0.205 0.005 39.047 0.000 0.195
## .Stst34r -0.020 0.004 -4.474 0.000 -0.029
## .Sts292D 0.255 0.004 61.629 0.000 0.247
## .Stst35t (.77.) -0.084 0.004 -22.546 0.000 -0.092
## .Stst36c (.78.) -0.119 0.004 -31.832 0.000 -0.127
## .Stst37b (.79.) -0.040 0.004 -10.702 0.000 -0.047
## .Stst28m 0.586 0.004 149.766 0.000 0.579
## .Sts303D (.81.) 0.248 0.004 56.212 0.000 0.240
## ci.upper Std.lv Std.all
## 0.253 0.244 0.258
## -0.045 -0.054 -0.056
## -0.123 -0.131 -0.132
## -0.105 -0.113 -0.118
## -0.134 -0.143 -0.149
## -0.122 -0.131 -0.134
## -0.107 -0.115 -0.115
## -0.027 -0.036 -0.036
## 0.060 0.050 0.051
## 0.116 0.108 0.110
## 0.185 0.175 0.180
## 0.291 0.282 0.303
## 0.215 0.205 0.208
## -0.011 -0.020 -0.021
## 0.264 0.255 0.265
## -0.077 -0.084 -0.085
## -0.112 -0.119 -0.122
## -0.032 -0.040 -0.039
## 0.594 0.586 0.682
## 0.257 0.248 0.250
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.307 0.002 141.509 0.000 0.303
## .Stst19dsgsdwrd 0.470 0.003 158.971 0.000 0.464
## .Stest20spellng 0.599 0.004 168.998 0.000 0.592
## .Stest21cptlztn 0.547 0.003 171.157 0.000 0.541
## .Stest22puncttn 0.366 0.003 142.858 0.000 0.361
## .Stest23english 0.556 0.004 144.075 0.000 0.549
## .Stest24exprssn 0.683 0.004 158.198 0.000 0.675
## .Stst25wrdfnctn 0.424 0.003 155.460 0.000 0.419
## .Stst26rdngcmpr 0.280 0.002 124.214 0.000 0.275
## .Stst31bstrctrs 0.491 0.003 151.541 0.000 0.485
## .Stst32rthrsnng 0.381 0.002 154.268 0.000 0.377
## .Stest5math 0.261 0.003 86.725 0.000 0.255
## .Stst33hghschlm 0.245 0.002 114.366 0.000 0.241
## .Stst34rthcmptt 0.516 0.004 142.191 0.000 0.509
## .Stst29vslztn2D 0.600 0.004 143.320 0.000 0.592
## .Stest35tblrdng 0.575 0.008 72.482 0.000 0.560
## .Stst36clrclchc 0.479 0.006 85.784 0.000 0.468
## .Stst37bjctnspc 0.665 0.005 135.666 0.000 0.655
## .Stst28mchnclrs 0.306 0.003 114.631 0.000 0.301
## .Stst30vslztn3D 0.457 0.004 126.546 0.000 0.450
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.311 0.307 0.344
## 0.476 0.470 0.498
## 0.606 0.599 0.607
## 0.553 0.547 0.593
## 0.371 0.366 0.394
## 0.564 0.556 0.581
## 0.692 0.683 0.683
## 0.430 0.424 0.435
## 0.284 0.280 0.291
## 0.498 0.491 0.518
## 0.386 0.381 0.402
## 0.267 0.261 0.302
## 0.249 0.245 0.251
## 0.524 0.516 0.550
## 0.608 0.600 0.647
## 0.591 0.575 0.580
## 0.490 0.479 0.501
## 0.674 0.665 0.647
## 0.311 0.306 0.415
## 0.464 0.457 0.465
## 1.000 0.175 0.175
## 1.000 0.127 0.127
## 1.000 0.939 0.939
## 1.000 0.521 0.521
## 1.000 0.971 0.971
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.320 0.003 116.906 0.000 0.314
## Stst19d (.p2.) 0.236 0.002 104.190 0.000 0.231
## Stst20s (.p3.) 0.260 0.002 108.945 0.000 0.255
## Stst21c (.p4.) 0.256 0.002 111.411 0.000 0.251
## Stst22p (.p5.) 0.313 0.003 116.214 0.000 0.308
## Stst23n (.p6.) 0.265 0.002 108.664 0.000 0.260
## Stst24x (.p7.) 0.235 0.002 105.908 0.000 0.231
## Stst25w (.p8.) 0.235 0.002 105.847 0.000 0.231
## Stst26r (.p9.) 0.345 0.003 116.201 0.000 0.339
## Stst31b (.10.) 0.118 0.001 81.952 0.000 0.115
## Stst32r (.11.) 0.095 0.002 60.594 0.000 0.092
## math =~
## Stst5mt (.12.) 0.276 0.004 75.242 0.000 0.269
## Stst25w (.13.) 0.072 0.001 49.947 0.000 0.069
## Stst32r (.14.) 0.196 0.002 81.166 0.000 0.191
## Stst33h (.15.) 0.304 0.004 72.923 0.000 0.296
## Stst34r (.16.) 0.168 0.002 69.070 0.000 0.163
## speed =~
## Stst19d (.17.) 0.280 0.003 108.189 0.000 0.275
## Sts292D (.18.) 0.209 0.003 73.058 0.000 0.203
## Stst34r (.19.) 0.341 0.003 125.565 0.000 0.336
## Stst35t (.20.) 0.626 0.003 188.026 0.000 0.619
## Stst36c (.21.) 0.669 0.003 200.879 0.000 0.662
## Stst37b (.22.) 0.547 0.003 174.516 0.000 0.541
## spatial =~
## Stst28m (.23.) 0.475 0.002 240.969 0.000 0.471
## Sts292D (.24.) 0.357 0.002 151.566 0.000 0.353
## Sts303D (.25.) 0.524 0.002 221.777 0.000 0.519
## Stst31b (.26.) 0.333 0.002 153.264 0.000 0.329
## Stst37b (.27.) 0.097 0.002 45.466 0.000 0.093
## g =~
## english (.28.) 2.143 0.022 97.481 0.000 2.100
## math (.29.) 2.589 0.040 65.316 0.000 2.511
## speed (.30.) 0.252 0.004 57.550 0.000 0.243
## spatial (.31.) 0.944 0.006 151.151 0.000 0.932
## ci.upper Std.lv Std.all
##
## 0.325 0.761 0.789
## 0.240 0.561 0.576
## 0.265 0.619 0.653
## 0.260 0.609 0.635
## 0.318 0.745 0.803
## 0.269 0.630 0.676
## 0.239 0.560 0.605
## 0.240 0.561 0.572
## 0.350 0.820 0.866
## 0.121 0.281 0.291
## 0.098 0.226 0.230
##
## 0.284 0.772 0.781
## 0.075 0.201 0.205
## 0.201 0.548 0.558
## 0.312 0.849 0.869
## 0.172 0.468 0.490
##
## 0.285 0.289 0.297
## 0.215 0.216 0.223
## 0.346 0.352 0.368
## 0.632 0.646 0.725
## 0.675 0.690 0.722
## 0.554 0.565 0.596
##
## 0.479 0.655 0.771
## 0.362 0.493 0.510
## 0.528 0.723 0.755
## 0.337 0.460 0.477
## 0.101 0.134 0.141
##
## 2.186 0.907 0.907
## 2.666 0.934 0.934
## 0.260 0.246 0.246
## 0.956 0.689 0.689
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.062 0.004 16.106 0.000 0.055
## age2 -0.049 0.003 -18.556 0.000 -0.055
## ci.upper Std.lv Std.all
##
## 0.070 0.062 0.074
## -0.044 -0.049 -0.082
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -0.533 0.006 -94.177 0.000 -0.544
## .Stst19d -0.259 0.005 -50.663 0.000 -0.269
## .Stst20s (.64.) -0.131 0.004 -31.429 0.000 -0.140
## .Stst21c (.65.) -0.113 0.004 -27.419 0.000 -0.121
## .Stst22p (.66.) -0.143 0.005 -31.148 0.000 -0.152
## .Stst23n (.67.) -0.131 0.004 -30.603 0.000 -0.139
## .Stst24x (.68.) -0.115 0.004 -27.889 0.000 -0.123
## .Stst25w (.69.) -0.036 0.005 -7.688 0.000 -0.045
## .Stst26r -0.367 0.006 -63.082 0.000 -0.379
## .Stst31b (.71.) 0.108 0.004 25.036 0.000 0.099
## .Stst32r (.72.) 0.175 0.005 36.552 0.000 0.166
## .Stst5mt (.73.) 0.282 0.005 61.618 0.000 0.273
## .Stst33h 0.421 0.006 67.108 0.000 0.409
## .Stst34r 0.333 0.005 63.179 0.000 0.322
## .Sts292D 0.036 0.005 7.120 0.000 0.026
## .Stst35t (.77.) -0.084 0.004 -22.546 0.000 -0.092
## .Stst36c (.78.) -0.119 0.004 -31.832 0.000 -0.127
## .Stst37b (.79.) -0.040 0.004 -10.702 0.000 -0.047
## .Stst28m -0.096 0.005 -18.595 0.000 -0.107
## .Sts303D (.81.) 0.248 0.004 56.212 0.000 0.240
## .english 1.701 0.011 156.390 0.000 1.680
## .math -1.226 0.009 -131.251 0.000 -1.244
## .speed 0.344 0.007 49.205 0.000 0.331
## .spatial -0.553 0.010 -55.770 0.000 -0.573
## .g -0.068 0.009 -7.319 0.000 -0.087
## ci.upper Std.lv Std.all
## -0.522 -0.533 -0.553
## -0.249 -0.259 -0.266
## -0.123 -0.131 -0.139
## -0.105 -0.113 -0.118
## -0.134 -0.143 -0.154
## -0.122 -0.131 -0.140
## -0.107 -0.115 -0.124
## -0.027 -0.036 -0.036
## -0.356 -0.367 -0.388
## 0.116 0.108 0.112
## 0.185 0.175 0.179
## 0.291 0.282 0.285
## 0.433 0.421 0.431
## 0.343 0.333 0.348
## 0.046 0.036 0.037
## -0.077 -0.084 -0.095
## -0.112 -0.119 -0.125
## -0.032 -0.040 -0.042
## -0.086 -0.096 -0.114
## 0.257 0.248 0.259
## 1.723 0.715 0.715
## -1.207 -0.439 -0.439
## 0.358 0.334 0.334
## -0.534 -0.401 -0.401
## -0.050 -0.068 -0.068
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.350 0.002 152.765 0.000 0.345
## .Stst19dsgsdwrd 0.478 0.003 162.884 0.000 0.472
## .Stest20spellng 0.515 0.003 172.210 0.000 0.509
## .Stest21cptlztn 0.550 0.003 169.812 0.000 0.543
## .Stest22puncttn 0.305 0.002 139.926 0.000 0.301
## .Stest23english 0.472 0.003 145.290 0.000 0.466
## .Stest24exprssn 0.542 0.004 149.292 0.000 0.535
## .Stst25wrdfnctn 0.414 0.003 150.650 0.000 0.409
## .Stst26rdngcmpr 0.225 0.002 120.439 0.000 0.222
## .Stst31bstrctrs 0.478 0.003 157.483 0.000 0.472
## .Stst32rthrsnng 0.404 0.003 161.191 0.000 0.399
## .Stest5math 0.382 0.004 104.462 0.000 0.375
## .Stst33hghschlm 0.234 0.002 109.593 0.000 0.230
## .Stst34rthcmptt 0.493 0.004 135.993 0.000 0.486
## .Stst29vslztn2D 0.610 0.004 162.099 0.000 0.602
## .Stest35tblrdng 0.377 0.005 69.306 0.000 0.366
## .Stst36clrclchc 0.438 0.004 97.638 0.000 0.429
## .Stst37bjctnspc 0.534 0.004 138.838 0.000 0.527
## .Stst28mchnclrs 0.293 0.002 121.391 0.000 0.288
## .Stst30vslztn3D 0.394 0.003 126.255 0.000 0.388
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.354 0.350 0.377
## 0.483 0.478 0.504
## 0.521 0.515 0.573
## 0.556 0.550 0.597
## 0.310 0.305 0.355
## 0.478 0.472 0.543
## 0.550 0.542 0.634
## 0.420 0.414 0.432
## 0.229 0.225 0.251
## 0.483 0.478 0.514
## 0.409 0.404 0.419
## 0.390 0.382 0.391
## 0.238 0.234 0.245
## 0.500 0.493 0.541
## 0.617 0.610 0.652
## 0.387 0.377 0.475
## 0.447 0.438 0.479
## 0.542 0.534 0.596
## 0.298 0.293 0.405
## 0.400 0.394 0.430
## 1.000 0.176 0.176
## 1.000 0.128 0.128
## 1.000 0.940 0.940
## 1.000 0.525 0.525
## 1.000 0.984 0.984
CHC Bifactor models (g varies depending on which intercept is freed,
S26 is freed instead of S5 because S26 has low loading on its
factor)
chc.bifactor.model <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g=~ Stest1vocab + Stest5math + 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", std.lv=T, orthogonal=T)
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 81850.530 145.000 0.000 0.943 0.063 0.048
## aic bic
## 6592591.839 6593430.338
Mc(baseline)
## [1] 0.7502267
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
## 55981.306 290.000 0.000 0.961 0.052 0.030
## aic bic
## 6462892.841 6464569.838
Mc(configural)
## [1] 0.8221101
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 33 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 170
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 55981.306 48244.345
## Degrees of freedom 290 290
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.160
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 30848.992 26585.471
## 1 25132.314 21658.873
##
## 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 =~
## Stst19dsgsdwrd 0.219 0.008 26.846 0.000 0.203
## Stest20spellng 0.389 0.008 49.254 0.000 0.374
## Stest21cptlztn 0.296 0.005 54.121 0.000 0.285
## Stest22puncttn 0.355 0.006 55.611 0.000 0.343
## Stest23english 0.269 0.007 40.633 0.000 0.256
## Stest24exprssn 0.177 0.007 23.661 0.000 0.162
## Stst25wrdfnctn 0.239 0.005 48.025 0.000 0.229
## Stst26rdngcmpr 0.082 0.007 12.134 0.000 0.069
## Stst31bstrctrs 0.077 0.006 13.926 0.000 0.066
## math =~
## Stest5math 0.247 0.004 62.339 0.000 0.239
## Stst25wrdfnctn 0.172 0.004 44.209 0.000 0.165
## Stst32rthrsnng 0.191 0.004 43.731 0.000 0.183
## Stst33hghschlm 0.574 0.006 102.575 0.000 0.563
## Stst34rthcmptt 0.275 0.005 55.024 0.000 0.265
## speed =~
## Stst19dsgsdwrd 0.268 0.004 74.361 0.000 0.261
## Stst29vslztn2D 0.230 0.004 57.194 0.000 0.222
## Stst34rthcmptt 0.378 0.004 97.384 0.000 0.370
## Stest35tblrdng 0.663 0.005 126.287 0.000 0.653
## Stst36clrclchc 0.715 0.005 154.246 0.000 0.706
## Stst37bjctnspc 0.612 0.005 134.086 0.000 0.603
## spatial =~
## Stst28mchnclrs 0.448 0.004 119.638 0.000 0.441
## Stst29vslztn2D 0.459 0.004 107.646 0.000 0.451
## Stst30vslztn3D 0.611 0.004 137.507 0.000 0.602
## Stst31bstrctrs 0.340 0.004 81.934 0.000 0.332
## Stst37bjctnspc 0.265 0.004 60.403 0.000 0.256
## g =~
## Stest1vocab 0.781 0.003 247.211 0.000 0.775
## Stest5math 0.729 0.003 229.457 0.000 0.723
## Stst19dsgsdwrd 0.601 0.004 163.985 0.000 0.594
## Stest20spellng 0.565 0.004 137.014 0.000 0.557
## Stest21cptlztn 0.591 0.004 163.087 0.000 0.584
## Stest22puncttn 0.729 0.003 210.301 0.000 0.722
## Stest23english 0.661 0.004 155.219 0.000 0.652
## Stest24exprssn 0.627 0.004 145.305 0.000 0.619
## Stst25wrdfnctn 0.667 0.003 211.905 0.000 0.660
## Stst26rdngcmpr 0.875 0.003 269.055 0.000 0.869
## Stst28mchnclrs 0.513 0.003 149.081 0.000 0.506
## Stst29vslztn2D 0.341 0.004 84.349 0.000 0.333
## Stst30vslztn3D 0.496 0.004 122.263 0.000 0.488
## Stst31bstrctrs 0.593 0.004 145.555 0.000 0.585
## Stst32rthrsnng 0.746 0.003 238.260 0.000 0.740
## Stst33hghschlm 0.794 0.003 240.374 0.000 0.787
## Stst34rthcmptt 0.500 0.004 121.540 0.000 0.492
## Stest35tblrdng 0.301 0.005 61.440 0.000 0.291
## Stst36clrclchc 0.118 0.004 27.434 0.000 0.110
## Stst37bjctnspc 0.126 0.004 28.690 0.000 0.118
## ci.upper Std.lv Std.all
##
## 0.235 0.219 0.225
## 0.405 0.389 0.389
## 0.306 0.296 0.302
## 0.368 0.355 0.359
## 0.282 0.269 0.264
## 0.192 0.177 0.169
## 0.248 0.239 0.246
## 0.095 0.082 0.080
## 0.087 0.077 0.078
##
## 0.255 0.247 0.263
## 0.180 0.172 0.178
## 0.200 0.191 0.194
## 0.585 0.574 0.552
## 0.284 0.275 0.278
##
## 0.275 0.268 0.276
## 0.238 0.230 0.235
## 0.385 0.378 0.382
## 0.673 0.663 0.641
## 0.724 0.715 0.716
## 0.621 0.612 0.593
##
## 0.455 0.448 0.505
## 0.467 0.459 0.470
## 0.619 0.611 0.599
## 0.349 0.340 0.346
## 0.273 0.265 0.257
##
## 0.787 0.781 0.835
## 0.735 0.729 0.775
## 0.608 0.601 0.617
## 0.574 0.565 0.565
## 0.598 0.591 0.604
## 0.735 0.729 0.736
## 0.669 0.661 0.647
## 0.636 0.627 0.599
## 0.673 0.667 0.688
## 0.882 0.875 0.858
## 0.520 0.513 0.579
## 0.349 0.341 0.349
## 0.504 0.496 0.487
## 0.601 0.593 0.602
## 0.752 0.746 0.755
## 0.800 0.794 0.763
## 0.508 0.500 0.505
## 0.310 0.301 0.291
## 0.127 0.118 0.118
## 0.135 0.126 0.123
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd -0.119 0.004 -30.513 0.000 -0.126
## .Stest20spellng -0.258 0.004 -64.136 0.000 -0.265
## .Stest21cptlztn -0.212 0.004 -54.084 0.000 -0.220
## .Stest22puncttn -0.208 0.004 -52.316 0.000 -0.216
## .Stest23english -0.144 0.004 -35.041 0.000 -0.152
## .Stest24exprssn -0.118 0.004 -28.047 0.000 -0.126
## .Stst25wrdfnctn -0.139 0.004 -35.813 0.000 -0.147
## .Stst26rdngcmpr -0.032 0.004 -7.896 0.000 -0.041
## .Stst31bstrctrs 0.055 0.004 13.853 0.000 0.047
## .Stest5math 0.193 0.004 51.128 0.000 0.186
## .Stst32rthrsnng 0.121 0.004 30.651 0.000 0.114
## .Stst33hghschlm 0.117 0.004 28.152 0.000 0.109
## .Stst34rthcmptt -0.078 0.004 -19.713 0.000 -0.086
## .Stst29vslztn2D 0.212 0.004 54.436 0.000 0.204
## .Stest35tblrdng -0.068 0.004 -16.347 0.000 -0.076
## .Stst36clrclchc -0.147 0.004 -37.322 0.000 -0.155
## .Stst37bjctnspc -0.095 0.004 -23.187 0.000 -0.103
## .Stst28mchnclrs 0.536 0.004 151.033 0.000 0.529
## .Stst30vslztn3D 0.190 0.004 46.616 0.000 0.182
## .Stest1vocab 0.167 0.004 44.518 0.000 0.160
## ci.upper Std.lv Std.all
## -0.111 -0.119 -0.122
## -0.250 -0.258 -0.257
## -0.204 -0.212 -0.217
## -0.200 -0.208 -0.210
## -0.136 -0.144 -0.141
## -0.110 -0.118 -0.113
## -0.132 -0.139 -0.144
## -0.024 -0.032 -0.032
## 0.063 0.055 0.056
## 0.201 0.193 0.205
## 0.129 0.121 0.123
## 0.125 0.117 0.113
## -0.070 -0.078 -0.079
## 0.219 0.212 0.217
## -0.060 -0.068 -0.066
## -0.140 -0.147 -0.148
## -0.087 -0.095 -0.092
## 0.543 0.536 0.605
## 0.198 0.190 0.186
## 0.175 0.167 0.179
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.467 0.003 140.747 0.000 0.460
## .Stest20spellng 0.530 0.005 105.813 0.000 0.520
## .Stest21cptlztn 0.520 0.004 147.447 0.000 0.513
## .Stest22puncttn 0.323 0.004 86.111 0.000 0.316
## .Stest23english 0.534 0.004 138.828 0.000 0.526
## .Stest24exprssn 0.672 0.004 154.760 0.000 0.663
## .Stst25wrdfnctn 0.408 0.003 137.023 0.000 0.402
## .Stst26rdngcmpr 0.267 0.003 100.892 0.000 0.262
## .Stst31bstrctrs 0.496 0.003 150.919 0.000 0.490
## .Stest5math 0.292 0.003 97.784 0.000 0.286
## .Stst32rthrsnng 0.382 0.002 154.296 0.000 0.377
## .Stst33hghschlm 0.121 0.006 21.829 0.000 0.111
## .Stst34rthcmptt 0.510 0.004 131.291 0.000 0.502
## .Stst29vslztn2D 0.573 0.005 124.530 0.000 0.564
## .Stest35tblrdng 0.538 0.007 72.188 0.000 0.524
## .Stst36clrclchc 0.472 0.006 83.606 0.000 0.461
## .Stst37bjctnspc 0.602 0.005 117.142 0.000 0.592
## .Stst28mchnclrs 0.322 0.003 114.109 0.000 0.316
## .Stst30vslztn3D 0.420 0.004 93.720 0.000 0.411
## .Stest1vocab 0.265 0.002 120.508 0.000 0.260
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.473 0.467 0.492
## 0.540 0.530 0.529
## 0.527 0.520 0.543
## 0.330 0.323 0.330
## 0.542 0.534 0.512
## 0.680 0.672 0.613
## 0.414 0.408 0.434
## 0.272 0.267 0.257
## 0.503 0.496 0.512
## 0.298 0.292 0.330
## 0.387 0.382 0.392
## 0.132 0.121 0.112
## 0.517 0.510 0.521
## 0.582 0.573 0.601
## 0.553 0.538 0.504
## 0.483 0.472 0.473
## 0.612 0.602 0.567
## 0.327 0.322 0.410
## 0.429 0.420 0.404
## 0.269 0.265 0.303
## 1.000 1.000 1.000
## 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 0.256 0.008 33.394 0.000 0.241
## Stest20spellng 0.385 0.008 50.963 0.000 0.370
## Stest21cptlztn 0.254 0.006 41.236 0.000 0.242
## Stest22puncttn 0.284 0.006 43.801 0.000 0.272
## Stest23english 0.245 0.006 44.516 0.000 0.234
## Stest24exprssn 0.136 0.006 21.898 0.000 0.124
## Stst25wrdfnctn 0.184 0.006 31.079 0.000 0.172
## Stst26rdngcmpr 0.043 0.005 8.139 0.000 0.032
## Stst31bstrctrs 0.074 0.006 12.185 0.000 0.062
## math =~
## Stest5math 0.354 0.005 78.665 0.000 0.345
## Stst25wrdfnctn 0.152 0.004 35.510 0.000 0.144
## Stst32rthrsnng 0.161 0.004 39.313 0.000 0.153
## Stst33hghschlm 0.560 0.005 102.740 0.000 0.549
## Stst34rthcmptt 0.233 0.005 50.592 0.000 0.224
## speed =~
## Stst19dsgsdwrd 0.291 0.004 80.473 0.000 0.283
## Stst29vslztn2D 0.210 0.004 51.401 0.000 0.202
## Stst34rthcmptt 0.334 0.004 87.455 0.000 0.327
## Stest35tblrdng 0.549 0.005 120.920 0.000 0.540
## Stst36clrclchc 0.656 0.004 151.021 0.000 0.648
## Stst37bjctnspc 0.537 0.004 129.535 0.000 0.529
## spatial =~
## Stst28mchnclrs 0.397 0.004 113.163 0.000 0.391
## Stst29vslztn2D 0.427 0.004 98.979 0.000 0.419
## Stst30vslztn3D 0.523 0.004 123.291 0.000 0.515
## Stst31bstrctrs 0.315 0.004 76.269 0.000 0.307
## Stst37bjctnspc 0.224 0.004 54.833 0.000 0.216
## g =~
## Stest1vocab 0.808 0.003 269.650 0.000 0.802
## Stest5math 0.675 0.003 197.244 0.000 0.669
## Stst19dsgsdwrd 0.576 0.004 156.735 0.000 0.569
## Stest20spellng 0.496 0.004 135.392 0.000 0.488
## Stest21cptlztn 0.506 0.004 134.750 0.000 0.499
## Stest22puncttn 0.671 0.003 209.121 0.000 0.665
## Stest23english 0.554 0.004 152.892 0.000 0.546
## Stest24exprssn 0.490 0.004 133.079 0.000 0.483
## Stst25wrdfnctn 0.711 0.003 225.335 0.000 0.704
## Stst26rdngcmpr 0.785 0.003 274.229 0.000 0.779
## Stst28mchnclrs 0.446 0.003 145.381 0.000 0.440
## Stst29vslztn2D 0.324 0.004 83.414 0.000 0.316
## Stst30vslztn3D 0.452 0.004 125.087 0.000 0.445
## Stst31bstrctrs 0.573 0.004 148.519 0.000 0.566
## Stst32rthrsnng 0.709 0.003 234.928 0.000 0.703
## Stst33hghschlm 0.636 0.003 196.219 0.000 0.630
## Stst34rthcmptt 0.441 0.004 110.456 0.000 0.433
## Stest35tblrdng 0.215 0.004 50.915 0.000 0.207
## Stst36clrclchc 0.121 0.004 30.319 0.000 0.113
## Stst37bjctnspc 0.147 0.004 37.267 0.000 0.139
## ci.upper Std.lv Std.all
##
## 0.271 0.256 0.265
## 0.400 0.385 0.423
## 0.266 0.254 0.275
## 0.297 0.284 0.314
## 0.256 0.245 0.270
## 0.148 0.136 0.152
## 0.196 0.184 0.187
## 0.053 0.043 0.047
## 0.086 0.074 0.078
##
## 0.363 0.354 0.358
## 0.161 0.152 0.155
## 0.170 0.161 0.167
## 0.570 0.560 0.607
## 0.242 0.233 0.251
##
## 0.298 0.291 0.301
## 0.218 0.210 0.219
## 0.342 0.334 0.359
## 0.558 0.549 0.637
## 0.665 0.656 0.704
## 0.545 0.537 0.578
##
## 0.404 0.397 0.483
## 0.435 0.427 0.446
## 0.532 0.523 0.563
## 0.323 0.315 0.330
## 0.232 0.224 0.242
##
## 0.814 0.808 0.827
## 0.682 0.675 0.683
## 0.583 0.576 0.597
## 0.503 0.496 0.544
## 0.514 0.506 0.549
## 0.678 0.671 0.743
## 0.561 0.554 0.610
## 0.497 0.490 0.547
## 0.717 0.711 0.721
## 0.790 0.785 0.864
## 0.452 0.446 0.543
## 0.331 0.324 0.338
## 0.459 0.452 0.486
## 0.581 0.573 0.600
## 0.715 0.709 0.735
## 0.642 0.636 0.690
## 0.449 0.441 0.474
## 0.223 0.215 0.250
## 0.129 0.121 0.130
## 0.154 0.147 0.158
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.150 0.004 38.967 0.000 0.142
## .Stest20spellng 0.280 0.004 77.302 0.000 0.273
## .Stest21cptlztn 0.276 0.004 74.784 0.000 0.268
## .Stest22puncttn 0.278 0.004 76.957 0.000 0.271
## .Stest23english 0.190 0.004 52.481 0.000 0.183
## .Stest24exprssn 0.165 0.004 46.240 0.000 0.158
## .Stst25wrdfnctn 0.196 0.004 50.126 0.000 0.189
## .Stst26rdngcmpr 0.105 0.004 29.044 0.000 0.098
## .Stst31bstrctrs 0.026 0.004 6.799 0.000 0.018
## .Stest5math -0.155 0.004 -39.596 0.000 -0.163
## .Stst32rthrsnng -0.040 0.004 -10.549 0.000 -0.048
## .Stst33hghschlm -0.072 0.004 -19.964 0.000 -0.080
## .Stst34rthcmptt 0.165 0.004 44.491 0.000 0.158
## .Stst29vslztn2D -0.150 0.004 -39.724 0.000 -0.157
## .Stest35tblrdng 0.085 0.003 24.796 0.000 0.078
## .Stst36clrclchc 0.094 0.004 25.710 0.000 0.087
## .Stst37bjctnspc 0.084 0.004 22.827 0.000 0.076
## .Stst28mchnclrs -0.428 0.003 -131.000 0.000 -0.434
## .Stst30vslztn3D -0.115 0.004 -31.342 0.000 -0.122
## .Stest1vocab -0.095 0.004 -24.615 0.000 -0.103
## ci.upper Std.lv Std.all
## 0.158 0.150 0.155
## 0.287 0.280 0.308
## 0.283 0.276 0.299
## 0.285 0.278 0.307
## 0.197 0.190 0.209
## 0.172 0.165 0.184
## 0.204 0.196 0.199
## 0.112 0.105 0.116
## 0.033 0.026 0.027
## -0.147 -0.155 -0.157
## -0.033 -0.040 -0.042
## -0.065 -0.072 -0.079
## 0.172 0.165 0.177
## -0.143 -0.150 -0.157
## 0.091 0.085 0.098
## 0.101 0.094 0.100
## 0.091 0.084 0.090
## -0.422 -0.428 -0.521
## -0.108 -0.115 -0.124
## -0.088 -0.095 -0.097
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.449 0.004 125.602 0.000 0.442
## .Stest20spellng 0.436 0.005 86.050 0.000 0.426
## .Stest21cptlztn 0.531 0.004 150.893 0.000 0.525
## .Stest22puncttn 0.286 0.003 100.584 0.000 0.280
## .Stest23english 0.458 0.003 142.008 0.000 0.452
## .Stest24exprssn 0.544 0.004 151.458 0.000 0.537
## .Stst25wrdfnctn 0.408 0.003 142.206 0.000 0.402
## .Stst26rdngcmpr 0.208 0.002 94.212 0.000 0.204
## .Stst31bstrctrs 0.478 0.003 152.794 0.000 0.471
## .Stest5math 0.397 0.004 104.882 0.000 0.390
## .Stst32rthrsnng 0.403 0.003 160.936 0.000 0.398
## .Stst33hghschlm 0.132 0.006 23.574 0.000 0.121
## .Stst34rthcmptt 0.504 0.004 131.955 0.000 0.497
## .Stst29vslztn2D 0.585 0.004 138.970 0.000 0.577
## .Stest35tblrdng 0.395 0.005 75.209 0.000 0.385
## .Stst36clrclchc 0.423 0.005 87.801 0.000 0.414
## .Stst37bjctnspc 0.503 0.004 123.127 0.000 0.495
## .Stst28mchnclrs 0.319 0.003 124.295 0.000 0.314
## .Stst30vslztn3D 0.386 0.004 101.273 0.000 0.379
## .Stest1vocab 0.301 0.002 121.242 0.000 0.296
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.456 0.449 0.482
## 0.446 0.436 0.525
## 0.538 0.531 0.624
## 0.292 0.286 0.350
## 0.464 0.458 0.555
## 0.551 0.544 0.678
## 0.414 0.408 0.421
## 0.212 0.208 0.252
## 0.484 0.478 0.524
## 0.404 0.397 0.406
## 0.408 0.403 0.432
## 0.143 0.132 0.156
## 0.512 0.504 0.583
## 0.593 0.585 0.639
## 0.405 0.395 0.532
## 0.433 0.423 0.487
## 0.511 0.503 0.583
## 0.324 0.319 0.472
## 0.394 0.386 0.447
## 0.306 0.301 0.315
## 1.000 1.000 1.000
## 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
## 225 math =~ Stest22punctuation 1
## 71 english ~~ math 1
## 252 spatial =~ Stest20spelling 1
## 634 Stest26readingcomprehension ~~ Stest1vocab 2
## 389 Stest26readingcomprehension ~~ Stest1vocab 1
## 459 english =~ Stest34arithcomputation 2
## 214 english =~ Stest34arithcomputation 1
## 497 spatial =~ Stest20spelling 2
## 482 speed =~ Stest20spelling 2
## 237 speed =~ Stest20spelling 1
## 177 english ~~ speed 2
## 470 math =~ Stest22punctuation 2
## 473 math =~ Stest26readingcomprehension 2
## 228 math =~ Stest26readingcomprehension 1
## 540 Stest20spelling ~~ Stest34arithcomputation 2
## 73 english ~~ spatial 1
## 295 Stest20spelling ~~ Stest34arithcomputation 1
## 266 Stest19disguisedwords ~~ Stest20spelling 1
## 262 spatial =~ Stest34arithcomputation 1
## 181 math ~~ spatial 2
## 511 Stest19disguisedwords ~~ Stest20spelling 2
## 76 math ~~ spatial 1
## 655 Stest5math ~~ Stest1vocab 2
## 323 Stest22punctuation ~~ Stest26readingcomprehension 1
## 229 math =~ Stest31abstractreasoning 1
## 178 english ~~ spatial 2
## 236 math =~ Stest1vocab 1
## 284 Stest19disguisedwords ~~ Stest1vocab 1
## 410 Stest5math ~~ Stest1vocab 1
## 280 Stest19disguisedwords ~~ Stest36clericalchecking 1
## group level mi epc sepc.lv sepc.all sepc.nox
## 225 1 1 3552.425 0.189 0.189 0.191 0.191
## 71 1 1 3074.617 0.511 0.511 0.511 0.511
## 252 1 1 2981.106 -0.200 -0.200 -0.200 -0.200
## 634 2 1 2954.047 0.088 0.088 0.351 0.351
## 389 1 1 2750.415 0.083 0.083 0.312 0.312
## 459 2 1 2629.008 0.234 0.234 0.251 0.251
## 214 1 1 2206.003 0.213 0.213 0.216 0.216
## 497 2 1 2073.207 -0.161 -0.161 -0.177 -0.177
## 482 2 1 1837.559 0.137 0.137 0.150 0.150
## 237 1 1 1702.470 0.140 0.140 0.140 0.140
## 177 2 1 1637.416 0.293 0.293 0.293 0.293
## 470 2 1 1537.390 0.113 0.113 0.125 0.125
## 473 2 1 1530.188 -0.114 -0.114 -0.126 -0.126
## 228 1 1 1507.054 -0.127 -0.127 -0.125 -0.125
## 540 2 1 1466.086 0.077 0.077 0.165 0.165
## 73 1 1 1465.756 -0.293 -0.293 -0.293 -0.293
## 295 1 1 1464.646 0.084 0.084 0.162 0.162
## 266 1 1 1434.317 0.090 0.090 0.181 0.181
## 262 1 1 1356.194 -0.131 -0.131 -0.133 -0.133
## 181 2 1 1348.079 0.228 0.228 0.228 0.228
## 511 2 1 1270.429 0.090 0.090 0.202 0.202
## 76 1 1 1211.281 0.212 0.212 0.212 0.212
## 655 2 1 1105.603 0.055 0.055 0.158 0.158
## 323 1 1 1089.215 -0.051 -0.051 -0.172 -0.172
## 229 1 1 1082.012 0.121 0.121 0.123 0.123
## 178 2 1 1075.882 -0.269 -0.269 -0.269 -0.269
## 236 1 1 1057.161 -0.113 -0.113 -0.121 -0.121
## 284 1 1 1030.213 0.053 0.053 0.151 0.151
## 410 1 1 1005.512 0.043 0.043 0.155 0.155
## 280 1 1 993.242 0.078 0.078 0.167 0.167
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
## 61754.707 330.000 0.000 0.957 0.051 0.038
## aic bic
## 6468586.243 6469868.652
Mc(metric)
## [1] 0.8056976
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 60 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 175
## Number of equality constraints 45
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 61754.707 52834.766
## Degrees of freedom 330 330
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.169
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 33532.795 28689.269
## 1 28221.912 24145.497
##
## 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.) 0.245 0.006 40.928 0.000 0.233
## Stst20s (.p2.) 0.406 0.006 67.522 0.000 0.394
## Stst21c (.p3.) 0.291 0.005 61.768 0.000 0.282
## Stst22p (.p4.) 0.339 0.005 62.192 0.000 0.328
## Stst23n (.p5.) 0.271 0.005 56.333 0.000 0.261
## Stst24x (.p6.) 0.165 0.005 30.905 0.000 0.154
## Stst25w (.p7.) 0.222 0.004 52.257 0.000 0.213
## Stst26r (.p8.) 0.066 0.005 14.520 0.000 0.057
## Stst31b (.p9.) 0.081 0.004 18.758 0.000 0.073
## math =~
## Stst5mt (.10.) 0.294 0.003 97.793 0.000 0.288
## Stst25w (.11.) 0.157 0.003 51.651 0.000 0.151
## Stst32r (.12.) 0.176 0.003 53.463 0.000 0.170
## Stst33h (.13.) 0.567 0.005 118.136 0.000 0.557
## Stst34r (.14.) 0.255 0.004 67.116 0.000 0.248
## speed =~
## Stst19d (.15.) 0.294 0.003 106.486 0.000 0.289
## Sts292D (.16.) 0.232 0.003 75.363 0.000 0.226
## Stst34r (.17.) 0.377 0.003 121.458 0.000 0.371
## Stst35t (.18.) 0.639 0.004 147.540 0.000 0.630
## Stst36c (.19.) 0.725 0.004 183.376 0.000 0.718
## Stst37b (.20.) 0.607 0.004 159.930 0.000 0.600
## spatial =~
## Stst28m (.21.) 0.449 0.003 147.351 0.000 0.443
## Sts292D (.22.) 0.469 0.003 136.247 0.000 0.463
## Sts303D (.23.) 0.603 0.004 160.415 0.000 0.596
## Stst31b (.24.) 0.348 0.003 107.176 0.000 0.342
## Stst37b (.25.) 0.260 0.003 78.725 0.000 0.254
## g =~
## Stst1vc (.26.) 0.819 0.003 300.751 0.000 0.813
## Stst5mt (.27.) 0.726 0.003 262.668 0.000 0.720
## Stst19d (.28.) 0.610 0.003 206.070 0.000 0.604
## Stst20s (.29.) 0.550 0.003 174.811 0.000 0.543
## Stst21c (.30.) 0.570 0.003 190.405 0.000 0.564
## Stst22p (.31.) 0.726 0.003 251.070 0.000 0.720
## Stst23n (.32.) 0.629 0.003 192.076 0.000 0.622
## Stst24x (.33.) 0.576 0.003 174.470 0.000 0.570
## Stst25w (.34.) 0.713 0.003 274.806 0.000 0.708
## Stst26r (.35.) 0.860 0.003 293.850 0.000 0.854
## Stst28m (.36.) 0.499 0.003 189.805 0.000 0.493
## Sts292D (.37.) 0.345 0.003 115.785 0.000 0.339
## Sts303D (.38.) 0.492 0.003 165.615 0.000 0.486
## Stst31b (.39.) 0.604 0.003 192.556 0.000 0.598
## Stst32r (.40.) 0.754 0.003 280.700 0.000 0.749
## Stst33h (.41.) 0.743 0.003 256.511 0.000 0.737
## Stst34r (.42.) 0.488 0.003 154.794 0.000 0.482
## Stst35t (.43.) 0.263 0.003 76.941 0.000 0.256
## Stst36c (.44.) 0.124 0.003 40.587 0.000 0.118
## Stst37b (.45.) 0.142 0.003 46.445 0.000 0.136
## ci.upper Std.lv Std.all
##
## 0.257 0.245 0.248
## 0.418 0.406 0.409
## 0.300 0.291 0.302
## 0.349 0.339 0.344
## 0.280 0.271 0.270
## 0.175 0.165 0.162
## 0.230 0.222 0.222
## 0.075 0.066 0.066
## 0.090 0.081 0.082
##
## 0.299 0.294 0.309
## 0.163 0.157 0.158
## 0.183 0.176 0.178
## 0.576 0.567 0.563
## 0.263 0.255 0.261
##
## 0.300 0.294 0.298
## 0.239 0.232 0.237
## 0.383 0.377 0.385
## 0.647 0.639 0.628
## 0.733 0.725 0.724
## 0.615 0.607 0.589
##
## 0.455 0.449 0.511
## 0.476 0.469 0.479
## 0.611 0.603 0.594
## 0.354 0.348 0.350
## 0.267 0.260 0.252
##
## 0.824 0.819 0.848
## 0.731 0.726 0.765
## 0.616 0.610 0.618
## 0.556 0.550 0.553
## 0.576 0.570 0.590
## 0.732 0.726 0.737
## 0.635 0.629 0.627
## 0.583 0.576 0.566
## 0.718 0.713 0.715
## 0.866 0.860 0.856
## 0.504 0.499 0.568
## 0.351 0.345 0.352
## 0.498 0.492 0.485
## 0.611 0.604 0.608
## 0.760 0.754 0.762
## 0.749 0.743 0.739
## 0.495 0.488 0.499
## 0.270 0.263 0.258
## 0.130 0.124 0.124
## 0.148 0.142 0.138
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd -0.119 0.004 -30.513 0.000 -0.126
## .Stest20spellng -0.258 0.004 -64.136 0.000 -0.265
## .Stest21cptlztn -0.212 0.004 -54.084 0.000 -0.220
## .Stest22puncttn -0.208 0.004 -52.316 0.000 -0.216
## .Stest23english -0.144 0.004 -35.041 0.000 -0.152
## .Stest24exprssn -0.118 0.004 -28.047 0.000 -0.126
## .Stst25wrdfnctn -0.139 0.004 -35.813 0.000 -0.147
## .Stst26rdngcmpr -0.032 0.004 -7.896 0.000 -0.041
## .Stst31bstrctrs 0.055 0.004 13.853 0.000 0.047
## .Stest5math 0.193 0.004 51.128 0.000 0.186
## .Stst32rthrsnng 0.121 0.004 30.651 0.000 0.114
## .Stst33hghschlm 0.117 0.004 28.152 0.000 0.109
## .Stst34rthcmptt -0.078 0.004 -19.713 0.000 -0.086
## .Stst29vslztn2D 0.212 0.004 54.436 0.000 0.204
## .Stest35tblrdng -0.068 0.004 -16.347 0.000 -0.076
## .Stst36clrclchc -0.147 0.004 -37.322 0.000 -0.155
## .Stst37bjctnspc -0.095 0.004 -23.187 0.000 -0.103
## .Stst28mchnclrs 0.536 0.004 151.033 0.000 0.529
## .Stst30vslztn3D 0.190 0.004 46.616 0.000 0.182
## .Stest1vocab 0.167 0.004 44.518 0.000 0.160
## ci.upper Std.lv Std.all
## -0.111 -0.119 -0.120
## -0.250 -0.258 -0.259
## -0.204 -0.212 -0.220
## -0.200 -0.208 -0.211
## -0.136 -0.144 -0.144
## -0.110 -0.118 -0.116
## -0.132 -0.139 -0.140
## -0.024 -0.032 -0.032
## 0.063 0.055 0.055
## 0.201 0.193 0.204
## 0.129 0.121 0.123
## 0.125 0.117 0.116
## -0.070 -0.078 -0.080
## 0.219 0.212 0.216
## -0.060 -0.068 -0.067
## -0.140 -0.147 -0.147
## -0.087 -0.095 -0.092
## 0.543 0.536 0.610
## 0.198 0.190 0.187
## 0.175 0.167 0.173
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.457 0.003 142.918 0.000 0.450
## .Stest20spellng 0.520 0.005 114.541 0.000 0.511
## .Stest21cptlztn 0.522 0.003 154.702 0.000 0.516
## .Stest22puncttn 0.329 0.003 104.599 0.000 0.323
## .Stest23english 0.536 0.004 139.986 0.000 0.528
## .Stest24exprssn 0.679 0.004 154.949 0.000 0.670
## .Stst25wrdfnctn 0.412 0.003 144.978 0.000 0.407
## .Stst26rdngcmpr 0.266 0.002 109.580 0.000 0.261
## .Stst31bstrctrs 0.495 0.003 152.542 0.000 0.488
## .Stest5math 0.287 0.003 94.818 0.000 0.281
## .Stst32rthrsnng 0.380 0.002 156.682 0.000 0.376
## .Stst33hghschlm 0.139 0.004 31.282 0.000 0.130
## .Stst34rthcmptt 0.512 0.004 138.451 0.000 0.505
## .Stst29vslztn2D 0.569 0.004 129.130 0.000 0.560
## .Stest35tblrdng 0.557 0.007 74.397 0.000 0.542
## .Stst36clrclchc 0.461 0.005 86.924 0.000 0.451
## .Stst37bjctnspc 0.608 0.005 125.026 0.000 0.598
## .Stst28mchnclrs 0.322 0.003 123.059 0.000 0.317
## .Stst30vslztn3D 0.426 0.004 106.416 0.000 0.418
## .Stest1vocab 0.261 0.002 120.523 0.000 0.257
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.463 0.457 0.468
## 0.529 0.520 0.527
## 0.529 0.522 0.561
## 0.335 0.329 0.339
## 0.543 0.536 0.533
## 0.687 0.679 0.654
## 0.418 0.412 0.415
## 0.271 0.266 0.263
## 0.501 0.495 0.501
## 0.293 0.287 0.319
## 0.385 0.380 0.388
## 0.148 0.139 0.137
## 0.519 0.512 0.534
## 0.577 0.569 0.591
## 0.572 0.557 0.539
## 0.471 0.461 0.460
## 0.617 0.608 0.571
## 0.327 0.322 0.417
## 0.434 0.426 0.413
## 0.265 0.261 0.280
## 1.000 1.000 1.000
## 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.) 0.245 0.006 40.928 0.000 0.233
## Stst20s (.p2.) 0.406 0.006 67.522 0.000 0.394
## Stst21c (.p3.) 0.291 0.005 61.768 0.000 0.282
## Stst22p (.p4.) 0.339 0.005 62.192 0.000 0.328
## Stst23n (.p5.) 0.271 0.005 56.333 0.000 0.261
## Stst24x (.p6.) 0.165 0.005 30.905 0.000 0.154
## Stst25w (.p7.) 0.222 0.004 52.257 0.000 0.213
## Stst26r (.p8.) 0.066 0.005 14.520 0.000 0.057
## Stst31b (.p9.) 0.081 0.004 18.758 0.000 0.073
## math =~
## Stst5mt (.10.) 0.294 0.003 97.793 0.000 0.288
## Stst25w (.11.) 0.157 0.003 51.651 0.000 0.151
## Stst32r (.12.) 0.176 0.003 53.463 0.000 0.170
## Stst33h (.13.) 0.567 0.005 118.136 0.000 0.557
## Stst34r (.14.) 0.255 0.004 67.116 0.000 0.248
## speed =~
## Stst19d (.15.) 0.294 0.003 106.486 0.000 0.289
## Sts292D (.16.) 0.232 0.003 75.363 0.000 0.226
## Stst34r (.17.) 0.377 0.003 121.458 0.000 0.371
## Stst35t (.18.) 0.639 0.004 147.540 0.000 0.630
## Stst36c (.19.) 0.725 0.004 183.376 0.000 0.718
## Stst37b (.20.) 0.607 0.004 159.930 0.000 0.600
## spatial =~
## Stst28m (.21.) 0.449 0.003 147.351 0.000 0.443
## Sts292D (.22.) 0.469 0.003 136.247 0.000 0.463
## Sts303D (.23.) 0.603 0.004 160.415 0.000 0.596
## Stst31b (.24.) 0.348 0.003 107.176 0.000 0.342
## Stst37b (.25.) 0.260 0.003 78.725 0.000 0.254
## g =~
## Stst1vc (.26.) 0.819 0.003 300.751 0.000 0.813
## Stst5mt (.27.) 0.726 0.003 262.668 0.000 0.720
## Stst19d (.28.) 0.610 0.003 206.070 0.000 0.604
## Stst20s (.29.) 0.550 0.003 174.811 0.000 0.543
## Stst21c (.30.) 0.570 0.003 190.405 0.000 0.564
## Stst22p (.31.) 0.726 0.003 251.070 0.000 0.720
## Stst23n (.32.) 0.629 0.003 192.076 0.000 0.622
## Stst24x (.33.) 0.576 0.003 174.470 0.000 0.570
## Stst25w (.34.) 0.713 0.003 274.806 0.000 0.708
## Stst26r (.35.) 0.860 0.003 293.850 0.000 0.854
## Stst28m (.36.) 0.499 0.003 189.805 0.000 0.493
## Sts292D (.37.) 0.345 0.003 115.785 0.000 0.339
## Sts303D (.38.) 0.492 0.003 165.615 0.000 0.486
## Stst31b (.39.) 0.604 0.003 192.556 0.000 0.598
## Stst32r (.40.) 0.754 0.003 280.700 0.000 0.749
## Stst33h (.41.) 0.743 0.003 256.511 0.000 0.737
## Stst34r (.42.) 0.488 0.003 154.794 0.000 0.482
## Stst35t (.43.) 0.263 0.003 76.941 0.000 0.256
## Stst36c (.44.) 0.124 0.003 40.587 0.000 0.118
## Stst37b (.45.) 0.142 0.003 46.445 0.000 0.136
## ci.upper Std.lv Std.all
##
## 0.257 0.221 0.233
## 0.418 0.367 0.400
## 0.300 0.263 0.281
## 0.349 0.306 0.337
## 0.280 0.245 0.264
## 0.175 0.149 0.162
## 0.230 0.200 0.210
## 0.075 0.060 0.065
## 0.090 0.073 0.078
##
## 0.299 0.293 0.301
## 0.163 0.157 0.164
## 0.183 0.176 0.183
## 0.576 0.566 0.591
## 0.263 0.255 0.271
##
## 0.300 0.262 0.276
## 0.239 0.207 0.217
## 0.383 0.336 0.357
## 0.647 0.569 0.649
## 0.733 0.646 0.694
## 0.615 0.540 0.582
##
## 0.455 0.396 0.477
## 0.476 0.414 0.435
## 0.611 0.532 0.570
## 0.354 0.307 0.325
## 0.267 0.230 0.247
##
## 0.824 0.759 0.806
## 0.731 0.672 0.691
## 0.616 0.565 0.595
## 0.556 0.509 0.555
## 0.576 0.528 0.564
## 0.732 0.673 0.740
## 0.635 0.583 0.629
## 0.583 0.534 0.579
## 0.718 0.660 0.691
## 0.866 0.797 0.865
## 0.504 0.462 0.557
## 0.351 0.320 0.336
## 0.498 0.456 0.489
## 0.611 0.560 0.593
## 0.760 0.699 0.727
## 0.749 0.689 0.720
## 0.495 0.453 0.481
## 0.270 0.244 0.278
## 0.130 0.115 0.124
## 0.148 0.132 0.142
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.150 0.004 38.967 0.000 0.142
## .Stest20spellng 0.280 0.004 77.302 0.000 0.273
## .Stest21cptlztn 0.276 0.004 74.784 0.000 0.268
## .Stest22puncttn 0.278 0.004 76.957 0.000 0.271
## .Stest23english 0.190 0.004 52.481 0.000 0.183
## .Stest24exprssn 0.165 0.004 46.240 0.000 0.158
## .Stst25wrdfnctn 0.196 0.004 50.126 0.000 0.189
## .Stst26rdngcmpr 0.105 0.004 29.044 0.000 0.098
## .Stst31bstrctrs 0.026 0.004 6.799 0.000 0.018
## .Stest5math -0.155 0.004 -39.596 0.000 -0.163
## .Stst32rthrsnng -0.040 0.004 -10.549 0.000 -0.048
## .Stst33hghschlm -0.072 0.004 -19.964 0.000 -0.080
## .Stst34rthcmptt 0.165 0.004 44.491 0.000 0.158
## .Stst29vslztn2D -0.150 0.004 -39.724 0.000 -0.157
## .Stest35tblrdng 0.085 0.003 24.796 0.000 0.078
## .Stst36clrclchc 0.094 0.004 25.710 0.000 0.087
## .Stst37bjctnspc 0.084 0.004 22.827 0.000 0.076
## .Stst28mchnclrs -0.428 0.003 -131.000 0.000 -0.434
## .Stst30vslztn3D -0.115 0.004 -31.342 0.000 -0.122
## .Stest1vocab -0.095 0.004 -24.615 0.000 -0.103
## ci.upper Std.lv Std.all
## 0.158 0.150 0.158
## 0.287 0.280 0.306
## 0.283 0.276 0.294
## 0.285 0.278 0.306
## 0.197 0.190 0.205
## 0.172 0.165 0.179
## 0.204 0.196 0.205
## 0.112 0.105 0.114
## 0.033 0.026 0.027
## -0.147 -0.155 -0.159
## -0.033 -0.040 -0.042
## -0.065 -0.072 -0.076
## 0.172 0.165 0.175
## -0.143 -0.150 -0.158
## 0.091 0.085 0.097
## 0.101 0.094 0.101
## 0.091 0.084 0.090
## -0.422 -0.428 -0.516
## -0.108 -0.115 -0.124
## -0.088 -0.095 -0.101
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.465 0.003 148.106 0.000 0.458
## .Stest20spellng 0.448 0.004 111.851 0.000 0.440
## .Stest21cptlztn 0.528 0.003 159.434 0.000 0.522
## .Stest22puncttn 0.279 0.003 107.447 0.000 0.274
## .Stest23english 0.458 0.003 143.620 0.000 0.452
## .Stest24exprssn 0.543 0.004 151.151 0.000 0.536
## .Stst25wrdfnctn 0.413 0.003 146.263 0.000 0.408
## .Stst26rdngcmpr 0.210 0.002 103.611 0.000 0.206
## .Stst31bstrctrs 0.480 0.003 156.821 0.000 0.474
## .Stest5math 0.410 0.004 111.475 0.000 0.403
## .Stst32rthrsnng 0.406 0.002 164.079 0.000 0.401
## .Stst33hghschlm 0.121 0.004 27.074 0.000 0.112
## .Stst34rthcmptt 0.502 0.004 133.799 0.000 0.495
## .Stst29vslztn2D 0.590 0.004 150.475 0.000 0.583
## .Stest35tblrdng 0.384 0.005 74.155 0.000 0.374
## .Stst36clrclchc 0.434 0.005 96.263 0.000 0.425
## .Stst37bjctnspc 0.499 0.004 129.907 0.000 0.492
## .Stst28mchnclrs 0.319 0.002 135.252 0.000 0.314
## .Stst30vslztn3D 0.380 0.003 112.675 0.000 0.373
## .Stest1vocab 0.310 0.002 136.984 0.000 0.306
## english 0.817 0.017 47.924 0.000 0.783
## math 0.996 0.016 60.940 0.000 0.964
## speed 0.792 0.010 78.896 0.000 0.772
## spatial 0.778 0.010 79.001 0.000 0.759
## g 0.859 0.007 126.604 0.000 0.845
## ci.upper Std.lv Std.all
## 0.471 0.465 0.515
## 0.455 0.448 0.532
## 0.535 0.528 0.603
## 0.284 0.279 0.338
## 0.464 0.458 0.534
## 0.550 0.543 0.638
## 0.419 0.413 0.452
## 0.214 0.210 0.247
## 0.486 0.480 0.537
## 0.418 0.410 0.433
## 0.411 0.406 0.438
## 0.130 0.121 0.132
## 0.509 0.502 0.568
## 0.598 0.590 0.651
## 0.394 0.384 0.501
## 0.443 0.434 0.502
## 0.507 0.499 0.580
## 0.323 0.319 0.463
## 0.387 0.380 0.436
## 0.315 0.310 0.350
## 0.850 1.000 1.000
## 1.028 1.000 1.000
## 0.812 1.000 1.000
## 0.797 1.000 1.000
## 0.872 1.000 1.000
lavTestScore(metric, release = 1:45)
## 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 5800.25 45 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p106. 162.858 1 0.000
## 2 .p2. == .p107. 4.751 1 0.029
## 3 .p3. == .p108. 1.891 1 0.169
## 4 .p4. == .p109. 31.086 1 0.000
## 5 .p5. == .p110. 3.107 1 0.078
## 6 .p6. == .p111. 40.770 1 0.000
## 7 .p7. == .p112. 5.512 1 0.019
## 8 .p8. == .p113. 107.429 1 0.000
## 9 .p9. == .p114. 8.500 1 0.004
## 10 .p10. == .p115. 855.629 1 0.000
## 11 .p11. == .p116. 11.197 1 0.001
## 12 .p12. == .p117. 119.009 1 0.000
## 13 .p13. == .p118. 139.456 1 0.000
## 14 .p14. == .p119. 177.651 1 0.000
## 15 .p15. == .p120. 185.219 1 0.000
## 16 .p16. == .p121. 0.638 1 0.425
## 17 .p17. == .p122. 0.163 1 0.686
## 18 .p18. == .p123. 103.954 1 0.000
## 19 .p19. == .p124. 5.486 1 0.019
## 20 .p20. == .p125. 0.431 1 0.512
## 21 .p21. == .p126. 0.889 1 0.346
## 22 .p22. == .p127. 18.785 1 0.000
## 23 .p23. == .p128. 19.736 1 0.000
## 24 .p24. == .p129. 8.332 1 0.004
## 25 .p25. == .p130. 2.096 1 0.148
## 26 .p26. == .p131. 1161.881 1 0.000
## 27 .p27. == .p132. 165.853 1 0.000
## 28 .p28. == .p133. 74.628 1 0.000
## 29 .p29. == .p134. 32.448 1 0.000
## 30 .p30. == .p135. 107.404 1 0.000
## 31 .p31. == .p136. 0.325 1 0.569
## 32 .p32. == .p137. 225.163 1 0.000
## 33 .p33. == .p138. 504.121 1 0.000
## 34 .p34. == .p139. 1028.719 1 0.000
## 35 .p35. == .p140. 194.864 1 0.000
## 36 .p36. == .p141. 99.405 1 0.000
## 37 .p37. == .p142. 10.362 1 0.001
## 38 .p38. == .p143. 4.352 1 0.037
## 39 .p39. == .p144. 64.919 1 0.000
## 40 .p40. == .p145. 103.869 1 0.000
## 41 .p41. == .p146. 1298.089 1 0.000
## 42 .p42. == .p147. 0.104 1 0.747
## 43 .p43. == .p148. 354.849 1 0.000
## 44 .p44. == .p149. 23.722 1 0.000
## 45 .p45. == .p150. 76.426 1 0.000
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"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 89153.670 345.000 0.000 0.938 0.060 0.045
## aic bic
## 6495955.205 6497089.645
Mc(scalar)
## [1] 0.7317156
summary(scalar, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 76 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 180
## Number of equality constraints 65
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 89153.670 76136.675
## Degrees of freedom 345 345
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.171
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 47762.728 40789.071
## 1 41390.941 35347.605
##
## 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.) 0.172 0.002 70.021 0.000 0.167
## Stst20s (.p2.) 0.351 0.003 104.419 0.000 0.344
## Stst21c (.p3.) 0.320 0.003 108.034 0.000 0.314
## Stst22p (.p4.) 0.347 0.003 111.679 0.000 0.341
## Stst23n (.p5.) 0.262 0.003 91.923 0.000 0.256
## Stst24x (.p6.) 0.219 0.003 82.928 0.000 0.213
## Stst25w (.p7.) 0.260 0.002 106.201 0.000 0.255
## Stst26r (.p8.) 0.168 0.002 89.797 0.000 0.164
## Stst31b (.p9.) 0.201 0.003 71.205 0.000 0.195
## math =~
## Stst5mt (.10.) 0.280 0.003 98.165 0.000 0.274
## Stst25w (.11.) 0.163 0.003 52.023 0.000 0.157
## Stst32r (.12.) 0.178 0.003 53.324 0.000 0.171
## Stst33h (.13.) 0.570 0.005 117.816 0.000 0.561
## Stst34r (.14.) 0.264 0.004 62.651 0.000 0.256
## speed =~
## Stst19d (.15.) 0.286 0.003 103.482 0.000 0.280
## Sts292D (.16.) 0.260 0.003 86.127 0.000 0.254
## Stst34r (.17.) 0.408 0.003 137.688 0.000 0.403
## Stst35t (.18.) 0.621 0.004 149.725 0.000 0.613
## Stst36c (.19.) 0.697 0.004 176.190 0.000 0.689
## Stst37b (.20.) 0.635 0.004 171.753 0.000 0.628
## spatial =~
## Stst28m (.21.) 0.609 0.003 195.661 0.000 0.603
## Sts292D (.22.) 0.377 0.004 94.467 0.000 0.369
## Sts303D (.23.) 0.355 0.004 88.759 0.000 0.347
## Stst31b (.24.) 0.277 0.005 57.508 0.000 0.268
## Stst37b (.25.) 0.175 0.003 54.214 0.000 0.168
## g =~
## Stst1vc (.26.) 0.823 0.003 306.064 0.000 0.818
## Stst5mt (.27.) 0.742 0.003 278.924 0.000 0.737
## Stst19d (.28.) 0.619 0.003 225.659 0.000 0.613
## Stst20s (.29.) 0.550 0.003 182.990 0.000 0.544
## Stst21c (.30.) 0.558 0.003 189.312 0.000 0.553
## Stst22p (.31.) 0.718 0.003 249.384 0.000 0.712
## Stst23n (.32.) 0.625 0.003 197.136 0.000 0.619
## Stst24x (.33.) 0.562 0.003 179.039 0.000 0.556
## Stst25w (.34.) 0.701 0.003 275.234 0.000 0.696
## Stst26r (.35.) 0.837 0.003 303.416 0.000 0.832
## Stst28m (.36.) 0.509 0.003 197.090 0.000 0.504
## Sts292D (.37.) 0.346 0.003 114.213 0.000 0.340
## Sts303D (.38.) 0.478 0.003 149.595 0.000 0.471
## Stst31b (.39.) 0.584 0.003 187.612 0.000 0.578
## Stst32r (.40.) 0.747 0.003 273.569 0.000 0.742
## Stst33h (.41.) 0.745 0.003 258.008 0.000 0.739
## Stst34r (.42.) 0.471 0.003 146.959 0.000 0.465
## Stst35t (.43.) 0.270 0.003 79.682 0.000 0.264
## Stst36c (.44.) 0.135 0.003 44.144 0.000 0.129
## Stst37b (.45.) 0.139 0.003 45.066 0.000 0.133
## ci.upper Std.lv Std.all
##
## 0.177 0.172 0.175
## 0.357 0.351 0.355
## 0.326 0.320 0.332
## 0.353 0.347 0.353
## 0.267 0.262 0.262
## 0.224 0.219 0.215
## 0.264 0.260 0.261
## 0.171 0.168 0.167
## 0.206 0.201 0.202
##
## 0.285 0.280 0.292
## 0.169 0.163 0.164
## 0.184 0.178 0.180
## 0.580 0.570 0.566
## 0.273 0.264 0.268
##
## 0.291 0.286 0.290
## 0.266 0.260 0.268
## 0.414 0.408 0.414
## 0.629 0.621 0.614
## 0.705 0.697 0.701
## 0.643 0.635 0.614
##
## 0.615 0.609 0.676
## 0.385 0.377 0.388
## 0.362 0.355 0.361
## 0.287 0.277 0.279
## 0.181 0.175 0.169
##
## 0.829 0.823 0.854
## 0.747 0.742 0.775
## 0.624 0.619 0.629
## 0.555 0.550 0.555
## 0.564 0.558 0.579
## 0.723 0.718 0.730
## 0.631 0.625 0.625
## 0.568 0.562 0.551
## 0.706 0.701 0.704
## 0.843 0.837 0.834
## 0.514 0.509 0.565
## 0.352 0.346 0.356
## 0.484 0.478 0.486
## 0.590 0.584 0.587
## 0.753 0.747 0.758
## 0.750 0.745 0.740
## 0.478 0.471 0.478
## 0.277 0.270 0.267
## 0.141 0.135 0.136
## 0.145 0.139 0.134
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.81.) -0.142 0.004 -37.317 0.000 -0.150
## .Stst20s (.82.) -0.269 0.004 -68.662 0.000 -0.276
## .Stst21c (.83.) -0.214 0.004 -55.968 0.000 -0.222
## .Stst22p (.84.) -0.215 0.004 -54.536 0.000 -0.223
## .Stst23n (.85.) -0.154 0.004 -37.763 0.000 -0.161
## .Stst24x (.86.) -0.117 0.004 -28.254 0.000 -0.125
## .Stst25w (.87.) -0.139 0.004 -36.221 0.000 -0.146
## .Stst26r (.88.) -0.007 0.004 -1.711 0.087 -0.015
## .Stst31b (.89.) 0.088 0.004 22.584 0.000 0.080
## .Stst5mt (.90.) 0.136 0.004 36.409 0.000 0.129
## .Stst32r (.91.) 0.148 0.004 40.328 0.000 0.141
## .Stst33h (.92.) 0.117 0.004 28.188 0.000 0.109
## .Stst34r (.93.) 0.001 0.004 0.286 0.775 -0.006
## .Sts292D (.94.) 0.240 0.003 68.901 0.000 0.234
## .Stst35t (.95.) -0.120 0.004 -32.027 0.000 -0.127
## .Stst36c (.96.) -0.189 0.004 -53.274 0.000 -0.196
## .Stst37b (.97.) -0.041 0.004 -10.402 0.000 -0.048
## .Stst28m (.98.) 0.497 0.004 114.006 0.000 0.488
## .Sts303D (.99.) 0.331 0.004 90.402 0.000 0.324
## .Stst1vc (.100) 0.162 0.004 42.311 0.000 0.155
## ci.upper Std.lv Std.all
## -0.135 -0.142 -0.144
## -0.261 -0.269 -0.271
## -0.207 -0.214 -0.222
## -0.207 -0.215 -0.219
## -0.146 -0.154 -0.153
## -0.109 -0.117 -0.115
## -0.131 -0.139 -0.139
## 0.001 -0.007 -0.007
## 0.095 0.088 0.088
## 0.143 0.136 0.142
## 0.155 0.148 0.150
## 0.126 0.117 0.117
## 0.008 0.001 0.001
## 0.247 0.240 0.247
## -0.112 -0.120 -0.118
## -0.182 -0.189 -0.190
## -0.033 -0.041 -0.039
## 0.505 0.497 0.551
## 0.339 0.331 0.337
## 0.170 0.162 0.168
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.473 0.003 161.013 0.000 0.468
## .Stest20spellng 0.554 0.003 158.994 0.000 0.548
## .Stest21cptlztn 0.517 0.003 161.688 0.000 0.511
## .Stest22puncttn 0.331 0.002 134.894 0.000 0.327
## .Stest23english 0.541 0.004 143.950 0.000 0.534
## .Stest24exprssn 0.674 0.004 156.175 0.000 0.666
## .Stst25wrdfnctn 0.406 0.003 151.641 0.000 0.401
## .Stst26rdngcmpr 0.280 0.002 124.029 0.000 0.275
## .Stst31bstrctrs 0.530 0.004 142.188 0.000 0.523
## .Stest5math 0.289 0.003 97.324 0.000 0.283
## .Stst32rthrsnng 0.383 0.002 156.153 0.000 0.378
## .Stst33hghschlm 0.134 0.005 29.609 0.000 0.125
## .Stst34rthcmptt 0.514 0.004 132.850 0.000 0.506
## .Stst29vslztn2D 0.617 0.005 126.236 0.000 0.607
## .Stest35tblrdng 0.564 0.007 78.522 0.000 0.550
## .Stst36clrclchc 0.485 0.006 88.093 0.000 0.474
## .Stst37bjctnspc 0.617 0.005 123.001 0.000 0.607
## .Stst28mchnclrs 0.182 0.005 37.706 0.000 0.172
## .Stst30vslztn3D 0.610 0.004 148.735 0.000 0.602
## .Stest1vocab 0.251 0.002 117.233 0.000 0.247
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.479 0.473 0.489
## 0.561 0.554 0.566
## 0.523 0.517 0.555
## 0.336 0.331 0.343
## 0.548 0.541 0.541
## 0.683 0.674 0.650
## 0.411 0.406 0.409
## 0.284 0.280 0.277
## 0.538 0.530 0.537
## 0.295 0.289 0.315
## 0.387 0.383 0.393
## 0.143 0.134 0.132
## 0.522 0.514 0.528
## 0.626 0.617 0.651
## 0.578 0.564 0.552
## 0.496 0.485 0.490
## 0.627 0.617 0.576
## 0.191 0.182 0.224
## 0.618 0.610 0.633
## 0.255 0.251 0.270
## 1.000 1.000 1.000
## 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.) 0.172 0.002 70.021 0.000 0.167
## Stst20s (.p2.) 0.351 0.003 104.419 0.000 0.344
## Stst21c (.p3.) 0.320 0.003 108.034 0.000 0.314
## Stst22p (.p4.) 0.347 0.003 111.679 0.000 0.341
## Stst23n (.p5.) 0.262 0.003 91.923 0.000 0.256
## Stst24x (.p6.) 0.219 0.003 82.928 0.000 0.213
## Stst25w (.p7.) 0.260 0.002 106.201 0.000 0.255
## Stst26r (.p8.) 0.168 0.002 89.797 0.000 0.164
## Stst31b (.p9.) 0.201 0.003 71.205 0.000 0.195
## math =~
## Stst5mt (.10.) 0.280 0.003 98.165 0.000 0.274
## Stst25w (.11.) 0.163 0.003 52.023 0.000 0.157
## Stst32r (.12.) 0.178 0.003 53.324 0.000 0.171
## Stst33h (.13.) 0.570 0.005 117.816 0.000 0.561
## Stst34r (.14.) 0.264 0.004 62.651 0.000 0.256
## speed =~
## Stst19d (.15.) 0.286 0.003 103.482 0.000 0.280
## Sts292D (.16.) 0.260 0.003 86.127 0.000 0.254
## Stst34r (.17.) 0.408 0.003 137.688 0.000 0.403
## Stst35t (.18.) 0.621 0.004 149.725 0.000 0.613
## Stst36c (.19.) 0.697 0.004 176.190 0.000 0.689
## Stst37b (.20.) 0.635 0.004 171.753 0.000 0.628
## spatial =~
## Stst28m (.21.) 0.609 0.003 195.661 0.000 0.603
## Sts292D (.22.) 0.377 0.004 94.467 0.000 0.369
## Sts303D (.23.) 0.355 0.004 88.759 0.000 0.347
## Stst31b (.24.) 0.277 0.005 57.508 0.000 0.268
## Stst37b (.25.) 0.175 0.003 54.214 0.000 0.168
## g =~
## Stst1vc (.26.) 0.823 0.003 306.064 0.000 0.818
## Stst5mt (.27.) 0.742 0.003 278.924 0.000 0.737
## Stst19d (.28.) 0.619 0.003 225.659 0.000 0.613
## Stst20s (.29.) 0.550 0.003 182.990 0.000 0.544
## Stst21c (.30.) 0.558 0.003 189.312 0.000 0.553
## Stst22p (.31.) 0.718 0.003 249.384 0.000 0.712
## Stst23n (.32.) 0.625 0.003 197.136 0.000 0.619
## Stst24x (.33.) 0.562 0.003 179.039 0.000 0.556
## Stst25w (.34.) 0.701 0.003 275.234 0.000 0.696
## Stst26r (.35.) 0.837 0.003 303.416 0.000 0.832
## Stst28m (.36.) 0.509 0.003 197.090 0.000 0.504
## Sts292D (.37.) 0.346 0.003 114.213 0.000 0.340
## Sts303D (.38.) 0.478 0.003 149.595 0.000 0.471
## Stst31b (.39.) 0.584 0.003 187.612 0.000 0.578
## Stst32r (.40.) 0.747 0.003 273.569 0.000 0.742
## Stst33h (.41.) 0.745 0.003 258.008 0.000 0.739
## Stst34r (.42.) 0.471 0.003 146.959 0.000 0.465
## Stst35t (.43.) 0.270 0.003 79.682 0.000 0.264
## Stst36c (.44.) 0.135 0.003 44.144 0.000 0.129
## Stst37b (.45.) 0.139 0.003 45.066 0.000 0.133
## ci.upper Std.lv Std.all
##
## 0.177 0.151 0.159
## 0.357 0.308 0.337
## 0.326 0.281 0.301
## 0.353 0.305 0.336
## 0.267 0.230 0.249
## 0.224 0.192 0.208
## 0.264 0.228 0.239
## 0.171 0.147 0.159
## 0.206 0.176 0.186
##
## 0.285 0.273 0.277
## 0.169 0.159 0.167
## 0.184 0.173 0.181
## 0.580 0.556 0.582
## 0.273 0.258 0.273
##
## 0.291 0.255 0.268
## 0.266 0.232 0.245
## 0.414 0.364 0.385
## 0.629 0.554 0.635
## 0.705 0.622 0.673
## 0.643 0.567 0.608
##
## 0.615 0.548 0.643
## 0.385 0.339 0.358
## 0.362 0.319 0.352
## 0.287 0.250 0.264
## 0.181 0.157 0.169
##
## 0.829 0.767 0.812
## 0.747 0.691 0.703
## 0.624 0.576 0.606
## 0.555 0.512 0.559
## 0.564 0.520 0.556
## 0.723 0.669 0.737
## 0.631 0.582 0.630
## 0.568 0.523 0.567
## 0.706 0.653 0.684
## 0.843 0.780 0.844
## 0.514 0.474 0.556
## 0.352 0.323 0.340
## 0.484 0.445 0.490
## 0.590 0.544 0.575
## 0.753 0.696 0.725
## 0.750 0.694 0.726
## 0.478 0.439 0.464
## 0.277 0.252 0.289
## 0.141 0.126 0.136
## 0.145 0.129 0.139
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.81.) -0.142 0.004 -37.317 0.000 -0.150
## .Stst20s (.82.) -0.269 0.004 -68.662 0.000 -0.276
## .Stst21c (.83.) -0.214 0.004 -55.968 0.000 -0.222
## .Stst22p (.84.) -0.215 0.004 -54.536 0.000 -0.223
## .Stst23n (.85.) -0.154 0.004 -37.763 0.000 -0.161
## .Stst24x (.86.) -0.117 0.004 -28.254 0.000 -0.125
## .Stst25w (.87.) -0.139 0.004 -36.221 0.000 -0.146
## .Stst26r (.88.) -0.007 0.004 -1.711 0.087 -0.015
## .Stst31b (.89.) 0.088 0.004 22.584 0.000 0.080
## .Stst5mt (.90.) 0.136 0.004 36.409 0.000 0.129
## .Stst32r (.91.) 0.148 0.004 40.328 0.000 0.141
## .Stst33h (.92.) 0.117 0.004 28.188 0.000 0.109
## .Stst34r (.93.) 0.001 0.004 0.286 0.775 -0.006
## .Sts292D (.94.) 0.240 0.003 68.901 0.000 0.234
## .Stst35t (.95.) -0.120 0.004 -32.027 0.000 -0.127
## .Stst36c (.96.) -0.189 0.004 -53.274 0.000 -0.196
## .Stst37b (.97.) -0.041 0.004 -10.402 0.000 -0.048
## .Stst28m (.98.) 0.497 0.004 114.006 0.000 0.488
## .Sts303D (.99.) 0.331 0.004 90.402 0.000 0.324
## .Stst1vc (.100) 0.162 0.004 42.311 0.000 0.155
## english 2.069 0.021 99.853 0.000 2.028
## math 0.064 0.009 6.861 0.000 0.046
## speed 0.520 0.008 65.126 0.000 0.504
## spatial -1.192 0.010 -114.260 0.000 -1.212
## g -0.305 0.007 -43.061 0.000 -0.319
## ci.upper Std.lv Std.all
## -0.135 -0.142 -0.150
## -0.261 -0.269 -0.294
## -0.207 -0.214 -0.229
## -0.207 -0.215 -0.237
## -0.146 -0.154 -0.166
## -0.109 -0.117 -0.127
## -0.131 -0.139 -0.145
## 0.001 -0.007 -0.008
## 0.095 0.088 0.093
## 0.143 0.136 0.138
## 0.155 0.148 0.154
## 0.126 0.117 0.123
## 0.008 0.001 0.001
## 0.247 0.240 0.253
## -0.112 -0.120 -0.137
## -0.182 -0.189 -0.204
## -0.033 -0.041 -0.044
## 0.505 0.497 0.583
## 0.339 0.331 0.365
## 0.170 0.162 0.172
## 2.110 2.355 2.355
## 0.082 0.066 0.066
## 0.536 0.583 0.583
## -1.171 -1.325 -1.325
## -0.291 -0.327 -0.327
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.483 0.003 164.605 0.000 0.477
## .Stest20spellng 0.480 0.003 159.244 0.000 0.474
## .Stest21cptlztn 0.525 0.003 163.303 0.000 0.519
## .Stest22puncttn 0.282 0.002 130.213 0.000 0.278
## .Stest23english 0.464 0.003 145.422 0.000 0.457
## .Stest24exprssn 0.540 0.004 149.125 0.000 0.532
## .Stst25wrdfnctn 0.409 0.003 145.017 0.000 0.404
## .Stst26rdngcmpr 0.224 0.002 122.885 0.000 0.221
## .Stst31bstrctrs 0.506 0.003 147.118 0.000 0.500
## .Stest5math 0.415 0.004 107.795 0.000 0.408
## .Stst32rthrsnng 0.408 0.002 164.227 0.000 0.403
## .Stst33hghschlm 0.122 0.005 25.963 0.000 0.113
## .Stst34rthcmptt 0.504 0.004 129.659 0.000 0.496
## .Stst29vslztn2D 0.628 0.004 154.681 0.000 0.620
## .Stest35tblrdng 0.390 0.005 74.896 0.000 0.380
## .Stst36clrclchc 0.452 0.004 105.681 0.000 0.443
## .Stst37bjctnspc 0.505 0.004 128.064 0.000 0.498
## .Stst28mchnclrs 0.202 0.004 48.895 0.000 0.193
## .Stst30vslztn3D 0.523 0.003 159.189 0.000 0.517
## .Stest1vocab 0.303 0.002 134.103 0.000 0.299
## english 0.772 0.017 46.276 0.000 0.739
## math 0.952 0.016 59.049 0.000 0.920
## speed 0.796 0.010 79.113 0.000 0.776
## spatial 0.809 0.010 79.351 0.000 0.789
## g 0.868 0.007 126.668 0.000 0.854
## ci.upper Std.lv Std.all
## 0.489 0.483 0.535
## 0.486 0.480 0.574
## 0.531 0.525 0.600
## 0.286 0.282 0.343
## 0.470 0.464 0.542
## 0.547 0.540 0.635
## 0.415 0.409 0.448
## 0.228 0.224 0.262
## 0.513 0.506 0.565
## 0.423 0.415 0.429
## 0.413 0.408 0.442
## 0.132 0.122 0.134
## 0.512 0.504 0.562
## 0.636 0.628 0.697
## 0.400 0.390 0.513
## 0.460 0.452 0.529
## 0.513 0.505 0.582
## 0.210 0.202 0.278
## 0.530 0.523 0.636
## 0.308 0.303 0.340
## 0.804 1.000 1.000
## 0.983 1.000 1.000
## 0.816 1.000 1.000
## 0.829 1.000 1.000
## 0.881 1.000 1.000
lavTestScore(scalar, release = 46:65)
## 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 28316.67 20 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p81. == .p186. 825.303 1 0.000
## 2 .p82. == .p187. 184.470 1 0.000
## 3 .p83. == .p188. 8.062 1 0.005
## 4 .p84. == .p189. 146.395 1 0.000
## 5 .p85. == .p190. 103.456 1 0.000
## 6 .p86. == .p191. 1.403 1 0.236
## 7 .p87. == .p192. 1.161 1 0.281
## 8 .p88. == .p193. 1722.897 1 0.000
## 9 .p89. == .p194. 1536.686 1 0.000
## 10 .p90. == .p195. 2417.385 1 0.000
## 11 .p91. == .p196. 338.923 1 0.000
## 12 .p92. == .p197. 2.004 1 0.157
## 13 .p93. == .p198. 2371.607 1 0.000
## 14 .p94. == .p199. 444.312 1 0.000
## 15 .p95. == .p200. 978.462 1 0.000
## 16 .p96. == .p201. 947.242 1 0.000
## 17 .p97. == .p202. 1413.995 1 0.000
## 18 .p98. == .p203. 18513.178 1 0.000
## 19 .p99. == .p204. 9565.303 1 0.000
## 20 .p100. == .p205. 51.116 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("Stest28mechanicalreasoning~1", "Stest34arithcomputation~1", "Stest29visualization2D~1", "Stest26readingcomprehension~1"))
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 64908.038 341.000 0.000 0.955 0.052 0.039
## aic bic
## 6471717.573 6472891.471
Mc(scalar2)
## [1] 0.7968417
summary(scalar2, standardized=T, ci=T) # -.367 but -.292 if math is released instead of reading comprehension
## lavaan 0.6-18 ended normally after 69 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 180
## Number of equality constraints 61
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 64908.038 55248.453
## Degrees of freedom 341 341
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.175
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 34674.798 29514.511
## 1 30233.239 25733.943
##
## 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.) 0.185 0.002 78.569 0.000 0.181
## Stst20s (.p2.) 0.354 0.003 110.677 0.000 0.348
## Stst21c (.p3.) 0.321 0.003 112.287 0.000 0.315
## Stst22p (.p4.) 0.353 0.003 118.424 0.000 0.348
## Stst23n (.p5.) 0.264 0.003 95.696 0.000 0.259
## Stst24x (.p6.) 0.213 0.003 81.026 0.000 0.208
## Stst25w (.p7.) 0.261 0.002 108.880 0.000 0.256
## Stst26r (.p8.) 0.066 0.004 18.539 0.000 0.059
## Stst31b (.p9.) 0.114 0.002 56.129 0.000 0.110
## math =~
## Stst5mt (.10.) 0.288 0.003 97.960 0.000 0.282
## Stst25w (.11.) 0.162 0.003 53.986 0.000 0.156
## Stst32r (.12.) 0.185 0.003 59.538 0.000 0.179
## Stst33h (.13.) 0.576 0.005 120.383 0.000 0.567
## Stst34r (.14.) 0.256 0.004 67.877 0.000 0.249
## speed =~
## Stst19d (.15.) 0.295 0.003 107.562 0.000 0.290
## Sts292D (.16.) 0.233 0.003 75.522 0.000 0.227
## Stst34r (.17.) 0.378 0.003 121.770 0.000 0.372
## Stst35t (.18.) 0.636 0.004 151.492 0.000 0.628
## Stst36c (.19.) 0.725 0.004 186.868 0.000 0.717
## Stst37b (.20.) 0.613 0.004 165.179 0.000 0.606
## spatial =~
## Stst28m (.21.) 0.451 0.003 149.561 0.000 0.445
## Sts292D (.22.) 0.470 0.003 137.079 0.000 0.463
## Sts303D (.23.) 0.607 0.004 163.823 0.000 0.600
## Stst31b (.24.) 0.355 0.003 114.253 0.000 0.349
## Stst37b (.25.) 0.258 0.003 78.423 0.000 0.252
## g =~
## Stst1vc (.26.) 0.820 0.003 305.119 0.000 0.815
## Stst5mt (.27.) 0.737 0.003 278.424 0.000 0.732
## Stst19d (.28.) 0.621 0.003 228.514 0.000 0.615
## Stst20s (.29.) 0.557 0.003 187.704 0.000 0.552
## Stst21c (.30.) 0.565 0.003 192.537 0.000 0.559
## Stst22p (.31.) 0.723 0.003 254.061 0.000 0.718
## Stst23n (.32.) 0.630 0.003 199.140 0.000 0.624
## Stst24x (.33.) 0.567 0.003 180.417 0.000 0.561
## Stst25w (.34.) 0.705 0.003 280.464 0.000 0.700
## Stst26r (.35.) 0.860 0.003 303.700 0.000 0.855
## Stst28m (.36.) 0.497 0.003 190.476 0.000 0.492
## Sts292D (.37.) 0.344 0.003 115.871 0.000 0.338
## Sts303D (.38.) 0.491 0.003 167.346 0.000 0.485
## Stst31b (.39.) 0.597 0.003 199.081 0.000 0.591
## Stst32r (.40.) 0.743 0.003 277.958 0.000 0.738
## Stst33h (.41.) 0.739 0.003 259.685 0.000 0.734
## Stst34r (.42.) 0.488 0.003 155.149 0.000 0.482
## Stst35t (.43.) 0.263 0.003 77.974 0.000 0.257
## Stst36c (.44.) 0.126 0.003 41.594 0.000 0.120
## Stst37b (.45.) 0.138 0.003 45.545 0.000 0.132
## ci.upper Std.lv Std.all
##
## 0.190 0.185 0.188
## 0.361 0.354 0.357
## 0.326 0.321 0.332
## 0.359 0.353 0.359
## 0.270 0.264 0.264
## 0.219 0.213 0.209
## 0.265 0.261 0.261
## 0.073 0.066 0.066
## 0.118 0.114 0.115
##
## 0.294 0.288 0.301
## 0.168 0.162 0.162
## 0.191 0.185 0.188
## 0.586 0.576 0.573
## 0.264 0.256 0.262
##
## 0.300 0.295 0.299
## 0.239 0.233 0.238
## 0.384 0.378 0.386
## 0.644 0.636 0.626
## 0.732 0.725 0.724
## 0.621 0.613 0.593
##
## 0.457 0.451 0.513
## 0.476 0.470 0.479
## 0.614 0.607 0.597
## 0.361 0.355 0.357
## 0.265 0.258 0.250
##
## 0.825 0.820 0.851
## 0.742 0.737 0.770
## 0.626 0.621 0.629
## 0.563 0.557 0.562
## 0.570 0.565 0.584
## 0.729 0.723 0.735
## 0.636 0.630 0.628
## 0.573 0.567 0.555
## 0.710 0.705 0.706
## 0.866 0.860 0.856
## 0.502 0.497 0.566
## 0.349 0.344 0.350
## 0.496 0.491 0.482
## 0.603 0.597 0.600
## 0.748 0.743 0.754
## 0.745 0.739 0.735
## 0.494 0.488 0.498
## 0.270 0.263 0.259
## 0.132 0.126 0.126
## 0.144 0.138 0.134
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.81.) -0.131 0.004 -34.288 0.000 -0.138
## .Stst20s (.82.) -0.265 0.004 -67.421 0.000 -0.272
## .Stst21c (.83.) -0.207 0.004 -54.046 0.000 -0.215
## .Stst22p (.84.) -0.212 0.004 -53.488 0.000 -0.219
## .Stst23n (.85.) -0.147 0.004 -36.127 0.000 -0.155
## .Stst24x (.86.) -0.102 0.004 -24.535 0.000 -0.110
## .Stst25w (.87.) -0.131 0.004 -34.258 0.000 -0.139
## .Stst26r -0.032 0.004 -7.898 0.000 -0.041
## .Stst31b (.89.) 0.059 0.004 15.327 0.000 0.052
## .Stst5mt (.90.) 0.143 0.004 38.807 0.000 0.136
## .Stst32r (.91.) 0.158 0.004 43.431 0.000 0.151
## .Stst33h (.92.) 0.124 0.004 29.550 0.000 0.115
## .Stst34r -0.078 0.004 -19.714 0.000 -0.086
## .Sts292D 0.212 0.004 54.435 0.000 0.204
## .Stst35t (.95.) -0.074 0.004 -20.578 0.000 -0.082
## .Stst36c (.96.) -0.150 0.004 -40.929 0.000 -0.157
## .Stst37b (.97.) -0.076 0.004 -20.581 0.000 -0.083
## .Stst28m 0.536 0.004 151.032 0.000 0.529
## .Sts303D (.99.) 0.182 0.004 45.187 0.000 0.175
## .Stst1vc (.100) 0.175 0.004 47.190 0.000 0.167
## ci.upper Std.lv Std.all
## -0.123 -0.131 -0.133
## -0.257 -0.265 -0.267
## -0.200 -0.207 -0.214
## -0.204 -0.212 -0.215
## -0.139 -0.147 -0.146
## -0.093 -0.102 -0.099
## -0.124 -0.131 -0.131
## -0.024 -0.032 -0.032
## 0.067 0.059 0.059
## 0.150 0.143 0.149
## 0.165 0.158 0.160
## 0.132 0.124 0.123
## -0.070 -0.078 -0.080
## 0.219 0.212 0.216
## -0.067 -0.074 -0.073
## -0.143 -0.150 -0.150
## -0.069 -0.076 -0.074
## 0.543 0.536 0.610
## 0.190 0.182 0.179
## 0.182 0.175 0.181
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.466 0.003 158.802 0.000 0.461
## .Stest20spellng 0.547 0.003 158.024 0.000 0.540
## .Stest21cptlztn 0.514 0.003 160.767 0.000 0.508
## .Stest22puncttn 0.322 0.002 131.826 0.000 0.317
## .Stest23english 0.538 0.004 143.389 0.000 0.530
## .Stest24exprssn 0.676 0.004 155.478 0.000 0.667
## .Stst25wrdfnctn 0.405 0.003 150.201 0.000 0.399
## .Stst26rdngcmpr 0.265 0.002 114.518 0.000 0.261
## .Stst31bstrctrs 0.493 0.003 152.043 0.000 0.487
## .Stest5math 0.290 0.003 97.237 0.000 0.285
## .Stst32rthrsnng 0.384 0.002 157.326 0.000 0.380
## .Stst33hghschlm 0.133 0.005 29.090 0.000 0.124
## .Stst34rthcmptt 0.512 0.004 138.405 0.000 0.505
## .Stst29vslztn2D 0.569 0.004 129.450 0.000 0.561
## .Stest35tblrdng 0.560 0.007 76.183 0.000 0.545
## .Stst36clrclchc 0.461 0.005 85.161 0.000 0.450
## .Stst37bjctnspc 0.606 0.005 124.320 0.000 0.597
## .Stst28mchnclrs 0.321 0.003 122.897 0.000 0.316
## .Stst30vslztn3D 0.425 0.004 106.360 0.000 0.418
## .Stest1vocab 0.255 0.002 123.012 0.000 0.251
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.472 0.466 0.479
## 0.554 0.547 0.556
## 0.520 0.514 0.549
## 0.326 0.322 0.332
## 0.545 0.538 0.535
## 0.684 0.676 0.648
## 0.410 0.405 0.407
## 0.270 0.265 0.263
## 0.500 0.493 0.499
## 0.296 0.290 0.317
## 0.389 0.384 0.396
## 0.142 0.133 0.132
## 0.519 0.512 0.534
## 0.578 0.569 0.592
## 0.574 0.560 0.542
## 0.471 0.461 0.460
## 0.616 0.606 0.568
## 0.326 0.321 0.416
## 0.433 0.425 0.411
## 0.260 0.255 0.275
## 1.000 1.000 1.000
## 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.) 0.185 0.002 78.569 0.000 0.181
## Stst20s (.p2.) 0.354 0.003 110.677 0.000 0.348
## Stst21c (.p3.) 0.321 0.003 112.287 0.000 0.315
## Stst22p (.p4.) 0.353 0.003 118.424 0.000 0.348
## Stst23n (.p5.) 0.264 0.003 95.696 0.000 0.259
## Stst24x (.p6.) 0.213 0.003 81.026 0.000 0.208
## Stst25w (.p7.) 0.261 0.002 108.880 0.000 0.256
## Stst26r (.p8.) 0.066 0.004 18.539 0.000 0.059
## Stst31b (.p9.) 0.114 0.002 56.129 0.000 0.110
## math =~
## Stst5mt (.10.) 0.288 0.003 97.960 0.000 0.282
## Stst25w (.11.) 0.162 0.003 53.986 0.000 0.156
## Stst32r (.12.) 0.185 0.003 59.538 0.000 0.179
## Stst33h (.13.) 0.576 0.005 120.383 0.000 0.567
## Stst34r (.14.) 0.256 0.004 67.877 0.000 0.249
## speed =~
## Stst19d (.15.) 0.295 0.003 107.562 0.000 0.290
## Sts292D (.16.) 0.233 0.003 75.522 0.000 0.227
## Stst34r (.17.) 0.378 0.003 121.770 0.000 0.372
## Stst35t (.18.) 0.636 0.004 151.492 0.000 0.628
## Stst36c (.19.) 0.725 0.004 186.868 0.000 0.717
## Stst37b (.20.) 0.613 0.004 165.179 0.000 0.606
## spatial =~
## Stst28m (.21.) 0.451 0.003 149.561 0.000 0.445
## Sts292D (.22.) 0.470 0.003 137.079 0.000 0.463
## Sts303D (.23.) 0.607 0.004 163.823 0.000 0.600
## Stst31b (.24.) 0.355 0.003 114.253 0.000 0.349
## Stst37b (.25.) 0.258 0.003 78.423 0.000 0.252
## g =~
## Stst1vc (.26.) 0.820 0.003 305.119 0.000 0.815
## Stst5mt (.27.) 0.737 0.003 278.424 0.000 0.732
## Stst19d (.28.) 0.621 0.003 228.514 0.000 0.615
## Stst20s (.29.) 0.557 0.003 187.704 0.000 0.552
## Stst21c (.30.) 0.565 0.003 192.537 0.000 0.559
## Stst22p (.31.) 0.723 0.003 254.061 0.000 0.718
## Stst23n (.32.) 0.630 0.003 199.140 0.000 0.624
## Stst24x (.33.) 0.567 0.003 180.417 0.000 0.561
## Stst25w (.34.) 0.705 0.003 280.464 0.000 0.700
## Stst26r (.35.) 0.860 0.003 303.700 0.000 0.855
## Stst28m (.36.) 0.497 0.003 190.476 0.000 0.492
## Sts292D (.37.) 0.344 0.003 115.871 0.000 0.338
## Sts303D (.38.) 0.491 0.003 167.346 0.000 0.485
## Stst31b (.39.) 0.597 0.003 199.081 0.000 0.591
## Stst32r (.40.) 0.743 0.003 277.958 0.000 0.738
## Stst33h (.41.) 0.739 0.003 259.685 0.000 0.734
## Stst34r (.42.) 0.488 0.003 155.149 0.000 0.482
## Stst35t (.43.) 0.263 0.003 77.974 0.000 0.257
## Stst36c (.44.) 0.126 0.003 41.594 0.000 0.120
## Stst37b (.45.) 0.138 0.003 45.545 0.000 0.132
## ci.upper Std.lv Std.all
##
## 0.190 0.164 0.173
## 0.361 0.314 0.343
## 0.326 0.284 0.304
## 0.359 0.313 0.345
## 0.270 0.235 0.253
## 0.219 0.189 0.205
## 0.265 0.231 0.242
## 0.073 0.059 0.064
## 0.118 0.101 0.107
##
## 0.294 0.285 0.290
## 0.168 0.160 0.167
## 0.191 0.183 0.191
## 0.586 0.570 0.597
## 0.264 0.253 0.270
##
## 0.300 0.262 0.276
## 0.239 0.207 0.218
## 0.384 0.336 0.357
## 0.644 0.566 0.647
## 0.732 0.645 0.694
## 0.621 0.546 0.587
##
## 0.457 0.398 0.479
## 0.476 0.414 0.435
## 0.614 0.535 0.573
## 0.361 0.313 0.331
## 0.265 0.228 0.245
##
## 0.825 0.761 0.809
## 0.742 0.684 0.696
## 0.626 0.576 0.606
## 0.563 0.517 0.565
## 0.570 0.524 0.559
## 0.729 0.671 0.740
## 0.636 0.584 0.631
## 0.573 0.526 0.570
## 0.710 0.654 0.683
## 0.866 0.798 0.866
## 0.502 0.461 0.556
## 0.349 0.319 0.335
## 0.496 0.455 0.487
## 0.603 0.554 0.586
## 0.748 0.689 0.719
## 0.745 0.686 0.718
## 0.494 0.452 0.481
## 0.270 0.244 0.279
## 0.132 0.117 0.126
## 0.144 0.128 0.138
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.81.) -0.131 0.004 -34.288 0.000 -0.138
## .Stst20s (.82.) -0.265 0.004 -67.421 0.000 -0.272
## .Stst21c (.83.) -0.207 0.004 -54.046 0.000 -0.215
## .Stst22p (.84.) -0.212 0.004 -53.488 0.000 -0.219
## .Stst23n (.85.) -0.147 0.004 -36.127 0.000 -0.155
## .Stst24x (.86.) -0.102 0.004 -24.535 0.000 -0.110
## .Stst25w (.87.) -0.131 0.004 -34.258 0.000 -0.139
## .Stst26r 0.260 0.008 31.183 0.000 0.243
## .Stst31b (.89.) 0.059 0.004 15.327 0.000 0.052
## .Stst5mt (.90.) 0.143 0.004 38.807 0.000 0.136
## .Stst32r (.91.) 0.158 0.004 43.431 0.000 0.151
## .Stst33h (.92.) 0.124 0.004 29.550 0.000 0.115
## .Stst34r 0.158 0.004 35.452 0.000 0.150
## .Sts292D -0.030 0.005 -6.141 0.000 -0.040
## .Stst35t (.95.) -0.074 0.004 -20.578 0.000 -0.082
## .Stst36c (.96.) -0.150 0.004 -40.929 0.000 -0.157
## .Stst37b (.97.) -0.076 0.004 -20.581 0.000 -0.083
## .Stst28m -0.167 0.004 -37.700 0.000 -0.176
## .Sts303D (.99.) 0.182 0.004 45.187 0.000 0.175
## .Stst1vc (.100) 0.175 0.004 47.190 0.000 0.167
## english 2.090 0.019 108.868 0.000 2.053
## math 0.086 0.009 10.017 0.000 0.069
## speed 0.398 0.007 55.129 0.000 0.384
## spatial -0.204 0.008 -24.801 0.000 -0.220
## g -0.340 0.007 -50.872 0.000 -0.353
## ci.upper Std.lv Std.all
## -0.123 -0.131 -0.138
## -0.257 -0.265 -0.289
## -0.200 -0.207 -0.221
## -0.204 -0.212 -0.233
## -0.139 -0.147 -0.159
## -0.093 -0.102 -0.110
## -0.124 -0.131 -0.137
## 0.276 0.260 0.282
## 0.067 0.059 0.062
## 0.150 0.143 0.146
## 0.165 0.158 0.164
## 0.132 0.124 0.129
## 0.167 0.158 0.168
## -0.021 -0.030 -0.032
## -0.067 -0.074 -0.085
## -0.143 -0.150 -0.161
## -0.069 -0.076 -0.082
## -0.158 -0.167 -0.201
## 0.190 0.182 0.195
## 0.182 0.175 0.186
## 2.128 2.357 2.357
## 0.102 0.087 0.087
## 0.412 0.447 0.447
## -0.188 -0.232 -0.232
## -0.327 -0.367 -0.367
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.475 0.003 162.699 0.000 0.470
## .Stest20spellng 0.472 0.003 157.964 0.000 0.466
## .Stest21cptlztn 0.522 0.003 162.584 0.000 0.516
## .Stest22puncttn 0.274 0.002 126.968 0.000 0.270
## .Stest23english 0.460 0.003 145.147 0.000 0.454
## .Stest24exprssn 0.540 0.004 149.343 0.000 0.533
## .Stst25wrdfnctn 0.409 0.003 144.478 0.000 0.403
## .Stst26rdngcmpr 0.209 0.002 109.759 0.000 0.205
## .Stst31bstrctrs 0.479 0.003 155.619 0.000 0.473
## .Stest5math 0.416 0.004 108.540 0.000 0.409
## .Stst32rthrsnng 0.411 0.002 165.829 0.000 0.406
## .Stst33hghschlm 0.117 0.005 25.324 0.000 0.108
## .Stst34rthcmptt 0.502 0.004 133.775 0.000 0.495
## .Stst29vslztn2D 0.591 0.004 150.776 0.000 0.583
## .Stest35tblrdng 0.386 0.005 73.999 0.000 0.375
## .Stst36clrclchc 0.434 0.004 99.411 0.000 0.426
## .Stst37bjctnspc 0.498 0.004 129.481 0.000 0.490
## .Stst28mchnclrs 0.318 0.002 135.096 0.000 0.314
## .Stst30vslztn3D 0.379 0.003 112.736 0.000 0.373
## .Stest1vocab 0.307 0.002 139.730 0.000 0.302
## english 0.787 0.016 47.872 0.000 0.754
## math 0.978 0.016 61.921 0.000 0.947
## speed 0.792 0.010 78.993 0.000 0.772
## spatial 0.778 0.010 79.652 0.000 0.759
## g 0.861 0.007 127.108 0.000 0.847
## ci.upper Std.lv Std.all
## 0.481 0.475 0.527
## 0.478 0.472 0.563
## 0.528 0.522 0.595
## 0.279 0.274 0.333
## 0.466 0.460 0.537
## 0.547 0.540 0.633
## 0.414 0.409 0.447
## 0.213 0.209 0.246
## 0.485 0.479 0.536
## 0.424 0.416 0.431
## 0.416 0.411 0.447
## 0.126 0.117 0.128
## 0.510 0.502 0.568
## 0.599 0.591 0.651
## 0.396 0.386 0.504
## 0.443 0.434 0.503
## 0.505 0.498 0.576
## 0.323 0.318 0.462
## 0.386 0.379 0.434
## 0.311 0.307 0.346
## 0.819 1.000 1.000
## 1.009 1.000 1.000
## 0.812 1.000 1.000
## 0.797 1.000 1.000
## 0.874 1.000 1.000
lavTestScore(scalar2, release = 46:61)
## 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 2976.258 16 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p81. == .p186. 225.418 1 0.000
## 2 .p82. == .p187. 74.580 1 0.000
## 3 .p83. == .p188. 34.737 1 0.000
## 4 .p84. == .p189. 41.833 1 0.000
## 5 .p85. == .p190. 7.302 1 0.007
## 6 .p86. == .p191. 244.387 1 0.000
## 7 .p87. == .p192. 135.652 1 0.000
## 8 .p89. == .p194. 25.461 1 0.000
## 9 .p90. == .p195. 1863.722 1 0.000
## 10 .p91. == .p196. 647.880 1 0.000
## 11 .p92. == .p197. 544.237 1 0.000
## 12 .p95. == .p200. 15.464 1 0.000
## 13 .p96. == .p201. 3.144 1 0.076
## 14 .p97. == .p202. 122.599 1 0.000
## 15 .p99. == .p204. 146.213 1 0.000
## 16 .p100. == .p205. 114.745 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("Stest28mechanicalreasoning~1", "Stest34arithcomputation~1", "Stest29visualization2D~1", "Stest26readingcomprehension~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 71764.852 361.000 0.000 0.950 0.053 0.042
## aic bic
## 6478534.388 6479510.992
Mc(strict)
## [1] 0.7779087
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("Stest28mechanicalreasoning~1", "Stest34arithcomputation~1", "Stest29visualization2D~1", "Stest26readingcomprehension~1"))
fitMeasures(chc.bifactor, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 66364.961 346.000 0.000 0.954 0.052 0.052
## aic bic
## 6473164.497 6474289.071
Mc(chc.bifactor)
## [1] 0.7927828
summary(chc.bifactor, standardized=T, ci=T) # -.352 but -.281 if math is released instead
## lavaan 0.6-18 ended normally after 54 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 175
## Number of equality constraints 61
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 66364.961 56481.427
## Degrees of freedom 346 346
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.175
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 35482.055 30197.819
## 1 30882.906 26283.608
##
## 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.) 0.175 0.002 82.839 0.000 0.171
## Stst20s (.p2.) 0.334 0.003 131.896 0.000 0.329
## Stst21c (.p3.) 0.303 0.002 135.463 0.000 0.299
## Stst22p (.p4.) 0.333 0.002 150.938 0.000 0.329
## Stst23n (.p5.) 0.249 0.002 111.469 0.000 0.245
## Stst24x (.p6.) 0.201 0.002 92.639 0.000 0.197
## Stst25w (.p7.) 0.246 0.002 126.821 0.000 0.242
## Stst26r (.p8.) 0.062 0.003 18.984 0.000 0.056
## Stst31b (.p9.) 0.108 0.002 58.157 0.000 0.104
## math =~
## Stst5mt (.10.) 0.287 0.003 98.509 0.000 0.281
## Stst25w (.11.) 0.161 0.003 56.263 0.000 0.155
## Stst32r (.12.) 0.184 0.003 64.377 0.000 0.178
## Stst33h (.13.) 0.573 0.004 141.812 0.000 0.565
## Stst34r (.14.) 0.255 0.003 74.228 0.000 0.248
## speed =~
## Stst19d (.15.) 0.280 0.003 110.730 0.000 0.276
## Sts292D (.16.) 0.221 0.003 76.999 0.000 0.215
## Stst34r (.17.) 0.357 0.003 131.064 0.000 0.352
## Stst35t (.18.) 0.597 0.003 177.324 0.000 0.591
## Stst36c (.19.) 0.686 0.003 219.686 0.000 0.679
## Stst37b (.20.) 0.578 0.003 192.524 0.000 0.572
## spatial =~
## Stst28m (.21.) 0.425 0.003 167.364 0.000 0.420
## Sts292D (.22.) 0.444 0.003 147.141 0.000 0.438
## Sts303D (.23.) 0.570 0.003 188.368 0.000 0.564
## Stst31b (.24.) 0.335 0.003 120.130 0.000 0.329
## Stst37b (.25.) 0.242 0.003 80.990 0.000 0.236
## g =~
## Stst1vc (.26.) 0.792 0.002 368.465 0.000 0.788
## Stst5mt (.27.) 0.712 0.002 317.539 0.000 0.707
## Stst19d (.28.) 0.599 0.002 252.509 0.000 0.594
## Stst20s (.29.) 0.538 0.003 206.381 0.000 0.533
## Stst21c (.30.) 0.545 0.003 211.779 0.000 0.540
## Stst22p (.31.) 0.698 0.002 300.515 0.000 0.693
## Stst23n (.32.) 0.607 0.003 224.093 0.000 0.602
## Stst24x (.33.) 0.547 0.003 199.656 0.000 0.541
## Stst25w (.34.) 0.681 0.002 318.810 0.000 0.676
## Stst26r (.35.) 0.829 0.002 398.807 0.000 0.825
## Stst28m (.36.) 0.479 0.002 208.222 0.000 0.475
## Sts292D (.37.) 0.331 0.003 118.487 0.000 0.326
## Sts303D (.38.) 0.473 0.003 176.480 0.000 0.468
## Stst31b (.39.) 0.576 0.003 215.099 0.000 0.571
## Stst32r (.40.) 0.717 0.002 334.414 0.000 0.713
## Stst33h (.41.) 0.713 0.002 309.959 0.000 0.709
## Stst34r (.42.) 0.470 0.003 164.348 0.000 0.465
## Stst35t (.43.) 0.253 0.003 78.963 0.000 0.247
## Stst36c (.44.) 0.122 0.003 41.660 0.000 0.116
## Stst37b (.45.) 0.134 0.003 45.618 0.000 0.128
## ci.upper Std.lv Std.all
##
## 0.179 0.175 0.181
## 0.339 0.334 0.343
## 0.307 0.303 0.318
## 0.338 0.333 0.347
## 0.254 0.249 0.253
## 0.205 0.201 0.199
## 0.250 0.246 0.252
## 0.068 0.062 0.063
## 0.111 0.108 0.111
##
## 0.292 0.287 0.306
## 0.166 0.161 0.165
## 0.189 0.184 0.190
## 0.581 0.573 0.581
## 0.262 0.255 0.265
##
## 0.285 0.280 0.290
## 0.226 0.221 0.229
## 0.363 0.357 0.371
## 0.604 0.597 0.601
## 0.692 0.686 0.703
## 0.584 0.578 0.572
##
## 0.430 0.425 0.496
## 0.450 0.444 0.461
## 0.576 0.570 0.574
## 0.340 0.335 0.344
## 0.248 0.242 0.239
##
## 0.796 0.792 0.842
## 0.716 0.712 0.759
## 0.604 0.599 0.619
## 0.543 0.538 0.551
## 0.550 0.545 0.573
## 0.702 0.698 0.727
## 0.613 0.607 0.617
## 0.552 0.547 0.543
## 0.685 0.681 0.696
## 0.833 0.829 0.847
## 0.484 0.479 0.559
## 0.337 0.331 0.344
## 0.479 0.473 0.477
## 0.581 0.576 0.591
## 0.721 0.717 0.743
## 0.718 0.713 0.724
## 0.476 0.470 0.489
## 0.260 0.253 0.255
## 0.128 0.122 0.125
## 0.139 0.134 0.132
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.81.) -0.132 0.004 -34.495 0.000 -0.139
## .Stst20s (.82.) -0.265 0.004 -67.441 0.000 -0.272
## .Stst21c (.83.) -0.208 0.004 -54.075 0.000 -0.215
## .Stst22p (.84.) -0.211 0.004 -53.421 0.000 -0.219
## .Stst23n (.85.) -0.147 0.004 -36.160 0.000 -0.155
## .Stst24x (.86.) -0.101 0.004 -24.496 0.000 -0.109
## .Stst25w (.87.) -0.131 0.004 -34.269 0.000 -0.139
## .Stst26r -0.032 0.004 -7.896 0.000 -0.041
## .Stst31b (.89.) 0.059 0.004 15.290 0.000 0.051
## .Stst5mt (.90.) 0.143 0.004 38.792 0.000 0.136
## .Stst32r (.91.) 0.158 0.004 43.423 0.000 0.150
## .Stst33h (.92.) 0.124 0.004 29.582 0.000 0.116
## .Stst34r -0.078 0.004 -19.713 0.000 -0.086
## .Sts292D 0.212 0.004 54.436 0.000 0.204
## .Stst35t (.95.) -0.074 0.004 -20.457 0.000 -0.081
## .Stst36c (.96.) -0.150 0.004 -40.962 0.000 -0.157
## .Stst37b (.97.) -0.076 0.004 -20.491 0.000 -0.083
## .Stst28m 0.536 0.004 151.033 0.000 0.529
## .Sts303D (.99.) 0.182 0.004 45.146 0.000 0.174
## .Stst1vc (.100) 0.175 0.004 47.238 0.000 0.168
## ci.upper Std.lv Std.all
## -0.124 -0.132 -0.136
## -0.257 -0.265 -0.271
## -0.200 -0.208 -0.218
## -0.204 -0.211 -0.220
## -0.139 -0.147 -0.149
## -0.093 -0.101 -0.100
## -0.124 -0.131 -0.134
## -0.024 -0.032 -0.033
## 0.066 0.059 0.060
## 0.150 0.143 0.153
## 0.165 0.158 0.163
## 0.132 0.124 0.126
## -0.070 -0.078 -0.081
## 0.219 0.212 0.220
## -0.067 -0.074 -0.074
## -0.143 -0.150 -0.154
## -0.068 -0.076 -0.075
## 0.543 0.536 0.625
## 0.190 0.182 0.184
## 0.182 0.175 0.186
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.467 0.003 159.143 0.000 0.461
## .Stest20spellng 0.550 0.003 159.797 0.000 0.544
## .Stest21cptlztn 0.516 0.003 162.030 0.000 0.510
## .Stest22puncttn 0.324 0.002 133.382 0.000 0.320
## .Stest23english 0.539 0.004 143.245 0.000 0.532
## .Stest24exprssn 0.676 0.004 155.476 0.000 0.668
## .Stst25wrdfnctn 0.405 0.003 150.963 0.000 0.400
## .Stst26rdngcmpr 0.267 0.002 116.184 0.000 0.263
## .Stst31bstrctrs 0.494 0.003 152.141 0.000 0.488
## .Stest5math 0.291 0.003 97.792 0.000 0.285
## .Stst32rthrsnng 0.384 0.002 157.737 0.000 0.380
## .Stst33hghschlm 0.135 0.004 30.861 0.000 0.126
## .Stst34rthcmptt 0.513 0.004 138.530 0.000 0.506
## .Stst29vslztn2D 0.571 0.004 130.187 0.000 0.563
## .Stest35tblrdng 0.566 0.007 76.300 0.000 0.552
## .Stst36clrclchc 0.467 0.005 86.150 0.000 0.457
## .Stst37bjctnspc 0.611 0.005 125.733 0.000 0.602
## .Stst28mchnclrs 0.324 0.003 124.968 0.000 0.319
## .Stst30vslztn3D 0.435 0.004 111.482 0.000 0.427
## .Stest1vocab 0.258 0.002 125.991 0.000 0.254
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.473 0.467 0.499
## 0.557 0.550 0.579
## 0.522 0.516 0.570
## 0.329 0.324 0.352
## 0.546 0.539 0.556
## 0.685 0.676 0.666
## 0.411 0.405 0.424
## 0.272 0.267 0.279
## 0.500 0.494 0.520
## 0.296 0.291 0.331
## 0.389 0.384 0.412
## 0.143 0.135 0.138
## 0.520 0.513 0.553
## 0.580 0.571 0.616
## 0.581 0.566 0.574
## 0.478 0.467 0.491
## 0.621 0.611 0.598
## 0.330 0.324 0.441
## 0.442 0.435 0.442
## 0.262 0.258 0.292
## 1.000 1.000 1.000
## 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.) 0.175 0.002 82.839 0.000 0.171
## Stst20s (.p2.) 0.334 0.003 131.896 0.000 0.329
## Stst21c (.p3.) 0.303 0.002 135.463 0.000 0.299
## Stst22p (.p4.) 0.333 0.002 150.938 0.000 0.329
## Stst23n (.p5.) 0.249 0.002 111.469 0.000 0.245
## Stst24x (.p6.) 0.201 0.002 92.639 0.000 0.197
## Stst25w (.p7.) 0.246 0.002 126.821 0.000 0.242
## Stst26r (.p8.) 0.062 0.003 18.984 0.000 0.056
## Stst31b (.p9.) 0.108 0.002 58.157 0.000 0.104
## math =~
## Stst5mt (.10.) 0.287 0.003 98.509 0.000 0.281
## Stst25w (.11.) 0.161 0.003 56.263 0.000 0.155
## Stst32r (.12.) 0.184 0.003 64.377 0.000 0.178
## Stst33h (.13.) 0.573 0.004 141.812 0.000 0.565
## Stst34r (.14.) 0.255 0.003 74.228 0.000 0.248
## speed =~
## Stst19d (.15.) 0.280 0.003 110.730 0.000 0.276
## Sts292D (.16.) 0.221 0.003 76.999 0.000 0.215
## Stst34r (.17.) 0.357 0.003 131.064 0.000 0.352
## Stst35t (.18.) 0.597 0.003 177.324 0.000 0.591
## Stst36c (.19.) 0.686 0.003 219.686 0.000 0.679
## Stst37b (.20.) 0.578 0.003 192.524 0.000 0.572
## spatial =~
## Stst28m (.21.) 0.425 0.003 167.364 0.000 0.420
## Sts292D (.22.) 0.444 0.003 147.141 0.000 0.438
## Sts303D (.23.) 0.570 0.003 188.368 0.000 0.564
## Stst31b (.24.) 0.335 0.003 120.130 0.000 0.329
## Stst37b (.25.) 0.242 0.003 80.990 0.000 0.236
## g =~
## Stst1vc (.26.) 0.792 0.002 368.465 0.000 0.788
## Stst5mt (.27.) 0.712 0.002 317.539 0.000 0.707
## Stst19d (.28.) 0.599 0.002 252.509 0.000 0.594
## Stst20s (.29.) 0.538 0.003 206.381 0.000 0.533
## Stst21c (.30.) 0.545 0.003 211.779 0.000 0.540
## Stst22p (.31.) 0.698 0.002 300.515 0.000 0.693
## Stst23n (.32.) 0.607 0.003 224.093 0.000 0.602
## Stst24x (.33.) 0.547 0.003 199.656 0.000 0.541
## Stst25w (.34.) 0.681 0.002 318.810 0.000 0.676
## Stst26r (.35.) 0.829 0.002 398.807 0.000 0.825
## Stst28m (.36.) 0.479 0.002 208.222 0.000 0.475
## Sts292D (.37.) 0.331 0.003 118.487 0.000 0.326
## Sts303D (.38.) 0.473 0.003 176.480 0.000 0.468
## Stst31b (.39.) 0.576 0.003 215.099 0.000 0.571
## Stst32r (.40.) 0.717 0.002 334.414 0.000 0.713
## Stst33h (.41.) 0.713 0.002 309.959 0.000 0.709
## Stst34r (.42.) 0.470 0.003 164.348 0.000 0.465
## Stst35t (.43.) 0.253 0.003 78.963 0.000 0.247
## Stst36c (.44.) 0.122 0.003 41.660 0.000 0.116
## Stst37b (.45.) 0.134 0.003 45.618 0.000 0.128
## ci.upper Std.lv Std.all
##
## 0.179 0.175 0.180
## 0.339 0.334 0.358
## 0.307 0.303 0.318
## 0.338 0.333 0.357
## 0.254 0.249 0.264
## 0.205 0.201 0.214
## 0.250 0.246 0.252
## 0.068 0.062 0.065
## 0.111 0.108 0.112
##
## 0.292 0.287 0.286
## 0.166 0.161 0.164
## 0.189 0.184 0.188
## 0.581 0.573 0.587
## 0.262 0.255 0.266
##
## 0.285 0.280 0.289
## 0.226 0.221 0.227
## 0.363 0.357 0.373
## 0.604 0.597 0.666
## 0.692 0.686 0.718
## 0.584 0.578 0.607
##
## 0.430 0.425 0.499
## 0.450 0.444 0.457
## 0.576 0.570 0.593
## 0.340 0.335 0.347
## 0.248 0.242 0.254
##
## 0.796 0.792 0.821
## 0.716 0.712 0.710
## 0.604 0.599 0.617
## 0.543 0.538 0.576
## 0.550 0.545 0.571
## 0.702 0.698 0.748
## 0.613 0.607 0.644
## 0.552 0.547 0.583
## 0.685 0.681 0.696
## 0.833 0.829 0.875
## 0.484 0.479 0.563
## 0.337 0.331 0.341
## 0.479 0.473 0.493
## 0.581 0.576 0.596
## 0.721 0.717 0.732
## 0.718 0.713 0.731
## 0.476 0.470 0.492
## 0.260 0.253 0.282
## 0.128 0.122 0.128
## 0.139 0.134 0.140
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.81.) -0.132 0.004 -34.495 0.000 -0.139
## .Stst20s (.82.) -0.265 0.004 -67.441 0.000 -0.272
## .Stst21c (.83.) -0.208 0.004 -54.075 0.000 -0.215
## .Stst22p (.84.) -0.211 0.004 -53.421 0.000 -0.219
## .Stst23n (.85.) -0.147 0.004 -36.160 0.000 -0.155
## .Stst24x (.86.) -0.101 0.004 -24.496 0.000 -0.109
## .Stst25w (.87.) -0.131 0.004 -34.269 0.000 -0.139
## .Stst26r 0.260 0.008 31.370 0.000 0.244
## .Stst31b (.89.) 0.059 0.004 15.290 0.000 0.051
## .Stst5mt (.90.) 0.143 0.004 38.792 0.000 0.136
## .Stst32r (.91.) 0.158 0.004 43.423 0.000 0.150
## .Stst33h (.92.) 0.124 0.004 29.582 0.000 0.116
## .Stst34r 0.158 0.004 35.425 0.000 0.149
## .Sts292D -0.030 0.005 -6.026 0.000 -0.039
## .Stst35t (.95.) -0.074 0.004 -20.457 0.000 -0.081
## .Stst36c (.96.) -0.150 0.004 -40.962 0.000 -0.157
## .Stst37b (.97.) -0.076 0.004 -20.491 0.000 -0.083
## .Stst28m -0.167 0.004 -37.580 0.000 -0.175
## .Sts303D (.99.) 0.182 0.004 45.146 0.000 0.174
## .Stst1vc (.100) 0.175 0.004 47.238 0.000 0.168
## english 2.214 0.017 128.054 0.000 2.180
## math 0.086 0.009 9.933 0.000 0.069
## speed 0.422 0.007 58.977 0.000 0.408
## spatial -0.218 0.009 -24.936 0.000 -0.235
## g -0.352 0.007 -52.257 0.000 -0.365
## ci.upper Std.lv Std.all
## -0.124 -0.132 -0.136
## -0.257 -0.265 -0.284
## -0.200 -0.208 -0.218
## -0.204 -0.211 -0.227
## -0.139 -0.147 -0.155
## -0.093 -0.101 -0.108
## -0.124 -0.131 -0.134
## 0.276 0.260 0.274
## 0.066 0.059 0.061
## 0.150 0.143 0.143
## 0.165 0.158 0.161
## 0.132 0.124 0.127
## 0.167 0.158 0.165
## -0.020 -0.030 -0.030
## -0.067 -0.074 -0.082
## -0.143 -0.150 -0.157
## -0.068 -0.076 -0.080
## -0.158 -0.167 -0.196
## 0.190 0.182 0.190
## 0.182 0.175 0.181
## 2.248 2.214 2.214
## 0.103 0.086 0.086
## 0.436 0.422 0.422
## -0.201 -0.218 -0.218
## -0.339 -0.352 -0.352
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.473 0.003 162.159 0.000 0.467
## .Stest20spellng 0.469 0.003 157.669 0.000 0.463
## .Stest21cptlztn 0.520 0.003 162.111 0.000 0.514
## .Stest22puncttn 0.272 0.002 126.160 0.000 0.268
## .Stest23english 0.459 0.003 144.992 0.000 0.453
## .Stest24exprssn 0.540 0.004 149.341 0.000 0.533
## .Stst25wrdfnctn 0.408 0.003 144.028 0.000 0.402
## .Stst26rdngcmpr 0.207 0.002 109.040 0.000 0.203
## .Stst31bstrctrs 0.477 0.003 155.347 0.000 0.471
## .Stest5math 0.416 0.004 108.467 0.000 0.408
## .Stst32rthrsnng 0.411 0.002 165.617 0.000 0.406
## .Stst33hghschlm 0.116 0.005 25.553 0.000 0.107
## .Stst34rthcmptt 0.502 0.004 133.597 0.000 0.494
## .Stst29vslztn2D 0.587 0.004 149.761 0.000 0.580
## .Stest35tblrdng 0.385 0.005 74.178 0.000 0.374
## .Stst36clrclchc 0.427 0.004 98.633 0.000 0.419
## .Stst37bjctnspc 0.496 0.004 128.776 0.000 0.488
## .Stst28mchnclrs 0.315 0.002 133.351 0.000 0.310
## .Stst30vslztn3D 0.374 0.003 110.592 0.000 0.367
## .Stest1vocab 0.303 0.002 138.919 0.000 0.298
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.479 0.473 0.503
## 0.475 0.469 0.539
## 0.527 0.520 0.572
## 0.276 0.272 0.313
## 0.466 0.459 0.516
## 0.547 0.540 0.614
## 0.413 0.408 0.426
## 0.211 0.207 0.231
## 0.483 0.477 0.512
## 0.423 0.416 0.414
## 0.416 0.411 0.428
## 0.125 0.116 0.121
## 0.509 0.502 0.548
## 0.595 0.587 0.623
## 0.395 0.385 0.477
## 0.436 0.427 0.468
## 0.503 0.496 0.547
## 0.320 0.315 0.434
## 0.380 0.374 0.405
## 0.307 0.303 0.325
## 1.000 1.000 1.000
## 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 =~ 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 math =~ Stest5math 1
## 11 math =~ Stest25wordfunctions 1
## 12 math =~ Stest32arithreasoning 1
## 13 math =~ Stest33highschoolmath 1
## 14 math =~ Stest34arithcomputation 1
## 15 speed =~ Stest19disguisedwords 1
## 16 speed =~ Stest29visualization2D 1
## 17 speed =~ Stest34arithcomputation 1
## 18 speed =~ Stest35tablereading 1
## 19 speed =~ Stest36clericalchecking 1
## 20 speed =~ Stest37objectinspection 1
## 21 spatial =~ Stest28mechanicalreasoning 1
## 22 spatial =~ Stest29visualization2D 1
## 23 spatial =~ Stest30visualization3D 1
## 24 spatial =~ Stest31abstractreasoning 1
## 25 spatial =~ Stest37objectinspection 1
## 26 g =~ Stest1vocab 1
## 27 g =~ Stest5math 1
## 28 g =~ Stest19disguisedwords 1
## 29 g =~ Stest20spelling 1
## 30 g =~ Stest21capitalization 1
## 31 g =~ Stest22punctuation 1
## 32 g =~ Stest23english 1
## 33 g =~ Stest24expression 1
## 34 g =~ Stest25wordfunctions 1
## 35 g =~ Stest26readingcomprehension 1
## 36 g =~ Stest28mechanicalreasoning 1
## 37 g =~ Stest29visualization2D 1
## 38 g =~ Stest30visualization3D 1
## 39 g =~ Stest31abstractreasoning 1
## 40 g =~ Stest32arithreasoning 1
## 41 g =~ Stest33highschoolmath 1
## 42 g =~ Stest34arithcomputation 1
## 43 g =~ Stest35tablereading 1
## 44 g =~ Stest36clericalchecking 1
## 45 g =~ Stest37objectinspection 1
## 46 Stest19disguisedwords ~~ Stest19disguisedwords 1
## 47 Stest20spelling ~~ Stest20spelling 1
## 48 Stest21capitalization ~~ Stest21capitalization 1
## 49 Stest22punctuation ~~ Stest22punctuation 1
## 50 Stest23english ~~ Stest23english 1
## 51 Stest24expression ~~ Stest24expression 1
## 52 Stest25wordfunctions ~~ Stest25wordfunctions 1
## 53 Stest26readingcomprehension ~~ Stest26readingcomprehension 1
## 54 Stest31abstractreasoning ~~ Stest31abstractreasoning 1
## 55 Stest5math ~~ Stest5math 1
## 56 Stest32arithreasoning ~~ Stest32arithreasoning 1
## 57 Stest33highschoolmath ~~ Stest33highschoolmath 1
## 58 Stest34arithcomputation ~~ Stest34arithcomputation 1
## 59 Stest29visualization2D ~~ Stest29visualization2D 1
## 60 Stest35tablereading ~~ Stest35tablereading 1
## 61 Stest36clericalchecking ~~ Stest36clericalchecking 1
## 62 Stest37objectinspection ~~ Stest37objectinspection 1
## 63 Stest28mechanicalreasoning ~~ Stest28mechanicalreasoning 1
## 64 Stest30visualization3D ~~ Stest30visualization3D 1
## 65 Stest1vocab ~~ Stest1vocab 1
## 66 english ~~ english 1
## 67 math ~~ math 1
## 68 speed ~~ speed 1
## 69 spatial ~~ spatial 1
## 70 g ~~ g 1
## 71 english ~~ math 1
## 72 english ~~ speed 1
## 73 english ~~ spatial 1
## 74 english ~~ g 1
## 75 math ~~ speed 1
## 76 math ~~ spatial 1
## 77 math ~~ g 1
## 78 speed ~~ spatial 1
## 79 speed ~~ g 1
## 80 spatial ~~ g 1
## 81 Stest19disguisedwords ~1 1
## 82 Stest20spelling ~1 1
## 83 Stest21capitalization ~1 1
## 84 Stest22punctuation ~1 1
## 85 Stest23english ~1 1
## 86 Stest24expression ~1 1
## 87 Stest25wordfunctions ~1 1
## 88 Stest26readingcomprehension ~1 1
## 89 Stest31abstractreasoning ~1 1
## 90 Stest5math ~1 1
## label est.std se z pvalue ci.lower ci.upper
## 1 .p1. 0.181 0.002 81.595 0 0.177 0.185
## 2 .p2. 0.343 0.003 130.957 0 0.338 0.348
## 3 .p3. 0.318 0.002 133.549 0 0.314 0.323
## 4 .p4. 0.347 0.002 150.971 0 0.342 0.351
## 5 .p5. 0.253 0.002 114.950 0 0.249 0.258
## 6 .p6. 0.199 0.002 96.291 0 0.195 0.204
## 7 .p7. 0.252 0.002 126.341 0 0.248 0.256
## 8 .p8. 0.063 0.003 19.000 0 0.057 0.070
## 9 .p9. 0.111 0.002 59.227 0 0.107 0.114
## 10 .p10. 0.306 0.003 100.011 0 0.300 0.312
## 11 .p11. 0.165 0.003 55.992 0 0.159 0.170
## 12 .p12. 0.190 0.003 64.388 0 0.185 0.196
## 13 .p13. 0.581 0.004 143.969 0 0.573 0.589
## 14 .p14. 0.265 0.004 74.295 0 0.258 0.272
## 15 .p15. 0.290 0.003 111.569 0 0.285 0.295
## 16 .p16. 0.229 0.003 76.025 0 0.223 0.235
## 17 .p17. 0.371 0.003 135.997 0 0.366 0.376
## 18 .p18. 0.601 0.003 178.394 0 0.595 0.608
## 19 .p19. 0.703 0.003 231.041 0 0.697 0.709
## 20 .p20. 0.572 0.003 203.823 0 0.566 0.577
## 21 .p21. 0.496 0.003 172.578 0 0.490 0.502
## 22 .p22. 0.461 0.003 149.435 0 0.455 0.467
## 23 .p23. 0.574 0.003 190.988 0 0.569 0.580
## 24 .p24. 0.344 0.003 122.682 0 0.338 0.349
## 25 .p25. 0.239 0.003 81.821 0 0.234 0.245
## 26 .p26. 0.842 0.001 675.415 0 0.839 0.844
## 27 .p27. 0.759 0.002 424.751 0 0.755 0.762
## 28 .p28. 0.619 0.002 308.944 0 0.615 0.623
## 29 .p29. 0.551 0.002 239.091 0 0.547 0.556
## 30 .p30. 0.573 0.002 249.159 0 0.568 0.577
## 31 .p31. 0.727 0.002 423.836 0 0.723 0.730
## 32 .p32. 0.617 0.002 288.456 0 0.612 0.621
## 33 .p33. 0.543 0.002 229.958 0 0.538 0.547
## 34 .p34. 0.696 0.002 415.312 0 0.693 0.700
## 35 .p35. 0.847 0.001 617.074 0 0.844 0.850
## 36 .p36. 0.559 0.002 243.253 0 0.555 0.564
## 37 .p37. 0.344 0.003 125.327 0 0.339 0.350
## 38 .p38. 0.477 0.002 193.493 0 0.473 0.482
## 39 .p39. 0.591 0.002 275.623 0 0.587 0.595
## 40 .p40. 0.743 0.002 453.154 0 0.739 0.746
## 41 .p41. 0.724 0.002 428.088 0 0.720 0.727
## 42 .p42. 0.489 0.003 189.991 0 0.484 0.494
## 43 .p43. 0.255 0.003 81.462 0 0.249 0.261
## 44 .p44. 0.125 0.003 41.424 0 0.119 0.131
## 45 .p45. 0.132 0.003 45.875 0 0.127 0.138
## 46 0.499 0.002 201.664 0 0.495 0.504
## 47 0.579 0.003 223.013 0 0.573 0.584
## 48 0.570 0.003 212.506 0 0.565 0.576
## 49 0.352 0.002 155.627 0 0.347 0.356
## 50 0.556 0.003 210.706 0 0.550 0.561
## 51 0.666 0.003 259.650 0 0.661 0.671
## 52 0.424 0.002 196.817 0 0.420 0.429
## 53 0.279 0.002 127.568 0 0.274 0.283
## 54 0.520 0.003 196.603 0 0.515 0.526
## 55 0.331 0.002 143.116 0 0.326 0.335
## 56 0.412 0.002 183.218 0 0.408 0.417
## 57 0.138 0.004 30.828 0 0.130 0.147
## 58 0.553 0.003 187.000 0 0.548 0.559
## 59 0.616 0.003 190.643 0 0.610 0.623
## 60 0.574 0.004 134.445 0 0.565 0.582
## 61 0.491 0.004 114.707 0 0.482 0.499
## 62 0.598 0.003 174.925 0 0.591 0.605
## 63 0.441 0.003 144.922 0 0.435 0.447
## 64 0.442 0.003 129.873 0 0.436 0.449
## 65 0.292 0.002 139.162 0 0.288 0.296
## 66 1.000 0.000 NA NA 1.000 1.000
## 67 1.000 0.000 NA NA 1.000 1.000
## 68 1.000 0.000 NA NA 1.000 1.000
## 69 1.000 0.000 NA NA 1.000 1.000
## 70 1.000 0.000 NA NA 1.000 1.000
## 71 0.000 0.000 NA NA 0.000 0.000
## 72 0.000 0.000 NA NA 0.000 0.000
## 73 0.000 0.000 NA NA 0.000 0.000
## 74 0.000 0.000 NA NA 0.000 0.000
## 75 0.000 0.000 NA NA 0.000 0.000
## 76 0.000 0.000 NA NA 0.000 0.000
## 77 0.000 0.000 NA NA 0.000 0.000
## 78 0.000 0.000 NA NA 0.000 0.000
## 79 0.000 0.000 NA NA 0.000 0.000
## 80 0.000 0.000 NA NA 0.000 0.000
## 81 .p81. -0.136 0.004 -34.144 0 -0.144 -0.128
## 82 .p82. -0.271 0.004 -67.257 0 -0.279 -0.263
## 83 .p83. -0.218 0.004 -53.788 0 -0.226 -0.210
## 84 .p84. -0.220 0.004 -54.170 0 -0.228 -0.212
## 85 .p85. -0.149 0.004 -37.098 0 -0.157 -0.141
## 86 .p86. -0.100 0.004 -25.186 0 -0.108 -0.093
## 87 .p87. -0.134 0.004 -34.404 0 -0.142 -0.127
## 88 -0.033 0.004 -7.941 0 -0.041 -0.025
## 89 .p89. 0.060 0.004 15.089 0 0.053 0.068
## 90 .p90. 0.153 0.004 36.801 0 0.144 0.161
## [ reached 'max' / getOption("max.print") -- omitted 120 rows ]
tests<-lavTestLRT(configural, metric, scalar2, chc.bifactor)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 4693.293 2326.845 1229.364
dfd=tests[2:4,"Df diff"]
dfd
## [1] 40 11 5
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04045611 0.05442424 0.05869543
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.03948273 0.04143782
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.05257352 0.05629796
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.0559577 0.0614805
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 0 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
## 1.000 1.000 1.000 0.223 0.000 0.000
tests<-lavTestLRT(configural, metric, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 4693.293 22493.463
dfd=tests[2:3,"Df diff"]
dfd
## [1] 40 15
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04045611 0.14520167
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.03948273 0.04143782
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.1436111 0.1467976
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] 4693.293 2326.845 4724.868
dfd=tests[2:4,"Df diff"]
dfd
## [1] 40 11 20
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-71381 + 70776 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04045611 0.05442424 0.05752977
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.03948273 0.04143782
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.05257352 0.05629796
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.05615469 0.05891662
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 0 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
## 1.000 1.000 1.000 0.002 0.000 0.000
bf.age <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest31abstractreasoning
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g=~ Stest1vocab + Stest5math + 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
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest19disguisedwords + Stest29visualization2D + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g=~ Stest1vocab + Stest5math + 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("Stest28mechanicalreasoning~1", "Stest34arithcomputation~1", "Stest29visualization2D~1", "Stest26readingcomprehension~1"))
fitMeasures(sem.age, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 74693.344 384.000 0.000 0.948 0.052 0.052
## ecvi aic bic
## 0.527 6471091.259 6472235.563
Mc(sem.age)
## [1] 0.7699994
summary(sem.age, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 54 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 177
## Number of equality constraints 61
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 74693.344 63653.071
## Degrees of freedom 384 384
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.173
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 38625.946 32916.722
## 1 36067.398 30736.348
##
## 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.) 0.175 0.002 82.740 0.000 0.171
## Stst20s (.p2.) 0.333 0.003 131.603 0.000 0.328
## Stst21c (.p3.) 0.302 0.002 134.895 0.000 0.298
## Stst22p (.p4.) 0.333 0.002 150.118 0.000 0.328
## Stst23n (.p5.) 0.249 0.002 111.258 0.000 0.244
## Stst24x (.p6.) 0.200 0.002 92.522 0.000 0.196
## Stst25w (.p7.) 0.246 0.002 126.334 0.000 0.242
## Stst26r (.p8.) 0.060 0.003 18.217 0.000 0.053
## Stst31b (.p9.) 0.108 0.002 58.213 0.000 0.104
## math =~
## Stst5mt (.10.) 0.288 0.003 99.031 0.000 0.283
## Stst25w (.11.) 0.161 0.003 56.677 0.000 0.156
## Stst32r (.12.) 0.185 0.003 65.111 0.000 0.180
## Stst33h (.13.) 0.575 0.004 142.964 0.000 0.567
## Stst34r (.14.) 0.255 0.003 74.634 0.000 0.248
## speed =~
## Stst19d (.15.) 0.280 0.003 110.489 0.000 0.275
## Sts292D (.16.) 0.221 0.003 77.031 0.000 0.215
## Stst34r (.17.) 0.357 0.003 130.893 0.000 0.352
## Stst35t (.18.) 0.597 0.003 177.204 0.000 0.590
## Stst36c (.19.) 0.685 0.003 219.539 0.000 0.679
## Stst37b (.20.) 0.578 0.003 192.469 0.000 0.572
## spatial =~
## Stst28m (.21.) 0.426 0.003 167.554 0.000 0.421
## Sts292D (.22.) 0.444 0.003 147.413 0.000 0.439
## Sts303D (.23.) 0.570 0.003 188.476 0.000 0.564
## Stst31b (.24.) 0.336 0.003 120.399 0.000 0.330
## Stst37b (.25.) 0.241 0.003 80.851 0.000 0.235
## g =~
## Stst1vc (.26.) 0.786 0.002 367.629 0.000 0.782
## Stst5mt (.27.) 0.705 0.002 313.791 0.000 0.701
## Stst19d (.28.) 0.594 0.002 251.537 0.000 0.590
## Stst20s (.29.) 0.534 0.003 207.498 0.000 0.529
## Stst21c (.30.) 0.541 0.003 211.574 0.000 0.536
## Stst22p (.31.) 0.692 0.002 298.921 0.000 0.688
## Stst23n (.32.) 0.603 0.003 224.398 0.000 0.598
## Stst24x (.33.) 0.543 0.003 200.603 0.000 0.538
## Stst25w (.34.) 0.675 0.002 317.342 0.000 0.671
## Stst26r (.35.) 0.823 0.002 397.988 0.000 0.819
## Stst28m (.36.) 0.475 0.002 207.356 0.000 0.471
## Sts292D (.37.) 0.328 0.003 118.109 0.000 0.323
## Sts303D (.38.) 0.470 0.003 176.515 0.000 0.464
## Stst31b (.39.) 0.571 0.003 213.492 0.000 0.566
## Stst32r (.40.) 0.711 0.002 332.590 0.000 0.707
## Stst33h (.41.) 0.706 0.002 305.953 0.000 0.702
## Stst34r (.42.) 0.467 0.003 164.927 0.000 0.462
## Stst35t (.43.) 0.252 0.003 79.489 0.000 0.246
## Stst36c (.44.) 0.122 0.003 41.994 0.000 0.116
## Stst37b (.45.) 0.134 0.003 45.976 0.000 0.128
## ci.upper Std.lv Std.all
##
## 0.179 0.175 0.181
## 0.338 0.333 0.342
## 0.307 0.302 0.318
## 0.337 0.333 0.346
## 0.253 0.249 0.252
## 0.204 0.200 0.198
## 0.249 0.246 0.252
## 0.066 0.060 0.061
## 0.112 0.108 0.111
##
## 0.294 0.288 0.308
## 0.167 0.161 0.165
## 0.191 0.185 0.192
## 0.583 0.575 0.584
## 0.261 0.255 0.265
##
## 0.285 0.280 0.290
## 0.226 0.221 0.229
## 0.362 0.357 0.371
## 0.604 0.597 0.601
## 0.691 0.685 0.702
## 0.584 0.578 0.572
##
## 0.431 0.426 0.497
## 0.450 0.444 0.462
## 0.575 0.570 0.574
## 0.341 0.336 0.344
## 0.247 0.241 0.239
##
## 0.790 0.792 0.841
## 0.709 0.710 0.758
## 0.599 0.599 0.619
## 0.539 0.538 0.552
## 0.546 0.545 0.573
## 0.697 0.698 0.726
## 0.608 0.607 0.617
## 0.549 0.547 0.543
## 0.679 0.680 0.696
## 0.827 0.829 0.847
## 0.480 0.479 0.559
## 0.334 0.331 0.344
## 0.475 0.473 0.477
## 0.576 0.575 0.590
## 0.715 0.716 0.742
## 0.711 0.712 0.722
## 0.473 0.471 0.489
## 0.259 0.254 0.256
## 0.128 0.123 0.126
## 0.139 0.135 0.133
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.097 0.004 26.719 0.000 0.090
## ci.upper Std.lv Std.all
##
## 0.104 0.097 0.120
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.79.) -0.125 0.004 -32.620 0.000 -0.133
## .Stst20s (.80.) -0.258 0.004 -65.684 0.000 -0.266
## .Stst21c (.81.) -0.202 0.004 -52.396 0.000 -0.209
## .Stst22p (.82.) -0.204 0.004 -51.258 0.000 -0.212
## .Stst23n (.83.) -0.140 0.004 -34.358 0.000 -0.148
## .Stst24x (.84.) -0.094 0.004 -22.870 0.000 -0.102
## .Stst25w (.85.) -0.124 0.004 -32.161 0.000 -0.131
## .Stst26r -0.023 0.004 -5.669 0.000 -0.031
## .Stst31b (.87.) 0.065 0.004 16.768 0.000 0.057
## .Stst5mt (.88.) 0.151 0.004 40.635 0.000 0.144
## .Stst32r (.89.) 0.165 0.004 45.356 0.000 0.158
## .Stst33h (.90.) 0.132 0.004 31.186 0.000 0.123
## .Stst34r -0.073 0.004 -18.406 0.000 -0.081
## .Sts292D 0.215 0.004 55.375 0.000 0.208
## .Stst35t (.93.) -0.071 0.004 -19.767 0.000 -0.078
## .Stst36c (.94.) -0.149 0.004 -40.695 0.000 -0.156
## .Stst37b (.95.) -0.074 0.004 -20.120 0.000 -0.081
## .Stst28m 0.541 0.004 152.651 0.000 0.534
## .Sts303D (.97.) 0.188 0.004 46.511 0.000 0.180
## .Stst1vc (.98.) 0.184 0.004 49.426 0.000 0.176
## ci.upper Std.lv Std.all
## -0.118 -0.125 -0.130
## -0.250 -0.258 -0.265
## -0.194 -0.202 -0.212
## -0.196 -0.204 -0.213
## -0.132 -0.140 -0.142
## -0.086 -0.094 -0.094
## -0.116 -0.124 -0.127
## -0.015 -0.023 -0.024
## 0.072 0.065 0.067
## 0.158 0.151 0.161
## 0.173 0.165 0.171
## 0.140 0.132 0.134
## -0.065 -0.073 -0.076
## 0.223 0.215 0.224
## -0.064 -0.071 -0.071
## -0.142 -0.149 -0.152
## -0.067 -0.074 -0.073
## 0.548 0.541 0.631
## 0.196 0.188 0.189
## 0.191 0.184 0.195
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.467 0.003 159.211 0.000 0.462
## .Stest20spellng 0.550 0.003 159.847 0.000 0.544
## .Stest21cptlztn 0.516 0.003 162.041 0.000 0.510
## .Stest22puncttn 0.325 0.002 133.413 0.000 0.320
## .Stest23english 0.539 0.004 143.180 0.000 0.531
## .Stest24exprssn 0.676 0.004 155.406 0.000 0.667
## .Stst25wrdfnctn 0.405 0.003 150.993 0.000 0.400
## .Stst26rdngcmpr 0.267 0.002 115.978 0.000 0.262
## .Stst31bstrctrs 0.494 0.003 152.103 0.000 0.488
## .Stest5math 0.291 0.003 97.704 0.000 0.285
## .Stst32rthrsnng 0.384 0.002 157.762 0.000 0.380
## .Stst33hghschlm 0.134 0.004 30.781 0.000 0.125
## .Stst34rthcmptt 0.513 0.004 138.721 0.000 0.506
## .Stst29vslztn2D 0.571 0.004 130.122 0.000 0.563
## .Stest35tblrdng 0.566 0.007 76.293 0.000 0.551
## .Stst36clrclchc 0.467 0.005 86.125 0.000 0.457
## .Stst37bjctnspc 0.612 0.005 125.753 0.000 0.602
## .Stst28mchnclrs 0.324 0.003 124.914 0.000 0.319
## .Stst30vslztn3D 0.435 0.004 111.593 0.000 0.427
## .Stest1vocab 0.258 0.002 126.073 0.000 0.254
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.473 0.467 0.500
## 0.557 0.550 0.579
## 0.522 0.516 0.571
## 0.330 0.325 0.352
## 0.546 0.539 0.556
## 0.684 0.676 0.666
## 0.411 0.405 0.425
## 0.271 0.267 0.278
## 0.501 0.494 0.521
## 0.297 0.291 0.331
## 0.389 0.384 0.413
## 0.142 0.134 0.138
## 0.520 0.513 0.554
## 0.580 0.571 0.616
## 0.581 0.566 0.573
## 0.478 0.467 0.491
## 0.621 0.612 0.598
## 0.329 0.324 0.441
## 0.443 0.435 0.442
## 0.262 0.258 0.292
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 0.985 0.985
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.175 0.002 82.740 0.000 0.171
## Stst20s (.p2.) 0.333 0.003 131.603 0.000 0.328
## Stst21c (.p3.) 0.302 0.002 134.895 0.000 0.298
## Stst22p (.p4.) 0.333 0.002 150.118 0.000 0.328
## Stst23n (.p5.) 0.249 0.002 111.258 0.000 0.244
## Stst24x (.p6.) 0.200 0.002 92.522 0.000 0.196
## Stst25w (.p7.) 0.246 0.002 126.334 0.000 0.242
## Stst26r (.p8.) 0.060 0.003 18.217 0.000 0.053
## Stst31b (.p9.) 0.108 0.002 58.213 0.000 0.104
## math =~
## Stst5mt (.10.) 0.288 0.003 99.031 0.000 0.283
## Stst25w (.11.) 0.161 0.003 56.677 0.000 0.156
## Stst32r (.12.) 0.185 0.003 65.111 0.000 0.180
## Stst33h (.13.) 0.575 0.004 142.964 0.000 0.567
## Stst34r (.14.) 0.255 0.003 74.634 0.000 0.248
## speed =~
## Stst19d (.15.) 0.280 0.003 110.489 0.000 0.275
## Sts292D (.16.) 0.221 0.003 77.031 0.000 0.215
## Stst34r (.17.) 0.357 0.003 130.893 0.000 0.352
## Stst35t (.18.) 0.597 0.003 177.204 0.000 0.590
## Stst36c (.19.) 0.685 0.003 219.539 0.000 0.679
## Stst37b (.20.) 0.578 0.003 192.469 0.000 0.572
## spatial =~
## Stst28m (.21.) 0.426 0.003 167.554 0.000 0.421
## Sts292D (.22.) 0.444 0.003 147.413 0.000 0.439
## Sts303D (.23.) 0.570 0.003 188.476 0.000 0.564
## Stst31b (.24.) 0.336 0.003 120.399 0.000 0.330
## Stst37b (.25.) 0.241 0.003 80.851 0.000 0.235
## g =~
## Stst1vc (.26.) 0.786 0.002 367.629 0.000 0.782
## Stst5mt (.27.) 0.705 0.002 313.791 0.000 0.701
## Stst19d (.28.) 0.594 0.002 251.537 0.000 0.590
## Stst20s (.29.) 0.534 0.003 207.498 0.000 0.529
## Stst21c (.30.) 0.541 0.003 211.574 0.000 0.536
## Stst22p (.31.) 0.692 0.002 298.921 0.000 0.688
## Stst23n (.32.) 0.603 0.003 224.398 0.000 0.598
## Stst24x (.33.) 0.543 0.003 200.603 0.000 0.538
## Stst25w (.34.) 0.675 0.002 317.342 0.000 0.671
## Stst26r (.35.) 0.823 0.002 397.988 0.000 0.819
## Stst28m (.36.) 0.475 0.002 207.356 0.000 0.471
## Sts292D (.37.) 0.328 0.003 118.109 0.000 0.323
## Sts303D (.38.) 0.470 0.003 176.515 0.000 0.464
## Stst31b (.39.) 0.571 0.003 213.492 0.000 0.566
## Stst32r (.40.) 0.711 0.002 332.590 0.000 0.707
## Stst33h (.41.) 0.706 0.002 305.953 0.000 0.702
## Stst34r (.42.) 0.467 0.003 164.927 0.000 0.462
## Stst35t (.43.) 0.252 0.003 79.489 0.000 0.246
## Stst36c (.44.) 0.122 0.003 41.994 0.000 0.116
## Stst37b (.45.) 0.134 0.003 45.976 0.000 0.128
## ci.upper Std.lv Std.all
##
## 0.179 0.175 0.180
## 0.338 0.333 0.357
## 0.307 0.302 0.317
## 0.337 0.333 0.356
## 0.253 0.249 0.263
## 0.204 0.200 0.213
## 0.249 0.246 0.251
## 0.066 0.060 0.063
## 0.112 0.108 0.112
##
## 0.294 0.288 0.288
## 0.167 0.161 0.165
## 0.191 0.185 0.189
## 0.583 0.575 0.589
## 0.261 0.255 0.266
##
## 0.285 0.280 0.288
## 0.226 0.221 0.227
## 0.362 0.357 0.373
## 0.604 0.597 0.665
## 0.691 0.685 0.718
## 0.584 0.578 0.607
##
## 0.431 0.426 0.499
## 0.450 0.444 0.458
## 0.575 0.570 0.593
## 0.341 0.336 0.347
## 0.247 0.241 0.253
##
## 0.790 0.793 0.822
## 0.709 0.711 0.709
## 0.599 0.599 0.618
## 0.539 0.539 0.578
## 0.546 0.546 0.572
## 0.697 0.699 0.749
## 0.608 0.608 0.644
## 0.549 0.548 0.584
## 0.679 0.681 0.696
## 0.827 0.830 0.876
## 0.480 0.479 0.563
## 0.334 0.331 0.341
## 0.475 0.474 0.493
## 0.576 0.576 0.596
## 0.715 0.717 0.732
## 0.711 0.713 0.730
## 0.473 0.471 0.492
## 0.259 0.255 0.284
## 0.128 0.123 0.129
## 0.139 0.135 0.142
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.111 0.003 31.847 0.000 0.105
## ci.upper Std.lv Std.all
##
## 0.118 0.110 0.132
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.79.) -0.125 0.004 -32.620 0.000 -0.133
## .Stst20s (.80.) -0.258 0.004 -65.684 0.000 -0.266
## .Stst21c (.81.) -0.202 0.004 -52.396 0.000 -0.209
## .Stst22p (.82.) -0.204 0.004 -51.258 0.000 -0.212
## .Stst23n (.83.) -0.140 0.004 -34.358 0.000 -0.148
## .Stst24x (.84.) -0.094 0.004 -22.870 0.000 -0.102
## .Stst25w (.85.) -0.124 0.004 -32.161 0.000 -0.131
## .Stst26r 0.274 0.008 32.945 0.000 0.258
## .Stst31b (.87.) 0.065 0.004 16.768 0.000 0.057
## .Stst5mt (.88.) 0.151 0.004 40.635 0.000 0.144
## .Stst32r (.89.) 0.165 0.004 45.356 0.000 0.158
## .Stst33h (.90.) 0.132 0.004 31.186 0.000 0.123
## .Stst34r 0.164 0.004 36.656 0.000 0.155
## .Sts292D -0.026 0.005 -5.266 0.000 -0.035
## .Stst35t (.93.) -0.071 0.004 -19.767 0.000 -0.078
## .Stst36c (.94.) -0.149 0.004 -40.695 0.000 -0.156
## .Stst37b (.95.) -0.074 0.004 -20.120 0.000 -0.081
## .Stst28m -0.161 0.004 -36.294 0.000 -0.170
## .Sts303D (.97.) 0.188 0.004 46.511 0.000 0.180
## .Stst1vc (.98.) 0.184 0.004 49.426 0.000 0.176
## english 2.220 0.017 127.578 0.000 2.186
## math 0.084 0.009 9.818 0.000 0.067
## speed 0.422 0.007 59.034 0.000 0.408
## spatial -0.219 0.009 -25.021 0.000 -0.236
## .g -0.342 0.007 -50.026 0.000 -0.356
## ci.upper Std.lv Std.all
## -0.118 -0.125 -0.129
## -0.250 -0.258 -0.277
## -0.194 -0.202 -0.212
## -0.196 -0.204 -0.219
## -0.132 -0.140 -0.148
## -0.086 -0.094 -0.100
## -0.116 -0.124 -0.127
## 0.290 0.274 0.289
## 0.072 0.065 0.067
## 0.158 0.151 0.150
## 0.173 0.165 0.169
## 0.140 0.132 0.135
## 0.172 0.164 0.171
## -0.016 -0.026 -0.027
## -0.064 -0.071 -0.079
## -0.142 -0.149 -0.156
## -0.067 -0.074 -0.078
## -0.152 -0.161 -0.189
## 0.196 0.188 0.195
## 0.191 0.184 0.190
## 2.254 2.220 2.220
## 0.101 0.084 0.084
## 0.436 0.422 0.422
## -0.202 -0.219 -0.219
## -0.329 -0.340 -0.340
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.473 0.003 162.230 0.000 0.468
## .Stest20spellng 0.469 0.003 157.781 0.000 0.463
## .Stest21cptlztn 0.520 0.003 162.118 0.000 0.514
## .Stest22puncttn 0.272 0.002 126.174 0.000 0.268
## .Stest23english 0.459 0.003 144.973 0.000 0.453
## .Stest24exprssn 0.540 0.004 149.395 0.000 0.533
## .Stst25wrdfnctn 0.408 0.003 144.039 0.000 0.402
## .Stst26rdngcmpr 0.206 0.002 108.687 0.000 0.202
## .Stst31bstrctrs 0.478 0.003 155.279 0.000 0.472
## .Stest5math 0.416 0.004 108.467 0.000 0.409
## .Stst32rthrsnng 0.411 0.002 165.706 0.000 0.406
## .Stst33hghschlm 0.115 0.005 25.469 0.000 0.106
## .Stst34rthcmptt 0.502 0.004 133.743 0.000 0.494
## .Stst29vslztn2D 0.587 0.004 149.676 0.000 0.580
## .Stest35tblrdng 0.385 0.005 74.180 0.000 0.374
## .Stst36clrclchc 0.427 0.004 98.622 0.000 0.419
## .Stst37bjctnspc 0.496 0.004 128.803 0.000 0.488
## .Stst28mchnclrs 0.315 0.002 133.328 0.000 0.311
## .Stst30vslztn3D 0.374 0.003 110.676 0.000 0.367
## .Stest1vocab 0.302 0.002 138.907 0.000 0.298
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.479 0.473 0.503
## 0.475 0.469 0.539
## 0.527 0.520 0.572
## 0.277 0.272 0.313
## 0.465 0.459 0.515
## 0.547 0.540 0.613
## 0.413 0.408 0.426
## 0.210 0.206 0.229
## 0.484 0.478 0.512
## 0.424 0.416 0.414
## 0.416 0.411 0.428
## 0.124 0.115 0.121
## 0.509 0.502 0.548
## 0.595 0.587 0.623
## 0.395 0.385 0.477
## 0.436 0.427 0.468
## 0.503 0.496 0.547
## 0.320 0.315 0.434
## 0.380 0.374 0.405
## 0.306 0.302 0.325
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 0.983 0.983
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("Stest28mechanicalreasoning~1", "Stest34arithcomputation~1", "Stest29visualization2D~1", "Stest26readingcomprehension~1"))
fitMeasures(sem.age2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 75367.055 422.000 0.000 0.948 0.050 0.050
## ecvi aic bic
## 0.532 6469900.248 6471064.281
Mc(sem.age2)
## [1] 0.7682797
summary(sem.age2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 56 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 179
## Number of equality constraints 61
##
## Number of observations per group:
## 0 70776
## 1 71381
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 75367.055 64231.063
## Degrees of freedom 422 422
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.173
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 38942.325 33188.333
## 1 36424.730 31042.730
##
## 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.) 0.175 0.002 82.826 0.000 0.171
## Stst20s (.p2.) 0.333 0.003 131.757 0.000 0.328
## Stst21c (.p3.) 0.302 0.002 135.047 0.000 0.298
## Stst22p (.p4.) 0.333 0.002 150.253 0.000 0.328
## Stst23n (.p5.) 0.249 0.002 111.347 0.000 0.244
## Stst24x (.p6.) 0.200 0.002 92.606 0.000 0.196
## Stst25w (.p7.) 0.246 0.002 126.446 0.000 0.242
## Stst26r (.p8.) 0.060 0.003 18.362 0.000 0.054
## Stst31b (.p9.) 0.108 0.002 58.235 0.000 0.104
## math =~
## Stst5mt (.10.) 0.288 0.003 98.879 0.000 0.282
## Stst25w (.11.) 0.161 0.003 56.582 0.000 0.156
## Stst32r (.12.) 0.185 0.003 65.062 0.000 0.180
## Stst33h (.13.) 0.575 0.004 142.729 0.000 0.567
## Stst34r (.14.) 0.255 0.003 74.534 0.000 0.248
## speed =~
## Stst19d (.15.) 0.280 0.003 110.410 0.000 0.275
## Sts292D (.16.) 0.221 0.003 77.013 0.000 0.215
## Stst34r (.17.) 0.357 0.003 130.846 0.000 0.351
## Stst35t (.18.) 0.597 0.003 177.176 0.000 0.590
## Stst36c (.19.) 0.685 0.003 219.483 0.000 0.679
## Stst37b (.20.) 0.578 0.003 192.436 0.000 0.572
## spatial =~
## Stst28m (.21.) 0.425 0.003 167.530 0.000 0.420
## Sts292D (.22.) 0.444 0.003 147.372 0.000 0.438
## Sts303D (.23.) 0.570 0.003 188.447 0.000 0.564
## Stst31b (.24.) 0.336 0.003 120.401 0.000 0.330
## Stst37b (.25.) 0.241 0.003 80.794 0.000 0.235
## g =~
## Stst1vc (.26.) 0.782 0.002 367.215 0.000 0.778
## Stst5mt (.27.) 0.702 0.002 314.497 0.000 0.698
## Stst19d (.28.) 0.592 0.002 251.798 0.000 0.587
## Stst20s (.29.) 0.532 0.003 207.485 0.000 0.527
## Stst21c (.30.) 0.538 0.003 211.737 0.000 0.533
## Stst22p (.31.) 0.689 0.002 298.864 0.000 0.685
## Stst23n (.32.) 0.600 0.003 224.467 0.000 0.595
## Stst24x (.33.) 0.541 0.003 200.730 0.000 0.536
## Stst25w (.34.) 0.672 0.002 317.397 0.000 0.668
## Stst26r (.35.) 0.819 0.002 397.430 0.000 0.815
## Stst28m (.36.) 0.473 0.002 207.502 0.000 0.469
## Sts292D (.37.) 0.327 0.003 118.266 0.000 0.322
## Sts303D (.38.) 0.467 0.003 176.440 0.000 0.462
## Stst31b (.39.) 0.568 0.003 213.616 0.000 0.563
## Stst32r (.40.) 0.708 0.002 332.203 0.000 0.704
## Stst33h (.41.) 0.703 0.002 306.178 0.000 0.699
## Stst34r (.42.) 0.465 0.003 165.068 0.000 0.460
## Stst35t (.43.) 0.252 0.003 79.641 0.000 0.245
## Stst36c (.44.) 0.122 0.003 42.129 0.000 0.116
## Stst37b (.45.) 0.133 0.003 46.130 0.000 0.128
## ci.upper Std.lv Std.all
##
## 0.179 0.175 0.181
## 0.338 0.333 0.341
## 0.307 0.302 0.318
## 0.337 0.333 0.346
## 0.253 0.249 0.252
## 0.204 0.200 0.198
## 0.249 0.246 0.251
## 0.066 0.060 0.061
## 0.112 0.108 0.111
##
## 0.293 0.288 0.307
## 0.167 0.161 0.165
## 0.191 0.185 0.192
## 0.583 0.575 0.583
## 0.261 0.255 0.264
##
## 0.285 0.280 0.289
## 0.226 0.221 0.229
## 0.362 0.357 0.370
## 0.603 0.597 0.601
## 0.691 0.685 0.702
## 0.584 0.578 0.572
##
## 0.430 0.425 0.496
## 0.450 0.444 0.462
## 0.575 0.570 0.574
## 0.341 0.336 0.344
## 0.247 0.241 0.239
##
## 0.786 0.793 0.842
## 0.706 0.712 0.759
## 0.596 0.600 0.620
## 0.537 0.539 0.553
## 0.543 0.546 0.574
## 0.694 0.699 0.727
## 0.605 0.608 0.617
## 0.546 0.548 0.544
## 0.676 0.681 0.697
## 0.823 0.831 0.848
## 0.478 0.480 0.559
## 0.332 0.331 0.344
## 0.473 0.474 0.478
## 0.573 0.576 0.591
## 0.712 0.717 0.743
## 0.708 0.713 0.723
## 0.471 0.472 0.490
## 0.258 0.255 0.257
## 0.127 0.123 0.126
## 0.139 0.135 0.134
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.089 0.004 25.116 0.000 0.082
## age2 -0.061 0.002 -24.957 0.000 -0.066
## ci.upper Std.lv Std.all
##
## 0.096 0.088 0.110
## -0.056 -0.060 -0.112
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.82.) -0.069 0.004 -15.410 0.000 -0.078
## .Stst20s (.83.) -0.208 0.004 -46.777 0.000 -0.216
## .Stst21c (.84.) -0.151 0.004 -34.595 0.000 -0.159
## .Stst22p (.85.) -0.139 0.005 -29.197 0.000 -0.148
## .Stst23n (.86.) -0.083 0.005 -17.885 0.000 -0.092
## .Stst24x (.87.) -0.043 0.005 -9.374 0.000 -0.052
## .Stst25w (.88.) -0.060 0.005 -12.855 0.000 -0.069
## .Stst26r 0.055 0.005 10.647 0.000 0.044
## .Stst31b (.90.) 0.119 0.004 27.142 0.000 0.110
## .Stst5mt (.91.) 0.218 0.005 47.612 0.000 0.209
## .Stst32r (.92.) 0.233 0.005 51.378 0.000 0.224
## .Stst33h (.93.) 0.198 0.005 39.122 0.000 0.188
## .Stst34r -0.029 0.004 -6.606 0.000 -0.037
## .Sts292D 0.246 0.004 60.733 0.000 0.239
## .Stst35t (.96.) -0.047 0.004 -12.836 0.000 -0.054
## .Stst36c (.97.) -0.137 0.004 -37.385 0.000 -0.144
## .Stst37b (.98.) -0.062 0.004 -16.540 0.000 -0.069
## .Stst28m 0.586 0.004 148.337 0.000 0.578
## .Sts303D (.100) 0.232 0.004 52.494 0.000 0.223
## .Stst1vc (.101) 0.258 0.005 54.682 0.000 0.249
## ci.upper Std.lv Std.all
## -0.060 -0.069 -0.071
## -0.199 -0.208 -0.213
## -0.142 -0.151 -0.158
## -0.129 -0.139 -0.144
## -0.074 -0.083 -0.084
## -0.034 -0.043 -0.043
## -0.051 -0.060 -0.061
## 0.065 0.055 0.056
## 0.127 0.119 0.122
## 0.227 0.218 0.232
## 0.242 0.233 0.241
## 0.208 0.198 0.201
## -0.020 -0.029 -0.030
## 0.254 0.246 0.256
## -0.040 -0.047 -0.047
## -0.130 -0.137 -0.141
## -0.054 -0.062 -0.061
## 0.594 0.586 0.684
## 0.241 0.232 0.234
## 0.267 0.258 0.274
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.468 0.003 159.231 0.000 0.462
## .Stest20spellng 0.550 0.003 159.840 0.000 0.544
## .Stest21cptlztn 0.516 0.003 162.046 0.000 0.510
## .Stest22puncttn 0.325 0.002 133.420 0.000 0.320
## .Stest23english 0.539 0.004 143.178 0.000 0.532
## .Stest24exprssn 0.676 0.004 155.396 0.000 0.667
## .Stst25wrdfnctn 0.405 0.003 151.004 0.000 0.400
## .Stst26rdngcmpr 0.267 0.002 116.129 0.000 0.262
## .Stst31bstrctrs 0.494 0.003 152.103 0.000 0.488
## .Stest5math 0.291 0.003 97.669 0.000 0.285
## .Stst32rthrsnng 0.385 0.002 157.780 0.000 0.380
## .Stst33hghschlm 0.134 0.004 30.694 0.000 0.125
## .Stst34rthcmptt 0.513 0.004 138.710 0.000 0.506
## .Stst29vslztn2D 0.571 0.004 130.127 0.000 0.563
## .Stest35tblrdng 0.566 0.007 76.289 0.000 0.551
## .Stst36clrclchc 0.467 0.005 86.122 0.000 0.457
## .Stst37bjctnspc 0.612 0.005 125.755 0.000 0.602
## .Stst28mchnclrs 0.324 0.003 124.903 0.000 0.319
## .Stst30vslztn3D 0.435 0.004 111.576 0.000 0.427
## .Stest1vocab 0.258 0.002 126.094 0.000 0.254
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.473 0.468 0.500
## 0.557 0.550 0.578
## 0.522 0.516 0.570
## 0.330 0.325 0.352
## 0.546 0.539 0.555
## 0.684 0.676 0.665
## 0.411 0.405 0.424
## 0.271 0.267 0.278
## 0.501 0.494 0.520
## 0.296 0.291 0.330
## 0.389 0.385 0.412
## 0.142 0.134 0.138
## 0.520 0.513 0.553
## 0.580 0.571 0.616
## 0.580 0.566 0.573
## 0.478 0.467 0.491
## 0.621 0.612 0.598
## 0.329 0.324 0.441
## 0.443 0.435 0.442
## 0.262 0.258 0.291
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 0.973 0.973
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.175 0.002 82.826 0.000 0.171
## Stst20s (.p2.) 0.333 0.003 131.757 0.000 0.328
## Stst21c (.p3.) 0.302 0.002 135.047 0.000 0.298
## Stst22p (.p4.) 0.333 0.002 150.253 0.000 0.328
## Stst23n (.p5.) 0.249 0.002 111.347 0.000 0.244
## Stst24x (.p6.) 0.200 0.002 92.606 0.000 0.196
## Stst25w (.p7.) 0.246 0.002 126.446 0.000 0.242
## Stst26r (.p8.) 0.060 0.003 18.362 0.000 0.054
## Stst31b (.p9.) 0.108 0.002 58.235 0.000 0.104
## math =~
## Stst5mt (.10.) 0.288 0.003 98.879 0.000 0.282
## Stst25w (.11.) 0.161 0.003 56.582 0.000 0.156
## Stst32r (.12.) 0.185 0.003 65.062 0.000 0.180
## Stst33h (.13.) 0.575 0.004 142.729 0.000 0.567
## Stst34r (.14.) 0.255 0.003 74.534 0.000 0.248
## speed =~
## Stst19d (.15.) 0.280 0.003 110.410 0.000 0.275
## Sts292D (.16.) 0.221 0.003 77.013 0.000 0.215
## Stst34r (.17.) 0.357 0.003 130.846 0.000 0.351
## Stst35t (.18.) 0.597 0.003 177.176 0.000 0.590
## Stst36c (.19.) 0.685 0.003 219.483 0.000 0.679
## Stst37b (.20.) 0.578 0.003 192.436 0.000 0.572
## spatial =~
## Stst28m (.21.) 0.425 0.003 167.530 0.000 0.420
## Sts292D (.22.) 0.444 0.003 147.372 0.000 0.438
## Sts303D (.23.) 0.570 0.003 188.447 0.000 0.564
## Stst31b (.24.) 0.336 0.003 120.401 0.000 0.330
## Stst37b (.25.) 0.241 0.003 80.794 0.000 0.235
## g =~
## Stst1vc (.26.) 0.782 0.002 367.215 0.000 0.778
## Stst5mt (.27.) 0.702 0.002 314.497 0.000 0.698
## Stst19d (.28.) 0.592 0.002 251.798 0.000 0.587
## Stst20s (.29.) 0.532 0.003 207.485 0.000 0.527
## Stst21c (.30.) 0.538 0.003 211.737 0.000 0.533
## Stst22p (.31.) 0.689 0.002 298.864 0.000 0.685
## Stst23n (.32.) 0.600 0.003 224.467 0.000 0.595
## Stst24x (.33.) 0.541 0.003 200.730 0.000 0.536
## Stst25w (.34.) 0.672 0.002 317.397 0.000 0.668
## Stst26r (.35.) 0.819 0.002 397.430 0.000 0.815
## Stst28m (.36.) 0.473 0.002 207.502 0.000 0.469
## Sts292D (.37.) 0.327 0.003 118.266 0.000 0.322
## Sts303D (.38.) 0.467 0.003 176.440 0.000 0.462
## Stst31b (.39.) 0.568 0.003 213.616 0.000 0.563
## Stst32r (.40.) 0.708 0.002 332.203 0.000 0.704
## Stst33h (.41.) 0.703 0.002 306.178 0.000 0.699
## Stst34r (.42.) 0.465 0.003 165.068 0.000 0.460
## Stst35t (.43.) 0.252 0.003 79.641 0.000 0.245
## Stst36c (.44.) 0.122 0.003 42.129 0.000 0.116
## Stst37b (.45.) 0.133 0.003 46.130 0.000 0.128
## ci.upper Std.lv Std.all
##
## 0.179 0.175 0.180
## 0.338 0.333 0.357
## 0.307 0.302 0.317
## 0.337 0.333 0.357
## 0.253 0.249 0.264
## 0.204 0.200 0.213
## 0.249 0.246 0.251
## 0.066 0.060 0.063
## 0.112 0.108 0.112
##
## 0.293 0.288 0.287
## 0.167 0.161 0.165
## 0.191 0.185 0.189
## 0.583 0.575 0.589
## 0.261 0.255 0.266
##
## 0.285 0.280 0.288
## 0.226 0.221 0.227
## 0.362 0.357 0.373
## 0.603 0.597 0.665
## 0.691 0.685 0.718
## 0.584 0.578 0.607
##
## 0.430 0.425 0.500
## 0.450 0.444 0.458
## 0.575 0.570 0.593
## 0.341 0.336 0.348
## 0.247 0.241 0.253
##
## 0.786 0.791 0.821
## 0.706 0.710 0.709
## 0.596 0.598 0.617
## 0.537 0.538 0.577
## 0.543 0.545 0.571
## 0.694 0.697 0.748
## 0.605 0.607 0.644
## 0.546 0.547 0.584
## 0.676 0.680 0.695
## 0.823 0.829 0.875
## 0.478 0.479 0.562
## 0.332 0.331 0.341
## 0.473 0.473 0.493
## 0.573 0.575 0.595
## 0.712 0.716 0.732
## 0.708 0.712 0.729
## 0.471 0.471 0.492
## 0.258 0.254 0.284
## 0.127 0.123 0.129
## 0.139 0.135 0.142
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.091 0.004 24.273 0.000 0.083
## age2 -0.048 0.003 -17.550 0.000 -0.053
## ci.upper Std.lv Std.all
##
## 0.098 0.090 0.107
## -0.042 -0.047 -0.079
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.82.) -0.069 0.004 -15.410 0.000 -0.078
## .Stst20s (.83.) -0.208 0.004 -46.777 0.000 -0.216
## .Stst21c (.84.) -0.151 0.004 -34.595 0.000 -0.159
## .Stst22p (.85.) -0.139 0.005 -29.197 0.000 -0.148
## .Stst23n (.86.) -0.083 0.005 -17.885 0.000 -0.092
## .Stst24x (.87.) -0.043 0.005 -9.374 0.000 -0.052
## .Stst25w (.88.) -0.060 0.005 -12.855 0.000 -0.069
## .Stst26r 0.351 0.009 39.549 0.000 0.334
## .Stst31b (.90.) 0.119 0.004 27.142 0.000 0.110
## .Stst5mt (.91.) 0.218 0.005 47.612 0.000 0.209
## .Stst32r (.92.) 0.233 0.005 51.378 0.000 0.224
## .Stst33h (.93.) 0.198 0.005 39.122 0.000 0.188
## .Stst34r 0.208 0.005 42.842 0.000 0.198
## .Sts292D 0.005 0.005 1.026 0.305 -0.005
## .Stst35t (.96.) -0.047 0.004 -12.836 0.000 -0.054
## .Stst36c (.97.) -0.137 0.004 -37.385 0.000 -0.144
## .Stst37b (.98.) -0.062 0.004 -16.540 0.000 -0.069
## .Stst28m -0.116 0.005 -24.081 0.000 -0.126
## .Sts303D (.100) 0.232 0.004 52.494 0.000 0.223
## .Stst1vc (.101) 0.258 0.005 54.682 0.000 0.249
## english 2.220 0.017 127.720 0.000 2.186
## math 0.085 0.009 9.868 0.000 0.068
## speed 0.422 0.007 59.058 0.000 0.408
## spatial -0.219 0.009 -25.011 0.000 -0.236
## .g -0.374 0.009 -43.246 0.000 -0.390
## ci.upper Std.lv Std.all
## -0.060 -0.069 -0.071
## -0.199 -0.208 -0.223
## -0.142 -0.151 -0.158
## -0.129 -0.139 -0.149
## -0.074 -0.083 -0.088
## -0.034 -0.043 -0.046
## -0.051 -0.060 -0.061
## 0.368 0.351 0.371
## 0.127 0.119 0.123
## 0.227 0.218 0.217
## 0.242 0.233 0.238
## 0.208 0.198 0.203
## 0.217 0.208 0.217
## 0.015 0.005 0.005
## -0.040 -0.047 -0.052
## -0.130 -0.137 -0.144
## -0.054 -0.062 -0.065
## -0.107 -0.116 -0.136
## 0.241 0.232 0.242
## 0.267 0.258 0.268
## 2.254 2.220 2.220
## 0.102 0.085 0.085
## 0.436 0.422 0.422
## -0.202 -0.219 -0.219
## -0.357 -0.369 -0.369
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.473 0.003 162.261 0.000 0.468
## .Stest20spellng 0.469 0.003 157.784 0.000 0.463
## .Stest21cptlztn 0.520 0.003 162.120 0.000 0.514
## .Stest22puncttn 0.272 0.002 126.179 0.000 0.268
## .Stest23english 0.459 0.003 144.988 0.000 0.453
## .Stest24exprssn 0.540 0.004 149.390 0.000 0.533
## .Stst25wrdfnctn 0.408 0.003 144.044 0.000 0.402
## .Stst26rdngcmpr 0.206 0.002 108.819 0.000 0.203
## .Stst31bstrctrs 0.478 0.003 155.284 0.000 0.472
## .Stest5math 0.416 0.004 108.461 0.000 0.409
## .Stst32rthrsnng 0.411 0.002 165.782 0.000 0.406
## .Stst33hghschlm 0.115 0.005 25.394 0.000 0.106
## .Stst34rthcmptt 0.502 0.004 133.732 0.000 0.494
## .Stst29vslztn2D 0.587 0.004 149.680 0.000 0.580
## .Stest35tblrdng 0.385 0.005 74.179 0.000 0.374
## .Stst36clrclchc 0.427 0.004 98.620 0.000 0.419
## .Stst37bjctnspc 0.496 0.004 128.811 0.000 0.488
## .Stst28mchnclrs 0.315 0.002 133.336 0.000 0.311
## .Stst30vslztn3D 0.374 0.003 110.654 0.000 0.367
## .Stest1vocab 0.302 0.002 138.922 0.000 0.298
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.479 0.473 0.503
## 0.475 0.469 0.539
## 0.527 0.520 0.573
## 0.277 0.272 0.313
## 0.465 0.459 0.516
## 0.547 0.540 0.614
## 0.413 0.408 0.426
## 0.210 0.206 0.230
## 0.484 0.478 0.512
## 0.424 0.416 0.415
## 0.416 0.411 0.429
## 0.124 0.115 0.121
## 0.509 0.502 0.548
## 0.595 0.587 0.623
## 0.395 0.385 0.477
## 0.436 0.427 0.468
## 0.503 0.496 0.547
## 0.320 0.315 0.435
## 0.380 0.374 0.405
## 0.306 0.302 0.325
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 0.977 0.977
MGCFA FOR BLACKS
dmale<- subset(db, sex==0)
dfemale<- subset(db, sex==1)
datamale<- select(dmale, starts_with("Stest"), -Stest2literature, -Stest3music, -Stest4socialstudies, -Stest6physicalscience, -Stest7biologicalscience, -Stest8aeronautics, -Stest9electronics, -Stest10mechanics, -Stest11art, -Stest12law, -Stest13health, -Stest14bible, -Stest15theater, -Stest16miscellaneous, -Stest17memsentences, -Stest18memwords, -Stest27creativity)
datafemale<- select(dfemale, starts_with("Stest"), -Stest2literature, -Stest3music, -Stest4socialstudies, -Stest6physicalscience, -Stest7biologicalscience, -Stest8aeronautics, -Stest9electronics, -Stest10mechanics, -Stest11art, -Stest12law, -Stest13health, -Stest14bible, -Stest15theater, -Stest16miscellaneous, -Stest17memsentences, -Stest18memwords, -Stest27creativity)
datagroup<- select(db, starts_with("Stest"), -Stest2literature, -Stest3music, -Stest4socialstudies, -Stest6physicalscience, -Stest7biologicalscience, -Stest8aeronautics, -Stest9electronics, -Stest10mechanics, -Stest11art, -Stest12law, -Stest13health, -Stest14bible, -Stest15theater, -Stest16miscellaneous, -Stest17memsentences, -Stest18memwords, -Stest27creativity)
dgroup<- select(db, starts_with("Stest"), wb, age, age2, sex, BY_WTA, -Stest2literature, -Stest3music, -Stest4socialstudies, -Stest6physicalscience, -Stest7biologicalscience, -Stest8aeronautics, -Stest9electronics, -Stest10mechanics, -Stest11art, -Stest12law, -Stest13health, -Stest14bible, -Stest15theater, -Stest16miscellaneous, -Stest17memsentences, -Stest18memwords, -Stest27creativity)
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
## Stest5math 2 2443 -0.79 1.05 -0.70 -0.76 1.13
## Stest19disguisedwords 3 2443 -0.97 0.88 -1.18 -1.07 0.87
## Stest20spelling 4 2443 -0.83 1.00 -0.93 -0.85 1.00
## Stest21capitalization 5 2443 -1.14 0.95 -1.41 -1.24 0.92
## Stest22punctuation 6 2443 -1.21 1.00 -1.28 -1.23 1.01
## Stest23english 7 2443 -1.04 1.18 -1.03 -1.01 0.95
## Stest24expression 8 2443 -0.95 1.17 -0.90 -0.92 1.36
## Stest25wordfunctions 9 2443 -0.86 0.78 -0.93 -0.91 0.77
## Stest26readingcomprehension 10 2443 -1.26 1.08 -1.46 -1.34 1.19
## Stest28mechanicalreasoning 11 2443 -0.69 0.90 -0.76 -0.75 1.05
## Stest29visualization2D 12 2443 -0.49 1.10 -0.45 -0.53 1.36
## Stest30visualization3D 13 2443 -0.69 0.95 -0.65 -0.73 0.93
## Stest31abstractreasoning 14 2443 -1.02 1.14 -0.90 -1.04 1.60
## Stest32arithreasoning 15 2443 -1.03 0.85 -1.18 -1.11 0.85
## Stest33highschoolmath 16 2443 -0.85 0.80 -0.93 -0.94 0.60
## Stest34arithcomputation 17 2443 -1.14 1.14 -1.18 -1.19 1.21
## Stest35tablereading 18 2443 -0.68 1.65 -0.49 -0.60 1.29
## Stest36clericalchecking 19 2443 0.00 1.30 -0.41 -0.09 1.18
## Stest37objectinspection 20 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
## Stest5math -3.10 1.58 4.68 -0.29 -0.19 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
## Stest5math 2 3642 -0.94 0.99 -0.70 -0.91 1.04
## Stest19disguisedwords 3 3642 -0.84 0.95 -1.03 -0.94 0.87
## Stest20spelling 4 3642 -0.42 0.97 -0.26 -0.42 1.00
## Stest21capitalization 5 3642 -0.86 1.02 -1.14 -0.94 1.18
## Stest22punctuation 6 3642 -0.90 0.98 -1.05 -0.92 1.01
## Stest23english 7 3642 -0.70 1.09 -0.71 -0.68 0.95
## Stest24expression 8 3642 -0.67 1.08 -0.44 -0.64 1.36
## Stest25wordfunctions 9 3642 -0.78 0.80 -0.93 -0.83 0.77
## Stest26readingcomprehension 10 3642 -1.19 0.98 -1.36 -1.25 1.04
## Stest28mechanicalreasoning 11 3642 -1.30 0.62 -1.47 -1.35 0.70
## Stest29visualization2D 12 3642 -0.90 0.99 -1.00 -0.98 1.08
## Stest30visualization3D 13 3642 -0.96 0.77 -0.97 -0.99 0.93
## Stest31abstractreasoning 14 3642 -1.20 1.10 -1.26 -1.24 1.06
## Stest32arithreasoning 15 3642 -1.17 0.74 -1.18 -1.24 0.85
## Stest33highschoolmath 16 3642 -0.92 0.70 -1.13 -0.98 0.60
## Stest34arithcomputation 17 3642 -1.01 1.13 -1.08 -1.04 1.06
## Stest35tablereading 18 3642 -0.50 1.59 -0.28 -0.41 1.18
## Stest36clericalchecking 19 3642 0.30 1.28 0.02 0.25 1.40
## Stest37objectinspection 20 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
## Stest5math -3.10 1.58 4.68 -0.35 -0.13 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] 8.6583961 1.8139087 1.2964261 0.8394189 0.6715033 0.6574052
## [7] 0.6062938 0.5585229 0.5293081 0.5094921 0.4730171 0.4523746
## [13] 0.4433373 0.4322079 0.4114139 0.4033314 0.3684169 0.3479582
## [19] 0.3240996 0.2031679
##
## $vectors
## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.27587266 -0.10282264 0.079699440 -0.004943307 -0.0003010366
## [2,] -0.23490802 -0.05383064 0.092226077 -0.407624215 -0.0437092848
## [3,] -0.24232997 0.04985263 0.166654652 0.155197989 0.3783830403
## [4,] -0.22087608 -0.09070136 0.362479102 0.180310911 0.1745655120
## [5,] -0.24952078 -0.08881315 0.081954710 0.209096489 0.0386618377
## [6,] -0.26571917 -0.09480855 0.088371026 0.134199229 0.0352794871
## [7,] -0.24757144 -0.07554141 0.096769961 0.340361709 -0.0361968976
## [8,] -0.20949649 -0.13920656 0.074492746 0.387528332 -0.4384058605
## [9,] -0.21081560 -0.08518498 0.030539915 -0.281954859 0.4709854580
## [10,] -0.28982442 -0.13578165 0.069881120 -0.001069219 0.0274009778
## [11,] -0.23279410 0.01572243 -0.376293285 0.008968547 0.0592197173
## [12,] -0.18013889 0.19478006 -0.385145593 0.247830712 0.1710201580
## [13,] -0.18725398 0.03049985 -0.528691130 -0.041076618 0.0794297081
## [14,] -0.23841109 -0.01621751 -0.308041425 0.015146618 -0.1126800400
## [15,] -0.24802767 -0.10710501 -0.050362916 -0.335679838 -0.1828278293
## [16,] -0.25725064 -0.08856373 0.005645796 -0.383065650 -0.1291394100
## [17,] -0.22471366 0.21505445 0.200145850 -0.130334250 -0.2538587959
## [18,] -0.15070074 0.45391647 0.094238940 -0.083569209 -0.4085552245
## [19,] -0.06946434 0.55426969 0.253221203 -0.083609985 0.2690004226
## [20,] -0.10216877 0.53848398 -0.103709225 0.127145391 0.0053410545
## [,6] [,7] [,8] [,9] [,10]
## [1,] 0.31378510 0.013977152 -0.0941892189 -0.02166546 0.17055764
## [2,] 0.30771782 -0.001122891 -0.2763833547 -0.34477574 0.11709507
## [3,] 0.26702281 -0.078573839 -0.0251530701 0.18542115 0.10279451
## [4,] -0.07544474 0.381377575 -0.0734527012 -0.07762637 -0.12763302
## [5,] -0.11886970 0.291158383 0.2871681261 0.04843912 0.06240718
## [6,] -0.16412736 0.109259720 0.2256829994 0.06368338 -0.06848582
## [7,] 0.10621666 -0.105315973 0.0125221386 0.03198304 0.04700293
## [8,] -0.06451370 -0.568614024 -0.1574225989 -0.12981041 -0.30805773
## [9,] -0.50766488 -0.504308582 0.1902546628 0.02946663 0.09784008
## [10,] 0.16209258 -0.064863109 -0.0121329123 0.07962908 0.09542644
## [11,] 0.28849273 -0.035330513 0.0340642736 0.16307908 0.09297491
## [12,] -0.34231253 0.090428198 -0.6535837466 -0.11849236 0.26698379
## [13,] 0.09280695 0.096347219 0.0712191850 0.17314336 -0.56950253
## [14,] -0.11858436 0.189404941 0.2433602308 -0.06593199 0.03412464
## [15,] 0.01667687 -0.096910074 -0.0002351783 0.09577629 -0.05231279
## [16,] -0.07052804 0.086160967 -0.0226086600 -0.13722586 -0.04788017
## [17,] -0.33980079 0.246179472 -0.0835687709 -0.16603595 -0.20534510
## [18,] -0.09276441 -0.034642578 0.0394627547 0.56966555 0.34533237
## [19,] 0.13403408 -0.085552370 -0.1691092064 0.13117256 -0.45798668
## [20,] 0.13775909 -0.134166345 0.4286641372 -0.58009556 0.15602867
## [,11] [,12] [,13] [,14] [,15]
## [1,] 0.03291043 -0.136070786 0.03849895 -0.007479012 -0.022406326
## [2,] 0.46600850 -0.081406443 -0.19201269 0.161494095 0.085967647
## [3,] -0.28719454 0.436029359 -0.20992183 -0.112208906 0.416003022
## [4,] 0.12015069 0.401881054 0.02178972 0.001796907 -0.575446774
## [5,] -0.10593163 -0.416407407 -0.35315772 0.429670254 0.216355018
## [6,] 0.05067500 -0.272153666 0.16821129 0.083807203 -0.162483007
## [7,] 0.29551248 -0.056284664 0.57812389 -0.105263311 0.231020932
## [8,] -0.02531616 0.029147399 -0.28304714 0.010024816 -0.089158320
## [9,] 0.20117584 0.017501563 0.02938124 -0.005469309 -0.023055635
## [10,] -0.10737056 -0.007263245 -0.06423536 -0.003620065 -0.001034437
## [11,] -0.08935490 -0.249453384 0.22764521 -0.250382490 -0.236208579
## [12,] -0.11610559 -0.052760965 -0.01415583 0.124860654 -0.039123234
## [13,] 0.25067602 0.285249292 0.03423453 0.339835385 0.128308814
## [14,] 0.13633306 0.021320082 -0.40682675 -0.648427001 -0.028434695
## [15,] -0.56570794 0.046879270 0.16396546 0.148168510 -0.197416639
## [16,] -0.15845216 0.075289487 0.01586886 -0.015141133 -0.013044307
## [17,] -0.09873062 0.033325531 0.26522812 -0.209078276 0.447979776
## [18,] 0.24637095 0.180120790 -0.07852809 0.144191651 -0.102028578
## [19,] -0.03328796 -0.398835961 -0.12296765 -0.162328132 -0.124659455
## [20,] -0.10724243 0.155130938 0.08536003 0.176464784 -0.111675015
## [,16] [,17] [,18] [,19] [,20]
## [1,] -0.23985689 0.441446035 -0.085985393 -0.428094313 0.5524085732
## [2,] 0.03689746 -0.065300222 -0.015610347 0.395543119 -0.0723313439
## [3,] -0.03154124 -0.205114409 -0.141946279 0.199235762 0.1243878181
## [4,] -0.06476584 0.001703979 0.236262917 0.045283911 -0.0113480707
## [5,] 0.03223332 -0.075190816 0.377279849 0.006721102 0.0216394271
## [6,] -0.06071606 -0.127504982 -0.758251084 0.243114370 0.0493833998
## [7,] 0.49585511 -0.070471838 0.199504697 -0.030013820 -0.0018296105
## [8,] -0.13927396 -0.105348460 0.035888918 0.026906019 0.0512466525
## [9,] -0.10421261 0.085558941 0.152677787 -0.031898160 0.0513987576
## [10,] -0.02432767 0.297614594 -0.137938645 -0.302300756 -0.7940741421
## [11,] -0.46483057 -0.311572938 0.288889765 0.186819487 -0.0864660765
## [12,] 0.10698234 0.011487168 -0.083799143 -0.023894461 -0.0014687845
## [13,] -0.03059368 0.112509218 -0.032383531 -0.083238700 0.0177381723
## [14,] 0.28541851 0.160367847 -0.018669441 0.054469564 0.0640062005
## [15,] 0.35420828 0.276546018 0.105800826 0.345856794 0.1183256226
## [16,] 0.15130516 -0.620412539 -0.065055847 -0.530435178 0.0606000591
## [17,] -0.39541859 0.157510817 0.084296033 0.103540531 -0.0662013613
## [18,] -0.01596519 -0.043759540 -0.007123298 -0.017983431 0.0166500427
## [19,] 0.19895764 0.010411563 0.022362003 -0.079147270 0.0003565032
## [20,] 0.00258874 0.033282479 -0.026867769 -0.041264880 -0.0325029568
eigen(femalecor) # all eigenvalues different from zero
## eigen() decomposition
## $values
## [1] 8.0218295 1.8291878 1.2389828 0.9232200 0.7076098 0.6672964
## [7] 0.6511390 0.6050737 0.6002025 0.5421577 0.5330719 0.5186053
## [13] 0.5010382 0.4565058 0.4454519 0.4363057 0.3958557 0.3569285
## [19] 0.3260553 0.2434826
##
## $vectors
## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.27549182 -0.09058894 -0.13391032 0.06465275 -0.154194043
## [2,] -0.20639785 -0.06937211 -0.02669664 0.52731342 0.276347821
## [3,] -0.26266049 0.10024704 -0.12719730 -0.09664043 -0.251497964
## [4,] -0.23320969 -0.01513397 -0.37305282 -0.11263146 -0.000675705
## [5,] -0.25892242 -0.06201150 -0.12485676 -0.18316663 -0.052568702
## [6,] -0.28480324 -0.08716956 -0.09286358 -0.10744280 0.102292421
## [7,] -0.25303471 -0.07007348 -0.12610928 -0.27821701 0.003314375
## [8,] -0.20242030 -0.10820614 -0.06806613 -0.46283102 0.140305356
## [9,] -0.23045259 -0.11901955 0.01382859 0.28698571 -0.022251697
## [10,] -0.29600735 -0.11092670 -0.08929235 -0.03397010 -0.117254025
## [11,] -0.19637241 -0.04866721 0.33767490 0.08876923 -0.674028575
## [12,] -0.16759997 0.10851243 0.47060980 -0.16971728 0.410769412
## [13,] -0.17163698 -0.01041844 0.54050174 -0.09606301 0.021440526
## [14,] -0.24049023 -0.06801830 0.26751966 -0.13810953 0.087936941
## [15,] -0.23363969 -0.14368283 0.09288839 0.24381527 -0.075770942
## [16,] -0.25331102 -0.09441883 0.01770885 0.35822632 0.190296038
## [17,] -0.22222910 0.25307608 -0.17891975 0.09805546 0.268682274
## [18,] -0.15790472 0.45677869 -0.06730470 -0.01509676 0.063241777
## [19,] -0.06219771 0.57454126 -0.07786850 0.11182326 -0.199061261
## [20,] -0.11556391 0.52051836 0.14946442 -0.02009681 -0.020723072
## [,6] [,7] [,8] [,9] [,10]
## [1,] -0.230649710 -0.018983709 -0.100148351 0.039987415 0.208674413
## [2,] -0.411474818 0.220436495 -0.380278395 0.230364552 0.009135734
## [3,] -0.295283218 -0.153414514 0.065790265 -0.160760415 0.118841940
## [4,] -0.110428517 -0.303083567 -0.002955792 -0.053116029 -0.200952826
## [5,] 0.135940801 -0.207894938 -0.049979785 0.044274645 0.096170042
## [6,] 0.058003885 -0.113459284 0.021842600 -0.041694971 -0.105397994
## [7,] -0.050177669 0.020131442 -0.113949979 0.031190892 -0.295702022
## [8,] 0.005020240 0.736936408 -0.020073852 0.020003507 -0.075165237
## [9,] 0.169881360 0.192408141 0.156084924 -0.533971475 0.016846754
## [10,] -0.098086731 -0.010550767 -0.041903802 0.003881148 0.187106811
## [11,] 0.003625086 0.063255720 0.168493696 0.451349589 -0.178206445
## [12,] -0.440266424 -0.140566967 0.522798050 0.024355863 0.032851759
## [13,] 0.108915269 -0.228440143 -0.592108193 -0.309332521 -0.063394166
## [14,] 0.159440091 -0.046465421 -0.065741759 0.088945236 0.295739927
## [15,] 0.298441159 0.143904436 0.316755572 -0.268714220 0.057372142
## [16,] 0.127582078 -0.005739864 0.088418845 0.188961171 -0.192941396
## [17,] 0.348415989 -0.224579651 0.122970674 0.177528692 -0.229766107
## [18,] 0.262047646 0.087918809 -0.055024580 0.233778489 0.610768350
## [19,] -0.272874795 0.114099743 0.022865178 -0.349342665 -0.033511124
## [20,] 0.119312755 0.170045364 -0.122858360 0.049247696 -0.401668167
## [,11] [,12] [,13] [,14] [,15]
## [1,] -0.048626535 0.244483529 -0.21687018 -0.20924159 -0.145767357
## [2,] -0.037686198 -0.044924827 0.04254792 0.16637066 0.155795730
## [3,] -0.030454283 0.092212750 0.01995326 -0.27720179 -0.250275148
## [4,] 0.193958036 -0.079474352 -0.02163109 -0.20817117 0.483456910
## [5,] -0.349331228 0.015954148 0.09741888 0.40005858 0.426148262
## [6,] -0.074997427 -0.079650673 0.08466285 0.20326646 0.055329285
## [7,] 0.015287947 -0.196112459 -0.21445099 0.48895510 -0.555197939
## [8,] 0.220129764 0.002457415 0.12837033 -0.19785823 0.160858032
## [9,] -0.325599717 -0.555403908 -0.07572860 -0.18754522 -0.008062176
## [10,] -0.028289025 0.178329130 -0.13816773 -0.13653237 -0.086177806
## [11,] 0.118934353 -0.263215854 0.06119673 -0.00408548 0.123359120
## [12,] 0.005639457 -0.077134726 -0.15925500 0.03368073 0.088663695
## [13,] 0.337505457 -0.044990617 -0.09613582 -0.08359312 0.069906129
## [14,] -0.290567592 0.140785827 0.60596051 -0.07504621 -0.172123968
## [15,] 0.272722506 0.521469576 -0.17451166 0.30857365 0.100020666
## [16,] 0.085260281 0.048490068 0.12088125 -0.08867167 -0.156669383
## [17,] 0.238685811 -0.039543879 0.16008183 -0.23858643 -0.173329291
## [18,] 0.161720236 -0.272664476 -0.30219836 0.08571279 0.033119842
## [19,] 0.206047754 0.008330159 0.44893117 0.27172755 -0.008654189
## [20,] -0.504738820 0.301185214 -0.27793193 -0.14142872 0.092083938
## [,16] [,17] [,18] [,19]
## [1,] -0.1208113564 0.048334049 0.547387682 0.135395194
## [2,] 0.0150558106 -0.301409929 -0.150660915 -0.102208894
## [3,] -0.1592731502 -0.047820679 -0.665955206 -0.200059778
## [4,] 0.5557937073 0.039678754 0.055200412 -0.105750715
## [5,] -0.4481154658 0.154103481 0.043765798 -0.317971839
## [6,] -0.0636631385 -0.101392542 -0.231350829 0.841068635
## [7,] 0.2252470783 -0.018792413 0.079761629 -0.209683904
## [8,] -0.1456698241 0.043181556 -0.028433873 -0.048971630
## [9,] 0.0103391007 -0.053211375 0.104143867 -0.069100009
## [10,] -0.0754360634 0.014364351 0.165001067 0.137269714
## [11,] -0.0002695756 -0.105721779 0.023197772 0.027905977
## [12,] -0.0336668275 0.003597163 0.096214026 -0.040986896
## [13,] -0.1143557531 0.059286644 -0.006857047 -0.015318112
## [14,] 0.4237702955 -0.116666117 0.069328372 -0.073897406
## [15,] 0.1495270111 -0.189539067 -0.104100780 -0.097962309
## [16,] -0.0131670524 0.771292294 -0.114977767 -0.006373877
## [17,] -0.3359503549 -0.417615455 0.165540253 -0.123182237
## [18,] 0.1484549821 0.104492641 -0.116596513 0.042233187
## [19,] -0.0386448798 0.138616415 0.220710962 0.072257374
## [20,] 0.1247829053 -0.001436042 -0.045022365 0.039477273
## [,20]
## [1,] 0.5021757761
## [2,] -0.0189771729
## [3,] 0.1291669483
## [4,] 0.0090738688
## [5,] 0.0282944471
## [6,] 0.1110277170
## [7,] -0.0003557049
## [8,] 0.0545581491
## [9,] 0.0023576905
## [10,] -0.8372348592
## [11,] 0.0084134772
## [12,] -0.0109352507
## [13,] 0.0182381115
## [14,] 0.0416188666
## [15,] 0.0681363164
## [16,] 0.0062511859
## [17,] -0.0227793453
## [18,] 0.0440730910
## [19,] -0.0636986976
## [20,] -0.0128485450
mpa<- fa.parallel(malecor, n.obs=2443, n.iter=1000)
## Parallel analysis suggests that the number of factors = 5 and the number of components = 3
fpa<- fa.parallel(femalecor, n.obs=3642, n.iter=1000)
## Parallel analysis suggests that the number of factors = 5 and the number of components = 3
mqqnorm(datafemale, main = "Multi-normal Q-Q Plot") # very minor
## 4858 3006
## 2415 563
mqqnorm(datamale, main = "Multi-normal Q-Q Plot") # very minor
## [1] 2159 2241
mqqnorm(datagroup, main = "Multi-normal Q-Q Plot") # very minor
## [1] 2159 3006
mvn(data = datamale, mvnTest = "mardia")
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 5198.45570681991 0 NO
## 2 Mardia Kurtosis 8.94471073737084 0 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value
## 1 Anderson-Darling Stest1vocab 17.2962 <0.001
## 2 Anderson-Darling Stest5math 19.8829 <0.001
## 3 Anderson-Darling Stest19disguisedwords 60.6622 <0.001
## 4 Anderson-Darling Stest20spelling 13.5916 <0.001
## 5 Anderson-Darling Stest21capitalization 79.2095 <0.001
## 6 Anderson-Darling Stest22punctuation 7.0268 <0.001
## 7 Anderson-Darling Stest23english 9.7213 <0.001
## 8 Anderson-Darling Stest24expression 21.4125 <0.001
## 9 Anderson-Darling Stest25wordfunctions 23.0605 <0.001
## 10 Anderson-Darling Stest26readingcomprehension 39.6555 <0.001
## 11 Anderson-Darling Stest28mechanicalreasoning 22.9034 <0.001
## 12 Anderson-Darling Stest29visualization2D 22.3567 <0.001
## 13 Anderson-Darling Stest30visualization3D 19.6763 <0.001
## 14 Anderson-Darling Stest31abstractreasoning 21.9210 <0.001
## 15 Anderson-Darling Stest32arithreasoning 48.8610 <0.001
## 16 Anderson-Darling Stest33highschoolmath 49.4632 <0.001
## 17 Anderson-Darling Stest34arithcomputation 5.6482 <0.001
## 18 Anderson-Darling Stest35tablereading 26.8353 <0.001
## 19 Anderson-Darling Stest36clericalchecking 70.2704 <0.001
## 20 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
##
## $Descriptives
## n Mean Std.Dev Median
## Stest1vocab 2443 -1.1095892563 1.0621130 -1.3076552
## Stest5math 2443 -0.7896922969 1.0531123 -0.7002896
## 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
## Stest5math -3.103322 1.578247 -1.4629972 -0.19790688
## 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 0.3451069 -0.5997669
## Stest5math -0.2883481 -0.1940244
## Stest19disguisedwords 1.0608678 0.7255663
## Stest20spelling 0.2312739 -0.3140564
## Stest21capitalization 0.8070777 -0.2315324
## Stest22punctuation 0.1822344 -0.2204551
## Stest23english -0.2516029 0.2185956
## Stest24expression -0.1804949 -0.6694891
## Stest25wordfunctions 0.4788478 0.4527625
## Stest26readingcomprehension 0.5876726 -0.5775554
## Stest28mechanicalreasoning 0.5402410 -0.1778992
## Stest29visualization2D 0.2211926 -0.9614718
## Stest30visualization3D 0.3515051 -0.4692480
## Stest31abstractreasoning 0.1504664 -0.8482587
## Stest32arithreasoning 0.8961258 0.5414459
## Stest33highschoolmath 1.1096846 1.4057803
## Stest34arithcomputation 0.5314790 0.7230444
## Stest35tablereading -0.4445734 0.5465100
## Stest36clericalchecking 0.5649866 -0.8859927
## Stest37objectinspection 0.4228243 -0.5425451
mvn(data = datafemale, mvnTest = "mardia")
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 6918.67023670638 0 NO
## 2 Mardia Kurtosis 12.4918121321916 0 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value
## 1 Anderson-Darling Stest1vocab 29.6155 <0.001
## 2 Anderson-Darling Stest5math 40.5679 <0.001
## 3 Anderson-Darling Stest19disguisedwords 77.7550 <0.001
## 4 Anderson-Darling Stest20spelling 18.8864 <0.001
## 5 Anderson-Darling Stest21capitalization 76.8646 <0.001
## 6 Anderson-Darling Stest22punctuation 10.1089 <0.001
## 7 Anderson-Darling Stest23english 14.3929 <0.001
## 8 Anderson-Darling Stest24expression 34.0889 <0.001
## 9 Anderson-Darling Stest25wordfunctions 41.3657 <0.001
## 10 Anderson-Darling Stest26readingcomprehension 36.4058 <0.001
## 11 Anderson-Darling Stest28mechanicalreasoning 44.7846 <0.001
## 12 Anderson-Darling Stest29visualization2D 55.7612 <0.001
## 13 Anderson-Darling Stest30visualization3D 34.3835 <0.001
## 14 Anderson-Darling Stest31abstractreasoning 35.9934 <0.001
## 15 Anderson-Darling Stest32arithreasoning 66.7532 <0.001
## 16 Anderson-Darling Stest33highschoolmath 51.9887 <0.001
## 17 Anderson-Darling Stest34arithcomputation 5.6984 <0.001
## 18 Anderson-Darling Stest35tablereading 49.6425 <0.001
## 19 Anderson-Darling Stest36clericalchecking 76.8501 <0.001
## 20 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
##
## $Descriptives
## n Mean Std.Dev Median
## Stest1vocab 3642 -1.3059162 0.9248888 -1.30765522
## Stest5math 3642 -0.9443045 0.9910145 -0.70028957
## 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
## Stest5math -3.103322 1.578247 -1.4629972 -0.19790688
## 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
## Stest5math -0.352819327 -0.127331788
## 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 10921.6134842946 0 NO
## 2 Mardia Kurtosis 16.6888411387986 0 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value
## 1 Anderson-Darling Stest1vocab 48.2718 <0.001
## 2 Anderson-Darling Stest5math 58.4651 <0.001
## 3 Anderson-Darling Stest19disguisedwords 139.9232 <0.001
## 4 Anderson-Darling Stest20spelling 30.1780 <0.001
## 5 Anderson-Darling Stest21capitalization 152.5606 <0.001
## 6 Anderson-Darling Stest22punctuation 16.1634 <0.001
## 7 Anderson-Darling Stest23english 23.6787 <0.001
## 8 Anderson-Darling Stest24expression 55.2359 <0.001
## 9 Anderson-Darling Stest25wordfunctions 64.1826 <0.001
## 10 Anderson-Darling Stest26readingcomprehension 72.4436 <0.001
## 11 Anderson-Darling Stest28mechanicalreasoning 97.9184 <0.001
## 12 Anderson-Darling Stest29visualization2D 78.4859 <0.001
## 13 Anderson-Darling Stest30visualization3D 57.8360 <0.001
## 14 Anderson-Darling Stest31abstractreasoning 57.5540 <0.001
## 15 Anderson-Darling Stest32arithreasoning 119.2201 <0.001
## 16 Anderson-Darling Stest33highschoolmath 102.6981 <0.001
## 17 Anderson-Darling Stest34arithcomputation 10.6258 <0.001
## 18 Anderson-Darling Stest35tablereading 76.0593 <0.001
## 19 Anderson-Darling Stest36clericalchecking 141.1956 <0.001
## 20 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
##
## $Descriptives
## n Mean Std.Dev Median
## Stest1vocab 6085 -1.2270951 0.9869065 -1.3076552
## Stest5math 6085 -0.8822309 1.0191384 -0.7002896
## 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
## Stest5math -3.103322 1.578247 -1.4629972 -0.19790688
## 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 -0.27969289
## Stest5math -0.30838742 -0.14354630
## Stest19disguisedwords 0.92528173 0.25002207
## Stest20spelling 0.07162174 -0.41402487
## Stest21capitalization 0.66079326 -0.45474924
## Stest22punctuation 0.13503261 -0.27371782
## Stest23english -0.27221625 0.19291627
## Stest24expression -0.25731040 -0.52677341
## Stest25wordfunctions 0.52426120 0.43972905
## Stest26readingcomprehension 0.55267240 -0.48267484
## Stest28mechanicalreasoning 0.89527624 0.74079782
## Stest29visualization2D 0.46617489 -0.71363353
## Stest30visualization3D 0.49007612 -0.05428675
## Stest31abstractreasoning 0.22160144 -0.81473251
## Stest32arithreasoning 0.96214821 0.92707276
## Stest33highschoolmath 1.05266420 1.46681124
## Stest34arithcomputation 0.45360729 0.61692702
## Stest35tablereading -0.52240978 0.72934119
## Stest36clericalchecking 0.42520016 -1.01692278
## Stest37objectinspection 0.36212399 -0.45668332
mvn(data = datamale, mvnTest = "hz", multivariatePlot = "qq", multivariateOutlierMethod = "quan") # no serious departure
## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 1.009486 0 NO
##
## $univariateNormality
## Test Variable Statistic p value
## 1 Anderson-Darling Stest1vocab 17.2962 <0.001
## 2 Anderson-Darling Stest5math 19.8829 <0.001
## 3 Anderson-Darling Stest19disguisedwords 60.6622 <0.001
## 4 Anderson-Darling Stest20spelling 13.5916 <0.001
## 5 Anderson-Darling Stest21capitalization 79.2095 <0.001
## 6 Anderson-Darling Stest22punctuation 7.0268 <0.001
## 7 Anderson-Darling Stest23english 9.7213 <0.001
## 8 Anderson-Darling Stest24expression 21.4125 <0.001
## 9 Anderson-Darling Stest25wordfunctions 23.0605 <0.001
## 10 Anderson-Darling Stest26readingcomprehension 39.6555 <0.001
## 11 Anderson-Darling Stest28mechanicalreasoning 22.9034 <0.001
## 12 Anderson-Darling Stest29visualization2D 22.3567 <0.001
## 13 Anderson-Darling Stest30visualization3D 19.6763 <0.001
## 14 Anderson-Darling Stest31abstractreasoning 21.9210 <0.001
## 15 Anderson-Darling Stest32arithreasoning 48.8610 <0.001
## 16 Anderson-Darling Stest33highschoolmath 49.4632 <0.001
## 17 Anderson-Darling Stest34arithcomputation 5.6482 <0.001
## 18 Anderson-Darling Stest35tablereading 26.8353 <0.001
## 19 Anderson-Darling Stest36clericalchecking 70.2704 <0.001
## 20 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
##
## $Descriptives
## n Mean Std.Dev Median
## Stest1vocab 2443 -1.1095892563 1.0621130 -1.3076552
## Stest5math 2443 -0.7896922969 1.0531123 -0.7002896
## 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
## Stest5math -3.103322 1.578247 -1.4629972 -0.19790688
## 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 0.3451069 -0.5997669
## Stest5math -0.2883481 -0.1940244
## Stest19disguisedwords 1.0608678 0.7255663
## Stest20spelling 0.2312739 -0.3140564
## Stest21capitalization 0.8070777 -0.2315324
## Stest22punctuation 0.1822344 -0.2204551
## Stest23english -0.2516029 0.2185956
## Stest24expression -0.1804949 -0.6694891
## Stest25wordfunctions 0.4788478 0.4527625
## Stest26readingcomprehension 0.5876726 -0.5775554
## Stest28mechanicalreasoning 0.5402410 -0.1778992
## Stest29visualization2D 0.2211926 -0.9614718
## Stest30visualization3D 0.3515051 -0.4692480
## Stest31abstractreasoning 0.1504664 -0.8482587
## Stest32arithreasoning 0.8961258 0.5414459
## Stest33highschoolmath 1.1096846 1.4057803
## Stest34arithcomputation 0.5314790 0.7230444
## Stest35tablereading -0.4445734 0.5465100
## Stest36clericalchecking 0.5649866 -0.8859927
## Stest37objectinspection 0.4228243 -0.5425451
mvn(data = datafemale, mvnTest = "hz", multivariatePlot = "qq", multivariateOutlierMethod = "quan") # no serious departure
## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 1.010121 0 NO
##
## $univariateNormality
## Test Variable Statistic p value
## 1 Anderson-Darling Stest1vocab 29.6155 <0.001
## 2 Anderson-Darling Stest5math 40.5679 <0.001
## 3 Anderson-Darling Stest19disguisedwords 77.7550 <0.001
## 4 Anderson-Darling Stest20spelling 18.8864 <0.001
## 5 Anderson-Darling Stest21capitalization 76.8646 <0.001
## 6 Anderson-Darling Stest22punctuation 10.1089 <0.001
## 7 Anderson-Darling Stest23english 14.3929 <0.001
## 8 Anderson-Darling Stest24expression 34.0889 <0.001
## 9 Anderson-Darling Stest25wordfunctions 41.3657 <0.001
## 10 Anderson-Darling Stest26readingcomprehension 36.4058 <0.001
## 11 Anderson-Darling Stest28mechanicalreasoning 44.7846 <0.001
## 12 Anderson-Darling Stest29visualization2D 55.7612 <0.001
## 13 Anderson-Darling Stest30visualization3D 34.3835 <0.001
## 14 Anderson-Darling Stest31abstractreasoning 35.9934 <0.001
## 15 Anderson-Darling Stest32arithreasoning 66.7532 <0.001
## 16 Anderson-Darling Stest33highschoolmath 51.9887 <0.001
## 17 Anderson-Darling Stest34arithcomputation 5.6984 <0.001
## 18 Anderson-Darling Stest35tablereading 49.6425 <0.001
## 19 Anderson-Darling Stest36clericalchecking 76.8501 <0.001
## 20 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
##
## $Descriptives
## n Mean Std.Dev Median
## Stest1vocab 3642 -1.3059162 0.9248888 -1.30765522
## Stest5math 3642 -0.9443045 0.9910145 -0.70028957
## 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
## Stest5math -3.103322 1.578247 -1.4629972 -0.19790688
## 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
## Stest5math -0.352819327 -0.127331788
## 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") # no serious departure
## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 1.015938 0 NO
##
## $univariateNormality
## Test Variable Statistic p value
## 1 Anderson-Darling Stest1vocab 48.2718 <0.001
## 2 Anderson-Darling Stest5math 58.4651 <0.001
## 3 Anderson-Darling Stest19disguisedwords 139.9232 <0.001
## 4 Anderson-Darling Stest20spelling 30.1780 <0.001
## 5 Anderson-Darling Stest21capitalization 152.5606 <0.001
## 6 Anderson-Darling Stest22punctuation 16.1634 <0.001
## 7 Anderson-Darling Stest23english 23.6787 <0.001
## 8 Anderson-Darling Stest24expression 55.2359 <0.001
## 9 Anderson-Darling Stest25wordfunctions 64.1826 <0.001
## 10 Anderson-Darling Stest26readingcomprehension 72.4436 <0.001
## 11 Anderson-Darling Stest28mechanicalreasoning 97.9184 <0.001
## 12 Anderson-Darling Stest29visualization2D 78.4859 <0.001
## 13 Anderson-Darling Stest30visualization3D 57.8360 <0.001
## 14 Anderson-Darling Stest31abstractreasoning 57.5540 <0.001
## 15 Anderson-Darling Stest32arithreasoning 119.2201 <0.001
## 16 Anderson-Darling Stest33highschoolmath 102.6981 <0.001
## 17 Anderson-Darling Stest34arithcomputation 10.6258 <0.001
## 18 Anderson-Darling Stest35tablereading 76.0593 <0.001
## 19 Anderson-Darling Stest36clericalchecking 141.1956 <0.001
## 20 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
##
## $Descriptives
## n Mean Std.Dev Median
## Stest1vocab 6085 -1.2270951 0.9869065 -1.3076552
## Stest5math 6085 -0.8822309 1.0191384 -0.7002896
## 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
## Stest5math -3.103322 1.578247 -1.4629972 -0.19790688
## 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 -0.27969289
## Stest5math -0.30838742 -0.14354630
## Stest19disguisedwords 0.92528173 0.25002207
## Stest20spelling 0.07162174 -0.41402487
## Stest21capitalization 0.66079326 -0.45474924
## Stest22punctuation 0.13503261 -0.27371782
## Stest23english -0.27221625 0.19291627
## Stest24expression -0.25731040 -0.52677341
## Stest25wordfunctions 0.52426120 0.43972905
## Stest26readingcomprehension 0.55267240 -0.48267484
## Stest28mechanicalreasoning 0.89527624 0.74079782
## Stest29visualization2D 0.46617489 -0.71363353
## Stest30visualization3D 0.49007612 -0.05428675
## Stest31abstractreasoning 0.22160144 -0.81473251
## Stest32arithreasoning 0.96214821 0.92707276
## Stest33highschoolmath 1.05266420 1.46681124
## Stest34arithcomputation 0.45360729 0.61692702
## Stest35tablereading -0.52240978 0.72934119
## Stest36clericalchecking 0.42520016 -1.01692278
## Stest37objectinspection 0.36212399 -0.45668332
# standardized loadings for Jensen's MCV
FAmale<-fa(r=datamale, nfactors=4, 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 = 4, 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 h2 u2 com
## Stest1vocab 0.80 -0.12 -0.08 -0.01 0.67 0.33 1.1
## Stest5math 0.66 -0.06 -0.08 -0.23 0.50 0.50 1.3
## Stest19disguisedwords 0.70 0.07 -0.14 0.10 0.52 0.48 1.1
## Stest20spelling 0.63 -0.10 -0.34 0.11 0.53 0.47 1.7
## Stest21capitalization 0.72 -0.10 -0.08 0.15 0.56 0.44 1.1
## Stest22punctuation 0.77 -0.11 -0.09 0.11 0.63 0.37 1.1
## Stest23english 0.72 -0.07 -0.11 0.22 0.58 0.42 1.3
## Stest24expression 0.58 -0.14 -0.06 0.12 0.38 0.62 1.2
## Stest25wordfunctions 0.58 -0.10 -0.02 -0.11 0.36 0.64 1.1
## Stest26readingcomprehension 0.85 -0.17 -0.08 0.01 0.76 0.24 1.1
## Stest28mechanicalreasoning 0.67 0.01 0.36 0.03 0.58 0.42 1.6
## Stest29visualization2D 0.51 0.20 0.30 0.12 0.40 0.60 2.1
## Stest30visualization3D 0.54 0.03 0.47 0.02 0.51 0.49 2.0
## Stest31abstractreasoning 0.69 -0.02 0.29 0.04 0.56 0.44 1.4
## Stest32arithreasoning 0.71 -0.12 0.06 -0.22 0.58 0.42 1.3
## Stest33highschoolmath 0.75 -0.11 0.00 -0.31 0.67 0.33 1.4
## Stest34arithcomputation 0.64 0.28 -0.17 -0.09 0.52 0.48 1.6
## Stest35tablereading 0.43 0.51 -0.05 -0.05 0.44 0.56 2.0
## Stest36clericalchecking 0.21 0.64 -0.21 -0.05 0.50 0.50 1.5
## Stest37objectinspection 0.30 0.61 0.09 0.06 0.48 0.52 1.5
##
## PA1 PA2 PA3 PA4
## SS loadings 8.26 1.30 0.80 0.37
## Proportion Var 0.41 0.07 0.04 0.02
## Cumulative Var 0.41 0.48 0.52 0.54
## Proportion Explained 0.77 0.12 0.07 0.03
## Cumulative Proportion 0.77 0.89 0.97 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 190 with the objective function = 10.2 0.1 with Chi Square = 24835.72
## df of the model are 116 and the objective function was 0.28
## 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 255.23 with prob < 1.8e-12
## 0.1The total n.obs was 2443 with Likelihood Chi Square = 689.36 with prob < 2.6e-82
## 0.1
## Tucker Lewis Index of factoring reliability = 0.962
## RMSEA index = 0.045 and the 90 % confidence intervals are 0.042 0.048 0.1
## BIC = -215.55
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA2 PA3 PA4
## Correlation of (regression) scores with factors 0.98 0.85 0.79 0.68
## Multiple R square of scores with factors 0.95 0.72 0.63 0.47
## Minimum correlation of possible factor scores 0.91 0.44 0.26 -0.07
FAfemale<-fa(r=datafemale, nfactors=4, 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 = 4, 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 h2 u2 com
## Stest1vocab 0.76 -0.10 -0.13 0.05 0.61 0.39 1.1
## Stest5math 0.55 -0.06 0.00 0.28 0.39 0.61 1.5
## Stest19disguisedwords 0.73 0.13 -0.13 -0.07 0.56 0.44 1.1
## Stest20spelling 0.63 0.00 -0.35 -0.06 0.52 0.48 1.6
## Stest21capitalization 0.72 -0.07 -0.10 -0.14 0.55 0.45 1.1
## Stest22punctuation 0.79 -0.11 -0.08 -0.09 0.66 0.34 1.1
## Stest23english 0.70 -0.08 -0.11 -0.19 0.54 0.46 1.2
## Stest24expression 0.54 -0.11 -0.06 -0.19 0.34 0.66 1.4
## Stest25wordfunctions 0.63 -0.14 0.04 0.18 0.44 0.56 1.3
## Stest26readingcomprehension 0.84 -0.14 -0.10 -0.03 0.73 0.27 1.1
## Stest28mechanicalreasoning 0.53 -0.06 0.24 0.02 0.35 0.65 1.4
## Stest29visualization2D 0.45 0.09 0.34 -0.09 0.33 0.67 2.1
## Stest30visualization3D 0.47 -0.04 0.44 -0.09 0.42 0.58 2.1
## Stest31abstractreasoning 0.66 -0.10 0.26 -0.12 0.53 0.47 1.4
## Stest32arithreasoning 0.63 -0.16 0.09 0.17 0.47 0.53 1.3
## Stest33highschoolmath 0.70 -0.11 0.06 0.30 0.60 0.40 1.4
## Stest34arithcomputation 0.60 0.31 -0.13 0.08 0.48 0.52 1.6
## Stest35tablereading 0.44 0.52 -0.02 0.01 0.46 0.54 2.0
## Stest36clericalchecking 0.18 0.66 -0.05 0.07 0.47 0.53 1.2
## Stest37objectinspection 0.34 0.59 0.16 -0.04 0.49 0.51 1.8
##
## PA1 PA2 PA3 PA4
## SS loadings 7.56 1.31 0.69 0.38
## Proportion Var 0.38 0.07 0.03 0.02
## Cumulative Var 0.38 0.44 0.48 0.50
## Proportion Explained 0.76 0.13 0.07 0.04
## Cumulative Proportion 0.76 0.89 0.96 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 190 with the objective function = 8.88 0.1 with Chi Square = 32272.14
## df of the model are 116 and the objective function was 0.24
## 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 3642 with the empirical chi square 368.51 with prob < 4.6e-28
## 0.1The total n.obs was 3642 with Likelihood Chi Square = 857.85 with prob < 1.7e-113
## 0.1
## Tucker Lewis Index of factoring reliability = 0.962
## RMSEA index = 0.042 and the 90 % confidence intervals are 0.039 0.045 0.1
## BIC = -93.38
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA2 PA3 PA4
## Correlation of (regression) scores with factors 0.97 0.85 0.75 0.66
## Multiple R square of scores with factors 0.94 0.72 0.56 0.44
## Minimum correlation of possible factor scores 0.89 0.44 0.12 -0.13
FA<-fa(r=datagroup, nfactors=4, 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 = 4, 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 h2 u2 com
## Stest1vocab 0.77 -0.12 -0.04 -0.09 0.62 0.38 1.1
## Stest5math 0.60 -0.07 0.03 -0.29 0.45 0.55 1.5
## Stest19disguisedwords 0.71 0.13 -0.12 0.04 0.54 0.46 1.1
## Stest20spelling 0.62 0.03 -0.40 0.03 0.54 0.46 1.7
## Stest21capitalization 0.71 -0.04 -0.18 0.16 0.56 0.44 1.2
## Stest22punctuation 0.78 -0.07 -0.19 0.12 0.66 0.34 1.2
## Stest23english 0.70 -0.03 -0.18 0.19 0.56 0.44 1.3
## Stest24expression 0.55 -0.09 -0.14 0.16 0.36 0.64 1.4
## Stest25wordfunctions 0.60 -0.11 -0.04 -0.12 0.39 0.61 1.1
## Stest26readingcomprehension 0.84 -0.14 -0.11 -0.01 0.74 0.26 1.1
## Stest28mechanicalreasoning 0.55 -0.14 0.43 -0.01 0.50 0.50 2.0
## Stest29visualization2D 0.47 0.06 0.38 0.13 0.38 0.62 2.1
## Stest30visualization3D 0.49 -0.10 0.45 0.13 0.47 0.53 2.2
## Stest31abstractreasoning 0.67 -0.11 0.25 0.14 0.54 0.46 1.4
## Stest32arithreasoning 0.67 -0.17 0.10 -0.17 0.51 0.49 1.3
## Stest33highschoolmath 0.72 -0.12 0.06 -0.26 0.61 0.39 1.3
## Stest34arithcomputation 0.62 0.32 -0.09 -0.09 0.50 0.50 1.6
## Stest35tablereading 0.43 0.51 0.05 -0.02 0.46 0.54 2.0
## Stest36clericalchecking 0.19 0.67 -0.02 -0.09 0.49 0.51 1.2
## Stest37objectinspection 0.32 0.58 0.20 0.07 0.48 0.52 1.9
##
## PA1 PA2 PA3 PA4
## SS loadings 7.71 1.31 0.97 0.38
## Proportion Var 0.39 0.07 0.05 0.02
## Cumulative Var 0.39 0.45 0.50 0.52
## Proportion Explained 0.74 0.13 0.09 0.04
## Cumulative Proportion 0.74 0.87 0.96 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 190 with the objective function = 9.39 0.1 with Chi Square = 57071.23
## df of the model are 116 and the objective function was 0.25
## 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 6085 with the empirical chi square 610.95 with prob < 2.9e-68
## 0.1The total n.obs was 6085 with Likelihood Chi Square = 1530.03 with prob < 3.6e-245
## 0.1
## Tucker Lewis Index of factoring reliability = 0.959
## RMSEA index = 0.045 and the 90 % confidence intervals are 0.043 0.047 0.1
## BIC = 519.26
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA2 PA3 PA4
## Correlation of (regression) scores with factors 0.97 0.85 0.81 0.67
## Multiple R square of scores with factors 0.95 0.72 0.66 0.45
## Minimum correlation of possible factor scores 0.89 0.44 0.32 -0.10
# 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.
male3<-fa(datamale, nfactors=3, rotate="promax", fm="minres", weight=dmale$BY_WTA)
print(male3, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datamale, nfactors = 3, rotate = "promax", fm = "minres",
## weight = dmale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## Stest1vocab 0.78 0.07 -0.04 0.67 0.33 1.0
## Stest5math 0.62 0.06 0.02 0.44 0.56 1.0
## Stest19disguisedwords 0.65 -0.02 0.17 0.51 0.49 1.1
## Stest20spelling 0.87 -0.30 0.03 0.52 0.48 1.2
## Stest21capitalization 0.70 0.06 -0.02 0.54 0.46 1.0
## Stest22punctuation 0.76 0.06 -0.02 0.62 0.38 1.0
## Stest23english 0.69 0.03 0.02 0.52 0.48 1.0
## Stest24expression 0.59 0.05 -0.08 0.36 0.64 1.0
## Stest25wordfunctions 0.54 0.10 -0.04 0.35 0.65 1.1
## Stest26readingcomprehension 0.85 0.08 -0.09 0.77 0.23 1.0
## Stest28mechanicalreasoning 0.16 0.65 -0.02 0.58 0.42 1.1
## Stest29visualization2D 0.00 0.53 0.18 0.38 0.62 1.2
## Stest30visualization3D -0.06 0.77 -0.04 0.52 0.48 1.0
## Stest31abstractreasoning 0.26 0.56 -0.03 0.56 0.44 1.4
## Stest32arithreasoning 0.57 0.23 -0.07 0.52 0.48 1.4
## Stest33highschoolmath 0.64 0.17 -0.04 0.56 0.44 1.2
## Stest34arithcomputation 0.50 -0.05 0.39 0.51 0.49 1.9
## Stest35tablereading 0.09 0.07 0.59 0.44 0.56 1.1
## Stest36clericalchecking 0.00 -0.20 0.76 0.50 0.50 1.1
## Stest37objectinspection -0.20 0.24 0.65 0.47 0.53 1.5
##
## MR1 MR3 MR2
## SS loadings 6.51 2.23 1.59
## Proportion Var 0.33 0.11 0.08
## Cumulative Var 0.33 0.44 0.52
## Proportion Explained 0.63 0.22 0.15
## Cumulative Proportion 0.63 0.85 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.67 0.38
## MR3 0.67 1.00 0.37
## MR2 0.38 0.37 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 190 with the objective function = 10.2 0.1 with Chi Square = 24835.72
## df of the model are 133 and the objective function was 0.46
## 0.1
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.03
## 0.1
## The harmonic n.obs is 2443 with the empirical chi square 529.29 with prob < 1.1e-48
## 0.1The total n.obs was 2443 with Likelihood Chi Square = 1114.79 with prob < 1.1e-154
## 0.1
## Tucker Lewis Index of factoring reliability = 0.943
## RMSEA index = 0.055 and the 90 % confidence intervals are 0.052 0.058 0.1
## BIC = 77.26
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.97 0.91 0.87
## Multiple R square of scores with factors 0.94 0.83 0.76
## Minimum correlation of possible factor scores 0.88 0.66 0.53
male4<-fa(datamale, nfactors=4, rotate="promax", fm="minres", weight=dmale$BY_WTA)
print(male4, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datamale, nfactors = 4, rotate = "promax", fm = "minres",
## weight = dmale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR4 MR2 h2 u2 com
## Stest1vocab 0.59 0.07 0.23 -0.03 0.67 0.33 1.3
## Stest5math 0.20 -0.02 0.54 0.05 0.50 0.50 1.3
## Stest19disguisedwords 0.64 0.01 0.00 0.16 0.52 0.48 1.1
## Stest20spelling 0.86 -0.27 0.00 0.02 0.53 0.47 1.2
## Stest21capitalization 0.72 0.10 -0.04 -0.04 0.56 0.44 1.1
## Stest22punctuation 0.72 0.09 0.03 -0.04 0.63 0.37 1.0
## Stest23english 0.82 0.09 -0.17 -0.01 0.58 0.42 1.1
## Stest24expression 0.60 0.09 -0.02 -0.09 0.38 0.62 1.1
## Stest25wordfunctions 0.27 0.06 0.33 -0.03 0.36 0.64 2.0
## Stest26readingcomprehension 0.66 0.08 0.23 -0.08 0.76 0.24 1.3
## Stest28mechanicalreasoning 0.08 0.64 0.11 -0.03 0.58 0.42 1.1
## Stest29visualization2D 0.07 0.57 -0.11 0.17 0.40 0.60 1.3
## Stest30visualization3D -0.11 0.75 0.08 -0.04 0.51 0.49 1.1
## Stest31abstractreasoning 0.18 0.56 0.10 -0.04 0.56 0.44 1.3
## Stest32arithreasoning 0.14 0.16 0.55 -0.05 0.58 0.42 1.3
## Stest33highschoolmath 0.10 0.07 0.70 0.00 0.67 0.33 1.1
## Stest34arithcomputation 0.30 -0.07 0.24 0.41 0.52 0.48 2.6
## Stest35tablereading 0.01 0.06 0.09 0.59 0.44 0.56 1.1
## Stest36clericalchecking -0.02 -0.20 0.01 0.76 0.50 0.50 1.1
## Stest37objectinspection -0.10 0.26 -0.14 0.65 0.48 0.52 1.5
##
## MR1 MR3 MR4 MR2
## SS loadings 4.91 2.18 2.04 1.60
## Proportion Var 0.25 0.11 0.10 0.08
## Cumulative Var 0.25 0.35 0.46 0.54
## Proportion Explained 0.46 0.20 0.19 0.15
## Cumulative Proportion 0.46 0.66 0.85 1.00
##
## With factor correlations of
## MR1 MR3 MR4 MR2
## MR1 1.00 0.65 0.77 0.39
## MR3 0.65 1.00 0.61 0.37
## MR4 0.77 0.61 1.00 0.31
## MR2 0.39 0.37 0.31 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 190 with the objective function = 10.2 0.1 with Chi Square = 24835.72
## df of the model are 116 and the objective function was 0.28
## 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 255.23 with prob < 1.8e-12
## 0.1The total n.obs was 2443 with Likelihood Chi Square = 689.45 with prob < 2.5e-82
## 0.1
## Tucker Lewis Index of factoring reliability = 0.962
## RMSEA index = 0.045 and the 90 % confidence intervals are 0.042 0.048 0.1
## BIC = -215.47
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR4 MR2
## Correlation of (regression) scores with factors 0.96 0.91 0.92 0.88
## Multiple R square of scores with factors 0.93 0.83 0.84 0.77
## Minimum correlation of possible factor scores 0.85 0.66 0.68 0.53
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 MR3 MR4 MR2 MR5 h2 u2 com
## Stest1vocab 0.60 0.07 0.20 0.02 0.30 0.73 0.27 1.8
## Stest5math 0.18 -0.02 0.55 0.07 0.15 0.52 0.48 1.4
## Stest19disguisedwords 0.65 0.01 -0.02 0.19 0.17 0.54 0.46 1.3
## Stest20spelling 0.86 -0.27 0.01 0.00 -0.02 0.53 0.47 1.2
## Stest21capitalization 0.73 0.10 -0.03 -0.06 -0.05 0.57 0.43 1.1
## Stest22punctuation 0.73 0.09 0.04 -0.07 -0.09 0.66 0.34 1.1
## Stest23english 0.82 0.09 -0.16 0.01 0.08 0.57 0.43 1.1
## Stest24expression 0.60 0.09 -0.02 -0.10 0.01 0.38 0.62 1.1
## Stest25wordfunctions 0.27 0.07 0.34 -0.04 0.00 0.36 0.64 2.0
## Stest26readingcomprehension 0.67 0.08 0.20 -0.04 0.24 0.80 0.20 1.5
## Stest28mechanicalreasoning 0.07 0.66 0.09 0.01 0.17 0.61 0.39 1.2
## Stest29visualization2D 0.07 0.57 -0.10 0.15 -0.05 0.41 0.59 1.3
## Stest30visualization3D -0.11 0.75 0.08 -0.04 0.04 0.51 0.49 1.1
## Stest31abstractreasoning 0.17 0.57 0.11 -0.06 -0.06 0.57 0.43 1.3
## Stest32arithreasoning 0.13 0.17 0.55 -0.06 0.03 0.57 0.43 1.3
## Stest33highschoolmath 0.05 0.07 0.76 -0.04 -0.07 0.70 0.30 1.1
## Stest34arithcomputation 0.29 -0.09 0.29 0.36 -0.20 0.57 0.43 3.6
## Stest35tablereading 0.01 0.07 0.10 0.57 -0.08 0.44 0.56 1.1
## Stest36clericalchecking -0.02 -0.20 0.00 0.78 0.03 0.52 0.48 1.1
## Stest37objectinspection -0.10 0.26 -0.14 0.64 -0.01 0.47 0.53 1.5
##
## MR1 MR3 MR4 MR2 MR5
## SS loadings 4.86 2.20 2.12 1.59 0.27
## Proportion Var 0.24 0.11 0.11 0.08 0.01
## Cumulative Var 0.24 0.35 0.46 0.54 0.55
## Proportion Explained 0.44 0.20 0.19 0.14 0.02
## Cumulative Proportion 0.44 0.64 0.83 0.98 1.00
##
## With factor correlations of
## MR1 MR3 MR4 MR2 MR5
## MR1 1.00 0.65 0.78 0.40 -0.09
## MR3 0.65 1.00 0.61 0.38 -0.07
## MR4 0.78 0.61 1.00 0.33 -0.01
## MR2 0.40 0.38 0.33 1.00 -0.15
## MR5 -0.09 -0.07 -0.01 -0.15 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 5 factors are sufficient.
##
## df null model = 190 with the objective function = 10.2 0.1 with Chi Square = 24835.72
## df of the model are 100 and the objective function was 0.13
## 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 121.92 with prob < 0.067
## 0.1The total n.obs was 2443 with Likelihood Chi Square = 323.37 with prob < 2.4e-25
## 0.1
## Tucker Lewis Index of factoring reliability = 0.983
## RMSEA index = 0.03 and the 90 % confidence intervals are 0.027 0.034 0.1
## BIC = -456.72
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR4 MR2
## Correlation of (regression) scores with factors 0.96 0.91 0.92 0.88
## Multiple R square of scores with factors 0.92 0.83 0.86 0.77
## Minimum correlation of possible factor scores 0.85 0.66 0.71 0.54
## MR5
## Correlation of (regression) scores with factors 0.67
## Multiple R square of scores with factors 0.44
## Minimum correlation of possible factor scores -0.11
female3<-fa(datafemale, nfactors=3, rotate="promax", fm="minres", weight=dfemale$BY_WTA)
print(female3, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datafemale, nfactors = 3, rotate = "promax", fm = "minres",
## weight = dfemale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## Stest1vocab 0.79 0.00 -0.03 0.61 0.39 1.0
## Stest5math 0.46 0.12 0.00 0.30 0.70 1.1
## Stest19disguisedwords 0.66 -0.02 0.21 0.56 0.44 1.2
## Stest20spelling 0.88 -0.32 0.06 0.52 0.48 1.3
## Stest21capitalization 0.70 0.03 0.00 0.53 0.47 1.0
## Stest22punctuation 0.76 0.09 -0.04 0.65 0.35 1.0
## Stest23english 0.69 0.03 -0.01 0.50 0.50 1.0
## Stest24expression 0.52 0.06 -0.05 0.30 0.70 1.0
## Stest25wordfunctions 0.52 0.19 -0.07 0.41 0.59 1.3
## Stest26readingcomprehension 0.84 0.06 -0.06 0.74 0.26 1.0
## Stest28mechanicalreasoning 0.19 0.45 -0.01 0.35 0.65 1.3
## Stest29visualization2D -0.04 0.54 0.15 0.33 0.67 1.2
## Stest30visualization3D -0.08 0.69 0.01 0.41 0.59 1.0
## Stest31abstractreasoning 0.29 0.50 -0.03 0.51 0.49 1.6
## Stest32arithreasoning 0.48 0.27 -0.10 0.43 0.57 1.7
## Stest33highschoolmath 0.54 0.23 -0.04 0.49 0.51 1.3
## Stest34arithcomputation 0.48 -0.07 0.40 0.48 0.52 2.0
## Stest35tablereading 0.15 0.02 0.60 0.46 0.54 1.1
## Stest36clericalchecking -0.08 -0.08 0.72 0.47 0.53 1.1
## Stest37objectinspection -0.15 0.23 0.67 0.48 0.52 1.4
##
## MR1 MR3 MR2
## SS loadings 6.04 1.86 1.62
## Proportion Var 0.30 0.09 0.08
## Cumulative Var 0.30 0.40 0.48
## Proportion Explained 0.63 0.20 0.17
## Cumulative Proportion 0.63 0.83 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.67 0.36
## MR3 0.67 1.00 0.27
## MR2 0.36 0.27 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 190 with the objective function = 8.88 0.1 with Chi Square = 32272.14
## df of the model are 133 and the objective function was 0.39
## 0.1
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.03
## 0.1
## The harmonic n.obs is 3642 with the empirical chi square 823.65 with prob < 4.6e-100
## 0.1The total n.obs was 3642 with Likelihood Chi Square = 1408.27 with prob < 8.6e-212
## 0.1
## Tucker Lewis Index of factoring reliability = 0.943
## RMSEA index = 0.051 and the 90 % confidence intervals are 0.049 0.054 0.1
## BIC = 317.63
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.97 0.88 0.87
## Multiple R square of scores with factors 0.93 0.78 0.76
## Minimum correlation of possible factor scores 0.87 0.56 0.52
female4<-fa(datafemale, nfactors=4, rotate="promax", fm="minres", weight=dfemale$BY_WTA)
print(female4, digits=2, cutoff=.10)
## Factor Analysis using method = minres
## Call: fa(r = datafemale, nfactors = 4, rotate = "promax", fm = "minres",
## weight = dfemale$BY_WTA)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR4 MR3 MR2 h2 u2 com
## Stest1vocab 0.54 0.31 -0.04 -0.02 0.61 0.39 1.6
## Stest5math -0.01 0.63 -0.03 0.03 0.39 0.61 1.0
## Stest19disguisedwords 0.59 0.06 0.01 0.20 0.56 0.44 1.3
## Stest20spelling 0.80 0.06 -0.28 0.05 0.52 0.48 1.3
## Stest21capitalization 0.71 -0.02 0.08 -0.02 0.55 0.45 1.0
## Stest22punctuation 0.68 0.10 0.10 -0.05 0.66 0.34 1.1
## Stest23english 0.76 -0.10 0.09 -0.03 0.54 0.46 1.1
## Stest24expression 0.63 -0.13 0.12 -0.08 0.34 0.66 1.2
## Stest25wordfunctions 0.14 0.51 0.08 -0.05 0.44 0.56 1.2
## Stest26readingcomprehension 0.66 0.22 0.05 -0.06 0.73 0.27 1.2
## Stest28mechanicalreasoning 0.05 0.22 0.39 -0.01 0.35 0.65 1.6
## Stest29visualization2D -0.01 -0.01 0.54 0.14 0.33 0.67 1.1
## Stest30visualization3D -0.07 0.03 0.67 0.00 0.42 0.58 1.0
## Stest31abstractreasoning 0.28 0.04 0.51 -0.05 0.53 0.47 1.6
## Stest32arithreasoning 0.10 0.51 0.16 -0.08 0.47 0.53 1.3
## Stest33highschoolmath 0.01 0.73 0.07 -0.01 0.60 0.40 1.0
## Stest34arithcomputation 0.30 0.22 -0.10 0.41 0.48 0.52 2.6
## Stest35tablereading 0.13 0.00 0.03 0.61 0.46 0.54 1.1
## Stest36clericalchecking -0.11 0.00 -0.09 0.74 0.47 0.53 1.1
## Stest37objectinspection -0.08 -0.11 0.25 0.67 0.49 0.51 1.4
##
## MR1 MR4 MR3 MR2
## SS loadings 4.42 2.26 1.64 1.63
## Proportion Var 0.22 0.11 0.08 0.08
## Cumulative Var 0.22 0.33 0.42 0.50
## Proportion Explained 0.44 0.23 0.16 0.16
## Cumulative Proportion 0.44 0.67 0.84 1.00
##
## With factor correlations of
## MR1 MR4 MR3 MR2
## MR1 1.00 0.79 0.62 0.39
## MR4 0.79 1.00 0.63 0.33
## MR3 0.62 0.63 1.00 0.29
## MR2 0.39 0.33 0.29 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 190 with the objective function = 8.88 0.1 with Chi Square = 32272.14
## df of the model are 116 and the objective function was 0.24
## 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 3642 with the empirical chi square 368.5 with prob < 4.6e-28
## 0.1The total n.obs was 3642 with Likelihood Chi Square = 857.85 with prob < 1.7e-113
## 0.1
## Tucker Lewis Index of factoring reliability = 0.962
## RMSEA index = 0.042 and the 90 % confidence intervals are 0.039 0.045 0.1
## BIC = -93.38
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR4 MR3 MR2
## Correlation of (regression) scores with factors 0.96 0.92 0.87 0.88
## Multiple R square of scores with factors 0.92 0.85 0.77 0.77
## Minimum correlation of possible factor scores 0.84 0.69 0.53 0.53
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 MR2 MR3 MR5 h2 u2 com
## Stest1vocab 0.51 0.25 0.02 -0.05 0.33 0.68 0.32 2.3
## Stest5math -0.01 0.61 0.03 -0.02 0.07 0.38 0.62 1.0
## Stest19disguisedwords 0.58 -0.01 0.24 0.01 0.25 0.60 0.40 1.7
## Stest20spelling 0.78 0.08 0.05 -0.28 0.04 0.52 0.48 1.3
## Stest21capitalization 0.70 -0.01 -0.02 0.08 0.04 0.55 0.45 1.0
## Stest22punctuation 0.69 0.12 -0.07 0.11 -0.06 0.68 0.32 1.1
## Stest23english 0.75 -0.08 -0.04 0.09 0.01 0.54 0.46 1.1
## Stest24expression 0.62 -0.12 -0.09 0.13 0.01 0.34 0.66 1.2
## Stest25wordfunctions 0.14 0.49 -0.06 0.09 0.04 0.44 0.56 1.3
## Stest26readingcomprehension 0.64 0.16 -0.04 0.05 0.27 0.77 0.23 1.5
## Stest28mechanicalreasoning 0.03 0.19 0.01 0.40 0.12 0.36 0.64 1.6
## Stest29visualization2D -0.01 -0.01 0.14 0.54 -0.02 0.33 0.67 1.1
## Stest30visualization3D -0.06 0.03 0.01 0.67 -0.01 0.42 0.58 1.0
## Stest31abstractreasoning 0.28 0.05 -0.06 0.50 -0.02 0.53 0.47 1.6
## Stest32arithreasoning 0.10 0.50 -0.09 0.17 0.03 0.46 0.54 1.4
## Stest33highschoolmath -0.03 0.82 -0.04 0.06 -0.11 0.64 0.36 1.1
## Stest34arithcomputation 0.30 0.30 0.39 -0.12 -0.18 0.55 0.45 3.5
## Stest35tablereading 0.13 0.02 0.60 0.03 -0.04 0.46 0.54 1.1
## Stest36clericalchecking -0.12 -0.03 0.76 -0.08 0.08 0.50 0.50 1.1
## Stest37objectinspection -0.08 -0.10 0.66 0.24 -0.04 0.48 0.52 1.4
##
## MR1 MR4 MR2 MR3 MR5
## SS loadings 4.29 2.25 1.65 1.64 0.40
## Proportion Var 0.21 0.11 0.08 0.08 0.02
## Cumulative Var 0.21 0.33 0.41 0.49 0.51
## Proportion Explained 0.42 0.22 0.16 0.16 0.04
## Cumulative Proportion 0.42 0.64 0.80 0.96 1.00
##
## With factor correlations of
## MR1 MR4 MR2 MR3 MR5
## MR1 1.00 0.79 0.40 0.61 0.12
## MR4 0.79 1.00 0.34 0.62 0.22
## MR2 0.40 0.34 1.00 0.29 -0.03
## MR3 0.61 0.62 0.29 1.00 0.17
## MR5 0.12 0.22 -0.03 0.17 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 5 factors are sufficient.
##
## df null model = 190 with the objective function = 8.88 0.1 with Chi Square = 32272.14
## df of the model are 100 and the objective function was 0.11
## 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 186.88 with prob < 3.2e-07
## 0.1The total n.obs was 3642 with Likelihood Chi Square = 402.51 with prob < 6.5e-38
## 0.1
## Tucker Lewis Index of factoring reliability = 0.982
## RMSEA index = 0.029 and the 90 % confidence intervals are 0.026 0.032 0.1
## BIC = -417.52
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR4 MR2 MR3
## Correlation of (regression) scores with factors 0.95 0.93 0.88 0.87
## Multiple R square of scores with factors 0.91 0.86 0.77 0.77
## Minimum correlation of possible factor scores 0.82 0.71 0.55 0.53
## MR5
## Correlation of (regression) scores with factors 0.67
## Multiple R square of scores with factors 0.45
## Minimum correlation of possible factor scores -0.10
CHC common factor model
chc.factor.model <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest26readingcomprehension + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest1vocab + Stest5math + Stest25wordfunctions + Stest26readingcomprehension + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
'
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
## 3330.952 158.000 0.000 0.944 0.057 0.043
## aic bic
## 294444.955 294928.333
Mc(baseline)
## [1] 0.7704643
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
## 3357.819 316.000 0.000 0.947 0.056 0.042
## aic bic
## 291291.549 292258.305
Mc(configural)
## [1] 0.7788124
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 60 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 144
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3357.819 2996.637
## Degrees of freedom 316 316
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.121
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1435.077 1280.714
## 1 1922.742 1715.923
##
## 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 0.543 0.070 7.712 0.000 0.405
## Stst19dsgsdwrd 0.619 0.018 34.938 0.000 0.585
## Stest20spellng 0.672 0.019 34.682 0.000 0.634
## Stest21cptlztn 0.708 0.016 44.489 0.000 0.677
## Stest22puncttn 0.792 0.018 44.049 0.000 0.757
## Stest23english 0.884 0.021 41.314 0.000 0.842
## Stest24exprssn 0.712 0.021 33.719 0.000 0.671
## Stst26rdngcmpr 0.600 0.067 8.915 0.000 0.468
## Stst31bstrctrs 0.244 0.035 6.907 0.000 0.175
## Stst34rthcmptt 0.258 0.064 4.041 0.000 0.133
## math =~
## Stest1vocab 0.366 0.072 5.123 0.000 0.226
## Stest5math 0.740 0.019 39.662 0.000 0.703
## Stst25wrdfnctn 0.476 0.018 26.400 0.000 0.440
## Stst26rdngcmpr 0.372 0.069 5.431 0.000 0.238
## Stst32rthrsnng 0.638 0.018 35.571 0.000 0.603
## Stst33hghschlm 0.624 0.019 33.149 0.000 0.587
## Stst34rthcmptt 0.285 0.065 4.380 0.000 0.157
## speed =~
## Stst34rthcmptt 0.469 0.031 15.369 0.000 0.409
## Stest35tblrdng 1.188 0.045 26.167 0.000 1.099
## Stst36clrclchc 0.801 0.032 25.052 0.000 0.739
## Stst37bjctnspc 0.735 0.035 21.021 0.000 0.666
## spatial =~
## Stst28mchnclrs 0.706 0.018 39.612 0.000 0.671
## Stst29vslztn2D 0.658 0.022 30.214 0.000 0.616
## Stst30vslztn3D 0.646 0.019 34.333 0.000 0.609
## Stst31bstrctrs 0.657 0.036 18.142 0.000 0.586
## Stst37bjctnspc 0.115 0.030 3.872 0.000 0.057
## ci.upper Std.lv Std.all
##
## 0.681 0.543 0.509
## 0.654 0.619 0.709
## 0.710 0.672 0.674
## 0.739 0.708 0.750
## 0.827 0.792 0.793
## 0.926 0.884 0.744
## 0.753 0.712 0.612
## 0.732 0.600 0.558
## 0.314 0.244 0.214
## 0.383 0.258 0.225
##
## 0.507 0.366 0.344
## 0.776 0.740 0.706
## 0.511 0.476 0.611
## 0.507 0.372 0.346
## 0.674 0.638 0.760
## 0.661 0.624 0.794
## 0.413 0.285 0.249
##
## 0.529 0.469 0.409
## 1.277 1.188 0.712
## 0.864 0.801 0.619
## 0.803 0.735 0.593
##
## 0.741 0.706 0.785
## 0.701 0.658 0.604
## 0.683 0.646 0.681
## 0.728 0.657 0.576
## 0.174 0.115 0.093
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.861 0.011 81.260 0.000 0.840
## speed 0.353 0.026 13.624 0.000 0.302
## spatial 0.703 0.018 39.244 0.000 0.668
## math ~~
## speed 0.317 0.027 11.833 0.000 0.264
## spatial 0.749 0.017 43.938 0.000 0.716
## speed ~~
## spatial 0.365 0.030 12.228 0.000 0.307
## ci.upper Std.lv Std.all
##
## 0.882 0.861 0.861
## 0.404 0.353 0.353
## 0.738 0.703 0.703
##
## 0.369 0.317 0.317
## 0.782 0.749 0.749
##
## 0.424 0.365 0.365
##
## 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
## .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
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.903
## .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
## .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 -1.136
## -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
## -1.248 -1.292 -1.202
## -1.022 -1.070 -0.937
## -1.104 -1.153 -1.006
## -0.770 -0.814 -0.777
## -0.838 -0.871 -1.119
## -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 -0.257
## -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 0.366 0.013 27.382 0.000 0.340
## .Stst19dsgsdwrd 0.379 0.014 27.124 0.000 0.351
## .Stest20spellng 0.542 0.018 30.368 0.000 0.507
## .Stest21cptlztn 0.390 0.016 25.109 0.000 0.360
## .Stest22puncttn 0.369 0.013 27.877 0.000 0.343
## .Stest23english 0.632 0.023 27.034 0.000 0.586
## .Stest24exprssn 0.848 0.026 32.988 0.000 0.798
## .Stst26rdngcmpr 0.273 0.011 24.254 0.000 0.251
## .Stst31bstrctrs 0.586 0.023 25.638 0.000 0.541
## .Stst34rthcmptt 0.648 0.030 21.843 0.000 0.590
## .Stest5math 0.550 0.021 26.331 0.000 0.509
## .Stst25wrdfnctn 0.379 0.012 31.698 0.000 0.356
## .Stst32rthrsnng 0.297 0.011 27.283 0.000 0.276
## .Stst33hghschlm 0.228 0.010 23.175 0.000 0.208
## .Stest35tblrdng 1.371 0.088 15.621 0.000 1.199
## .Stst36clrclchc 1.036 0.048 21.733 0.000 0.943
## .Stst37bjctnspc 0.920 0.040 23.088 0.000 0.842
## .Stst28mchnclrs 0.310 0.015 20.015 0.000 0.280
## .Stst29vslztn2D 0.756 0.027 28.152 0.000 0.703
## .Stst30vslztn3D 0.481 0.017 27.531 0.000 0.447
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.392 0.366 0.321
## 0.406 0.379 0.497
## 0.577 0.542 0.546
## 0.420 0.390 0.438
## 0.395 0.369 0.370
## 0.678 0.632 0.447
## 0.899 0.848 0.626
## 0.295 0.273 0.236
## 0.630 0.586 0.450
## 0.706 0.648 0.494
## 0.591 0.550 0.501
## 0.403 0.379 0.626
## 0.319 0.297 0.422
## 0.247 0.228 0.369
## 1.543 1.371 0.493
## 1.129 1.036 0.617
## 0.998 0.920 0.599
## 0.341 0.310 0.383
## 0.808 0.756 0.636
## 0.515 0.481 0.536
## 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 0.517 0.043 12.062 0.000 0.433
## Stst19dsgsdwrd 0.690 0.014 48.821 0.000 0.663
## Stest20spellng 0.642 0.015 43.261 0.000 0.613
## Stest21cptlztn 0.749 0.014 54.541 0.000 0.723
## Stest22puncttn 0.797 0.014 56.336 0.000 0.769
## Stest23english 0.784 0.017 47.284 0.000 0.751
## Stest24exprssn 0.602 0.017 35.254 0.000 0.568
## Stst26rdngcmpr 0.633 0.039 16.125 0.000 0.556
## Stst31bstrctrs 0.282 0.030 9.324 0.000 0.223
## Stst34rthcmptt 0.291 0.048 6.117 0.000 0.198
## math =~
## Stest1vocab 0.226 0.046 4.948 0.000 0.137
## Stest5math 0.595 0.016 37.277 0.000 0.563
## Stst25wrdfnctn 0.539 0.015 36.593 0.000 0.510
## Stst26rdngcmpr 0.223 0.041 5.389 0.000 0.142
## Stst32rthrsnng 0.512 0.015 33.488 0.000 0.482
## Stst33hghschlm 0.526 0.014 37.512 0.000 0.498
## Stst34rthcmptt 0.203 0.046 4.447 0.000 0.114
## speed =~
## Stst34rthcmptt 0.490 0.027 18.414 0.000 0.438
## Stest35tblrdng 1.184 0.038 31.392 0.000 1.110
## Stst36clrclchc 0.766 0.026 29.587 0.000 0.715
## Stst37bjctnspc 0.706 0.027 26.207 0.000 0.654
## spatial =~
## Stst28mchnclrs 0.379 0.013 29.236 0.000 0.354
## Stst29vslztn2D 0.548 0.019 29.282 0.000 0.511
## Stst30vslztn3D 0.471 0.015 31.370 0.000 0.442
## Stst31bstrctrs 0.559 0.032 17.693 0.000 0.497
## Stst37bjctnspc 0.109 0.024 4.576 0.000 0.063
## ci.upper Std.lv Std.all
##
## 0.601 0.517 0.562
## 0.718 0.690 0.735
## 0.671 0.642 0.667
## 0.776 0.749 0.741
## 0.825 0.797 0.808
## 0.816 0.784 0.718
## 0.635 0.602 0.557
## 0.710 0.633 0.653
## 0.341 0.282 0.258
## 0.385 0.291 0.252
##
## 0.316 0.226 0.246
## 0.626 0.595 0.603
## 0.568 0.539 0.676
## 0.303 0.223 0.229
## 0.542 0.512 0.694
## 0.553 0.526 0.756
## 0.293 0.203 0.176
##
## 0.542 0.490 0.424
## 1.258 1.184 0.729
## 0.817 0.766 0.598
## 0.759 0.706 0.615
##
## 0.405 0.379 0.619
## 0.585 0.548 0.554
## 0.501 0.471 0.610
## 0.621 0.559 0.511
## 0.156 0.109 0.095
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.840 0.010 87.880 0.000 0.821
## speed 0.389 0.022 17.678 0.000 0.346
## spatial 0.695 0.017 41.519 0.000 0.662
## math ~~
## speed 0.291 0.022 13.104 0.000 0.248
## spatial 0.749 0.018 42.221 0.000 0.714
## speed ~~
## spatial 0.330 0.027 12.298 0.000 0.277
## ci.upper Std.lv Std.all
##
## 0.859 0.840 0.840
## 0.432 0.389 0.389
## 0.727 0.695 0.695
##
## 0.335 0.291 0.291
## 0.784 0.749 0.749
##
## 0.382 0.330 0.330
##
## 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
## .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
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.816
## .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
## .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 -1.455
## -0.846 -0.878 -0.935
## -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
## -1.193 -1.226 -1.265
## -1.222 -1.260 -1.152
## -0.963 -1.004 -0.868
## -0.931 -0.965 -0.978
## -0.761 -0.788 -0.989
## -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
## -1.303 -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 0.331 0.010 34.380 0.000 0.312
## .Stst19dsgsdwrd 0.406 0.012 34.677 0.000 0.383
## .Stest20spellng 0.516 0.014 37.393 0.000 0.489
## .Stest21cptlztn 0.461 0.014 32.923 0.000 0.434
## .Stest22puncttn 0.337 0.011 30.531 0.000 0.315
## .Stest23english 0.576 0.017 34.094 0.000 0.543
## .Stest24exprssn 0.805 0.021 37.943 0.000 0.763
## .Stst26rdngcmpr 0.254 0.008 29.918 0.000 0.237
## .Stst31bstrctrs 0.585 0.019 31.567 0.000 0.548
## .Stst34rthcmptt 0.703 0.027 26.377 0.000 0.651
## .Stest5math 0.620 0.017 35.640 0.000 0.586
## .Stst25wrdfnctn 0.346 0.010 33.725 0.000 0.326
## .Stst32rthrsnng 0.282 0.008 34.343 0.000 0.266
## .Stst33hghschlm 0.207 0.007 28.975 0.000 0.193
## .Stest35tblrdng 1.235 0.073 16.839 0.000 1.091
## .Stst36clrclchc 1.055 0.036 29.157 0.000 0.984
## .Stst37bjctnspc 0.756 0.031 24.423 0.000 0.696
## .Stst28mchnclrs 0.231 0.007 33.590 0.000 0.218
## .Stst29vslztn2D 0.677 0.020 33.905 0.000 0.638
## .Stst30vslztn3D 0.375 0.011 33.037 0.000 0.353
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.350 0.331 0.391
## 0.429 0.406 0.460
## 0.543 0.516 0.556
## 0.489 0.461 0.451
## 0.358 0.337 0.346
## 0.609 0.576 0.484
## 0.846 0.805 0.690
## 0.270 0.254 0.270
## 0.621 0.585 0.489
## 0.755 0.703 0.525
## 0.654 0.620 0.637
## 0.366 0.346 0.543
## 0.299 0.282 0.518
## 0.221 0.207 0.428
## 1.379 1.235 0.468
## 1.126 1.055 0.643
## 0.817 0.756 0.574
## 0.245 0.231 0.616
## 0.716 0.677 0.693
## 0.398 0.375 0.628
## 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
## 409 english =~ Stest35tablereading 2 2
## 422 math =~ Stest35tablereading 2 2
## 465 Stest1vocab ~~ Stest26readingcomprehension 2 2
## 429 speed =~ Stest19disguisedwords 2 2
## 457 spatial =~ Stest35tablereading 2 2
## 491 Stest19disguisedwords ~~ Stest36clericalchecking 2 2
## 178 math =~ Stest35tablereading 1 1
## 446 spatial =~ Stest20spelling 2 2
## 213 spatial =~ Stest35tablereading 1 1
## 221 Stest1vocab ~~ Stest26readingcomprehension 1 1
## 165 english =~ Stest35tablereading 1 1
## 410 english =~ Stest36clericalchecking 2 2
## 423 math =~ Stest36clericalchecking 2 2
## 458 spatial =~ Stest36clericalchecking 2 2
## 202 spatial =~ Stest20spelling 1 1
## 639 Stest36clericalchecking ~~ Stest37objectinspection 2 2
## 425 math =~ Stest28mechanicalreasoning 2 2
## 214 spatial =~ Stest36clericalchecking 1 1
## 180 math =~ Stest37objectinspection 1 1
## 597 Stest34arithcomputation ~~ Stest33highschoolmath 2 2
## 185 speed =~ Stest19disguisedwords 1 1
## 198 speed =~ Stest29visualization2D 1 1
## 462 Stest1vocab ~~ Stest22punctuation 2 2
## 424 math =~ Stest37objectinspection 2 2
## 247 Stest19disguisedwords ~~ Stest36clericalchecking 1 1
## 418 math =~ Stest22punctuation 2 2
## 635 Stest35tablereading ~~ Stest37objectinspection 2 2
## 167 english =~ Stest37objectinspection 1 1
## 395 Stest36clericalchecking ~~ Stest37objectinspection 1 1
## 412 english =~ Stest28mechanicalreasoning 2 2
## level mi epc sepc.lv sepc.all sepc.nox
## 409 1 246.736 0.562 0.562 0.346 0.346
## 422 1 238.265 0.551 0.551 0.339 0.339
## 465 1 200.392 0.083 0.083 0.286 0.286
## 429 1 189.846 0.205 0.205 0.218 0.218
## 457 1 184.916 0.546 0.546 0.336 0.336
## 491 1 173.523 0.162 0.162 0.248 0.248
## 178 1 169.046 0.561 0.561 0.336 0.336
## 446 1 159.565 -0.315 -0.315 -0.326 -0.326
## 213 1 148.124 0.580 0.580 0.347 0.347
## 221 1 146.514 0.096 0.096 0.305 0.305
## 165 1 137.695 0.499 0.499 0.299 0.299
## 410 1 124.214 -0.276 -0.276 -0.215 -0.215
## 423 1 122.977 -0.270 -0.270 -0.211 -0.211
## 458 1 121.094 -0.296 -0.296 -0.231 -0.231
## 202 1 120.462 -0.316 -0.316 -0.317 -0.317
## 639 1 115.014 0.257 0.257 0.287 0.287
## 425 1 102.412 0.244 0.244 0.399 0.399
## 214 1 101.302 -0.332 -0.332 -0.256 -0.256
## 180 1 93.404 -0.423 -0.423 -0.341 -0.341
## 597 1 87.319 0.076 0.076 0.199 0.199
## 185 1 84.673 0.158 0.158 0.181 0.181
## 198 1 82.881 0.230 0.230 0.211 0.211
## 462 1 76.495 -0.059 -0.059 -0.177 -0.177
## 424 1 71.564 -0.309 -0.309 -0.269 -0.269
## 247 1 70.411 0.122 0.122 0.194 0.194
## 418 1 66.010 0.266 0.266 0.270 0.270
## 635 1 64.523 -0.303 -0.303 -0.313 -0.313
## 167 1 64.317 -0.314 -0.314 -0.254 -0.254
## 395 1 63.268 0.262 0.262 0.268 0.268
## 412 1 62.656 0.163 0.163 0.266 0.266
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
## 3678.537 338.000 0.000 0.941 0.057 0.052
## aic bic
## 291568.267 292387.324
Mc(metric)
## [1] 0.7599257
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 78 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 148
## Number of equality constraints 26
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3678.537 3267.595
## Degrees of freedom 338 338
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.126
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1599.587 1420.892
## 1 2078.949 1846.703
##
## 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.) 0.490 0.042 11.781 0.000 0.408
## Stst19d (.p2.) 0.669 0.014 48.664 0.000 0.642
## Stst20s (.p3.) 0.665 0.014 46.410 0.000 0.637
## Stst21c (.p4.) 0.742 0.013 56.244 0.000 0.716
## Stst22p (.p5.) 0.808 0.014 55.773 0.000 0.780
## Stst23n (.p6.) 0.835 0.017 49.265 0.000 0.802
## Stst24x (.p7.) 0.655 0.016 40.443 0.000 0.624
## Stst26r (.p8.) 0.597 0.039 15.399 0.000 0.521
## Stst31b (.p9.) 0.309 0.022 14.145 0.000 0.266
## Stst34r (.10.) 0.289 0.038 7.650 0.000 0.215
## math =~
## Stst1vc (.11.) 0.363 0.046 7.858 0.000 0.272
## Stst5mt (.12.) 0.724 0.017 41.584 0.000 0.690
## Stst25w (.13.) 0.559 0.014 39.318 0.000 0.531
## Stst26r (.14.) 0.349 0.042 8.287 0.000 0.267
## Stst32r (.15.) 0.622 0.016 39.121 0.000 0.591
## Stst33h (.16.) 0.623 0.016 39.334 0.000 0.592
## Stst34r (.17.) 0.252 0.041 6.213 0.000 0.173
## speed =~
## Stst34r (.18.) 0.484 0.021 22.561 0.000 0.442
## Stst35t (.19.) 1.193 0.035 33.611 0.000 1.123
## Stst36c (.20.) 0.784 0.025 31.453 0.000 0.735
## Stst37b (.21.) 0.722 0.026 28.068 0.000 0.672
## spatial =~
## Stst28m (.22.) 0.625 0.018 34.353 0.000 0.589
## Sts292D (.23.) 0.713 0.018 39.987 0.000 0.678
## Sts303D (.24.) 0.661 0.016 40.248 0.000 0.629
## Stst31b (.25.) 0.671 0.025 26.409 0.000 0.621
## Stst37b (.26.) 0.134 0.022 6.019 0.000 0.090
## ci.upper Std.lv Std.all
##
## 0.572 0.490 0.476
## 0.696 0.669 0.737
## 0.693 0.665 0.670
## 0.767 0.742 0.767
## 0.837 0.808 0.801
## 0.868 0.835 0.721
## 0.687 0.655 0.577
## 0.673 0.597 0.564
## 0.351 0.309 0.260
## 0.364 0.289 0.251
##
## 0.453 0.363 0.352
## 0.758 0.724 0.697
## 0.587 0.559 0.674
## 0.432 0.349 0.330
## 0.653 0.622 0.750
## 0.655 0.623 0.794
## 0.332 0.252 0.219
##
## 0.526 0.484 0.420
## 1.262 1.193 0.715
## 0.833 0.784 0.608
## 0.773 0.722 0.583
##
## 0.661 0.625 0.727
## 0.748 0.713 0.640
## 0.693 0.661 0.694
## 0.721 0.671 0.566
## 0.177 0.134 0.108
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.869 0.010 86.350 0.000 0.849
## speed 0.353 0.024 14.525 0.000 0.306
## spatial 0.689 0.017 40.224 0.000 0.655
## math ~~
## speed 0.319 0.025 12.763 0.000 0.270
## spatial 0.737 0.017 43.609 0.000 0.704
## speed ~~
## spatial 0.368 0.028 13.255 0.000 0.314
## ci.upper Std.lv Std.all
##
## 0.888 0.869 0.869
## 0.401 0.353 0.353
## 0.722 0.689 0.689
##
## 0.368 0.319 0.319
## 0.771 0.737 0.737
##
## 0.423 0.368 0.368
##
## 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
## .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
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.903
## .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
## .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 -1.122
## -0.956 -0.992 -1.092
## -0.806 -0.848 -0.855
## -1.128 -1.167 -1.207
## -1.184 -1.226 -1.215
## -1.012 -1.062 -0.917
## -0.916 -0.965 -0.850
## -1.248 -1.292 -1.222
## -1.022 -1.070 -0.903
## -1.104 -1.153 -1.001
## -0.770 -0.814 -0.783
## -0.838 -0.871 -1.050
## -1.017 -1.052 -1.267
## -0.843 -0.875 -1.114
## -0.640 -0.712 -0.427
## 0.023 -0.032 -0.025
## -0.266 -0.318 -0.257
## -0.677 -0.715 -0.832
## -0.466 -0.512 -0.459
## -0.683 -0.723 -0.760
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.378 0.013 28.551 0.000 0.353
## .Stst19dsgsdwrd 0.377 0.014 26.911 0.000 0.349
## .Stest20spellng 0.542 0.017 31.525 0.000 0.508
## .Stest21cptlztn 0.385 0.015 25.142 0.000 0.355
## .Stest22puncttn 0.365 0.013 29.218 0.000 0.341
## .Stest23english 0.645 0.024 27.175 0.000 0.599
## .Stest24exprssn 0.860 0.025 33.905 0.000 0.810
## .Stst26rdngcmpr 0.279 0.011 25.149 0.000 0.257
## .Stst31bstrctrs 0.574 0.022 26.015 0.000 0.530
## .Stst34rthcmptt 0.642 0.030 21.327 0.000 0.583
## .Stest5math 0.555 0.021 26.584 0.000 0.514
## .Stst25wrdfnctn 0.376 0.012 31.211 0.000 0.352
## .Stst32rthrsnng 0.302 0.011 28.467 0.000 0.281
## .Stst33hghschlm 0.228 0.009 25.416 0.000 0.211
## .Stest35tblrdng 1.361 0.076 17.939 0.000 1.212
## .Stst36clrclchc 1.047 0.041 25.343 0.000 0.966
## .Stst37bjctnspc 0.925 0.036 25.958 0.000 0.855
## .Stst28mchnclrs 0.348 0.016 21.868 0.000 0.317
## .Stst29vslztn2D 0.732 0.026 28.058 0.000 0.681
## .Stst30vslztn3D 0.469 0.017 27.506 0.000 0.435
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.404 0.378 0.357
## 0.404 0.377 0.457
## 0.575 0.542 0.550
## 0.415 0.385 0.412
## 0.390 0.365 0.359
## 0.692 0.645 0.481
## 0.909 0.860 0.667
## 0.300 0.279 0.249
## 0.617 0.574 0.409
## 0.701 0.642 0.484
## 0.596 0.555 0.514
## 0.399 0.376 0.546
## 0.322 0.302 0.438
## 0.246 0.228 0.370
## 1.509 1.361 0.489
## 1.128 1.047 0.630
## 0.995 0.925 0.602
## 0.380 0.348 0.471
## 0.783 0.732 0.590
## 0.502 0.469 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
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.490 0.042 11.781 0.000 0.408
## Stst19d (.p2.) 0.669 0.014 48.664 0.000 0.642
## Stst20s (.p3.) 0.665 0.014 46.410 0.000 0.637
## Stst21c (.p4.) 0.742 0.013 56.244 0.000 0.716
## Stst22p (.p5.) 0.808 0.014 55.773 0.000 0.780
## Stst23n (.p6.) 0.835 0.017 49.265 0.000 0.802
## Stst24x (.p7.) 0.655 0.016 40.443 0.000 0.624
## Stst26r (.p8.) 0.597 0.039 15.399 0.000 0.521
## Stst31b (.p9.) 0.309 0.022 14.145 0.000 0.266
## Stst34r (.10.) 0.289 0.038 7.650 0.000 0.215
## math =~
## Stst1vc (.11.) 0.363 0.046 7.858 0.000 0.272
## Stst5mt (.12.) 0.724 0.017 41.584 0.000 0.690
## Stst25w (.13.) 0.559 0.014 39.318 0.000 0.531
## Stst26r (.14.) 0.349 0.042 8.287 0.000 0.267
## Stst32r (.15.) 0.622 0.016 39.121 0.000 0.591
## Stst33h (.16.) 0.623 0.016 39.334 0.000 0.592
## Stst34r (.17.) 0.252 0.041 6.213 0.000 0.173
## speed =~
## Stst34r (.18.) 0.484 0.021 22.561 0.000 0.442
## Stst35t (.19.) 1.193 0.035 33.611 0.000 1.123
## Stst36c (.20.) 0.784 0.025 31.453 0.000 0.735
## Stst37b (.21.) 0.722 0.026 28.068 0.000 0.672
## spatial =~
## Stst28m (.22.) 0.625 0.018 34.353 0.000 0.589
## Sts292D (.23.) 0.713 0.018 39.987 0.000 0.678
## Sts303D (.24.) 0.661 0.016 40.248 0.000 0.629
## Stst31b (.25.) 0.671 0.025 26.409 0.000 0.621
## Stst37b (.26.) 0.134 0.022 6.019 0.000 0.090
## ci.upper Std.lv Std.all
##
## 0.572 0.478 0.506
## 0.696 0.653 0.713
## 0.693 0.649 0.671
## 0.767 0.723 0.728
## 0.837 0.788 0.806
## 0.868 0.815 0.734
## 0.687 0.639 0.582
## 0.673 0.582 0.594
## 0.351 0.301 0.284
## 0.364 0.282 0.245
##
## 0.453 0.304 0.322
## 0.758 0.608 0.612
## 0.587 0.469 0.614
## 0.432 0.293 0.299
## 0.653 0.522 0.701
## 0.655 0.523 0.753
## 0.332 0.212 0.184
##
## 0.526 0.479 0.416
## 1.262 1.181 0.727
## 0.833 0.776 0.604
## 0.773 0.715 0.623
##
## 0.661 0.434 0.683
## 0.748 0.495 0.509
## 0.693 0.459 0.595
## 0.721 0.466 0.440
## 0.177 0.093 0.081
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.685 0.031 22.212 0.000 0.624
## speed 0.379 0.025 15.243 0.000 0.330
## spatial 0.471 0.022 21.366 0.000 0.427
## math ~~
## speed 0.243 0.020 12.367 0.000 0.205
## spatial 0.442 0.025 17.586 0.000 0.392
## speed ~~
## spatial 0.228 0.020 11.578 0.000 0.190
## ci.upper Std.lv Std.all
##
## 0.745 0.836 0.836
## 0.427 0.392 0.392
## 0.514 0.695 0.695
##
## 0.282 0.293 0.293
## 0.491 0.758 0.758
##
## 0.267 0.332 0.332
##
## 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
## .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
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.816
## .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
## .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 -1.417
## -0.846 -0.878 -0.960
## -0.417 -0.450 -0.466
## -0.865 -0.899 -0.905
## -0.895 -0.929 -0.949
## -0.706 -0.744 -0.670
## -0.667 -0.704 -0.641
## -1.193 -1.226 -1.250
## -1.222 -1.260 -1.189
## -0.963 -1.004 -0.871
## -0.931 -0.965 -0.971
## -0.761 -0.788 -1.033
## -1.159 -1.184 -1.589
## -0.919 -0.942 -1.357
## -0.466 -0.524 -0.323
## 0.344 0.300 0.233
## -0.176 -0.217 -0.189
## -1.303 -1.323 -2.083
## -0.882 -0.916 -0.942
## -0.955 -0.982 -1.274
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.328 0.010 33.988 0.000 0.309
## .Stst19dsgsdwrd 0.412 0.012 34.908 0.000 0.388
## .Stest20spellng 0.514 0.014 37.489 0.000 0.487
## .Stest21cptlztn 0.464 0.014 33.629 0.000 0.437
## .Stest22puncttn 0.336 0.011 30.650 0.000 0.315
## .Stest23english 0.568 0.017 33.821 0.000 0.535
## .Stest24exprssn 0.800 0.021 37.830 0.000 0.758
## .Stst26rdngcmpr 0.252 0.008 30.313 0.000 0.235
## .Stst31bstrctrs 0.620 0.017 35.902 0.000 0.586
## .Stst34rthcmptt 0.707 0.027 26.023 0.000 0.654
## .Stest5math 0.618 0.017 35.613 0.000 0.584
## .Stst25wrdfnctn 0.363 0.011 34.531 0.000 0.342
## .Stst32rthrsnng 0.282 0.008 34.254 0.000 0.266
## .Stst33hghschlm 0.209 0.007 29.344 0.000 0.195
## .Stest35tblrdng 1.241 0.067 18.544 0.000 1.110
## .Stst36clrclchc 1.050 0.033 32.026 0.000 0.986
## .Stst37bjctnspc 0.753 0.028 26.583 0.000 0.697
## .Stst28mchnclrs 0.215 0.007 32.089 0.000 0.202
## .Stst29vslztn2D 0.700 0.019 36.866 0.000 0.663
## .Stst30vslztn3D 0.383 0.011 34.809 0.000 0.362
## english 0.952 0.038 25.049 0.000 0.877
## math 0.705 0.043 16.345 0.000 0.620
## speed 0.981 0.059 16.623 0.000 0.865
## spatial 0.482 0.028 17.114 0.000 0.427
## ci.upper Std.lv Std.all
## 0.347 0.328 0.367
## 0.435 0.412 0.491
## 0.540 0.514 0.549
## 0.491 0.464 0.470
## 0.358 0.336 0.351
## 0.601 0.568 0.461
## 0.841 0.800 0.662
## 0.268 0.252 0.261
## 0.654 0.620 0.552
## 0.761 0.707 0.533
## 0.652 0.618 0.626
## 0.384 0.363 0.623
## 0.298 0.282 0.508
## 0.223 0.209 0.432
## 1.373 1.241 0.471
## 1.114 1.050 0.635
## 0.808 0.753 0.571
## 0.229 0.215 0.534
## 0.737 0.700 0.741
## 0.405 0.383 0.645
## 1.026 1.000 1.000
## 0.789 1.000 1.000
## 1.096 1.000 1.000
## 0.537 1.000 1.000
lavTestScore(metric, release = 1:26)
## 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 304.318 26 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p81. 31.462 1 0.000
## 2 .p2. == .p82. 31.410 1 0.000
## 3 .p3. == .p83. 0.479 1 0.489
## 4 .p4. == .p84. 13.716 1 0.000
## 5 .p5. == .p85. 3.070 1 0.080
## 6 .p6. == .p86. 14.217 1 0.000
## 7 .p7. == .p87. 14.056 1 0.000
## 8 .p8. == .p88. 7.267 1 0.007
## 9 .p9. == .p89. 37.614 1 0.000
## 10 .p10. == .p90. 0.316 1 0.574
## 11 .p11. == .p91. 30.202 1 0.000
## 12 .p12. == .p92. 1.979 1 0.159
## 13 .p13. == .p93. 92.543 1 0.000
## 14 .p14. == .p94. 9.880 1 0.002
## 15 .p15. == .p95. 4.008 1 0.045
## 16 .p16. == .p96. 0.001 1 0.979
## 17 .p17. == .p97. 0.033 1 0.856
## 18 .p18. == .p98. 1.365 1 0.243
## 19 .p19. == .p99. 0.000 1 0.994
## 20 .p20. == .p100. 0.961 1 0.327
## 21 .p21. == .p101. 0.000 1 0.994
## 22 .p22. == .p102. 94.547 1 0.000
## 23 .p23. == .p103. 16.481 1 0.000
## 24 .p24. == .p104. 0.645 1 0.422
## 25 .p25. == .p105. 46.734 1 0.000
## 26 .p26. == .p106. 0.504 1 0.478
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("spatial=~Stest28mechanicalreasoning", "math=~Stest25wordfunctions"))
fitMeasures(metric2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 3481.375 336.000 0.000 0.945 0.055 0.046
## aic bic
## 291375.106 292207.590
Mc(metric2)
## [1] 0.7722124
summary(metric2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 81 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 148
## Number of equality constraints 24
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3481.375 3092.289
## Degrees of freedom 336 336
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.126
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1503.010 1335.030
## 1 1978.365 1757.258
##
## 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.) 0.487 0.039 12.472 0.000 0.410
## Stst19d (.p2.) 0.668 0.014 48.564 0.000 0.641
## Stst20s (.p3.) 0.664 0.014 46.262 0.000 0.636
## Stst21c (.p4.) 0.740 0.013 56.045 0.000 0.715
## Stst22p (.p5.) 0.807 0.015 55.471 0.000 0.778
## Stst23n (.p6.) 0.834 0.017 49.016 0.000 0.800
## Stst24x (.p7.) 0.654 0.016 40.291 0.000 0.622
## Stst26r (.p8.) 0.597 0.036 16.371 0.000 0.525
## Stst31b (.p9.) 0.283 0.023 12.511 0.000 0.238
## Stst34r (.10.) 0.297 0.037 8.075 0.000 0.225
## math =~
## Stst1vc (.11.) 0.377 0.044 8.573 0.000 0.291
## Stst5mt (.12.) 0.743 0.017 43.201 0.000 0.709
## Stst25w 0.476 0.018 26.562 0.000 0.441
## Stst26r (.14.) 0.359 0.040 8.942 0.000 0.280
## Stst32r (.15.) 0.640 0.016 40.041 0.000 0.609
## Stst33h (.16.) 0.640 0.016 40.312 0.000 0.609
## Stst34r (.17.) 0.250 0.041 6.168 0.000 0.170
## speed =~
## Stst34r (.18.) 0.484 0.021 22.614 0.000 0.442
## Stst35t (.19.) 1.194 0.036 33.616 0.000 1.124
## Stst36c (.20.) 0.785 0.025 31.411 0.000 0.736
## Stst37b (.21.) 0.722 0.026 28.013 0.000 0.671
## spatial =~
## Stst28m 0.708 0.018 39.675 0.000 0.673
## Sts292D (.23.) 0.667 0.019 36.006 0.000 0.631
## Sts303D (.24.) 0.611 0.017 35.794 0.000 0.577
## Stst31b (.25.) 0.657 0.026 25.323 0.000 0.606
## Stst37b (.26.) 0.126 0.021 6.073 0.000 0.085
## ci.upper Std.lv Std.all
##
## 0.563 0.487 0.470
## 0.695 0.668 0.736
## 0.692 0.664 0.670
## 0.766 0.740 0.766
## 0.835 0.807 0.800
## 0.867 0.834 0.720
## 0.686 0.654 0.576
## 0.668 0.597 0.561
## 0.327 0.283 0.243
## 0.369 0.297 0.257
##
## 0.463 0.377 0.364
## 0.777 0.743 0.708
## 0.511 0.476 0.611
## 0.438 0.359 0.337
## 0.672 0.640 0.761
## 0.671 0.640 0.803
## 0.329 0.250 0.216
##
## 0.525 0.484 0.419
## 1.263 1.194 0.715
## 0.834 0.785 0.609
## 0.772 0.722 0.583
##
## 0.743 0.708 0.787
## 0.703 0.667 0.609
## 0.644 0.611 0.657
## 0.708 0.657 0.565
## 0.167 0.126 0.102
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.865 0.010 83.548 0.000 0.845
## speed 0.353 0.024 14.531 0.000 0.306
## spatial 0.699 0.017 41.691 0.000 0.666
## math ~~
## speed 0.319 0.025 12.833 0.000 0.270
## spatial 0.747 0.016 45.273 0.000 0.714
## speed ~~
## spatial 0.364 0.027 13.272 0.000 0.311
## ci.upper Std.lv Std.all
##
## 0.885 0.865 0.865
## 0.401 0.353 0.353
## 0.732 0.699 0.699
##
## 0.367 0.319 0.319
## 0.779 0.747 0.747
##
## 0.418 0.364 0.364
##
## 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
## .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
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.903
## .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
## .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 -1.115
## -0.956 -0.992 -1.094
## -0.806 -0.848 -0.855
## -1.128 -1.167 -1.208
## -1.184 -1.226 -1.216
## -1.012 -1.062 -0.918
## -0.916 -0.965 -0.850
## -1.248 -1.292 -1.214
## -1.022 -1.070 -0.919
## -1.104 -1.153 -0.998
## -0.770 -0.814 -0.775
## -0.838 -0.871 -1.119
## -1.017 -1.052 -1.250
## -0.843 -0.875 -1.098
## -0.640 -0.712 -0.427
## 0.023 -0.032 -0.025
## -0.266 -0.318 -0.257
## -0.677 -0.715 -0.795
## -0.466 -0.512 -0.468
## -0.683 -0.723 -0.778
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.375 0.013 28.283 0.000 0.349
## .Stst19dsgsdwrd 0.376 0.014 26.905 0.000 0.349
## .Stest20spellng 0.542 0.017 31.530 0.000 0.508
## .Stest21cptlztn 0.385 0.015 25.159 0.000 0.355
## .Stest22puncttn 0.366 0.013 29.233 0.000 0.341
## .Stest23english 0.645 0.024 27.165 0.000 0.598
## .Stest24exprssn 0.860 0.025 33.906 0.000 0.810
## .Stst26rdngcmpr 0.277 0.011 25.007 0.000 0.255
## .Stst31bstrctrs 0.584 0.022 26.364 0.000 0.540
## .Stst34rthcmptt 0.642 0.030 21.363 0.000 0.583
## .Stest5math 0.550 0.021 26.495 0.000 0.510
## .Stst25wrdfnctn 0.379 0.012 31.876 0.000 0.356
## .Stst32rthrsnng 0.298 0.011 28.079 0.000 0.277
## .Stst33hghschlm 0.226 0.009 25.073 0.000 0.208
## .Stest35tblrdng 1.360 0.076 17.898 0.000 1.211
## .Stst36clrclchc 1.046 0.041 25.302 0.000 0.965
## .Stst37bjctnspc 0.927 0.036 25.987 0.000 0.858
## .Stst28mchnclrs 0.308 0.015 20.057 0.000 0.278
## .Stst29vslztn2D 0.753 0.026 28.940 0.000 0.702
## .Stst30vslztn3D 0.490 0.017 28.556 0.000 0.457
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.401 0.375 0.350
## 0.404 0.376 0.458
## 0.576 0.542 0.551
## 0.415 0.385 0.413
## 0.390 0.366 0.360
## 0.691 0.645 0.481
## 0.909 0.860 0.668
## 0.299 0.277 0.244
## 0.627 0.584 0.431
## 0.701 0.642 0.481
## 0.591 0.550 0.499
## 0.403 0.379 0.626
## 0.319 0.298 0.421
## 0.243 0.226 0.355
## 1.509 1.360 0.488
## 1.127 1.046 0.629
## 0.997 0.927 0.606
## 0.338 0.308 0.381
## 0.804 0.753 0.629
## 0.524 0.490 0.568
## 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.) 0.487 0.039 12.472 0.000 0.410
## Stst19d (.p2.) 0.668 0.014 48.564 0.000 0.641
## Stst20s (.p3.) 0.664 0.014 46.262 0.000 0.636
## Stst21c (.p4.) 0.740 0.013 56.045 0.000 0.715
## Stst22p (.p5.) 0.807 0.015 55.471 0.000 0.778
## Stst23n (.p6.) 0.834 0.017 49.016 0.000 0.800
## Stst24x (.p7.) 0.654 0.016 40.291 0.000 0.622
## Stst26r (.p8.) 0.597 0.036 16.371 0.000 0.525
## Stst31b (.p9.) 0.283 0.023 12.511 0.000 0.238
## Stst34r (.10.) 0.297 0.037 8.075 0.000 0.225
## math =~
## Stst1vc (.11.) 0.377 0.044 8.573 0.000 0.291
## Stst5mt (.12.) 0.743 0.017 43.201 0.000 0.709
## Stst25w 0.676 0.021 32.070 0.000 0.635
## Stst26r (.14.) 0.359 0.040 8.942 0.000 0.280
## Stst32r (.15.) 0.640 0.016 40.041 0.000 0.609
## Stst33h (.16.) 0.640 0.016 40.312 0.000 0.609
## Stst34r (.17.) 0.250 0.041 6.168 0.000 0.170
## speed =~
## Stst34r (.18.) 0.484 0.021 22.614 0.000 0.442
## Stst35t (.19.) 1.194 0.036 33.616 0.000 1.124
## Stst36c (.20.) 0.785 0.025 31.411 0.000 0.736
## Stst37b (.21.) 0.722 0.026 28.013 0.000 0.671
## spatial =~
## Stst28m 0.467 0.021 22.632 0.000 0.427
## Sts292D (.23.) 0.667 0.019 36.006 0.000 0.631
## Sts303D (.24.) 0.611 0.017 35.794 0.000 0.577
## Stst31b (.25.) 0.657 0.026 25.323 0.000 0.606
## Stst37b (.26.) 0.126 0.021 6.073 0.000 0.085
## ci.upper Std.lv Std.all
##
## 0.563 0.476 0.506
## 0.695 0.654 0.714
## 0.692 0.650 0.672
## 0.766 0.725 0.729
## 0.835 0.790 0.806
## 0.867 0.816 0.734
## 0.686 0.640 0.582
## 0.668 0.584 0.598
## 0.327 0.277 0.257
## 0.369 0.291 0.253
##
## 0.463 0.300 0.319
## 0.777 0.591 0.600
## 0.717 0.537 0.674
## 0.438 0.286 0.292
## 0.672 0.509 0.691
## 0.671 0.509 0.741
## 0.329 0.199 0.173
##
## 0.525 0.478 0.416
## 1.263 1.180 0.727
## 0.834 0.776 0.604
## 0.772 0.714 0.621
##
## 0.508 0.380 0.620
## 0.703 0.542 0.549
## 0.644 0.496 0.633
## 0.708 0.534 0.496
## 0.167 0.103 0.089
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.652 0.029 22.348 0.000 0.595
## speed 0.378 0.025 15.140 0.000 0.329
## spatial 0.549 0.025 21.792 0.000 0.499
## math ~~
## speed 0.229 0.019 12.286 0.000 0.193
## spatial 0.484 0.026 18.359 0.000 0.432
## speed ~~
## spatial 0.267 0.023 11.530 0.000 0.222
## ci.upper Std.lv Std.all
##
## 0.709 0.838 0.838
## 0.427 0.390 0.390
## 0.598 0.690 0.690
##
## 0.266 0.292 0.292
## 0.536 0.750 0.750
##
## 0.313 0.332 0.332
##
## 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
## .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
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.816
## .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
## .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 -1.423
## -0.846 -0.878 -0.959
## -0.417 -0.450 -0.466
## -0.865 -0.899 -0.905
## -0.895 -0.929 -0.949
## -0.706 -0.744 -0.669
## -0.667 -0.704 -0.641
## -1.193 -1.226 -1.255
## -1.222 -1.260 -1.170
## -0.963 -1.004 -0.873
## -0.931 -0.965 -0.980
## -0.761 -0.788 -0.989
## -1.159 -1.184 -1.607
## -0.919 -0.942 -1.373
## -0.466 -0.524 -0.323
## 0.344 0.300 0.233
## -0.176 -0.217 -0.189
## -1.303 -1.323 -2.162
## -0.882 -0.916 -0.928
## -0.955 -0.982 -1.252
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.329 0.010 34.123 0.000 0.310
## .Stst19dsgsdwrd 0.412 0.012 34.906 0.000 0.388
## .Stest20spellng 0.513 0.014 37.506 0.000 0.486
## .Stest21cptlztn 0.464 0.014 33.658 0.000 0.437
## .Stest22puncttn 0.336 0.011 30.746 0.000 0.314
## .Stest23english 0.568 0.017 33.822 0.000 0.535
## .Stest24exprssn 0.800 0.021 37.836 0.000 0.758
## .Stst26rdngcmpr 0.253 0.008 30.333 0.000 0.236
## .Stst31bstrctrs 0.594 0.018 33.961 0.000 0.560
## .Stst34rthcmptt 0.708 0.027 26.041 0.000 0.655
## .Stest5math 0.621 0.017 35.726 0.000 0.587
## .Stst25wrdfnctn 0.347 0.010 33.771 0.000 0.327
## .Stst32rthrsnng 0.284 0.008 34.625 0.000 0.268
## .Stst33hghschlm 0.212 0.007 30.197 0.000 0.199
## .Stest35tblrdng 1.243 0.067 18.514 0.000 1.111
## .Stst36clrclchc 1.049 0.033 31.908 0.000 0.985
## .Stst37bjctnspc 0.752 0.028 26.583 0.000 0.696
## .Stst28mchnclrs 0.231 0.007 33.555 0.000 0.217
## .Stst29vslztn2D 0.679 0.019 35.425 0.000 0.641
## .Stst30vslztn3D 0.369 0.011 33.327 0.000 0.347
## english 0.957 0.038 24.914 0.000 0.882
## math 0.632 0.038 16.464 0.000 0.557
## speed 0.978 0.059 16.618 0.000 0.863
## spatial 0.660 0.040 16.519 0.000 0.582
## ci.upper Std.lv Std.all
## 0.348 0.329 0.371
## 0.435 0.412 0.491
## 0.540 0.513 0.549
## 0.491 0.464 0.469
## 0.357 0.336 0.350
## 0.601 0.568 0.461
## 0.841 0.800 0.661
## 0.269 0.253 0.265
## 0.629 0.594 0.512
## 0.761 0.708 0.536
## 0.655 0.621 0.640
## 0.368 0.347 0.546
## 0.300 0.284 0.523
## 0.226 0.212 0.451
## 1.374 1.243 0.471
## 1.114 1.049 0.635
## 0.807 0.752 0.569
## 0.244 0.231 0.616
## 0.717 0.679 0.698
## 0.391 0.369 0.600
## 1.033 1.000 1.000
## 0.707 1.000 1.000
## 1.093 1.000 1.000
## 0.738 1.000 1.000
lavTestScore(metric2, release = 1:24)
## 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 120.134 24 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p81. 23.012 1 0.000
## 2 .p2. == .p82. 29.788 1 0.000
## 3 .p3. == .p83. 0.618 1 0.432
## 4 .p4. == .p84. 12.670 1 0.000
## 5 .p5. == .p85. 2.597 1 0.107
## 6 .p6. == .p86. 15.494 1 0.000
## 7 .p7. == .p87. 14.748 1 0.000
## 8 .p8. == .p88. 2.959 1 0.085
## 9 .p9. == .p89. 11.849 1 0.001
## 10 .p10. == .p90. 1.100 1 0.294
## 11 .p11. == .p91. 22.250 1 0.000
## 12 .p12. == .p92. 0.166 1 0.684
## 13 .p14. == .p94. 4.450 1 0.035
## 14 .p15. == .p95. 0.155 1 0.694
## 15 .p16. == .p96. 8.430 1 0.004
## 16 .p17. == .p97. 0.471 1 0.492
## 17 .p18. == .p98. 1.946 1 0.163
## 18 .p19. == .p99. 0.004 1 0.952
## 19 .p20. == .p100. 0.881 1 0.348
## 20 .p21. == .p101. 0.083 1 0.773
## 21 .p23. == .p103. 0.428 1 0.513
## 22 .p24. == .p104. 16.178 1 0.000
## 23 .p25. == .p105. 12.499 1 0.000
## 24 .p26. == .p106. 0.084 1 0.773
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("spatial=~Stest28mechanicalreasoning", "math=~Stest25wordfunctions"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 4344.202 352.000 0.000 0.930 0.061 0.051
## aic bic
## 292205.933 292930.999
Mc(scalar)
## [1] 0.720298
summary(scalar, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 81 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 152
## Number of equality constraints 44
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 4344.202 3872.484
## Degrees of freedom 352 352
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.122
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1938.876 1728.342
## 1 2405.326 2144.142
##
## 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.) 0.186 0.042 4.429 0.000 0.104
## Stst19d (.p2.) 0.647 0.014 47.366 0.000 0.621
## Stst20s (.p3.) 0.672 0.014 46.870 0.000 0.644
## Stst21c (.p4.) 0.737 0.013 55.913 0.000 0.711
## Stst22p (.p5.) 0.805 0.015 54.515 0.000 0.776
## Stst23n (.p6.) 0.828 0.017 48.083 0.000 0.794
## Stst24x (.p7.) 0.651 0.016 40.123 0.000 0.619
## Stst26r (.p8.) 0.437 0.032 13.650 0.000 0.374
## Stst31b (.p9.) 0.377 0.016 22.930 0.000 0.345
## Stst34r (.10.) 0.285 0.031 9.060 0.000 0.223
## math =~
## Stst1vc (.11.) 0.706 0.047 15.168 0.000 0.615
## Stst5mt (.12.) 0.735 0.017 43.160 0.000 0.701
## Stst25w 0.461 0.018 25.254 0.000 0.426
## Stst26r (.14.) 0.529 0.035 15.247 0.000 0.461
## Stst32r (.15.) 0.628 0.016 38.782 0.000 0.596
## Stst33h (.16.) 0.620 0.016 38.892 0.000 0.589
## Stst34r (.17.) 0.256 0.035 7.419 0.000 0.189
## speed =~
## Stst34r (.18.) 0.480 0.022 22.259 0.000 0.438
## Stst35t (.19.) 1.176 0.036 32.804 0.000 1.106
## Stst36c (.20.) 0.798 0.024 32.649 0.000 0.750
## Stst37b (.21.) 0.731 0.024 30.758 0.000 0.684
## spatial =~
## Stst28m 0.717 0.019 37.587 0.000 0.679
## Sts292D (.23.) 0.682 0.019 36.457 0.000 0.645
## Sts303D (.24.) 0.601 0.018 34.279 0.000 0.566
## Stst31b (.25.) 0.569 0.020 28.747 0.000 0.530
## Stst37b (.26.) 0.127 0.019 6.549 0.000 0.089
## ci.upper Std.lv Std.all
##
## 0.268 0.186 0.175
## 0.674 0.647 0.723
## 0.700 0.672 0.672
## 0.763 0.737 0.767
## 0.834 0.805 0.803
## 0.862 0.828 0.718
## 0.682 0.651 0.574
## 0.500 0.437 0.407
## 0.409 0.377 0.323
## 0.347 0.285 0.247
##
## 0.798 0.706 0.663
## 0.768 0.735 0.700
## 0.497 0.461 0.590
## 0.597 0.529 0.493
## 0.660 0.628 0.747
## 0.651 0.620 0.780
## 0.324 0.256 0.222
##
## 0.522 0.480 0.416
## 1.246 1.176 0.706
## 0.846 0.798 0.615
## 0.777 0.731 0.590
##
## 0.754 0.717 0.786
## 0.718 0.682 0.619
## 0.635 0.601 0.645
## 0.608 0.569 0.487
## 0.164 0.127 0.102
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.889 0.011 78.857 0.000 0.867
## speed 0.357 0.025 14.446 0.000 0.309
## spatial 0.687 0.017 39.653 0.000 0.653
## math ~~
## speed 0.319 0.025 12.796 0.000 0.270
## spatial 0.748 0.016 45.527 0.000 0.715
## speed ~~
## spatial 0.365 0.028 13.124 0.000 0.311
## ci.upper Std.lv Std.all
##
## 0.912 0.889 0.889
## 0.405 0.357 0.357
## 0.721 0.687 0.687
##
## 0.368 0.319 0.319
## 0.780 0.748 0.748
##
## 0.420 0.365 0.365
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.57.) -1.297 0.027 -47.511 0.000 -1.351
## .Stst19d (.58.) -1.101 0.018 -61.328 0.000 -1.136
## .Stst20s (.59.) -0.794 0.021 -37.150 0.000 -0.836
## .Stst21c (.60.) -1.211 0.021 -57.826 0.000 -1.252
## .Stst22p (.61.) -1.272 0.023 -54.912 0.000 -1.317
## .Stst23n (.62.) -1.101 0.025 -43.196 0.000 -1.151
## .Stst24x (.63.) -0.989 0.022 -44.677 0.000 -1.033
## .Stst26r (.64.) -1.357 0.026 -51.432 0.000 -1.409
## .Stst31b (.65.) -1.083 0.026 -41.699 0.000 -1.134
## .Stst34r (.66.) -1.216 0.025 -48.085 0.000 -1.266
## .Stst5mt (.67.) -0.879 0.022 -40.477 0.000 -0.922
## .Stst25w (.68.) -0.792 0.017 -47.547 0.000 -0.825
## .Stst32r (.69.) -1.111 0.018 -62.550 0.000 -1.146
## .Stst33h (.70.) -0.895 0.017 -51.763 0.000 -0.929
## .Stst35t (.71.) -0.804 0.035 -22.805 0.000 -0.873
## .Stst36c (.72.) 0.030 0.026 1.141 0.254 -0.021
## .Stst37b (.73.) -0.337 0.025 -13.698 0.000 -0.385
## .Stst28m (.74.) -0.861 0.028 -30.946 0.000 -0.915
## .Sts292D (.75.) -0.506 0.023 -22.416 0.000 -0.550
## .Sts303D (.76.) -0.652 0.019 -33.484 0.000 -0.690
## ci.upper Std.lv Std.all
## -1.244 -1.297 -1.218
## -1.066 -1.101 -1.229
## -0.752 -0.794 -0.794
## -1.170 -1.211 -1.261
## -1.226 -1.272 -1.268
## -1.051 -1.101 -0.954
## -0.946 -0.989 -0.873
## -1.305 -1.357 -1.263
## -1.032 -1.083 -0.927
## -1.167 -1.216 -1.055
## -0.837 -0.879 -0.839
## -0.759 -0.792 -1.013
## -1.076 -1.111 -1.321
## -0.861 -0.895 -1.126
## -0.735 -0.804 -0.483
## 0.080 0.030 0.023
## -0.289 -0.337 -0.272
## -0.806 -0.861 -0.945
## -0.462 -0.506 -0.459
## -0.614 -0.652 -0.700
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.367 0.015 23.953 0.000 0.337
## .Stst19dsgsdwrd 0.383 0.015 26.073 0.000 0.355
## .Stest20spellng 0.548 0.018 31.250 0.000 0.514
## .Stest21cptlztn 0.380 0.015 24.942 0.000 0.351
## .Stest22puncttn 0.358 0.012 28.987 0.000 0.334
## .Stest23english 0.646 0.024 27.080 0.000 0.599
## .Stest24exprssn 0.860 0.025 33.757 0.000 0.810
## .Stst26rdngcmpr 0.272 0.011 23.915 0.000 0.249
## .Stst31bstrctrs 0.605 0.022 27.892 0.000 0.563
## .Stst34rthcmptt 0.645 0.030 21.480 0.000 0.586
## .Stest5math 0.560 0.021 26.691 0.000 0.519
## .Stst25wrdfnctn 0.399 0.013 31.459 0.000 0.374
## .Stst32rthrsnng 0.313 0.011 27.868 0.000 0.291
## .Stst33hghschlm 0.247 0.009 26.135 0.000 0.228
## .Stest35tblrdng 1.392 0.075 18.649 0.000 1.246
## .Stst36clrclchc 1.045 0.042 24.793 0.000 0.962
## .Stst37bjctnspc 0.918 0.036 25.692 0.000 0.848
## .Stst28mchnclrs 0.317 0.017 18.355 0.000 0.283
## .Stst29vslztn2D 0.748 0.026 28.392 0.000 0.696
## .Stst30vslztn3D 0.507 0.018 28.601 0.000 0.472
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.397 0.367 0.324
## 0.412 0.383 0.478
## 0.582 0.548 0.548
## 0.410 0.380 0.412
## 0.382 0.358 0.356
## 0.692 0.646 0.485
## 0.910 0.860 0.670
## 0.294 0.272 0.235
## 0.648 0.605 0.443
## 0.704 0.645 0.486
## 0.601 0.560 0.509
## 0.424 0.399 0.652
## 0.335 0.313 0.442
## 0.265 0.247 0.391
## 1.538 1.392 0.502
## 1.127 1.045 0.621
## 0.988 0.918 0.598
## 0.350 0.317 0.381
## 0.800 0.748 0.617
## 0.542 0.507 0.584
## 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.) 0.186 0.042 4.429 0.000 0.104
## Stst19d (.p2.) 0.647 0.014 47.366 0.000 0.621
## Stst20s (.p3.) 0.672 0.014 46.870 0.000 0.644
## Stst21c (.p4.) 0.737 0.013 55.913 0.000 0.711
## Stst22p (.p5.) 0.805 0.015 54.515 0.000 0.776
## Stst23n (.p6.) 0.828 0.017 48.083 0.000 0.794
## Stst24x (.p7.) 0.651 0.016 40.123 0.000 0.619
## Stst26r (.p8.) 0.437 0.032 13.650 0.000 0.374
## Stst31b (.p9.) 0.377 0.016 22.930 0.000 0.345
## Stst34r (.10.) 0.285 0.031 9.060 0.000 0.223
## math =~
## Stst1vc (.11.) 0.706 0.047 15.168 0.000 0.615
## Stst5mt (.12.) 0.735 0.017 43.160 0.000 0.701
## Stst25w 0.644 0.021 31.210 0.000 0.604
## Stst26r (.14.) 0.529 0.035 15.247 0.000 0.461
## Stst32r (.15.) 0.628 0.016 38.782 0.000 0.596
## Stst33h (.16.) 0.620 0.016 38.892 0.000 0.589
## Stst34r (.17.) 0.256 0.035 7.419 0.000 0.189
## speed =~
## Stst34r (.18.) 0.480 0.022 22.259 0.000 0.438
## Stst35t (.19.) 1.176 0.036 32.804 0.000 1.106
## Stst36c (.20.) 0.798 0.024 32.649 0.000 0.750
## Stst37b (.21.) 0.731 0.024 30.758 0.000 0.684
## spatial =~
## Stst28m 0.648 0.033 19.787 0.000 0.584
## Sts292D (.23.) 0.682 0.019 36.457 0.000 0.645
## Sts303D (.24.) 0.601 0.018 34.279 0.000 0.566
## Stst31b (.25.) 0.569 0.020 28.747 0.000 0.530
## Stst37b (.26.) 0.127 0.019 6.549 0.000 0.089
## ci.upper Std.lv Std.all
##
## 0.268 0.185 0.200
## 0.674 0.645 0.706
## 0.700 0.670 0.682
## 0.763 0.734 0.735
## 0.834 0.803 0.816
## 0.862 0.825 0.740
## 0.682 0.649 0.588
## 0.500 0.436 0.448
## 0.409 0.376 0.352
## 0.347 0.284 0.247
##
## 0.798 0.565 0.609
## 0.768 0.588 0.595
## 0.685 0.516 0.648
## 0.597 0.423 0.436
## 0.660 0.502 0.679
## 0.651 0.496 0.721
## 0.324 0.205 0.178
##
## 0.522 0.475 0.413
## 1.246 1.164 0.718
## 0.846 0.789 0.611
## 0.777 0.723 0.630
##
## 0.712 0.453 0.703
## 0.718 0.477 0.492
## 0.635 0.420 0.553
## 0.608 0.398 0.372
## 0.164 0.088 0.077
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.696 0.030 22.828 0.000 0.636
## speed 0.388 0.025 15.252 0.000 0.338
## spatial 0.480 0.027 17.525 0.000 0.427
## math ~~
## speed 0.241 0.019 12.673 0.000 0.204
## spatial 0.424 0.026 16.199 0.000 0.372
## speed ~~
## spatial 0.228 0.022 10.452 0.000 0.186
## ci.upper Std.lv Std.all
##
## 0.756 0.873 0.873
## 0.438 0.394 0.394
## 0.534 0.690 0.690
##
## 0.279 0.305 0.305
## 0.475 0.757 0.757
##
## 0.271 0.330 0.330
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.57.) -1.297 0.027 -47.511 0.000 -1.351
## .Stst19d (.58.) -1.101 0.018 -61.328 0.000 -1.136
## .Stst20s (.59.) -0.794 0.021 -37.150 0.000 -0.836
## .Stst21c (.60.) -1.211 0.021 -57.826 0.000 -1.252
## .Stst22p (.61.) -1.272 0.023 -54.912 0.000 -1.317
## .Stst23n (.62.) -1.101 0.025 -43.196 0.000 -1.151
## .Stst24x (.63.) -0.989 0.022 -44.677 0.000 -1.033
## .Stst26r (.64.) -1.357 0.026 -51.432 0.000 -1.409
## .Stst31b (.65.) -1.083 0.026 -41.699 0.000 -1.134
## .Stst34r (.66.) -1.216 0.025 -48.085 0.000 -1.266
## .Stst5mt (.67.) -0.879 0.022 -40.477 0.000 -0.922
## .Stst25w (.68.) -0.792 0.017 -47.547 0.000 -0.825
## .Stst32r (.69.) -1.111 0.018 -62.550 0.000 -1.146
## .Stst33h (.70.) -0.895 0.017 -51.763 0.000 -0.929
## .Stst35t (.71.) -0.804 0.035 -22.805 0.000 -0.873
## .Stst36c (.72.) 0.030 0.026 1.141 0.254 -0.021
## .Stst37b (.73.) -0.337 0.025 -13.698 0.000 -0.385
## .Stst28m (.74.) -0.861 0.028 -30.946 0.000 -0.915
## .Sts292D (.75.) -0.506 0.023 -22.416 0.000 -0.550
## .Sts303D (.76.) -0.652 0.019 -33.484 0.000 -0.690
## english 0.423 0.036 11.789 0.000 0.353
## math -0.099 0.031 -3.167 0.002 -0.160
## speed 0.271 0.037 7.324 0.000 0.198
## spatial -0.644 0.033 -19.590 0.000 -0.708
## ci.upper Std.lv Std.all
## -1.244 -1.297 -1.398
## -1.066 -1.101 -1.204
## -0.752 -0.794 -0.809
## -1.170 -1.211 -1.212
## -1.226 -1.272 -1.293
## -1.051 -1.101 -0.987
## -0.946 -0.989 -0.896
## -1.305 -1.357 -1.397
## -1.032 -1.083 -1.015
## -1.167 -1.216 -1.057
## -0.837 -0.879 -0.890
## -0.759 -0.792 -0.996
## -1.076 -1.111 -1.502
## -0.861 -0.895 -1.301
## -0.735 -0.804 -0.496
## 0.080 0.030 0.023
## -0.289 -0.337 -0.293
## -0.806 -0.861 -1.336
## -0.462 -0.506 -0.523
## -0.614 -0.652 -0.859
## 0.494 0.425 0.425
## -0.038 -0.123 -0.123
## 0.343 0.274 0.274
## -0.579 -0.921 -0.921
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.325 0.011 30.042 0.000 0.304
## .Stst19dsgsdwrd 0.420 0.012 35.078 0.000 0.396
## .Stest20spellng 0.515 0.014 37.148 0.000 0.488
## .Stest21cptlztn 0.459 0.014 33.703 0.000 0.432
## .Stest22puncttn 0.324 0.011 30.604 0.000 0.303
## .Stest23english 0.563 0.017 33.614 0.000 0.530
## .Stest24exprssn 0.797 0.021 37.751 0.000 0.755
## .Stst26rdngcmpr 0.253 0.008 30.128 0.000 0.236
## .Stst31bstrctrs 0.635 0.018 35.704 0.000 0.600
## .Stst34rthcmptt 0.708 0.027 26.200 0.000 0.655
## .Stest5math 0.631 0.018 35.887 0.000 0.597
## .Stst25wrdfnctn 0.366 0.011 34.235 0.000 0.345
## .Stst32rthrsnng 0.295 0.009 34.337 0.000 0.278
## .Stst33hghschlm 0.227 0.007 31.060 0.000 0.212
## .Stest35tblrdng 1.270 0.067 18.923 0.000 1.138
## .Stst36clrclchc 1.045 0.033 31.685 0.000 0.980
## .Stst37bjctnspc 0.746 0.028 26.918 0.000 0.691
## .Stst28mchnclrs 0.210 0.008 27.044 0.000 0.195
## .Stst29vslztn2D 0.710 0.020 35.081 0.000 0.671
## .Stst30vslztn3D 0.400 0.012 33.395 0.000 0.376
## english 0.994 0.040 25.010 0.000 0.916
## math 0.640 0.034 18.654 0.000 0.573
## speed 0.979 0.058 16.774 0.000 0.864
## spatial 0.488 0.044 11.162 0.000 0.403
## ci.upper Std.lv Std.all
## 0.346 0.325 0.377
## 0.443 0.420 0.502
## 0.542 0.515 0.534
## 0.486 0.459 0.460
## 0.345 0.324 0.335
## 0.596 0.563 0.453
## 0.838 0.797 0.655
## 0.269 0.253 0.268
## 0.670 0.635 0.557
## 0.761 0.708 0.535
## 0.666 0.631 0.646
## 0.387 0.366 0.580
## 0.312 0.295 0.539
## 0.241 0.227 0.480
## 1.401 1.270 0.484
## 1.110 1.045 0.626
## 0.800 0.746 0.566
## 0.225 0.210 0.506
## 0.750 0.710 0.758
## 0.423 0.400 0.694
## 1.072 1.000 1.000
## 0.707 1.000 1.000
## 1.093 1.000 1.000
## 0.574 1.000 1.000
lavTestScore(scalar, release = 25:44)
## 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 811.527 20 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p57. == .p137. 159.014 1 0.000
## 2 .p58. == .p138. 66.786 1 0.000
## 3 .p59. == .p139. 76.309 1 0.000
## 4 .p60. == .p140. 0.000 1 0.985
## 5 .p61. == .p141. 0.130 1 0.718
## 6 .p62. == .p142. 0.947 1 0.330
## 7 .p63. == .p143. 1.142 1 0.285
## 8 .p64. == .p144. 0.292 1 0.589
## 9 .p65. == .p145. 33.469 1 0.000
## 10 .p66. == .p146. 4.032 1 0.045
## 11 .p67. == .p147. 2.519 1 0.113
## 12 .p68. == .p148. 151.028 1 0.000
## 13 .p69. == .p149. 4.780 1 0.029
## 14 .p70. == .p150. 10.606 1 0.001
## 15 .p71. == .p151. 21.643 1 0.000
## 16 .p72. == .p152. 35.696 1 0.000
## 17 .p73. == .p153. 0.327 1 0.567
## 18 .p74. == .p154. 333.514 1 0.000
## 19 .p75. == .p155. 17.610 1 0.000
## 20 .p76. == .p156. 138.215 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("spatial=~Stest28mechanicalreasoning", "math=~Stest25wordfunctions", "Stest28mechanicalreasoning~1", "Stest1vocab~1", "Stest25wordfunctions~1"))
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 3701.089 349.000 0.000 0.941 0.056 0.048
## aic bic
## 291568.819 292314.027
Mc(scalar2)
## [1] 0.7592046
summary(scalar2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 82 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 152
## Number of equality constraints 41
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3701.089 3285.760
## Degrees of freedom 349 349
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.126
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1619.009 1437.328
## 1 2082.079 1848.432
##
## 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.) 0.446 0.035 12.894 0.000 0.378
## Stst19d (.p2.) 0.654 0.014 48.104 0.000 0.627
## Stst20s (.p3.) 0.677 0.014 47.856 0.000 0.650
## Stst21c (.p4.) 0.740 0.013 56.921 0.000 0.715
## Stst22p (.p5.) 0.808 0.015 55.465 0.000 0.779
## Stst23n (.p6.) 0.835 0.017 48.930 0.000 0.801
## Stst24x (.p7.) 0.655 0.016 40.591 0.000 0.624
## Stst26r (.p8.) 0.525 0.026 19.840 0.000 0.473
## Stst31b (.p9.) 0.297 0.018 16.243 0.000 0.261
## Stst34r (.10.) 0.283 0.029 9.647 0.000 0.226
## math =~
## Stst1vc (.11.) 0.422 0.039 10.791 0.000 0.346
## Stst5mt (.12.) 0.742 0.017 43.911 0.000 0.709
## Stst25w 0.475 0.018 26.540 0.000 0.440
## Stst26r (.14.) 0.438 0.030 14.739 0.000 0.380
## Stst32r (.15.) 0.639 0.016 40.087 0.000 0.608
## Stst33h (.16.) 0.633 0.016 40.514 0.000 0.602
## Stst34r (.17.) 0.267 0.032 8.327 0.000 0.204
## speed =~
## Stst34r (.18.) 0.482 0.021 22.475 0.000 0.440
## Stst35t (.19.) 1.177 0.036 32.708 0.000 1.107
## Stst36c (.20.) 0.799 0.025 32.395 0.000 0.751
## Stst37b (.21.) 0.722 0.024 29.908 0.000 0.675
## spatial =~
## Stst28m 0.709 0.018 39.724 0.000 0.674
## Sts292D (.23.) 0.681 0.018 37.724 0.000 0.646
## Sts303D (.24.) 0.605 0.017 36.124 0.000 0.572
## Stst31b (.25.) 0.641 0.022 29.632 0.000 0.598
## Stst37b (.26.) 0.132 0.019 6.819 0.000 0.094
## ci.upper Std.lv Std.all
##
## 0.514 0.446 0.430
## 0.680 0.654 0.726
## 0.705 0.677 0.675
## 0.766 0.740 0.767
## 0.836 0.808 0.802
## 0.868 0.835 0.721
## 0.687 0.655 0.577
## 0.577 0.525 0.491
## 0.332 0.297 0.255
## 0.341 0.283 0.245
##
## 0.499 0.422 0.407
## 0.775 0.742 0.706
## 0.510 0.475 0.610
## 0.496 0.438 0.410
## 0.671 0.639 0.759
## 0.663 0.633 0.796
## 0.329 0.267 0.231
##
## 0.524 0.482 0.418
## 1.248 1.177 0.707
## 0.848 0.799 0.616
## 0.770 0.722 0.584
##
## 0.744 0.709 0.788
## 0.716 0.681 0.618
## 0.638 0.605 0.653
## 0.683 0.641 0.551
## 0.170 0.132 0.107
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.867 0.010 83.162 0.000 0.847
## speed 0.351 0.025 14.275 0.000 0.303
## spatial 0.695 0.017 41.627 0.000 0.662
## math ~~
## speed 0.312 0.025 12.419 0.000 0.263
## spatial 0.747 0.016 45.824 0.000 0.715
## speed ~~
## spatial 0.360 0.028 13.006 0.000 0.306
## ci.upper Std.lv Std.all
##
## 0.887 0.867 0.867
## 0.399 0.351 0.351
## 0.727 0.695 0.695
##
## 0.361 0.312 0.312
## 0.779 0.747 0.747
##
## 0.415 0.360 0.360
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -1.155 0.023 -50.361 0.000 -1.200
## .Stst19d (.58.) -1.061 0.016 -67.747 0.000 -1.091
## .Stst20s (.59.) -0.752 0.019 -40.069 0.000 -0.789
## .Stst21c (.60.) -1.165 0.018 -63.972 0.000 -1.201
## .Stst22p (.61.) -1.220 0.020 -61.472 0.000 -1.259
## .Stst23n (.62.) -1.049 0.022 -46.960 0.000 -1.093
## .Stst24x (.63.) -0.948 0.020 -47.823 0.000 -0.987
## .Stst26r (.64.) -1.318 0.022 -59.422 0.000 -1.362
## .Stst31b (.65.) -1.060 0.023 -45.830 0.000 -1.105
## .Stst34r (.66.) -1.164 0.022 -51.809 0.000 -1.208
## .Stst5mt (.67.) -0.823 0.019 -42.704 0.000 -0.861
## .Stst25w -0.871 0.017 -52.726 0.000 -0.903
## .Stst32r (.69.) -1.062 0.016 -65.712 0.000 -1.094
## .Stst33h (.70.) -0.846 0.016 -54.505 0.000 -0.877
## .Stst35t (.71.) -0.772 0.034 -22.881 0.000 -0.838
## .Stst36c (.72.) 0.051 0.025 2.044 0.041 0.002
## .Stst37b (.73.) -0.324 0.023 -13.987 0.000 -0.369
## .Stst28m -0.715 0.019 -36.895 0.000 -0.753
## .Sts292D (.75.) -0.556 0.021 -26.509 0.000 -0.597
## .Sts303D (.76.) -0.699 0.018 -38.478 0.000 -0.734
## ci.upper Std.lv Std.all
## -1.110 -1.155 -1.113
## -1.030 -1.061 -1.179
## -0.715 -0.752 -0.749
## -1.129 -1.165 -1.207
## -1.181 -1.220 -1.212
## -1.005 -1.049 -0.906
## -0.909 -0.948 -0.835
## -1.275 -1.318 -1.233
## -1.014 -1.060 -0.912
## -1.120 -1.164 -1.008
## -0.785 -0.823 -0.784
## -0.838 -0.871 -1.119
## -1.030 -1.062 -1.261
## -0.816 -0.846 -1.064
## -0.706 -0.772 -0.463
## 0.100 0.051 0.040
## -0.278 -0.324 -0.262
## -0.677 -0.715 -0.795
## -0.515 -0.556 -0.505
## -0.663 -0.699 -0.754
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.373 0.013 28.081 0.000 0.347
## .Stst19dsgsdwrd 0.382 0.015 26.172 0.000 0.354
## .Stest20spellng 0.549 0.018 31.251 0.000 0.515
## .Stest21cptlztn 0.383 0.015 25.032 0.000 0.353
## .Stest22puncttn 0.362 0.012 29.130 0.000 0.338
## .Stest23english 0.643 0.024 27.124 0.000 0.596
## .Stest24exprssn 0.859 0.025 33.817 0.000 0.809
## .Stst26rdngcmpr 0.277 0.011 24.623 0.000 0.255
## .Stst31bstrctrs 0.588 0.022 27.043 0.000 0.545
## .Stst34rthcmptt 0.642 0.030 21.373 0.000 0.583
## .Stest5math 0.553 0.021 26.561 0.000 0.512
## .Stst25wrdfnctn 0.380 0.012 31.966 0.000 0.357
## .Stst32rthrsnng 0.300 0.011 28.101 0.000 0.279
## .Stst33hghschlm 0.232 0.009 25.933 0.000 0.214
## .Stest35tblrdng 1.390 0.075 18.563 0.000 1.243
## .Stst36clrclchc 1.043 0.042 24.703 0.000 0.960
## .Stst37bjctnspc 0.923 0.036 25.827 0.000 0.853
## .Stst28mchnclrs 0.306 0.015 19.975 0.000 0.276
## .Stst29vslztn2D 0.751 0.026 28.630 0.000 0.700
## .Stst30vslztn3D 0.493 0.017 28.932 0.000 0.459
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.399 0.373 0.346
## 0.411 0.382 0.472
## 0.583 0.549 0.545
## 0.413 0.383 0.411
## 0.387 0.362 0.357
## 0.689 0.643 0.480
## 0.909 0.859 0.667
## 0.299 0.277 0.242
## 0.631 0.588 0.435
## 0.701 0.642 0.482
## 0.593 0.553 0.501
## 0.404 0.380 0.628
## 0.321 0.300 0.423
## 0.249 0.232 0.366
## 1.536 1.390 0.501
## 1.126 1.043 0.620
## 0.993 0.923 0.603
## 0.336 0.306 0.379
## 0.803 0.751 0.618
## 0.526 0.493 0.574
## 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.) 0.446 0.035 12.894 0.000 0.378
## Stst19d (.p2.) 0.654 0.014 48.104 0.000 0.627
## Stst20s (.p3.) 0.677 0.014 47.856 0.000 0.650
## Stst21c (.p4.) 0.740 0.013 56.921 0.000 0.715
## Stst22p (.p5.) 0.808 0.015 55.465 0.000 0.779
## Stst23n (.p6.) 0.835 0.017 48.930 0.000 0.801
## Stst24x (.p7.) 0.655 0.016 40.591 0.000 0.624
## Stst26r (.p8.) 0.525 0.026 19.840 0.000 0.473
## Stst31b (.p9.) 0.297 0.018 16.243 0.000 0.261
## Stst34r (.10.) 0.283 0.029 9.647 0.000 0.226
## math =~
## Stst1vc (.11.) 0.422 0.039 10.791 0.000 0.346
## Stst5mt (.12.) 0.742 0.017 43.911 0.000 0.709
## Stst25w 0.672 0.021 32.493 0.000 0.632
## Stst26r (.14.) 0.438 0.030 14.739 0.000 0.380
## Stst32r (.15.) 0.639 0.016 40.087 0.000 0.608
## Stst33h (.16.) 0.633 0.016 40.514 0.000 0.602
## Stst34r (.17.) 0.267 0.032 8.327 0.000 0.204
## speed =~
## Stst34r (.18.) 0.482 0.021 22.475 0.000 0.440
## Stst35t (.19.) 1.177 0.036 32.708 0.000 1.107
## Stst36c (.20.) 0.799 0.025 32.395 0.000 0.751
## Stst37b (.21.) 0.722 0.024 29.908 0.000 0.675
## spatial =~
## Stst28m 0.468 0.021 22.527 0.000 0.427
## Sts292D (.23.) 0.681 0.018 37.724 0.000 0.646
## Sts303D (.24.) 0.605 0.017 36.124 0.000 0.572
## Stst31b (.25.) 0.641 0.022 29.632 0.000 0.598
## Stst37b (.26.) 0.132 0.019 6.819 0.000 0.094
## ci.upper Std.lv Std.all
##
## 0.514 0.439 0.467
## 0.680 0.643 0.705
## 0.705 0.666 0.680
## 0.766 0.728 0.731
## 0.836 0.794 0.810
## 0.868 0.821 0.737
## 0.687 0.644 0.585
## 0.577 0.516 0.531
## 0.332 0.292 0.271
## 0.341 0.278 0.242
##
## 0.499 0.336 0.358
## 0.775 0.590 0.599
## 0.713 0.535 0.671
## 0.496 0.348 0.358
## 0.671 0.509 0.689
## 0.663 0.503 0.734
## 0.329 0.212 0.185
##
## 0.524 0.477 0.416
## 1.248 1.165 0.719
## 0.848 0.791 0.612
## 0.770 0.715 0.622
##
## 0.509 0.380 0.621
## 0.716 0.553 0.558
## 0.638 0.491 0.628
## 0.683 0.520 0.483
## 0.170 0.107 0.093
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.659 0.029 22.646 0.000 0.602
## speed 0.378 0.025 14.976 0.000 0.328
## spatial 0.547 0.025 21.861 0.000 0.498
## math ~~
## speed 0.227 0.019 12.077 0.000 0.190
## spatial 0.483 0.026 18.620 0.000 0.433
## speed ~~
## spatial 0.264 0.023 11.330 0.000 0.219
## ci.upper Std.lv Std.all
##
## 0.716 0.842 0.842
## 0.427 0.388 0.388
## 0.596 0.685 0.685
##
## 0.264 0.289 0.289
## 0.534 0.749 0.749
##
## 0.310 0.329 0.329
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -1.421 0.027 -53.038 0.000 -1.474
## .Stst19d (.58.) -1.061 0.016 -67.747 0.000 -1.091
## .Stst20s (.59.) -0.752 0.019 -40.069 0.000 -0.789
## .Stst21c (.60.) -1.165 0.018 -63.972 0.000 -1.201
## .Stst22p (.61.) -1.220 0.020 -61.472 0.000 -1.259
## .Stst23n (.62.) -1.049 0.022 -46.960 0.000 -1.093
## .Stst24x (.63.) -0.948 0.020 -47.823 0.000 -0.987
## .Stst26r (.64.) -1.318 0.022 -59.422 0.000 -1.362
## .Stst31b (.65.) -1.060 0.023 -45.830 0.000 -1.105
## .Stst34r (.66.) -1.164 0.022 -51.809 0.000 -1.208
## .Stst5mt (.67.) -0.823 0.019 -42.704 0.000 -0.861
## .Stst25w -0.667 0.020 -33.985 0.000 -0.705
## .Stst32r (.69.) -1.062 0.016 -65.712 0.000 -1.094
## .Stst33h (.70.) -0.846 0.016 -54.505 0.000 -0.877
## .Stst35t (.71.) -0.772 0.034 -22.881 0.000 -0.838
## .Stst36c (.72.) 0.051 0.025 2.044 0.041 0.002
## .Stst37b (.73.) -0.324 0.023 -13.987 0.000 -0.369
## .Stst28m -1.095 0.019 -56.172 0.000 -1.133
## .Sts292D (.75.) -0.556 0.021 -26.509 0.000 -0.597
## .Sts303D (.76.) -0.699 0.018 -38.478 0.000 -0.734
## english 0.356 0.031 11.414 0.000 0.295
## math -0.181 0.027 -6.820 0.000 -0.233
## speed 0.241 0.036 6.758 0.000 0.171
## spatial -0.489 0.033 -14.655 0.000 -0.554
## ci.upper Std.lv Std.all
## -1.369 -1.421 -1.513
## -1.030 -1.061 -1.164
## -0.715 -0.752 -0.768
## -1.129 -1.165 -1.170
## -1.181 -1.220 -1.244
## -1.005 -1.049 -0.942
## -0.909 -0.948 -0.861
## -1.275 -1.318 -1.356
## -1.014 -1.060 -0.983
## -1.120 -1.164 -1.014
## -0.785 -0.823 -0.835
## -0.628 -0.667 -0.836
## -1.030 -1.062 -1.440
## -0.816 -0.846 -1.235
## -0.706 -0.772 -0.476
## 0.100 0.051 0.040
## -0.278 -0.324 -0.282
## -1.057 -1.095 -1.788
## -0.515 -0.556 -0.561
## -0.663 -0.699 -0.894
## 0.417 0.362 0.362
## -0.129 -0.227 -0.227
## 0.311 0.244 0.244
## -0.423 -0.602 -0.602
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.329 0.010 33.898 0.000 0.310
## .Stst19dsgsdwrd 0.417 0.012 35.283 0.000 0.394
## .Stest20spellng 0.515 0.014 37.207 0.000 0.488
## .Stest21cptlztn 0.461 0.014 33.861 0.000 0.435
## .Stest22puncttn 0.332 0.011 30.968 0.000 0.311
## .Stest23english 0.565 0.017 33.686 0.000 0.532
## .Stest24exprssn 0.799 0.021 37.775 0.000 0.757
## .Stst26rdngcmpr 0.255 0.008 30.451 0.000 0.238
## .Stst31bstrctrs 0.597 0.017 34.466 0.000 0.563
## .Stst34rthcmptt 0.708 0.027 26.131 0.000 0.655
## .Stest5math 0.623 0.017 35.887 0.000 0.589
## .Stst25wrdfnctn 0.350 0.010 33.984 0.000 0.330
## .Stst32rthrsnng 0.286 0.008 34.649 0.000 0.269
## .Stst33hghschlm 0.216 0.007 30.920 0.000 0.203
## .Stest35tblrdng 1.267 0.068 18.741 0.000 1.134
## .Stst36clrclchc 1.043 0.033 31.292 0.000 0.977
## .Stst37bjctnspc 0.747 0.028 27.025 0.000 0.693
## .Stst28mchnclrs 0.230 0.007 33.374 0.000 0.217
## .Stst29vslztn2D 0.676 0.019 34.939 0.000 0.638
## .Stst30vslztn3D 0.370 0.011 33.455 0.000 0.348
## english 0.967 0.038 25.189 0.000 0.892
## math 0.633 0.037 16.918 0.000 0.560
## speed 0.979 0.059 16.702 0.000 0.864
## spatial 0.659 0.040 16.446 0.000 0.580
## ci.upper Std.lv Std.all
## 0.348 0.329 0.373
## 0.441 0.417 0.502
## 0.542 0.515 0.537
## 0.488 0.461 0.465
## 0.353 0.332 0.345
## 0.598 0.565 0.456
## 0.840 0.799 0.658
## 0.271 0.255 0.269
## 0.631 0.597 0.515
## 0.761 0.708 0.536
## 0.657 0.623 0.641
## 0.370 0.350 0.550
## 0.302 0.286 0.525
## 0.230 0.216 0.461
## 1.399 1.267 0.483
## 1.108 1.043 0.625
## 0.801 0.747 0.566
## 0.244 0.230 0.615
## 0.714 0.676 0.689
## 0.391 0.370 0.605
## 1.043 1.000 1.000
## 0.706 1.000 1.000
## 1.094 1.000 1.000
## 0.737 1.000 1.000
lavTestScore(scalar2, release = 25:41)
## 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 216.626 17 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p58. == .p138. 63.451 1 0.000
## 2 .p59. == .p139. 78.141 1 0.000
## 3 .p60. == .p140. 0.065 1 0.798
## 4 .p61. == .p141. 0.540 1 0.463
## 5 .p62. == .p142. 1.354 1 0.245
## 6 .p63. == .p143. 1.434 1 0.231
## 7 .p64. == .p144. 19.174 1 0.000
## 8 .p65. == .p145. 1.751 1 0.186
## 9 .p66. == .p146. 1.664 1 0.197
## 10 .p67. == .p147. 0.901 1 0.342
## 11 .p69. == .p149. 1.931 1 0.165
## 12 .p70. == .p150. 24.142 1 0.000
## 13 .p71. == .p151. 18.580 1 0.000
## 14 .p72. == .p152. 37.320 1 0.000
## 15 .p73. == .p153. 0.200 1 0.655
## 16 .p75. == .p155. 17.076 1 0.000
## 17 .p76. == .p156. 8.604 1 0.003
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("spatial=~Stest28mechanicalreasoning", "math=~Stest25wordfunctions", "Stest28mechanicalreasoning~1", "Stest1vocab~1", "Stest25wordfunctions~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 3893.336 369.000 0.000 0.938 0.056 0.049
## aic bic
## 291721.067 292332.003
Mc(strict)
## [1] 0.7485332
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("spatial=~Stest28mechanicalreasoning", "math=~Stest25wordfunctions", "Stest28mechanicalreasoning~1", "Stest1vocab~1", "Stest25wordfunctions~1"))
fitMeasures(chc.cov, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 3797.809 355.000 0.000 0.939 0.056 0.065
## aic bic
## 291653.540 292358.466
Mc(chc.cov)
## [1] 0.7535653
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("spatial=~Stest28mechanicalreasoning", "math=~Stest25wordfunctions", "Stest28mechanicalreasoning~1", "Stest1vocab~1", "Stest25wordfunctions~1"))
fitMeasures(chc.vcov, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 3857.530 359.000 0.000 0.938 0.057 0.066
## aic bic
## 291705.261 292383.333
Mc(chc.vcov)
## [1] 0.7501224
summary(chc.vcov, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 58 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 148
## Number of equality constraints 47
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3857.530 3417.796
## Degrees of freedom 359 359
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.129
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1707.701 1513.034
## 1 2149.830 1904.763
##
## 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.) 0.462 0.033 14.177 0.000 0.398
## Stst19d (.p2.) 0.646 0.011 57.094 0.000 0.623
## Stst20s (.p3.) 0.671 0.011 58.695 0.000 0.649
## Stst21c (.p4.) 0.731 0.010 71.665 0.000 0.711
## Stst22p (.p5.) 0.799 0.011 73.368 0.000 0.778
## Stst23n (.p6.) 0.828 0.013 64.089 0.000 0.803
## Stst24x (.p7.) 0.650 0.013 49.063 0.000 0.624
## Stst26r (.p8.) 0.528 0.025 21.419 0.000 0.480
## Stst31b (.p9.) 0.293 0.018 16.279 0.000 0.257
## Stst34r (.10.) 0.274 0.029 9.390 0.000 0.217
## math =~
## Stst1vc (.11.) 0.351 0.034 10.443 0.000 0.285
## Stst5mt (.12.) 0.657 0.012 54.397 0.000 0.633
## Stst25w 0.443 0.015 28.836 0.000 0.413
## Stst26r (.14.) 0.377 0.025 14.821 0.000 0.327
## Stst32r (.15.) 0.564 0.012 48.281 0.000 0.541
## Stst33h (.16.) 0.559 0.011 49.308 0.000 0.537
## Stst34r (.17.) 0.243 0.029 8.450 0.000 0.186
## speed =~
## Stst34r (.18.) 0.480 0.020 24.043 0.000 0.441
## Stst35t (.19.) 1.168 0.029 40.066 0.000 1.111
## Stst36c (.20.) 0.796 0.020 40.207 0.000 0.757
## Stst37b (.21.) 0.718 0.020 35.968 0.000 0.678
## spatial =~
## Stst28m 0.673 0.016 42.494 0.000 0.642
## Sts292D (.23.) 0.607 0.013 45.093 0.000 0.580
## Sts303D (.24.) 0.534 0.012 45.331 0.000 0.511
## Stst31b (.25.) 0.574 0.019 30.698 0.000 0.537
## Stst37b (.26.) 0.119 0.017 6.886 0.000 0.085
## ci.upper Std.lv Std.all
##
## 0.526 0.462 0.465
## 0.668 0.646 0.723
## 0.693 0.671 0.671
## 0.751 0.731 0.763
## 0.821 0.799 0.799
## 0.854 0.828 0.720
## 0.676 0.650 0.575
## 0.577 0.528 0.518
## 0.328 0.293 0.262
## 0.331 0.274 0.242
##
## 0.416 0.351 0.353
## 0.681 0.657 0.660
## 0.473 0.443 0.584
## 0.427 0.377 0.370
## 0.587 0.564 0.715
## 0.582 0.559 0.756
## 0.299 0.243 0.214
##
## 0.519 0.480 0.423
## 1.225 1.168 0.703
## 0.835 0.796 0.615
## 0.757 0.718 0.583
##
## 0.704 0.673 0.776
## 0.633 0.607 0.570
## 0.558 0.534 0.600
## 0.611 0.574 0.515
## 0.153 0.119 0.097
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math (.51.) 0.849 0.007 115.504 0.000 0.835
## speed (.52.) 0.372 0.017 21.717 0.000 0.339
## spatial (.53.) 0.686 0.012 57.959 0.000 0.663
## math ~~
## speed (.54.) 0.297 0.017 17.076 0.000 0.263
## spatial (.55.) 0.745 0.012 61.604 0.000 0.721
## speed ~~
## spatial (.56.) 0.340 0.020 16.908 0.000 0.301
## ci.upper Std.lv Std.all
##
## 0.864 0.849 0.849
## 0.406 0.372 0.372
## 0.709 0.686 0.686
##
## 0.331 0.297 0.297
## 0.769 0.745 0.745
##
## 0.379 0.340 0.340
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -1.155 0.023 -50.360 0.000 -1.200
## .Stst19d (.58.) -1.060 0.016 -67.795 0.000 -1.090
## .Stst20s (.59.) -0.752 0.019 -40.006 0.000 -0.788
## .Stst21c (.60.) -1.164 0.018 -64.027 0.000 -1.200
## .Stst22p (.61.) -1.220 0.020 -61.385 0.000 -1.259
## .Stst23n (.62.) -1.049 0.022 -46.823 0.000 -1.093
## .Stst24x (.63.) -0.948 0.020 -47.743 0.000 -0.987
## .Stst26r (.64.) -1.321 0.022 -59.654 0.000 -1.364
## .Stst31b (.65.) -1.058 0.023 -45.663 0.000 -1.103
## .Stst34r (.66.) -1.162 0.022 -51.742 0.000 -1.206
## .Stst5mt (.67.) -0.823 0.019 -42.522 0.000 -0.861
## .Stst25w -0.871 0.017 -52.726 0.000 -0.903
## .Stst32r (.69.) -1.062 0.016 -65.764 0.000 -1.094
## .Stst33h (.70.) -0.845 0.016 -54.403 0.000 -0.876
## .Stst35t (.71.) -0.773 0.034 -22.904 0.000 -0.839
## .Stst36c (.72.) 0.050 0.025 1.998 0.046 0.001
## .Stst37b (.73.) -0.324 0.023 -13.965 0.000 -0.369
## .Stst28m -0.715 0.019 -36.895 0.000 -0.753
## .Sts292D (.75.) -0.556 0.021 -26.449 0.000 -0.598
## .Sts303D (.76.) -0.700 0.018 -38.657 0.000 -0.735
## ci.upper Std.lv Std.all
## -1.110 -1.155 -1.162
## -1.029 -1.060 -1.186
## -0.715 -0.752 -0.752
## -1.128 -1.164 -1.215
## -1.181 -1.220 -1.219
## -1.005 -1.049 -0.911
## -0.909 -0.948 -0.838
## -1.278 -1.321 -1.296
## -1.012 -1.058 -0.949
## -1.118 -1.162 -1.025
## -0.785 -0.823 -0.827
## -0.838 -0.871 -1.148
## -1.030 -1.062 -1.347
## -0.815 -0.845 -1.142
## -0.707 -0.773 -0.466
## 0.100 0.050 0.039
## -0.278 -0.324 -0.263
## -0.677 -0.715 -0.824
## -0.515 -0.556 -0.523
## -0.664 -0.700 -0.785
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.376 0.013 28.548 0.000 0.350
## .Stst19dsgsdwrd 0.381 0.015 26.241 0.000 0.353
## .Stest20spellng 0.549 0.018 31.215 0.000 0.515
## .Stest21cptlztn 0.384 0.015 25.048 0.000 0.354
## .Stest22puncttn 0.362 0.012 29.044 0.000 0.338
## .Stest23english 0.638 0.024 27.158 0.000 0.592
## .Stest24exprssn 0.857 0.025 33.781 0.000 0.808
## .Stst26rdngcmpr 0.279 0.011 25.031 0.000 0.258
## .Stst31bstrctrs 0.598 0.022 27.799 0.000 0.556
## .Stst34rthcmptt 0.643 0.030 21.320 0.000 0.584
## .Stest5math 0.559 0.021 26.624 0.000 0.518
## .Stst25wrdfnctn 0.379 0.012 31.829 0.000 0.355
## .Stst32rthrsnng 0.304 0.011 28.286 0.000 0.283
## .Stst33hghschlm 0.235 0.009 25.899 0.000 0.217
## .Stest35tblrdng 1.392 0.075 18.627 0.000 1.246
## .Stst36clrclchc 1.043 0.041 25.195 0.000 0.962
## .Stst37bjctnspc 0.928 0.035 26.258 0.000 0.859
## .Stst28mchnclrs 0.300 0.015 19.659 0.000 0.270
## .Stst29vslztn2D 0.765 0.025 30.076 0.000 0.716
## .Stst30vslztn3D 0.509 0.017 30.581 0.000 0.476
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.402 0.376 0.381
## 0.410 0.381 0.478
## 0.584 0.549 0.550
## 0.414 0.384 0.418
## 0.387 0.362 0.362
## 0.685 0.638 0.482
## 0.907 0.857 0.670
## 0.301 0.279 0.269
## 0.640 0.598 0.481
## 0.702 0.643 0.499
## 0.600 0.559 0.564
## 0.402 0.379 0.659
## 0.325 0.304 0.489
## 0.252 0.235 0.429
## 1.538 1.392 0.505
## 1.124 1.043 0.622
## 0.998 0.928 0.613
## 0.330 0.300 0.398
## 0.815 0.765 0.675
## 0.541 0.509 0.640
## 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.) 0.462 0.033 14.177 0.000 0.398
## Stst19d (.p2.) 0.646 0.011 57.094 0.000 0.623
## Stst20s (.p3.) 0.671 0.011 58.695 0.000 0.649
## Stst21c (.p4.) 0.731 0.010 71.665 0.000 0.711
## Stst22p (.p5.) 0.799 0.011 73.368 0.000 0.778
## Stst23n (.p6.) 0.828 0.013 64.089 0.000 0.803
## Stst24x (.p7.) 0.650 0.013 49.063 0.000 0.624
## Stst26r (.p8.) 0.528 0.025 21.419 0.000 0.480
## Stst31b (.p9.) 0.293 0.018 16.279 0.000 0.257
## Stst34r (.10.) 0.274 0.029 9.390 0.000 0.217
## math =~
## Stst1vc (.11.) 0.351 0.034 10.443 0.000 0.285
## Stst5mt (.12.) 0.657 0.012 54.397 0.000 0.633
## Stst25w 0.565 0.014 39.316 0.000 0.537
## Stst26r (.14.) 0.377 0.025 14.821 0.000 0.327
## Stst32r (.15.) 0.564 0.012 48.281 0.000 0.541
## Stst33h (.16.) 0.559 0.011 49.308 0.000 0.537
## Stst34r (.17.) 0.243 0.029 8.450 0.000 0.186
## speed =~
## Stst34r (.18.) 0.480 0.020 24.043 0.000 0.441
## Stst35t (.19.) 1.168 0.029 40.066 0.000 1.111
## Stst36c (.20.) 0.796 0.020 40.207 0.000 0.757
## Stst37b (.21.) 0.718 0.020 35.968 0.000 0.678
## spatial =~
## Stst28m 0.392 0.013 29.688 0.000 0.366
## Sts292D (.23.) 0.607 0.013 45.093 0.000 0.580
## Sts303D (.24.) 0.534 0.012 45.331 0.000 0.511
## Stst31b (.25.) 0.574 0.019 30.698 0.000 0.537
## Stst37b (.26.) 0.119 0.017 6.886 0.000 0.085
## ci.upper Std.lv Std.all
##
## 0.526 0.462 0.477
## 0.668 0.646 0.706
## 0.693 0.671 0.683
## 0.751 0.731 0.732
## 0.821 0.799 0.811
## 0.854 0.828 0.741
## 0.676 0.650 0.588
## 0.577 0.528 0.525
## 0.328 0.293 0.264
## 0.331 0.274 0.236
##
## 0.416 0.351 0.362
## 0.681 0.657 0.641
## 0.593 0.565 0.690
## 0.427 0.377 0.374
## 0.587 0.564 0.727
## 0.582 0.559 0.773
## 0.299 0.243 0.209
##
## 0.519 0.480 0.413
## 1.225 1.168 0.719
## 0.835 0.796 0.616
## 0.757 0.718 0.622
##
## 0.418 0.392 0.630
## 0.633 0.607 0.597
## 0.558 0.534 0.664
## 0.611 0.574 0.517
## 0.153 0.119 0.103
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math (.51.) 0.849 0.007 115.504 0.000 0.835
## speed (.52.) 0.372 0.017 21.717 0.000 0.339
## spatial (.53.) 0.686 0.012 57.959 0.000 0.663
## math ~~
## speed (.54.) 0.297 0.017 17.076 0.000 0.263
## spatial (.55.) 0.745 0.012 61.604 0.000 0.721
## speed ~~
## spatial (.56.) 0.340 0.020 16.908 0.000 0.301
## ci.upper Std.lv Std.all
##
## 0.864 0.849 0.849
## 0.406 0.372 0.372
## 0.709 0.686 0.686
##
## 0.331 0.297 0.297
## 0.769 0.745 0.745
##
## 0.379 0.340 0.340
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -1.432 0.027 -53.612 0.000 -1.485
## .Stst19d (.58.) -1.060 0.016 -67.795 0.000 -1.090
## .Stst20s (.59.) -0.752 0.019 -40.006 0.000 -0.788
## .Stst21c (.60.) -1.164 0.018 -64.027 0.000 -1.200
## .Stst22p (.61.) -1.220 0.020 -61.385 0.000 -1.259
## .Stst23n (.62.) -1.049 0.022 -46.823 0.000 -1.093
## .Stst24x (.63.) -0.948 0.020 -47.743 0.000 -0.987
## .Stst26r (.64.) -1.321 0.022 -59.654 0.000 -1.364
## .Stst31b (.65.) -1.058 0.023 -45.663 0.000 -1.103
## .Stst34r (.66.) -1.162 0.022 -51.742 0.000 -1.206
## .Stst5mt (.67.) -0.823 0.019 -42.522 0.000 -0.861
## .Stst25w -0.672 0.019 -35.878 0.000 -0.709
## .Stst32r (.69.) -1.062 0.016 -65.764 0.000 -1.094
## .Stst33h (.70.) -0.845 0.016 -54.403 0.000 -0.876
## .Stst35t (.71.) -0.773 0.034 -22.904 0.000 -0.839
## .Stst36c (.72.) 0.050 0.025 1.998 0.046 0.001
## .Stst37b (.73.) -0.324 0.023 -13.965 0.000 -0.369
## .Stst28m -1.108 0.018 -61.081 0.000 -1.144
## .Sts292D (.75.) -0.556 0.021 -26.449 0.000 -0.598
## .Sts303D (.76.) -0.700 0.018 -38.657 0.000 -0.735
## english 0.359 0.030 11.829 0.000 0.300
## math -0.206 0.032 -6.498 0.000 -0.268
## speed 0.245 0.035 6.952 0.000 0.176
## spatial -0.549 0.039 -14.183 0.000 -0.625
## ci.upper Std.lv Std.all
## -1.380 -1.432 -1.477
## -1.029 -1.060 -1.158
## -0.715 -0.752 -0.765
## -1.128 -1.164 -1.166
## -1.181 -1.220 -1.237
## -1.005 -1.049 -0.938
## -0.909 -0.948 -0.858
## -1.278 -1.321 -1.312
## -1.012 -1.058 -0.953
## -1.118 -1.162 -1.000
## -0.785 -0.823 -0.803
## -0.636 -0.672 -0.822
## -1.030 -1.062 -1.370
## -0.815 -0.845 -1.168
## -0.707 -0.773 -0.476
## 0.100 0.050 0.039
## -0.278 -0.324 -0.281
## -1.073 -1.108 -1.780
## -0.515 -0.556 -0.547
## -0.664 -0.700 -0.869
## 0.418 0.359 0.359
## -0.144 -0.206 -0.206
## 0.314 0.245 0.245
## -0.473 -0.549 -0.549
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.328 0.010 33.891 0.000 0.309
## .Stst19dsgsdwrd 0.420 0.012 35.357 0.000 0.397
## .Stest20spellng 0.515 0.014 37.209 0.000 0.488
## .Stest21cptlztn 0.463 0.014 34.108 0.000 0.437
## .Stest22puncttn 0.334 0.011 31.073 0.000 0.313
## .Stest23english 0.565 0.017 33.632 0.000 0.532
## .Stest24exprssn 0.798 0.021 37.788 0.000 0.756
## .Stst26rdngcmpr 0.254 0.008 30.352 0.000 0.238
## .Stst31bstrctrs 0.587 0.017 34.565 0.000 0.554
## .Stst34rthcmptt 0.707 0.027 25.998 0.000 0.654
## .Stest5math 0.618 0.017 35.836 0.000 0.584
## .Stst25wrdfnctn 0.351 0.010 34.163 0.000 0.331
## .Stst32rthrsnng 0.283 0.008 34.479 0.000 0.267
## .Stst33hghschlm 0.211 0.007 30.509 0.000 0.198
## .Stest35tblrdng 1.274 0.068 18.758 0.000 1.141
## .Stst36clrclchc 1.038 0.033 31.533 0.000 0.974
## .Stst37bjctnspc 0.743 0.027 27.066 0.000 0.689
## .Stst28mchnclrs 0.234 0.007 33.990 0.000 0.220
## .Stst29vslztn2D 0.665 0.019 34.743 0.000 0.627
## .Stst30vslztn3D 0.362 0.011 33.364 0.000 0.341
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## ci.upper Std.lv Std.all
## 0.347 0.328 0.349
## 0.444 0.420 0.502
## 0.542 0.515 0.533
## 0.490 0.463 0.465
## 0.355 0.334 0.343
## 0.598 0.565 0.452
## 0.839 0.798 0.654
## 0.271 0.254 0.251
## 0.620 0.587 0.476
## 0.760 0.707 0.523
## 0.652 0.618 0.589
## 0.371 0.351 0.524
## 0.299 0.283 0.471
## 0.225 0.211 0.403
## 1.407 1.274 0.483
## 1.103 1.038 0.621
## 0.796 0.743 0.558
## 0.247 0.234 0.603
## 0.702 0.665 0.644
## 0.383 0.362 0.559
## 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.cov, chc.vcov)
Td=tests[2:5,"Chisq diff"]
Td
## [1] 102.15504 192.50532 85.79648 44.98320
dfd=tests[2:5,"Df diff"]
dfd
## [1] 20 13 6 4
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.03675007 0.06737877 0.06612601 0.05804022
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.02986334 0.04396147
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.05913788 0.07595623
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.05413869 0.07887196
RMSEA.CI(T=Td[4],df=dfd[4],N=N,G=2)
## [1] 0.04349355 0.07387053
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 0.930 0.007 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 0.986 0.807 0.036 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 0.828 0.446 0.010 0.000
tests<-lavTestLRT(configural, metric2, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 102.1550 831.5914
dfd=tests[2:3,"Df diff"]
dfd
## [1] 20 16
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.03675007 0.12945905
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.02986334 0.04396147
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.1220363 0.1370161
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, metric2, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 102.1550 192.5053 157.8302
dfd=tests[2:4,"Df diff"]
dfd
## [1] 20 13 20
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.03675007 0.06737877 0.04760069
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.02986334 0.04396147
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.05913788 0.07595623
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.04084678 0.05463936
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 0.930 0.007 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 0.297 0.002 0.000 0.000
CHC higher order models
chc.hof.model <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest26readingcomprehension + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest1vocab + Stest5math + Stest25wordfunctions + Stest26readingcomprehension + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g =~ english + math + speed + spatial
'
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
## 3521.742 160.000 0.000 0.941 0.059 0.046
## aic bic
## 294631.745 295101.696
Mc(baseline)
## [1] 0.7586026
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
## 3440.210 320.000 0.000 0.945 0.057 0.044
## aic bic
## 291365.940 292305.842
Mc(configural)
## [1] 0.7738111
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 117 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 140
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3440.210 3068.656
## Degrees of freedom 320 320
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.121
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1461.162 1303.351
## 1 1979.048 1765.304
##
## 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 0.237 0.028 8.582 0.000 0.183
## Stst19dsgsdwrd 0.261 0.016 16.445 0.000 0.230
## Stest20spellng 0.283 0.019 14.824 0.000 0.246
## Stest21cptlztn 0.299 0.019 16.098 0.000 0.263
## Stest22puncttn 0.334 0.021 16.221 0.000 0.294
## Stest23english 0.374 0.024 15.846 0.000 0.327
## Stest24exprssn 0.301 0.019 15.597 0.000 0.263
## Stst26rdngcmpr 0.263 0.028 9.484 0.000 0.209
## Stst31bstrctrs 0.102 0.016 6.246 0.000 0.070
## Stst34rthcmptt 0.116 0.029 3.928 0.000 0.058
## math =~
## Stest1vocab 0.111 0.023 4.784 0.000 0.066
## Stest5math 0.238 0.024 9.763 0.000 0.190
## Stst25wrdfnctn 0.152 0.015 9.863 0.000 0.122
## Stst26rdngcmpr 0.112 0.022 4.991 0.000 0.068
## Stst32rthrsnng 0.205 0.021 9.783 0.000 0.164
## Stst33hghschlm 0.201 0.021 9.589 0.000 0.160
## Stst34rthcmptt 0.087 0.024 3.601 0.000 0.040
## speed =~
## Stst34rthcmptt 0.436 0.029 14.949 0.000 0.379
## Stest35tblrdng 1.103 0.039 28.513 0.000 1.027
## Stst36clrclchc 0.753 0.035 21.768 0.000 0.685
## Stst37bjctnspc 0.667 0.033 19.948 0.000 0.602
## spatial =~
## Stst28mchnclrs 0.437 0.017 26.301 0.000 0.405
## Stst29vslztn2D 0.403 0.019 20.846 0.000 0.365
## Stst30vslztn3D 0.399 0.018 22.480 0.000 0.364
## Stst31bstrctrs 0.406 0.022 18.835 0.000 0.364
## Stst37bjctnspc 0.085 0.019 4.550 0.000 0.048
## g =~
## english 2.145 0.154 13.940 0.000 1.844
## math 2.955 0.328 9.016 0.000 2.313
## speed 0.397 0.034 11.751 0.000 0.331
## spatial 1.274 0.069 18.461 0.000 1.139
## ci.upper Std.lv Std.all
##
## 0.291 0.562 0.527
## 0.292 0.618 0.708
## 0.321 0.670 0.672
## 0.335 0.708 0.750
## 0.375 0.792 0.793
## 0.420 0.884 0.743
## 0.339 0.712 0.612
## 0.317 0.623 0.579
## 0.135 0.242 0.212
## 0.174 0.274 0.239
##
## 0.157 0.348 0.326
## 0.285 0.742 0.708
## 0.183 0.476 0.611
## 0.156 0.349 0.324
## 0.246 0.638 0.760
## 0.242 0.626 0.797
## 0.134 0.271 0.237
##
## 0.493 0.469 0.409
## 1.179 1.187 0.711
## 0.820 0.810 0.625
## 0.733 0.718 0.581
##
## 0.470 0.709 0.788
## 0.441 0.653 0.599
## 0.434 0.647 0.682
## 0.449 0.658 0.576
## 0.121 0.137 0.111
##
## 2.447 0.906 0.906
## 3.597 0.947 0.947
## 0.464 0.369 0.369
## 1.409 0.787 0.787
##
## 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
## .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
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.903
## .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
## .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 -1.136
## -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
## -1.248 -1.292 -1.202
## -1.022 -1.070 -0.937
## -1.104 -1.153 -1.006
## -0.770 -0.814 -0.777
## -0.838 -0.871 -1.119
## -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 -0.257
## -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 0.366 0.013 27.385 0.000 0.340
## .Stst19dsgsdwrd 0.380 0.014 27.160 0.000 0.353
## .Stest20spellng 0.544 0.018 30.626 0.000 0.510
## .Stest21cptlztn 0.390 0.016 25.078 0.000 0.360
## .Stest22puncttn 0.369 0.013 27.832 0.000 0.343
## .Stest23english 0.633 0.023 27.043 0.000 0.587
## .Stest24exprssn 0.848 0.026 32.983 0.000 0.798
## .Stst26rdngcmpr 0.274 0.011 24.183 0.000 0.251
## .Stst31bstrctrs 0.584 0.023 25.401 0.000 0.539
## .Stst34rthcmptt 0.643 0.029 21.854 0.000 0.585
## .Stest5math 0.547 0.021 26.321 0.000 0.507
## .Stst25wrdfnctn 0.380 0.012 31.705 0.000 0.356
## .Stst32rthrsnng 0.297 0.011 27.430 0.000 0.276
## .Stst33hghschlm 0.225 0.009 23.765 0.000 0.207
## .Stest35tblrdng 1.375 0.091 15.157 0.000 1.197
## .Stst36clrclchc 1.022 0.049 21.002 0.000 0.927
## .Stst37bjctnspc 0.938 0.039 24.183 0.000 0.862
## .Stst28mchnclrs 0.307 0.015 19.878 0.000 0.277
## .Stst29vslztn2D 0.762 0.027 28.484 0.000 0.710
## .Stst30vslztn3D 0.480 0.017 27.461 0.000 0.446
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.392 0.366 0.322
## 0.408 0.380 0.499
## 0.579 0.544 0.548
## 0.421 0.390 0.438
## 0.395 0.369 0.371
## 0.679 0.633 0.447
## 0.898 0.848 0.626
## 0.296 0.274 0.237
## 0.629 0.584 0.448
## 0.700 0.643 0.489
## 0.588 0.547 0.499
## 0.403 0.380 0.627
## 0.319 0.297 0.422
## 0.244 0.225 0.366
## 1.553 1.375 0.494
## 1.118 1.022 0.609
## 1.014 0.938 0.613
## 0.337 0.307 0.379
## 0.815 0.762 0.641
## 0.514 0.480 0.534
## 1.000 0.179 0.179
## 1.000 0.103 0.103
## 1.000 0.864 0.864
## 1.000 0.381 0.381
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stest1vocab 0.225 0.022 10.251 0.000 0.182
## Stst19dsgsdwrd 0.293 0.016 18.694 0.000 0.262
## Stest20spellng 0.273 0.016 17.415 0.000 0.242
## Stest21cptlztn 0.320 0.017 18.460 0.000 0.286
## Stest22puncttn 0.340 0.018 18.723 0.000 0.305
## Stest23english 0.334 0.019 17.985 0.000 0.298
## Stest24exprssn 0.257 0.015 16.979 0.000 0.227
## Stst26rdngcmpr 0.279 0.021 13.215 0.000 0.238
## Stst31bstrctrs 0.114 0.015 7.689 0.000 0.085
## Stst34rthcmptt 0.140 0.023 6.022 0.000 0.094
## math =~
## Stest1vocab 0.080 0.019 4.197 0.000 0.043
## Stest5math 0.222 0.017 12.999 0.000 0.188
## Stst25wrdfnctn 0.200 0.015 13.168 0.000 0.170
## Stst26rdngcmpr 0.074 0.017 4.378 0.000 0.041
## Stst32rthrsnng 0.189 0.015 13.018 0.000 0.161
## Stst33hghschlm 0.195 0.015 12.858 0.000 0.166
## Stst34rthcmptt 0.063 0.019 3.295 0.001 0.025
## speed =~
## Stst34rthcmptt 0.451 0.024 18.436 0.000 0.403
## Stest35tblrdng 1.093 0.031 34.907 0.000 1.031
## Stst36clrclchc 0.710 0.028 25.410 0.000 0.656
## Stst37bjctnspc 0.650 0.027 24.283 0.000 0.598
## spatial =~
## Stst28mchnclrs 0.232 0.010 23.156 0.000 0.212
## Stst29vslztn2D 0.334 0.018 18.383 0.000 0.299
## Stst30vslztn3D 0.288 0.015 19.229 0.000 0.259
## Stst31bstrctrs 0.350 0.020 17.319 0.000 0.311
## Stst37bjctnspc 0.070 0.015 4.554 0.000 0.040
## g =~
## english 2.121 0.135 15.656 0.000 1.855
## math 2.505 0.212 11.825 0.000 2.090
## speed 0.413 0.029 14.145 0.000 0.355
## spatial 1.292 0.075 17.127 0.000 1.144
## ci.upper Std.lv Std.all
##
## 0.268 0.527 0.573
## 0.324 0.687 0.732
## 0.304 0.640 0.664
## 0.354 0.749 0.741
## 0.376 0.798 0.809
## 0.371 0.784 0.719
## 0.287 0.603 0.558
## 0.320 0.654 0.675
## 0.144 0.268 0.245
## 0.185 0.327 0.283
##
## 0.117 0.215 0.234
## 0.255 0.598 0.606
## 0.229 0.539 0.676
## 0.107 0.200 0.206
## 0.218 0.510 0.692
## 0.225 0.527 0.759
## 0.100 0.169 0.146
##
## 0.499 0.488 0.422
## 1.154 1.182 0.728
## 0.765 0.768 0.600
## 0.703 0.703 0.613
##
## 0.251 0.378 0.618
## 0.370 0.546 0.552
## 0.317 0.470 0.608
## 0.390 0.572 0.523
## 0.100 0.115 0.100
##
## 2.386 0.904 0.904
## 2.921 0.929 0.929
## 0.470 0.381 0.381
## 1.440 0.791 0.791
##
## 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
## .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
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.816
## .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
## .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 -1.455
## -0.846 -0.878 -0.935
## -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
## -1.193 -1.226 -1.265
## -1.222 -1.260 -1.151
## -0.963 -1.004 -0.869
## -0.931 -0.965 -0.978
## -0.761 -0.788 -0.989
## -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
## -1.303 -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 0.331 0.010 34.359 0.000 0.312
## .Stst19dsgsdwrd 0.410 0.012 34.685 0.000 0.387
## .Stest20spellng 0.519 0.014 37.426 0.000 0.492
## .Stest21cptlztn 0.461 0.014 32.742 0.000 0.434
## .Stest22puncttn 0.335 0.011 30.447 0.000 0.314
## .Stest23english 0.576 0.017 34.050 0.000 0.543
## .Stest24exprssn 0.804 0.021 37.862 0.000 0.762
## .Stst26rdngcmpr 0.253 0.009 29.539 0.000 0.236
## .Stst31bstrctrs 0.578 0.019 30.850 0.000 0.541
## .Stst34rthcmptt 0.700 0.026 26.444 0.000 0.648
## .Stest5math 0.616 0.017 35.549 0.000 0.582
## .Stst25wrdfnctn 0.346 0.010 33.692 0.000 0.326
## .Stst32rthrsnng 0.284 0.008 34.461 0.000 0.268
## .Stst33hghschlm 0.205 0.007 29.123 0.000 0.191
## .Stest35tblrdng 1.240 0.074 16.825 0.000 1.096
## .Stst36clrclchc 1.051 0.037 28.711 0.000 0.979
## .Stst37bjctnspc 0.760 0.030 24.951 0.000 0.701
## .Stst28mchnclrs 0.232 0.007 33.675 0.000 0.218
## .Stst29vslztn2D 0.679 0.020 34.073 0.000 0.640
## .Stst30vslztn3D 0.377 0.011 33.065 0.000 0.354
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.350 0.331 0.391
## 0.433 0.410 0.465
## 0.546 0.519 0.559
## 0.489 0.461 0.451
## 0.357 0.335 0.345
## 0.609 0.576 0.484
## 0.845 0.804 0.689
## 0.270 0.253 0.269
## 0.615 0.578 0.483
## 0.752 0.700 0.524
## 0.650 0.616 0.633
## 0.366 0.346 0.544
## 0.301 0.284 0.522
## 0.219 0.205 0.425
## 1.384 1.240 0.470
## 1.123 1.051 0.640
## 0.820 0.760 0.577
## 0.245 0.232 0.618
## 0.718 0.679 0.695
## 0.399 0.377 0.630
## 1.000 0.182 0.182
## 1.000 0.137 0.137
## 1.000 0.855 0.855
## 1.000 0.375 0.375
## 1.000 1.000 1.000
modificationIndices(configural, sort=T, maximum.number=30)
## lhs op rhs block group
## 439 english =~ Stest35tablereading 2 2
## 503 g =~ Stest35tablereading 2 2
## 452 math =~ Stest35tablereading 2 2
## 459 speed =~ Stest19disguisedwords 2 2
## 515 Stest1vocab ~~ Stest26readingcomprehension 2 2
## 229 g =~ Stest35tablereading 1 1
## 541 Stest19disguisedwords ~~ Stest36clericalchecking 2 2
## 487 spatial =~ Stest35tablereading 2 2
## 476 spatial =~ Stest20spelling 2 2
## 178 math =~ Stest35tablereading 1 1
## 213 spatial =~ Stest35tablereading 1 1
## 241 Stest1vocab ~~ Stest26readingcomprehension 1 1
## 165 english =~ Stest35tablereading 1 1
## 504 g =~ Stest36clericalchecking 2 2
## 453 math =~ Stest36clericalchecking 2 2
## 202 spatial =~ Stest20spelling 1 1
## 689 Stest36clericalchecking ~~ Stest37objectinspection 2 2
## 180 math =~ Stest37objectinspection 1 1
## 440 english =~ Stest36clericalchecking 2 2
## 488 spatial =~ Stest36clericalchecking 2 2
## 231 g =~ Stest37objectinspection 1 1
## 455 math =~ Stest28mechanicalreasoning 2 2
## 506 g =~ Stest28mechanicalreasoning 2 2
## 198 speed =~ Stest29visualization2D 1 1
## 185 speed =~ Stest19disguisedwords 1 1
## 454 math =~ Stest37objectinspection 2 2
## 505 g =~ Stest37objectinspection 2 2
## 647 Stest34arithcomputation ~~ Stest33highschoolmath 2 2
## 512 Stest1vocab ~~ Stest22punctuation 2 2
## 214 spatial =~ Stest36clericalchecking 1 1
## level mi epc sepc.lv sepc.all sepc.nox
## 439 1 271.873 0.243 0.569 0.350 0.350
## 503 1 270.559 0.627 0.627 0.386 0.386
## 452 1 218.517 0.200 0.541 0.333 0.333
## 459 1 209.951 0.193 0.208 0.222 0.222
## 515 1 202.044 0.083 0.083 0.288 0.288
## 229 1 184.618 0.615 0.615 0.369 0.369
## 541 1 181.924 0.167 0.167 0.254 0.254
## 487 1 178.931 0.300 0.490 0.302 0.302
## 476 1 174.776 -0.210 -0.344 -0.357 -0.357
## 178 1 170.769 0.184 0.574 0.344 0.344
## 213 1 156.715 0.324 0.525 0.315 0.315
## 241 1 148.644 0.097 0.097 0.307 0.307
## 165 1 148.249 0.215 0.510 0.305 0.305
## 504 1 136.179 -0.301 -0.301 -0.235 -0.235
## 453 1 135.653 -0.109 -0.294 -0.229 -0.229
## 202 1 128.511 -0.205 -0.332 -0.333 -0.333
## 689 1 119.736 0.265 0.265 0.296 0.296
## 180 1 112.799 -0.149 -0.465 -0.376 -0.376
## 440 1 110.384 -0.108 -0.253 -0.197 -0.197
## 488 1 110.147 -0.166 -0.272 -0.212 -0.212
## 231 1 106.574 -0.518 -0.518 -0.419 -0.419
## 455 1 99.960 0.086 0.232 0.378 0.378
## 506 1 94.505 0.279 0.279 0.456 0.456
## 198 1 88.546 0.207 0.223 0.204 0.204
## 185 1 88.304 0.147 0.158 0.181 0.181
## 454 1 84.409 -0.120 -0.322 -0.281 -0.281
## 505 1 80.467 -0.376 -0.376 -0.328 -0.328
## 647 1 79.890 0.073 0.073 0.193 0.193
## 512 1 78.722 -0.060 -0.060 -0.180 -0.180
## 214 1 74.596 -0.163 -0.263 -0.203 -0.203
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
## 3824.723 345.000 0.000 0.939 0.058 0.056
## aic bic
## 291700.454 292472.516
Mc(metric)
## [1] 0.7512827
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 106 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 145
## Number of equality constraints 30
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3824.723 3394.340
## Degrees of freedom 345 345
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.127
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1672.258 1484.084
## 1 2152.465 1910.255
##
## 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 =~
## Stst1vc (.p1.) 0.188 0.020 9.263 0.000 0.148
## Stst19d (.p2.) 0.240 0.018 13.338 0.000 0.204
## Stst20s (.p3.) 0.239 0.018 12.915 0.000 0.203
## Stst21c (.p4.) 0.267 0.020 13.276 0.000 0.227
## Stst22p (.p5.) 0.291 0.022 13.301 0.000 0.248
## Stst23n (.p6.) 0.301 0.023 13.113 0.000 0.256
## Stst24x (.p7.) 0.237 0.018 12.972 0.000 0.201
## Stst26r (.p8.) 0.227 0.022 10.409 0.000 0.184
## Stst31b (.p9.) 0.107 0.011 9.830 0.000 0.085
## Stst34r (.10.) 0.115 0.017 6.905 0.000 0.083
## math =~
## Stst1vc (.11.) 0.115 0.019 6.159 0.000 0.079
## Stst5mt (.12.) 0.256 0.021 12.148 0.000 0.215
## Stst25w (.13.) 0.197 0.016 12.590 0.000 0.167
## Stst26r (.14.) 0.110 0.017 6.321 0.000 0.076
## Stst32r (.15.) 0.219 0.018 12.273 0.000 0.184
## Stst33h (.16.) 0.221 0.018 12.169 0.000 0.185
## Stst34r (.17.) 0.078 0.016 4.748 0.000 0.046
## speed =~
## Stst34r (.18.) 0.448 0.020 22.019 0.000 0.408
## Stst35t (.19.) 1.103 0.032 34.111 0.000 1.040
## Stst36c (.20.) 0.735 0.026 28.020 0.000 0.683
## Stst37b (.21.) 0.662 0.025 26.495 0.000 0.613
## spatial =~
## Stst28m (.22.) 0.406 0.015 27.273 0.000 0.376
## Sts292D (.23.) 0.469 0.018 26.694 0.000 0.435
## Sts303D (.24.) 0.435 0.016 27.006 0.000 0.404
## Stst31b (.25.) 0.453 0.018 25.218 0.000 0.418
## Stst37b (.26.) 0.101 0.015 6.665 0.000 0.072
## g =~
## english (.27.) 2.656 0.218 12.201 0.000 2.229
## math (.28.) 2.619 0.229 11.422 0.000 2.169
## speed (.29.) 0.430 0.025 17.021 0.000 0.381
## spatial (.30.) 1.041 0.049 21.278 0.000 0.945
## ci.upper Std.lv Std.all
##
## 0.228 0.533 0.515
## 0.275 0.680 0.742
## 0.275 0.678 0.676
## 0.306 0.757 0.772
## 0.334 0.826 0.807
## 0.346 0.855 0.729
## 0.272 0.672 0.587
## 0.270 0.645 0.605
## 0.128 0.303 0.261
## 0.148 0.328 0.282
##
## 0.152 0.324 0.313
## 0.298 0.719 0.696
## 0.228 0.553 0.671
## 0.144 0.308 0.289
## 0.254 0.614 0.744
## 0.256 0.619 0.793
## 0.111 0.220 0.189
##
## 0.488 0.488 0.419
## 1.166 1.201 0.717
## 0.786 0.800 0.618
## 0.711 0.721 0.581
##
## 0.435 0.585 0.699
## 0.503 0.677 0.620
## 0.467 0.628 0.677
## 0.488 0.654 0.563
## 0.131 0.146 0.118
##
## 3.082 0.936 0.936
## 3.068 0.934 0.934
## 0.480 0.395 0.395
## 1.137 0.721 0.721
##
## 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
## .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
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.903
## .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
## .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 -1.082
## -0.806 -0.848 -0.846
## -1.128 -1.167 -1.191
## -1.184 -1.226 -1.197
## -1.012 -1.062 -0.906
## -0.916 -0.965 -0.843
## -1.248 -1.292 -1.212
## -1.022 -1.070 -0.921
## -1.104 -1.153 -0.991
## -0.770 -0.814 -0.787
## -0.838 -0.871 -1.056
## -1.017 -1.052 -1.275
## -0.843 -0.875 -1.121
## -0.640 -0.712 -0.425
## 0.023 -0.032 -0.025
## -0.266 -0.318 -0.256
## -0.677 -0.715 -0.854
## -0.466 -0.512 -0.469
## -0.683 -0.723 -0.779
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.379 0.013 28.708 0.000 0.353
## .Stst19dsgsdwrd 0.378 0.014 26.993 0.000 0.351
## .Stest20spellng 0.545 0.017 31.687 0.000 0.512
## .Stest21cptlztn 0.387 0.015 25.159 0.000 0.357
## .Stest22puncttn 0.366 0.013 29.258 0.000 0.342
## .Stest23english 0.646 0.024 27.268 0.000 0.599
## .Stest24exprssn 0.858 0.025 33.888 0.000 0.809
## .Stst26rdngcmpr 0.279 0.011 25.194 0.000 0.257
## .Stst31bstrctrs 0.564 0.022 25.458 0.000 0.520
## .Stst34rthcmptt 0.636 0.030 21.343 0.000 0.578
## .Stest5math 0.551 0.021 26.470 0.000 0.510
## .Stst25wrdfnctn 0.374 0.012 31.213 0.000 0.351
## .Stst32rthrsnng 0.303 0.011 28.556 0.000 0.283
## .Stst33hghschlm 0.227 0.009 25.550 0.000 0.209
## .Stest35tblrdng 1.363 0.077 17.692 0.000 1.212
## .Stst36clrclchc 1.036 0.042 24.824 0.000 0.954
## .Stst37bjctnspc 0.940 0.035 26.630 0.000 0.871
## .Stst28mchnclrs 0.358 0.016 22.394 0.000 0.327
## .Stst29vslztn2D 0.734 0.026 28.204 0.000 0.683
## .Stst30vslztn3D 0.466 0.017 27.106 0.000 0.432
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.404 0.379 0.354
## 0.406 0.378 0.450
## 0.579 0.545 0.543
## 0.417 0.387 0.403
## 0.391 0.366 0.349
## 0.692 0.646 0.469
## 0.908 0.858 0.656
## 0.301 0.279 0.245
## 0.607 0.564 0.417
## 0.695 0.636 0.470
## 0.592 0.551 0.516
## 0.398 0.374 0.550
## 0.324 0.303 0.446
## 0.244 0.227 0.372
## 1.514 1.363 0.486
## 1.117 1.036 0.618
## 1.009 0.940 0.610
## 0.389 0.358 0.511
## 0.785 0.734 0.616
## 0.499 0.466 0.541
## 1.000 0.124 0.124
## 1.000 0.127 0.127
## 1.000 0.844 0.844
## 1.000 0.480 0.480
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.188 0.020 9.263 0.000 0.148
## Stst19d (.p2.) 0.240 0.018 13.338 0.000 0.204
## Stst20s (.p3.) 0.239 0.018 12.915 0.000 0.203
## Stst21c (.p4.) 0.267 0.020 13.276 0.000 0.227
## Stst22p (.p5.) 0.291 0.022 13.301 0.000 0.248
## Stst23n (.p6.) 0.301 0.023 13.113 0.000 0.256
## Stst24x (.p7.) 0.237 0.018 12.972 0.000 0.201
## Stst26r (.p8.) 0.227 0.022 10.409 0.000 0.184
## Stst31b (.p9.) 0.107 0.011 9.830 0.000 0.085
## Stst34r (.10.) 0.115 0.017 6.905 0.000 0.083
## math =~
## Stst1vc (.11.) 0.115 0.019 6.159 0.000 0.079
## Stst5mt (.12.) 0.256 0.021 12.148 0.000 0.215
## Stst25w (.13.) 0.197 0.016 12.590 0.000 0.167
## Stst26r (.14.) 0.110 0.017 6.321 0.000 0.076
## Stst32r (.15.) 0.219 0.018 12.273 0.000 0.184
## Stst33h (.16.) 0.221 0.018 12.169 0.000 0.185
## Stst34r (.17.) 0.078 0.016 4.748 0.000 0.046
## speed =~
## Stst34r (.18.) 0.448 0.020 22.019 0.000 0.408
## Stst35t (.19.) 1.103 0.032 34.111 0.000 1.040
## Stst36c (.20.) 0.735 0.026 28.020 0.000 0.683
## Stst37b (.21.) 0.662 0.025 26.495 0.000 0.613
## spatial =~
## Stst28m (.22.) 0.406 0.015 27.273 0.000 0.376
## Sts292D (.23.) 0.469 0.018 26.694 0.000 0.435
## Sts303D (.24.) 0.435 0.016 27.006 0.000 0.404
## Stst31b (.25.) 0.453 0.018 25.218 0.000 0.418
## Stst37b (.26.) 0.101 0.015 6.665 0.000 0.072
## g =~
## english (.27.) 2.656 0.218 12.201 0.000 2.229
## math (.28.) 2.619 0.229 11.422 0.000 2.169
## speed (.29.) 0.430 0.025 17.021 0.000 0.381
## spatial (.30.) 1.041 0.049 21.278 0.000 0.945
## ci.upper Std.lv Std.all
##
## 0.228 0.498 0.530
## 0.275 0.635 0.701
## 0.275 0.633 0.661
## 0.306 0.707 0.720
## 0.334 0.772 0.799
## 0.346 0.798 0.727
## 0.272 0.627 0.575
## 0.270 0.602 0.620
## 0.128 0.283 0.265
## 0.148 0.306 0.268
##
## 0.152 0.278 0.296
## 0.298 0.617 0.619
## 0.228 0.475 0.619
## 0.144 0.264 0.272
## 0.254 0.527 0.704
## 0.256 0.531 0.761
## 0.111 0.188 0.165
##
## 0.488 0.474 0.416
## 1.166 1.169 0.722
## 0.786 0.778 0.607
## 0.711 0.702 0.614
##
## 0.435 0.446 0.691
## 0.503 0.515 0.525
## 0.467 0.478 0.612
## 0.488 0.498 0.466
## 0.131 0.111 0.097
##
## 3.082 0.870 0.870
## 3.068 0.945 0.945
## 0.480 0.352 0.352
## 1.137 0.822 0.822
##
## 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
## .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
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.816
## .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
## .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 -1.427
## -0.846 -0.878 -0.969
## -0.417 -0.450 -0.470
## -0.865 -0.899 -0.916
## -0.895 -0.929 -0.962
## -0.706 -0.744 -0.677
## -0.667 -0.704 -0.645
## -1.193 -1.226 -1.262
## -1.222 -1.260 -1.179
## -0.963 -1.004 -0.880
## -0.931 -0.965 -0.967
## -0.761 -0.788 -1.029
## -1.159 -1.184 -1.582
## -0.919 -0.942 -1.351
## -0.466 -0.524 -0.324
## 0.344 0.300 0.234
## -0.176 -0.217 -0.190
## -1.303 -1.323 -2.053
## -0.882 -0.916 -0.932
## -0.955 -0.982 -1.256
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.328 0.010 34.155 0.000 0.310
## .Stst19dsgsdwrd 0.417 0.012 34.949 0.000 0.394
## .Stest20spellng 0.516 0.014 37.434 0.000 0.489
## .Stest21cptlztn 0.465 0.014 33.570 0.000 0.438
## .Stest22puncttn 0.336 0.011 30.719 0.000 0.315
## .Stest23english 0.567 0.017 33.753 0.000 0.534
## .Stest24exprssn 0.798 0.021 37.747 0.000 0.756
## .Stst26rdngcmpr 0.251 0.008 30.053 0.000 0.235
## .Stst31bstrctrs 0.613 0.017 35.558 0.000 0.579
## .Stst34rthcmptt 0.705 0.027 26.032 0.000 0.652
## .Stest5math 0.613 0.017 35.594 0.000 0.580
## .Stst25wrdfnctn 0.362 0.010 34.582 0.000 0.342
## .Stst32rthrsnng 0.282 0.008 34.380 0.000 0.266
## .Stst33hghschlm 0.205 0.007 29.657 0.000 0.191
## .Stest35tblrdng 1.257 0.068 18.503 0.000 1.124
## .Stst36clrclchc 1.038 0.033 31.200 0.000 0.973
## .Stst37bjctnspc 0.757 0.028 27.206 0.000 0.702
## .Stst28mchnclrs 0.217 0.007 32.673 0.000 0.204
## .Stst29vslztn2D 0.699 0.019 36.957 0.000 0.662
## .Stst30vslztn3D 0.383 0.011 34.955 0.000 0.361
## .english 1.713 0.255 6.729 0.000 1.214
## .math 0.621 0.142 4.365 0.000 0.342
## .speed 0.983 0.065 15.188 0.000 0.856
## .spatial 0.391 0.038 10.423 0.000 0.317
## g 0.753 0.035 21.320 0.000 0.684
## ci.upper Std.lv Std.all
## 0.347 0.328 0.373
## 0.441 0.417 0.508
## 0.543 0.516 0.563
## 0.492 0.465 0.482
## 0.358 0.336 0.361
## 0.600 0.567 0.471
## 0.839 0.798 0.670
## 0.267 0.251 0.266
## 0.647 0.613 0.537
## 0.758 0.705 0.541
## 0.647 0.613 0.617
## 0.383 0.362 0.616
## 0.299 0.282 0.504
## 0.219 0.205 0.421
## 1.391 1.257 0.479
## 1.103 1.038 0.631
## 0.811 0.757 0.579
## 0.230 0.217 0.522
## 0.736 0.699 0.725
## 0.404 0.383 0.626
## 2.212 0.244 0.244
## 0.900 0.107 0.107
## 1.110 0.876 0.876
## 0.464 0.324 0.324
## 0.822 1.000 1.000
lavTestScore(metric, release = 1:30)
## 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 359.705 30 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p81. 28.307 1 0.000
## 2 .p2. == .p82. 38.562 1 0.000
## 3 .p3. == .p83. 0.017 1 0.897
## 4 .p4. == .p84. 21.921 1 0.000
## 5 .p5. == .p85. 8.879 1 0.003
## 6 .p6. == .p86. 7.482 1 0.006
## 7 .p7. == .p87. 9.463 1 0.002
## 8 .p8. == .p88. 4.678 1 0.031
## 9 .p9. == .p89. 20.850 1 0.000
## 10 .p10. == .p90. 1.448 1 0.229
## 11 .p11. == .p91. 26.994 1 0.000
## 12 .p12. == .p92. 3.985 1 0.046
## 13 .p13. == .p93. 78.112 1 0.000
## 14 .p14. == .p94. 7.026 1 0.008
## 15 .p15. == .p95. 7.274 1 0.007
## 16 .p16. == .p96. 0.559 1 0.455
## 17 .p17. == .p97. 0.290 1 0.590
## 18 .p18. == .p98. 1.672 1 0.196
## 19 .p19. == .p99. 0.004 1 0.949
## 20 .p20. == .p100. 0.489 1 0.485
## 21 .p21. == .p101. 0.282 1 0.596
## 22 .p22. == .p102. 123.827 1 0.000
## 23 .p23. == .p103. 5.906 1 0.015
## 24 .p24. == .p104. 2.021 1 0.155
## 25 .p25. == .p105. 30.313 1 0.000
## 26 .p26. == .p106. 0.166 1 0.684
## 27 .p27. == .p107. 35.986 1 0.000
## 28 .p28. == .p108. 3.117 1 0.077
## 29 .p29. == .p109. 2.782 1 0.095
## 30 .p30. == .p110. 31.816 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("spatial=~Stest28mechanicalreasoning", "math=~Stest25wordfunctions"))
fitMeasures(metric2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 3611.485 343.000 0.000 0.943 0.056 0.050
## aic bic
## 291491.216 292276.705
Mc(metric2)
## [1] 0.7644389
summary(metric2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 114 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 145
## Number of equality constraints 28
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3611.485 3207.091
## Degrees of freedom 343 343
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.126
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1553.071 1379.166
## 1 2058.415 1827.924
##
## 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.) 0.187 0.019 9.716 0.000 0.149
## Stst19d (.p2.) 0.240 0.017 13.888 0.000 0.206
## Stst20s (.p3.) 0.239 0.018 13.420 0.000 0.204
## Stst21c (.p4.) 0.267 0.019 13.837 0.000 0.229
## Stst22p (.p5.) 0.292 0.021 13.847 0.000 0.250
## Stst23n (.p6.) 0.302 0.022 13.616 0.000 0.258
## Stst24x (.p7.) 0.237 0.018 13.475 0.000 0.202
## Stst26r (.p8.) 0.227 0.021 10.902 0.000 0.186
## Stst31b (.p9.) 0.101 0.011 9.570 0.000 0.080
## Stst34r (.10.) 0.117 0.017 7.079 0.000 0.084
## math =~
## Stst1vc (.11.) 0.129 0.019 6.757 0.000 0.091
## Stst5mt (.12.) 0.282 0.020 14.226 0.000 0.243
## Stst25w 0.183 0.013 14.460 0.000 0.158
## Stst26r (.14.) 0.122 0.018 6.928 0.000 0.087
## Stst32r (.15.) 0.241 0.017 14.325 0.000 0.208
## Stst33h (.16.) 0.242 0.017 14.225 0.000 0.209
## Stst34r (.17.) 0.085 0.017 4.859 0.000 0.050
## speed =~
## Stst34r (.18.) 0.448 0.020 22.028 0.000 0.408
## Stst35t (.19.) 1.102 0.032 34.134 0.000 1.039
## Stst36c (.20.) 0.734 0.026 27.977 0.000 0.683
## Stst37b (.21.) 0.662 0.025 26.505 0.000 0.613
## spatial =~
## Stst28m 0.450 0.015 29.971 0.000 0.421
## Sts292D (.23.) 0.415 0.018 23.396 0.000 0.380
## Sts303D (.24.) 0.381 0.016 23.617 0.000 0.350
## Stst31b (.25.) 0.414 0.018 22.488 0.000 0.378
## Stst37b (.26.) 0.089 0.014 6.566 0.000 0.063
## g =~
## english (.27.) 2.650 0.208 12.763 0.000 2.243
## math (.28.) 2.375 0.183 13.004 0.000 2.017
## speed (.29.) 0.429 0.025 16.974 0.000 0.380
## spatial (.30.) 1.209 0.059 20.653 0.000 1.094
## ci.upper Std.lv Std.all
##
## 0.225 0.530 0.512
## 0.274 0.680 0.742
## 0.274 0.677 0.676
## 0.305 0.756 0.773
## 0.333 0.826 0.807
## 0.345 0.854 0.729
## 0.271 0.671 0.587
## 0.267 0.642 0.602
## 0.121 0.285 0.245
## 0.149 0.331 0.284
##
## 0.166 0.331 0.320
## 0.321 0.726 0.701
## 0.208 0.472 0.609
## 0.156 0.314 0.295
## 0.274 0.621 0.751
## 0.276 0.625 0.798
## 0.119 0.218 0.188
##
## 0.487 0.487 0.419
## 1.166 1.200 0.717
## 0.786 0.799 0.617
## 0.711 0.720 0.580
##
## 0.480 0.707 0.789
## 0.450 0.651 0.599
## 0.413 0.598 0.649
## 0.450 0.649 0.558
## 0.116 0.140 0.113
##
## 3.057 0.936 0.936
## 2.732 0.922 0.922
## 0.479 0.395 0.395
## 1.324 0.771 0.771
##
## 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
## .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
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.903
## .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
## .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 -1.082
## -0.806 -0.848 -0.846
## -1.128 -1.167 -1.192
## -1.184 -1.226 -1.198
## -1.012 -1.062 -0.906
## -0.916 -0.965 -0.844
## -1.248 -1.292 -1.212
## -1.022 -1.070 -0.920
## -1.104 -1.153 -0.991
## -0.770 -0.814 -0.785
## -0.838 -0.871 -1.123
## -1.017 -1.052 -1.271
## -0.843 -0.875 -1.118
## -0.640 -0.712 -0.426
## 0.023 -0.032 -0.025
## -0.266 -0.318 -0.256
## -0.677 -0.715 -0.798
## -0.466 -0.512 -0.470
## -0.683 -0.723 -0.784
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.376 0.013 28.554 0.000 0.350
## .Stst19dsgsdwrd 0.378 0.014 27.004 0.000 0.350
## .Stest20spellng 0.547 0.017 31.669 0.000 0.513
## .Stest21cptlztn 0.386 0.015 25.153 0.000 0.356
## .Stest22puncttn 0.366 0.013 29.187 0.000 0.341
## .Stest23english 0.644 0.024 27.249 0.000 0.597
## .Stest24exprssn 0.858 0.025 33.866 0.000 0.809
## .Stst26rdngcmpr 0.278 0.011 25.187 0.000 0.257
## .Stst31bstrctrs 0.583 0.022 26.152 0.000 0.539
## .Stst34rthcmptt 0.637 0.030 21.364 0.000 0.579
## .Stest5math 0.546 0.021 26.354 0.000 0.506
## .Stst25wrdfnctn 0.378 0.012 31.716 0.000 0.355
## .Stst32rthrsnng 0.299 0.011 28.115 0.000 0.278
## .Stst33hghschlm 0.223 0.009 25.066 0.000 0.205
## .Stest35tblrdng 1.361 0.077 17.689 0.000 1.211
## .Stst36clrclchc 1.036 0.042 24.826 0.000 0.954
## .Stst37bjctnspc 0.942 0.035 26.666 0.000 0.873
## .Stst28mchnclrs 0.303 0.015 19.713 0.000 0.273
## .Stst29vslztn2D 0.758 0.026 29.349 0.000 0.708
## .Stst30vslztn3D 0.493 0.017 28.783 0.000 0.459
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.402 0.376 0.352
## 0.405 0.378 0.450
## 0.581 0.547 0.544
## 0.417 0.386 0.403
## 0.391 0.366 0.349
## 0.690 0.644 0.469
## 0.908 0.858 0.656
## 0.300 0.278 0.245
## 0.627 0.583 0.431
## 0.696 0.637 0.471
## 0.587 0.546 0.509
## 0.402 0.378 0.629
## 0.320 0.299 0.437
## 0.240 0.223 0.363
## 1.512 1.361 0.486
## 1.118 1.036 0.619
## 1.011 0.942 0.611
## 0.334 0.303 0.378
## 0.809 0.758 0.641
## 0.526 0.493 0.579
## 1.000 0.125 0.125
## 1.000 0.151 0.151
## 1.000 0.844 0.844
## 1.000 0.406 0.406
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.187 0.019 9.716 0.000 0.149
## Stst19d (.p2.) 0.240 0.017 13.888 0.000 0.206
## Stst20s (.p3.) 0.239 0.018 13.420 0.000 0.204
## Stst21c (.p4.) 0.267 0.019 13.837 0.000 0.229
## Stst22p (.p5.) 0.292 0.021 13.847 0.000 0.250
## Stst23n (.p6.) 0.302 0.022 13.616 0.000 0.258
## Stst24x (.p7.) 0.237 0.018 13.475 0.000 0.202
## Stst26r (.p8.) 0.227 0.021 10.902 0.000 0.186
## Stst31b (.p9.) 0.101 0.011 9.570 0.000 0.080
## Stst34r (.10.) 0.117 0.017 7.079 0.000 0.084
## math =~
## Stst1vc (.11.) 0.129 0.019 6.757 0.000 0.091
## Stst5mt (.12.) 0.282 0.020 14.226 0.000 0.243
## Stst25w 0.249 0.018 13.513 0.000 0.213
## Stst26r (.14.) 0.122 0.018 6.928 0.000 0.087
## Stst32r (.15.) 0.241 0.017 14.325 0.000 0.208
## Stst33h (.16.) 0.242 0.017 14.225 0.000 0.209
## Stst34r (.17.) 0.085 0.017 4.859 0.000 0.050
## speed =~
## Stst34r (.18.) 0.448 0.020 22.028 0.000 0.408
## Stst35t (.19.) 1.102 0.032 34.134 0.000 1.039
## Stst36c (.20.) 0.734 0.026 27.977 0.000 0.683
## Stst37b (.21.) 0.662 0.025 26.505 0.000 0.613
## spatial =~
## Stst28m 0.289 0.016 18.534 0.000 0.258
## Sts292D (.23.) 0.415 0.018 23.396 0.000 0.380
## Sts303D (.24.) 0.381 0.016 23.617 0.000 0.350
## Stst31b (.25.) 0.414 0.018 22.488 0.000 0.378
## Stst37b (.26.) 0.089 0.014 6.566 0.000 0.063
## g =~
## english (.27.) 2.650 0.208 12.763 0.000 2.243
## math (.28.) 2.375 0.183 13.004 0.000 2.017
## speed (.29.) 0.429 0.025 16.974 0.000 0.380
## spatial (.30.) 1.209 0.059 20.653 0.000 1.094
## ci.upper Std.lv Std.all
##
## 0.225 0.495 0.528
## 0.274 0.636 0.701
## 0.274 0.633 0.662
## 0.305 0.707 0.720
## 0.333 0.772 0.800
## 0.345 0.799 0.728
## 0.271 0.627 0.575
## 0.267 0.600 0.618
## 0.121 0.266 0.247
## 0.149 0.309 0.271
##
## 0.166 0.278 0.296
## 0.321 0.608 0.612
## 0.286 0.539 0.674
## 0.156 0.263 0.271
## 0.274 0.520 0.699
## 0.276 0.523 0.753
## 0.119 0.183 0.160
##
## 0.487 0.475 0.416
## 1.166 1.169 0.722
## 0.786 0.779 0.607
## 0.711 0.702 0.614
##
## 0.319 0.381 0.621
## 0.450 0.547 0.553
## 0.413 0.503 0.638
## 0.450 0.545 0.506
## 0.116 0.118 0.103
##
## 3.057 0.868 0.868
## 2.732 0.955 0.955
## 0.479 0.351 0.351
## 1.324 0.796 0.796
##
## 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
## .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
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.816
## .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
## .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 -1.428
## -0.846 -0.878 -0.969
## -0.417 -0.450 -0.470
## -0.865 -0.899 -0.916
## -0.895 -0.929 -0.962
## -0.706 -0.744 -0.677
## -0.667 -0.704 -0.645
## -1.193 -1.226 -1.263
## -1.222 -1.260 -1.170
## -0.963 -1.004 -0.880
## -0.931 -0.965 -0.971
## -0.761 -0.788 -0.987
## -1.159 -1.184 -1.590
## -0.919 -0.942 -1.357
## -0.466 -0.524 -0.323
## 0.344 0.300 0.234
## -0.176 -0.217 -0.189
## -1.303 -1.323 -2.159
## -0.882 -0.916 -0.925
## -0.955 -0.982 -1.246
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.329 0.010 34.227 0.000 0.310
## .Stst19dsgsdwrd 0.418 0.012 34.935 0.000 0.394
## .Stest20spellng 0.515 0.014 37.421 0.000 0.488
## .Stest21cptlztn 0.465 0.014 33.610 0.000 0.438
## .Stest22puncttn 0.336 0.011 30.815 0.000 0.315
## .Stest23english 0.568 0.017 33.760 0.000 0.535
## .Stest24exprssn 0.798 0.021 37.776 0.000 0.756
## .Stst26rdngcmpr 0.252 0.008 30.048 0.000 0.235
## .Stst31bstrctrs 0.590 0.017 33.841 0.000 0.556
## .Stst34rthcmptt 0.705 0.027 26.029 0.000 0.652
## .Stest5math 0.616 0.017 35.718 0.000 0.583
## .Stst25wrdfnctn 0.349 0.010 33.868 0.000 0.328
## .Stst32rthrsnng 0.284 0.008 34.723 0.000 0.268
## .Stst33hghschlm 0.209 0.007 30.268 0.000 0.195
## .Stest35tblrdng 1.259 0.068 18.487 0.000 1.125
## .Stst36clrclchc 1.037 0.033 31.122 0.000 0.972
## .Stst37bjctnspc 0.755 0.028 27.178 0.000 0.701
## .Stst28mchnclrs 0.231 0.007 33.858 0.000 0.218
## .Stst29vslztn2D 0.681 0.019 35.545 0.000 0.643
## .Stst30vslztn3D 0.369 0.011 33.334 0.000 0.347
## .english 1.726 0.249 6.935 0.000 1.238
## .math 0.412 0.102 4.028 0.000 0.212
## .speed 0.986 0.065 15.203 0.000 0.859
## .spatial 0.637 0.069 9.237 0.000 0.502
## g 0.753 0.034 21.921 0.000 0.686
## ci.upper Std.lv Std.all
## 0.348 0.329 0.374
## 0.441 0.418 0.508
## 0.542 0.515 0.562
## 0.492 0.465 0.482
## 0.357 0.336 0.360
## 0.600 0.568 0.471
## 0.839 0.798 0.670
## 0.268 0.252 0.267
## 0.625 0.590 0.509
## 0.758 0.705 0.542
## 0.650 0.616 0.625
## 0.369 0.349 0.546
## 0.300 0.284 0.512
## 0.222 0.209 0.432
## 1.392 1.259 0.479
## 1.103 1.037 0.631
## 0.810 0.755 0.577
## 0.244 0.231 0.614
## 0.718 0.681 0.694
## 0.390 0.369 0.593
## 2.214 0.246 0.246
## 0.613 0.089 0.089
## 1.113 0.877 0.877
## 0.772 0.367 0.367
## 0.820 1.000 1.000
lavTestScore(metric2, release = 1:28)
## 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 167.523 28 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p81. 24.994 1 0.000
## 2 .p2. == .p82. 37.529 1 0.000
## 3 .p3. == .p83. 0.037 1 0.847
## 4 .p4. == .p84. 21.163 1 0.000
## 5 .p5. == .p85. 8.608 1 0.003
## 6 .p6. == .p86. 8.153 1 0.004
## 7 .p7. == .p87. 9.699 1 0.002
## 8 .p8. == .p88. 3.038 1 0.081
## 9 .p9. == .p89. 9.322 1 0.002
## 10 .p10. == .p90. 2.124 1 0.145
## 11 .p11. == .p91. 24.183 1 0.000
## 12 .p12. == .p92. 1.000 1 0.317
## 13 .p14. == .p94. 4.951 1 0.026
## 14 .p15. == .p95. 2.145 1 0.143
## 15 .p16. == .p96. 0.419 1 0.517
## 16 .p17. == .p97. 0.567 1 0.451
## 17 .p18. == .p98. 2.028 1 0.154
## 18 .p19. == .p99. 0.000 1 0.987
## 19 .p20. == .p100. 0.420 1 0.517
## 20 .p21. == .p101. 0.078 1 0.781
## 21 .p23. == .p103. 0.007 1 0.934
## 22 .p24. == .p104. 19.907 1 0.000
## 23 .p25. == .p105. 9.603 1 0.002
## 24 .p26. == .p106. 0.117 1 0.732
## 25 .p27. == .p107. 35.149 1 0.000
## 26 .p28. == .p108. 27.942 1 0.000
## 27 .p29. == .p109. 2.056 1 0.152
## 28 .p30. == .p110. 1.933 1 0.164
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("spatial=~Stest28mechanicalreasoning", "math=~Stest25wordfunctions"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov)
## does not appear to be positive definite! The smallest eigenvalue
## (= 5.569568e-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
## 4525.936 358.000 0.000 0.927 0.062 0.055
## aic bic
## 292375.667 293060.452
Mc(scalar)
## [1] 0.70997
summary(scalar, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 139 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 150
## 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 4525.936 4020.142
## Degrees of freedom 358 358
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.126
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 2048.268 1819.364
## 1 2477.668 2200.778
##
## 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.) 0.070 0.017 4.121 0.000 0.037
## Stst19d (.p2.) 0.212 0.021 10.139 0.000 0.171
## Stst20s (.p3.) 0.221 0.022 9.926 0.000 0.178
## Stst21c (.p4.) 0.243 0.024 10.128 0.000 0.196
## Stst22p (.p5.) 0.266 0.026 10.134 0.000 0.215
## Stst23n (.p6.) 0.274 0.027 10.015 0.000 0.221
## Stst24x (.p7.) 0.216 0.022 9.956 0.000 0.173
## Stst26r (.p8.) 0.152 0.021 7.412 0.000 0.112
## Stst31b (.p9.) 0.123 0.013 9.759 0.000 0.099
## Stst34r (.10.) 0.101 0.015 6.806 0.000 0.072
## math =~
## Stst1vc (.11.) 0.229 0.022 10.329 0.000 0.185
## Stst5mt (.12.) 0.251 0.022 11.209 0.000 0.207
## Stst25w 0.158 0.014 11.256 0.000 0.131
## Stst26r (.14.) 0.170 0.017 9.851 0.000 0.136
## Stst32r (.15.) 0.213 0.019 11.229 0.000 0.176
## Stst33h (.16.) 0.211 0.019 11.136 0.000 0.174
## Stst34r (.17.) 0.080 0.014 5.592 0.000 0.052
## speed =~
## Stst34r (.18.) 0.445 0.020 22.111 0.000 0.406
## Stst35t (.19.) 1.089 0.033 33.295 0.000 1.025
## Stst36c (.20.) 0.750 0.026 28.987 0.000 0.699
## Stst37b (.21.) 0.673 0.024 28.470 0.000 0.626
## spatial =~
## Stst28m 0.482 0.015 32.724 0.000 0.453
## Sts292D (.23.) 0.433 0.019 22.741 0.000 0.396
## Sts303D (.24.) 0.381 0.017 22.685 0.000 0.348
## Stst31b (.25.) 0.364 0.018 20.714 0.000 0.330
## Stst37b (.26.) 0.092 0.013 7.008 0.000 0.066
## g =~
## english (.27.) 2.958 0.308 9.591 0.000 2.354
## math (.28.) 2.712 0.261 10.405 0.000 2.201
## speed (.29.) 0.421 0.025 16.549 0.000 0.371
## spatial (.30.) 1.079 0.058 18.482 0.000 0.965
## ci.upper Std.lv Std.all
##
## 0.104 0.220 0.208
## 0.253 0.663 0.731
## 0.265 0.691 0.681
## 0.290 0.759 0.776
## 0.318 0.832 0.812
## 0.328 0.857 0.730
## 0.258 0.674 0.589
## 0.192 0.475 0.442
## 0.148 0.385 0.334
## 0.130 0.316 0.271
##
## 0.272 0.661 0.626
## 0.294 0.724 0.697
## 0.186 0.458 0.587
## 0.204 0.492 0.457
## 0.250 0.615 0.740
## 0.248 0.610 0.777
## 0.109 0.233 0.200
##
## 0.485 0.483 0.416
## 1.153 1.182 0.707
## 0.800 0.813 0.625
## 0.719 0.730 0.588
##
## 0.511 0.709 0.786
## 0.471 0.637 0.591
## 0.414 0.560 0.615
## 0.398 0.536 0.465
## 0.117 0.135 0.109
##
## 3.563 0.947 0.947
## 3.223 0.938 0.938
## 0.471 0.388 0.388
## 1.194 0.734 0.734
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.56.) -1.315 0.027 -49.293 0.000 -1.367
## .Stst19d (.57.) -1.108 0.018 -61.652 0.000 -1.144
## .Stst20s (.58.) -0.803 0.022 -37.216 0.000 -0.845
## .Stst21c (.59.) -1.222 0.021 -57.917 0.000 -1.263
## .Stst22p (.60.) -1.283 0.023 -54.801 0.000 -1.329
## .Stst23n (.61.) -1.113 0.026 -43.261 0.000 -1.164
## .Stst24x (.62.) -0.999 0.022 -44.813 0.000 -1.043
## .Stst26r (.63.) -1.375 0.026 -53.208 0.000 -1.426
## .Stst31b (.64.) -1.093 0.026 -41.466 0.000 -1.145
## .Stst34r (.65.) -1.232 0.025 -49.229 0.000 -1.281
## .Stst5mt (.66.) -0.885 0.021 -41.530 0.000 -0.927
## .Stst25w (.67.) -0.797 0.016 -49.013 0.000 -0.829
## .Stst32r (.68.) -1.116 0.017 -64.343 0.000 -1.150
## .Stst33h (.69.) -0.899 0.017 -53.211 0.000 -0.932
## .Stst35t (.70.) -0.813 0.035 -23.204 0.000 -0.882
## .Stst36c (.71.) 0.021 0.026 0.812 0.417 -0.030
## .Stst37b (.72.) -0.337 0.024 -13.752 0.000 -0.384
## .Stst28m (.73.) -0.883 0.026 -34.379 0.000 -0.934
## .Sts292D (.74.) -0.514 0.023 -22.564 0.000 -0.558
## .Sts303D (.75.) -0.658 0.020 -33.598 0.000 -0.696
## ci.upper Std.lv Std.all
## -1.262 -1.315 -1.244
## -1.073 -1.108 -1.221
## -0.761 -0.803 -0.790
## -1.180 -1.222 -1.249
## -1.238 -1.283 -1.253
## -1.063 -1.113 -0.949
## -0.955 -0.999 -0.873
## -1.324 -1.375 -1.278
## -1.041 -1.093 -0.948
## -1.183 -1.232 -1.060
## -0.843 -0.885 -0.852
## -0.765 -0.797 -1.022
## -1.082 -1.116 -1.342
## -0.866 -0.899 -1.146
## -0.745 -0.813 -0.487
## 0.072 0.021 0.016
## -0.289 -0.337 -0.271
## -0.833 -0.883 -0.979
## -0.469 -0.514 -0.476
## -0.620 -0.658 -0.723
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.372 0.015 24.347 0.000 0.342
## .Stst19dsgsdwrd 0.384 0.015 26.226 0.000 0.355
## .Stest20spellng 0.554 0.018 31.369 0.000 0.519
## .Stest21cptlztn 0.381 0.015 24.934 0.000 0.351
## .Stest22puncttn 0.357 0.012 28.943 0.000 0.333
## .Stest23english 0.642 0.024 27.163 0.000 0.596
## .Stest24exprssn 0.857 0.025 33.668 0.000 0.807
## .Stst26rdngcmpr 0.274 0.011 24.206 0.000 0.252
## .Stst31bstrctrs 0.606 0.022 27.715 0.000 0.563
## .Stst34rthcmptt 0.640 0.030 21.341 0.000 0.581
## .Stest5math 0.554 0.021 26.553 0.000 0.513
## .Stst25wrdfnctn 0.398 0.013 31.360 0.000 0.373
## .Stst32rthrsnng 0.313 0.011 27.904 0.000 0.291
## .Stst33hghschlm 0.244 0.009 25.858 0.000 0.226
## .Stest35tblrdng 1.395 0.076 18.401 0.000 1.246
## .Stst36clrclchc 1.031 0.043 24.154 0.000 0.948
## .Stst37bjctnspc 0.933 0.035 26.310 0.000 0.864
## .Stst28mchnclrs 0.311 0.018 17.141 0.000 0.276
## .Stst29vslztn2D 0.758 0.026 28.839 0.000 0.706
## .Stst30vslztn3D 0.515 0.018 28.623 0.000 0.480
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.402 0.372 0.333
## 0.413 0.384 0.466
## 0.588 0.554 0.537
## 0.411 0.381 0.398
## 0.382 0.357 0.341
## 0.688 0.642 0.467
## 0.907 0.857 0.654
## 0.296 0.274 0.237
## 0.649 0.606 0.456
## 0.698 0.640 0.474
## 0.595 0.554 0.514
## 0.423 0.398 0.655
## 0.335 0.313 0.453
## 0.263 0.244 0.397
## 1.543 1.395 0.500
## 1.115 1.031 0.609
## 1.003 0.933 0.606
## 0.347 0.311 0.382
## 0.809 0.758 0.651
## 0.551 0.515 0.622
## 1.000 0.103 0.103
## 1.000 0.120 0.120
## 1.000 0.849 0.849
## 1.000 0.462 0.462
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.070 0.017 4.121 0.000 0.037
## Stst19d (.p2.) 0.212 0.021 10.139 0.000 0.171
## Stst20s (.p3.) 0.221 0.022 9.926 0.000 0.178
## Stst21c (.p4.) 0.243 0.024 10.128 0.000 0.196
## Stst22p (.p5.) 0.266 0.026 10.134 0.000 0.215
## Stst23n (.p6.) 0.274 0.027 10.015 0.000 0.221
## Stst24x (.p7.) 0.216 0.022 9.956 0.000 0.173
## Stst26r (.p8.) 0.152 0.021 7.412 0.000 0.112
## Stst31b (.p9.) 0.123 0.013 9.759 0.000 0.099
## Stst34r (.10.) 0.101 0.015 6.806 0.000 0.072
## math =~
## Stst1vc (.11.) 0.229 0.022 10.329 0.000 0.185
## Stst5mt (.12.) 0.251 0.022 11.209 0.000 0.207
## Stst25w 0.215 0.020 10.809 0.000 0.176
## Stst26r (.14.) 0.170 0.017 9.851 0.000 0.136
## Stst32r (.15.) 0.213 0.019 11.229 0.000 0.176
## Stst33h (.16.) 0.211 0.019 11.136 0.000 0.174
## Stst34r (.17.) 0.080 0.014 5.592 0.000 0.052
## speed =~
## Stst34r (.18.) 0.445 0.020 22.111 0.000 0.406
## Stst35t (.19.) 1.089 0.033 33.295 0.000 1.025
## Stst36c (.20.) 0.750 0.026 28.987 0.000 0.699
## Stst37b (.21.) 0.673 0.024 28.470 0.000 0.626
## spatial =~
## Stst28m 0.389 0.022 17.364 0.000 0.345
## Sts292D (.23.) 0.433 0.019 22.741 0.000 0.396
## Sts303D (.24.) 0.381 0.017 22.685 0.000 0.348
## Stst31b (.25.) 0.364 0.018 20.714 0.000 0.330
## Stst37b (.26.) 0.092 0.013 7.008 0.000 0.066
## g =~
## english (.27.) 2.958 0.308 9.591 0.000 2.354
## math (.28.) 2.712 0.261 10.405 0.000 2.201
## speed (.29.) 0.421 0.025 16.549 0.000 0.371
## spatial (.30.) 1.079 0.058 18.482 0.000 0.965
## ci.upper Std.lv Std.all
##
## 0.104 0.207 0.222
## 0.253 0.623 0.690
## 0.265 0.649 0.670
## 0.290 0.712 0.725
## 0.318 0.781 0.809
## 0.328 0.804 0.732
## 0.258 0.633 0.579
## 0.192 0.446 0.462
## 0.148 0.362 0.337
## 0.130 0.296 0.260
##
## 0.272 0.549 0.590
## 0.294 0.602 0.605
## 0.255 0.517 0.650
## 0.204 0.408 0.423
## 0.250 0.511 0.686
## 0.248 0.506 0.732
## 0.109 0.193 0.170
##
## 0.485 0.471 0.414
## 1.153 1.152 0.713
## 0.800 0.793 0.616
## 0.719 0.712 0.622
##
## 0.433 0.457 0.702
## 0.471 0.508 0.518
## 0.414 0.446 0.580
## 0.398 0.427 0.397
## 0.117 0.107 0.094
##
## 3.563 0.873 0.873
## 3.223 0.977 0.977
## 0.471 0.344 0.344
## 1.194 0.796 0.796
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc (.56.) -1.315 0.027 -49.293 0.000 -1.367
## .Stst19d (.57.) -1.108 0.018 -61.652 0.000 -1.144
## .Stst20s (.58.) -0.803 0.022 -37.216 0.000 -0.845
## .Stst21c (.59.) -1.222 0.021 -57.917 0.000 -1.263
## .Stst22p (.60.) -1.283 0.023 -54.801 0.000 -1.329
## .Stst23n (.61.) -1.113 0.026 -43.261 0.000 -1.164
## .Stst24x (.62.) -0.999 0.022 -44.813 0.000 -1.043
## .Stst26r (.63.) -1.375 0.026 -53.208 0.000 -1.426
## .Stst31b (.64.) -1.093 0.026 -41.466 0.000 -1.145
## .Stst34r (.65.) -1.232 0.025 -49.229 0.000 -1.281
## .Stst5mt (.66.) -0.885 0.021 -41.530 0.000 -0.927
## .Stst25w (.67.) -0.797 0.016 -49.013 0.000 -0.829
## .Stst32r (.68.) -1.116 0.017 -64.343 0.000 -1.150
## .Stst33h (.69.) -0.899 0.017 -53.211 0.000 -0.932
## .Stst35t (.70.) -0.813 0.035 -23.204 0.000 -0.882
## .Stst36c (.71.) 0.021 0.026 0.812 0.417 -0.030
## .Stst37b (.72.) -0.337 0.024 -13.752 0.000 -0.384
## .Stst28m (.73.) -0.883 0.026 -34.379 0.000 -0.934
## .Sts292D (.74.) -0.514 0.023 -22.564 0.000 -0.558
## .Sts303D (.75.) -0.658 0.020 -33.598 0.000 -0.696
## .english 1.146 0.067 17.070 0.000 1.014
## .math -0.435 0.060 -7.287 0.000 -0.552
## .speed 0.278 0.038 7.231 0.000 0.202
## .spatial -1.062 0.056 -19.016 0.000 -1.171
## g 0.059 0.037 1.582 0.114 -0.014
## ci.upper Std.lv Std.all
## -1.262 -1.315 -1.412
## -1.073 -1.108 -1.228
## -0.761 -0.803 -0.829
## -1.180 -1.222 -1.243
## -1.238 -1.283 -1.330
## -1.063 -1.113 -1.014
## -0.955 -0.999 -0.915
## -1.324 -1.375 -1.425
## -1.041 -1.093 -1.017
## -1.183 -1.232 -1.083
## -0.843 -0.885 -0.890
## -0.765 -0.797 -1.001
## -1.082 -1.116 -1.498
## -0.866 -0.899 -1.299
## -0.745 -0.813 -0.503
## 0.072 0.021 0.016
## -0.289 -0.337 -0.294
## -0.833 -0.883 -1.359
## -0.469 -0.514 -0.524
## -0.620 -0.658 -0.855
## 1.277 0.391 0.391
## -0.318 -0.181 -0.181
## 0.353 0.262 0.262
## -0.952 -0.905 -0.905
## 0.132 0.068 0.068
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.329 0.011 30.858 0.000 0.308
## .Stst19dsgsdwrd 0.428 0.012 35.131 0.000 0.404
## .Stest20spellng 0.516 0.014 37.062 0.000 0.489
## .Stest21cptlztn 0.459 0.014 33.679 0.000 0.432
## .Stest22puncttn 0.322 0.011 30.578 0.000 0.301
## .Stest23english 0.559 0.017 33.463 0.000 0.527
## .Stest24exprssn 0.793 0.021 37.653 0.000 0.752
## .Stst26rdngcmpr 0.255 0.008 30.429 0.000 0.238
## .Stst31bstrctrs 0.626 0.017 36.001 0.000 0.592
## .Stst34rthcmptt 0.706 0.027 26.230 0.000 0.653
## .Stest5math 0.626 0.017 35.867 0.000 0.591
## .Stst25wrdfnctn 0.366 0.011 34.168 0.000 0.345
## .Stst32rthrsnng 0.294 0.009 34.332 0.000 0.277
## .Stst33hghschlm 0.223 0.007 30.791 0.000 0.209
## .Stest35tblrdng 1.285 0.068 18.795 0.000 1.151
## .Stst36clrclchc 1.031 0.033 30.859 0.000 0.965
## .Stst37bjctnspc 0.750 0.027 27.435 0.000 0.696
## .Stst28mchnclrs 0.214 0.007 29.056 0.000 0.200
## .Stst29vslztn2D 0.704 0.020 35.770 0.000 0.665
## .Stst30vslztn3D 0.394 0.012 34.027 0.000 0.371
## .english 2.042 0.367 5.563 0.000 1.322
## .math 0.258 0.104 2.480 0.013 0.054
## .speed 0.987 0.064 15.346 0.000 0.861
## .spatial 0.503 0.064 7.872 0.000 0.378
## g 0.749 0.034 22.124 0.000 0.682
## ci.upper Std.lv Std.all
## 0.350 0.329 0.379
## 0.451 0.428 0.524
## 0.543 0.516 0.551
## 0.485 0.459 0.475
## 0.342 0.322 0.345
## 0.592 0.559 0.464
## 0.834 0.793 0.665
## 0.271 0.255 0.274
## 0.660 0.626 0.543
## 0.759 0.706 0.545
## 0.660 0.626 0.633
## 0.387 0.366 0.578
## 0.310 0.294 0.529
## 0.237 0.223 0.465
## 1.419 1.285 0.492
## 1.096 1.031 0.621
## 0.803 0.750 0.572
## 0.229 0.214 0.507
## 0.743 0.704 0.732
## 0.416 0.394 0.664
## 2.761 0.238 0.238
## 0.462 0.045 0.045
## 1.113 0.881 0.881
## 0.628 0.366 0.366
## 0.815 1.000 1.000
lavTestScore(scalar, release = 29:48)
## 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 859.512 20 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p56. == .p136. 179.043 1 0.000
## 2 .p57. == .p137. 61.444 1 0.000
## 3 .p58. == .p138. 79.357 1 0.000
## 4 .p59. == .p139. 0.048 1 0.826
## 5 .p60. == .p140. 0.347 1 0.556
## 6 .p61. == .p141. 1.247 1 0.264
## 7 .p62. == .p142. 1.327 1 0.249
## 8 .p63. == .p143. 2.025 1 0.155
## 9 .p64. == .p144. 44.154 1 0.000
## 10 .p65. == .p145. 7.056 1 0.008
## 11 .p66. == .p146. 1.778 1 0.182
## 12 .p67. == .p147. 151.454 1 0.000
## 13 .p68. == .p148. 3.698 1 0.054
## 14 .p69. == .p149. 13.339 1 0.000
## 15 .p70. == .p150. 22.520 1 0.000
## 16 .p71. == .p151. 33.968 1 0.000
## 17 .p72. == .p152. 1.526 1 0.217
## 18 .p73. == .p153. 356.031 1 0.000
## 19 .p74. == .p154. 19.300 1 0.000
## 20 .p75. == .p155. 140.958 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("spatial=~Stest28mechanicalreasoning", "math=~Stest25wordfunctions", "Stest28mechanicalreasoning~1", "Stest1vocab~1", "Stest25wordfunctions~1", "Stest20spelling~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
## (= 2.568926e-14) 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
## 3759.229 354.000 0.000 0.940 0.056 0.051
## aic bic
## 291616.959 292328.599
Mc(scalar2)
## [1] 0.7558963
summary(scalar2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 128 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 150
## Number of equality constraints 44
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3759.229 3327.059
## Degrees of freedom 354 354
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.130
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1628.849 1441.593
## 1 2130.380 1885.466
##
## 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.) 0.174 0.018 9.479 0.000 0.138
## Stst19d (.p2.) 0.237 0.017 13.556 0.000 0.202
## Stst20s (.p3.) 0.239 0.018 13.115 0.000 0.204
## Stst21c (.p4.) 0.268 0.020 13.526 0.000 0.230
## Stst22p (.p5.) 0.293 0.022 13.519 0.000 0.251
## Stst23n (.p6.) 0.304 0.023 13.298 0.000 0.259
## Stst24x (.p7.) 0.239 0.018 13.161 0.000 0.203
## Stst26r (.p8.) 0.203 0.018 11.010 0.000 0.167
## Stst31b (.p9.) 0.108 0.010 10.798 0.000 0.088
## Stst34r (.10.) 0.112 0.014 7.910 0.000 0.084
## math =~
## Stst1vc (.11.) 0.144 0.018 8.137 0.000 0.109
## Stst5mt (.12.) 0.280 0.020 14.025 0.000 0.241
## Stst25w 0.181 0.013 14.173 0.000 0.156
## Stst26r (.14.) 0.149 0.015 9.844 0.000 0.119
## Stst32r (.15.) 0.239 0.017 14.088 0.000 0.206
## Stst33h (.16.) 0.238 0.017 13.990 0.000 0.205
## Stst34r (.17.) 0.091 0.014 6.319 0.000 0.063
## speed =~
## Stst34r (.18.) 0.446 0.020 22.196 0.000 0.407
## Stst35t (.19.) 1.089 0.033 33.253 0.000 1.025
## Stst36c (.20.) 0.750 0.026 28.750 0.000 0.699
## Stst37b (.21.) 0.665 0.024 27.827 0.000 0.618
## spatial =~
## Stst28m 0.454 0.015 31.149 0.000 0.426
## Sts292D (.23.) 0.427 0.017 24.449 0.000 0.393
## Sts303D (.24.) 0.380 0.016 24.529 0.000 0.350
## Stst31b (.25.) 0.402 0.017 23.521 0.000 0.368
## Stst37b (.26.) 0.093 0.013 7.232 0.000 0.068
## g =~
## english (.27.) 2.645 0.212 12.492 0.000 2.230
## math (.28.) 2.396 0.187 12.783 0.000 2.029
## speed (.29.) 0.422 0.026 16.497 0.000 0.372
## spatial (.30.) 1.194 0.056 21.167 0.000 1.083
## ci.upper Std.lv Std.all
##
## 0.210 0.491 0.474
## 0.271 0.669 0.735
## 0.275 0.677 0.676
## 0.307 0.759 0.775
## 0.336 0.830 0.809
## 0.348 0.859 0.731
## 0.274 0.675 0.589
## 0.239 0.574 0.537
## 0.127 0.305 0.263
## 0.139 0.315 0.271
##
## 0.178 0.373 0.360
## 0.319 0.726 0.700
## 0.207 0.471 0.608
## 0.178 0.387 0.362
## 0.273 0.621 0.750
## 0.272 0.619 0.792
## 0.120 0.237 0.204
##
## 0.486 0.484 0.417
## 1.153 1.182 0.708
## 0.801 0.814 0.625
## 0.712 0.722 0.581
##
## 0.483 0.708 0.790
## 0.461 0.665 0.607
## 0.411 0.592 0.644
## 0.435 0.625 0.539
## 0.118 0.145 0.116
##
## 3.060 0.935 0.935
## 2.764 0.923 0.923
## 0.472 0.389 0.389
## 1.304 0.767 0.767
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -1.155 0.023 -50.360 0.000 -1.200
## .Stst19d (.57.) -1.047 0.016 -66.268 0.000 -1.078
## .Stst20s -0.848 0.021 -39.900 0.000 -0.890
## .Stst21c (.59.) -1.151 0.018 -62.631 0.000 -1.187
## .Stst22p (.60.) -1.203 0.020 -60.306 0.000 -1.242
## .Stst23n (.61.) -1.031 0.022 -46.025 0.000 -1.075
## .Stst24x (.62.) -0.935 0.020 -47.002 0.000 -0.974
## .Stst26r (.63.) -1.319 0.022 -60.053 0.000 -1.362
## .Stst31b (.64.) -1.056 0.023 -45.756 0.000 -1.101
## .Stst34r (.65.) -1.166 0.022 -52.444 0.000 -1.210
## .Stst5mt (.66.) -0.824 0.019 -42.554 0.000 -0.862
## .Stst25w -0.871 0.017 -52.726 0.000 -0.903
## .Stst32r (.68.) -1.063 0.016 -65.835 0.000 -1.095
## .Stst33h (.69.) -0.847 0.016 -54.408 0.000 -0.877
## .Stst35t (.70.) -0.773 0.034 -22.898 0.000 -0.839
## .Stst36c (.71.) 0.049 0.025 1.925 0.054 -0.001
## .Stst37b (.72.) -0.320 0.023 -13.815 0.000 -0.365
## .Stst28m -0.715 0.019 -36.895 0.000 -0.753
## .Sts292D (.74.) -0.559 0.021 -26.704 0.000 -0.600
## .Sts303D (.75.) -0.701 0.018 -38.563 0.000 -0.736
## ci.upper Std.lv Std.all
## -1.110 -1.155 -1.115
## -1.016 -1.047 -1.150
## -0.806 -0.848 -0.846
## -1.115 -1.151 -1.174
## -1.164 -1.203 -1.173
## -0.987 -1.031 -0.878
## -0.896 -0.935 -0.816
## -1.276 -1.319 -1.235
## -1.011 -1.056 -0.910
## -1.123 -1.166 -1.004
## -0.786 -0.824 -0.795
## -0.838 -0.871 -1.123
## -1.031 -1.063 -1.283
## -0.816 -0.847 -1.083
## -0.707 -0.773 -0.463
## 0.098 0.049 0.037
## -0.274 -0.320 -0.257
## -0.677 -0.715 -0.798
## -0.518 -0.559 -0.510
## -0.665 -0.701 -0.762
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.375 0.013 28.397 0.000 0.349
## .Stst19dsgsdwrd 0.382 0.014 26.449 0.000 0.353
## .Stest20spellng 0.545 0.017 31.652 0.000 0.512
## .Stest21cptlztn 0.384 0.015 25.106 0.000 0.354
## .Stest22puncttn 0.363 0.013 28.981 0.000 0.339
## .Stest23english 0.641 0.024 27.117 0.000 0.595
## .Stest24exprssn 0.858 0.025 33.700 0.000 0.808
## .Stst26rdngcmpr 0.279 0.011 25.036 0.000 0.257
## .Stst31bstrctrs 0.589 0.022 26.946 0.000 0.546
## .Stst34rthcmptt 0.638 0.030 21.272 0.000 0.579
## .Stest5math 0.548 0.021 26.400 0.000 0.507
## .Stst25wrdfnctn 0.379 0.012 31.796 0.000 0.356
## .Stst32rthrsnng 0.301 0.011 28.116 0.000 0.280
## .Stst33hghschlm 0.228 0.009 25.730 0.000 0.211
## .Stest35tblrdng 1.392 0.076 18.358 0.000 1.244
## .Stst36clrclchc 1.031 0.043 24.145 0.000 0.948
## .Stst37bjctnspc 0.937 0.035 26.414 0.000 0.867
## .Stst28mchnclrs 0.301 0.015 19.590 0.000 0.271
## .Stst29vslztn2D 0.757 0.026 28.974 0.000 0.706
## .Stst30vslztn3D 0.495 0.017 29.091 0.000 0.461
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.401 0.375 0.350
## 0.410 0.382 0.460
## 0.579 0.545 0.543
## 0.414 0.384 0.400
## 0.388 0.363 0.345
## 0.688 0.641 0.465
## 0.908 0.858 0.653
## 0.301 0.279 0.245
## 0.631 0.589 0.437
## 0.696 0.638 0.472
## 0.588 0.548 0.509
## 0.402 0.379 0.630
## 0.322 0.301 0.438
## 0.246 0.228 0.373
## 1.541 1.392 0.499
## 1.115 1.031 0.609
## 1.006 0.937 0.608
## 0.331 0.301 0.375
## 0.808 0.757 0.631
## 0.528 0.495 0.585
## 1.000 0.125 0.125
## 1.000 0.148 0.148
## 1.000 0.849 0.849
## 1.000 0.412 0.412
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.174 0.018 9.479 0.000 0.138
## Stst19d (.p2.) 0.237 0.017 13.556 0.000 0.202
## Stst20s (.p3.) 0.239 0.018 13.115 0.000 0.204
## Stst21c (.p4.) 0.268 0.020 13.526 0.000 0.230
## Stst22p (.p5.) 0.293 0.022 13.519 0.000 0.251
## Stst23n (.p6.) 0.304 0.023 13.298 0.000 0.259
## Stst24x (.p7.) 0.239 0.018 13.161 0.000 0.203
## Stst26r (.p8.) 0.203 0.018 11.010 0.000 0.167
## Stst31b (.p9.) 0.108 0.010 10.798 0.000 0.088
## Stst34r (.10.) 0.112 0.014 7.910 0.000 0.084
## math =~
## Stst1vc (.11.) 0.144 0.018 8.137 0.000 0.109
## Stst5mt (.12.) 0.280 0.020 14.025 0.000 0.241
## Stst25w 0.247 0.019 13.330 0.000 0.211
## Stst26r (.14.) 0.149 0.015 9.844 0.000 0.119
## Stst32r (.15.) 0.239 0.017 14.088 0.000 0.206
## Stst33h (.16.) 0.238 0.017 13.990 0.000 0.205
## Stst34r (.17.) 0.091 0.014 6.319 0.000 0.063
## speed =~
## Stst34r (.18.) 0.446 0.020 22.196 0.000 0.407
## Stst35t (.19.) 1.089 0.033 33.253 0.000 1.025
## Stst36c (.20.) 0.750 0.026 28.750 0.000 0.699
## Stst37b (.21.) 0.665 0.024 27.827 0.000 0.618
## spatial =~
## Stst28m 0.291 0.016 18.719 0.000 0.261
## Sts292D (.23.) 0.427 0.017 24.449 0.000 0.393
## Sts303D (.24.) 0.380 0.016 24.529 0.000 0.350
## Stst31b (.25.) 0.402 0.017 23.521 0.000 0.368
## Stst37b (.26.) 0.093 0.013 7.232 0.000 0.068
## g =~
## english (.27.) 2.645 0.212 12.492 0.000 2.230
## math (.28.) 2.396 0.187 12.783 0.000 2.029
## speed (.29.) 0.422 0.026 16.497 0.000 0.372
## spatial (.30.) 1.194 0.056 21.167 0.000 1.083
## ci.upper Std.lv Std.all
##
## 0.210 0.461 0.492
## 0.271 0.628 0.695
## 0.275 0.635 0.663
## 0.307 0.712 0.723
## 0.336 0.778 0.804
## 0.348 0.806 0.731
## 0.274 0.633 0.579
## 0.239 0.538 0.556
## 0.127 0.286 0.266
## 0.139 0.296 0.260
##
## 0.178 0.312 0.333
## 0.319 0.607 0.611
## 0.283 0.537 0.671
## 0.178 0.323 0.334
## 0.273 0.520 0.697
## 0.272 0.518 0.747
## 0.120 0.198 0.174
##
## 0.486 0.473 0.415
## 1.153 1.154 0.713
## 0.801 0.794 0.616
## 0.712 0.704 0.616
##
## 0.321 0.382 0.622
## 0.461 0.560 0.562
## 0.411 0.499 0.635
## 0.435 0.527 0.489
## 0.118 0.122 0.106
##
## 3.060 0.866 0.866
## 2.764 0.959 0.959
## 0.472 0.346 0.346
## 1.304 0.791 0.791
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -1.424 0.026 -55.430 0.000 -1.474
## .Stst19d (.57.) -1.047 0.016 -66.268 0.000 -1.078
## .Stst20s -0.663 0.021 -31.842 0.000 -0.703
## .Stst21c (.59.) -1.151 0.018 -62.631 0.000 -1.187
## .Stst22p (.60.) -1.203 0.020 -60.306 0.000 -1.242
## .Stst23n (.61.) -1.031 0.022 -46.025 0.000 -1.075
## .Stst24x (.62.) -0.935 0.020 -47.002 0.000 -0.974
## .Stst26r (.63.) -1.319 0.022 -60.053 0.000 -1.362
## .Stst31b (.64.) -1.056 0.023 -45.756 0.000 -1.101
## .Stst34r (.65.) -1.166 0.022 -52.444 0.000 -1.210
## .Stst5mt (.66.) -0.824 0.019 -42.554 0.000 -0.862
## .Stst25w -0.671 0.019 -34.829 0.000 -0.709
## .Stst32r (.68.) -1.063 0.016 -65.835 0.000 -1.095
## .Stst33h (.69.) -0.847 0.016 -54.408 0.000 -0.877
## .Stst35t (.70.) -0.773 0.034 -22.898 0.000 -0.839
## .Stst36c (.71.) 0.049 0.025 1.925 0.054 -0.001
## .Stst37b (.72.) -0.320 0.023 -13.815 0.000 -0.365
## .Stst28m -1.100 0.019 -57.480 0.000 -1.137
## .Sts292D (.74.) -0.559 0.021 -26.704 0.000 -0.600
## .Sts303D (.75.) -0.701 0.018 -38.563 0.000 -0.736
## .english 0.971 0.049 19.844 0.000 0.875
## .math -0.400 0.044 -9.018 0.000 -0.487
## .speed 0.277 0.037 7.423 0.000 0.204
## .spatial -0.731 0.048 -15.382 0.000 -0.824
## g -0.032 0.030 -1.069 0.285 -0.090
## ci.upper Std.lv Std.all
## -1.374 -1.424 -1.520
## -1.016 -1.047 -1.159
## -0.622 -0.663 -0.692
## -1.115 -1.151 -1.169
## -1.164 -1.203 -1.243
## -0.987 -1.031 -0.936
## -0.896 -0.935 -0.854
## -1.276 -1.319 -1.362
## -1.011 -1.056 -0.980
## -1.123 -1.166 -1.023
## -0.786 -0.824 -0.829
## -0.633 -0.671 -0.840
## -1.031 -1.063 -1.426
## -0.816 -0.847 -1.222
## -0.707 -0.773 -0.478
## 0.098 0.049 0.038
## -0.274 -0.320 -0.279
## -1.062 -1.100 -1.793
## -0.518 -0.559 -0.561
## -0.665 -0.701 -0.892
## 1.067 0.366 0.366
## -0.313 -0.184 -0.184
## 0.350 0.261 0.261
## -0.638 -0.558 -0.558
## 0.027 -0.037 -0.037
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.330 0.010 34.167 0.000 0.311
## .Stst19dsgsdwrd 0.422 0.012 35.254 0.000 0.399
## .Stest20spellng 0.514 0.014 37.462 0.000 0.487
## .Stest21cptlztn 0.462 0.014 33.716 0.000 0.435
## .Stest22puncttn 0.332 0.011 31.016 0.000 0.311
## .Stest23english 0.564 0.017 33.653 0.000 0.531
## .Stest24exprssn 0.796 0.021 37.726 0.000 0.755
## .Stst26rdngcmpr 0.255 0.008 30.477 0.000 0.238
## .Stst31bstrctrs 0.594 0.017 34.436 0.000 0.561
## .Stst34rthcmptt 0.705 0.027 26.169 0.000 0.652
## .Stest5math 0.618 0.017 35.812 0.000 0.584
## .Stst25wrdfnctn 0.351 0.010 34.003 0.000 0.330
## .Stst32rthrsnng 0.285 0.008 34.685 0.000 0.269
## .Stst33hghschlm 0.212 0.007 30.774 0.000 0.199
## .Stest35tblrdng 1.284 0.069 18.651 0.000 1.149
## .Stst36clrclchc 1.029 0.034 30.547 0.000 0.963
## .Stst37bjctnspc 0.750 0.027 27.504 0.000 0.697
## .Stst28mchnclrs 0.230 0.007 33.668 0.000 0.217
## .Stst29vslztn2D 0.678 0.019 35.036 0.000 0.640
## .Stst30vslztn3D 0.369 0.011 33.449 0.000 0.347
## .english 1.757 0.257 6.846 0.000 1.254
## .math 0.380 0.100 3.817 0.000 0.185
## .speed 0.988 0.065 15.255 0.000 0.861
## .spatial 0.643 0.070 9.230 0.000 0.507
## g 0.755 0.034 22.034 0.000 0.688
## ci.upper Std.lv Std.all
## 0.349 0.330 0.376
## 0.446 0.422 0.517
## 0.541 0.514 0.560
## 0.489 0.462 0.477
## 0.353 0.332 0.354
## 0.597 0.564 0.465
## 0.838 0.796 0.665
## 0.271 0.255 0.272
## 0.628 0.594 0.512
## 0.758 0.705 0.543
## 0.652 0.618 0.626
## 0.371 0.351 0.549
## 0.301 0.285 0.514
## 0.226 0.212 0.442
## 1.419 1.284 0.491
## 1.095 1.029 0.620
## 0.804 0.750 0.574
## 0.244 0.230 0.613
## 0.715 0.678 0.684
## 0.390 0.369 0.597
## 2.260 0.250 0.250
## 0.576 0.081 0.081
## 1.115 0.880 0.880
## 0.780 0.374 0.374
## 0.822 1.000 1.000
lavTestScore(scalar2, release = 29:44)
## 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 145.572 16 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p57. == .p137. 41.483 1 0.000
## 2 .p59. == .p139. 3.937 1 0.047
## 3 .p60. == .p140. 8.218 1 0.004
## 4 .p61. == .p141. 7.325 1 0.007
## 5 .p62. == .p142. 4.698 1 0.030
## 6 .p63. == .p143. 19.142 1 0.000
## 7 .p64. == .p144. 3.177 1 0.075
## 8 .p65. == .p145. 2.272 1 0.132
## 9 .p66. == .p146. 1.012 1 0.314
## 10 .p68. == .p148. 2.317 1 0.128
## 11 .p69. == .p149. 24.102 1 0.000
## 12 .p70. == .p150. 19.191 1 0.000
## 13 .p71. == .p151. 35.719 1 0.000
## 14 .p72. == .p152. 0.013 1 0.908
## 15 .p74. == .p154. 18.927 1 0.000
## 16 .p75. == .p155. 7.254 1 0.007
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("spatial=~Stest28mechanicalreasoning", "math=~Stest25wordfunctions", "Stest28mechanicalreasoning~1", "Stest1vocab~1", "Stest25wordfunctions~1", "Stest20spelling~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
## (= 5.301684e-15) 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
## 3954.351 374.000 0.000 0.937 0.056 0.052
## aic bic
## 291772.082 292349.450
Mc(strict)
## [1] 0.7450953
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("spatial=~Stest28mechanicalreasoning", "math=~Stest25wordfunctions", "Stest28mechanicalreasoning~1", "Stest1vocab~1", "Stest25wordfunctions~1", "Stest20spelling~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
## (= 6.431896e-15) 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
## 3861.594 359.000 0.000 0.938 0.057 0.066
## aic bic
## 291709.325 292387.397
Mc(chc.hof)
## [1] 0.7498719
summary(chc.hof, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 87 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 145
## Number of equality constraints 44
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3861.594 3411.698
## Degrees of freedom 359 359
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.132
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1690.065 1493.163
## 1 2171.530 1918.535
##
## 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.) 0.209 0.016 12.695 0.000 0.177
## Stst19d (.p2.) 0.281 0.011 26.142 0.000 0.260
## Stst20s (.p3.) 0.285 0.012 24.322 0.000 0.262
## Stst21c (.p4.) 0.319 0.012 26.060 0.000 0.295
## Stst22p (.p5.) 0.349 0.013 26.660 0.000 0.324
## Stst23n (.p6.) 0.362 0.014 25.679 0.000 0.334
## Stst24x (.p7.) 0.284 0.012 24.418 0.000 0.261
## Stst26r (.p8.) 0.243 0.015 16.695 0.000 0.215
## Stst31b (.p9.) 0.127 0.009 13.777 0.000 0.109
## Stst34r (.10.) 0.131 0.014 9.041 0.000 0.102
## math =~
## Stst1vc (.11.) 0.113 0.013 8.593 0.000 0.087
## Stst5mt (.12.) 0.225 0.015 15.458 0.000 0.197
## Stst25w 0.151 0.010 14.659 0.000 0.131
## Stst26r (.14.) 0.118 0.011 10.883 0.000 0.097
## Stst32r (.15.) 0.192 0.012 15.486 0.000 0.168
## Stst33h (.16.) 0.192 0.013 15.243 0.000 0.167
## Stst34r (.17.) 0.075 0.012 6.326 0.000 0.052
## speed =~
## Stst34r (.18.) 0.444 0.019 23.988 0.000 0.408
## Stst35t (.19.) 1.085 0.024 44.398 0.000 1.037
## Stst36c (.20.) 0.743 0.022 34.342 0.000 0.701
## Stst37b (.21.) 0.660 0.020 33.104 0.000 0.621
## spatial =~
## Stst28m 0.423 0.013 31.784 0.000 0.397
## Sts292D (.23.) 0.378 0.012 30.268 0.000 0.353
## Sts303D (.24.) 0.334 0.011 31.245 0.000 0.313
## Stst31b (.25.) 0.359 0.013 27.518 0.000 0.333
## Stst37b (.26.) 0.081 0.011 7.262 0.000 0.059
## g =~
## english (.27.) 2.067 0.094 21.993 0.000 1.883
## math (.28.) 2.756 0.194 14.212 0.000 2.376
## speed (.29.) 0.398 0.022 17.735 0.000 0.354
## spatial (.30.) 1.248 0.047 26.488 0.000 1.156
## ci.upper Std.lv Std.all
##
## 0.242 0.481 0.484
## 0.303 0.646 0.723
## 0.308 0.654 0.664
## 0.343 0.733 0.764
## 0.375 0.802 0.800
## 0.389 0.831 0.720
## 0.307 0.653 0.576
## 0.272 0.559 0.548
## 0.145 0.291 0.261
## 0.159 0.300 0.265
##
## 0.139 0.332 0.334
## 0.254 0.660 0.664
## 0.171 0.443 0.584
## 0.139 0.345 0.339
## 0.217 0.563 0.715
## 0.216 0.562 0.760
## 0.098 0.219 0.193
##
## 0.481 0.478 0.422
## 1.132 1.167 0.704
## 0.786 0.800 0.618
## 0.699 0.710 0.577
##
## 0.449 0.677 0.779
## 0.402 0.605 0.567
## 0.355 0.535 0.600
## 0.384 0.574 0.514
## 0.103 0.130 0.106
##
## 2.251 0.900 0.900
## 3.136 0.940 0.940
## 0.442 0.370 0.370
## 1.341 0.780 0.780
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -1.155 0.023 -50.360 0.000 -1.200
## .Stst19d (.57.) -1.047 0.016 -66.292 0.000 -1.078
## .Stst20s -0.848 0.021 -39.900 0.000 -0.890
## .Stst21c (.59.) -1.150 0.018 -62.637 0.000 -1.186
## .Stst22p (.60.) -1.203 0.020 -60.251 0.000 -1.242
## .Stst23n (.61.) -1.031 0.022 -45.957 0.000 -1.075
## .Stst24x (.62.) -0.935 0.020 -46.962 0.000 -0.974
## .Stst26r (.63.) -1.320 0.022 -60.225 0.000 -1.363
## .Stst31b (.64.) -1.054 0.023 -45.471 0.000 -1.099
## .Stst34r (.65.) -1.165 0.022 -52.221 0.000 -1.209
## .Stst5mt (.66.) -0.824 0.019 -42.425 0.000 -0.862
## .Stst25w -0.871 0.017 -52.726 0.000 -0.903
## .Stst32r (.68.) -1.063 0.016 -65.865 0.000 -1.095
## .Stst33h (.69.) -0.846 0.016 -54.309 0.000 -0.877
## .Stst35t (.70.) -0.774 0.034 -22.908 0.000 -0.840
## .Stst36c (.71.) 0.049 0.025 1.937 0.053 -0.001
## .Stst37b (.72.) -0.320 0.023 -13.822 0.000 -0.365
## .Stst28m -0.715 0.019 -36.895 0.000 -0.753
## .Sts292D (.74.) -0.560 0.021 -26.694 0.000 -0.601
## .Sts303D (.75.) -0.702 0.018 -38.744 0.000 -0.737
## ci.upper Std.lv Std.all
## -1.110 -1.155 -1.162
## -1.016 -1.047 -1.171
## -0.806 -0.848 -0.861
## -1.114 -1.150 -1.199
## -1.164 -1.203 -1.199
## -0.987 -1.031 -0.894
## -0.896 -0.935 -0.825
## -1.277 -1.320 -1.295
## -1.008 -1.054 -0.944
## -1.121 -1.165 -1.028
## -0.785 -0.824 -0.828
## -0.838 -0.871 -1.148
## -1.031 -1.063 -1.349
## -0.816 -0.846 -1.144
## -0.707 -0.774 -0.466
## 0.098 0.049 0.038
## -0.275 -0.320 -0.260
## -0.677 -0.715 -0.823
## -0.519 -0.560 -0.525
## -0.666 -0.702 -0.787
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.377 0.013 28.616 0.000 0.351
## .Stst19dsgsdwrd 0.382 0.014 26.438 0.000 0.354
## .Stest20spellng 0.543 0.017 31.575 0.000 0.509
## .Stest21cptlztn 0.384 0.015 25.056 0.000 0.354
## .Stest22puncttn 0.363 0.013 28.836 0.000 0.338
## .Stest23english 0.639 0.024 27.048 0.000 0.593
## .Stest24exprssn 0.856 0.025 33.686 0.000 0.806
## .Stst26rdngcmpr 0.281 0.011 25.292 0.000 0.259
## .Stst31bstrctrs 0.597 0.022 27.682 0.000 0.555
## .Stst34rthcmptt 0.638 0.030 21.184 0.000 0.579
## .Stest5math 0.554 0.021 26.512 0.000 0.513
## .Stst25wrdfnctn 0.379 0.012 31.784 0.000 0.355
## .Stst32rthrsnng 0.304 0.011 28.289 0.000 0.283
## .Stst33hghschlm 0.232 0.009 25.788 0.000 0.214
## .Stest35tblrdng 1.388 0.076 18.344 0.000 1.240
## .Stst36clrclchc 1.036 0.042 24.775 0.000 0.954
## .Stst37bjctnspc 0.941 0.035 26.789 0.000 0.872
## .Stst28mchnclrs 0.297 0.015 19.506 0.000 0.267
## .Stst29vslztn2D 0.770 0.025 30.194 0.000 0.720
## .Stst30vslztn3D 0.509 0.017 30.573 0.000 0.476
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.403 0.377 0.382
## 0.410 0.382 0.478
## 0.577 0.543 0.559
## 0.414 0.384 0.417
## 0.387 0.363 0.361
## 0.686 0.639 0.481
## 0.906 0.856 0.668
## 0.303 0.281 0.270
## 0.640 0.597 0.479
## 0.697 0.638 0.497
## 0.595 0.554 0.559
## 0.402 0.379 0.658
## 0.325 0.304 0.489
## 0.249 0.232 0.423
## 1.536 1.388 0.505
## 1.118 1.036 0.618
## 1.010 0.941 0.621
## 0.327 0.297 0.394
## 0.820 0.770 0.678
## 0.541 0.509 0.640
## 1.000 0.190 0.190
## 1.000 0.116 0.116
## 1.000 0.863 0.863
## 1.000 0.391 0.391
## 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.209 0.016 12.695 0.000 0.177
## Stst19d (.p2.) 0.281 0.011 26.142 0.000 0.260
## Stst20s (.p3.) 0.285 0.012 24.322 0.000 0.262
## Stst21c (.p4.) 0.319 0.012 26.060 0.000 0.295
## Stst22p (.p5.) 0.349 0.013 26.660 0.000 0.324
## Stst23n (.p6.) 0.362 0.014 25.679 0.000 0.334
## Stst24x (.p7.) 0.284 0.012 24.418 0.000 0.261
## Stst26r (.p8.) 0.243 0.015 16.695 0.000 0.215
## Stst31b (.p9.) 0.127 0.009 13.777 0.000 0.109
## Stst34r (.10.) 0.131 0.014 9.041 0.000 0.102
## math =~
## Stst1vc (.11.) 0.113 0.013 8.593 0.000 0.087
## Stst5mt (.12.) 0.225 0.015 15.458 0.000 0.197
## Stst25w 0.193 0.013 15.076 0.000 0.168
## Stst26r (.14.) 0.118 0.011 10.883 0.000 0.097
## Stst32r (.15.) 0.192 0.012 15.486 0.000 0.168
## Stst33h (.16.) 0.192 0.013 15.243 0.000 0.167
## Stst34r (.17.) 0.075 0.012 6.326 0.000 0.052
## speed =~
## Stst34r (.18.) 0.444 0.019 23.988 0.000 0.408
## Stst35t (.19.) 1.085 0.024 44.398 0.000 1.037
## Stst36c (.20.) 0.743 0.022 34.342 0.000 0.701
## Stst37b (.21.) 0.660 0.020 33.104 0.000 0.621
## spatial =~
## Stst28m 0.245 0.009 28.468 0.000 0.228
## Sts292D (.23.) 0.378 0.012 30.268 0.000 0.353
## Sts303D (.24.) 0.334 0.011 31.245 0.000 0.313
## Stst31b (.25.) 0.359 0.013 27.518 0.000 0.333
## Stst37b (.26.) 0.081 0.011 7.262 0.000 0.059
## g =~
## english (.27.) 2.067 0.094 21.993 0.000 1.883
## math (.28.) 2.756 0.194 14.212 0.000 2.376
## speed (.29.) 0.398 0.022 17.735 0.000 0.354
## spatial (.30.) 1.248 0.047 26.488 0.000 1.156
## ci.upper Std.lv Std.all
##
## 0.242 0.481 0.496
## 0.303 0.646 0.705
## 0.308 0.654 0.674
## 0.343 0.733 0.733
## 0.375 0.802 0.812
## 0.389 0.831 0.741
## 0.307 0.653 0.590
## 0.272 0.559 0.555
## 0.145 0.291 0.262
## 0.159 0.300 0.258
##
## 0.139 0.332 0.342
## 0.254 0.660 0.645
## 0.218 0.565 0.690
## 0.139 0.345 0.343
## 0.217 0.563 0.727
## 0.216 0.562 0.776
## 0.098 0.219 0.189
##
## 0.481 0.478 0.412
## 1.132 1.167 0.718
## 0.786 0.800 0.619
## 0.699 0.710 0.617
##
## 0.262 0.392 0.630
## 0.402 0.605 0.595
## 0.355 0.535 0.665
## 0.384 0.574 0.517
## 0.103 0.130 0.113
##
## 2.251 0.900 0.900
## 3.136 0.940 0.940
## 0.442 0.370 0.370
## 1.341 0.780 0.780
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -1.427 0.026 -55.108 0.000 -1.478
## .Stst19d (.57.) -1.047 0.016 -66.292 0.000 -1.078
## .Stst20s -0.662 0.021 -31.802 0.000 -0.703
## .Stst21c (.59.) -1.150 0.018 -62.637 0.000 -1.186
## .Stst22p (.60.) -1.203 0.020 -60.251 0.000 -1.242
## .Stst23n (.61.) -1.031 0.022 -45.957 0.000 -1.075
## .Stst24x (.62.) -0.935 0.020 -46.962 0.000 -0.974
## .Stst26r (.63.) -1.320 0.022 -60.225 0.000 -1.363
## .Stst31b (.64.) -1.054 0.023 -45.471 0.000 -1.099
## .Stst34r (.65.) -1.165 0.022 -52.221 0.000 -1.209
## .Stst5mt (.66.) -0.824 0.019 -42.425 0.000 -0.862
## .Stst25w -0.674 0.019 -35.921 0.000 -0.711
## .Stst32r (.68.) -1.063 0.016 -65.865 0.000 -1.095
## .Stst33h (.69.) -0.846 0.016 -54.309 0.000 -0.877
## .Stst35t (.70.) -0.774 0.034 -22.908 0.000 -0.840
## .Stst36c (.71.) 0.049 0.025 1.937 0.053 -0.001
## .Stst37b (.72.) -0.320 0.023 -13.822 0.000 -0.365
## .Stst28m -1.111 0.018 -61.451 0.000 -1.146
## .Sts292D (.74.) -0.560 0.021 -26.694 0.000 -0.601
## .Sts303D (.75.) -0.702 0.018 -38.744 0.000 -0.737
## .english 0.913 0.042 21.778 0.000 0.830
## .math -0.369 0.036 -10.364 0.000 -0.439
## .speed 0.297 0.036 8.367 0.000 0.228
## .spatial -0.766 0.049 -15.573 0.000 -0.863
## g -0.082 0.030 -2.726 0.006 -0.140
## ci.upper Std.lv Std.all
## -1.376 -1.427 -1.472
## -1.016 -1.047 -1.142
## -0.622 -0.662 -0.682
## -1.114 -1.150 -1.150
## -1.164 -1.203 -1.218
## -0.987 -1.031 -0.920
## -0.896 -0.935 -0.845
## -1.277 -1.320 -1.312
## -1.008 -1.054 -0.949
## -1.121 -1.165 -1.003
## -0.785 -0.824 -0.804
## -0.637 -0.674 -0.824
## -1.031 -1.063 -1.371
## -0.816 -0.846 -1.168
## -0.707 -0.774 -0.476
## 0.098 0.049 0.038
## -0.275 -0.320 -0.278
## -1.075 -1.111 -1.786
## -0.519 -0.560 -0.551
## -0.666 -0.702 -0.872
## 0.995 0.397 0.397
## -0.299 -0.126 -0.126
## 0.367 0.276 0.276
## -0.670 -0.479 -0.479
## -0.023 -0.082 -0.082
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.329 0.010 34.083 0.000 0.310
## .Stst19dsgsdwrd 0.422 0.012 35.277 0.000 0.399
## .Stest20spellng 0.516 0.014 37.592 0.000 0.489
## .Stest21cptlztn 0.463 0.014 33.888 0.000 0.437
## .Stest22puncttn 0.333 0.011 31.112 0.000 0.312
## .Stest23english 0.565 0.017 33.656 0.000 0.532
## .Stest24exprssn 0.797 0.021 37.747 0.000 0.755
## .Stst26rdngcmpr 0.254 0.008 30.425 0.000 0.238
## .Stst31bstrctrs 0.583 0.017 34.255 0.000 0.550
## .Stst34rthcmptt 0.704 0.027 26.045 0.000 0.651
## .Stest5math 0.614 0.017 35.740 0.000 0.580
## .Stst25wrdfnctn 0.350 0.010 34.096 0.000 0.330
## .Stst32rthrsnng 0.284 0.008 34.509 0.000 0.268
## .Stst33hghschlm 0.209 0.007 30.406 0.000 0.196
## .Stest35tblrdng 1.277 0.069 18.555 0.000 1.142
## .Stst36clrclchc 1.031 0.033 30.930 0.000 0.966
## .Stst37bjctnspc 0.750 0.027 27.583 0.000 0.697
## .Stst28mchnclrs 0.233 0.007 34.012 0.000 0.220
## .Stst29vslztn2D 0.667 0.019 34.791 0.000 0.630
## .Stst30vslztn3D 0.362 0.011 33.404 0.000 0.340
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.348 0.329 0.350
## 0.446 0.422 0.503
## 0.542 0.516 0.546
## 0.490 0.463 0.463
## 0.354 0.333 0.341
## 0.598 0.565 0.450
## 0.838 0.797 0.652
## 0.271 0.254 0.251
## 0.617 0.583 0.474
## 0.757 0.704 0.521
## 0.647 0.614 0.585
## 0.371 0.350 0.523
## 0.300 0.284 0.472
## 0.223 0.209 0.398
## 1.412 1.277 0.484
## 1.097 1.031 0.617
## 0.803 0.750 0.566
## 0.247 0.233 0.603
## 0.705 0.667 0.646
## 0.383 0.362 0.558
## 1.000 0.190 0.190
## 1.000 0.116 0.116
## 1.000 0.863 0.863
## 1.000 0.391 0.391
## 1.000 1.000 1.000
standardizedSolution(chc.hof) # 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 =~ Stest26readingcomprehension 1
## 9 english =~ Stest31abstractreasoning 1
## 10 english =~ Stest34arithcomputation 1
## 11 math =~ Stest1vocab 1
## 12 math =~ Stest5math 1
## 13 math =~ Stest25wordfunctions 1
## 14 math =~ Stest26readingcomprehension 1
## 15 math =~ Stest32arithreasoning 1
## 16 math =~ Stest33highschoolmath 1
## 17 math =~ Stest34arithcomputation 1
## 18 speed =~ Stest34arithcomputation 1
## 19 speed =~ Stest35tablereading 1
## 20 speed =~ Stest36clericalchecking 1
## 21 speed =~ Stest37objectinspection 1
## 22 spatial =~ Stest28mechanicalreasoning 1
## 23 spatial =~ Stest29visualization2D 1
## 24 spatial =~ Stest30visualization3D 1
## 25 spatial =~ Stest31abstractreasoning 1
## 26 spatial =~ Stest37objectinspection 1
## 27 g =~ english 1
## 28 g =~ math 1
## 29 g =~ speed 1
## 30 g =~ spatial 1
## 31 Stest1vocab ~~ Stest1vocab 1
## 32 Stest19disguisedwords ~~ Stest19disguisedwords 1
## 33 Stest20spelling ~~ Stest20spelling 1
## 34 Stest21capitalization ~~ Stest21capitalization 1
## 35 Stest22punctuation ~~ Stest22punctuation 1
## 36 Stest23english ~~ Stest23english 1
## 37 Stest24expression ~~ Stest24expression 1
## 38 Stest26readingcomprehension ~~ Stest26readingcomprehension 1
## 39 Stest31abstractreasoning ~~ Stest31abstractreasoning 1
## 40 Stest34arithcomputation ~~ Stest34arithcomputation 1
## 41 Stest5math ~~ Stest5math 1
## 42 Stest25wordfunctions ~~ Stest25wordfunctions 1
## 43 Stest32arithreasoning ~~ Stest32arithreasoning 1
## 44 Stest33highschoolmath ~~ Stest33highschoolmath 1
## 45 Stest35tablereading ~~ Stest35tablereading 1
## 46 Stest36clericalchecking ~~ Stest36clericalchecking 1
## 47 Stest37objectinspection ~~ Stest37objectinspection 1
## 48 Stest28mechanicalreasoning ~~ Stest28mechanicalreasoning 1
## 49 Stest29visualization2D ~~ Stest29visualization2D 1
## 50 Stest30visualization3D ~~ Stest30visualization3D 1
## 51 english ~~ english 1
## 52 math ~~ math 1
## 53 speed ~~ speed 1
## 54 spatial ~~ spatial 1
## 55 g ~~ g 1
## 56 Stest1vocab ~1 1
## 57 Stest19disguisedwords ~1 1
## 58 Stest20spelling ~1 1
## 59 Stest21capitalization ~1 1
## 60 Stest22punctuation ~1 1
## 61 Stest23english ~1 1
## 62 Stest24expression ~1 1
## 63 Stest26readingcomprehension ~1 1
## 64 Stest31abstractreasoning ~1 1
## 65 Stest34arithcomputation ~1 1
## 66 Stest5math ~1 1
## 67 Stest25wordfunctions ~1 1
## 68 Stest32arithreasoning ~1 1
## 69 Stest33highschoolmath ~1 1
## 70 Stest35tablereading ~1 1
## 71 Stest36clericalchecking ~1 1
## 72 Stest37objectinspection ~1 1
## 73 Stest28mechanicalreasoning ~1 1
## 74 Stest29visualization2D ~1 1
## 75 Stest30visualization3D ~1 1
## 76 english ~1 1
## 77 math ~1 1
## 78 speed ~1 1
## 79 spatial ~1 1
## 80 g ~1 1
## 81 english =~ Stest1vocab 2
## 82 english =~ Stest19disguisedwords 2
## 83 english =~ Stest20spelling 2
## 84 english =~ Stest21capitalization 2
## 85 english =~ Stest22punctuation 2
## 86 english =~ Stest23english 2
## 87 english =~ Stest24expression 2
## 88 english =~ Stest26readingcomprehension 2
## 89 english =~ Stest31abstractreasoning 2
## 90 english =~ Stest34arithcomputation 2
## label est.std se z pvalue ci.lower ci.upper
## 1 .p1. 0.484 0.032 14.976 0.000 0.420 0.547
## 2 .p2. 0.723 0.008 85.466 0.000 0.706 0.739
## 3 .p3. 0.664 0.010 69.643 0.000 0.645 0.683
## 4 .p4. 0.764 0.008 95.573 0.000 0.748 0.779
## 5 .p5. 0.800 0.007 120.504 0.000 0.787 0.813
## 6 .p6. 0.720 0.008 85.545 0.000 0.704 0.737
## 7 .p7. 0.576 0.011 54.113 0.000 0.556 0.597
## 8 .p8. 0.548 0.024 22.989 0.000 0.502 0.595
## 9 .p9. 0.261 0.017 15.774 0.000 0.229 0.293
## 10 .p10. 0.265 0.026 10.281 0.000 0.214 0.315
## 11 .p11. 0.334 0.034 9.888 0.000 0.268 0.400
## 12 .p12. 0.664 0.011 62.543 0.000 0.643 0.685
## 13 0.584 0.015 38.183 0.000 0.554 0.614
## 14 .p14. 0.339 0.025 13.555 0.000 0.290 0.388
## 15 .p15. 0.715 0.010 69.512 0.000 0.695 0.735
## 16 .p16. 0.760 0.009 80.519 0.000 0.741 0.778
## 17 .p17. 0.193 0.026 7.557 0.000 0.143 0.244
## 18 .p18. 0.422 0.016 27.185 0.000 0.391 0.452
## 19 .p19. 0.704 0.016 45.300 0.000 0.673 0.734
## 20 .p20. 0.618 0.015 40.052 0.000 0.588 0.648
## 21 .p21. 0.577 0.015 38.383 0.000 0.547 0.606
## 22 0.779 0.013 62.101 0.000 0.754 0.803
## 23 .p23. 0.567 0.012 45.686 0.000 0.543 0.592
## 24 .p24. 0.600 0.012 49.675 0.000 0.576 0.624
## 25 .p25. 0.514 0.017 29.744 0.000 0.480 0.548
## 26 .p26. 0.106 0.014 7.752 0.000 0.079 0.133
## 27 .p27. 0.900 0.008 115.960 0.000 0.885 0.915
## 28 .p28. 0.940 0.008 122.137 0.000 0.925 0.955
## 29 .p29. 0.370 0.018 20.546 0.000 0.335 0.405
## 30 .p30. 0.780 0.012 67.770 0.000 0.758 0.803
## 31 0.382 0.012 31.971 0.000 0.358 0.405
## 32 0.478 0.012 39.093 0.000 0.454 0.502
## 33 0.559 0.013 44.131 0.000 0.534 0.584
## 34 0.417 0.012 34.155 0.000 0.393 0.441
## 35 0.361 0.011 33.985 0.000 0.340 0.381
## 36 0.481 0.012 39.640 0.000 0.457 0.505
## 37 0.668 0.012 54.369 0.000 0.644 0.692
## 38 0.270 0.010 27.587 0.000 0.251 0.290
## 39 0.479 0.013 36.611 0.000 0.454 0.505
## 40 0.497 0.015 33.810 0.000 0.468 0.526
## 41 0.559 0.014 39.710 0.000 0.532 0.587
## 42 0.658 0.018 36.799 0.000 0.623 0.693
## 43 0.489 0.015 33.259 0.000 0.460 0.518
## 44 0.423 0.014 29.528 0.000 0.395 0.451
## 45 0.505 0.022 23.071 0.000 0.462 0.547
## 46 0.618 0.019 32.402 0.000 0.581 0.655
## 47 0.621 0.017 36.824 0.000 0.588 0.654
## 48 0.394 0.020 20.153 0.000 0.355 0.432
## 49 0.678 0.014 48.102 0.000 0.650 0.706
## 50 0.640 0.014 44.150 0.000 0.612 0.668
## 51 0.190 0.014 13.571 0.000 0.162 0.217
## 52 0.116 0.014 8.041 0.000 0.088 0.145
## 53 0.863 0.013 64.821 0.000 0.837 0.889
## 54 0.391 0.018 21.742 0.000 0.356 0.426
## 55 1.000 0.000 NA NA 1.000 1.000
## 56 -1.162 0.027 -42.519 0.000 -1.215 -1.108
## 57 .p57. -1.171 0.028 -41.200 0.000 -1.226 -1.115
## 58 -0.861 0.025 -35.120 0.000 -0.909 -0.812
## 59 .p59. -1.199 0.028 -42.898 0.000 -1.253 -1.144
## 60 .p60. -1.199 0.024 -50.084 0.000 -1.246 -1.153
## 61 .p61. -0.894 0.020 -44.009 0.000 -0.934 -0.855
## 62 .p62. -0.825 0.018 -45.197 0.000 -0.861 -0.790
## 63 .p63. -1.295 0.028 -46.603 0.000 -1.350 -1.241
## 64 .p64. -0.944 0.024 -39.902 0.000 -0.990 -0.897
## 65 .p65. -1.028 0.028 -36.602 0.000 -1.083 -0.973
## 66 .p66. -0.828 0.020 -42.346 0.000 -0.866 -0.789
## 67 -1.148 0.031 -37.594 0.000 -1.208 -1.088
## 68 .p68. -1.349 0.032 -42.513 0.000 -1.411 -1.287
## 69 .p69. -1.144 0.032 -36.251 0.000 -1.206 -1.082
## 70 .p70. -0.466 0.019 -23.997 0.000 -0.505 -0.428
## 71 .p71. 0.038 0.019 1.952 0.051 0.000 0.076
## 72 .p72. -0.260 0.020 -13.150 0.000 -0.299 -0.221
## 73 -0.823 0.029 -28.694 0.000 -0.879 -0.767
## 74 .p74. -0.525 0.022 -24.355 0.000 -0.568 -0.483
## 75 .p75. -0.787 0.024 -32.879 0.000 -0.834 -0.740
## 76 0.000 0.000 NA NA 0.000 0.000
## 77 0.000 0.000 NA NA 0.000 0.000
## 78 0.000 0.000 NA NA 0.000 0.000
## 79 0.000 0.000 NA NA 0.000 0.000
## 80 0.000 0.000 NA NA 0.000 0.000
## 81 .p1. 0.496 0.033 14.962 0.000 0.431 0.561
## 82 .p2. 0.705 0.009 82.222 0.000 0.688 0.722
## 83 .p3. 0.674 0.009 75.617 0.000 0.656 0.691
## 84 .p4. 0.733 0.008 94.864 0.000 0.718 0.748
## 85 .p5. 0.812 0.006 127.971 0.000 0.799 0.824
## 86 .p6. 0.741 0.007 103.673 0.000 0.727 0.755
## 87 .p7. 0.590 0.010 59.101 0.000 0.571 0.610
## 88 .p8. 0.555 0.024 22.688 0.000 0.507 0.603
## 89 .p9. 0.262 0.017 15.842 0.000 0.230 0.295
## 90 .p10. 0.258 0.025 10.374 0.000 0.209 0.307
## [ reached 'max' / getOption("max.print") -- omitted 70 rows ]
tests<-lavTestLRT(configural, metric2, scalar2, chc.hof)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 143.22533 118.34290 80.50238
dfd=tests[2:4,"Df diff"]
dfd
## [1] 23 11 5
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04145626 0.05664302 0.07046142
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.03509080 0.04808945
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.04767390 0.06607564
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.05737893 0.08440863
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 0.017 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 0.891 0.290 0.000 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 0.994 0.908 0.134 0.000
tests<-lavTestLRT(configural, metric2, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 143.2253 816.8842
dfd=tests[2:3,"Df diff"]
dfd
## [1] 23 15
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04145626 0.13257642
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.03509080 0.04808945
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.1249128 0.1403804
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 0.017 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, metric2, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 143.2253 118.3429 160.2079
dfd=tests[2:4,"Df diff"]
dfd
## [1] 23 11 20
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04145626 0.05664302 0.04800951
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.03509080 0.04808945
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.04767390 0.06607564
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.04125861 0.05504353
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 0.017 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 0.891 0.290 0.000 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 0.332 0.002 0.000 0.000
hof.age <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest26readingcomprehension + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest1vocab + Stest5math + Stest25wordfunctions + Stest26readingcomprehension + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g =~ english + math + speed + spatial
g ~ age
'
hof.age2 <-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest26readingcomprehension + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest1vocab + Stest5math + Stest25wordfunctions + Stest26readingcomprehension + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g =~ english + math + speed + spatial
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("spatial=~Stest28mechanicalreasoning", "math=~Stest25wordfunctions", "Stest28mechanicalreasoning~1", "Stest1vocab~1", "Stest25wordfunctions~1", "Stest20spelling~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
## (= 8.379761e-16) is close to zero. This may be a symptom that the
## model is not identified.
fitMeasures(sem.age, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 4066.353 397.000 0.000 0.936 0.055 0.064
## ecvi aic bic
## 0.702 291710.827 292402.326
Mc(sem.age)
## [1] 0.7396652
summary(sem.age, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 89 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 147
## Number of equality constraints 44
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 4066.353 3593.693
## Degrees of freedom 397 397
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.132
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1757.553 1553.260
## 1 2308.801 2040.433
##
## 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.) 0.209 0.017 12.664 0.000 0.177
## Stst19d (.p2.) 0.281 0.011 26.018 0.000 0.260
## Stst20s (.p3.) 0.285 0.012 24.219 0.000 0.262
## Stst21c (.p4.) 0.319 0.012 25.955 0.000 0.295
## Stst22p (.p5.) 0.349 0.013 26.510 0.000 0.323
## Stst23n (.p6.) 0.361 0.014 25.554 0.000 0.334
## Stst24x (.p7.) 0.284 0.012 24.308 0.000 0.261
## Stst26r (.p8.) 0.243 0.015 16.649 0.000 0.214
## Stst31b (.p9.) 0.127 0.009 13.762 0.000 0.109
## Stst34r (.10.) 0.130 0.014 9.025 0.000 0.102
## math =~
## Stst1vc (.11.) 0.113 0.013 8.589 0.000 0.087
## Stst5mt (.12.) 0.226 0.015 15.486 0.000 0.197
## Stst25w 0.151 0.010 14.682 0.000 0.131
## Stst26r (.14.) 0.118 0.011 10.890 0.000 0.097
## Stst32r (.15.) 0.193 0.012 15.519 0.000 0.168
## Stst33h (.16.) 0.192 0.013 15.283 0.000 0.167
## Stst34r (.17.) 0.075 0.012 6.333 0.000 0.052
## speed =~
## Stst34r (.18.) 0.444 0.019 23.988 0.000 0.408
## Stst35t (.19.) 1.084 0.024 44.402 0.000 1.037
## Stst36c (.20.) 0.743 0.022 34.344 0.000 0.701
## Stst37b (.21.) 0.660 0.020 33.101 0.000 0.621
## spatial =~
## Stst28m 0.423 0.013 31.743 0.000 0.397
## Sts292D (.23.) 0.378 0.012 30.242 0.000 0.354
## Sts303D (.24.) 0.334 0.011 31.224 0.000 0.313
## Stst31b (.25.) 0.359 0.013 27.516 0.000 0.333
## Stst37b (.26.) 0.081 0.011 7.260 0.000 0.059
## g =~
## english (.27.) 2.070 0.095 21.888 0.000 1.884
## math (.28.) 2.749 0.193 14.234 0.000 2.370
## speed (.29.) 0.398 0.022 17.744 0.000 0.354
## spatial (.30.) 1.248 0.047 26.435 0.000 1.155
## ci.upper Std.lv Std.all
##
## 0.241 0.481 0.484
## 0.302 0.646 0.723
## 0.308 0.655 0.664
## 0.343 0.733 0.764
## 0.375 0.802 0.800
## 0.389 0.831 0.720
## 0.307 0.653 0.577
## 0.272 0.559 0.548
## 0.145 0.291 0.261
## 0.159 0.300 0.264
##
## 0.139 0.332 0.334
## 0.254 0.661 0.664
## 0.172 0.443 0.585
## 0.139 0.346 0.339
## 0.217 0.564 0.715
## 0.217 0.562 0.760
## 0.098 0.219 0.194
##
## 0.481 0.478 0.422
## 1.132 1.167 0.704
## 0.786 0.800 0.618
## 0.699 0.710 0.577
##
## 0.449 0.677 0.779
## 0.403 0.605 0.568
## 0.355 0.535 0.600
## 0.384 0.574 0.514
## 0.103 0.130 0.106
##
## 2.255 0.901 0.901
## 3.127 0.940 0.940
## 0.442 0.370 0.370
## 1.340 0.781 0.781
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age -0.023 0.016 -1.466 0.143 -0.053
## ci.upper Std.lv Std.all
##
## 0.008 -0.023 -0.033
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -1.154 0.023 -50.350 0.000 -1.199
## .Stst19d (.59.) -1.046 0.016 -66.382 0.000 -1.077
## .Stst20s -0.847 0.021 -39.900 0.000 -0.889
## .Stst21c (.61.) -1.150 0.018 -62.677 0.000 -1.186
## .Stst22p (.62.) -1.202 0.020 -60.289 0.000 -1.241
## .Stst23n (.63.) -1.030 0.022 -45.961 0.000 -1.074
## .Stst24x (.64.) -0.934 0.020 -46.969 0.000 -0.973
## .Stst26r (.65.) -1.320 0.022 -60.267 0.000 -1.363
## .Stst31b (.66.) -1.053 0.023 -45.530 0.000 -1.098
## .Stst34r (.67.) -1.164 0.022 -52.280 0.000 -1.208
## .Stst5mt (.68.) -0.823 0.019 -42.416 0.000 -0.861
## .Stst25w -0.870 0.017 -52.706 0.000 -0.903
## .Stst32r (.70.) -1.062 0.016 -65.910 0.000 -1.094
## .Stst33h (.71.) -0.846 0.016 -54.354 0.000 -0.876
## .Stst35t (.72.) -0.773 0.034 -22.907 0.000 -0.839
## .Stst36c (.73.) 0.049 0.025 1.950 0.051 -0.000
## .Stst37b (.74.) -0.320 0.023 -13.816 0.000 -0.365
## .Stst28m -0.714 0.019 -36.913 0.000 -0.752
## .Sts292D (.76.) -0.559 0.021 -26.686 0.000 -0.600
## .Sts303D (.77.) -0.701 0.018 -38.761 0.000 -0.737
## ci.upper Std.lv Std.all
## -1.109 -1.154 -1.161
## -1.015 -1.046 -1.170
## -0.806 -0.847 -0.860
## -1.114 -1.150 -1.198
## -1.163 -1.202 -1.199
## -0.986 -1.030 -0.894
## -0.895 -0.934 -0.825
## -1.277 -1.320 -1.294
## -1.008 -1.053 -0.943
## -1.121 -1.164 -1.027
## -0.785 -0.823 -0.827
## -0.838 -0.870 -1.148
## -1.031 -1.062 -1.348
## -0.815 -0.846 -1.143
## -0.707 -0.773 -0.466
## 0.099 0.049 0.038
## -0.274 -0.320 -0.260
## -0.676 -0.714 -0.822
## -0.518 -0.559 -0.525
## -0.666 -0.701 -0.786
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.377 0.013 28.621 0.000 0.351
## .Stst19dsgsdwrd 0.382 0.014 26.429 0.000 0.354
## .Stest20spellng 0.543 0.017 31.582 0.000 0.509
## .Stest21cptlztn 0.384 0.015 25.056 0.000 0.354
## .Stest22puncttn 0.363 0.013 28.838 0.000 0.338
## .Stest23english 0.639 0.024 27.050 0.000 0.593
## .Stest24exprssn 0.856 0.025 33.686 0.000 0.806
## .Stst26rdngcmpr 0.281 0.011 25.289 0.000 0.259
## .Stst31bstrctrs 0.597 0.022 27.672 0.000 0.555
## .Stst34rthcmptt 0.638 0.030 21.184 0.000 0.579
## .Stest5math 0.554 0.021 26.508 0.000 0.513
## .Stst25wrdfnctn 0.379 0.012 31.786 0.000 0.355
## .Stst32rthrsnng 0.304 0.011 28.291 0.000 0.283
## .Stst33hghschlm 0.232 0.009 25.775 0.000 0.214
## .Stest35tblrdng 1.388 0.076 18.345 0.000 1.240
## .Stst36clrclchc 1.036 0.042 24.777 0.000 0.954
## .Stst37bjctnspc 0.941 0.035 26.789 0.000 0.872
## .Stst28mchnclrs 0.297 0.015 19.512 0.000 0.267
## .Stst29vslztn2D 0.770 0.025 30.191 0.000 0.720
## .Stst30vslztn3D 0.509 0.017 30.572 0.000 0.476
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.403 0.377 0.382
## 0.410 0.382 0.478
## 0.577 0.543 0.559
## 0.414 0.384 0.417
## 0.388 0.363 0.361
## 0.686 0.639 0.481
## 0.906 0.856 0.668
## 0.303 0.281 0.270
## 0.640 0.597 0.479
## 0.697 0.638 0.497
## 0.595 0.554 0.559
## 0.402 0.379 0.658
## 0.325 0.304 0.489
## 0.249 0.232 0.423
## 1.536 1.388 0.505
## 1.118 1.036 0.618
## 1.010 0.941 0.621
## 0.327 0.297 0.394
## 0.820 0.770 0.678
## 0.541 0.509 0.640
## 1.000 0.189 0.189
## 1.000 0.117 0.117
## 1.000 0.863 0.863
## 1.000 0.391 0.391
## 1.000 0.999 0.999
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.209 0.017 12.664 0.000 0.177
## Stst19d (.p2.) 0.281 0.011 26.018 0.000 0.260
## Stst20s (.p3.) 0.285 0.012 24.219 0.000 0.262
## Stst21c (.p4.) 0.319 0.012 25.955 0.000 0.295
## Stst22p (.p5.) 0.349 0.013 26.510 0.000 0.323
## Stst23n (.p6.) 0.361 0.014 25.554 0.000 0.334
## Stst24x (.p7.) 0.284 0.012 24.308 0.000 0.261
## Stst26r (.p8.) 0.243 0.015 16.649 0.000 0.214
## Stst31b (.p9.) 0.127 0.009 13.762 0.000 0.109
## Stst34r (.10.) 0.130 0.014 9.025 0.000 0.102
## math =~
## Stst1vc (.11.) 0.113 0.013 8.589 0.000 0.087
## Stst5mt (.12.) 0.226 0.015 15.486 0.000 0.197
## Stst25w 0.193 0.013 15.103 0.000 0.168
## Stst26r (.14.) 0.118 0.011 10.890 0.000 0.097
## Stst32r (.15.) 0.193 0.012 15.519 0.000 0.168
## Stst33h (.16.) 0.192 0.013 15.283 0.000 0.167
## Stst34r (.17.) 0.075 0.012 6.333 0.000 0.052
## speed =~
## Stst34r (.18.) 0.444 0.019 23.988 0.000 0.408
## Stst35t (.19.) 1.084 0.024 44.402 0.000 1.037
## Stst36c (.20.) 0.743 0.022 34.344 0.000 0.701
## Stst37b (.21.) 0.660 0.020 33.101 0.000 0.621
## spatial =~
## Stst28m 0.245 0.009 28.456 0.000 0.228
## Sts292D (.23.) 0.378 0.012 30.242 0.000 0.354
## Sts303D (.24.) 0.334 0.011 31.224 0.000 0.313
## Stst31b (.25.) 0.359 0.013 27.516 0.000 0.333
## Stst37b (.26.) 0.081 0.011 7.260 0.000 0.059
## g =~
## english (.27.) 2.070 0.095 21.888 0.000 1.884
## math (.28.) 2.749 0.193 14.234 0.000 2.370
## speed (.29.) 0.398 0.022 17.744 0.000 0.354
## spatial (.30.) 1.248 0.047 26.435 0.000 1.155
## ci.upper Std.lv Std.all
##
## 0.241 0.480 0.496
## 0.302 0.646 0.705
## 0.308 0.654 0.674
## 0.343 0.733 0.733
## 0.375 0.802 0.812
## 0.389 0.830 0.741
## 0.307 0.653 0.590
## 0.272 0.559 0.555
## 0.145 0.291 0.262
## 0.159 0.300 0.258
##
## 0.139 0.332 0.342
## 0.254 0.660 0.644
## 0.218 0.565 0.690
## 0.139 0.345 0.343
## 0.217 0.563 0.726
## 0.217 0.562 0.776
## 0.098 0.219 0.189
##
## 0.481 0.478 0.412
## 1.132 1.167 0.718
## 0.786 0.800 0.619
## 0.699 0.710 0.617
##
## 0.262 0.392 0.630
## 0.403 0.605 0.595
## 0.355 0.535 0.665
## 0.384 0.574 0.517
## 0.103 0.130 0.113
##
## 2.255 0.900 0.900
## 3.127 0.940 0.940
## 0.442 0.370 0.370
## 1.340 0.780 0.780
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.006 0.013 0.462 0.644 -0.019
## ci.upper Std.lv Std.all
##
## 0.031 0.006 0.008
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -1.426 0.026 -55.119 0.000 -1.477
## .Stst19d (.59.) -1.046 0.016 -66.382 0.000 -1.077
## .Stst20s -0.662 0.021 -31.805 0.000 -0.703
## .Stst21c (.61.) -1.150 0.018 -62.677 0.000 -1.186
## .Stst22p (.62.) -1.202 0.020 -60.289 0.000 -1.241
## .Stst23n (.63.) -1.030 0.022 -45.961 0.000 -1.074
## .Stst24x (.64.) -0.934 0.020 -46.969 0.000 -0.973
## .Stst26r (.65.) -1.320 0.022 -60.267 0.000 -1.363
## .Stst31b (.66.) -1.053 0.023 -45.530 0.000 -1.098
## .Stst34r (.67.) -1.164 0.022 -52.280 0.000 -1.208
## .Stst5mt (.68.) -0.823 0.019 -42.416 0.000 -0.861
## .Stst25w -0.674 0.019 -35.920 0.000 -0.710
## .Stst32r (.70.) -1.062 0.016 -65.910 0.000 -1.094
## .Stst33h (.71.) -0.846 0.016 -54.354 0.000 -0.876
## .Stst35t (.72.) -0.773 0.034 -22.907 0.000 -0.839
## .Stst36c (.73.) 0.049 0.025 1.950 0.051 -0.000
## .Stst37b (.74.) -0.320 0.023 -13.816 0.000 -0.365
## .Stst28m -1.111 0.018 -61.455 0.000 -1.146
## .Sts292D (.76.) -0.559 0.021 -26.686 0.000 -0.600
## .Sts303D (.77.) -0.701 0.018 -38.761 0.000 -0.737
## .english 0.908 0.042 21.689 0.000 0.826
## .math -0.376 0.036 -10.539 0.000 -0.446
## .speed 0.296 0.036 8.337 0.000 0.227
## .spatial -0.769 0.049 -15.638 0.000 -0.866
## .g -0.078 0.030 -2.595 0.009 -0.138
## ci.upper Std.lv Std.all
## -1.376 -1.426 -1.472
## -1.015 -1.046 -1.142
## -0.621 -0.662 -0.681
## -1.114 -1.150 -1.150
## -1.163 -1.202 -1.217
## -0.986 -1.030 -0.920
## -0.895 -0.934 -0.845
## -1.277 -1.320 -1.311
## -1.008 -1.053 -0.949
## -1.121 -1.164 -1.002
## -0.785 -0.823 -0.803
## -0.637 -0.674 -0.823
## -1.031 -1.062 -1.370
## -0.815 -0.846 -1.168
## -0.707 -0.773 -0.476
## 0.099 0.049 0.038
## -0.274 -0.320 -0.278
## -1.075 -1.111 -1.785
## -0.518 -0.559 -0.550
## -0.666 -0.701 -0.871
## 0.990 0.395 0.395
## -0.306 -0.129 -0.129
## 0.366 0.275 0.275
## -0.673 -0.481 -0.481
## -0.019 -0.078 -0.078
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.329 0.010 34.080 0.000 0.310
## .Stst19dsgsdwrd 0.422 0.012 35.277 0.000 0.399
## .Stest20spellng 0.516 0.014 37.592 0.000 0.489
## .Stest21cptlztn 0.463 0.014 33.888 0.000 0.437
## .Stest22puncttn 0.333 0.011 31.115 0.000 0.312
## .Stest23english 0.565 0.017 33.650 0.000 0.532
## .Stest24exprssn 0.797 0.021 37.748 0.000 0.755
## .Stst26rdngcmpr 0.254 0.008 30.422 0.000 0.238
## .Stst31bstrctrs 0.583 0.017 34.253 0.000 0.550
## .Stst34rthcmptt 0.704 0.027 26.045 0.000 0.651
## .Stest5math 0.614 0.017 35.742 0.000 0.580
## .Stst25wrdfnctn 0.350 0.010 34.093 0.000 0.330
## .Stst32rthrsnng 0.284 0.008 34.506 0.000 0.268
## .Stst33hghschlm 0.209 0.007 30.367 0.000 0.196
## .Stest35tblrdng 1.277 0.069 18.554 0.000 1.142
## .Stst36clrclchc 1.031 0.033 30.933 0.000 0.966
## .Stst37bjctnspc 0.750 0.027 27.584 0.000 0.697
## .Stst28mchnclrs 0.233 0.007 34.010 0.000 0.220
## .Stst29vslztn2D 0.667 0.019 34.788 0.000 0.630
## .Stst30vslztn3D 0.362 0.011 33.404 0.000 0.340
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.348 0.329 0.350
## 0.446 0.422 0.503
## 0.542 0.516 0.546
## 0.490 0.463 0.463
## 0.354 0.333 0.341
## 0.598 0.565 0.450
## 0.838 0.797 0.652
## 0.271 0.254 0.251
## 0.617 0.583 0.474
## 0.757 0.704 0.521
## 0.647 0.614 0.585
## 0.371 0.350 0.523
## 0.300 0.284 0.472
## 0.223 0.209 0.399
## 1.412 1.277 0.484
## 1.097 1.031 0.617
## 0.803 0.750 0.566
## 0.247 0.233 0.603
## 0.705 0.667 0.646
## 0.383 0.362 0.558
## 1.000 0.189 0.189
## 1.000 0.117 0.117
## 1.000 0.863 0.863
## 1.000 0.391 0.391
## 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("spatial=~Stest28mechanicalreasoning", "math=~Stest25wordfunctions", "Stest28mechanicalreasoning~1", "Stest1vocab~1", "Stest25wordfunctions~1", "Stest20spelling~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
## (= 5.347335e-15) is close to zero. This may be a symptom that the
## model is not identified.
fitMeasures(sem.age2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 4152.567 435.000 0.000 0.935 0.053 0.060
## ecvi aic bic
## 0.717 291656.675 292361.601
Mc(sem.age2)
## [1] 0.7367402
summary(sem.age2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 88 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 149
## Number of equality constraints 44
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 4152.567 3676.658
## Degrees of freedom 435 435
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.129
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1799.410 1593.187
## 1 2353.156 2083.471
##
## 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.) 0.210 0.016 12.791 0.000 0.178
## Stst19d (.p2.) 0.283 0.011 26.551 0.000 0.262
## Stst20s (.p3.) 0.287 0.012 24.658 0.000 0.264
## Stst21c (.p4.) 0.321 0.012 26.517 0.000 0.297
## Stst22p (.p5.) 0.351 0.013 27.076 0.000 0.326
## Stst23n (.p6.) 0.364 0.014 26.066 0.000 0.336
## Stst24x (.p7.) 0.286 0.012 24.741 0.000 0.263
## Stst26r (.p8.) 0.245 0.015 16.849 0.000 0.216
## Stst31b (.p9.) 0.128 0.009 13.842 0.000 0.110
## Stst34r (.10.) 0.132 0.014 9.111 0.000 0.103
## math =~
## Stst1vc (.11.) 0.113 0.013 8.596 0.000 0.087
## Stst5mt (.12.) 0.224 0.015 15.343 0.000 0.196
## Stst25w 0.150 0.010 14.559 0.000 0.130
## Stst26r (.14.) 0.117 0.011 10.864 0.000 0.096
## Stst32r (.15.) 0.191 0.012 15.343 0.000 0.167
## Stst33h (.16.) 0.191 0.013 15.127 0.000 0.166
## Stst34r (.17.) 0.074 0.012 6.318 0.000 0.051
## speed =~
## Stst34r (.18.) 0.444 0.019 23.970 0.000 0.408
## Stst35t (.19.) 1.084 0.024 44.406 0.000 1.037
## Stst36c (.20.) 0.743 0.022 34.349 0.000 0.701
## Stst37b (.21.) 0.660 0.020 33.107 0.000 0.621
## spatial =~
## Stst28m 0.422 0.013 31.755 0.000 0.396
## Sts292D (.23.) 0.378 0.012 30.242 0.000 0.353
## Sts303D (.24.) 0.334 0.011 31.193 0.000 0.313
## Stst31b (.25.) 0.358 0.013 27.505 0.000 0.333
## Stst37b (.26.) 0.081 0.011 7.254 0.000 0.059
## g =~
## english (.27.) 2.042 0.092 22.289 0.000 1.863
## math (.28.) 2.756 0.196 14.093 0.000 2.373
## speed (.29.) 0.396 0.022 17.777 0.000 0.353
## spatial (.30.) 1.243 0.047 26.459 0.000 1.151
## ci.upper Std.lv Std.all
##
## 0.243 0.483 0.484
## 0.304 0.649 0.724
## 0.309 0.658 0.666
## 0.345 0.736 0.765
## 0.376 0.806 0.801
## 0.391 0.834 0.722
## 0.308 0.656 0.578
## 0.273 0.562 0.549
## 0.146 0.293 0.262
## 0.160 0.302 0.266
##
## 0.138 0.333 0.334
## 0.253 0.664 0.666
## 0.170 0.445 0.586
## 0.138 0.347 0.339
## 0.216 0.566 0.716
## 0.215 0.565 0.761
## 0.097 0.220 0.193
##
## 0.480 0.478 0.421
## 1.132 1.168 0.704
## 0.786 0.801 0.618
## 0.699 0.711 0.577
##
## 0.449 0.679 0.780
## 0.402 0.607 0.569
## 0.355 0.537 0.601
## 0.384 0.575 0.514
## 0.103 0.131 0.106
##
## 2.222 0.900 0.900
## 3.139 0.941 0.941
## 0.440 0.372 0.372
## 1.335 0.783 0.783
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.009 0.017 0.513 0.608 -0.024
## age2 -0.055 0.008 -7.039 0.000 -0.070
## ci.upper Std.lv Std.all
##
## 0.042 0.009 0.012
## -0.039 -0.054 -0.152
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -1.071 0.027 -39.728 0.000 -1.124
## .Stst19d (.62.) -0.981 0.019 -50.542 0.000 -1.019
## .Stst20s -0.782 0.024 -32.861 0.000 -0.828
## .Stst21c (.64.) -1.076 0.022 -48.405 0.000 -1.120
## .Stst22p (.65.) -1.122 0.024 -46.226 0.000 -1.169
## .Stst23n (.66.) -0.947 0.027 -35.667 0.000 -0.999
## .Stst24x (.67.) -0.869 0.023 -38.372 0.000 -0.913
## .Stst26r (.68.) -1.227 0.027 -45.132 0.000 -1.281
## .Stst31b (.69.) -0.974 0.027 -36.235 0.000 -1.026
## .Stst34r (.70.) -1.092 0.026 -42.471 0.000 -1.142
## .Stst5mt (.71.) -0.754 0.023 -32.580 0.000 -0.799
## .Stst25w -0.824 0.019 -43.589 0.000 -0.861
## .Stst32r (.73.) -1.003 0.020 -50.873 0.000 -1.042
## .Stst33h (.74.) -0.787 0.019 -40.784 0.000 -0.825
## .Stst35t (.75.) -0.725 0.034 -21.073 0.000 -0.792
## .Stst36c (.76.) 0.082 0.026 3.181 0.001 0.032
## .Stst37b (.77.) -0.279 0.024 -11.443 0.000 -0.327
## .Stst28m -0.655 0.022 -29.297 0.000 -0.699
## .Sts292D (.79.) -0.506 0.023 -22.114 0.000 -0.551
## .Sts303D (.80.) -0.655 0.020 -32.794 0.000 -0.694
## ci.upper Std.lv Std.all
## -1.018 -1.071 -1.074
## -0.943 -0.981 -1.095
## -0.735 -0.782 -0.792
## -1.032 -1.076 -1.118
## -1.074 -1.122 -1.115
## -0.895 -0.947 -0.819
## -0.824 -0.869 -0.766
## -1.174 -1.227 -1.199
## -0.921 -0.974 -0.870
## -1.041 -1.092 -0.961
## -0.708 -0.754 -0.756
## -0.787 -0.824 -1.085
## -0.965 -1.003 -1.270
## -0.749 -0.787 -1.061
## -0.657 -0.725 -0.437
## 0.133 0.082 0.064
## -0.231 -0.279 -0.226
## -0.612 -0.655 -0.753
## -0.462 -0.506 -0.475
## -0.615 -0.655 -0.733
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.377 0.013 28.612 0.000 0.351
## .Stst19dsgsdwrd 0.382 0.014 26.431 0.000 0.354
## .Stest20spellng 0.543 0.017 31.562 0.000 0.509
## .Stest21cptlztn 0.384 0.015 25.057 0.000 0.354
## .Stest22puncttn 0.363 0.013 28.841 0.000 0.338
## .Stest23english 0.640 0.024 27.052 0.000 0.593
## .Stest24exprssn 0.856 0.025 33.692 0.000 0.806
## .Stst26rdngcmpr 0.281 0.011 25.313 0.000 0.259
## .Stst31bstrctrs 0.598 0.022 27.691 0.000 0.555
## .Stst34rthcmptt 0.638 0.030 21.184 0.000 0.579
## .Stest5math 0.553 0.021 26.491 0.000 0.513
## .Stst25wrdfnctn 0.379 0.012 31.783 0.000 0.355
## .Stst32rthrsnng 0.304 0.011 28.248 0.000 0.283
## .Stst33hghschlm 0.231 0.009 25.794 0.000 0.214
## .Stest35tblrdng 1.387 0.076 18.346 0.000 1.239
## .Stst36clrclchc 1.036 0.042 24.779 0.000 0.954
## .Stst37bjctnspc 0.941 0.035 26.792 0.000 0.872
## .Stst28mchnclrs 0.297 0.015 19.496 0.000 0.267
## .Stst29vslztn2D 0.770 0.025 30.205 0.000 0.720
## .Stst30vslztn3D 0.509 0.017 30.563 0.000 0.476
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.403 0.377 0.379
## 0.410 0.382 0.476
## 0.576 0.543 0.556
## 0.414 0.384 0.415
## 0.388 0.363 0.359
## 0.686 0.640 0.479
## 0.906 0.856 0.666
## 0.303 0.281 0.268
## 0.640 0.598 0.477
## 0.697 0.638 0.495
## 0.594 0.553 0.557
## 0.402 0.379 0.657
## 0.325 0.304 0.487
## 0.249 0.231 0.420
## 1.536 1.387 0.504
## 1.118 1.036 0.618
## 1.010 0.941 0.620
## 0.327 0.297 0.392
## 0.820 0.770 0.677
## 0.541 0.509 0.638
## 1.000 0.190 0.190
## 1.000 0.114 0.114
## 1.000 0.862 0.862
## 1.000 0.387 0.387
## 1.000 0.978 0.978
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst1vc (.p1.) 0.210 0.016 12.791 0.000 0.178
## Stst19d (.p2.) 0.283 0.011 26.551 0.000 0.262
## Stst20s (.p3.) 0.287 0.012 24.658 0.000 0.264
## Stst21c (.p4.) 0.321 0.012 26.517 0.000 0.297
## Stst22p (.p5.) 0.351 0.013 27.076 0.000 0.326
## Stst23n (.p6.) 0.364 0.014 26.066 0.000 0.336
## Stst24x (.p7.) 0.286 0.012 24.741 0.000 0.263
## Stst26r (.p8.) 0.245 0.015 16.849 0.000 0.216
## Stst31b (.p9.) 0.128 0.009 13.842 0.000 0.110
## Stst34r (.10.) 0.132 0.014 9.111 0.000 0.103
## math =~
## Stst1vc (.11.) 0.113 0.013 8.596 0.000 0.087
## Stst5mt (.12.) 0.224 0.015 15.343 0.000 0.196
## Stst25w 0.192 0.013 14.956 0.000 0.167
## Stst26r (.14.) 0.117 0.011 10.864 0.000 0.096
## Stst32r (.15.) 0.191 0.012 15.343 0.000 0.167
## Stst33h (.16.) 0.191 0.013 15.127 0.000 0.166
## Stst34r (.17.) 0.074 0.012 6.318 0.000 0.051
## speed =~
## Stst34r (.18.) 0.444 0.019 23.970 0.000 0.408
## Stst35t (.19.) 1.084 0.024 44.406 0.000 1.037
## Stst36c (.20.) 0.743 0.022 34.349 0.000 0.701
## Stst37b (.21.) 0.660 0.020 33.107 0.000 0.621
## spatial =~
## Stst28m 0.245 0.009 28.426 0.000 0.228
## Sts292D (.23.) 0.378 0.012 30.242 0.000 0.353
## Sts303D (.24.) 0.334 0.011 31.193 0.000 0.313
## Stst31b (.25.) 0.358 0.013 27.505 0.000 0.333
## Stst37b (.26.) 0.081 0.011 7.254 0.000 0.059
## g =~
## english (.27.) 2.042 0.092 22.289 0.000 1.863
## math (.28.) 2.756 0.196 14.093 0.000 2.373
## speed (.29.) 0.396 0.022 17.777 0.000 0.353
## spatial (.30.) 1.243 0.047 26.459 0.000 1.151
## ci.upper Std.lv Std.all
##
## 0.243 0.479 0.495
## 0.304 0.644 0.704
## 0.309 0.653 0.673
## 0.345 0.731 0.732
## 0.376 0.800 0.811
## 0.391 0.828 0.740
## 0.308 0.651 0.589
## 0.273 0.558 0.555
## 0.146 0.291 0.262
## 0.160 0.300 0.258
##
## 0.138 0.330 0.342
## 0.253 0.658 0.643
## 0.217 0.563 0.689
## 0.138 0.344 0.343
## 0.216 0.562 0.725
## 0.215 0.560 0.775
## 0.097 0.218 0.188
##
## 0.480 0.478 0.412
## 1.132 1.167 0.718
## 0.786 0.800 0.619
## 0.699 0.710 0.617
##
## 0.262 0.391 0.629
## 0.402 0.603 0.594
## 0.355 0.534 0.664
## 0.384 0.572 0.516
## 0.103 0.130 0.113
##
## 2.222 0.898 0.898
## 3.139 0.940 0.940
## 0.440 0.369 0.369
## 1.335 0.780 0.780
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.001 0.013 0.056 0.956 -0.024
## age2 -0.028 0.007 -3.926 0.000 -0.042
## ci.upper Std.lv Std.all
##
## 0.025 0.001 0.001
## -0.014 -0.028 -0.063
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst1vc -1.343 0.030 -45.213 0.000 -1.402
## .Stst19d (.62.) -0.981 0.019 -50.542 0.000 -1.019
## .Stst20s -0.596 0.023 -25.403 0.000 -0.642
## .Stst21c (.64.) -1.076 0.022 -48.405 0.000 -1.120
## .Stst22p (.65.) -1.122 0.024 -46.226 0.000 -1.169
## .Stst23n (.66.) -0.947 0.027 -35.667 0.000 -0.999
## .Stst24x (.67.) -0.869 0.023 -38.372 0.000 -0.913
## .Stst26r (.68.) -1.227 0.027 -45.132 0.000 -1.281
## .Stst31b (.69.) -0.974 0.027 -36.235 0.000 -1.026
## .Stst34r (.70.) -1.092 0.026 -42.471 0.000 -1.142
## .Stst5mt (.71.) -0.754 0.023 -32.580 0.000 -0.799
## .Stst25w -0.614 0.022 -28.041 0.000 -0.657
## .Stst32r (.73.) -1.003 0.020 -50.873 0.000 -1.042
## .Stst33h (.74.) -0.787 0.019 -40.784 0.000 -0.825
## .Stst35t (.75.) -0.725 0.034 -21.073 0.000 -0.792
## .Stst36c (.76.) 0.082 0.026 3.181 0.001 0.032
## .Stst37b (.77.) -0.279 0.024 -11.443 0.000 -0.327
## .Stst28m -1.076 0.020 -55.021 0.000 -1.115
## .Sts292D (.79.) -0.506 0.023 -22.114 0.000 -0.551
## .Sts303D (.80.) -0.655 0.020 -32.794 0.000 -0.694
## .english 0.901 0.042 21.519 0.000 0.819
## .math -0.379 0.036 -10.580 0.000 -0.450
## .speed 0.296 0.036 8.324 0.000 0.226
## .spatial -0.771 0.049 -15.633 0.000 -0.867
## .g -0.142 0.039 -3.686 0.000 -0.218
## ci.upper Std.lv Std.all
## -1.285 -1.343 -1.389
## -0.943 -0.981 -1.072
## -0.550 -0.596 -0.614
## -1.032 -1.076 -1.078
## -1.074 -1.122 -1.138
## -0.895 -0.947 -0.847
## -0.824 -0.869 -0.786
## -1.174 -1.227 -1.223
## -0.921 -0.974 -0.879
## -1.041 -1.092 -0.941
## -0.708 -0.754 -0.736
## -0.571 -0.614 -0.751
## -0.965 -1.003 -1.296
## -0.749 -0.787 -1.088
## -0.657 -0.725 -0.446
## 0.133 0.082 0.064
## -0.231 -0.279 -0.242
## -1.038 -1.076 -1.732
## -0.462 -0.506 -0.499
## -0.615 -0.655 -0.814
## 0.983 0.396 0.396
## -0.309 -0.129 -0.129
## 0.366 0.275 0.275
## -0.674 -0.482 -0.482
## -0.067 -0.142 -0.142
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stest1vocab 0.329 0.010 34.072 0.000 0.310
## .Stst19dsgsdwrd 0.422 0.012 35.272 0.000 0.399
## .Stest20spellng 0.515 0.014 37.585 0.000 0.488
## .Stest21cptlztn 0.463 0.014 33.885 0.000 0.437
## .Stest22puncttn 0.333 0.011 31.114 0.000 0.312
## .Stest23english 0.565 0.017 33.642 0.000 0.532
## .Stest24exprssn 0.797 0.021 37.746 0.000 0.755
## .Stst26rdngcmpr 0.254 0.008 30.428 0.000 0.238
## .Stst31bstrctrs 0.583 0.017 34.269 0.000 0.550
## .Stst34rthcmptt 0.704 0.027 26.049 0.000 0.651
## .Stest5math 0.614 0.017 35.743 0.000 0.580
## .Stst25wrdfnctn 0.350 0.010 34.085 0.000 0.330
## .Stst32rthrsnng 0.284 0.008 34.509 0.000 0.268
## .Stst33hghschlm 0.209 0.007 30.382 0.000 0.196
## .Stest35tblrdng 1.277 0.069 18.558 0.000 1.142
## .Stst36clrclchc 1.031 0.033 30.947 0.000 0.966
## .Stst37bjctnspc 0.750 0.027 27.591 0.000 0.697
## .Stst28mchnclrs 0.233 0.007 33.999 0.000 0.220
## .Stst29vslztn2D 0.667 0.019 34.796 0.000 0.630
## .Stst30vslztn3D 0.362 0.011 33.392 0.000 0.340
## .english 1.000 1.000
## .math 1.000 1.000
## .speed 1.000 1.000
## .spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.348 0.329 0.352
## 0.446 0.422 0.504
## 0.542 0.515 0.547
## 0.490 0.463 0.465
## 0.354 0.333 0.342
## 0.598 0.565 0.452
## 0.838 0.797 0.653
## 0.271 0.254 0.252
## 0.617 0.583 0.475
## 0.757 0.704 0.523
## 0.648 0.614 0.586
## 0.371 0.350 0.525
## 0.300 0.284 0.474
## 0.223 0.209 0.400
## 1.412 1.277 0.484
## 1.097 1.031 0.617
## 0.803 0.750 0.567
## 0.247 0.233 0.604
## 0.705 0.667 0.647
## 0.383 0.362 0.559
## 1.000 0.193 0.193
## 1.000 0.116 0.116
## 1.000 0.864 0.864
## 1.000 0.392 0.392
## 1.000 0.996 0.996
CHC Bifactor models (vocabulary and reading comprehension load on
english and math, given EFA, but these loadings are zero, because their
loading on g is already very high)
chc.bifactor.failed<-'
english =~ Stest1vocab + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest26readingcomprehension + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g=~ Stest1vocab + Stest5math + Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest25wordfunctions + Stest26readingcomprehension + Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
'
configural<-cfa(chc.bifactor.failed, 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
## 2390.689 292.000 0.000 0.963 0.049 0.030
## aic bic
## 290372.419 291500.301
Mc(configural)
## [1] 0.8415784
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 55 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 168
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2390.689 2253.503
## Degrees of freedom 292 292
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.061
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 997.257 940.031
## 1 1393.432 1313.472
##
## 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 -0.023 0.087 -0.264 0.791 -0.194
## Stst19dsgsdwrd 0.098 0.069 1.426 0.154 -0.037
## Stest20spellng 0.326 0.095 3.412 0.001 0.139
## Stest21cptlztn 0.271 0.038 7.161 0.000 0.197
## Stest22puncttn 0.315 0.027 11.743 0.000 0.262
## Stest23english 0.285 0.080 3.545 0.000 0.127
## Stest24exprssn 0.193 0.058 3.345 0.001 0.080
## Stst26rdngcmpr -0.005 0.090 -0.058 0.953 -0.182
## Stst31bstrctrs 0.113 0.033 3.438 0.001 0.049
## Stst34rthcmptt 0.257 0.045 5.702 0.000 0.169
## math =~
## Stest5math 0.231 0.027 8.409 0.000 0.177
## Stst25wrdfnctn 0.135 0.023 5.913 0.000 0.090
## Stst32rthrsnng 0.214 0.025 8.449 0.000 0.164
## Stst33hghschlm 0.374 0.030 12.271 0.000 0.314
## Stst34rthcmptt 0.245 0.039 6.323 0.000 0.169
## speed =~
## Stst34rthcmptt 0.447 0.029 15.573 0.000 0.391
## Stest35tblrdng 0.955 0.043 22.337 0.000 0.871
## Stst36clrclchc 0.867 0.029 30.265 0.000 0.811
## Stst37bjctnspc 0.735 0.029 25.263 0.000 0.678
## spatial =~
## Stst28mchnclrs 0.385 0.022 17.337 0.000 0.342
## Stst29vslztn2D 0.468 0.028 16.568 0.000 0.412
## Stst30vslztn3D 0.509 0.025 20.210 0.000 0.459
## Stst31bstrctrs 0.440 0.025 17.765 0.000 0.391
## Stst37bjctnspc 0.318 0.028 11.315 0.000 0.263
## g =~
## Stest1vocab 0.904 0.017 52.243 0.000 0.870
## Stest5math 0.691 0.020 33.740 0.000 0.651
## Stst19dsgsdwrd 0.603 0.021 28.976 0.000 0.562
## Stest20spellng 0.612 0.033 18.455 0.000 0.547
## Stest21cptlztn 0.663 0.023 29.041 0.000 0.618
## Stest22puncttn 0.744 0.025 30.350 0.000 0.696
## Stest23english 0.832 0.029 28.733 0.000 0.775
## Stest24exprssn 0.681 0.025 27.495 0.000 0.633
## Stst25wrdfnctn 0.447 0.018 25.069 0.000 0.412
## Stst26rdngcmpr 0.965 0.018 53.513 0.000 0.930
## Stst28mchnclrs 0.568 0.021 27.349 0.000 0.527
## Stst29vslztn2D 0.475 0.021 22.126 0.000 0.433
## Stst30vslztn3D 0.451 0.022 20.700 0.000 0.408
## Stst31bstrctrs 0.721 0.020 35.638 0.000 0.682
## Stst32rthrsnng 0.589 0.019 30.691 0.000 0.551
## Stst33hghschlm 0.561 0.018 30.867 0.000 0.525
## Stst34rthcmptt 0.635 0.028 22.974 0.000 0.581
## Stest35tblrdng 0.596 0.032 18.679 0.000 0.534
## Stst36clrclchc 0.173 0.028 6.254 0.000 0.119
## Stst37bjctnspc 0.250 0.026 9.508 0.000 0.199
## ci.upper Std.lv Std.all
##
## 0.148 -0.023 -0.022
## 0.233 0.098 0.112
## 0.513 0.326 0.327
## 0.345 0.271 0.287
## 0.367 0.315 0.315
## 0.442 0.285 0.239
## 0.306 0.193 0.166
## 0.172 -0.005 -0.005
## 0.177 0.113 0.099
## 0.346 0.257 0.225
##
## 0.285 0.231 0.221
## 0.179 0.135 0.173
## 0.264 0.214 0.255
## 0.434 0.374 0.476
## 0.321 0.245 0.215
##
## 0.503 0.447 0.391
## 1.038 0.955 0.572
## 0.923 0.867 0.669
## 0.792 0.735 0.597
##
## 0.429 0.385 0.428
## 0.523 0.468 0.429
## 0.558 0.509 0.537
## 0.488 0.440 0.385
## 0.373 0.318 0.258
##
## 0.937 0.904 0.847
## 0.732 0.691 0.660
## 0.644 0.603 0.691
## 0.677 0.612 0.614
## 0.708 0.663 0.702
## 0.792 0.744 0.746
## 0.888 0.832 0.699
## 0.730 0.681 0.585
## 0.482 0.447 0.574
## 1.000 0.965 0.898
## 0.608 0.568 0.631
## 0.517 0.475 0.436
## 0.494 0.451 0.476
## 0.761 0.721 0.632
## 0.627 0.589 0.702
## 0.596 0.561 0.714
## 0.689 0.635 0.556
## 0.659 0.596 0.357
## 0.227 0.173 0.133
## 0.302 0.250 0.203
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## 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
## .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
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.903
## .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
## .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 -1.136
## -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
## -1.248 -1.292 -1.202
## -1.022 -1.070 -0.937
## -1.104 -1.153 -1.009
## -0.770 -0.814 -0.777
## -0.838 -0.871 -1.119
## -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
## -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 0.321 0.017 18.557 0.000 0.287
## .Stst19dsgsdwrd 0.389 0.014 27.413 0.000 0.361
## .Stest20spellng 0.513 0.032 16.020 0.000 0.450
## .Stest21cptlztn 0.378 0.016 23.495 0.000 0.346
## .Stest22puncttn 0.343 0.023 15.121 0.000 0.298
## .Stest23english 0.642 0.025 25.218 0.000 0.592
## .Stest24exprssn 0.854 0.026 32.768 0.000 0.803
## .Stst26rdngcmpr 0.225 0.019 11.999 0.000 0.188
## .Stst31bstrctrs 0.577 0.023 24.854 0.000 0.532
## .Stst34rthcmptt 0.576 0.031 18.729 0.000 0.516
## .Stest5math 0.566 0.021 27.063 0.000 0.525
## .Stst25wrdfnctn 0.388 0.012 32.251 0.000 0.364
## .Stst32rthrsnng 0.312 0.012 26.317 0.000 0.289
## .Stst33hghschlm 0.162 0.019 8.677 0.000 0.126
## .Stest35tblrdng 1.516 0.075 20.200 0.000 1.369
## .Stst36clrclchc 0.896 0.046 19.440 0.000 0.806
## .Stst37bjctnspc 0.814 0.038 21.280 0.000 0.739
## .Stst28mchnclrs 0.338 0.015 22.247 0.000 0.309
## .Stst29vslztn2D 0.745 0.029 26.116 0.000 0.689
## .Stst30vslztn3D 0.436 0.021 21.044 0.000 0.395
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.354 0.321 0.282
## 0.417 0.389 0.510
## 0.576 0.513 0.516
## 0.410 0.378 0.424
## 0.387 0.343 0.344
## 0.691 0.642 0.454
## 0.905 0.854 0.630
## 0.261 0.225 0.194
## 0.623 0.577 0.443
## 0.636 0.576 0.441
## 0.607 0.566 0.516
## 0.411 0.388 0.640
## 0.336 0.312 0.443
## 0.199 0.162 0.263
## 1.663 1.516 0.545
## 0.987 0.896 0.534
## 0.889 0.814 0.536
## 0.368 0.338 0.418
## 0.801 0.745 0.626
## 0.476 0.436 0.485
## 1.000 1.000 1.000
## 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 0.122 0.156 0.783 0.434 -0.183
## Stst19dsgsdwrd 0.226 0.125 1.806 0.071 -0.019
## Stest20spellng 0.423 0.109 3.901 0.000 0.211
## Stest21cptlztn 0.292 0.039 7.446 0.000 0.215
## Stest22puncttn 0.300 0.027 11.152 0.000 0.247
## Stest23english 0.356 0.033 10.778 0.000 0.291
## Stest24exprssn 0.235 0.036 6.589 0.000 0.165
## Stst26rdngcmpr 0.161 0.142 1.135 0.257 -0.117
## Stst31bstrctrs 0.085 0.036 2.355 0.018 0.014
## Stst34rthcmptt 0.353 0.038 9.222 0.000 0.278
## math =~
## Stest5math 0.234 0.039 6.053 0.000 0.158
## Stst25wrdfnctn 0.130 0.051 2.523 0.012 0.029
## Stst32rthrsnng 0.136 0.044 3.107 0.002 0.050
## Stst33hghschlm 0.318 0.034 9.275 0.000 0.251
## Stst34rthcmptt 0.302 0.064 4.678 0.000 0.175
## speed =~
## Stst34rthcmptt 0.469 0.025 19.063 0.000 0.421
## Stest35tblrdng 0.971 0.037 26.415 0.000 0.899
## Stst36clrclchc 0.831 0.023 36.146 0.000 0.786
## Stst37bjctnspc 0.703 0.023 30.373 0.000 0.658
## spatial =~
## Stst28mchnclrs 0.145 0.025 5.786 0.000 0.096
## Stst29vslztn2D 0.401 0.030 13.547 0.000 0.343
## Stst30vslztn3D 0.381 0.028 13.654 0.000 0.327
## Stst31bstrctrs 0.344 0.041 8.371 0.000 0.264
## Stst37bjctnspc 0.246 0.026 9.486 0.000 0.195
## g =~
## Stest1vocab 0.716 0.043 16.678 0.000 0.632
## Stest5math 0.547 0.020 26.915 0.000 0.507
## Stst19dsgsdwrd 0.644 0.042 15.438 0.000 0.562
## Stest20spellng 0.538 0.054 9.952 0.000 0.432
## Stest21cptlztn 0.688 0.024 28.779 0.000 0.641
## Stest22puncttn 0.738 0.016 46.613 0.000 0.707
## Stest23english 0.704 0.027 26.373 0.000 0.651
## Stest24exprssn 0.553 0.021 26.663 0.000 0.513
## Stst25wrdfnctn 0.505 0.024 21.118 0.000 0.459
## Stst26rdngcmpr 0.823 0.040 20.494 0.000 0.744
## Stst28mchnclrs 0.328 0.017 19.066 0.000 0.295
## Stst29vslztn2D 0.405 0.023 17.320 0.000 0.359
## Stst30vslztn3D 0.341 0.024 14.305 0.000 0.295
## Stst31bstrctrs 0.697 0.026 27.311 0.000 0.647
## Stst32rthrsnng 0.478 0.023 20.497 0.000 0.432
## Stst33hghschlm 0.475 0.022 22.020 0.000 0.433
## Stst34rthcmptt 0.557 0.038 14.777 0.000 0.483
## Stest35tblrdng 0.605 0.029 20.724 0.000 0.548
## Stst36clrclchc 0.131 0.028 4.626 0.000 0.075
## Stst37bjctnspc 0.281 0.021 13.228 0.000 0.240
## ci.upper Std.lv Std.all
##
## 0.427 0.122 0.133
## 0.472 0.226 0.241
## 0.636 0.423 0.439
## 0.369 0.292 0.289
## 0.352 0.300 0.304
## 0.421 0.356 0.327
## 0.305 0.235 0.218
## 0.439 0.161 0.166
## 0.156 0.085 0.078
## 0.428 0.353 0.307
##
## 0.309 0.234 0.237
## 0.230 0.130 0.163
## 0.221 0.136 0.184
## 0.385 0.318 0.458
## 0.428 0.302 0.262
##
## 0.517 0.469 0.408
## 1.043 0.971 0.598
## 0.876 0.831 0.649
## 0.749 0.703 0.614
##
## 0.194 0.145 0.236
## 0.459 0.401 0.406
## 0.436 0.381 0.493
## 0.425 0.344 0.314
## 0.296 0.246 0.214
##
## 0.800 0.716 0.778
## 0.587 0.547 0.554
## 0.726 0.644 0.685
## 0.644 0.538 0.558
## 0.735 0.688 0.680
## 0.769 0.738 0.749
## 0.756 0.704 0.645
## 0.594 0.553 0.512
## 0.552 0.505 0.634
## 0.901 0.823 0.848
## 0.362 0.328 0.537
## 0.451 0.405 0.410
## 0.388 0.341 0.441
## 0.747 0.697 0.637
## 0.524 0.478 0.648
## 0.517 0.475 0.683
## 0.631 0.557 0.484
## 0.662 0.605 0.372
## 0.186 0.131 0.102
## 0.323 0.281 0.245
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## 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
## .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
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.816
## .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
## .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 -1.455
## -0.846 -0.878 -0.935
## -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
## -1.193 -1.226 -1.265
## -1.222 -1.260 -1.151
## -0.963 -1.004 -0.873
## -0.931 -0.965 -0.978
## -0.761 -0.788 -0.989
## -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
## -1.303 -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 0.319 0.022 14.469 0.000 0.276
## .Stst19dsgsdwrd 0.417 0.013 31.793 0.000 0.391
## .Stest20spellng 0.460 0.039 11.864 0.000 0.384
## .Stest21cptlztn 0.464 0.016 29.074 0.000 0.433
## .Stest22puncttn 0.338 0.020 16.851 0.000 0.298
## .Stest23english 0.568 0.025 22.907 0.000 0.519
## .Stest24exprssn 0.806 0.023 34.996 0.000 0.760
## .Stst26rdngcmpr 0.237 0.018 12.868 0.000 0.201
## .Stst31bstrctrs 0.586 0.018 32.188 0.000 0.550
## .Stst34rthcmptt 0.577 0.041 13.973 0.000 0.496
## .Stest5math 0.620 0.018 34.941 0.000 0.585
## .Stst25wrdfnctn 0.364 0.012 29.622 0.000 0.340
## .Stst32rthrsnng 0.298 0.010 29.348 0.000 0.278
## .Stst33hghschlm 0.156 0.014 10.800 0.000 0.128
## .Stest35tblrdng 1.329 0.062 21.406 0.000 1.207
## .Stst36clrclchc 0.934 0.036 26.253 0.000 0.864
## .Stst37bjctnspc 0.678 0.029 23.026 0.000 0.621
## .Stst28mchnclrs 0.246 0.007 37.204 0.000 0.233
## .Stst29vslztn2D 0.653 0.023 28.712 0.000 0.608
## .Stst30vslztn3D 0.336 0.015 21.788 0.000 0.305
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.363 0.319 0.377
## 0.443 0.417 0.472
## 0.536 0.460 0.495
## 0.495 0.464 0.454
## 0.377 0.338 0.347
## 0.616 0.568 0.477
## 0.851 0.806 0.690
## 0.274 0.237 0.252
## 0.622 0.586 0.489
## 0.658 0.577 0.436
## 0.654 0.620 0.637
## 0.388 0.364 0.572
## 0.318 0.298 0.547
## 0.184 0.156 0.323
## 1.451 1.329 0.504
## 1.003 0.934 0.569
## 0.736 0.678 0.517
## 0.259 0.246 0.656
## 0.697 0.653 0.668
## 0.366 0.336 0.562
## 1.000 1.000 1.000
## 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.bifactor.model <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g=~ Stest1vocab + Stest5math + 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", std.lv=T, orthogonal=T)
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 2554.784 148.000 0.000 0.958 0.052 0.034
## aic bic
## 293688.788 294239.301
Mc(baseline)
## [1] 0.820537
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
## 2389.613 296.000 0.000 0.963 0.048 0.031
## aic bic
## 290363.343 291464.371
Mc(configural)
## [1] 0.8419296
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 39 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 164
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2389.613 2133.878
## Degrees of freedom 296 296
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.120
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 997.884 891.091
## 1 1391.729 1242.787
##
## 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 0.105 0.029 3.662 0.000 0.049
## Stest20spellng 0.337 0.035 9.705 0.000 0.269
## Stest21cptlztn 0.275 0.024 11.566 0.000 0.228
## Stest22puncttn 0.316 0.026 12.288 0.000 0.266
## Stest23english 0.295 0.034 8.616 0.000 0.228
## Stest24exprssn 0.198 0.035 5.598 0.000 0.129
## Stst31bstrctrs 0.111 0.033 3.378 0.001 0.047
## Stst34rthcmptt 0.263 0.034 7.642 0.000 0.196
## math =~
## Stest5math 0.230 0.023 9.906 0.000 0.184
## Stst25wrdfnctn 0.133 0.022 6.126 0.000 0.091
## Stst32rthrsnng 0.212 0.022 9.661 0.000 0.169
## Stst33hghschlm 0.372 0.028 13.335 0.000 0.317
## Stst34rthcmptt 0.249 0.030 8.429 0.000 0.191
## speed =~
## Stst34rthcmptt 0.447 0.028 15.726 0.000 0.392
## Stest35tblrdng 0.955 0.043 22.422 0.000 0.872
## Stst36clrclchc 0.867 0.029 30.258 0.000 0.811
## Stst37bjctnspc 0.735 0.029 25.250 0.000 0.678
## spatial =~
## Stst28mchnclrs 0.384 0.019 19.846 0.000 0.346
## Stst29vslztn2D 0.468 0.028 16.523 0.000 0.412
## Stst30vslztn3D 0.508 0.024 21.532 0.000 0.462
## Stst31bstrctrs 0.439 0.024 18.261 0.000 0.392
## Stst37bjctnspc 0.318 0.028 11.291 0.000 0.262
## g =~
## Stest1vocab 0.901 0.017 53.764 0.000 0.868
## Stest5math 0.692 0.019 36.114 0.000 0.654
## Stst19dsgsdwrd 0.602 0.018 32.832 0.000 0.566
## Stest20spellng 0.609 0.020 31.116 0.000 0.570
## Stest21cptlztn 0.661 0.017 39.468 0.000 0.628
## Stest22puncttn 0.742 0.018 40.297 0.000 0.706
## Stest23english 0.829 0.021 38.964 0.000 0.787
## Stest24exprssn 0.680 0.021 31.981 0.000 0.638
## Stst25wrdfnctn 0.447 0.018 25.291 0.000 0.413
## Stst26rdngcmpr 0.965 0.016 59.769 0.000 0.934
## Stst28mchnclrs 0.568 0.018 30.997 0.000 0.533
## Stst29vslztn2D 0.475 0.021 22.340 0.000 0.434
## Stst30vslztn3D 0.452 0.020 23.031 0.000 0.414
## Stst31bstrctrs 0.722 0.020 35.802 0.000 0.682
## Stst32rthrsnng 0.590 0.018 33.510 0.000 0.556
## Stst33hghschlm 0.562 0.017 32.309 0.000 0.528
## Stst34rthcmptt 0.632 0.022 28.334 0.000 0.588
## Stest35tblrdng 0.597 0.032 18.846 0.000 0.535
## Stst36clrclchc 0.172 0.028 6.243 0.000 0.118
## Stst37bjctnspc 0.250 0.026 9.526 0.000 0.199
## ci.upper Std.lv Std.all
##
## 0.161 0.105 0.120
## 0.405 0.337 0.338
## 0.321 0.275 0.291
## 0.367 0.316 0.317
## 0.362 0.295 0.248
## 0.267 0.198 0.170
## 0.175 0.111 0.097
## 0.331 0.263 0.230
##
## 0.275 0.230 0.220
## 0.176 0.133 0.171
## 0.255 0.212 0.253
## 0.427 0.372 0.474
## 0.307 0.249 0.218
##
## 0.503 0.447 0.392
## 1.039 0.955 0.573
## 0.923 0.867 0.669
## 0.792 0.735 0.597
##
## 0.422 0.384 0.427
## 0.523 0.468 0.429
## 0.554 0.508 0.536
## 0.486 0.439 0.384
## 0.373 0.318 0.258
##
## 0.934 0.901 0.845
## 0.729 0.692 0.660
## 0.638 0.602 0.690
## 0.647 0.609 0.611
## 0.694 0.661 0.700
## 0.778 0.742 0.744
## 0.871 0.829 0.697
## 0.721 0.680 0.584
## 0.482 0.447 0.575
## 0.997 0.965 0.898
## 0.604 0.568 0.632
## 0.517 0.475 0.436
## 0.491 0.452 0.477
## 0.761 0.722 0.632
## 0.625 0.590 0.703
## 0.596 0.562 0.715
## 0.676 0.632 0.553
## 0.659 0.597 0.358
## 0.227 0.172 0.133
## 0.302 0.250 0.203
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .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
## .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
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.903
## .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
## .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
## .Stest1vocab -1.155 0.023 -50.360 0.000 -1.200
## .Stst26rdngcmpr -1.292 0.023 -56.802 0.000 -1.337
## ci.upper Std.lv Std.all
## -0.956 -0.992 -1.136
## -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
## -1.022 -1.070 -0.937
## -1.104 -1.153 -1.009
## -0.770 -0.814 -0.777
## -0.838 -0.871 -1.119
## -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
## -0.677 -0.715 -0.795
## -0.466 -0.512 -0.469
## -0.683 -0.723 -0.763
## -1.110 -1.155 -1.083
## -1.248 -1.292 -1.202
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.389 0.014 27.514 0.000 0.361
## .Stest20spellng 0.510 0.022 23.302 0.000 0.467
## .Stest21cptlztn 0.379 0.015 24.488 0.000 0.348
## .Stest22puncttn 0.345 0.015 22.714 0.000 0.315
## .Stest23english 0.640 0.025 26.078 0.000 0.592
## .Stest24exprssn 0.854 0.026 32.820 0.000 0.803
## .Stst31bstrctrs 0.578 0.023 25.282 0.000 0.533
## .Stst34rthcmptt 0.573 0.030 19.412 0.000 0.516
## .Stest5math 0.566 0.021 27.318 0.000 0.525
## .Stst25wrdfnctn 0.388 0.012 32.327 0.000 0.364
## .Stst32rthrsnng 0.312 0.011 27.446 0.000 0.289
## .Stst33hghschlm 0.163 0.018 8.858 0.000 0.127
## .Stest35tblrdng 1.514 0.074 20.455 0.000 1.369
## .Stst36clrclchc 0.897 0.046 19.519 0.000 0.807
## .Stst37bjctnspc 0.814 0.038 21.293 0.000 0.739
## .Stst28mchnclrs 0.338 0.015 22.172 0.000 0.308
## .Stst29vslztn2D 0.745 0.029 26.102 0.000 0.689
## .Stst30vslztn3D 0.436 0.021 21.046 0.000 0.395
## .Stest1vocab 0.325 0.013 25.300 0.000 0.300
## .Stst26rdngcmpr 0.224 0.011 20.206 0.000 0.202
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.416 0.389 0.510
## 0.552 0.510 0.513
## 0.409 0.379 0.425
## 0.375 0.345 0.347
## 0.689 0.640 0.453
## 0.905 0.854 0.630
## 0.623 0.578 0.443
## 0.631 0.573 0.440
## 0.606 0.566 0.516
## 0.411 0.388 0.640
## 0.334 0.312 0.442
## 0.199 0.163 0.264
## 1.659 1.514 0.544
## 0.987 0.897 0.534
## 0.889 0.814 0.536
## 0.368 0.338 0.418
## 0.800 0.745 0.626
## 0.477 0.436 0.485
## 0.350 0.325 0.286
## 0.246 0.224 0.194
## 1.000 1.000 1.000
## 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 0.099 0.027 3.672 0.000 0.046
## Stest20spellng 0.286 0.034 8.288 0.000 0.218
## Stest21cptlztn 0.248 0.023 10.975 0.000 0.203
## Stest22puncttn 0.304 0.026 11.868 0.000 0.254
## Stest23english 0.316 0.028 11.108 0.000 0.260
## Stest24exprssn 0.211 0.035 6.065 0.000 0.143
## Stst31bstrctrs 0.097 0.032 3.016 0.003 0.034
## Stst34rthcmptt 0.276 0.038 7.330 0.000 0.202
## math =~
## Stest5math 0.267 0.024 11.341 0.000 0.221
## Stst25wrdfnctn 0.173 0.025 6.929 0.000 0.124
## Stst32rthrsnng 0.172 0.021 8.231 0.000 0.131
## Stst33hghschlm 0.336 0.024 13.947 0.000 0.289
## Stst34rthcmptt 0.228 0.027 8.481 0.000 0.176
## speed =~
## Stst34rthcmptt 0.467 0.025 18.870 0.000 0.418
## Stest35tblrdng 0.959 0.034 27.973 0.000 0.892
## Stst36clrclchc 0.834 0.023 36.430 0.000 0.790
## Stst37bjctnspc 0.704 0.023 30.466 0.000 0.659
## spatial =~
## Stst28mchnclrs 0.165 0.013 12.237 0.000 0.139
## Stst29vslztn2D 0.413 0.025 16.638 0.000 0.365
## Stst30vslztn3D 0.396 0.020 19.358 0.000 0.356
## Stst31bstrctrs 0.370 0.022 16.614 0.000 0.326
## Stst37bjctnspc 0.253 0.024 10.531 0.000 0.206
## g =~
## Stest1vocab 0.738 0.014 53.399 0.000 0.711
## Stest5math 0.532 0.017 31.693 0.000 0.499
## Stst19dsgsdwrd 0.674 0.015 45.340 0.000 0.645
## Stest20spellng 0.589 0.016 37.977 0.000 0.559
## Stest21cptlztn 0.710 0.015 48.882 0.000 0.681
## Stest22puncttn 0.752 0.014 51.955 0.000 0.724
## Stest23english 0.731 0.016 44.645 0.000 0.699
## Stest24exprssn 0.569 0.017 33.094 0.000 0.535
## Stst25wrdfnctn 0.488 0.015 33.321 0.000 0.460
## Stst26rdngcmpr 0.854 0.012 68.557 0.000 0.830
## Stst28mchnclrs 0.316 0.012 26.650 0.000 0.293
## Stst29vslztn2D 0.390 0.017 22.948 0.000 0.357
## Stst30vslztn3D 0.325 0.014 22.653 0.000 0.297
## Stst31bstrctrs 0.682 0.016 41.905 0.000 0.651
## Stst32rthrsnng 0.461 0.015 31.544 0.000 0.433
## Stst33hghschlm 0.460 0.013 34.670 0.000 0.434
## Stst34rthcmptt 0.599 0.019 31.088 0.000 0.562
## Stest35tblrdng 0.609 0.027 22.682 0.000 0.557
## Stst36clrclchc 0.139 0.023 6.178 0.000 0.095
## Stst37bjctnspc 0.280 0.021 13.400 0.000 0.239
## ci.upper Std.lv Std.all
##
## 0.152 0.099 0.106
## 0.353 0.286 0.296
## 0.292 0.248 0.245
## 0.355 0.304 0.309
## 0.371 0.316 0.289
## 0.280 0.211 0.196
## 0.160 0.097 0.089
## 0.350 0.276 0.239
##
## 0.313 0.267 0.271
## 0.222 0.173 0.217
## 0.213 0.172 0.233
## 0.383 0.336 0.484
## 0.281 0.228 0.198
##
## 0.516 0.467 0.404
## 1.026 0.959 0.590
## 0.879 0.834 0.651
## 0.750 0.704 0.614
##
## 0.192 0.165 0.270
## 0.462 0.413 0.418
## 0.436 0.396 0.512
## 0.414 0.370 0.338
## 0.300 0.253 0.220
##
## 0.765 0.738 0.803
## 0.565 0.532 0.539
## 0.703 0.674 0.717
## 0.619 0.589 0.611
## 0.738 0.710 0.702
## 0.781 0.752 0.763
## 0.763 0.731 0.670
## 0.602 0.569 0.527
## 0.517 0.488 0.612
## 0.878 0.854 0.881
## 0.339 0.316 0.516
## 0.424 0.390 0.395
## 0.353 0.325 0.421
## 0.714 0.682 0.624
## 0.490 0.461 0.625
## 0.486 0.460 0.663
## 0.637 0.599 0.519
## 0.662 0.609 0.375
## 0.183 0.139 0.109
## 0.321 0.280 0.244
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .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
## .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
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.816
## .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
## .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
## .Stest1vocab -1.339 0.016 -83.554 0.000 -1.370
## .Stst26rdngcmpr -1.226 0.017 -72.842 0.000 -1.259
## ci.upper Std.lv Std.all
## -0.846 -0.878 -0.935
## -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
## -1.222 -1.260 -1.152
## -0.963 -1.004 -0.869
## -0.931 -0.965 -0.978
## -0.761 -0.788 -0.989
## -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
## -1.303 -1.323 -2.162
## -0.882 -0.916 -0.926
## -0.955 -0.982 -1.270
## -1.307 -1.339 -1.455
## -1.193 -1.226 -1.265
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.419 0.012 34.963 0.000 0.395
## .Stest20spellng 0.500 0.018 27.637 0.000 0.464
## .Stest21cptlztn 0.458 0.014 32.202 0.000 0.430
## .Stest22puncttn 0.313 0.014 22.435 0.000 0.286
## .Stest23english 0.556 0.019 29.983 0.000 0.520
## .Stest24exprssn 0.799 0.022 36.043 0.000 0.755
## .Stst31bstrctrs 0.584 0.018 31.858 0.000 0.548
## .Stst34rthcmptt 0.627 0.031 20.548 0.000 0.567
## .Stest5math 0.619 0.018 34.402 0.000 0.584
## .Stst25wrdfnctn 0.368 0.011 32.666 0.000 0.346
## .Stst32rthrsnng 0.302 0.009 33.488 0.000 0.285
## .Stst33hghschlm 0.158 0.016 10.142 0.000 0.127
## .Stest35tblrdng 1.346 0.060 22.328 0.000 1.228
## .Stst36clrclchc 0.926 0.035 26.369 0.000 0.857
## .Stst37bjctnspc 0.676 0.029 22.975 0.000 0.618
## .Stst28mchnclrs 0.248 0.007 37.617 0.000 0.235
## .Stst29vslztn2D 0.654 0.022 29.492 0.000 0.611
## .Stst30vslztn3D 0.335 0.015 22.649 0.000 0.306
## .Stest1vocab 0.301 0.010 31.643 0.000 0.283
## .Stst26rdngcmpr 0.211 0.008 25.505 0.000 0.195
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.442 0.419 0.474
## 0.535 0.500 0.538
## 0.486 0.458 0.448
## 0.340 0.313 0.322
## 0.592 0.556 0.467
## 0.842 0.799 0.684
## 0.620 0.584 0.488
## 0.687 0.627 0.471
## 0.654 0.619 0.636
## 0.390 0.368 0.578
## 0.320 0.302 0.555
## 0.188 0.158 0.327
## 1.464 1.346 0.511
## 0.995 0.926 0.564
## 0.733 0.676 0.514
## 0.261 0.248 0.661
## 0.698 0.654 0.669
## 0.364 0.335 0.561
## 0.320 0.301 0.356
## 0.227 0.211 0.224
## 1.000 1.000 1.000
## 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
## 480 speed =~ Stest19disguisedwords 2 2
## 523 Stest19disguisedwords ~~ Stest36clericalchecking 2 2
## 497 spatial =~ Stest20spelling 2 2
## 249 spatial =~ Stest20spelling 1 1
## 232 speed =~ Stest19disguisedwords 1 1
## 244 speed =~ Stest29visualization2D 1 1
## 175 math ~~ spatial 2 2
## 275 Stest19disguisedwords ~~ Stest36clericalchecking 1 1
## 396 Stest5math ~~ Stest1vocab 1 1
## 468 math =~ Stest22punctuation 2 2
## 492 speed =~ Stest29visualization2D 2 2
## 700 Stest1vocab ~~ Stest26readingcomprehension 2 2
## 646 Stest25wordfunctions ~~ Stest32arithreasoning 2 2
## 509 spatial =~ Stest1vocab 2 2
## 644 Stest5math ~~ Stest1vocab 2 2
## 581 Stest23english ~~ Stest24expression 2 2
## 73 math ~~ spatial 1 1
## 511 Stest19disguisedwords ~~ Stest20spelling 2 2
## 259 spatial =~ Stest35tablereading 1 1
## 499 spatial =~ Stest22punctuation 2 2
## 263 Stest19disguisedwords ~~ Stest20spelling 1 1
## 505 spatial =~ Stest32arithreasoning 2 2
## 534 Stest20spelling ~~ Stest31abstractreasoning 2 2
## 247 speed =~ Stest26readingcomprehension 1 1
## 506 spatial =~ Stest33highschoolmath 2 2
## 579 Stest22punctuation ~~ Stest1vocab 2 2
## 535 Stest20spelling ~~ Stest34arithcomputation 2 2
## 262 spatial =~ Stest26readingcomprehension 1 1
## 452 Stest1vocab ~~ Stest26readingcomprehension 1 1
## 223 math =~ Stest31abstractreasoning 1 1
## level mi epc sepc.lv sepc.all sepc.nox
## 480 1 242.532 0.207 0.207 0.220 0.220
## 523 1 166.962 0.157 0.157 0.252 0.252
## 497 1 162.921 -0.224 -0.224 -0.232 -0.232
## 249 1 118.508 -0.219 -0.219 -0.219 -0.219
## 232 1 99.392 0.155 0.155 0.177 0.177
## 244 1 91.965 0.213 0.213 0.196 0.196
## 175 1 66.437 0.287 0.287 0.287 0.287
## 275 1 65.187 0.115 0.115 0.194 0.194
## 396 1 60.989 0.080 0.080 0.188 0.188
## 468 1 59.176 0.122 0.122 0.124 0.124
## 492 1 57.427 0.131 0.131 0.132 0.132
## 700 1 57.271 0.050 0.050 0.199 0.199
## 646 1 51.434 0.047 0.047 0.140 0.140
## 509 1 48.675 -0.100 -0.100 -0.109 -0.109
## 644 1 45.633 0.056 0.056 0.129 0.129
## 581 1 43.926 0.086 0.086 0.129 0.129
## 73 1 42.037 0.251 0.251 0.251 0.251
## 511 1 40.721 0.056 0.056 0.122 0.122
## 259 1 38.023 0.228 0.228 0.137 0.137
## 499 1 37.800 0.091 0.091 0.092 0.092
## 263 1 34.346 0.062 0.062 0.140 0.140
## 505 1 32.489 0.077 0.077 0.104 0.104
## 534 1 31.920 -0.060 -0.060 -0.111 -0.111
## 247 1 31.736 -0.078 -0.078 -0.073 -0.073
## 506 1 31.562 0.066 0.066 0.095 0.095
## 579 1 30.772 -0.036 -0.036 -0.117 -0.117
## 535 1 30.759 0.069 0.069 0.123 0.123
## 262 1 29.311 -0.086 -0.086 -0.080 -0.080
## 452 1 29.059 0.049 0.049 0.181 0.181
## 223 1 28.611 0.131 0.131 0.115 0.115
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
## 2865.137 333.000 0.000 0.955 0.050 0.050
## aic bic
## 290764.868 291617.493
Mc(metric)
## [1] 0.8121274
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 80 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 169
## Number of equality constraints 42
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2865.137 2542.778
## Degrees of freedom 333 333
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.127
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1263.735 1121.551
## 1 1601.402 1421.227
##
## 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.) 0.113 0.018 6.214 0.000 0.077
## Stst20s (.p2.) 0.298 0.026 11.541 0.000 0.248
## Stst21c (.p3.) 0.264 0.018 14.779 0.000 0.229
## Stst22p (.p4.) 0.307 0.020 15.243 0.000 0.267
## Stst23n (.p5.) 0.294 0.023 12.612 0.000 0.248
## Stst24x (.p6.) 0.194 0.024 8.258 0.000 0.148
## Stst31b (.p7.) 0.108 0.021 5.108 0.000 0.067
## Stst34r (.p8.) 0.267 0.026 10.403 0.000 0.216
## math =~
## Stst5mt (.p9.) 0.259 0.018 14.510 0.000 0.224
## Stst25w (.10.) 0.155 0.016 9.448 0.000 0.123
## Stst32r (.11.) 0.194 0.017 11.282 0.000 0.161
## Stst33h (.12.) 0.372 0.023 16.497 0.000 0.328
## Stst34r (.13.) 0.250 0.021 11.837 0.000 0.209
## speed =~
## Stst34r (.14.) 0.461 0.020 22.919 0.000 0.422
## Stst35t (.15.) 0.968 0.032 30.721 0.000 0.906
## Stst36c (.16.) 0.853 0.024 35.174 0.000 0.805
## Stst37b (.17.) 0.722 0.023 31.616 0.000 0.677
## spatial =~
## Stst28m (.18.) 0.311 0.019 16.767 0.000 0.274
## Sts292D (.19.) 0.508 0.022 22.745 0.000 0.464
## Sts303D (.20.) 0.530 0.020 25.966 0.000 0.490
## Stst31b (.21.) 0.466 0.020 23.718 0.000 0.427
## Stst37b (.22.) 0.326 0.022 14.745 0.000 0.283
## g =~
## Stst1vc (.23.) 0.861 0.016 54.710 0.000 0.830
## Stst5mt (.24.) 0.644 0.016 41.322 0.000 0.613
## Stst19d (.25.) 0.681 0.014 47.799 0.000 0.653
## Stst20s (.26.) 0.637 0.015 43.045 0.000 0.608
## Stst21c (.27.) 0.728 0.014 53.144 0.000 0.701
## Stst22p (.28.) 0.798 0.015 53.871 0.000 0.769
## Stst23n (.29.) 0.823 0.017 47.994 0.000 0.789
## Stst24x (.30.) 0.657 0.017 39.318 0.000 0.624
## Stst25w (.31.) 0.504 0.013 38.673 0.000 0.478
## Stst26r (.32.) 0.965 0.016 61.691 0.000 0.934
## Stst28m (.33.) 0.427 0.013 32.594 0.000 0.401
## Sts292D (.34.) 0.449 0.015 29.907 0.000 0.420
## Sts303D (.35.) 0.396 0.014 28.987 0.000 0.369
## Stst31b (.36.) 0.738 0.016 47.029 0.000 0.707
## Stst32r (.37.) 0.551 0.014 39.746 0.000 0.524
## Stst33h (.38.) 0.538 0.013 40.998 0.000 0.512
## Stst34r (.39.) 0.652 0.017 38.308 0.000 0.618
## Stst35t (.40.) 0.644 0.023 28.129 0.000 0.599
## Stst36c (.41.) 0.163 0.019 8.657 0.000 0.126
## Stst37b (.42.) 0.282 0.018 15.945 0.000 0.248
## ci.upper Std.lv Std.all
##
## 0.149 0.113 0.122
## 0.349 0.298 0.296
## 0.299 0.264 0.267
## 0.346 0.307 0.296
## 0.340 0.294 0.248
## 0.240 0.194 0.169
## 0.150 0.108 0.094
## 0.317 0.267 0.231
##
## 0.294 0.259 0.253
## 0.187 0.155 0.190
## 0.228 0.194 0.239
## 0.417 0.372 0.484
## 0.292 0.250 0.217
##
## 0.501 0.461 0.399
## 1.030 0.968 0.573
## 0.900 0.853 0.661
## 0.767 0.722 0.583
##
## 0.347 0.311 0.380
## 0.551 0.508 0.466
## 0.570 0.530 0.570
## 0.504 0.466 0.403
## 0.370 0.326 0.264
##
## 0.892 0.861 0.829
## 0.674 0.644 0.629
## 0.709 0.681 0.732
## 0.666 0.637 0.632
## 0.755 0.728 0.736
## 0.827 0.798 0.769
## 0.857 0.823 0.694
## 0.690 0.657 0.570
## 0.529 0.504 0.618
## 0.995 0.965 0.898
## 0.452 0.427 0.522
## 0.479 0.449 0.412
## 0.423 0.396 0.426
## 0.768 0.738 0.637
## 0.579 0.551 0.679
## 0.563 0.538 0.698
## 0.685 0.652 0.563
## 0.689 0.644 0.381
## 0.200 0.163 0.126
## 0.317 0.282 0.228
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .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
## .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
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.903
## .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
## .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
## .Stest1vocab -1.155 0.023 -50.360 0.000 -1.200
## .Stst26rdngcmpr -1.292 0.023 -56.802 0.000 -1.337
## ci.upper Std.lv Std.all
## -0.956 -0.992 -1.067
## -0.806 -0.848 -0.842
## -1.128 -1.167 -1.180
## -1.184 -1.226 -1.183
## -1.012 -1.062 -0.896
## -0.916 -0.965 -0.838
## -1.022 -1.070 -0.925
## -1.104 -1.153 -0.997
## -0.770 -0.814 -0.795
## -0.838 -0.871 -1.069
## -1.017 -1.052 -1.295
## -0.843 -0.875 -1.137
## -0.640 -0.712 -0.422
## 0.023 -0.032 -0.025
## -0.266 -0.318 -0.257
## -0.677 -0.715 -0.875
## -0.466 -0.512 -0.470
## -0.683 -0.723 -0.778
## -1.110 -1.155 -1.112
## -1.248 -1.292 -1.204
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.388 0.014 27.264 0.000 0.360
## .Stest20spellng 0.520 0.019 27.623 0.000 0.483
## .Stest21cptlztn 0.379 0.015 24.840 0.000 0.349
## .Stest22puncttn 0.345 0.013 25.635 0.000 0.319
## .Stest23english 0.642 0.024 26.689 0.000 0.595
## .Stest24exprssn 0.857 0.025 33.773 0.000 0.808
## .Stst31bstrctrs 0.566 0.022 25.649 0.000 0.523
## .Stst34rthcmptt 0.566 0.029 19.499 0.000 0.509
## .Stest5math 0.566 0.021 27.111 0.000 0.525
## .Stst25wrdfnctn 0.386 0.012 32.102 0.000 0.362
## .Stst32rthrsnng 0.319 0.011 29.525 0.000 0.297
## .Stst33hghschlm 0.165 0.015 11.352 0.000 0.137
## .Stest35tblrdng 1.499 0.069 21.694 0.000 1.363
## .Stst36clrclchc 0.911 0.040 22.714 0.000 0.832
## .Stst37bjctnspc 0.824 0.035 23.794 0.000 0.757
## .Stst28mchnclrs 0.389 0.016 24.279 0.000 0.357
## .Stst29vslztn2D 0.727 0.027 26.715 0.000 0.674
## .Stst30vslztn3D 0.426 0.020 21.470 0.000 0.387
## .Stest1vocab 0.337 0.013 26.586 0.000 0.313
## .Stst26rdngcmpr 0.223 0.011 20.715 0.000 0.202
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.416 0.388 0.449
## 0.557 0.520 0.513
## 0.409 0.379 0.387
## 0.371 0.345 0.321
## 0.689 0.642 0.457
## 0.907 0.857 0.646
## 0.609 0.566 0.423
## 0.623 0.566 0.423
## 0.607 0.566 0.540
## 0.410 0.386 0.581
## 0.340 0.319 0.482
## 0.194 0.165 0.279
## 1.634 1.499 0.526
## 0.989 0.911 0.547
## 0.892 0.824 0.538
## 0.420 0.389 0.583
## 0.781 0.727 0.613
## 0.465 0.426 0.494
## 0.362 0.337 0.313
## 0.244 0.223 0.193
## 1.000 1.000 1.000
## 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.) 0.113 0.018 6.214 0.000 0.077
## Stst20s (.p2.) 0.298 0.026 11.541 0.000 0.248
## Stst21c (.p3.) 0.264 0.018 14.779 0.000 0.229
## Stst22p (.p4.) 0.307 0.020 15.243 0.000 0.267
## Stst23n (.p5.) 0.294 0.023 12.612 0.000 0.248
## Stst24x (.p6.) 0.194 0.024 8.258 0.000 0.148
## Stst31b (.p7.) 0.108 0.021 5.108 0.000 0.067
## Stst34r (.p8.) 0.267 0.026 10.403 0.000 0.216
## math =~
## Stst5mt (.p9.) 0.259 0.018 14.510 0.000 0.224
## Stst25w (.10.) 0.155 0.016 9.448 0.000 0.123
## Stst32r (.11.) 0.194 0.017 11.282 0.000 0.161
## Stst33h (.12.) 0.372 0.023 16.497 0.000 0.328
## Stst34r (.13.) 0.250 0.021 11.837 0.000 0.209
## speed =~
## Stst34r (.14.) 0.461 0.020 22.919 0.000 0.422
## Stst35t (.15.) 0.968 0.032 30.721 0.000 0.906
## Stst36c (.16.) 0.853 0.024 35.174 0.000 0.805
## Stst37b (.17.) 0.722 0.023 31.616 0.000 0.677
## spatial =~
## Stst28m (.18.) 0.311 0.019 16.767 0.000 0.274
## Sts292D (.19.) 0.508 0.022 22.745 0.000 0.464
## Sts303D (.20.) 0.530 0.020 25.966 0.000 0.490
## Stst31b (.21.) 0.466 0.020 23.718 0.000 0.427
## Stst37b (.22.) 0.326 0.022 14.745 0.000 0.283
## g =~
## Stst1vc (.23.) 0.861 0.016 54.710 0.000 0.830
## Stst5mt (.24.) 0.644 0.016 41.322 0.000 0.613
## Stst19d (.25.) 0.681 0.014 47.799 0.000 0.653
## Stst20s (.26.) 0.637 0.015 43.045 0.000 0.608
## Stst21c (.27.) 0.728 0.014 53.144 0.000 0.701
## Stst22p (.28.) 0.798 0.015 53.871 0.000 0.769
## Stst23n (.29.) 0.823 0.017 47.994 0.000 0.789
## Stst24x (.30.) 0.657 0.017 39.318 0.000 0.624
## Stst25w (.31.) 0.504 0.013 38.673 0.000 0.478
## Stst26r (.32.) 0.965 0.016 61.691 0.000 0.934
## Stst28m (.33.) 0.427 0.013 32.594 0.000 0.401
## Sts292D (.34.) 0.449 0.015 29.907 0.000 0.420
## Sts303D (.35.) 0.396 0.014 28.987 0.000 0.369
## Stst31b (.36.) 0.738 0.016 47.029 0.000 0.707
## Stst32r (.37.) 0.551 0.014 39.746 0.000 0.524
## Stst33h (.38.) 0.538 0.013 40.998 0.000 0.512
## Stst34r (.39.) 0.652 0.017 38.308 0.000 0.618
## Stst35t (.40.) 0.644 0.023 28.129 0.000 0.599
## Stst36c (.41.) 0.163 0.019 8.657 0.000 0.126
## Stst37b (.42.) 0.282 0.018 15.945 0.000 0.248
## ci.upper Std.lv Std.all
##
## 0.149 0.119 0.133
## 0.349 0.314 0.329
## 0.299 0.278 0.285
## 0.346 0.323 0.337
## 0.340 0.310 0.284
## 0.240 0.205 0.188
## 0.150 0.114 0.106
## 0.317 0.281 0.246
##
## 0.294 0.240 0.239
## 0.187 0.143 0.186
## 0.228 0.180 0.238
## 0.417 0.345 0.490
## 0.292 0.232 0.203
##
## 0.501 0.456 0.399
## 1.030 0.956 0.593
## 0.900 0.842 0.655
## 0.767 0.713 0.625
##
## 0.347 0.225 0.342
## 0.551 0.367 0.372
## 0.570 0.383 0.490
## 0.504 0.337 0.313
## 0.370 0.236 0.207
##
## 0.892 0.765 0.815
## 0.674 0.572 0.569
## 0.709 0.604 0.673
## 0.666 0.565 0.591
## 0.755 0.646 0.662
## 0.827 0.708 0.739
## 0.857 0.731 0.670
## 0.690 0.583 0.536
## 0.529 0.447 0.579
## 0.995 0.856 0.882
## 0.452 0.379 0.576
## 0.479 0.399 0.405
## 0.423 0.351 0.449
## 0.768 0.655 0.609
## 0.579 0.489 0.647
## 0.563 0.477 0.677
## 0.685 0.578 0.506
## 0.689 0.572 0.355
## 0.200 0.144 0.112
## 0.317 0.251 0.220
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .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
## .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
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.816
## .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
## .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
## .Stest1vocab -1.339 0.016 -83.554 0.000 -1.370
## .Stst26rdngcmpr -1.226 0.017 -72.842 0.000 -1.259
## ci.upper Std.lv Std.all
## -0.846 -0.878 -0.977
## -0.417 -0.450 -0.471
## -0.865 -0.899 -0.921
## -0.895 -0.929 -0.969
## -0.706 -0.744 -0.682
## -0.667 -0.704 -0.648
## -1.222 -1.260 -1.172
## -0.963 -1.004 -0.879
## -0.931 -0.965 -0.961
## -0.761 -0.788 -1.020
## -1.159 -1.184 -1.564
## -0.919 -0.942 -1.337
## -0.466 -0.524 -0.325
## 0.344 0.300 0.233
## -0.176 -0.217 -0.190
## -1.303 -1.323 -2.014
## -0.882 -0.916 -0.929
## -0.955 -0.982 -1.256
## -1.307 -1.339 -1.426
## -1.193 -1.226 -1.263
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.428 0.012 35.541 0.000 0.404
## .Stest20spellng 0.495 0.016 30.986 0.000 0.464
## .Stest21cptlztn 0.459 0.014 32.634 0.000 0.431
## .Stest22puncttn 0.313 0.013 24.751 0.000 0.288
## .Stest23english 0.561 0.017 32.293 0.000 0.527
## .Stest24exprssn 0.801 0.021 37.384 0.000 0.759
## .Stst31bstrctrs 0.600 0.017 35.148 0.000 0.567
## .Stst34rthcmptt 0.630 0.028 22.388 0.000 0.575
## .Stest5math 0.624 0.017 35.783 0.000 0.590
## .Stst25wrdfnctn 0.377 0.011 35.866 0.000 0.356
## .Stst32rthrsnng 0.301 0.009 34.808 0.000 0.284
## .Stst33hghschlm 0.150 0.012 12.502 0.000 0.127
## .Stest35tblrdng 1.355 0.058 23.443 0.000 1.241
## .Stst36clrclchc 0.921 0.032 28.611 0.000 0.858
## .Stst37bjctnspc 0.675 0.027 24.945 0.000 0.622
## .Stst28mchnclrs 0.238 0.007 35.239 0.000 0.225
## .Stst29vslztn2D 0.677 0.020 34.519 0.000 0.639
## .Stst30vslztn3D 0.341 0.012 27.520 0.000 0.317
## .Stest1vocab 0.296 0.009 31.510 0.000 0.278
## .Stst26rdngcmpr 0.209 0.008 26.166 0.000 0.193
## english 1.109 0.123 8.985 0.000 0.867
## math 0.859 0.093 9.273 0.000 0.678
## speed 0.975 0.060 16.294 0.000 0.858
## spatial 0.523 0.043 12.203 0.000 0.439
## g 0.788 0.033 24.140 0.000 0.724
## ci.upper Std.lv Std.all
## 0.452 0.428 0.530
## 0.526 0.495 0.542
## 0.486 0.459 0.481
## 0.338 0.313 0.341
## 0.595 0.561 0.471
## 0.843 0.801 0.677
## 0.634 0.600 0.519
## 0.685 0.630 0.483
## 0.658 0.624 0.619
## 0.398 0.377 0.631
## 0.318 0.301 0.525
## 0.174 0.150 0.302
## 1.468 1.355 0.522
## 0.984 0.921 0.558
## 0.728 0.675 0.518
## 0.251 0.238 0.551
## 0.716 0.677 0.697
## 0.365 0.341 0.558
## 0.315 0.296 0.336
## 0.224 0.209 0.222
## 1.351 1.000 1.000
## 1.041 1.000 1.000
## 1.093 1.000 1.000
## 0.607 1.000 1.000
## 0.852 1.000 1.000
lavTestScore(metric, release = 1:42)
## 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 467.332 42 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p103. 3.739 1 0.053
## 2 .p2. == .p104. 3.176 1 0.075
## 3 .p3. == .p105. 0.002 1 0.965
## 4 .p4. == .p106. 0.003 1 0.953
## 5 .p5. == .p107. 0.120 1 0.729
## 6 .p6. == .p108. 0.000 1 0.988
## 7 .p7. == .p109. 0.214 1 0.644
## 8 .p8. == .p110. 0.039 1 0.844
## 9 .p9. == .p111. 0.935 1 0.334
## 10 .p10. == .p112. 7.033 1 0.008
## 11 .p11. == .p113. 6.693 1 0.010
## 12 .p12. == .p114. 0.146 1 0.702
## 13 .p13. == .p115. 0.015 1 0.903
## 14 .p14. == .p116. 0.999 1 0.317
## 15 .p15. == .p117. 0.204 1 0.651
## 16 .p16. == .p118. 0.529 1 0.467
## 17 .p17. == .p119. 0.298 1 0.585
## 18 .p18. == .p120. 64.864 1 0.000
## 19 .p19. == .p121. 8.553 1 0.003
## 20 .p20. == .p122. 2.104 1 0.147
## 21 .p21. == .p123. 6.644 1 0.010
## 22 .p22. == .p124. 1.405 1 0.236
## 23 .p23. == .p125. 19.880 1 0.000
## 24 .p24. == .p126. 10.559 1 0.001
## 25 .p25. == .p127. 61.526 1 0.000
## 26 .p26. == .p128. 0.023 1 0.880
## 27 .p27. == .p129. 29.579 1 0.000
## 28 .p28. == .p130. 15.174 1 0.000
## 29 .p29. == .p131. 4.995 1 0.025
## 30 .p30. == .p132. 6.757 1 0.009
## 31 .p31. == .p133. 44.352 1 0.000
## 32 .p32. == .p134. 0.074 1 0.786
## 33 .p33. == .p135. 147.712 1 0.000
## 34 .p34. == .p136. 0.385 1 0.535
## 35 .p35. == .p137. 4.457 1 0.035
## 36 .p36. == .p138. 13.873 1 0.000
## 37 .p37. == .p139. 14.625 1 0.000
## 38 .p38. == .p140. 4.661 1 0.031
## 39 .p39. == .p141. 0.002 1 0.961
## 40 .p40. == .p142. 2.347 1 0.125
## 41 .p41. == .p143. 5.489 1 0.019
## 42 .p42. == .p144. 8.659 1 0.003
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=~Stest28mechanicalreasoning", "g=~Stest19disguisedwords", "spatial=~Stest28mechanicalreasoning"))
fitMeasures(metric2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 2603.557 330.000 0.000 0.960 0.048 0.041
## aic bic
## 290509.288 291382.054
Mc(metric2)
## [1] 0.8295704
summary(metric2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 78 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 169
## Number of equality constraints 39
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2603.557 2311.470
## Degrees of freedom 330 330
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.126
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1112.382 987.586
## 1 1491.176 1323.884
##
## 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.) 0.102 0.019 5.392 0.000 0.065
## Stst20s (.p2.) 0.300 0.026 11.322 0.000 0.248
## Stst21c (.p3.) 0.265 0.018 14.829 0.000 0.230
## Stst22p (.p4.) 0.309 0.020 15.454 0.000 0.270
## Stst23n (.p5.) 0.297 0.024 12.652 0.000 0.251
## Stst24x (.p6.) 0.199 0.024 8.382 0.000 0.152
## Stst31b (.p7.) 0.108 0.021 5.073 0.000 0.066
## Stst34r (.p8.) 0.269 0.026 10.331 0.000 0.218
## math =~
## Stst5mt (.p9.) 0.259 0.018 14.556 0.000 0.224
## Stst25w (.10.) 0.155 0.016 9.515 0.000 0.123
## Stst32r (.11.) 0.194 0.017 11.366 0.000 0.160
## Stst33h (.12.) 0.371 0.023 16.464 0.000 0.326
## Stst34r (.13.) 0.248 0.021 11.770 0.000 0.207
## speed =~
## Stst34r (.14.) 0.463 0.020 22.947 0.000 0.423
## Stst35t (.15.) 0.968 0.032 30.693 0.000 0.906
## Stst36c (.16.) 0.854 0.024 35.279 0.000 0.806
## Stst37b (.17.) 0.723 0.023 31.619 0.000 0.678
## spatial =~
## Stst28m 0.387 0.019 19.993 0.000 0.349
## Sts292D (.19.) 0.484 0.022 21.699 0.000 0.440
## Sts303D (.20.) 0.498 0.021 24.099 0.000 0.458
## Stst31b (.21.) 0.443 0.020 22.396 0.000 0.404
## Stst37b (.22.) 0.311 0.021 14.491 0.000 0.269
## g =~
## Stst1vc (.23.) 0.863 0.016 55.383 0.000 0.832
## Stst5mt (.24.) 0.644 0.015 41.642 0.000 0.614
## Stst19d 0.610 0.018 34.047 0.000 0.574
## Stst20s (.26.) 0.638 0.015 42.999 0.000 0.609
## Stst21c (.27.) 0.729 0.014 53.408 0.000 0.702
## Stst22p (.28.) 0.799 0.015 54.244 0.000 0.771
## Stst23n (.29.) 0.825 0.017 48.516 0.000 0.791
## Stst24x (.30.) 0.658 0.017 39.600 0.000 0.625
## Stst25w (.31.) 0.504 0.013 38.852 0.000 0.478
## Stst26r (.32.) 0.965 0.015 62.525 0.000 0.935
## Stst28m 0.558 0.018 31.515 0.000 0.524
## Sts292D (.34.) 0.455 0.015 30.312 0.000 0.426
## Sts303D (.35.) 0.399 0.014 29.413 0.000 0.373
## Stst31b (.36.) 0.745 0.016 47.846 0.000 0.714
## Stst32r (.37.) 0.552 0.014 40.158 0.000 0.525
## Stst33h (.38.) 0.538 0.013 41.332 0.000 0.512
## Stst34r (.39.) 0.653 0.017 38.302 0.000 0.620
## Stst35t (.40.) 0.646 0.023 28.178 0.000 0.601
## Stst36c (.41.) 0.165 0.019 8.727 0.000 0.128
## Stst37b (.42.) 0.287 0.018 16.166 0.000 0.252
## ci.upper Std.lv Std.all
##
## 0.139 0.102 0.116
## 0.352 0.300 0.297
## 0.301 0.265 0.268
## 0.349 0.309 0.298
## 0.344 0.297 0.251
## 0.245 0.199 0.172
## 0.150 0.108 0.094
## 0.320 0.269 0.232
##
## 0.294 0.259 0.253
## 0.187 0.155 0.191
## 0.227 0.194 0.239
## 0.415 0.371 0.481
## 0.290 0.248 0.215
##
## 0.502 0.463 0.400
## 1.030 0.968 0.573
## 0.901 0.854 0.661
## 0.768 0.723 0.585
##
## 0.425 0.387 0.432
## 0.527 0.484 0.445
## 0.539 0.498 0.539
## 0.482 0.443 0.383
## 0.353 0.311 0.252
##
## 0.893 0.863 0.830
## 0.674 0.644 0.629
## 0.645 0.610 0.695
## 0.667 0.638 0.633
## 0.755 0.729 0.736
## 0.828 0.799 0.770
## 0.858 0.825 0.695
## 0.690 0.658 0.571
## 0.529 0.504 0.618
## 0.995 0.965 0.898
## 0.593 0.558 0.624
## 0.484 0.455 0.419
## 0.426 0.399 0.432
## 0.775 0.745 0.644
## 0.579 0.552 0.679
## 0.563 0.538 0.699
## 0.687 0.653 0.564
## 0.691 0.646 0.383
## 0.202 0.165 0.127
## 0.321 0.287 0.232
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .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
## .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
## .Stst25wrdfnctn -0.871 0.017 -52.726 0.000 -0.903
## .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
## .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
## .Stest1vocab -1.155 0.023 -50.360 0.000 -1.200
## .Stst26rdngcmpr -1.292 0.023 -56.802 0.000 -1.337
## ci.upper Std.lv Std.all
## -0.956 -0.992 -1.130
## -0.806 -0.848 -0.841
## -1.128 -1.167 -1.179
## -1.184 -1.226 -1.181
## -1.012 -1.062 -0.895
## -0.916 -0.965 -0.837
## -1.022 -1.070 -0.925
## -1.104 -1.153 -0.995
## -0.770 -0.814 -0.795
## -0.838 -0.871 -1.068
## -1.017 -1.052 -1.295
## -0.843 -0.875 -1.137
## -0.640 -0.712 -0.422
## 0.023 -0.032 -0.025
## -0.266 -0.318 -0.257
## -0.677 -0.715 -0.799
## -0.466 -0.512 -0.471
## -0.683 -0.723 -0.783
## -1.110 -1.155 -1.111
## -1.248 -1.292 -1.202
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.388 0.014 27.477 0.000 0.361
## .Stest20spellng 0.521 0.019 27.405 0.000 0.483
## .Stest21cptlztn 0.379 0.015 24.831 0.000 0.349
## .Stest22puncttn 0.343 0.013 25.448 0.000 0.317
## .Stest23english 0.641 0.024 26.645 0.000 0.594
## .Stest24exprssn 0.856 0.025 33.677 0.000 0.806
## .Stst31bstrctrs 0.575 0.022 26.332 0.000 0.532
## .Stst34rthcmptt 0.565 0.029 19.523 0.000 0.509
## .Stest5math 0.566 0.021 27.083 0.000 0.525
## .Stst25wrdfnctn 0.386 0.012 32.075 0.000 0.363
## .Stst32rthrsnng 0.318 0.011 29.512 0.000 0.297
## .Stst33hghschlm 0.166 0.014 11.460 0.000 0.137
## .Stest35tblrdng 1.498 0.069 21.722 0.000 1.363
## .Stst36clrclchc 0.911 0.040 22.709 0.000 0.832
## .Stst37bjctnspc 0.826 0.035 23.882 0.000 0.758
## .Stst28mchnclrs 0.339 0.015 22.171 0.000 0.309
## .Stst29vslztn2D 0.738 0.027 27.656 0.000 0.685
## .Stst30vslztn3D 0.445 0.019 23.212 0.000 0.408
## .Stest1vocab 0.336 0.013 26.545 0.000 0.311
## .Stst26rdngcmpr 0.224 0.011 20.842 0.000 0.203
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.416 0.388 0.504
## 0.558 0.521 0.511
## 0.409 0.379 0.386
## 0.370 0.343 0.318
## 0.688 0.641 0.455
## 0.906 0.856 0.645
## 0.618 0.575 0.430
## 0.622 0.565 0.422
## 0.606 0.566 0.540
## 0.410 0.386 0.581
## 0.339 0.318 0.482
## 0.194 0.166 0.280
## 1.633 1.498 0.525
## 0.989 0.911 0.546
## 0.893 0.826 0.541
## 0.368 0.339 0.423
## 0.790 0.738 0.626
## 0.483 0.445 0.522
## 0.361 0.336 0.311
## 0.245 0.224 0.194
## 1.000 1.000 1.000
## 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.) 0.102 0.019 5.392 0.000 0.065
## Stst20s (.p2.) 0.300 0.026 11.322 0.000 0.248
## Stst21c (.p3.) 0.265 0.018 14.829 0.000 0.230
## Stst22p (.p4.) 0.309 0.020 15.454 0.000 0.270
## Stst23n (.p5.) 0.297 0.024 12.652 0.000 0.251
## Stst24x (.p6.) 0.199 0.024 8.382 0.000 0.152
## Stst31b (.p7.) 0.108 0.021 5.073 0.000 0.066
## Stst34r (.p8.) 0.269 0.026 10.331 0.000 0.218
## math =~
## Stst5mt (.p9.) 0.259 0.018 14.556 0.000 0.224
## Stst25w (.10.) 0.155 0.016 9.515 0.000 0.123
## Stst32r (.11.) 0.194 0.017 11.366 0.000 0.160
## Stst33h (.12.) 0.371 0.023 16.464 0.000 0.326
## Stst34r (.13.) 0.248 0.021 11.770 0.000 0.207
## speed =~
## Stst34r (.14.) 0.463 0.020 22.947 0.000 0.423
## Stst35t (.15.) 0.968 0.032 30.693 0.000 0.906
## Stst36c (.16.) 0.854 0.024 35.279 0.000 0.806
## Stst37b (.17.) 0.723 0.023 31.619 0.000 0.678
## spatial =~
## Stst28m 0.200 0.018 11.126 0.000 0.165
## Sts292D (.19.) 0.484 0.022 21.699 0.000 0.440
## Sts303D (.20.) 0.498 0.021 24.099 0.000 0.458
## Stst31b (.21.) 0.443 0.020 22.396 0.000 0.404
## Stst37b (.22.) 0.311 0.021 14.491 0.000 0.269
## g =~
## Stst1vc (.23.) 0.863 0.016 55.383 0.000 0.832
## Stst5mt (.24.) 0.644 0.015 41.642 0.000 0.614
## Stst19d 0.754 0.019 40.617 0.000 0.717
## Stst20s (.26.) 0.638 0.015 42.999 0.000 0.609
## Stst21c (.27.) 0.729 0.014 53.408 0.000 0.702
## Stst22p (.28.) 0.799 0.015 54.244 0.000 0.771
## Stst23n (.29.) 0.825 0.017 48.516 0.000 0.791
## Stst24x (.30.) 0.658 0.017 39.600 0.000 0.625
## Stst25w (.31.) 0.504 0.013 38.852 0.000 0.478
## Stst26r (.32.) 0.965 0.015 62.525 0.000 0.935
## Stst28m 0.360 0.013 27.477 0.000 0.334
## Sts292D (.34.) 0.455 0.015 30.312 0.000 0.426
## Sts303D (.35.) 0.399 0.014 29.413 0.000 0.373
## Stst31b (.36.) 0.745 0.016 47.846 0.000 0.714
## Stst32r (.37.) 0.552 0.014 40.158 0.000 0.525
## Stst33h (.38.) 0.538 0.013 41.332 0.000 0.512
## Stst34r (.39.) 0.653 0.017 38.302 0.000 0.620
## Stst35t (.40.) 0.646 0.023 28.178 0.000 0.601
## Stst36c (.41.) 0.165 0.019 8.727 0.000 0.128
## Stst37b (.42.) 0.287 0.018 16.166 0.000 0.252
## ci.upper Std.lv Std.all
##
## 0.139 0.106 0.113
## 0.352 0.311 0.325
## 0.301 0.275 0.282
## 0.349 0.320 0.334
## 0.344 0.308 0.282
## 0.245 0.206 0.189
## 0.150 0.112 0.104
## 0.320 0.279 0.244
##
## 0.294 0.242 0.241
## 0.187 0.145 0.188
## 0.227 0.181 0.239
## 0.415 0.346 0.491
## 0.290 0.232 0.203
##
## 0.502 0.456 0.399
## 1.030 0.953 0.592
## 0.901 0.841 0.655
## 0.768 0.712 0.623
##
## 0.236 0.164 0.268
## 0.527 0.396 0.400
## 0.539 0.408 0.519
## 0.482 0.363 0.336
## 0.353 0.255 0.223
##
## 0.893 0.764 0.815
## 0.674 0.571 0.568
## 0.790 0.668 0.714
## 0.667 0.565 0.592
## 0.755 0.646 0.662
## 0.828 0.708 0.739
## 0.858 0.731 0.670
## 0.690 0.583 0.536
## 0.529 0.447 0.578
## 0.995 0.855 0.882
## 0.385 0.319 0.520
## 0.484 0.403 0.407
## 0.426 0.354 0.450
## 0.775 0.660 0.610
## 0.579 0.489 0.646
## 0.563 0.477 0.676
## 0.687 0.579 0.507
## 0.691 0.572 0.355
## 0.202 0.146 0.114
## 0.321 0.254 0.222
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .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
## .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
## .Stst25wrdfnctn -0.788 0.014 -57.181 0.000 -0.816
## .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
## .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
## .Stest1vocab -1.339 0.016 -83.554 0.000 -1.370
## .Stst26rdngcmpr -1.226 0.017 -72.842 0.000 -1.259
## ci.upper Std.lv Std.all
## -0.846 -0.878 -0.938
## -0.417 -0.450 -0.472
## -0.865 -0.899 -0.922
## -0.895 -0.929 -0.969
## -0.706 -0.744 -0.682
## -0.667 -0.704 -0.648
## -1.222 -1.260 -1.165
## -0.963 -1.004 -0.879
## -0.931 -0.965 -0.961
## -0.761 -0.788 -1.020
## -1.159 -1.184 -1.564
## -0.919 -0.942 -1.337
## -0.466 -0.524 -0.325
## 0.344 0.300 0.233
## -0.176 -0.217 -0.189
## -1.303 -1.323 -2.158
## -0.882 -0.916 -0.924
## -0.955 -0.982 -1.247
## -1.307 -1.339 -1.427
## -1.193 -1.226 -1.264
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.419 0.012 35.100 0.000 0.395
## .Stest20spellng 0.495 0.016 31.067 0.000 0.464
## .Stest21cptlztn 0.460 0.014 32.690 0.000 0.432
## .Stest22puncttn 0.314 0.013 24.680 0.000 0.289
## .Stest23english 0.560 0.017 32.219 0.000 0.526
## .Stest24exprssn 0.800 0.021 37.338 0.000 0.758
## .Stst31bstrctrs 0.589 0.017 34.397 0.000 0.556
## .Stst34rthcmptt 0.631 0.028 22.368 0.000 0.575
## .Stest5math 0.624 0.017 35.749 0.000 0.590
## .Stst25wrdfnctn 0.377 0.011 35.802 0.000 0.356
## .Stst32rthrsnng 0.301 0.009 34.773 0.000 0.284
## .Stst33hghschlm 0.150 0.012 12.476 0.000 0.126
## .Stest35tblrdng 1.357 0.058 23.488 0.000 1.244
## .Stst36clrclchc 0.921 0.032 28.629 0.000 0.858
## .Stst37bjctnspc 0.671 0.027 24.794 0.000 0.618
## .Stst28mchnclrs 0.248 0.007 37.712 0.000 0.235
## .Stst29vslztn2D 0.663 0.020 33.287 0.000 0.624
## .Stst30vslztn3D 0.327 0.013 25.521 0.000 0.302
## .Stest1vocab 0.296 0.009 31.700 0.000 0.278
## .Stst26rdngcmpr 0.209 0.008 26.399 0.000 0.194
## english 1.072 0.118 9.052 0.000 0.840
## math 0.874 0.094 9.314 0.000 0.690
## speed 0.970 0.060 16.293 0.000 0.854
## spatial 0.672 0.053 12.619 0.000 0.568
## g 0.785 0.032 24.587 0.000 0.723
## ci.upper Std.lv Std.all
## 0.442 0.419 0.478
## 0.527 0.495 0.543
## 0.487 0.460 0.483
## 0.339 0.314 0.342
## 0.595 0.560 0.471
## 0.842 0.800 0.677
## 0.623 0.589 0.504
## 0.686 0.631 0.483
## 0.658 0.624 0.619
## 0.398 0.377 0.631
## 0.318 0.301 0.526
## 0.174 0.150 0.302
## 1.470 1.357 0.523
## 0.984 0.921 0.558
## 0.724 0.671 0.513
## 0.260 0.248 0.658
## 0.702 0.663 0.675
## 0.353 0.327 0.529
## 0.314 0.296 0.336
## 0.225 0.209 0.223
## 1.305 1.000 1.000
## 1.058 1.000 1.000
## 1.087 1.000 1.000
## 0.776 1.000 1.000
## 0.848 1.000 1.000
lavTestScore(metric2, release = 1:39)
## 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 211.464 39 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p103. 0.796 1 0.372
## 2 .p2. == .p104. 3.142 1 0.076
## 3 .p3. == .p105. 0.036 1 0.849
## 4 .p4. == .p106. 0.077 1 0.782
## 5 .p5. == .p107. 0.262 1 0.609
## 6 .p6. == .p108. 0.005 1 0.945
## 7 .p7. == .p109. 0.036 1 0.850
## 8 .p8. == .p110. 0.095 1 0.758
## 9 .p9. == .p111. 0.966 1 0.326
## 10 .p10. == .p112. 7.049 1 0.008
## 11 .p11. == .p113. 6.126 1 0.013
## 12 .p12. == .p114. 0.187 1 0.665
## 13 .p13. == .p115. 0.053 1 0.818
## 14 .p14. == .p116. 1.081 1 0.298
## 15 .p15. == .p117. 0.139 1 0.710
## 16 .p16. == .p118. 0.393 1 0.531
## 17 .p17. == .p119. 0.363 1 0.547
## 18 .p19. == .p121. 0.983 1 0.322
## 19 .p20. == .p122. 1.908 1 0.167
## 20 .p21. == .p123. 0.331 1 0.565
## 21 .p22. == .p124. 0.036 1 0.850
## 22 .p23. == .p125. 19.707 1 0.000
## 23 .p24. == .p126. 10.684 1 0.001
## 24 .p26. == .p128. 0.481 1 0.488
## 25 .p27. == .p129. 34.550 1 0.000
## 26 .p28. == .p130. 19.538 1 0.000
## 27 .p29. == .p131. 3.520 1 0.061
## 28 .p30. == .p132. 5.862 1 0.015
## 29 .p31. == .p133. 44.857 1 0.000
## 30 .p32. == .p134. 0.003 1 0.959
## 31 .p34. == .p136. 0.606 1 0.436
## 32 .p35. == .p137. 19.114 1 0.000
## 33 .p36. == .p138. 5.846 1 0.016
## 34 .p37. == .p139. 15.250 1 0.000
## 35 .p38. == .p140. 5.112 1 0.024
## 36 .p39. == .p141. 0.156 1 0.693
## 37 .p40. == .p142. 2.877 1 0.090
## 38 .p41. == .p143. 4.205 1 0.040
## 39 .p42. == .p144. 4.634 1 0.031
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=~Stest28mechanicalreasoning", "g=~Stest19disguisedwords", "spatial=~Stest28mechanicalreasoning"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 3373.141 345.000 0.000 0.947 0.054 0.044
## aic bic
## 291248.872 292020.934
Mc(scalar)
## [1] 0.7796883
summary(scalar, standardized=T, ci=T) # +.008
## lavaan 0.6-18 ended normally after 92 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 174
## Number of equality constraints 59
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3373.141 2998.976
## Degrees of freedom 345 345
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.125
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1379.950 1226.879
## 1 1993.192 1772.097
##
## 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.) 0.111 0.013 8.468 0.000 0.085
## Stst20s (.p2.) 0.336 0.021 16.186 0.000 0.295
## Stst21c (.p3.) 0.261 0.015 17.603 0.000 0.232
## Stst22p (.p4.) 0.296 0.016 18.131 0.000 0.264
## Stst23n (.p5.) 0.308 0.019 16.020 0.000 0.271
## Stst24x (.p6.) 0.224 0.018 12.420 0.000 0.188
## Stst31b (.p7.) 0.112 0.018 6.059 0.000 0.076
## Stst34r (.p8.) 0.184 0.023 8.160 0.000 0.140
## math =~
## Stst5mt (.p9.) 0.271 0.018 14.883 0.000 0.235
## Stst25w (.10.) 0.138 0.015 9.078 0.000 0.108
## Stst32r (.11.) 0.204 0.018 11.590 0.000 0.169
## Stst33h (.12.) 0.349 0.023 15.239 0.000 0.304
## Stst34r (.13.) 0.258 0.024 10.564 0.000 0.210
## speed =~
## Stst34r (.14.) 0.446 0.020 21.962 0.000 0.406
## Stst35t (.15.) 0.953 0.032 30.185 0.000 0.891
## Stst36c (.16.) 0.864 0.024 36.376 0.000 0.817
## Stst37b (.17.) 0.737 0.022 32.833 0.000 0.693
## spatial =~
## Stst28m 0.379 0.020 19.246 0.000 0.341
## Sts292D (.19.) 0.520 0.022 23.875 0.000 0.477
## Sts303D (.20.) 0.469 0.020 23.993 0.000 0.430
## Stst31b (.21.) 0.455 0.021 21.480 0.000 0.413
## Stst37b (.22.) 0.286 0.022 12.862 0.000 0.243
## g =~
## Stst1vc (.23.) 0.859 0.016 53.059 0.000 0.827
## Stst5mt (.24.) 0.644 0.016 41.038 0.000 0.613
## Stst19d 0.609 0.018 33.888 0.000 0.574
## Stst20s (.26.) 0.633 0.015 43.171 0.000 0.604
## Stst21c (.27.) 0.729 0.014 53.361 0.000 0.703
## Stst22p (.28.) 0.802 0.015 54.354 0.000 0.773
## Stst23n (.29.) 0.823 0.017 48.604 0.000 0.790
## Stst24x (.30.) 0.655 0.016 39.894 0.000 0.623
## Stst25w (.31.) 0.505 0.013 39.277 0.000 0.480
## Stst26r (.32.) 0.961 0.015 63.053 0.000 0.931
## Stst28m 0.564 0.018 31.590 0.000 0.529
## Sts292D (.34.) 0.462 0.015 30.230 0.000 0.432
## Sts303D (.35.) 0.409 0.014 29.730 0.000 0.382
## Stst31b (.36.) 0.748 0.016 47.681 0.000 0.717
## Stst32r (.37.) 0.552 0.014 39.742 0.000 0.525
## Stst33h (.38.) 0.539 0.013 41.550 0.000 0.514
## Stst34r (.39.) 0.663 0.017 38.259 0.000 0.629
## Stst35t (.40.) 0.649 0.023 28.091 0.000 0.603
## Stst36c (.41.) 0.164 0.019 8.737 0.000 0.127
## Stst37b (.42.) 0.292 0.018 16.392 0.000 0.257
## ci.upper Std.lv Std.all
##
## 0.136 0.111 0.126
## 0.377 0.336 0.332
## 0.290 0.261 0.263
## 0.328 0.296 0.285
## 0.346 0.308 0.260
## 0.259 0.224 0.194
## 0.148 0.112 0.096
## 0.228 0.184 0.159
##
## 0.307 0.271 0.264
## 0.168 0.138 0.169
## 0.238 0.204 0.250
## 0.393 0.349 0.454
## 0.306 0.258 0.223
##
## 0.486 0.446 0.386
## 1.015 0.953 0.565
## 0.910 0.864 0.667
## 0.781 0.737 0.595
##
## 0.418 0.379 0.423
## 0.563 0.520 0.474
## 0.507 0.469 0.508
## 0.496 0.455 0.391
## 0.330 0.286 0.231
##
## 0.891 0.859 0.823
## 0.674 0.644 0.628
## 0.644 0.609 0.694
## 0.662 0.633 0.626
## 0.756 0.729 0.737
## 0.831 0.802 0.772
## 0.857 0.823 0.694
## 0.687 0.655 0.567
## 0.530 0.505 0.618
## 0.991 0.961 0.894
## 0.599 0.564 0.628
## 0.491 0.462 0.421
## 0.436 0.409 0.443
## 0.779 0.748 0.644
## 0.580 0.552 0.678
## 0.565 0.539 0.702
## 0.697 0.663 0.574
## 0.694 0.649 0.385
## 0.201 0.164 0.127
## 0.327 0.292 0.236
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.78.) -1.005 0.018 -57.043 0.000 -1.040
## .Stst20s (.79.) -0.838 0.021 -40.031 0.000 -0.879
## .Stst21c (.80.) -1.187 0.019 -61.403 0.000 -1.225
## .Stst22p (.81.) -1.253 0.022 -58.210 0.000 -1.295
## .Stst23n (.82.) -1.085 0.025 -43.483 0.000 -1.134
## .Stst24x (.83.) -0.964 0.023 -41.576 0.000 -1.009
## .Stst31b (.84.) -1.051 0.023 -45.255 0.000 -1.096
## .Stst34r (.85.) -1.232 0.023 -54.004 0.000 -1.277
## .Stst5mt (.86.) -0.868 0.020 -43.190 0.000 -0.908
## .Stst25w (.87.) -0.806 0.014 -56.442 0.000 -0.834
## .Stst32r (.88.) -1.107 0.016 -68.457 0.000 -1.139
## .Stst33h (.89.) -0.866 0.017 -51.552 0.000 -0.899
## .Stst35t (.90.) -0.790 0.033 -23.802 0.000 -0.855
## .Stst36c (.91.) 0.002 0.026 0.081 0.935 -0.049
## .Stst37b (.92.) -0.259 0.025 -10.171 0.000 -0.309
## .Stst28m (.93.) -0.755 0.023 -32.428 0.000 -0.801
## .Sts292D (.94.) -0.511 0.022 -23.168 0.000 -0.554
## .Sts303D (.95.) -0.657 0.018 -35.709 0.000 -0.693
## .Stst1vc (.96.) -1.283 0.022 -58.394 0.000 -1.326
## .Stst26r (.97.) -1.265 0.023 -54.000 0.000 -1.311
## ci.upper Std.lv Std.all
## -0.971 -1.005 -1.145
## -0.797 -0.838 -0.828
## -1.150 -1.187 -1.199
## -1.211 -1.253 -1.207
## -1.036 -1.085 -0.914
## -0.918 -0.964 -0.835
## -1.005 -1.051 -0.905
## -1.188 -1.232 -1.067
## -0.829 -0.868 -0.847
## -0.778 -0.806 -0.986
## -1.075 -1.107 -1.359
## -0.834 -0.866 -1.127
## -0.725 -0.790 -0.468
## 0.054 0.002 0.002
## -0.209 -0.259 -0.209
## -0.709 -0.755 -0.841
## -0.468 -0.511 -0.466
## -0.621 -0.657 -0.712
## -1.240 -1.283 -1.229
## -1.219 -1.265 -1.178
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.388 0.014 27.415 0.000 0.360
## .Stest20spellng 0.509 0.019 27.324 0.000 0.473
## .Stest21cptlztn 0.380 0.016 24.373 0.000 0.350
## .Stest22puncttn 0.348 0.012 27.890 0.000 0.323
## .Stest23english 0.636 0.024 27.030 0.000 0.590
## .Stest24exprssn 0.854 0.025 33.614 0.000 0.804
## .Stst31bstrctrs 0.570 0.022 25.735 0.000 0.527
## .Stst34rthcmptt 0.596 0.031 19.361 0.000 0.535
## .Stest5math 0.564 0.021 26.547 0.000 0.522
## .Stst25wrdfnctn 0.393 0.012 31.896 0.000 0.369
## .Stst32rthrsnng 0.317 0.011 28.873 0.000 0.295
## .Stst33hghschlm 0.178 0.014 12.814 0.000 0.151
## .Stest35tblrdng 1.517 0.068 22.397 0.000 1.384
## .Stst36clrclchc 0.903 0.041 22.084 0.000 0.823
## .Stst37bjctnspc 0.824 0.035 23.602 0.000 0.756
## .Stst28mchnclrs 0.343 0.015 22.328 0.000 0.313
## .Stst29vslztn2D 0.720 0.027 26.702 0.000 0.667
## .Stst30vslztn3D 0.465 0.018 25.536 0.000 0.429
## .Stest1vocab 0.352 0.014 25.982 0.000 0.326
## .Stst26rdngcmpr 0.231 0.011 20.564 0.000 0.209
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.415 0.388 0.503
## 0.546 0.509 0.498
## 0.411 0.380 0.388
## 0.372 0.348 0.322
## 0.682 0.636 0.451
## 0.903 0.854 0.641
## 0.614 0.570 0.423
## 0.656 0.596 0.446
## 0.605 0.564 0.536
## 0.417 0.393 0.589
## 0.338 0.317 0.478
## 0.206 0.178 0.302
## 1.650 1.517 0.533
## 0.983 0.903 0.539
## 0.893 0.824 0.537
## 0.373 0.343 0.426
## 0.772 0.720 0.598
## 0.501 0.465 0.546
## 0.379 0.352 0.323
## 0.253 0.231 0.200
## 1.000 1.000 1.000
## 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.) 0.111 0.013 8.468 0.000 0.085
## Stst20s (.p2.) 0.336 0.021 16.186 0.000 0.295
## Stst21c (.p3.) 0.261 0.015 17.603 0.000 0.232
## Stst22p (.p4.) 0.296 0.016 18.131 0.000 0.264
## Stst23n (.p5.) 0.308 0.019 16.020 0.000 0.271
## Stst24x (.p6.) 0.224 0.018 12.420 0.000 0.188
## Stst31b (.p7.) 0.112 0.018 6.059 0.000 0.076
## Stst34r (.p8.) 0.184 0.023 8.160 0.000 0.140
## math =~
## Stst5mt (.p9.) 0.271 0.018 14.883 0.000 0.235
## Stst25w (.10.) 0.138 0.015 9.078 0.000 0.108
## Stst32r (.11.) 0.204 0.018 11.590 0.000 0.169
## Stst33h (.12.) 0.349 0.023 15.239 0.000 0.304
## Stst34r (.13.) 0.258 0.024 10.564 0.000 0.210
## speed =~
## Stst34r (.14.) 0.446 0.020 21.962 0.000 0.406
## Stst35t (.15.) 0.953 0.032 30.185 0.000 0.891
## Stst36c (.16.) 0.864 0.024 36.376 0.000 0.817
## Stst37b (.17.) 0.737 0.022 32.833 0.000 0.693
## spatial =~
## Stst28m 0.720 0.051 14.017 0.000 0.619
## Sts292D (.19.) 0.520 0.022 23.875 0.000 0.477
## Sts303D (.20.) 0.469 0.020 23.993 0.000 0.430
## Stst31b (.21.) 0.455 0.021 21.480 0.000 0.413
## Stst37b (.22.) 0.286 0.022 12.862 0.000 0.243
## g =~
## Stst1vc (.23.) 0.859 0.016 53.059 0.000 0.827
## Stst5mt (.24.) 0.644 0.016 41.038 0.000 0.613
## Stst19d 0.751 0.018 41.621 0.000 0.716
## Stst20s (.26.) 0.633 0.015 43.171 0.000 0.604
## Stst21c (.27.) 0.729 0.014 53.361 0.000 0.703
## Stst22p (.28.) 0.802 0.015 54.354 0.000 0.773
## Stst23n (.29.) 0.823 0.017 48.604 0.000 0.790
## Stst24x (.30.) 0.655 0.016 39.894 0.000 0.623
## Stst25w (.31.) 0.505 0.013 39.277 0.000 0.480
## Stst26r (.32.) 0.961 0.015 63.053 0.000 0.931
## Stst28m 0.356 0.013 27.077 0.000 0.330
## Sts292D (.34.) 0.462 0.015 30.230 0.000 0.432
## Sts303D (.35.) 0.409 0.014 29.730 0.000 0.382
## Stst31b (.36.) 0.748 0.016 47.681 0.000 0.717
## Stst32r (.37.) 0.552 0.014 39.742 0.000 0.525
## Stst33h (.38.) 0.539 0.013 41.550 0.000 0.514
## Stst34r (.39.) 0.663 0.017 38.259 0.000 0.629
## Stst35t (.40.) 0.649 0.023 28.091 0.000 0.603
## Stst36c (.41.) 0.164 0.019 8.737 0.000 0.127
## Stst37b (.42.) 0.292 0.018 16.392 0.000 0.257
## ci.upper Std.lv Std.all
##
## 0.136 0.113 0.121
## 0.377 0.344 0.358
## 0.290 0.267 0.274
## 0.328 0.303 0.317
## 0.346 0.316 0.289
## 0.259 0.229 0.210
## 0.148 0.115 0.107
## 0.228 0.188 0.165
##
## 0.307 0.253 0.251
## 0.168 0.129 0.166
## 0.238 0.190 0.250
## 0.393 0.325 0.461
## 0.306 0.241 0.211
##
## 0.486 0.439 0.386
## 1.015 0.938 0.584
## 0.910 0.850 0.660
## 0.781 0.725 0.634
##
## 0.821 0.335 0.535
## 0.563 0.242 0.246
## 0.507 0.218 0.281
## 0.496 0.211 0.197
## 0.330 0.133 0.116
##
## 0.891 0.762 0.810
## 0.674 0.571 0.568
## 0.786 0.667 0.712
## 0.662 0.562 0.585
## 0.756 0.647 0.664
## 0.831 0.712 0.743
## 0.857 0.731 0.670
## 0.687 0.581 0.534
## 0.530 0.448 0.580
## 0.991 0.853 0.878
## 0.381 0.316 0.504
## 0.491 0.410 0.416
## 0.436 0.363 0.468
## 0.779 0.664 0.619
## 0.580 0.490 0.646
## 0.565 0.479 0.680
## 0.697 0.589 0.517
## 0.694 0.576 0.358
## 0.201 0.145 0.113
## 0.327 0.259 0.226
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.78.) -1.005 0.018 -57.043 0.000 -1.040
## .Stst20s (.79.) -0.838 0.021 -40.031 0.000 -0.879
## .Stst21c (.80.) -1.187 0.019 -61.403 0.000 -1.225
## .Stst22p (.81.) -1.253 0.022 -58.210 0.000 -1.295
## .Stst23n (.82.) -1.085 0.025 -43.483 0.000 -1.134
## .Stst24x (.83.) -0.964 0.023 -41.576 0.000 -1.009
## .Stst31b (.84.) -1.051 0.023 -45.255 0.000 -1.096
## .Stst34r (.85.) -1.232 0.023 -54.004 0.000 -1.277
## .Stst5mt (.86.) -0.868 0.020 -43.190 0.000 -0.908
## .Stst25w (.87.) -0.806 0.014 -56.442 0.000 -0.834
## .Stst32r (.88.) -1.107 0.016 -68.457 0.000 -1.139
## .Stst33h (.89.) -0.866 0.017 -51.552 0.000 -0.899
## .Stst35t (.90.) -0.790 0.033 -23.802 0.000 -0.855
## .Stst36c (.91.) 0.002 0.026 0.081 0.935 -0.049
## .Stst37b (.92.) -0.259 0.025 -10.171 0.000 -0.309
## .Stst28m (.93.) -0.755 0.023 -32.428 0.000 -0.801
## .Sts292D (.94.) -0.511 0.022 -23.168 0.000 -0.554
## .Sts303D (.95.) -0.657 0.018 -35.709 0.000 -0.693
## .Stst1vc (.96.) -1.283 0.022 -58.394 0.000 -1.326
## .Stst26r (.97.) -1.265 0.023 -54.000 0.000 -1.311
## english 1.090 0.079 13.775 0.000 0.935
## math -0.268 0.059 -4.510 0.000 -0.385
## speed 0.313 0.038 8.316 0.000 0.239
## spatial -0.773 0.040 -19.150 0.000 -0.852
## g 0.007 0.030 0.235 0.814 -0.051
## ci.upper Std.lv Std.all
## -0.971 -1.005 -1.074
## -0.797 -0.838 -0.873
## -1.150 -1.187 -1.217
## -1.211 -1.253 -1.309
## -1.036 -1.085 -0.995
## -0.918 -0.964 -0.885
## -1.005 -1.051 -0.979
## -1.188 -1.232 -1.083
## -0.829 -0.868 -0.863
## -0.778 -0.806 -1.042
## -1.075 -1.107 -1.459
## -0.834 -0.866 -1.230
## -0.725 -0.790 -0.492
## 0.054 0.002 0.002
## -0.209 -0.259 -0.227
## -0.709 -0.755 -1.206
## -0.468 -0.511 -0.519
## -0.621 -0.657 -0.847
## -1.240 -1.283 -1.363
## -1.219 -1.265 -1.303
## 1.245 1.065 1.065
## -0.152 -0.288 -0.288
## 0.387 0.318 0.318
## -0.694 -1.662 -1.662
## 0.065 0.008 0.008
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.419 0.012 35.147 0.000 0.396
## .Stest20spellng 0.487 0.015 32.051 0.000 0.458
## .Stest21cptlztn 0.462 0.013 34.457 0.000 0.435
## .Stest22puncttn 0.318 0.011 28.516 0.000 0.296
## .Stest23english 0.556 0.017 32.133 0.000 0.522
## .Stest24exprssn 0.795 0.022 36.960 0.000 0.753
## .Stst31bstrctrs 0.653 0.018 37.072 0.000 0.619
## .Stst34rthcmptt 0.662 0.028 23.751 0.000 0.607
## .Stest5math 0.622 0.017 35.692 0.000 0.588
## .Stst25wrdfnctn 0.381 0.010 36.514 0.000 0.360
## .Stst32rthrsnng 0.300 0.009 33.871 0.000 0.282
## .Stst33hghschlm 0.161 0.012 13.984 0.000 0.138
## .Stest35tblrdng 1.370 0.058 23.562 0.000 1.256
## .Stst36clrclchc 0.915 0.032 28.512 0.000 0.852
## .Stst37bjctnspc 0.697 0.027 25.534 0.000 0.644
## .Stst28mchnclrs 0.180 0.009 20.742 0.000 0.163
## .Stst29vslztn2D 0.743 0.020 36.585 0.000 0.703
## .Stst30vslztn3D 0.423 0.012 35.119 0.000 0.400
## .Stest1vocab 0.305 0.010 31.699 0.000 0.286
## .Stst26rdngcmpr 0.215 0.008 26.673 0.000 0.199
## english 1.048 0.116 9.026 0.000 0.821
## math 0.868 0.098 8.847 0.000 0.676
## speed 0.969 0.059 16.504 0.000 0.854
## spatial 0.216 0.031 6.952 0.000 0.155
## g 0.788 0.032 24.517 0.000 0.725
## ci.upper Std.lv Std.all
## 0.442 0.419 0.478
## 0.517 0.487 0.529
## 0.488 0.462 0.485
## 0.340 0.318 0.347
## 0.590 0.556 0.467
## 0.838 0.795 0.671
## 0.688 0.653 0.567
## 0.717 0.662 0.511
## 0.656 0.622 0.614
## 0.401 0.381 0.636
## 0.317 0.300 0.520
## 0.184 0.161 0.325
## 1.484 1.370 0.531
## 0.978 0.915 0.551
## 0.751 0.697 0.533
## 0.197 0.180 0.460
## 0.783 0.743 0.766
## 0.447 0.423 0.702
## 0.324 0.305 0.344
## 0.231 0.215 0.228
## 1.276 1.000 1.000
## 1.060 1.000 1.000
## 1.084 1.000 1.000
## 0.277 1.000 1.000
## 0.851 1.000 1.000
lavTestScore(scalar, release = 40:59)
## 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 824.01 20 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p78. == .p180. 0.090 1 0.765
## 2 .p79. == .p181. 14.903 1 0.000
## 3 .p80. == .p182. 0.082 1 0.774
## 4 .p81. == .p183. 1.277 1 0.259
## 5 .p82. == .p184. 0.020 1 0.888
## 6 .p83. == .p185. 2.823 1 0.093
## 7 .p84. == .p186. 8.307 1 0.004
## 8 .p85. == .p187. 68.845 1 0.000
## 9 .p86. == .p188. 13.284 1 0.000
## 10 .p87. == .p189. 70.243 1 0.000
## 11 .p88. == .p190. 26.319 1 0.000
## 12 .p89. == .p191. 38.868 1 0.000
## 13 .p90. == .p192. 15.050 1 0.000
## 14 .p91. == .p193. 11.780 1 0.001
## 15 .p92. == .p194. 31.956 1 0.000
## 16 .p93. == .p195. 419.771 1 0.000
## 17 .p94. == .p196. 0.946 1 0.331
## 18 .p95. == .p197. 73.010 1 0.000
## 19 .p96. == .p198. 177.689 1 0.000
## 20 .p97. == .p199. 106.080 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=~Stest28mechanicalreasoning", "g=~Stest19disguisedwords", "spatial=~Stest28mechanicalreasoning", "Stest28mechanicalreasoning~1", "Stest1vocab~1"))
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 2833.057 343.000 0.000 0.956 0.049 0.042
## aic bic
## 290712.787 291498.277
Mc(scalar2)
## [1] 0.8149408
summary(scalar2, standardized=T, ci=T) # +.068
## lavaan 0.6-18 ended normally after 106 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 174
## Number of equality constraints 57
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2833.057 2515.417
## Degrees of freedom 343 343
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.126
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1239.588 1100.607
## 1 1593.468 1414.810
##
## 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.) 0.100 0.014 6.960 0.000 0.072
## Stst20s (.p2.) 0.342 0.021 15.912 0.000 0.300
## Stst21c (.p3.) 0.260 0.016 16.639 0.000 0.229
## Stst22p (.p4.) 0.298 0.017 17.373 0.000 0.264
## Stst23n (.p5.) 0.307 0.020 15.307 0.000 0.268
## Stst24x (.p6.) 0.217 0.019 11.188 0.000 0.179
## Stst31b (.p7.) 0.092 0.018 5.071 0.000 0.056
## Stst34r (.p8.) 0.224 0.025 9.065 0.000 0.175
## math =~
## Stst5mt (.p9.) 0.283 0.018 16.039 0.000 0.249
## Stst25w (.10.) 0.136 0.015 9.093 0.000 0.106
## Stst32r (.11.) 0.220 0.017 12.895 0.000 0.187
## Stst33h (.12.) 0.327 0.021 15.627 0.000 0.286
## Stst34r (.13.) 0.280 0.024 11.559 0.000 0.232
## speed =~
## Stst34r (.14.) 0.452 0.020 22.237 0.000 0.412
## Stst35t (.15.) 0.951 0.032 30.015 0.000 0.889
## Stst36c (.16.) 0.865 0.024 36.421 0.000 0.818
## Stst37b (.17.) 0.733 0.022 32.649 0.000 0.689
## spatial =~
## Stst28m 0.385 0.020 19.729 0.000 0.347
## Sts292D (.19.) 0.519 0.021 24.761 0.000 0.478
## Sts303D (.20.) 0.472 0.019 24.573 0.000 0.434
## Stst31b (.21.) 0.447 0.019 23.118 0.000 0.409
## Stst37b (.22.) 0.280 0.020 14.228 0.000 0.242
## g =~
## Stst1vc (.23.) 0.861 0.016 55.250 0.000 0.830
## Stst5mt (.24.) 0.641 0.016 41.052 0.000 0.611
## Stst19d 0.609 0.018 33.974 0.000 0.574
## Stst20s (.26.) 0.636 0.015 43.507 0.000 0.607
## Stst21c (.27.) 0.729 0.014 53.314 0.000 0.703
## Stst22p (.28.) 0.800 0.015 54.207 0.000 0.772
## Stst23n (.29.) 0.824 0.017 48.617 0.000 0.790
## Stst24x (.30.) 0.656 0.016 39.866 0.000 0.624
## Stst25w (.31.) 0.507 0.013 39.540 0.000 0.482
## Stst26r (.32.) 0.964 0.015 62.301 0.000 0.933
## Stst28m 0.559 0.018 31.460 0.000 0.524
## Sts292D (.34.) 0.452 0.015 29.925 0.000 0.423
## Sts303D (.35.) 0.401 0.013 29.736 0.000 0.375
## Stst31b (.36.) 0.747 0.016 48.056 0.000 0.716
## Stst32r (.37.) 0.549 0.014 39.654 0.000 0.522
## Stst33h (.38.) 0.540 0.013 41.668 0.000 0.515
## Stst34r (.39.) 0.655 0.017 37.918 0.000 0.621
## Stst35t (.40.) 0.643 0.023 27.874 0.000 0.598
## Stst36c (.41.) 0.165 0.019 8.811 0.000 0.128
## Stst37b (.42.) 0.289 0.018 16.352 0.000 0.255
## ci.upper Std.lv Std.all
##
## 0.128 0.100 0.114
## 0.384 0.342 0.337
## 0.290 0.260 0.262
## 0.331 0.298 0.287
## 0.346 0.307 0.259
## 0.255 0.217 0.188
## 0.127 0.092 0.079
## 0.272 0.224 0.193
##
## 0.318 0.283 0.276
## 0.165 0.136 0.166
## 0.254 0.220 0.270
## 0.368 0.327 0.425
## 0.327 0.280 0.242
##
## 0.492 0.452 0.391
## 1.013 0.951 0.564
## 0.911 0.865 0.667
## 0.777 0.733 0.593
##
## 0.423 0.385 0.430
## 0.561 0.519 0.475
## 0.510 0.472 0.514
## 0.485 0.447 0.386
## 0.319 0.280 0.227
##
## 0.892 0.861 0.829
## 0.672 0.641 0.626
## 0.644 0.609 0.695
## 0.664 0.636 0.627
## 0.756 0.729 0.737
## 0.829 0.800 0.771
## 0.857 0.824 0.694
## 0.688 0.656 0.568
## 0.533 0.507 0.621
## 0.994 0.964 0.897
## 0.594 0.559 0.625
## 0.482 0.452 0.413
## 0.428 0.401 0.437
## 0.777 0.747 0.645
## 0.576 0.549 0.674
## 0.566 0.540 0.703
## 0.688 0.655 0.566
## 0.689 0.643 0.382
## 0.202 0.165 0.128
## 0.324 0.289 0.234
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.78.) -1.001 0.017 -58.132 0.000 -1.035
## .Stst20s (.79.) -0.807 0.021 -38.871 0.000 -0.848
## .Stst21c (.80.) -1.166 0.019 -62.854 0.000 -1.202
## .Stst22p (.81.) -1.230 0.021 -59.562 0.000 -1.270
## .Stst23n (.82.) -1.058 0.024 -44.105 0.000 -1.105
## .Stst24x (.83.) -0.943 0.022 -42.784 0.000 -0.986
## .Stst31b (.84.) -1.074 0.023 -46.398 0.000 -1.119
## .Stst34r (.85.) -1.199 0.023 -51.892 0.000 -1.244
## .Stst5mt (.86.) -0.848 0.020 -41.638 0.000 -0.888
## .Stst25w (.87.) -0.801 0.014 -56.258 0.000 -0.829
## .Stst32r (.88.) -1.091 0.017 -65.583 0.000 -1.124
## .Stst33h (.89.) -0.844 0.016 -51.460 0.000 -0.877
## .Stst35t (.90.) -0.784 0.033 -24.012 0.000 -0.848
## .Stst36c (.91.) 0.016 0.026 0.621 0.535 -0.035
## .Stst37b (.92.) -0.272 0.025 -10.909 0.000 -0.321
## .Stst28m -0.712 0.019 -36.731 0.000 -0.750
## .Sts292D (.94.) -0.559 0.022 -25.384 0.000 -0.602
## .Sts303D (.95.) -0.696 0.018 -37.764 0.000 -0.732
## .Stst1vc -1.151 0.023 -50.235 0.000 -1.196
## .Stst26r (.97.) -1.286 0.023 -56.930 0.000 -1.330
## ci.upper Std.lv Std.all
## -0.967 -1.001 -1.142
## -0.767 -0.807 -0.796
## -1.129 -1.166 -1.177
## -1.189 -1.230 -1.185
## -1.011 -1.058 -0.891
## -0.900 -0.943 -0.817
## -1.029 -1.074 -0.928
## -1.153 -1.199 -1.037
## -0.808 -0.848 -0.827
## -0.773 -0.801 -0.981
## -1.059 -1.091 -1.340
## -0.812 -0.844 -1.099
## -0.720 -0.784 -0.465
## 0.067 0.016 0.013
## -0.223 -0.272 -0.220
## -0.674 -0.712 -0.796
## -0.516 -0.559 -0.510
## -0.660 -0.696 -0.758
## -1.106 -1.151 -1.108
## -1.242 -1.286 -1.197
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.388 0.014 27.320 0.000 0.360
## .Stest20spellng 0.507 0.019 26.652 0.000 0.470
## .Stest21cptlztn 0.381 0.016 24.456 0.000 0.350
## .Stest22puncttn 0.348 0.013 27.573 0.000 0.323
## .Stest23english 0.637 0.024 27.000 0.000 0.591
## .Stest24exprssn 0.854 0.025 33.644 0.000 0.805
## .Stst31bstrctrs 0.574 0.022 26.424 0.000 0.532
## .Stst34rthcmptt 0.574 0.030 18.887 0.000 0.515
## .Stest5math 0.559 0.021 26.135 0.000 0.517
## .Stst25wrdfnctn 0.391 0.012 31.997 0.000 0.367
## .Stst32rthrsnng 0.313 0.011 28.427 0.000 0.292
## .Stst33hghschlm 0.192 0.012 16.043 0.000 0.168
## .Stest35tblrdng 1.521 0.068 22.440 0.000 1.388
## .Stst36clrclchc 0.904 0.041 22.110 0.000 0.824
## .Stst37bjctnspc 0.828 0.035 23.920 0.000 0.760
## .Stst28mchnclrs 0.339 0.015 22.336 0.000 0.309
## .Stst29vslztn2D 0.724 0.027 26.744 0.000 0.671
## .Stst30vslztn3D 0.460 0.018 25.350 0.000 0.424
## .Stest1vocab 0.337 0.013 26.601 0.000 0.312
## .Stst26rdngcmpr 0.225 0.011 20.838 0.000 0.204
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.416 0.388 0.505
## 0.545 0.507 0.494
## 0.411 0.381 0.388
## 0.372 0.348 0.323
## 0.683 0.637 0.452
## 0.904 0.854 0.641
## 0.617 0.574 0.429
## 0.634 0.574 0.430
## 0.601 0.559 0.532
## 0.415 0.391 0.587
## 0.335 0.313 0.472
## 0.215 0.192 0.325
## 1.654 1.521 0.536
## 0.984 0.904 0.538
## 0.895 0.828 0.542
## 0.369 0.339 0.424
## 0.777 0.724 0.604
## 0.496 0.460 0.545
## 0.362 0.337 0.313
## 0.246 0.225 0.195
## 1.000 1.000 1.000
## 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.) 0.100 0.014 6.960 0.000 0.072
## Stst20s (.p2.) 0.342 0.021 15.912 0.000 0.300
## Stst21c (.p3.) 0.260 0.016 16.639 0.000 0.229
## Stst22p (.p4.) 0.298 0.017 17.373 0.000 0.264
## Stst23n (.p5.) 0.307 0.020 15.307 0.000 0.268
## Stst24x (.p6.) 0.217 0.019 11.188 0.000 0.179
## Stst31b (.p7.) 0.092 0.018 5.071 0.000 0.056
## Stst34r (.p8.) 0.224 0.025 9.065 0.000 0.175
## math =~
## Stst5mt (.p9.) 0.283 0.018 16.039 0.000 0.249
## Stst25w (.10.) 0.136 0.015 9.093 0.000 0.106
## Stst32r (.11.) 0.220 0.017 12.895 0.000 0.187
## Stst33h (.12.) 0.327 0.021 15.627 0.000 0.286
## Stst34r (.13.) 0.280 0.024 11.559 0.000 0.232
## speed =~
## Stst34r (.14.) 0.452 0.020 22.237 0.000 0.412
## Stst35t (.15.) 0.951 0.032 30.015 0.000 0.889
## Stst36c (.16.) 0.865 0.024 36.421 0.000 0.818
## Stst37b (.17.) 0.733 0.022 32.649 0.000 0.689
## spatial =~
## Stst28m 0.198 0.018 10.985 0.000 0.162
## Sts292D (.19.) 0.519 0.021 24.761 0.000 0.478
## Sts303D (.20.) 0.472 0.019 24.573 0.000 0.434
## Stst31b (.21.) 0.447 0.019 23.118 0.000 0.409
## Stst37b (.22.) 0.280 0.020 14.228 0.000 0.242
## g =~
## Stst1vc (.23.) 0.861 0.016 55.250 0.000 0.830
## Stst5mt (.24.) 0.641 0.016 41.052 0.000 0.611
## Stst19d 0.752 0.018 41.050 0.000 0.716
## Stst20s (.26.) 0.636 0.015 43.507 0.000 0.607
## Stst21c (.27.) 0.729 0.014 53.314 0.000 0.703
## Stst22p (.28.) 0.800 0.015 54.207 0.000 0.772
## Stst23n (.29.) 0.824 0.017 48.617 0.000 0.790
## Stst24x (.30.) 0.656 0.016 39.866 0.000 0.624
## Stst25w (.31.) 0.507 0.013 39.540 0.000 0.482
## Stst26r (.32.) 0.964 0.015 62.301 0.000 0.933
## Stst28m 0.359 0.013 27.497 0.000 0.334
## Sts292D (.34.) 0.452 0.015 29.925 0.000 0.423
## Sts303D (.35.) 0.401 0.013 29.736 0.000 0.375
## Stst31b (.36.) 0.747 0.016 48.056 0.000 0.716
## Stst32r (.37.) 0.549 0.014 39.654 0.000 0.522
## Stst33h (.38.) 0.540 0.013 41.668 0.000 0.515
## Stst34r (.39.) 0.655 0.017 37.918 0.000 0.621
## Stst35t (.40.) 0.643 0.023 27.874 0.000 0.598
## Stst36c (.41.) 0.165 0.019 8.811 0.000 0.128
## Stst37b (.42.) 0.289 0.018 16.352 0.000 0.255
## ci.upper Std.lv Std.all
##
## 0.128 0.102 0.109
## 0.384 0.349 0.363
## 0.290 0.265 0.272
## 0.331 0.304 0.317
## 0.346 0.314 0.287
## 0.255 0.222 0.204
## 0.127 0.094 0.087
## 0.272 0.228 0.200
##
## 0.318 0.264 0.262
## 0.165 0.126 0.163
## 0.254 0.205 0.270
## 0.368 0.304 0.432
## 0.327 0.260 0.229
##
## 0.492 0.445 0.391
## 1.013 0.936 0.583
## 0.911 0.851 0.661
## 0.777 0.721 0.631
##
## 0.233 0.163 0.266
## 0.561 0.428 0.430
## 0.510 0.389 0.496
## 0.485 0.368 0.341
## 0.319 0.231 0.202
##
## 0.892 0.764 0.814
## 0.672 0.569 0.566
## 0.788 0.668 0.714
## 0.664 0.564 0.587
## 0.756 0.647 0.664
## 0.829 0.710 0.742
## 0.857 0.731 0.670
## 0.688 0.582 0.535
## 0.533 0.450 0.582
## 0.994 0.855 0.881
## 0.385 0.319 0.520
## 0.482 0.401 0.403
## 0.428 0.356 0.453
## 0.777 0.663 0.613
## 0.576 0.487 0.642
## 0.566 0.479 0.681
## 0.688 0.581 0.510
## 0.689 0.571 0.356
## 0.202 0.147 0.114
## 0.324 0.257 0.224
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.78.) -1.001 0.017 -58.132 0.000 -1.035
## .Stst20s (.79.) -0.807 0.021 -38.871 0.000 -0.848
## .Stst21c (.80.) -1.166 0.019 -62.854 0.000 -1.202
## .Stst22p (.81.) -1.230 0.021 -59.562 0.000 -1.270
## .Stst23n (.82.) -1.058 0.024 -44.105 0.000 -1.105
## .Stst24x (.83.) -0.943 0.022 -42.784 0.000 -0.986
## .Stst31b (.84.) -1.074 0.023 -46.398 0.000 -1.119
## .Stst34r (.85.) -1.199 0.023 -51.892 0.000 -1.244
## .Stst5mt (.86.) -0.848 0.020 -41.638 0.000 -0.888
## .Stst25w (.87.) -0.801 0.014 -56.258 0.000 -0.829
## .Stst32r (.88.) -1.091 0.017 -65.583 0.000 -1.124
## .Stst33h (.89.) -0.844 0.016 -51.460 0.000 -0.877
## .Stst35t (.90.) -0.784 0.033 -24.012 0.000 -0.848
## .Stst36c (.91.) 0.016 0.026 0.621 0.535 -0.035
## .Stst37b (.92.) -0.272 0.025 -10.909 0.000 -0.321
## .Stst28m -1.210 0.018 -66.111 0.000 -1.246
## .Sts292D (.94.) -0.559 0.022 -25.384 0.000 -0.602
## .Sts303D (.95.) -0.696 0.018 -37.764 0.000 -0.732
## .Stst1vc -1.391 0.023 -59.737 0.000 -1.436
## .Stst26r (.97.) -1.286 0.023 -56.930 0.000 -1.330
## english 0.861 0.069 12.407 0.000 0.725
## math -0.453 0.064 -7.098 0.000 -0.578
## speed 0.279 0.037 7.560 0.000 0.207
## spatial -0.683 0.041 -16.552 0.000 -0.764
## g 0.061 0.029 2.053 0.040 0.003
## ci.upper Std.lv Std.all
## -0.967 -1.001 -1.070
## -0.767 -0.807 -0.840
## -1.129 -1.166 -1.195
## -1.189 -1.230 -1.284
## -1.011 -1.058 -0.970
## -0.900 -0.943 -0.866
## -1.029 -1.074 -0.993
## -1.153 -1.199 -1.052
## -0.808 -0.848 -0.843
## -0.773 -0.801 -1.036
## -1.059 -1.091 -1.438
## -0.812 -0.844 -1.200
## -0.720 -0.784 -0.488
## 0.067 0.016 0.013
## -0.223 -0.272 -0.238
## -1.174 -1.210 -1.973
## -0.516 -0.559 -0.561
## -0.660 -0.696 -0.886
## -1.345 -1.391 -1.481
## -1.242 -1.286 -1.325
## 0.997 0.843 0.843
## -0.328 -0.487 -0.487
## 0.352 0.284 0.284
## -0.602 -0.828 -0.828
## 0.118 0.068 0.068
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.419 0.012 35.095 0.000 0.395
## .Stest20spellng 0.483 0.015 31.148 0.000 0.452
## .Stest21cptlztn 0.462 0.013 34.337 0.000 0.436
## .Stest22puncttn 0.320 0.012 27.764 0.000 0.297
## .Stest23english 0.557 0.017 32.096 0.000 0.523
## .Stest24exprssn 0.798 0.022 37.076 0.000 0.755
## .Stst31bstrctrs 0.587 0.017 34.194 0.000 0.553
## .Stst34rthcmptt 0.642 0.029 22.471 0.000 0.586
## .Stest5math 0.618 0.017 35.706 0.000 0.585
## .Stst25wrdfnctn 0.379 0.010 36.636 0.000 0.359
## .Stst32rthrsnng 0.297 0.009 33.272 0.000 0.279
## .Stst33hghschlm 0.173 0.010 17.416 0.000 0.154
## .Stest35tblrdng 1.377 0.058 23.591 0.000 1.263
## .Stst36clrclchc 0.914 0.032 28.463 0.000 0.851
## .Stst37bjctnspc 0.669 0.027 24.646 0.000 0.616
## .Stst28mchnclrs 0.248 0.007 37.673 0.000 0.235
## .Stst29vslztn2D 0.647 0.021 31.489 0.000 0.607
## .Stst30vslztn3D 0.339 0.012 28.098 0.000 0.315
## .Stest1vocab 0.297 0.009 31.818 0.000 0.279
## .Stst26rdngcmpr 0.211 0.008 26.476 0.000 0.195
## english 1.043 0.114 9.148 0.000 0.820
## math 0.865 0.098 8.872 0.000 0.674
## speed 0.969 0.059 16.453 0.000 0.854
## spatial 0.680 0.054 12.524 0.000 0.574
## g 0.788 0.032 24.571 0.000 0.725
## ci.upper Std.lv Std.all
## 0.442 0.419 0.479
## 0.513 0.483 0.523
## 0.489 0.462 0.486
## 0.343 0.320 0.349
## 0.591 0.557 0.468
## 0.840 0.798 0.672
## 0.620 0.587 0.501
## 0.698 0.642 0.495
## 0.652 0.618 0.611
## 0.400 0.379 0.634
## 0.314 0.297 0.515
## 0.193 0.173 0.350
## 1.491 1.377 0.534
## 0.977 0.914 0.550
## 0.722 0.669 0.511
## 0.261 0.248 0.659
## 0.687 0.647 0.652
## 0.362 0.339 0.549
## 0.316 0.297 0.337
## 0.226 0.211 0.224
## 1.267 1.000 1.000
## 1.056 1.000 1.000
## 1.084 1.000 1.000
## 0.787 1.000 1.000
## 0.851 1.000 1.000
lavTestScore(scalar2, release = 40:57)
## 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 233.876 18 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p78. == .p180. 2.632 1 0.105
## 2 .p79. == .p181. 24.664 1 0.000
## 3 .p80. == .p182. 0.083 1 0.774
## 4 .p81. == .p183. 1.167 1 0.280
## 5 .p82. == .p184. 0.004 1 0.952
## 6 .p83. == .p185. 2.570 1 0.109
## 7 .p84. == .p186. 0.892 1 0.345
## 8 .p85. == .p187. 42.218 1 0.000
## 9 .p86. == .p188. 14.315 1 0.000
## 10 .p87. == .p189. 57.219 1 0.000
## 11 .p88. == .p190. 31.727 1 0.000
## 12 .p89. == .p191. 52.936 1 0.000
## 13 .p90. == .p192. 21.710 1 0.000
## 14 .p91. == .p193. 17.275 1 0.000
## 15 .p92. == .p194. 17.915 1 0.000
## 16 .p94. == .p196. 25.673 1 0.000
## 17 .p95. == .p197. 12.250 1 0.000
## 18 .p97. == .p199. 0.416 1 0.519
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=~Stest28mechanicalreasoning", "g=~Stest19disguisedwords", "spatial=~Stest28mechanicalreasoning", "Stest28mechanicalreasoning~1", "Stest1vocab~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 3031.434 363.000 0.000 0.953 0.049 0.043
## aic bic
## 290871.165 291522.382
Mc(strict)
## [1] 0.8030813
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=~Stest28mechanicalreasoning", "g=~Stest19disguisedwords", "spatial=~Stest28mechanicalreasoning", "Stest28mechanicalreasoning~1", "Stest1vocab~1"))
fitMeasures(chc.bifactor, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 2896.832 348.000 0.000 0.955 0.049 0.057
## aic bic
## 290766.563 291518.484
Mc(chc.bifactor)
## [1] 0.8110139
summary(chc.bifactor, standardized=T, ci=T) # +.066
## lavaan 0.6-18 ended normally after 55 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 169
## Number of equality constraints 57
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2896.832 2569.672
## Degrees of freedom 348 348
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.127
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1281.577 1136.839
## 1 1615.256 1432.833
##
## 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.) 0.101 0.014 7.124 0.000 0.073
## Stst20s (.p2.) 0.346 0.017 20.516 0.000 0.313
## Stst21c (.p3.) 0.260 0.014 18.903 0.000 0.233
## Stst22p (.p4.) 0.299 0.014 20.896 0.000 0.271
## Stst23n (.p5.) 0.310 0.017 18.365 0.000 0.277
## Stst24x (.p6.) 0.220 0.018 11.909 0.000 0.184
## Stst31b (.p7.) 0.091 0.018 4.940 0.000 0.055
## Stst34r (.p8.) 0.225 0.023 9.655 0.000 0.179
## math =~
## Stst5mt (.p9.) 0.274 0.016 17.091 0.000 0.242
## Stst25w (.10.) 0.130 0.015 8.972 0.000 0.102
## Stst32r (.11.) 0.210 0.014 15.539 0.000 0.183
## Stst33h (.12.) 0.313 0.017 18.053 0.000 0.279
## Stst34r (.13.) 0.268 0.022 12.340 0.000 0.225
## speed =~
## Stst34r (.14.) 0.448 0.019 23.885 0.000 0.411
## Stst35t (.15.) 0.942 0.027 35.300 0.000 0.890
## Stst36c (.16.) 0.856 0.018 48.927 0.000 0.822
## Stst37b (.17.) 0.726 0.018 40.761 0.000 0.691
## spatial =~
## Stst28m 0.383 0.020 19.367 0.000 0.344
## Sts292D (.19.) 0.465 0.017 28.146 0.000 0.433
## Sts303D (.20.) 0.418 0.014 29.607 0.000 0.390
## Stst31b (.21.) 0.399 0.016 25.532 0.000 0.369
## Stst37b (.22.) 0.249 0.017 14.799 0.000 0.216
## g =~
## Stst1vc (.23.) 0.803 0.011 73.616 0.000 0.782
## Stst5mt (.24.) 0.599 0.013 47.210 0.000 0.574
## Stst19d 0.574 0.016 36.394 0.000 0.543
## Stst20s (.26.) 0.594 0.012 49.480 0.000 0.571
## Stst21c (.27.) 0.683 0.011 62.029 0.000 0.662
## Stst22p (.28.) 0.749 0.011 65.764 0.000 0.726
## Stst23n (.29.) 0.770 0.013 59.253 0.000 0.744
## Stst24x (.30.) 0.613 0.013 46.093 0.000 0.587
## Stst25w (.31.) 0.475 0.011 41.761 0.000 0.452
## Stst26r (.32.) 0.900 0.010 90.292 0.000 0.880
## Stst28m 0.527 0.016 33.859 0.000 0.497
## Sts292D (.34.) 0.424 0.013 31.903 0.000 0.398
## Sts303D (.35.) 0.375 0.012 32.015 0.000 0.352
## Stst31b (.36.) 0.700 0.012 56.013 0.000 0.676
## Stst32r (.37.) 0.513 0.011 45.069 0.000 0.491
## Stst33h (.38.) 0.505 0.011 47.482 0.000 0.484
## Stst34r (.39.) 0.613 0.015 42.249 0.000 0.585
## Stst35t (.40.) 0.602 0.020 29.404 0.000 0.562
## Stst36c (.41.) 0.154 0.017 8.849 0.000 0.120
## Stst37b (.42.) 0.272 0.016 16.536 0.000 0.239
## ci.upper Std.lv Std.all
##
## 0.128 0.101 0.118
## 0.379 0.346 0.350
## 0.287 0.260 0.272
## 0.328 0.299 0.300
## 0.343 0.310 0.269
## 0.256 0.220 0.194
## 0.127 0.091 0.082
## 0.271 0.225 0.199
##
## 0.305 0.274 0.275
## 0.159 0.130 0.164
## 0.236 0.210 0.266
## 0.347 0.313 0.423
## 0.310 0.268 0.237
##
## 0.485 0.448 0.397
## 0.994 0.942 0.566
## 0.891 0.856 0.664
## 0.761 0.726 0.593
##
## 0.422 0.383 0.441
## 0.497 0.465 0.437
## 0.445 0.418 0.469
## 0.430 0.399 0.358
## 0.282 0.249 0.204
##
## 0.825 0.803 0.809
## 0.624 0.599 0.601
## 0.605 0.574 0.673
## 0.618 0.594 0.600
## 0.705 0.683 0.714
## 0.771 0.749 0.750
## 0.795 0.770 0.668
## 0.639 0.613 0.542
## 0.497 0.475 0.597
## 0.919 0.900 0.883
## 0.558 0.527 0.607
## 0.450 0.424 0.398
## 0.398 0.375 0.421
## 0.725 0.700 0.628
## 0.535 0.513 0.651
## 0.526 0.505 0.682
## 0.642 0.613 0.543
## 0.642 0.602 0.362
## 0.188 0.154 0.119
## 0.304 0.272 0.222
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.78.) -1.002 0.017 -58.289 0.000 -1.035
## .Stst20s (.79.) -0.809 0.021 -38.981 0.000 -0.849
## .Stst21c (.80.) -1.166 0.019 -62.988 0.000 -1.202
## .Stst22p (.81.) -1.230 0.021 -59.686 0.000 -1.270
## .Stst23n (.82.) -1.059 0.024 -44.206 0.000 -1.106
## .Stst24x (.83.) -0.944 0.022 -42.833 0.000 -0.987
## .Stst31b (.84.) -1.073 0.023 -46.306 0.000 -1.119
## .Stst34r (.85.) -1.199 0.023 -52.114 0.000 -1.244
## .Stst5mt (.86.) -0.848 0.020 -41.543 0.000 -0.888
## .Stst25w (.87.) -0.802 0.014 -56.284 0.000 -0.830
## .Stst32r (.88.) -1.092 0.017 -66.162 0.000 -1.124
## .Stst33h (.89.) -0.845 0.016 -51.431 0.000 -0.877
## .Stst35t (.90.) -0.784 0.033 -24.055 0.000 -0.848
## .Stst36c (.91.) 0.016 0.026 0.629 0.529 -0.035
## .Stst37b (.92.) -0.272 0.025 -10.895 0.000 -0.321
## .Stst28m -0.713 0.019 -36.804 0.000 -0.751
## .Sts292D (.94.) -0.558 0.022 -25.348 0.000 -0.602
## .Sts303D (.95.) -0.697 0.018 -37.941 0.000 -0.733
## .Stst1vc -1.152 0.023 -50.350 0.000 -1.196
## .Stst26r (.97.) -1.287 0.023 -57.038 0.000 -1.331
## ci.upper Std.lv Std.all
## -0.968 -1.002 -1.174
## -0.768 -0.809 -0.817
## -1.130 -1.166 -1.219
## -1.190 -1.230 -1.232
## -1.012 -1.059 -0.920
## -0.901 -0.944 -0.835
## -1.028 -1.073 -0.963
## -1.154 -1.199 -1.062
## -0.808 -0.848 -0.850
## -0.774 -0.802 -1.007
## -1.060 -1.092 -1.385
## -0.812 -0.845 -1.140
## -0.720 -0.784 -0.471
## 0.068 0.016 0.013
## -0.223 -0.272 -0.222
## -0.675 -0.713 -0.821
## -0.515 -0.558 -0.525
## -0.661 -0.697 -0.783
## -1.107 -1.152 -1.160
## -1.243 -1.287 -1.263
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.388 0.014 27.275 0.000 0.360
## .Stest20spellng 0.507 0.019 26.876 0.000 0.470
## .Stest21cptlztn 0.381 0.016 24.461 0.000 0.350
## .Stest22puncttn 0.347 0.013 27.650 0.000 0.322
## .Stest23english 0.637 0.024 26.939 0.000 0.591
## .Stest24exprssn 0.855 0.025 33.654 0.000 0.805
## .Stst31bstrctrs 0.585 0.022 27.103 0.000 0.542
## .Stst34rthcmptt 0.576 0.031 18.859 0.000 0.516
## .Stest5math 0.560 0.021 26.119 0.000 0.518
## .Stst25wrdfnctn 0.391 0.012 32.022 0.000 0.367
## .Stst32rthrsnng 0.315 0.011 28.579 0.000 0.293
## .Stst33hghschlm 0.196 0.012 16.965 0.000 0.173
## .Stest35tblrdng 1.518 0.068 22.437 0.000 1.386
## .Stst36clrclchc 0.907 0.040 22.722 0.000 0.829
## .Stst37bjctnspc 0.835 0.034 24.412 0.000 0.768
## .Stst28mchnclrs 0.330 0.016 21.155 0.000 0.300
## .Stst29vslztn2D 0.737 0.026 27.999 0.000 0.685
## .Stst30vslztn3D 0.478 0.017 27.489 0.000 0.444
## .Stest1vocab 0.340 0.013 26.798 0.000 0.316
## .Stst26rdngcmpr 0.229 0.011 21.178 0.000 0.208
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.416 0.388 0.534
## 0.544 0.507 0.517
## 0.411 0.381 0.416
## 0.371 0.347 0.348
## 0.684 0.637 0.481
## 0.905 0.855 0.668
## 0.627 0.585 0.470
## 0.636 0.576 0.452
## 0.602 0.560 0.563
## 0.415 0.391 0.617
## 0.336 0.315 0.506
## 0.218 0.196 0.357
## 1.651 1.518 0.549
## 0.986 0.907 0.545
## 0.902 0.835 0.558
## 0.361 0.330 0.438
## 0.788 0.737 0.650
## 0.513 0.478 0.603
## 0.365 0.340 0.345
## 0.250 0.229 0.221
## 1.000 1.000 1.000
## 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.) 0.101 0.014 7.124 0.000 0.073
## Stst20s (.p2.) 0.346 0.017 20.516 0.000 0.313
## Stst21c (.p3.) 0.260 0.014 18.903 0.000 0.233
## Stst22p (.p4.) 0.299 0.014 20.896 0.000 0.271
## Stst23n (.p5.) 0.310 0.017 18.365 0.000 0.277
## Stst24x (.p6.) 0.220 0.018 11.909 0.000 0.184
## Stst31b (.p7.) 0.091 0.018 4.940 0.000 0.055
## Stst34r (.p8.) 0.225 0.023 9.655 0.000 0.179
## math =~
## Stst5mt (.p9.) 0.274 0.016 17.091 0.000 0.242
## Stst25w (.10.) 0.130 0.015 8.972 0.000 0.102
## Stst32r (.11.) 0.210 0.014 15.539 0.000 0.183
## Stst33h (.12.) 0.313 0.017 18.053 0.000 0.279
## Stst34r (.13.) 0.268 0.022 12.340 0.000 0.225
## speed =~
## Stst34r (.14.) 0.448 0.019 23.885 0.000 0.411
## Stst35t (.15.) 0.942 0.027 35.300 0.000 0.890
## Stst36c (.16.) 0.856 0.018 48.927 0.000 0.822
## Stst37b (.17.) 0.726 0.018 40.761 0.000 0.691
## spatial =~
## Stst28m 0.164 0.013 12.290 0.000 0.138
## Sts292D (.19.) 0.465 0.017 28.146 0.000 0.433
## Sts303D (.20.) 0.418 0.014 29.607 0.000 0.390
## Stst31b (.21.) 0.399 0.016 25.532 0.000 0.369
## Stst37b (.22.) 0.249 0.017 14.799 0.000 0.216
## g =~
## Stst1vc (.23.) 0.803 0.011 73.616 0.000 0.782
## Stst5mt (.24.) 0.599 0.013 47.210 0.000 0.574
## Stst19d 0.698 0.014 48.918 0.000 0.670
## Stst20s (.26.) 0.594 0.012 49.480 0.000 0.571
## Stst21c (.27.) 0.683 0.011 62.029 0.000 0.662
## Stst22p (.28.) 0.749 0.011 65.764 0.000 0.726
## Stst23n (.29.) 0.770 0.013 59.253 0.000 0.744
## Stst24x (.30.) 0.613 0.013 46.093 0.000 0.587
## Stst25w (.31.) 0.475 0.011 41.761 0.000 0.452
## Stst26r (.32.) 0.900 0.010 90.292 0.000 0.880
## Stst28m 0.334 0.012 28.548 0.000 0.311
## Sts292D (.34.) 0.424 0.013 31.903 0.000 0.398
## Sts303D (.35.) 0.375 0.012 32.015 0.000 0.352
## Stst31b (.36.) 0.700 0.012 56.013 0.000 0.676
## Stst32r (.37.) 0.513 0.011 45.069 0.000 0.491
## Stst33h (.38.) 0.505 0.011 47.482 0.000 0.484
## Stst34r (.39.) 0.613 0.015 42.249 0.000 0.585
## Stst35t (.40.) 0.602 0.020 29.404 0.000 0.562
## Stst36c (.41.) 0.154 0.017 8.849 0.000 0.120
## Stst37b (.42.) 0.272 0.016 16.536 0.000 0.239
## ci.upper Std.lv Std.all
##
## 0.128 0.101 0.105
## 0.379 0.346 0.354
## 0.287 0.260 0.261
## 0.328 0.299 0.304
## 0.343 0.310 0.278
## 0.256 0.220 0.199
## 0.127 0.091 0.082
## 0.271 0.225 0.194
##
## 0.305 0.274 0.267
## 0.159 0.130 0.166
## 0.236 0.210 0.270
## 0.347 0.313 0.433
## 0.310 0.268 0.231
##
## 0.485 0.448 0.387
## 0.994 0.942 0.581
## 0.891 0.856 0.663
## 0.761 0.726 0.630
##
## 0.190 0.164 0.264
## 0.497 0.465 0.457
## 0.445 0.418 0.519
## 0.430 0.399 0.359
## 0.282 0.249 0.216
##
## 0.825 0.803 0.828
## 0.624 0.599 0.584
## 0.726 0.698 0.729
## 0.618 0.594 0.608
## 0.705 0.683 0.684
## 0.771 0.749 0.760
## 0.795 0.770 0.690
## 0.639 0.613 0.555
## 0.497 0.475 0.602
## 0.919 0.900 0.892
## 0.357 0.334 0.536
## 0.450 0.424 0.417
## 0.398 0.375 0.466
## 0.725 0.700 0.629
## 0.535 0.513 0.660
## 0.526 0.505 0.698
## 0.642 0.613 0.530
## 0.642 0.602 0.371
## 0.188 0.154 0.119
## 0.304 0.272 0.236
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## g 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.78.) -1.002 0.017 -58.289 0.000 -1.035
## .Stst20s (.79.) -0.809 0.021 -38.981 0.000 -0.849
## .Stst21c (.80.) -1.166 0.019 -62.988 0.000 -1.202
## .Stst22p (.81.) -1.230 0.021 -59.686 0.000 -1.270
## .Stst23n (.82.) -1.059 0.024 -44.206 0.000 -1.106
## .Stst24x (.83.) -0.944 0.022 -42.833 0.000 -0.987
## .Stst31b (.84.) -1.073 0.023 -46.306 0.000 -1.119
## .Stst34r (.85.) -1.199 0.023 -52.114 0.000 -1.244
## .Stst5mt (.86.) -0.848 0.020 -41.543 0.000 -0.888
## .Stst25w (.87.) -0.802 0.014 -56.284 0.000 -0.830
## .Stst32r (.88.) -1.092 0.017 -66.162 0.000 -1.124
## .Stst33h (.89.) -0.845 0.016 -51.431 0.000 -0.877
## .Stst35t (.90.) -0.784 0.033 -24.055 0.000 -0.848
## .Stst36c (.91.) 0.016 0.026 0.629 0.529 -0.035
## .Stst37b (.92.) -0.272 0.025 -10.895 0.000 -0.321
## .Stst28m -1.219 0.017 -70.441 0.000 -1.253
## .Sts292D (.94.) -0.558 0.022 -25.348 0.000 -0.602
## .Sts303D (.95.) -0.697 0.018 -37.941 0.000 -0.733
## .Stst1vc -1.392 0.023 -59.831 0.000 -1.437
## .Stst26r (.97.) -1.287 0.023 -57.038 0.000 -1.331
## english 0.854 0.060 14.120 0.000 0.736
## math -0.473 0.066 -7.130 0.000 -0.603
## speed 0.282 0.036 7.890 0.000 0.212
## spatial -0.768 0.046 -16.632 0.000 -0.858
## g 0.066 0.031 2.114 0.034 0.005
## ci.upper Std.lv Std.all
## -0.968 -1.002 -1.046
## -0.768 -0.809 -0.827
## -1.130 -1.166 -1.168
## -1.190 -1.230 -1.248
## -1.012 -1.059 -0.949
## -0.901 -0.944 -0.854
## -1.028 -1.073 -0.964
## -1.154 -1.199 -1.036
## -0.808 -0.848 -0.827
## -0.774 -0.802 -1.017
## -1.060 -1.092 -1.405
## -0.812 -0.845 -1.167
## -0.720 -0.784 -0.484
## 0.068 0.016 0.013
## -0.223 -0.272 -0.236
## -1.185 -1.219 -1.960
## -0.515 -0.558 -0.549
## -0.661 -0.697 -0.866
## -1.346 -1.392 -1.434
## -1.243 -1.287 -1.275
## 0.973 0.854 0.854
## -0.343 -0.473 -0.473
## 0.351 0.282 0.282
## -0.677 -0.768 -0.768
## 0.127 0.066 0.066
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.419 0.012 35.135 0.000 0.395
## .Stest20spellng 0.482 0.015 31.207 0.000 0.452
## .Stest21cptlztn 0.462 0.013 34.512 0.000 0.436
## .Stest22puncttn 0.321 0.011 28.055 0.000 0.298
## .Stest23english 0.557 0.017 32.051 0.000 0.523
## .Stest24exprssn 0.798 0.022 37.092 0.000 0.755
## .Stst31bstrctrs 0.581 0.017 33.804 0.000 0.547
## .Stst34rthcmptt 0.641 0.029 22.383 0.000 0.585
## .Stest5math 0.617 0.017 35.729 0.000 0.584
## .Stst25wrdfnctn 0.379 0.010 36.627 0.000 0.359
## .Stst32rthrsnng 0.297 0.009 33.227 0.000 0.279
## .Stst33hghschlm 0.171 0.010 17.166 0.000 0.151
## .Stest35tblrdng 1.376 0.058 23.573 0.000 1.261
## .Stst36clrclchc 0.913 0.032 28.741 0.000 0.851
## .Stst37bjctnspc 0.666 0.027 24.600 0.000 0.613
## .Stst28mchnclrs 0.249 0.007 38.113 0.000 0.236
## .Stst29vslztn2D 0.639 0.021 30.778 0.000 0.598
## .Stst30vslztn3D 0.333 0.012 27.185 0.000 0.309
## .Stest1vocab 0.297 0.009 31.871 0.000 0.278
## .Stst26rdngcmpr 0.209 0.008 26.374 0.000 0.193
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.442 0.419 0.457
## 0.513 0.482 0.505
## 0.489 0.462 0.464
## 0.343 0.321 0.330
## 0.591 0.557 0.447
## 0.840 0.798 0.653
## 0.615 0.581 0.469
## 0.698 0.641 0.478
## 0.651 0.617 0.587
## 0.399 0.379 0.610
## 0.314 0.297 0.491
## 0.190 0.171 0.326
## 1.490 1.376 0.524
## 0.975 0.913 0.547
## 0.719 0.666 0.501
## 0.262 0.249 0.643
## 0.679 0.639 0.617
## 0.357 0.333 0.514
## 0.315 0.297 0.315
## 0.224 0.209 0.205
## 1.000 1.000 1.000
## 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 =~ Stest19disguisedwords 1
## 2 english =~ Stest20spelling 1
## 3 english =~ Stest21capitalization 1
## 4 english =~ Stest22punctuation 1
## 5 english =~ Stest23english 1
## 6 english =~ Stest24expression 1
## 7 english =~ Stest31abstractreasoning 1
## 8 english =~ Stest34arithcomputation 1
## 9 math =~ Stest5math 1
## 10 math =~ Stest25wordfunctions 1
## 11 math =~ Stest32arithreasoning 1
## 12 math =~ Stest33highschoolmath 1
## 13 math =~ Stest34arithcomputation 1
## 14 speed =~ Stest34arithcomputation 1
## 15 speed =~ Stest35tablereading 1
## 16 speed =~ Stest36clericalchecking 1
## 17 speed =~ Stest37objectinspection 1
## 18 spatial =~ Stest28mechanicalreasoning 1
## 19 spatial =~ Stest29visualization2D 1
## 20 spatial =~ Stest30visualization3D 1
## 21 spatial =~ Stest31abstractreasoning 1
## 22 spatial =~ Stest37objectinspection 1
## 23 g =~ Stest1vocab 1
## 24 g =~ Stest5math 1
## 25 g =~ Stest19disguisedwords 1
## 26 g =~ Stest20spelling 1
## 27 g =~ Stest21capitalization 1
## 28 g =~ Stest22punctuation 1
## 29 g =~ Stest23english 1
## 30 g =~ Stest24expression 1
## 31 g =~ Stest25wordfunctions 1
## 32 g =~ Stest26readingcomprehension 1
## 33 g =~ Stest28mechanicalreasoning 1
## 34 g =~ Stest29visualization2D 1
## 35 g =~ Stest30visualization3D 1
## 36 g =~ Stest31abstractreasoning 1
## 37 g =~ Stest32arithreasoning 1
## 38 g =~ Stest33highschoolmath 1
## 39 g =~ Stest34arithcomputation 1
## 40 g =~ Stest35tablereading 1
## 41 g =~ Stest36clericalchecking 1
## 42 g =~ Stest37objectinspection 1
## 43 Stest19disguisedwords ~~ Stest19disguisedwords 1
## 44 Stest20spelling ~~ Stest20spelling 1
## 45 Stest21capitalization ~~ Stest21capitalization 1
## 46 Stest22punctuation ~~ Stest22punctuation 1
## 47 Stest23english ~~ Stest23english 1
## 48 Stest24expression ~~ Stest24expression 1
## 49 Stest31abstractreasoning ~~ Stest31abstractreasoning 1
## 50 Stest34arithcomputation ~~ Stest34arithcomputation 1
## 51 Stest5math ~~ Stest5math 1
## 52 Stest25wordfunctions ~~ Stest25wordfunctions 1
## 53 Stest32arithreasoning ~~ Stest32arithreasoning 1
## 54 Stest33highschoolmath ~~ Stest33highschoolmath 1
## 55 Stest35tablereading ~~ Stest35tablereading 1
## 56 Stest36clericalchecking ~~ Stest36clericalchecking 1
## 57 Stest37objectinspection ~~ Stest37objectinspection 1
## 58 Stest28mechanicalreasoning ~~ Stest28mechanicalreasoning 1
## 59 Stest29visualization2D ~~ Stest29visualization2D 1
## 60 Stest30visualization3D ~~ Stest30visualization3D 1
## 61 Stest1vocab ~~ Stest1vocab 1
## 62 Stest26readingcomprehension ~~ Stest26readingcomprehension 1
## 63 english ~~ english 1
## 64 math ~~ math 1
## 65 speed ~~ speed 1
## 66 spatial ~~ spatial 1
## 67 g ~~ g 1
## 68 english ~~ math 1
## 69 english ~~ speed 1
## 70 english ~~ spatial 1
## 71 english ~~ g 1
## 72 math ~~ speed 1
## 73 math ~~ spatial 1
## 74 math ~~ g 1
## 75 speed ~~ spatial 1
## 76 speed ~~ g 1
## 77 spatial ~~ g 1
## 78 Stest19disguisedwords ~1 1
## 79 Stest20spelling ~1 1
## 80 Stest21capitalization ~1 1
## 81 Stest22punctuation ~1 1
## 82 Stest23english ~1 1
## 83 Stest24expression ~1 1
## 84 Stest31abstractreasoning ~1 1
## 85 Stest34arithcomputation ~1 1
## 86 Stest5math ~1 1
## 87 Stest25wordfunctions ~1 1
## 88 Stest32arithreasoning ~1 1
## 89 Stest33highschoolmath ~1 1
## 90 Stest35tablereading ~1 1
## label est.std se z pvalue ci.lower ci.upper
## 1 .p1. 0.118 0.017 7.033 0 0.085 0.151
## 2 .p2. 0.350 0.017 20.237 0 0.316 0.383
## 3 .p3. 0.272 0.015 18.438 0 0.243 0.301
## 4 .p4. 0.300 0.014 20.927 0 0.272 0.328
## 5 .p5. 0.269 0.014 18.791 0 0.241 0.297
## 6 .p6. 0.194 0.016 11.995 0 0.163 0.226
## 7 .p7. 0.082 0.017 4.946 0 0.049 0.114
## 8 .p8. 0.199 0.021 9.700 0 0.159 0.240
## 9 .p9. 0.275 0.016 16.763 0 0.242 0.307
## 10 .p10. 0.164 0.018 9.063 0 0.128 0.199
## 11 .p11. 0.266 0.017 15.920 0 0.233 0.299
## 12 .p12. 0.423 0.023 18.633 0 0.378 0.467
## 13 .p13. 0.237 0.019 12.388 0 0.200 0.275
## 14 .p14. 0.397 0.015 26.885 0 0.368 0.426
## 15 .p15. 0.566 0.014 39.156 0 0.538 0.595
## 16 .p16. 0.664 0.014 48.467 0 0.637 0.691
## 17 .p17. 0.593 0.014 43.236 0 0.566 0.620
## 18 0.441 0.022 20.027 0 0.398 0.484
## 19 .p19. 0.437 0.016 28.007 0 0.406 0.468
## 20 .p20. 0.469 0.015 30.342 0 0.439 0.499
## 21 .p21. 0.358 0.014 25.427 0 0.331 0.386
## 22 .p22. 0.204 0.014 14.794 0 0.177 0.231
## 23 .p23. 0.809 0.007 110.412 0 0.795 0.823
## 24 .p24. 0.601 0.011 54.158 0 0.579 0.623
## 25 0.673 0.012 54.850 0 0.649 0.697
## 26 .p26. 0.600 0.010 59.735 0 0.581 0.620
## 27 .p27. 0.714 0.009 82.540 0 0.697 0.731
## 28 .p28. 0.750 0.007 101.904 0 0.735 0.764
## 29 .p29. 0.668 0.009 74.511 0 0.651 0.686
## 30 .p30. 0.542 0.011 49.705 0 0.521 0.563
## 31 .p31. 0.597 0.011 55.289 0 0.575 0.618
## 32 .p32. 0.883 0.006 159.300 0 0.872 0.894
## 33 0.607 0.014 43.228 0 0.579 0.634
## 34 .p34. 0.398 0.012 32.263 0 0.374 0.422
## 35 .p35. 0.421 0.012 34.006 0 0.397 0.445
## 36 .p36. 0.628 0.010 63.399 0 0.609 0.648
## 37 .p37. 0.651 0.010 62.031 0 0.630 0.671
## 38 .p38. 0.682 0.009 72.553 0 0.663 0.700
## 39 .p39. 0.543 0.013 43.337 0 0.518 0.568
## 40 .p40. 0.362 0.011 31.776 0 0.339 0.384
## 41 .p41. 0.119 0.013 8.858 0 0.093 0.146
## 42 .p42. 0.222 0.013 16.905 0 0.196 0.248
## 43 0.534 0.016 33.890 0 0.503 0.564
## 44 0.517 0.015 35.543 0 0.489 0.546
## 45 0.416 0.012 33.869 0 0.392 0.440
## 46 0.348 0.011 32.189 0 0.327 0.369
## 47 0.481 0.012 38.977 0 0.456 0.505
## 48 0.668 0.012 54.199 0 0.644 0.693
## 49 0.470 0.013 34.975 0 0.444 0.497
## 50 0.452 0.017 26.349 0 0.418 0.485
## 51 0.563 0.014 39.194 0 0.535 0.592
## 52 0.617 0.013 47.224 0 0.592 0.643
## 53 0.506 0.015 33.700 0 0.476 0.535
## 54 0.357 0.020 17.756 0 0.317 0.396
## 55 0.549 0.017 32.062 0 0.515 0.582
## 56 0.545 0.018 29.624 0 0.509 0.581
## 57 0.558 0.017 32.244 0 0.524 0.591
## 58 0.438 0.019 22.881 0 0.400 0.475
## 59 0.650 0.016 41.263 0 0.619 0.681
## 60 0.603 0.017 36.484 0 0.571 0.635
## 61 0.345 0.012 29.129 0 0.322 0.369
## 62 0.221 0.010 22.549 0 0.201 0.240
## 63 1.000 0.000 NA NA 1.000 1.000
## 64 1.000 0.000 NA NA 1.000 1.000
## 65 1.000 0.000 NA NA 1.000 1.000
## 66 1.000 0.000 NA NA 1.000 1.000
## 67 1.000 0.000 NA NA 1.000 1.000
## 68 0.000 0.000 NA NA 0.000 0.000
## 69 0.000 0.000 NA NA 0.000 0.000
## 70 0.000 0.000 NA NA 0.000 0.000
## 71 0.000 0.000 NA NA 0.000 0.000
## 72 0.000 0.000 NA NA 0.000 0.000
## 73 0.000 0.000 NA NA 0.000 0.000
## 74 0.000 0.000 NA NA 0.000 0.000
## 75 0.000 0.000 NA NA 0.000 0.000
## 76 0.000 0.000 NA NA 0.000 0.000
## 77 0.000 0.000 NA NA 0.000 0.000
## 78 .p78. -1.174 0.034 -34.763 0 -1.241 -1.108
## 79 .p79. -0.817 0.024 -34.708 0 -0.863 -0.771
## 80 .p80. -1.219 0.029 -42.435 0 -1.275 -1.162
## 81 .p81. -1.232 0.025 -49.133 0 -1.281 -1.183
## 82 .p82. -0.920 0.022 -42.656 0 -0.962 -0.878
## 83 .p83. -0.835 0.020 -41.603 0 -0.874 -0.796
## 84 .p84. -0.963 0.024 -40.625 0 -1.009 -0.916
## 85 .p85. -1.062 0.029 -36.449 0 -1.119 -1.005
## 86 .p86. -0.850 0.020 -42.299 0 -0.890 -0.811
## 87 .p87. -1.007 0.025 -40.427 0 -1.056 -0.959
## 88 .p88. -1.385 0.032 -43.176 0 -1.447 -1.322
## 89 .p89. -1.140 0.032 -35.487 0 -1.203 -1.077
## 90 .p90. -0.471 0.019 -25.165 0 -0.508 -0.435
## [ reached 'max' / getOption("max.print") -- omitted 114 rows ]
tests<-lavTestLRT(configural, metric2, scalar2, chc.bifactor)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 180.83120 204.16843 53.20924
dfd=tests[2:4,"Df diff"]
dfd
## [1] 34 13 5
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.03768129 0.06953324 0.05630361
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.03237787 0.04317091
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.06129601 0.07809757
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.04320978 0.07044331
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
## 1.000 1.000 1.000 0.971 0.022 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 0.797 0.353 0.003 0.000
tests<-lavTestLRT(configural, metric2, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 180.8312 706.3221
dfd=tests[2:3,"Df diff"]
dfd
## [1] 34 15
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.03768129 0.12309791
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.03237787 0.04317091
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.1154357 0.1309140
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] 180.8312 204.1684 165.0430
dfd=tests[2:4,"Df diff"]
dfd
## [1] 34 13 20
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<- 2443 + 3642 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.03768129 0.06953324 0.04883031
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.03237787 0.04317091
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.06129601 0.07809757
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.04208516 0.05585526
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
## 1.000 1.000 1.000 0.971 0.022 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 0.405 0.004 0.000 0.000
bf.age <-'
english =~ Stest19disguisedwords + Stest20spelling + Stest21capitalization + Stest22punctuation + Stest23english + Stest24expression + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g=~ Stest1vocab + Stest5math + 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 + Stest31abstractreasoning + Stest34arithcomputation
math =~ Stest5math + Stest25wordfunctions + Stest32arithreasoning + Stest33highschoolmath + Stest34arithcomputation
speed =~ Stest34arithcomputation + Stest35tablereading + Stest36clericalchecking + Stest37objectinspection
spatial =~ Stest28mechanicalreasoning + Stest29visualization2D + Stest30visualization3D + Stest31abstractreasoning + Stest37objectinspection
g=~ Stest1vocab + Stest5math + 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=~Stest28mechanicalreasoning", "g=~Stest19disguisedwords", "spatial=~Stest28mechanicalreasoning", "Stest28mechanicalreasoning~1", "Stest1vocab~1"))
fitMeasures(sem.age, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 3099.933 386.000 0.000 0.952 0.048 0.055
## ecvi aic bic
## 0.547 290766.407 291531.756
Mc(sem.age)
## [1] 0.800084
summary(sem.age, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 56 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 171
## Number of equality constraints 57
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3099.933 2749.649
## Degrees of freedom 386 386
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.127
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1348.770 1196.362
## 1 1751.164 1553.287
##
## 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.) 0.100 0.014 7.120 0.000 0.073
## Stst20s (.p2.) 0.346 0.017 20.506 0.000 0.313
## Stst21c (.p3.) 0.260 0.014 18.894 0.000 0.233
## Stst22p (.p4.) 0.300 0.014 20.889 0.000 0.271
## Stst23n (.p5.) 0.310 0.017 18.353 0.000 0.277
## Stst24x (.p6.) 0.220 0.018 11.903 0.000 0.184
## Stst31b (.p7.) 0.091 0.018 4.934 0.000 0.055
## Stst34r (.p8.) 0.225 0.023 9.655 0.000 0.179
## math =~
## Stst5mt (.p9.) 0.274 0.016 17.100 0.000 0.243
## Stst25w (.10.) 0.131 0.015 8.982 0.000 0.102
## Stst32r (.11.) 0.210 0.014 15.545 0.000 0.184
## Stst33h (.12.) 0.313 0.017 18.066 0.000 0.279
## Stst34r (.13.) 0.268 0.022 12.344 0.000 0.225
## speed =~
## Stst34r (.14.) 0.448 0.019 23.885 0.000 0.411
## Stst35t (.15.) 0.942 0.027 35.299 0.000 0.890
## Stst36c (.16.) 0.856 0.018 48.925 0.000 0.822
## Stst37b (.17.) 0.726 0.018 40.762 0.000 0.691
## spatial =~
## Stst28m 0.383 0.020 19.361 0.000 0.344
## Sts292D (.19.) 0.465 0.017 28.150 0.000 0.433
## Sts303D (.20.) 0.418 0.014 29.613 0.000 0.390
## Stst31b (.21.) 0.399 0.016 25.533 0.000 0.369
## Stst37b (.22.) 0.249 0.017 14.801 0.000 0.216
## g =~
## Stst1vc (.23.) 0.803 0.011 73.502 0.000 0.782
## Stst5mt (.24.) 0.599 0.013 47.130 0.000 0.574
## Stst19d 0.574 0.016 36.428 0.000 0.543
## Stst20s (.26.) 0.594 0.012 49.462 0.000 0.571
## Stst21c (.27.) 0.683 0.011 62.085 0.000 0.661
## Stst22p (.28.) 0.748 0.011 65.697 0.000 0.726
## Stst23n (.29.) 0.769 0.013 59.210 0.000 0.744
## Stst24x (.30.) 0.613 0.013 46.055 0.000 0.587
## Stst25w (.31.) 0.475 0.011 41.764 0.000 0.452
## Stst26r (.32.) 0.899 0.010 90.227 0.000 0.880
## Stst28m 0.527 0.016 33.832 0.000 0.496
## Sts292D (.34.) 0.424 0.013 31.865 0.000 0.398
## Sts303D (.35.) 0.375 0.012 31.989 0.000 0.352
## Stst31b (.36.) 0.700 0.013 55.965 0.000 0.675
## Stst32r (.37.) 0.513 0.011 45.038 0.000 0.491
## Stst33h (.38.) 0.505 0.011 47.401 0.000 0.484
## Stst34r (.39.) 0.613 0.015 42.233 0.000 0.584
## Stst35t (.40.) 0.602 0.020 29.403 0.000 0.561
## Stst36c (.41.) 0.154 0.017 8.854 0.000 0.120
## Stst37b (.42.) 0.272 0.016 16.532 0.000 0.239
## ci.upper Std.lv Std.all
##
## 0.128 0.100 0.118
## 0.379 0.346 0.349
## 0.287 0.260 0.272
## 0.328 0.300 0.300
## 0.343 0.310 0.269
## 0.256 0.220 0.194
## 0.127 0.091 0.082
## 0.271 0.225 0.199
##
## 0.305 0.274 0.275
## 0.159 0.131 0.164
## 0.237 0.210 0.266
## 0.347 0.313 0.423
## 0.310 0.268 0.237
##
## 0.485 0.448 0.397
## 0.994 0.942 0.566
## 0.891 0.856 0.664
## 0.761 0.726 0.593
##
## 0.422 0.383 0.441
## 0.498 0.465 0.437
## 0.445 0.418 0.469
## 0.430 0.399 0.358
## 0.282 0.249 0.204
##
## 0.824 0.803 0.809
## 0.624 0.599 0.601
## 0.605 0.574 0.673
## 0.618 0.595 0.601
## 0.705 0.683 0.714
## 0.771 0.749 0.750
## 0.795 0.770 0.669
## 0.639 0.613 0.542
## 0.497 0.475 0.597
## 0.919 0.900 0.883
## 0.557 0.527 0.607
## 0.450 0.424 0.398
## 0.398 0.375 0.421
## 0.724 0.700 0.628
## 0.535 0.513 0.651
## 0.525 0.505 0.682
## 0.641 0.613 0.543
## 0.642 0.602 0.362
## 0.188 0.154 0.119
## 0.304 0.272 0.222
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age -0.024 0.015 -1.579 0.114 -0.054
## ci.upper Std.lv Std.all
##
## 0.006 -0.024 -0.035
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.76.) -1.001 0.017 -58.350 0.000 -1.034
## .Stst20s (.77.) -0.808 0.021 -38.964 0.000 -0.849
## .Stst21c (.78.) -1.165 0.018 -62.994 0.000 -1.201
## .Stst22p (.79.) -1.229 0.021 -59.715 0.000 -1.270
## .Stst23n (.80.) -1.059 0.024 -44.200 0.000 -1.106
## .Stst24x (.81.) -0.944 0.022 -42.836 0.000 -0.987
## .Stst31b (.82.) -1.073 0.023 -46.363 0.000 -1.118
## .Stst34r (.83.) -1.199 0.023 -52.172 0.000 -1.244
## .Stst5mt (.84.) -0.847 0.020 -41.512 0.000 -0.887
## .Stst25w (.85.) -0.801 0.014 -56.288 0.000 -0.829
## .Stst32r (.86.) -1.092 0.016 -66.207 0.000 -1.124
## .Stst33h (.87.) -0.844 0.016 -51.454 0.000 -0.876
## .Stst35t (.88.) -0.783 0.033 -24.054 0.000 -0.847
## .Stst36c (.89.) 0.017 0.026 0.636 0.525 -0.035
## .Stst37b (.90.) -0.272 0.025 -10.889 0.000 -0.320
## .Stst28m -0.712 0.019 -36.815 0.000 -0.750
## .Sts292D (.92.) -0.558 0.022 -25.340 0.000 -0.601
## .Sts303D (.93.) -0.697 0.018 -37.958 0.000 -0.733
## .Stst1vc -1.151 0.023 -50.325 0.000 -1.196
## .Stst26r (.95.) -1.286 0.023 -57.083 0.000 -1.330
## ci.upper Std.lv Std.all
## -0.967 -1.001 -1.173
## -0.767 -0.808 -0.816
## -1.129 -1.165 -1.218
## -1.189 -1.229 -1.231
## -1.012 -1.059 -0.919
## -0.900 -0.944 -0.834
## -1.027 -1.073 -0.962
## -1.154 -1.199 -1.062
## -0.807 -0.847 -0.850
## -0.773 -0.801 -1.007
## -1.059 -1.092 -1.384
## -0.812 -0.844 -1.139
## -0.720 -0.783 -0.471
## 0.068 0.017 0.013
## -0.223 -0.272 -0.222
## -0.674 -0.712 -0.820
## -0.515 -0.558 -0.524
## -0.661 -0.697 -0.782
## -1.106 -1.151 -1.159
## -1.242 -1.286 -1.262
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.388 0.014 27.262 0.000 0.360
## .Stest20spellng 0.507 0.019 26.873 0.000 0.470
## .Stest21cptlztn 0.380 0.016 24.464 0.000 0.350
## .Stest22puncttn 0.347 0.013 27.648 0.000 0.322
## .Stest23english 0.637 0.024 26.940 0.000 0.591
## .Stest24exprssn 0.855 0.025 33.654 0.000 0.805
## .Stst31bstrctrs 0.584 0.022 27.102 0.000 0.542
## .Stst34rthcmptt 0.576 0.031 18.863 0.000 0.516
## .Stest5math 0.560 0.021 26.118 0.000 0.518
## .Stst25wrdfnctn 0.391 0.012 32.024 0.000 0.367
## .Stst32rthrsnng 0.315 0.011 28.580 0.000 0.293
## .Stst33hghschlm 0.196 0.012 16.959 0.000 0.173
## .Stest35tblrdng 1.519 0.068 22.437 0.000 1.386
## .Stst36clrclchc 0.907 0.040 22.722 0.000 0.829
## .Stst37bjctnspc 0.835 0.034 24.411 0.000 0.768
## .Stst28mchnclrs 0.330 0.016 21.156 0.000 0.300
## .Stst29vslztn2D 0.737 0.026 27.997 0.000 0.685
## .Stst30vslztn3D 0.478 0.017 27.489 0.000 0.444
## .Stest1vocab 0.341 0.013 26.804 0.000 0.316
## .Stst26rdngcmpr 0.229 0.011 21.171 0.000 0.208
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.416 0.388 0.533
## 0.544 0.507 0.517
## 0.411 0.380 0.416
## 0.371 0.347 0.348
## 0.684 0.637 0.481
## 0.905 0.855 0.668
## 0.627 0.584 0.470
## 0.636 0.576 0.452
## 0.602 0.560 0.563
## 0.415 0.391 0.617
## 0.336 0.315 0.506
## 0.218 0.196 0.356
## 1.651 1.519 0.549
## 0.986 0.907 0.545
## 0.902 0.835 0.558
## 0.361 0.330 0.438
## 0.788 0.737 0.650
## 0.513 0.478 0.603
## 0.365 0.341 0.345
## 0.250 0.229 0.220
## 1.000 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 =~
## Stst19d (.p1.) 0.100 0.014 7.120 0.000 0.073
## Stst20s (.p2.) 0.346 0.017 20.506 0.000 0.313
## Stst21c (.p3.) 0.260 0.014 18.894 0.000 0.233
## Stst22p (.p4.) 0.300 0.014 20.889 0.000 0.271
## Stst23n (.p5.) 0.310 0.017 18.353 0.000 0.277
## Stst24x (.p6.) 0.220 0.018 11.903 0.000 0.184
## Stst31b (.p7.) 0.091 0.018 4.934 0.000 0.055
## Stst34r (.p8.) 0.225 0.023 9.655 0.000 0.179
## math =~
## Stst5mt (.p9.) 0.274 0.016 17.100 0.000 0.243
## Stst25w (.10.) 0.131 0.015 8.982 0.000 0.102
## Stst32r (.11.) 0.210 0.014 15.545 0.000 0.184
## Stst33h (.12.) 0.313 0.017 18.066 0.000 0.279
## Stst34r (.13.) 0.268 0.022 12.344 0.000 0.225
## speed =~
## Stst34r (.14.) 0.448 0.019 23.885 0.000 0.411
## Stst35t (.15.) 0.942 0.027 35.299 0.000 0.890
## Stst36c (.16.) 0.856 0.018 48.925 0.000 0.822
## Stst37b (.17.) 0.726 0.018 40.762 0.000 0.691
## spatial =~
## Stst28m 0.164 0.013 12.298 0.000 0.138
## Sts292D (.19.) 0.465 0.017 28.150 0.000 0.433
## Sts303D (.20.) 0.418 0.014 29.613 0.000 0.390
## Stst31b (.21.) 0.399 0.016 25.533 0.000 0.369
## Stst37b (.22.) 0.249 0.017 14.801 0.000 0.216
## g =~
## Stst1vc (.23.) 0.803 0.011 73.502 0.000 0.782
## Stst5mt (.24.) 0.599 0.013 47.130 0.000 0.574
## Stst19d 0.698 0.014 48.889 0.000 0.670
## Stst20s (.26.) 0.594 0.012 49.462 0.000 0.571
## Stst21c (.27.) 0.683 0.011 62.085 0.000 0.661
## Stst22p (.28.) 0.748 0.011 65.697 0.000 0.726
## Stst23n (.29.) 0.769 0.013 59.210 0.000 0.744
## Stst24x (.30.) 0.613 0.013 46.055 0.000 0.587
## Stst25w (.31.) 0.475 0.011 41.764 0.000 0.452
## Stst26r (.32.) 0.899 0.010 90.227 0.000 0.880
## Stst28m 0.334 0.012 28.529 0.000 0.311
## Sts292D (.34.) 0.424 0.013 31.865 0.000 0.398
## Sts303D (.35.) 0.375 0.012 31.989 0.000 0.352
## Stst31b (.36.) 0.700 0.013 55.965 0.000 0.675
## Stst32r (.37.) 0.513 0.011 45.038 0.000 0.491
## Stst33h (.38.) 0.505 0.011 47.401 0.000 0.484
## Stst34r (.39.) 0.613 0.015 42.233 0.000 0.584
## Stst35t (.40.) 0.602 0.020 29.403 0.000 0.561
## Stst36c (.41.) 0.154 0.017 8.854 0.000 0.120
## Stst37b (.42.) 0.272 0.016 16.532 0.000 0.239
## ci.upper Std.lv Std.all
##
## 0.128 0.100 0.105
## 0.379 0.346 0.354
## 0.287 0.260 0.261
## 0.328 0.300 0.304
## 0.343 0.310 0.278
## 0.256 0.220 0.199
## 0.127 0.091 0.082
## 0.271 0.225 0.194
##
## 0.305 0.274 0.267
## 0.159 0.131 0.166
## 0.237 0.210 0.270
## 0.347 0.313 0.433
## 0.310 0.268 0.231
##
## 0.485 0.448 0.387
## 0.994 0.942 0.581
## 0.891 0.856 0.663
## 0.761 0.726 0.630
##
## 0.191 0.164 0.264
## 0.498 0.465 0.457
## 0.445 0.418 0.519
## 0.430 0.399 0.359
## 0.282 0.249 0.216
##
## 0.824 0.803 0.828
## 0.624 0.599 0.584
## 0.726 0.698 0.729
## 0.618 0.594 0.608
## 0.705 0.683 0.684
## 0.771 0.749 0.760
## 0.795 0.770 0.690
## 0.639 0.613 0.555
## 0.497 0.475 0.602
## 0.919 0.900 0.892
## 0.356 0.334 0.536
## 0.450 0.424 0.417
## 0.398 0.375 0.466
## 0.724 0.700 0.629
## 0.535 0.513 0.660
## 0.525 0.505 0.698
## 0.641 0.613 0.529
## 0.642 0.602 0.371
## 0.188 0.154 0.119
## 0.304 0.272 0.236
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.016 0.013 1.266 0.206 -0.009
## ci.upper Std.lv Std.all
##
## 0.040 0.016 0.021
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.76.) -1.001 0.017 -58.350 0.000 -1.034
## .Stst20s (.77.) -0.808 0.021 -38.964 0.000 -0.849
## .Stst21c (.78.) -1.165 0.018 -62.994 0.000 -1.201
## .Stst22p (.79.) -1.229 0.021 -59.715 0.000 -1.270
## .Stst23n (.80.) -1.059 0.024 -44.200 0.000 -1.106
## .Stst24x (.81.) -0.944 0.022 -42.836 0.000 -0.987
## .Stst31b (.82.) -1.073 0.023 -46.363 0.000 -1.118
## .Stst34r (.83.) -1.199 0.023 -52.172 0.000 -1.244
## .Stst5mt (.84.) -0.847 0.020 -41.512 0.000 -0.887
## .Stst25w (.85.) -0.801 0.014 -56.288 0.000 -0.829
## .Stst32r (.86.) -1.092 0.016 -66.207 0.000 -1.124
## .Stst33h (.87.) -0.844 0.016 -51.454 0.000 -0.876
## .Stst35t (.88.) -0.783 0.033 -24.054 0.000 -0.847
## .Stst36c (.89.) 0.017 0.026 0.636 0.525 -0.035
## .Stst37b (.90.) -0.272 0.025 -10.889 0.000 -0.320
## .Stst28m -1.219 0.017 -70.460 0.000 -1.253
## .Sts292D (.92.) -0.558 0.022 -25.340 0.000 -0.601
## .Sts303D (.93.) -0.697 0.018 -37.958 0.000 -0.733
## .Stst1vc -1.391 0.023 -59.864 0.000 -1.436
## .Stst26r (.95.) -1.286 0.023 -57.083 0.000 -1.330
## english 0.854 0.061 14.117 0.000 0.736
## math -0.473 0.066 -7.132 0.000 -0.602
## speed 0.281 0.036 7.889 0.000 0.212
## spatial -0.768 0.046 -16.633 0.000 -0.858
## .g 0.069 0.031 2.190 0.029 0.007
## ci.upper Std.lv Std.all
## -0.967 -1.001 -1.046
## -0.767 -0.808 -0.827
## -1.129 -1.165 -1.167
## -1.189 -1.229 -1.248
## -1.012 -1.059 -0.948
## -0.900 -0.944 -0.854
## -1.027 -1.073 -0.964
## -1.154 -1.199 -1.035
## -0.807 -0.847 -0.826
## -0.773 -0.801 -1.017
## -1.059 -1.092 -1.404
## -0.812 -0.844 -1.167
## -0.720 -0.783 -0.484
## 0.068 0.017 0.013
## -0.223 -0.272 -0.236
## -1.185 -1.219 -1.959
## -0.515 -0.558 -0.548
## -0.661 -0.697 -0.866
## -1.345 -1.391 -1.433
## -1.242 -1.286 -1.275
## 0.973 0.854 0.854
## -0.343 -0.473 -0.473
## 0.351 0.281 0.281
## -0.677 -0.768 -0.768
## 0.130 0.069 0.069
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.419 0.012 35.138 0.000 0.395
## .Stest20spellng 0.482 0.015 31.208 0.000 0.452
## .Stest21cptlztn 0.462 0.013 34.514 0.000 0.436
## .Stest22puncttn 0.321 0.011 28.052 0.000 0.298
## .Stest23english 0.557 0.017 32.050 0.000 0.523
## .Stest24exprssn 0.798 0.022 37.092 0.000 0.755
## .Stst31bstrctrs 0.581 0.017 33.805 0.000 0.547
## .Stst34rthcmptt 0.641 0.029 22.388 0.000 0.585
## .Stest5math 0.617 0.017 35.729 0.000 0.583
## .Stst25wrdfnctn 0.379 0.010 36.627 0.000 0.359
## .Stst32rthrsnng 0.297 0.009 33.228 0.000 0.279
## .Stst33hghschlm 0.171 0.010 17.163 0.000 0.151
## .Stest35tblrdng 1.376 0.058 23.572 0.000 1.261
## .Stst36clrclchc 0.913 0.032 28.741 0.000 0.851
## .Stst37bjctnspc 0.666 0.027 24.600 0.000 0.613
## .Stst28mchnclrs 0.249 0.007 38.111 0.000 0.236
## .Stst29vslztn2D 0.639 0.021 30.776 0.000 0.598
## .Stst30vslztn3D 0.333 0.012 27.185 0.000 0.309
## .Stest1vocab 0.297 0.009 31.878 0.000 0.278
## .Stst26rdngcmpr 0.209 0.008 26.361 0.000 0.193
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.442 0.419 0.457
## 0.513 0.482 0.505
## 0.489 0.462 0.464
## 0.343 0.321 0.330
## 0.591 0.557 0.447
## 0.840 0.798 0.653
## 0.615 0.581 0.469
## 0.698 0.641 0.479
## 0.651 0.617 0.587
## 0.399 0.379 0.610
## 0.314 0.297 0.491
## 0.190 0.171 0.326
## 1.490 1.376 0.524
## 0.975 0.913 0.547
## 0.719 0.666 0.501
## 0.262 0.249 0.643
## 0.679 0.639 0.617
## 0.357 0.333 0.514
## 0.315 0.297 0.315
## 0.224 0.209 0.205
## 1.000 1.000 1.000
## 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=~Stest28mechanicalreasoning", "g=~Stest19disguisedwords", "spatial=~Stest28mechanicalreasoning", "Stest28mechanicalreasoning~1", "Stest1vocab~1"))
fitMeasures(sem.age2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr
## 3190.849 424.000 0.000 0.952 0.046 0.052
## ecvi aic bic
## 0.563 290716.957 291495.733
Mc(sem.age2)
## [1] 0.7966122
summary(sem.age2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 60 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 173
## Number of equality constraints 57
##
## Number of observations per group:
## 0 2443
## 1 3642
## Sampling weights variable BY_WTA
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3190.849 2834.475
## Degrees of freedom 424 424
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.126
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1396.433 1240.471
## 1 1794.416 1594.004
##
## 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.) 0.105 0.014 7.422 0.000 0.077
## Stst20s (.p2.) 0.346 0.017 20.590 0.000 0.313
## Stst21c (.p3.) 0.260 0.014 18.849 0.000 0.233
## Stst22p (.p4.) 0.299 0.014 20.785 0.000 0.271
## Stst23n (.p5.) 0.311 0.017 18.374 0.000 0.278
## Stst24x (.p6.) 0.220 0.019 11.862 0.000 0.183
## Stst31b (.p7.) 0.091 0.019 4.904 0.000 0.055
## Stst34r (.p8.) 0.226 0.023 9.689 0.000 0.180
## math =~
## Stst5mt (.p9.) 0.274 0.016 17.083 0.000 0.242
## Stst25w (.10.) 0.130 0.015 8.952 0.000 0.102
## Stst32r (.11.) 0.210 0.013 15.578 0.000 0.184
## Stst33h (.12.) 0.312 0.017 18.022 0.000 0.278
## Stst34r (.13.) 0.268 0.022 12.362 0.000 0.226
## speed =~
## Stst34r (.14.) 0.448 0.019 23.877 0.000 0.411
## Stst35t (.15.) 0.942 0.027 35.276 0.000 0.890
## Stst36c (.16.) 0.856 0.018 48.914 0.000 0.822
## Stst37b (.17.) 0.726 0.018 40.753 0.000 0.691
## spatial =~
## Stst28m 0.382 0.020 19.320 0.000 0.343
## Sts292D (.19.) 0.465 0.017 28.161 0.000 0.433
## Sts303D (.20.) 0.417 0.014 29.614 0.000 0.390
## Stst31b (.21.) 0.399 0.016 25.526 0.000 0.369
## Stst37b (.22.) 0.249 0.017 14.788 0.000 0.216
## g =~
## Stst1vc (.23.) 0.799 0.011 73.804 0.000 0.778
## Stst5mt (.24.) 0.596 0.013 47.356 0.000 0.572
## Stst19d 0.570 0.016 36.620 0.000 0.539
## Stst20s (.26.) 0.591 0.012 49.617 0.000 0.568
## Stst21c (.27.) 0.680 0.011 61.813 0.000 0.658
## Stst22p (.28.) 0.745 0.011 65.673 0.000 0.722
## Stst23n (.29.) 0.766 0.013 59.037 0.000 0.740
## Stst24x (.30.) 0.610 0.013 46.099 0.000 0.584
## Stst25w (.31.) 0.472 0.011 41.859 0.000 0.450
## Stst26r (.32.) 0.895 0.010 90.403 0.000 0.876
## Stst28m 0.525 0.015 34.018 0.000 0.494
## Sts292D (.34.) 0.422 0.013 31.891 0.000 0.396
## Sts303D (.35.) 0.373 0.012 31.999 0.000 0.350
## Stst31b (.36.) 0.697 0.012 56.015 0.000 0.672
## Stst32r (.37.) 0.511 0.011 45.189 0.000 0.488
## Stst33h (.38.) 0.502 0.011 47.640 0.000 0.482
## Stst34r (.39.) 0.610 0.014 42.294 0.000 0.582
## Stst35t (.40.) 0.599 0.020 29.417 0.000 0.559
## Stst36c (.41.) 0.153 0.017 8.860 0.000 0.119
## Stst37b (.42.) 0.271 0.016 16.552 0.000 0.238
## ci.upper Std.lv Std.all
##
## 0.133 0.105 0.123
## 0.379 0.346 0.349
## 0.288 0.260 0.272
## 0.327 0.299 0.299
## 0.344 0.311 0.269
## 0.256 0.220 0.194
## 0.127 0.091 0.081
## 0.272 0.226 0.200
##
## 0.305 0.274 0.274
## 0.159 0.130 0.163
## 0.237 0.210 0.266
## 0.346 0.312 0.421
## 0.311 0.268 0.237
##
## 0.485 0.448 0.396
## 0.994 0.942 0.566
## 0.890 0.856 0.664
## 0.761 0.726 0.593
##
## 0.421 0.382 0.439
## 0.497 0.465 0.437
## 0.445 0.417 0.468
## 0.430 0.399 0.358
## 0.282 0.249 0.203
##
## 0.821 0.807 0.810
## 0.621 0.602 0.603
## 0.600 0.575 0.673
## 0.615 0.597 0.602
## 0.701 0.686 0.716
## 0.767 0.752 0.751
## 0.791 0.773 0.670
## 0.636 0.616 0.544
## 0.495 0.477 0.598
## 0.915 0.904 0.884
## 0.555 0.530 0.609
## 0.448 0.426 0.400
## 0.396 0.377 0.423
## 0.721 0.703 0.630
## 0.533 0.515 0.652
## 0.523 0.507 0.683
## 0.638 0.616 0.544
## 0.639 0.604 0.363
## 0.187 0.155 0.120
## 0.303 0.273 0.223
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.004 0.017 0.269 0.788 -0.028
## age2 -0.049 0.008 -6.537 0.000 -0.064
## ci.upper Std.lv Std.all
##
## 0.037 0.004 0.006
## -0.035 -0.049 -0.138
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.79.) -0.940 0.021 -45.446 0.000 -0.980
## .Stst20s (.80.) -0.749 0.023 -32.137 0.000 -0.795
## .Stst21c (.81.) -1.097 0.022 -49.578 0.000 -1.141
## .Stst22p (.82.) -1.155 0.025 -46.471 0.000 -1.204
## .Stst23n (.83.) -0.983 0.028 -35.148 0.000 -1.037
## .Stst24x (.84.) -0.883 0.025 -35.697 0.000 -0.931
## .Stst31b (.85.) -1.003 0.026 -37.859 0.000 -1.055
## .Stst34r (.86.) -1.137 0.026 -43.901 0.000 -1.188
## .Stst5mt (.87.) -0.787 0.023 -33.562 0.000 -0.833
## .Stst25w (.88.) -0.754 0.017 -44.569 0.000 -0.787
## .Stst32r (.89.) -1.040 0.020 -53.092 0.000 -1.079
## .Stst33h (.90.) -0.794 0.019 -40.702 0.000 -0.832
## .Stst35t (.91.) -0.724 0.034 -21.355 0.000 -0.790
## .Stst36c (.92.) 0.032 0.026 1.222 0.222 -0.019
## .Stst37b (.93.) -0.244 0.025 -9.597 0.000 -0.294
## .Stst28m -0.660 0.022 -29.817 0.000 -0.703
## .Sts292D (.95.) -0.516 0.023 -22.103 0.000 -0.561
## .Sts303D (.96.) -0.659 0.020 -33.420 0.000 -0.698
## .Stst1vc -1.071 0.027 -39.480 0.000 -1.124
## .Stst26r (.98.) -1.198 0.028 -43.181 0.000 -1.252
## ci.upper Std.lv Std.all
## -0.899 -0.940 -1.100
## -0.703 -0.749 -0.756
## -1.054 -1.097 -1.145
## -1.106 -1.155 -1.154
## -0.928 -0.983 -0.852
## -0.834 -0.883 -0.779
## -0.951 -1.003 -0.898
## -1.087 -1.137 -1.006
## -0.741 -0.787 -0.789
## -0.721 -0.754 -0.946
## -1.002 -1.040 -1.316
## -0.755 -0.794 -1.069
## -0.658 -0.724 -0.435
## 0.083 0.032 0.025
## -0.194 -0.244 -0.200
## -0.616 -0.660 -0.758
## -0.470 -0.516 -0.484
## -0.621 -0.659 -0.740
## -1.017 -1.071 -1.075
## -1.143 -1.198 -1.171
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.388 0.014 27.282 0.000 0.360
## .Stest20spellng 0.507 0.019 26.853 0.000 0.470
## .Stest21cptlztn 0.381 0.016 24.465 0.000 0.350
## .Stest22puncttn 0.347 0.013 27.663 0.000 0.323
## .Stest23english 0.638 0.024 26.939 0.000 0.591
## .Stest24exprssn 0.855 0.025 33.672 0.000 0.805
## .Stst31bstrctrs 0.585 0.022 27.108 0.000 0.542
## .Stst34rthcmptt 0.575 0.031 18.848 0.000 0.515
## .Stest5math 0.560 0.021 26.106 0.000 0.518
## .Stst25wrdfnctn 0.391 0.012 32.021 0.000 0.367
## .Stst32rthrsnng 0.315 0.011 28.544 0.000 0.293
## .Stst33hghschlm 0.196 0.011 17.034 0.000 0.173
## .Stest35tblrdng 1.518 0.068 22.438 0.000 1.386
## .Stst36clrclchc 0.907 0.040 22.724 0.000 0.829
## .Stst37bjctnspc 0.835 0.034 24.412 0.000 0.768
## .Stst28mchnclrs 0.330 0.016 21.167 0.000 0.300
## .Stst29vslztn2D 0.736 0.026 27.997 0.000 0.685
## .Stst30vslztn3D 0.478 0.017 27.490 0.000 0.444
## .Stest1vocab 0.340 0.013 26.768 0.000 0.315
## .Stst26rdngcmpr 0.229 0.011 21.214 0.000 0.208
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.416 0.388 0.532
## 0.544 0.507 0.515
## 0.411 0.381 0.414
## 0.372 0.347 0.347
## 0.684 0.638 0.479
## 0.905 0.855 0.667
## 0.627 0.585 0.469
## 0.635 0.575 0.450
## 0.602 0.560 0.561
## 0.415 0.391 0.615
## 0.336 0.315 0.504
## 0.218 0.196 0.356
## 1.651 1.518 0.548
## 0.986 0.907 0.545
## 0.902 0.835 0.557
## 0.361 0.330 0.436
## 0.788 0.736 0.649
## 0.513 0.478 0.602
## 0.365 0.340 0.343
## 0.251 0.229 0.219
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 1.000 1.000
## 1.000 0.981 0.981
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english =~
## Stst19d (.p1.) 0.105 0.014 7.422 0.000 0.077
## Stst20s (.p2.) 0.346 0.017 20.590 0.000 0.313
## Stst21c (.p3.) 0.260 0.014 18.849 0.000 0.233
## Stst22p (.p4.) 0.299 0.014 20.785 0.000 0.271
## Stst23n (.p5.) 0.311 0.017 18.374 0.000 0.278
## Stst24x (.p6.) 0.220 0.019 11.862 0.000 0.183
## Stst31b (.p7.) 0.091 0.019 4.904 0.000 0.055
## Stst34r (.p8.) 0.226 0.023 9.689 0.000 0.180
## math =~
## Stst5mt (.p9.) 0.274 0.016 17.083 0.000 0.242
## Stst25w (.10.) 0.130 0.015 8.952 0.000 0.102
## Stst32r (.11.) 0.210 0.013 15.578 0.000 0.184
## Stst33h (.12.) 0.312 0.017 18.022 0.000 0.278
## Stst34r (.13.) 0.268 0.022 12.362 0.000 0.226
## speed =~
## Stst34r (.14.) 0.448 0.019 23.877 0.000 0.411
## Stst35t (.15.) 0.942 0.027 35.276 0.000 0.890
## Stst36c (.16.) 0.856 0.018 48.914 0.000 0.822
## Stst37b (.17.) 0.726 0.018 40.753 0.000 0.691
## spatial =~
## Stst28m 0.164 0.013 12.299 0.000 0.138
## Sts292D (.19.) 0.465 0.017 28.161 0.000 0.433
## Sts303D (.20.) 0.417 0.014 29.614 0.000 0.390
## Stst31b (.21.) 0.399 0.016 25.526 0.000 0.369
## Stst37b (.22.) 0.249 0.017 14.788 0.000 0.216
## g =~
## Stst1vc (.23.) 0.799 0.011 73.804 0.000 0.778
## Stst5mt (.24.) 0.596 0.013 47.356 0.000 0.572
## Stst19d 0.695 0.014 49.722 0.000 0.668
## Stst20s (.26.) 0.591 0.012 49.617 0.000 0.568
## Stst21c (.27.) 0.680 0.011 61.813 0.000 0.658
## Stst22p (.28.) 0.745 0.011 65.673 0.000 0.722
## Stst23n (.29.) 0.766 0.013 59.037 0.000 0.740
## Stst24x (.30.) 0.610 0.013 46.099 0.000 0.584
## Stst25w (.31.) 0.472 0.011 41.859 0.000 0.450
## Stst26r (.32.) 0.895 0.010 90.403 0.000 0.876
## Stst28m 0.332 0.012 28.502 0.000 0.309
## Sts292D (.34.) 0.422 0.013 31.891 0.000 0.396
## Sts303D (.35.) 0.373 0.012 31.999 0.000 0.350
## Stst31b (.36.) 0.697 0.012 56.015 0.000 0.672
## Stst32r (.37.) 0.511 0.011 45.189 0.000 0.488
## Stst33h (.38.) 0.502 0.011 47.640 0.000 0.482
## Stst34r (.39.) 0.610 0.014 42.294 0.000 0.582
## Stst35t (.40.) 0.599 0.020 29.417 0.000 0.559
## Stst36c (.41.) 0.153 0.017 8.860 0.000 0.119
## Stst37b (.42.) 0.271 0.016 16.552 0.000 0.238
## ci.upper Std.lv Std.all
##
## 0.133 0.105 0.110
## 0.379 0.346 0.355
## 0.288 0.260 0.261
## 0.327 0.299 0.304
## 0.344 0.311 0.279
## 0.256 0.220 0.199
## 0.127 0.091 0.082
## 0.272 0.226 0.195
##
## 0.305 0.274 0.267
## 0.159 0.130 0.165
## 0.237 0.210 0.271
## 0.346 0.312 0.432
## 0.311 0.268 0.232
##
## 0.485 0.448 0.387
## 0.994 0.942 0.582
## 0.890 0.856 0.663
## 0.761 0.726 0.630
##
## 0.191 0.164 0.264
## 0.497 0.465 0.457
## 0.445 0.417 0.519
## 0.430 0.399 0.359
## 0.282 0.249 0.216
##
## 0.821 0.801 0.827
## 0.621 0.598 0.584
## 0.722 0.697 0.728
## 0.615 0.593 0.607
## 0.701 0.681 0.683
## 0.767 0.746 0.759
## 0.791 0.767 0.688
## 0.636 0.611 0.554
## 0.495 0.474 0.601
## 0.915 0.897 0.891
## 0.355 0.333 0.535
## 0.448 0.423 0.416
## 0.396 0.374 0.465
## 0.721 0.698 0.628
## 0.533 0.512 0.659
## 0.523 0.504 0.697
## 0.638 0.611 0.528
## 0.639 0.600 0.371
## 0.187 0.154 0.119
## 0.303 0.271 0.235
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower
## g ~
## age 0.011 0.012 0.878 0.380 -0.013
## age2 -0.028 0.007 -4.156 0.000 -0.042
## ci.upper Std.lv Std.all
##
## 0.035 0.011 0.014
## -0.015 -0.028 -0.064
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## english ~~
## math 0.000 0.000
## speed 0.000 0.000
## spatial 0.000 0.000
## math ~~
## speed 0.000 0.000
## spatial 0.000 0.000
## speed ~~
## 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
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19d (.79.) -0.940 0.021 -45.446 0.000 -0.980
## .Stst20s (.80.) -0.749 0.023 -32.137 0.000 -0.795
## .Stst21c (.81.) -1.097 0.022 -49.578 0.000 -1.141
## .Stst22p (.82.) -1.155 0.025 -46.471 0.000 -1.204
## .Stst23n (.83.) -0.983 0.028 -35.148 0.000 -1.037
## .Stst24x (.84.) -0.883 0.025 -35.697 0.000 -0.931
## .Stst31b (.85.) -1.003 0.026 -37.859 0.000 -1.055
## .Stst34r (.86.) -1.137 0.026 -43.901 0.000 -1.188
## .Stst5mt (.87.) -0.787 0.023 -33.562 0.000 -0.833
## .Stst25w (.88.) -0.754 0.017 -44.569 0.000 -0.787
## .Stst32r (.89.) -1.040 0.020 -53.092 0.000 -1.079
## .Stst33h (.90.) -0.794 0.019 -40.702 0.000 -0.832
## .Stst35t (.91.) -0.724 0.034 -21.355 0.000 -0.790
## .Stst36c (.92.) 0.032 0.026 1.222 0.222 -0.019
## .Stst37b (.93.) -0.244 0.025 -9.597 0.000 -0.294
## .Stst28m -1.186 0.018 -64.354 0.000 -1.222
## .Sts292D (.95.) -0.516 0.023 -22.103 0.000 -0.561
## .Sts303D (.96.) -0.659 0.020 -33.420 0.000 -0.698
## .Stst1vc -1.313 0.027 -48.110 0.000 -1.366
## .Stst26r (.98.) -1.198 0.028 -43.181 0.000 -1.252
## english 0.851 0.060 14.079 0.000 0.732
## math -0.479 0.067 -7.175 0.000 -0.609
## speed 0.281 0.036 7.874 0.000 0.211
## spatial -0.770 0.046 -16.660 0.000 -0.861
## .g 0.021 0.039 0.528 0.597 -0.056
## ci.upper Std.lv Std.all
## -0.899 -0.940 -0.982
## -0.703 -0.749 -0.767
## -1.054 -1.097 -1.101
## -1.106 -1.155 -1.174
## -0.928 -0.983 -0.881
## -0.834 -0.883 -0.799
## -0.951 -1.003 -0.902
## -1.087 -1.137 -0.983
## -0.741 -0.787 -0.769
## -0.721 -0.754 -0.958
## -1.002 -1.040 -1.340
## -0.755 -0.794 -1.098
## -0.658 -0.724 -0.447
## 0.083 0.032 0.025
## -0.194 -0.244 -0.212
## -1.150 -1.186 -1.907
## -0.470 -0.516 -0.507
## -0.621 -0.659 -0.820
## -1.259 -1.313 -1.355
## -1.143 -1.198 -1.190
## 0.969 0.851 0.851
## -0.348 -0.479 -0.479
## 0.351 0.281 0.281
## -0.680 -0.770 -0.770
## 0.097 0.020 0.020
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower
## .Stst19dsgsdwrd 0.419 0.012 35.157 0.000 0.395
## .Stest20spellng 0.482 0.015 31.180 0.000 0.452
## .Stest21cptlztn 0.462 0.013 34.507 0.000 0.436
## .Stest22puncttn 0.321 0.011 28.072 0.000 0.299
## .Stest23english 0.557 0.017 32.050 0.000 0.523
## .Stest24exprssn 0.798 0.022 37.104 0.000 0.756
## .Stst31bstrctrs 0.581 0.017 33.807 0.000 0.547
## .Stst34rthcmptt 0.641 0.029 22.336 0.000 0.585
## .Stest5math 0.617 0.017 35.736 0.000 0.583
## .Stst25wrdfnctn 0.379 0.010 36.628 0.000 0.359
## .Stst32rthrsnng 0.297 0.009 33.211 0.000 0.279
## .Stst33hghschlm 0.171 0.010 17.254 0.000 0.152
## .Stest35tblrdng 1.376 0.058 23.570 0.000 1.261
## .Stst36clrclchc 0.913 0.032 28.742 0.000 0.851
## .Stst37bjctnspc 0.666 0.027 24.596 0.000 0.613
## .Stst28mchnclrs 0.249 0.007 38.103 0.000 0.236
## .Stst29vslztn2D 0.639 0.021 30.778 0.000 0.598
## .Stst30vslztn3D 0.333 0.012 27.195 0.000 0.309
## .Stest1vocab 0.297 0.009 31.852 0.000 0.278
## .Stst26rdngcmpr 0.209 0.008 26.343 0.000 0.193
## english 1.000 1.000
## math 1.000 1.000
## speed 1.000 1.000
## spatial 1.000 1.000
## .g 1.000 1.000
## ci.upper Std.lv Std.all
## 0.442 0.419 0.457
## 0.512 0.482 0.506
## 0.489 0.462 0.465
## 0.344 0.321 0.332
## 0.591 0.557 0.449
## 0.840 0.798 0.654
## 0.615 0.581 0.470
## 0.697 0.641 0.479
## 0.651 0.617 0.588
## 0.399 0.379 0.611
## 0.314 0.297 0.492
## 0.190 0.171 0.327
## 1.490 1.376 0.524
## 0.975 0.913 0.547
## 0.719 0.666 0.502
## 0.262 0.249 0.644
## 0.679 0.639 0.618
## 0.357 0.333 0.514
## 0.315 0.297 0.316
## 0.224 0.209 0.206
## 1.000 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