Sys.setenv(LANG = "en") # make R environment in english
require(haven)
require(srvyr)
require(tidyverse)
require(MASS)
require(MVN)
require(RVAideMemoire)
require(lavaan) # get SEM, CFA, MGCFA programs
require(leaps) # FactoMineR() doesn't seem to work without leaps installed or loaded
require(FactoMineR) # get PCA() function
require(nFactors) # get nScree() and parallel() functions
require(GPArotation) # get quartimax rotation
require(psych) # get fa.parallel() and VSS() functions
require(semPlot)
require(psy)
require(dplyr)
require(mice)
require(rms) # for rcs()
require(NlsyLinks)
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)$root)
l.min.tol
RMSEA.mintol<-sqrt(l.min.tol*G/((N-1)*df))
RMSEA.mintol
out<-c(l.min.tol,RMSEA.mintol)
names(out)<-c("ncp(T)","RMSEA.pop")
return(out)
}
d<-read_csv(file = "C:\\Users\\mh198\\OneDrive\\Documents\\Data\\NLSY\\NLSY79 IQ wage.csv")
## Rows: 12686 Columns: 165
## ── Column specification ───────────────────────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (165): E5780100, E5780200, E5780300, E5780400, E5780500, E5780600, E5780700, E5780800, E578...
##
## â„ą Use `spec()` to retrieve the full column specification for this data.
## â„ą Specify the column types or set `show_col_types = FALSE` to quiet this message.
d$weight2000<- d$R7006200
d$sweight<- d$R0614600
d$cweight<- d$R0614601
d$asvabweight<- d$R0614700
sum(d$sweight == 0)
## [1] 491
sum(d$cweight == 0)
## [1] 6794
cor(d$sweight, d$cweight)
## [1] 0.7864714
cor(d$sweight, d$asvabweight)
## [1] 0.9439677
# R0214700 has no white category, the value 3 indicates the respondent is neither hispanic nor black
d$bhw<- rep(NA)
d$bhw[d$R0214700==2] <- 1
d$bhw[d$R0214700==1] <- 2
d$bhw[d$R0214700==3] <- 3
d$bw<- rep(NA)
d$bw[d$R0214700==2] <- 0
d$bw[d$R0214700==3] <- 1
d<- d %>% mutate(nonwhite = case_when(
R0009600==0 ~ 1, # none
R0009600==2 ~ 1, # chinese
R0009600==4 ~ 1, # filipino
R0009600==8 ~ 1, # hawaiian
R0009600==9 ~ 1, # native american
R0009600==10 ~ 1, # asian indian
R0009600==13 ~ 1, # japanese
R0009600==14 ~ 1, # korean
R0009600==26 ~ 1, # vietnamese
R0009600==28 ~ 1)) # others
d$id<-d$R0000100
d$hhid<-d$R0000149
d$momeduc<-ifelse(d$R0006500 < 0, NA, d$R0006500)
d$dadeduc<-ifelse(d$R0007900 < 0, NA, d$R0007900)
d$pareduc<- rowMeans(d[, c("momeduc", "dadeduc")], na.rm = TRUE)
d$educ2000<- ifelse(d$R7007300 < 0, NA, d$R7007300)
d$sex<-d$R0214800-1 # where 0 is male 1 is female
d$age<-d$R0000600-18
d$age2<- d$age^2
d$agesex<-d$sex*d$age
d$agesex2<- d$agesex^2
d$age14<- as.numeric(d$R0000600==14)
d$age15<- as.numeric(d$R0000600==15)
d$age16<- as.numeric(d$R0000600==16)
d$age17<- as.numeric(d$R0000600==17)
d$age18<- as.numeric(d$R0000600==18)
d$age19<- as.numeric(d$R0000600==19)
d$age20<- as.numeric(d$R0000600==20)
d$age21<- as.numeric(d$R0000600==21)
d$age22<- as.numeric(d$R0000600==22)
d$ssgs <- ifelse(d$R0615000 < 0, NA, d$R0615000)
d$ssar <- ifelse(d$R0615100 < 0, NA, d$R0615100)
d$sswk <- ifelse(d$R0615200 < 0, NA, d$R0615200)
d$sspc <- ifelse(d$R0615300 < 0, NA, d$R0615300)
d$ssno <- ifelse(d$R0615400 < 0, NA, d$R0615400)
d$sscs <- ifelse(d$R0615500 < 0, NA, d$R0615500)
d$ssasi <- ifelse(d$R0615600 < 0, NA, d$R0615600)
d$ssmk <- ifelse(d$R0615700 < 0, NA, d$R0615700)
d$ssmc <- ifelse(d$R0615800 < 0, NA, d$R0615800)
d$ssei <- ifelse(d$R0615900 < 0, NA, d$R0615900)
d$R0618301<- ifelse(d$R0618301 < 0, NA, d$R0618301)
d$afqtz<- scale(d$R0618301, center = TRUE, scale = TRUE)
d$afqt<- d$afqtz*15+100
cor(d$afqtz, d$afqt, use="pairwise.complete.obs", method="pearson")
## [,1]
## [1,] 1
d %>% as_survey_design(ids = id, weights = sweight) %>% group_by(sex) %>% summarise(MEAN = survey_mean(afqt, na.rm = TRUE), SD = survey_sd(afqt, na.rm = TRUE))
## # A tibble: 2 Ă— 4
## sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl>
## 1 0 104. 0.254 15.5
## 2 1 104. 0.242 14.7
datagroup <- dplyr::select(d, starts_with("ss"))
efa_fit = fa(datagroup[,1:10], nfactors=1, rotate="none", scores="Bartlett") # Bartlett necessary if the factor is used as dependent variable in a regression but here produces same numbers as the default "regression", also could use weight=datagroup$sweight but it didn't change the results
d$efa = efa_fit$scores[, 1]
d$efa<- d$efa*15+100
describeBy(d$efa)
## Warning in describeBy(d$efa): no grouping variable requested
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 11914 100 15.36 100.38 100.18 18.15 54.86 133.69 78.84 -0.11 -0.85 0.14
describeBy(d$afqt)
## Warning in describeBy(d$afqt): no grouping variable requested
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 11914 100 15 98.03 99.3 18.62 77.91 130.02 52.11 0.31 -1.11 0.14
cor(d$efa, d$afqt, use="pairwise.complete.obs", method="pearson")
## [,1]
## [1,] 0.9249239
datagroup<- na.omit(datagroup)
d_clean <- d %>% filter(sweight > 0) # summarise by subgroup doesn't work with weights if there are zero
d_survey_clean <- d_clean %>% as_survey_design(ids = id, weights = sweight)
survey_results <- d_survey_clean %>%
group_by(age, sex) %>%
summarise(
MEAN = survey_mean(efa, na.rm = TRUE),
SD = survey_sd(efa, na.rm = TRUE)
)
print(survey_results)
## # A tibble: 18 Ă— 5
## # Groups: age [9]
## age sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -4 0 98.6 0.759 14.5
## 2 -4 1 99.4 0.711 12.7
## 3 -3 0 103. 0.632 15.0
## 4 -3 1 98.9 0.571 12.8
## 5 -2 0 104. 0.636 15.3
## 6 -2 1 100. 0.556 12.6
## 7 -1 0 106. 0.658 14.9
## 8 -1 1 102. 0.561 12.9
## 9 0 0 106. 0.666 15.6
## 10 0 1 102. 0.565 13.4
## 11 1 0 108. 0.689 15.3
## 12 1 1 103. 0.603 13.8
## 13 2 0 111. 0.671 14.8
## 14 2 1 104. 0.620 13.4
## 15 3 0 110. 0.695 15.2
## 16 3 1 105. 0.608 13.7
## 17 4 0 110. 1.37 15.1
## 18 4 1 106. 1.16 11.9
describeBy(d$efa, d$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 5975 101.55 16.38 102.74 101.93 19.89 54.86 133.69 78.84 -0.19 -0.97 0.21
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 5939 98.44 14.09 98.68 98.57 16.32 54.86 130.66 75.8 -0.1 -0.73 0.18
d <- d %>% filter(!is.na(afqt)) # n=11914
d <- d %>% filter(!(nonwhite %in% c(1))) # remove cases that self-identify with a race/ethnicity other than black, white or hispanic, n=10918
d<- d %>% mutate(sibling = case_when(
R0000151>=6 & R0000151<=7 ~ 0, # brother and sister
R0000151==16 ~ 1, # cousin
R0000151>=26 & R0000151<=27 ~ 1, # brother/sister in law
R0000151==36 ~ 1, # other non relative
R0000151>=39 & R0000151<=40 ~ 1, # step brother/sister
R0000151>=52 & R0000151<=53 ~ 1, # foster brother/sister
R0000151>=59 & R0000151<=65 ~ 1)) # adopted, cousin, etc
nrow(d) # 10918
## [1] 10918
#d <- d %>% filter(!(R4521500 %in% c(1))) ## remove twins and triplets
#d <- d %>% mutate(across(starts_with("ss"), ~scale(.x, center = TRUE, scale = TRUE)))
d$ssno<- scale(d$ssno, center = TRUE, scale = TRUE)
d$sscs<- scale(d$sscs, center = TRUE, scale = TRUE)
dk<-d
d %>%
as_survey_design(ids = id, weights = sweight) %>%
group_by(sex) %>%
summarise(across(starts_with("ss"), list(MEAN = ~ survey_mean(.), SD = ~ survey_sd(.)),
.names = "{.col}_{.fn}")) %>%
pivot_longer(cols = starts_with("ss"), names_to = c(".value", "variable"), names_sep = "_")
## Warning: Expected 2 pieces. Additional pieces discarded in 10 rows [2, 5, 8, 11, 14, 17, 20, 23,
## 26, 29].
## # A tibble: 6 Ă— 12
## sex variable ssgs ssar sswk sspc ssno sscs ssasi ssmk ssmc ssei
## <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0 MEAN 16.4 18.4 25.5 10.4 0.0839 -0.0418 16.3 13.6 15.6 12.5
## 2 0 MEAN 0.0869 0.130 0.130 0.0593 0.0162 0.0161 0.0920 0.116 0.0920 0.0718
## 3 0 SD 5.29 7.54 8.11 3.60 0.967 0.937 5.59 6.59 5.49 4.37
## 4 1 MEAN 14.7 16.6 25.6 11.1 0.302 0.380 11.0 13.2 11.8 9.61
## 5 1 MEAN 0.0782 0.123 0.123 0.0527 0.0154 0.0157 0.0638 0.108 0.0756 0.0615
## 6 1 SD 4.65 7.00 7.64 3.28 0.928 0.940 3.76 6.13 4.31 3.58
# NORMALITY TEST
dblack<- subset(dk, bhw==1)
dwhite<- subset(dk, bhw==3)
datablack<- dplyr::select(dblack, starts_with("ss"))
datawhite<- dplyr::select(dwhite, starts_with("ss"))
mqqnorm(datablack, main = "Multi-normal Q-Q Plot")
## [1] 1836 911
mqqnorm(datawhite, main = "Multi-normal Q-Q Plot")
## [1] 1118 3799
mqqnorm(datagroup, main = "Multi-normal Q-Q Plot")
## [1] 1624 5291
mvn(data = datablack, mvnTest = "mardia")
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 2266.64009628387 0 NO
## 2 Mardia Kurtosis 7.22063301630499 5.17363929475323e-13 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling ssgs 13.9795 <0.001 NO
## 2 Anderson-Darling ssar 62.5313 <0.001 NO
## 3 Anderson-Darling sswk 15.1514 <0.001 NO
## 4 Anderson-Darling sspc 28.7517 <0.001 NO
## 5 Anderson-Darling ssno 3.5004 <0.001 NO
## 6 Anderson-Darling sscs 10.3566 <0.001 NO
## 7 Anderson-Darling ssasi 41.7441 <0.001 NO
## 8 Anderson-Darling ssmk 76.9507 <0.001 NO
## 9 Anderson-Darling ssmc 43.4728 <0.001 NO
## 10 Anderson-Darling ssei 35.0841 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## ssgs 2994 11.1295925 4.3875000 11.0000000 0.000000 25.000000 8.000000 14.0000000 0.38540936
## ssar 2994 11.4709419 5.1077914 10.0000000 0.000000 30.000000 8.000000 14.0000000 1.04113313
## sswk 2994 18.2321309 8.0379086 18.0000000 0.000000 35.000000 12.000000 24.0000000 0.17098981
## sspc 2994 7.9605878 3.5484970 8.0000000 0.000000 15.000000 5.000000 11.0000000 0.02888516
## ssno 2994 -0.4624243 0.9780054 -0.4846101 -2.736272 1.593847 -1.177429 0.2082090 0.01695172
## sscs 2994 -0.4952273 0.9395854 -0.4134647 -2.494567 2.500078 -1.245906 0.1811359 -0.04248575
## ssasi 2994 9.0845023 3.9480261 8.0000000 0.000000 25.000000 6.000000 11.0000000 0.86959273
## ssmk 2994 9.1686707 4.6889845 8.0000000 0.000000 25.000000 6.000000 11.0000000 1.09271693
## ssmc 2994 9.3326653 3.7531884 9.0000000 0.000000 25.000000 7.000000 11.0000000 0.88087552
## ssei 2994 7.5871743 3.4443574 7.0000000 0.000000 20.000000 5.000000 10.0000000 0.68646918
## Kurtosis
## ssgs -0.0839087
## ssar 1.0747015
## sswk -0.8296500
## sspc -0.9983582
## ssno -0.5549781
## sscs -0.5168196
## ssasi 0.8856102
## ssmk 0.9828757
## ssmc 1.0471244
## ssei 0.2876448
mvn(data = datawhite, mvnTest = "mardia")
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 3922.29814591995 0 NO
## 2 Mardia Kurtosis 7.57356303505293 3.64153152077051e-14 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling ssgs 24.0746 <0.001 NO
## 2 Anderson-Darling ssar 58.6086 <0.001 NO
## 3 Anderson-Darling sswk 195.7633 <0.001 NO
## 4 Anderson-Darling sspc 227.1347 <0.001 NO
## 5 Anderson-Darling ssno 42.8925 <0.001 NO
## 6 Anderson-Darling sscs 21.2531 <0.001 NO
## 7 Anderson-Darling ssasi 40.4712 <0.001 NO
## 8 Anderson-Darling ssmk 76.0697 <0.001 NO
## 9 Anderson-Darling ssmc 29.9868 <0.001 NO
## 10 Anderson-Darling ssei 32.5599 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## ssgs 6161 16.3905210 4.6302297 17.0000000 0.000000 25.000000 13.0000000 20.0000000 -0.32932101
## ssar 6161 18.5177731 7.0450119 18.0000000 1.000000 30.000000 13.0000000 25.0000000 -0.07617875
## sswk 6161 26.9009901 7.1039316 29.0000000 1.000000 35.000000 23.0000000 32.0000000 -1.07500497
## sspc 6161 11.2325921 3.1699609 12.0000000 0.000000 15.000000 10.0000000 14.0000000 -1.09930729
## ssno 6161 0.3009822 0.8994054 0.3814138 -2.736272 1.593847 -0.3114053 0.9876305 -0.47240273
## sscs 6161 0.3011659 0.9183528 0.3595161 -2.494567 2.500078 -0.2350845 0.8946566 -0.36095948
## ssasi 6161 14.6955040 5.2252006 14.0000000 0.000000 25.000000 11.0000000 19.0000000 0.09167924
## ssmk 6161 13.8805389 6.2191065 13.0000000 0.000000 25.000000 9.0000000 19.0000000 0.16202921
## ssmc 6161 14.6033112 5.0708054 14.0000000 0.000000 25.000000 11.0000000 19.0000000 0.01735101
## ssei 6161 11.8375264 4.0214596 12.0000000 0.000000 20.000000 9.0000000 15.0000000 -0.16635923
## Kurtosis
## ssgs -0.31350403
## ssar -1.08144547
## sswk 0.51822397
## sspc 0.58495264
## ssno -0.32573652
## sscs 0.08674834
## ssasi -0.82617255
## ssmk -1.10238320
## ssmc -0.81454486
## ssei -0.69895259
mvn(data = datagroup, mvnTest = "mardia")
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 5293.37990043677 0 NO
## 2 Mardia Kurtosis -0.735865642639813 0.461812468016037 YES
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling ssgs 36.4896 <0.001 NO
## 2 Anderson-Darling ssar 169.0011 <0.001 NO
## 3 Anderson-Darling sswk 210.0292 <0.001 NO
## 4 Anderson-Darling sspc 272.6056 <0.001 NO
## 5 Anderson-Darling ssno 49.8691 <0.001 NO
## 6 Anderson-Darling sscs 44.7109 <0.001 NO
## 7 Anderson-Darling ssasi 105.4991 <0.001 NO
## 8 Anderson-Darling ssmk 222.0899 <0.001 NO
## 9 Anderson-Darling ssmc 109.0926 <0.001 NO
## 10 Anderson-Darling ssei 75.8909 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew Kurtosis
## ssgs 11914 14.320631 5.253142 14 0 25 10 18 -0.08615219 -0.6257330
## ssar 11914 15.821303 7.222702 15 0 30 10 22 0.33542654 -0.9638784
## sswk 11914 23.554474 8.527227 25 0 35 17 31 -0.54412481 -0.7162933
## sspc 11914 9.944015 3.705358 11 0 15 7 13 -0.59653344 -0.6670781
## ssno 11914 31.728555 11.519421 32 0 50 24 40 -0.31092027 -0.5541453
## sscs 11914 42.192463 16.764929 44 0 84 32 54 -0.26701668 -0.2781619
## ssasi 11914 12.607437 5.548932 12 0 25 8 17 0.33518543 -0.6939238
## ssmk 11914 12.000671 6.174238 11 0 25 7 17 0.49615130 -0.7889924
## ssmc 11914 12.633121 5.297491 12 0 25 8 16 0.32689991 -0.7116053
## ssei 11914 10.184405 4.366969 10 0 20 7 14 0.13085884 -0.8024524
mvn(data = datablack, mvnTest = "hz", multivariatePlot = "qq", multivariateOutlierMethod = "quan")
## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 1.316072 0 NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling ssgs 13.9795 <0.001 NO
## 2 Anderson-Darling ssar 62.5313 <0.001 NO
## 3 Anderson-Darling sswk 15.1514 <0.001 NO
## 4 Anderson-Darling sspc 28.7517 <0.001 NO
## 5 Anderson-Darling ssno 3.5004 <0.001 NO
## 6 Anderson-Darling sscs 10.3566 <0.001 NO
## 7 Anderson-Darling ssasi 41.7441 <0.001 NO
## 8 Anderson-Darling ssmk 76.9507 <0.001 NO
## 9 Anderson-Darling ssmc 43.4728 <0.001 NO
## 10 Anderson-Darling ssei 35.0841 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## ssgs 2994 11.1295925 4.3875000 11.0000000 0.000000 25.000000 8.000000 14.0000000 0.38540936
## ssar 2994 11.4709419 5.1077914 10.0000000 0.000000 30.000000 8.000000 14.0000000 1.04113313
## sswk 2994 18.2321309 8.0379086 18.0000000 0.000000 35.000000 12.000000 24.0000000 0.17098981
## sspc 2994 7.9605878 3.5484970 8.0000000 0.000000 15.000000 5.000000 11.0000000 0.02888516
## ssno 2994 -0.4624243 0.9780054 -0.4846101 -2.736272 1.593847 -1.177429 0.2082090 0.01695172
## sscs 2994 -0.4952273 0.9395854 -0.4134647 -2.494567 2.500078 -1.245906 0.1811359 -0.04248575
## ssasi 2994 9.0845023 3.9480261 8.0000000 0.000000 25.000000 6.000000 11.0000000 0.86959273
## ssmk 2994 9.1686707 4.6889845 8.0000000 0.000000 25.000000 6.000000 11.0000000 1.09271693
## ssmc 2994 9.3326653 3.7531884 9.0000000 0.000000 25.000000 7.000000 11.0000000 0.88087552
## ssei 2994 7.5871743 3.4443574 7.0000000 0.000000 20.000000 5.000000 10.0000000 0.68646918
## Kurtosis
## ssgs -0.0839087
## ssar 1.0747015
## sswk -0.8296500
## sspc -0.9983582
## ssno -0.5549781
## sscs -0.5168196
## ssasi 0.8856102
## ssmk 0.9828757
## ssmc 1.0471244
## ssei 0.2876448
mvn(data = datawhite, mvnTest = "hz", multivariatePlot = "qq", multivariateOutlierMethod = "quan")
## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 1.807967 0 NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling ssgs 24.0746 <0.001 NO
## 2 Anderson-Darling ssar 58.6086 <0.001 NO
## 3 Anderson-Darling sswk 195.7633 <0.001 NO
## 4 Anderson-Darling sspc 227.1347 <0.001 NO
## 5 Anderson-Darling ssno 42.8925 <0.001 NO
## 6 Anderson-Darling sscs 21.2531 <0.001 NO
## 7 Anderson-Darling ssasi 40.4712 <0.001 NO
## 8 Anderson-Darling ssmk 76.0697 <0.001 NO
## 9 Anderson-Darling ssmc 29.9868 <0.001 NO
## 10 Anderson-Darling ssei 32.5599 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## ssgs 6161 16.3905210 4.6302297 17.0000000 0.000000 25.000000 13.0000000 20.0000000 -0.32932101
## ssar 6161 18.5177731 7.0450119 18.0000000 1.000000 30.000000 13.0000000 25.0000000 -0.07617875
## sswk 6161 26.9009901 7.1039316 29.0000000 1.000000 35.000000 23.0000000 32.0000000 -1.07500497
## sspc 6161 11.2325921 3.1699609 12.0000000 0.000000 15.000000 10.0000000 14.0000000 -1.09930729
## ssno 6161 0.3009822 0.8994054 0.3814138 -2.736272 1.593847 -0.3114053 0.9876305 -0.47240273
## sscs 6161 0.3011659 0.9183528 0.3595161 -2.494567 2.500078 -0.2350845 0.8946566 -0.36095948
## ssasi 6161 14.6955040 5.2252006 14.0000000 0.000000 25.000000 11.0000000 19.0000000 0.09167924
## ssmk 6161 13.8805389 6.2191065 13.0000000 0.000000 25.000000 9.0000000 19.0000000 0.16202921
## ssmc 6161 14.6033112 5.0708054 14.0000000 0.000000 25.000000 11.0000000 19.0000000 0.01735101
## ssei 6161 11.8375264 4.0214596 12.0000000 0.000000 20.000000 9.0000000 15.0000000 -0.16635923
## Kurtosis
## ssgs -0.31350403
## ssar -1.08144547
## sswk 0.51822397
## sspc 0.58495264
## ssno -0.32573652
## sscs 0.08674834
## ssasi -0.82617255
## ssmk -1.10238320
## ssmc -0.81454486
## ssei -0.69895259
mvn(data = datagroup, mvnTest = "hz", multivariatePlot = "qq", multivariateOutlierMethod = "quan")
## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 1.859271 0 NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling ssgs 36.4896 <0.001 NO
## 2 Anderson-Darling ssar 169.0011 <0.001 NO
## 3 Anderson-Darling sswk 210.0292 <0.001 NO
## 4 Anderson-Darling sspc 272.6056 <0.001 NO
## 5 Anderson-Darling ssno 49.8691 <0.001 NO
## 6 Anderson-Darling sscs 44.7109 <0.001 NO
## 7 Anderson-Darling ssasi 105.4991 <0.001 NO
## 8 Anderson-Darling ssmk 222.0899 <0.001 NO
## 9 Anderson-Darling ssmc 109.0926 <0.001 NO
## 10 Anderson-Darling ssei 75.8909 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew Kurtosis
## ssgs 11914 14.320631 5.253142 14 0 25 10 18 -0.08615219 -0.6257330
## ssar 11914 15.821303 7.222702 15 0 30 10 22 0.33542654 -0.9638784
## sswk 11914 23.554474 8.527227 25 0 35 17 31 -0.54412481 -0.7162933
## sspc 11914 9.944015 3.705358 11 0 15 7 13 -0.59653344 -0.6670781
## ssno 11914 31.728555 11.519421 32 0 50 24 40 -0.31092027 -0.5541453
## sscs 11914 42.192463 16.764929 44 0 84 32 54 -0.26701668 -0.2781619
## ssasi 11914 12.607437 5.548932 12 0 25 8 17 0.33518543 -0.6939238
## ssmk 11914 12.000671 6.174238 11 0 25 7 17 0.49615130 -0.7889924
## ssmc 11914 12.633121 5.297491 12 0 25 8 16 0.32689991 -0.7116053
## ssei 11914 10.184405 4.366969 10 0 20 7 14 0.13085884 -0.8024524
dwhitem<- subset(dk, sex==0 & bhw==3)
dwhitef<- subset(dk, sex==1 & bhw==3)
datawhitem<- dplyr::select(dwhitem, starts_with("ss"))
datawhitef<- dplyr::select(dwhitef, starts_with("ss"))
mqqnorm(datawhitem, main = "Multi-normal Q-Q Plot")
## [1] 562 1895
mqqnorm(datawhitef, main = "Multi-normal Q-Q Plot")
## [1] 1039 956
mvn(data = datawhitem, mvnTest = "mardia")
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 2302.1409596443 0 NO
## 2 Mardia Kurtosis 11.0991151376095 0 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling ssgs 22.7194 <0.001 NO
## 2 Anderson-Darling ssar 40.8422 <0.001 NO
## 3 Anderson-Darling sswk 108.7868 <0.001 NO
## 4 Anderson-Darling sspc 99.3066 <0.001 NO
## 5 Anderson-Darling ssno 15.7588 <0.001 NO
## 6 Anderson-Darling sscs 10.6851 <0.001 NO
## 7 Anderson-Darling ssasi 40.9097 <0.001 NO
## 8 Anderson-Darling ssmk 45.4680 <0.001 NO
## 9 Anderson-Darling ssmc 30.9151 <0.001 NO
## 10 Anderson-Darling ssei 45.4217 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## ssgs 3094 17.18584357 4.8815964 18.0000000 1.000000 25.000000 14.0000000 21.0000000 -0.5414934
## ssar 3094 19.27925016 7.2242436 20.0000000 1.000000 30.000000 13.0000000 26.0000000 -0.2153913
## sswk 3094 26.66451196 7.4398062 29.0000000 1.000000 35.000000 23.0000000 32.0000000 -1.0835362
## sspc 3094 10.80607628 3.3852558 12.0000000 0.000000 15.000000 9.0000000 13.0000000 -0.9263760
## ssno 3094 0.18167408 0.9276262 0.2082090 -2.736272 1.593847 -0.3980077 0.9010281 -0.3981409
## sscs 3094 0.06955699 0.9060932 0.1514059 -2.494567 2.500078 -0.4729248 0.7162764 -0.3047979
## ssasi 3094 17.56367162 4.9874384 18.0000000 1.000000 25.000000 14.0000000 22.0000000 -0.6553983
## ssmk 3094 13.99547511 6.4515388 13.0000000 0.000000 25.000000 9.0000000 20.0000000 0.1545661
## ssmc 3094 16.53878474 5.0961288 17.0000000 0.000000 25.000000 13.0000000 21.0000000 -0.4267266
## ssei 3094 13.26470588 4.0674958 14.0000000 0.000000 20.000000 11.0000000 16.0000000 -0.6330201
## Kurtosis
## ssgs -0.15634130
## ssar -1.09662380
## sswk 0.42239473
## sspc 0.06419374
## ssno -0.41565716
## sscs -0.05418987
## ssasi -0.21015230
## ssmk -1.15911506
## ssmc -0.63766334
## ssei -0.27373198
mvn(data = datawhitef, mvnTest = "mardia")
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 2189.55223689514 5.21239256362515e-321 NO
## 2 Mardia Kurtosis 5.88517570047261 3.9763135006865e-09 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling ssgs 10.6312 <0.001 NO
## 2 Anderson-Darling ssar 21.5122 <0.001 NO
## 3 Anderson-Darling sswk 87.2707 <0.001 NO
## 4 Anderson-Darling sspc 120.1071 <0.001 NO
## 5 Anderson-Darling ssno 27.6213 <0.001 NO
## 6 Anderson-Darling sscs 11.0897 <0.001 NO
## 7 Anderson-Darling ssasi 11.7323 <0.001 NO
## 8 Anderson-Darling ssmk 32.4684 <0.001 NO
## 9 Anderson-Darling ssmc 10.7403 <0.001 NO
## 10 Anderson-Darling ssei 12.3650 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## ssgs 3067 15.5881969 4.2132836 16.0000000 0.000000 25.000000 13.00000000 19.000000 -0.223824802
## ssar 3067 17.7495924 6.7744312 18.0000000 2.000000 30.000000 12.00000000 23.000000 0.044765417
## sswk 3067 27.1395500 6.7409980 29.0000000 1.000000 35.000000 23.00000000 32.000000 -1.034766286
## sspc 3067 11.6628627 2.8739217 12.0000000 0.000000 15.000000 10.00000000 14.000000 -1.262123159
## ssno 3067 0.4213407 0.8534192 0.4680162 -2.649670 1.593847 -0.13820052 1.160835 -0.518285524
## sscs 3067 0.5348137 0.8703272 0.5973563 -2.316187 2.500078 0.06221577 1.132497 -0.437710800
## ssasi 3067 11.8020867 3.6173310 12.0000000 0.000000 23.000000 9.00000000 14.000000 0.135557410
## ssmk 3067 13.7645908 5.9742881 13.0000000 0.000000 25.000000 9.00000000 19.000000 0.161130374
## ssmc 3067 12.6507988 4.2270448 12.0000000 2.000000 25.000000 10.00000000 16.000000 0.188030513
## ssei 3067 10.3977828 3.4165432 10.0000000 1.000000 20.000000 8.00000000 13.000000 0.006430677
## Kurtosis
## ssgs -0.3366270
## ssar -1.0011772
## sswk 0.5179849
## sspc 1.2372973
## ssno -0.2680411
## sscs 0.3893419
## ssasi -0.1061248
## ssmk -1.0567015
## ssmc -0.4274462
## ssei -0.4650131
mvn(data = datawhitem, mvnTest = "hz", multivariatePlot = "qq", multivariateOutlierMethod = "quan")
## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 1.90853 0 NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling ssgs 22.7194 <0.001 NO
## 2 Anderson-Darling ssar 40.8422 <0.001 NO
## 3 Anderson-Darling sswk 108.7868 <0.001 NO
## 4 Anderson-Darling sspc 99.3066 <0.001 NO
## 5 Anderson-Darling ssno 15.7588 <0.001 NO
## 6 Anderson-Darling sscs 10.6851 <0.001 NO
## 7 Anderson-Darling ssasi 40.9097 <0.001 NO
## 8 Anderson-Darling ssmk 45.4680 <0.001 NO
## 9 Anderson-Darling ssmc 30.9151 <0.001 NO
## 10 Anderson-Darling ssei 45.4217 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## ssgs 3094 17.18584357 4.8815964 18.0000000 1.000000 25.000000 14.0000000 21.0000000 -0.5414934
## ssar 3094 19.27925016 7.2242436 20.0000000 1.000000 30.000000 13.0000000 26.0000000 -0.2153913
## sswk 3094 26.66451196 7.4398062 29.0000000 1.000000 35.000000 23.0000000 32.0000000 -1.0835362
## sspc 3094 10.80607628 3.3852558 12.0000000 0.000000 15.000000 9.0000000 13.0000000 -0.9263760
## ssno 3094 0.18167408 0.9276262 0.2082090 -2.736272 1.593847 -0.3980077 0.9010281 -0.3981409
## sscs 3094 0.06955699 0.9060932 0.1514059 -2.494567 2.500078 -0.4729248 0.7162764 -0.3047979
## ssasi 3094 17.56367162 4.9874384 18.0000000 1.000000 25.000000 14.0000000 22.0000000 -0.6553983
## ssmk 3094 13.99547511 6.4515388 13.0000000 0.000000 25.000000 9.0000000 20.0000000 0.1545661
## ssmc 3094 16.53878474 5.0961288 17.0000000 0.000000 25.000000 13.0000000 21.0000000 -0.4267266
## ssei 3094 13.26470588 4.0674958 14.0000000 0.000000 20.000000 11.0000000 16.0000000 -0.6330201
## Kurtosis
## ssgs -0.15634130
## ssar -1.09662380
## sswk 0.42239473
## sspc 0.06419374
## ssno -0.41565716
## sscs -0.05418987
## ssasi -0.21015230
## ssmk -1.15911506
## ssmc -0.63766334
## ssei -0.27373198
mvn(data = datawhitef, mvnTest = "hz", multivariatePlot = "qq", multivariateOutlierMethod = "quan")
## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 1.296356 0 NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling ssgs 10.6312 <0.001 NO
## 2 Anderson-Darling ssar 21.5122 <0.001 NO
## 3 Anderson-Darling sswk 87.2707 <0.001 NO
## 4 Anderson-Darling sspc 120.1071 <0.001 NO
## 5 Anderson-Darling ssno 27.6213 <0.001 NO
## 6 Anderson-Darling sscs 11.0897 <0.001 NO
## 7 Anderson-Darling ssasi 11.7323 <0.001 NO
## 8 Anderson-Darling ssmk 32.4684 <0.001 NO
## 9 Anderson-Darling ssmc 10.7403 <0.001 NO
## 10 Anderson-Darling ssei 12.3650 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## ssgs 3067 15.5881969 4.2132836 16.0000000 0.000000 25.000000 13.00000000 19.000000 -0.223824802
## ssar 3067 17.7495924 6.7744312 18.0000000 2.000000 30.000000 12.00000000 23.000000 0.044765417
## sswk 3067 27.1395500 6.7409980 29.0000000 1.000000 35.000000 23.00000000 32.000000 -1.034766286
## sspc 3067 11.6628627 2.8739217 12.0000000 0.000000 15.000000 10.00000000 14.000000 -1.262123159
## ssno 3067 0.4213407 0.8534192 0.4680162 -2.649670 1.593847 -0.13820052 1.160835 -0.518285524
## sscs 3067 0.5348137 0.8703272 0.5973563 -2.316187 2.500078 0.06221577 1.132497 -0.437710800
## ssasi 3067 11.8020867 3.6173310 12.0000000 0.000000 23.000000 9.00000000 14.000000 0.135557410
## ssmk 3067 13.7645908 5.9742881 13.0000000 0.000000 25.000000 9.00000000 19.000000 0.161130374
## ssmc 3067 12.6507988 4.2270448 12.0000000 2.000000 25.000000 10.00000000 16.000000 0.188030513
## ssei 3067 10.3977828 3.4165432 10.0000000 1.000000 20.000000 8.00000000 13.000000 0.006430677
## Kurtosis
## ssgs -0.3366270
## ssar -1.0011772
## sswk 0.5179849
## sspc 1.2372973
## ssno -0.2680411
## sscs 0.3893419
## ssasi -0.1061248
## ssmk -1.0567015
## ssmc -0.4274462
## ssei -0.4650131
dfullm<- subset(dk, sex==0)
dfullf<- subset(dk, sex==1)
datafullm<- dplyr::select(dfullm, starts_with("ss"))
datafullf<- dplyr::select(dfullf, starts_with("ss"))
mqqnorm(datafullm, main = "Multi-normal Q-Q Plot")
## [1] 736 2341
mqqnorm(datafullf, main = "Multi-normal Q-Q Plot")
## [1] 4423 1381
mvn(data = datafullm, mvnTest = "mardia")
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 2474.87778333186 0 NO
## 2 Mardia Kurtosis 2.69992921890835 0.0069354229573364 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling ssgs 25.6066 <0.001 NO
## 2 Anderson-Darling ssar 82.1725 <0.001 NO
## 3 Anderson-Darling sswk 107.1790 <0.001 NO
## 4 Anderson-Darling sspc 108.3298 <0.001 NO
## 5 Anderson-Darling ssno 15.6332 <0.001 NO
## 6 Anderson-Darling sscs 16.2744 <0.001 NO
## 7 Anderson-Darling ssasi 48.5724 <0.001 NO
## 8 Anderson-Darling ssmk 117.7090 <0.001 NO
## 9 Anderson-Darling ssmc 46.4374 <0.001 NO
## 10 Anderson-Darling ssei 49.8168 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## ssgs 5469 14.8816968 5.5995424 15.00000000 0.000000 25.000000 11.0000000 19.0000000 -0.170443464
## ssar 5469 16.3731944 7.4874109 15.00000000 0.000000 30.000000 10.0000000 23.0000000 0.247810262
## sswk 5469 23.2607424 8.8425860 25.00000000 0.000000 35.000000 17.0000000 31.0000000 -0.541274236
## sspc 5469 9.5258731 3.8203434 10.00000000 0.000000 15.000000 6.0000000 13.0000000 -0.448278169
## ssno 5469 -0.1147645 1.0039385 -0.05159814 -2.736272 1.593847 -0.8310196 0.6412209 -0.206562599
## sscs 5469 -0.2106656 0.9611496 -0.11616442 -2.494567 2.500078 -0.8296851 0.4784362 -0.164910391
## ssasi 5469 14.8299506 5.8952676 15.00000000 0.000000 25.000000 10.0000000 20.0000000 -0.152023273
## ssmk 5469 12.0501006 6.3309465 11.00000000 0.000000 25.000000 7.0000000 17.0000000 0.522992232
## ssmc 5469 14.1078808 5.6870075 14.00000000 0.000000 25.000000 9.0000000 19.0000000 0.002940784
## ssei 5469 11.3316877 4.6378015 12.00000000 0.000000 20.000000 8.0000000 15.0000000 -0.172415213
## Kurtosis
## ssgs -0.7532686
## ssar -1.0967571
## sswk -0.7953042
## sspc -0.8989933
## ssno -0.6209683
## sscs -0.3922488
## ssasi -0.9894640
## ssmk -0.8155823
## ssmc -0.9975137
## ssei -0.9446280
mvn(data = datafullf, mvnTest = "mardia")
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 2794.89854987819 0 NO
## 2 Mardia Kurtosis 0.812585556592171 0.416455715301972 YES
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling ssgs 15.3243 <0.001 NO
## 2 Anderson-Darling ssar 74.2353 <0.001 NO
## 3 Anderson-Darling sswk 85.1263 <0.001 NO
## 4 Anderson-Darling sspc 135.9202 <0.001 NO
## 5 Anderson-Darling ssno 30.8167 <0.001 NO
## 6 Anderson-Darling sscs 32.6009 <0.001 NO
## 7 Anderson-Darling ssasi 23.0705 <0.001 NO
## 8 Anderson-Darling ssmk 89.7146 <0.001 NO
## 9 Anderson-Darling ssmc 43.3883 <0.001 NO
## 10 Anderson-Darling ssei 30.8359 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## ssgs 5449 13.5966232 4.8268358 14.0000000 0.000000 25.000000 10.0000000 17.0000000 -0.06431556
## ssar 5449 15.0348688 6.8554856 14.0000000 0.000000 30.000000 9.0000000 20.0000000 0.44455878
## sswk 5449 23.6298403 8.3077771 25.0000000 0.000000 35.000000 17.0000000 31.0000000 -0.49370237
## sspc 5449 10.2780327 3.5711712 11.0000000 0.000000 15.000000 8.0000000 13.0000000 -0.71377382
## ssno 5449 0.1151857 0.9827361 0.2082090 -2.736272 1.593847 -0.5712124 0.9010281 -0.41323831
## sscs 5449 0.2114388 0.9936746 0.3595161 -2.494567 2.500078 -0.3540047 0.8351966 -0.42469524
## ssasi 5449 10.1367223 3.9416900 10.0000000 0.000000 23.000000 7.0000000 13.0000000 0.26289126
## ssmk 5449 11.8249220 5.9750303 11.0000000 0.000000 25.000000 7.0000000 16.0000000 0.48018621
## ssmc 5449 10.9427418 4.3022323 10.0000000 0.000000 25.000000 8.0000000 14.0000000 0.45501842
## ssei 5449 8.8537346 3.6843227 9.0000000 0.000000 20.000000 6.0000000 11.0000000 0.25437200
## Kurtosis
## ssgs -0.52108084
## ssar -0.75090205
## sswk -0.72724367
## sspc -0.41291365
## ssno -0.44056651
## sscs -0.01971192
## ssasi -0.20025521
## ssmk -0.75440722
## ssmc -0.18157957
## ssei -0.45930917
mvn(data = datafullm, mvnTest = "hz", multivariatePlot = "qq", multivariateOutlierMethod = "quan")
## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 1.759128 0 NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling ssgs 25.6066 <0.001 NO
## 2 Anderson-Darling ssar 82.1725 <0.001 NO
## 3 Anderson-Darling sswk 107.1790 <0.001 NO
## 4 Anderson-Darling sspc 108.3298 <0.001 NO
## 5 Anderson-Darling ssno 15.6332 <0.001 NO
## 6 Anderson-Darling sscs 16.2744 <0.001 NO
## 7 Anderson-Darling ssasi 48.5724 <0.001 NO
## 8 Anderson-Darling ssmk 117.7090 <0.001 NO
## 9 Anderson-Darling ssmc 46.4374 <0.001 NO
## 10 Anderson-Darling ssei 49.8168 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## ssgs 5469 14.8816968 5.5995424 15.00000000 0.000000 25.000000 11.0000000 19.0000000 -0.170443464
## ssar 5469 16.3731944 7.4874109 15.00000000 0.000000 30.000000 10.0000000 23.0000000 0.247810262
## sswk 5469 23.2607424 8.8425860 25.00000000 0.000000 35.000000 17.0000000 31.0000000 -0.541274236
## sspc 5469 9.5258731 3.8203434 10.00000000 0.000000 15.000000 6.0000000 13.0000000 -0.448278169
## ssno 5469 -0.1147645 1.0039385 -0.05159814 -2.736272 1.593847 -0.8310196 0.6412209 -0.206562599
## sscs 5469 -0.2106656 0.9611496 -0.11616442 -2.494567 2.500078 -0.8296851 0.4784362 -0.164910391
## ssasi 5469 14.8299506 5.8952676 15.00000000 0.000000 25.000000 10.0000000 20.0000000 -0.152023273
## ssmk 5469 12.0501006 6.3309465 11.00000000 0.000000 25.000000 7.0000000 17.0000000 0.522992232
## ssmc 5469 14.1078808 5.6870075 14.00000000 0.000000 25.000000 9.0000000 19.0000000 0.002940784
## ssei 5469 11.3316877 4.6378015 12.00000000 0.000000 20.000000 8.0000000 15.0000000 -0.172415213
## Kurtosis
## ssgs -0.7532686
## ssar -1.0967571
## sswk -0.7953042
## sspc -0.8989933
## ssno -0.6209683
## sscs -0.3922488
## ssasi -0.9894640
## ssmk -0.8155823
## ssmc -0.9975137
## ssei -0.9446280
mvn(data = datafullf, mvnTest = "hz", multivariatePlot = "qq", multivariateOutlierMethod = "quan")
## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 1.347076 0 NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling ssgs 15.3243 <0.001 NO
## 2 Anderson-Darling ssar 74.2353 <0.001 NO
## 3 Anderson-Darling sswk 85.1263 <0.001 NO
## 4 Anderson-Darling sspc 135.9202 <0.001 NO
## 5 Anderson-Darling ssno 30.8167 <0.001 NO
## 6 Anderson-Darling sscs 32.6009 <0.001 NO
## 7 Anderson-Darling ssasi 23.0705 <0.001 NO
## 8 Anderson-Darling ssmk 89.7146 <0.001 NO
## 9 Anderson-Darling ssmc 43.3883 <0.001 NO
## 10 Anderson-Darling ssei 30.8359 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## ssgs 5449 13.5966232 4.8268358 14.0000000 0.000000 25.000000 10.0000000 17.0000000 -0.06431556
## ssar 5449 15.0348688 6.8554856 14.0000000 0.000000 30.000000 9.0000000 20.0000000 0.44455878
## sswk 5449 23.6298403 8.3077771 25.0000000 0.000000 35.000000 17.0000000 31.0000000 -0.49370237
## sspc 5449 10.2780327 3.5711712 11.0000000 0.000000 15.000000 8.0000000 13.0000000 -0.71377382
## ssno 5449 0.1151857 0.9827361 0.2082090 -2.736272 1.593847 -0.5712124 0.9010281 -0.41323831
## sscs 5449 0.2114388 0.9936746 0.3595161 -2.494567 2.500078 -0.3540047 0.8351966 -0.42469524
## ssasi 5449 10.1367223 3.9416900 10.0000000 0.000000 23.000000 7.0000000 13.0000000 0.26289126
## ssmk 5449 11.8249220 5.9750303 11.0000000 0.000000 25.000000 7.0000000 16.0000000 0.48018621
## ssmc 5449 10.9427418 4.3022323 10.0000000 0.000000 25.000000 8.0000000 14.0000000 0.45501842
## ssei 5449 8.8537346 3.6843227 9.0000000 0.000000 20.000000 6.0000000 11.0000000 0.25437200
## Kurtosis
## ssgs -0.52108084
## ssar -0.75090205
## sswk -0.72724367
## sspc -0.41291365
## ssno -0.44056651
## sscs -0.01971192
## ssasi -0.20025521
## ssmk -0.75440722
## ssmc -0.18157957
## ssei -0.45930917
# NLSYLINKS
d<- dplyr::select(d, id, hhid, starts_with("ss"), afqt, efa, momeduc, dadeduc, pareduc, educ2000, age, sex, agesex, age2, agesex2, age14:age22, bhw, bw, sweight, weight2000, cweight, asvabweight, sibling)
dh <- d %>% group_by(hhid) %>% filter(n() == 1) %>% ungroup() # Keep cases with one count in hhid
dh %>% group_by(bhw, sex) %>% summarise(mean=mean(afqt), sd=sd(afqt))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 92.6 12.0
## 2 1 1 91.9 11.4
## 3 2 0 95.8 14.0
## 4 2 1 93.6 13.4
## 5 3 0 106. 14.4
## 6 3 1 106. 13.6
dh %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(afqt), SD = survey_sd(afqt))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 92.6 0.564 12.2
## 2 1 1 91.7 0.514 11.5
## 3 2 0 96.6 0.895 14.5
## 4 2 1 92.9 0.662 12.9
## 5 3 0 108. 0.441 14.2
## 6 3 1 106. 0.428 13.7
dh %>% group_by(bhw, sex) %>% summarise(mean=mean(efa), sd=sd(efa))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 93.0 13.5
## 2 1 1 90.6 11.2
## 3 2 0 96.4 16.1
## 4 2 1 91.0 14.2
## 5 3 0 110. 13.4
## 6 3 1 105. 11.9
dh %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(efa), SD = survey_sd(efa))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 92.5 0.631 13.7
## 2 1 1 90.2 0.500 11.2
## 3 2 0 97.0 1.02 16.6
## 4 2 1 90.3 0.746 14.1
## 5 3 0 111. 0.397 13.0
## 6 3 1 105. 0.358 11.5
links79<- subset(Links79PairExpanded, RelationshipPath == "Gen1Housemates")
links79$hhid<-links79$ExtendedID
links79<- dplyr::select(links79, hhid, RelationshipPath, R, RFull)
matching_indices<- match(d$hhid, links79$hhid)
d$R<- links79$R[matching_indices]
d<- subset(d, R==0.5)
nrow(d) # N=4410
## [1] 4410
result <- d %>% group_by(hhid) %>% summarise(identical_count = n()) %>% group_by(identical_count) %>% summarise(case_count = n())
print(result)
## # A tibble: 6 Ă— 2
## identical_count case_count
## <int> <int>
## 1 1 175
## 2 2 1211
## 3 3 421
## 4 4 109
## 5 5 18
## 6 6 4
d<- d %>% group_by(hhid) %>% filter(n() > 1) %>% ungroup() # remove cases with one count in hhid
d<- d %>% group_by(hhid) %>% filter(any(sex == 0) & any(sex == 1)) %>% ungroup() # retain hhid with 2 distinct sexes
nrow(d) # N=2586
## [1] 2586
result <- d %>% group_by(hhid) %>% summarise(identical_count = n()) %>% group_by(identical_count) %>% summarise(case_count = n())
print(result)
## # A tibble: 5 Ă— 2
## identical_count case_count
## <int> <int>
## 1 2 592
## 2 3 298
## 3 4 101
## 4 5 16
## 5 6 4
result <- d %>% group_by(hhid) %>% summarise(sex_distinct = n_distinct(sex)) %>% ungroup() # calculates the number of distinct values of sex within each group
result$all_same_sex <- result$sex_distinct == 1
result$all_same_sex # check if number of distinct sex = 1
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [16] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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## [ reached getOption("max.print") -- omitted 11 entries ]
# SELECTING HOUSEHOLDS WITH EQUAL NUMBER OF OPPOSITE SEX SIBLINGS
two<- d %>% group_by(hhid) %>% filter(n() == 2) %>% ungroup() # keep hhid with 2 members
# among cases sharing the same hhid value, if there are 2 individuals with sex=0 or sex=1, removes the youngest individual in the respective category.
three<- d %>% group_by(hhid) %>% filter(n() == 3) %>% ungroup() # keep hhid with 3 members
three <- three %>%
group_by(hhid, sex) %>%
arrange(desc(age)) %>%
filter(row_number() <= ifelse(n() == 2, 1, n())) %>%
arrange(hhid) %>%
ungroup()
four<- d %>% group_by(hhid) %>% filter(n() == 4) %>% ungroup() # keep hhid with 4 members
four <- four %>%
group_by(hhid, sex) %>%
arrange(desc(age)) %>%
filter(row_number() <= ifelse(n() == 3, 1, n())) %>%
arrange(hhid) %>%
ungroup()
# among cases sharing the same hhid value, if there are 4 same sex individuals then remove 3 of youngest individuals in the respective categories, if there are 3 same sex individuals then remove the 1 youngest individual in the respective categories.
five<- d %>% group_by(hhid) %>% filter(n() == 5) %>% ungroup() # keep hhid with 5 members
five <- five %>%
group_by(hhid, sex) %>%
arrange(desc(age)) %>%
filter(row_number() <= ifelse(n() == 3, 2, ifelse(n() == 4, 1, n()))) %>%
arrange(hhid) %>%
ungroup()
six<- d %>% group_by(hhid) %>% filter(n() == 6) %>% ungroup() # keep hhid with 6 members
six <- six %>%
group_by(hhid, sex) %>%
arrange(desc(age)) %>%
filter(row_number() <= ifelse(n() == 4, 2, ifelse(n() == 5, 1, n()))) %>%
arrange(hhid) %>%
ungroup()
d<- bind_rows(two, three, four, five, six) %>% arrange(id)
nrow(d) # N=2134
## [1] 2134
result <- d %>% group_by(hhid) %>% summarise(identical_count = n()) %>% group_by(identical_count) %>% summarise(case_count = n())
print(result)
## # A tibble: 3 Ă— 2
## identical_count case_count
## <int> <int>
## 1 2 957
## 2 4 52
## 3 6 2
result <- d %>% group_by(hhid) %>% summarise(sex_distinct = n_distinct(sex)) %>% ungroup() # calculates the number of distinct values of sex within each group
result$all_same_sex <- result$sex_distinct == 1
result$all_same_sex # check if number of distinct sex = 1
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [16] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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## [ reached getOption("max.print") -- omitted 11 entries ]
hist(d$age)
# DESCRIPTIVE STATS
describeBy(d$age, d$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1067 -0.53 2.07 -1 -0.58 2.97 -4 4 8 0.15 -0.84 0.06
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1067 -0.49 2.06 -1 -0.53 2.97 -4 4 8 0.12 -0.89 0.06
describeBy(dk$age, dk$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 5469 -0.18 2.34 0 -0.17 2.97 -4 4 8 0 -1.16 0.03
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 5449 -0.12 2.28 0 -0.09 2.97 -4 4 8 -0.06 -1.14 0.03
describeBy(d$pareduc, d$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1035 10.71 3.36 11.5 10.86 2.22 0 20 20 -0.5 0.4 0.1
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1043 10.57 3.4 11 10.76 2.97 0 19 19 -0.56 0.26 0.11
describeBy(dk$pareduc, dk$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 5249 10.9 3.28 11.5 11.08 2.22 0 20 20 -0.64 1.06 0.05
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 5304 10.77 3.26 11.5 10.96 2.22 0 20 20 -0.63 0.9 0.04
describeBy(d$momeduc, d$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1006 10.73 3.22 12 10.95 1.48 0 18 18 -0.78 0.83 0.1
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1016 10.65 3.27 12 10.84 2.97 0 19 19 -0.69 0.68 0.1
describeBy(dk$momeduc, dk$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 5083 10.95 3.18 12 11.16 1.48 0 20 20 -0.85 1.62 0.04
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 5172 10.8 3.16 12 11.02 1.48 0 20 20 -0.83 1.41 0.04
describeBy(d$dadeduc, d$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 943 10.74 4.08 12 10.9 2.97 0 20 20 -0.33 0.02 0.13
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 954 10.61 4.17 12 10.82 3.71 0 20 20 -0.42 0.01 0.14
describeBy(dk$dadeduc, dk$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 4674 11.02 3.92 12 11.17 2.97 0 20 20 -0.39 0.51 0.06
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 4678 10.9 3.95 12 11.07 2.97 0 20 20 -0.44 0.48 0.06
t.test(age ~ sex, data = d)
##
## Welch Two Sample t-test
##
## data: age by sex
## t = -0.50277, df = 2132, p-value = 0.6152
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## -0.2204563 0.1304844
## sample estimates:
## mean in group 0 mean in group 1
## -0.5313964 -0.4864105
t.test(age ~ sex, data = dk)
##
## Welch Two Sample t-test
##
## data: age by sex
## t = -1.4394, df = 10911, p-value = 0.1501
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## -0.1501208 0.0229964
## sample estimates:
## mean in group 0 mean in group 1
## -0.1824831 -0.1189209
t.test(pareduc ~ sex, data = d)
##
## Welch Two Sample t-test
##
## data: pareduc by sex
## t = 0.96146, df = 2075.9, p-value = 0.3364
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## -0.1482291 0.4333616
## sample estimates:
## mean in group 0 mean in group 1
## 10.71208 10.56951
t.test(pareduc ~ sex, data = dk)
##
## Welch Two Sample t-test
##
## data: pareduc by sex
## t = 2.0138, df = 10549, p-value = 0.04405
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## 0.003413779 0.252980279
## sample estimates:
## mean in group 0 mean in group 1
## 10.89922 10.77102
t.test(momeduc ~ sex, data = d)
##
## Welch Two Sample t-test
##
## data: momeduc by sex
## t = 0.58927, df = 2019.9, p-value = 0.5557
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## -0.1977636 0.3676576
## sample estimates:
## mean in group 0 mean in group 1
## 10.73062 10.64567
t.test(momeduc ~ sex, data = dk)
##
## Welch Two Sample t-test
##
## data: momeduc by sex
## t = 2.2978, df = 10248, p-value = 0.0216
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## 0.02113875 0.26663578
## sample estimates:
## mean in group 0 mean in group 1
## 10.94590 10.80201
t.test(dadeduc ~ sex, data = d)
##
## Welch Two Sample t-test
##
## data: dadeduc by sex
## t = 0.69215, df = 1894.8, p-value = 0.4889
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## -0.2405111 0.5028635
## sample estimates:
## mean in group 0 mean in group 1
## 10.74019 10.60901
t.test(dadeduc ~ sex, data = dk)
##
## Welch Two Sample t-test
##
## data: dadeduc by sex
## t = 1.4966, df = 9349.4, p-value = 0.1345
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## -0.03774794 0.28147110
## sample estimates:
## mean in group 0 mean in group 1
## 11.01712 10.89525
describeBy(d$educ2000, d$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 838 13.04 2.4 12 12.92 1.48 4 20 16 0.64 0.86 0.08
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 866 13.49 2.34 13 13.37 1.48 6 20 14 0.4 0.07 0.08
describeBy(dk$educ2000, dk$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 3482 13.06 2.49 12 12.95 1.48 1 20 19 0.47 0.96 0.04
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 3678 13.31 2.46 12 13.22 1.48 0 20 20 0.16 1.09 0.04
t.test(educ2000 ~ sex, data = dk)
##
## Welch Two Sample t-test
##
## data: educ2000 by sex
## t = -4.1832, df = 7128.7, p-value = 2.909e-05
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## -0.3593938 -0.1300388
## sample estimates:
## mean in group 0 mean in group 1
## 13.06088 13.30560
t.test(educ2000 ~ sex, data = d)
##
## Welch Two Sample t-test
##
## data: educ2000 by sex
## t = -3.9092, df = 1696.9, p-value = 9.623e-05
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## -0.6741527 -0.2236850
## sample estimates:
## mean in group 0 mean in group 1
## 13.04415 13.49307
# FACTOR ANALYSIS (fa uses "minres" by default while factanal uses "ml")
d %>% group_by(bhw, sex) %>% summarise(mean=mean(age), sd=sd(age))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 -0.512 2.00
## 2 1 1 -0.387 2.08
## 3 2 0 -0.673 1.98
## 4 2 1 -0.639 2.05
## 5 3 0 -0.489 2.15
## 6 3 1 -0.490 2.06
d %>% group_by(bhw, sex) %>% summarise(mean=mean(ssgs), sd=sd(ssgs))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 10.7 4.65
## 2 1 1 10.5 3.86
## 3 2 0 12.8 5.47
## 4 2 1 11.7 4.53
## 5 3 0 17.3 4.88
## 6 3 1 15.5 4.22
d %>% group_by(bhw, sex) %>% summarise(mean=mean(ssar), sd=sd(ssar))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 11.4 5.22
## 2 1 1 11.0 4.78
## 3 2 0 14.6 6.91
## 4 2 1 12.4 5.32
## 5 3 0 19.5 7.28
## 6 3 1 17.9 6.80
d %>% group_by(bhw, sex) %>% summarise(mean=mean(sswk), sd=sd(sswk))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 16.9 8.39
## 2 1 1 17.7 7.41
## 3 2 0 20.6 8.22
## 4 2 1 20.6 7.47
## 5 3 0 26.6 7.40
## 6 3 1 27.0 6.77
d %>% group_by(bhw, sex) %>% summarise(mean=mean(sspc), sd=sd(sspc))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 7.19 3.44
## 2 1 1 8.08 3.26
## 3 2 0 8.29 3.93
## 4 2 1 8.86 3.40
## 5 3 0 10.9 3.32
## 6 3 1 11.7 2.81
d %>% group_by(bhw, sex) %>% summarise(mean=mean(ssno), sd=sd(ssno))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 -0.664 0.919
## 2 1 1 -0.385 0.996
## 3 2 0 -0.293 0.977
## 4 2 1 -0.0710 0.972
## 5 3 0 0.173 0.912
## 6 3 1 0.433 0.870
d %>% group_by(bhw, sex) %>% summarise(mean=mean(sscs), sd=sd(sscs))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 -0.739 0.851
## 2 1 1 -0.324 0.948
## 3 2 0 -0.397 0.897
## 4 2 1 -0.0149 0.886
## 5 3 0 0.0177 0.857
## 6 3 1 0.564 0.852
d %>% group_by(bhw, sex) %>% summarise(mean=mean(ssasi), sd=sd(ssasi))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 10.1 4.08
## 2 1 1 7.60 2.91
## 3 2 0 12.9 5.64
## 4 2 1 8.36 3.48
## 5 3 0 17.3 4.95
## 6 3 1 11.5 3.49
d %>% group_by(bhw, sex) %>% summarise(mean=mean(ssmk), sd=sd(ssmk))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 8.93 4.78
## 2 1 1 9.29 4.78
## 3 2 0 11.0 6.13
## 4 2 1 9.96 5.38
## 5 3 0 14.6 6.66
## 6 3 1 14.3 6.24
d %>% group_by(bhw, sex) %>% summarise(mean=mean(ssmc), sd=sd(ssmc))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 9.81 4.16
## 2 1 1 8.40 2.86
## 3 2 0 13.0 5.26
## 4 2 1 9.25 3.65
## 5 3 0 16.6 5.09
## 6 3 1 12.6 4.03
d %>% group_by(bhw, sex) %>% summarise(mean=mean(ssei), sd=sd(ssei))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 7.97 3.81
## 2 1 1 6.51 2.54
## 3 2 0 9.41 4.36
## 4 2 1 7.27 3.15
## 5 3 0 13.1 4.13
## 6 3 1 10.0 3.15
d %>% group_by(bhw, sex) %>% summarise(mean=mean(afqt), sd=sd(afqt))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 89.7 11.3
## 2 1 1 90.2 10.2
## 3 2 0 95.6 14.0
## 4 2 1 93.9 12.3
## 5 3 0 107. 15.0
## 6 3 1 107. 14.0
d %>% group_by(bhw, sex) %>% summarise(mean=mean(efa), sd=sd(efa))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 88.3 12.7
## 2 1 1 88.1 10.6
## 3 2 0 95.7 15.6
## 4 2 1 92.2 12.0
## 5 3 0 109. 14.3
## 6 3 1 105. 12.0
d %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(age), SD = survey_sd(age))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 -0.385 0.132 2.12
## 2 1 1 -0.312 0.128 2.16
## 3 2 0 -0.604 0.162 2.06
## 4 2 1 -0.563 0.162 2.13
## 5 3 0 -0.240 0.106 2.21
## 6 3 1 -0.317 0.105 2.16
d %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(ssgs), SD = survey_sd(ssgs))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 10.7 0.287 4.76
## 2 1 1 10.6 0.228 3.95
## 3 2 0 12.8 0.447 5.69
## 4 2 1 11.9 0.348 4.64
## 5 3 0 17.9 0.210 4.54
## 6 3 1 16.1 0.190 4.10
d %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(ssar), SD = survey_sd(ssar))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 11.3 0.309 5.23
## 2 1 1 11.1 0.285 4.92
## 3 2 0 14.9 0.603 7.26
## 4 2 1 12.4 0.401 5.41
## 5 3 0 20.3 0.336 7.14
## 6 3 1 18.6 0.312 6.67
d %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(sswk), SD = survey_sd(sswk))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 16.8 0.505 8.51
## 2 1 1 17.8 0.435 7.56
## 3 2 0 20.9 0.654 8.37
## 4 2 1 20.7 0.567 7.62
## 5 3 0 27.6 0.309 6.72
## 6 3 1 28.0 0.286 6.25
d %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(sspc), SD = survey_sd(sspc))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 7.21 0.201 3.44
## 2 1 1 8.11 0.185 3.26
## 3 2 0 8.44 0.319 4.06
## 4 2 1 8.88 0.260 3.47
## 5 3 0 11.2 0.144 3.11
## 6 3 1 12.1 0.116 2.55
d %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(ssno), SD = survey_sd(ssno))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 -0.692 0.0534 0.910
## 2 1 1 -0.384 0.0560 0.991
## 3 2 0 -0.248 0.0764 0.991
## 4 2 1 -0.0350 0.0698 0.960
## 5 3 0 0.244 0.0415 0.886
## 6 3 1 0.511 0.0393 0.847
d %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(sscs), SD = survey_sd(sscs))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 -0.733 0.0497 0.848
## 2 1 1 -0.329 0.0559 0.965
## 3 2 0 -0.343 0.0809 0.947
## 4 2 1 0.0247 0.0630 0.870
## 5 3 0 0.0761 0.0399 0.841
## 6 3 1 0.629 0.0386 0.832
d %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(ssasi), SD = survey_sd(ssasi))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 10.0 0.240 4.09
## 2 1 1 7.58 0.176 2.99
## 3 2 0 12.9 0.448 5.79
## 4 2 1 8.40 0.251 3.44
## 5 3 0 17.8 0.221 4.74
## 6 3 1 11.7 0.159 3.41
d %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(ssmk), SD = survey_sd(ssmk))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 8.91 0.290 4.86
## 2 1 1 9.38 0.276 4.84
## 3 2 0 11.2 0.521 6.37
## 4 2 1 10.1 0.405 5.44
## 5 3 0 15.3 0.316 6.66
## 6 3 1 15.0 0.291 6.21
d %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(ssmc), SD = survey_sd(ssmc))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 9.82 0.239 4.12
## 2 1 1 8.46 0.169 2.92
## 3 2 0 13.1 0.402 5.32
## 4 2 1 9.42 0.269 3.66
## 5 3 0 17.1 0.231 4.94
## 6 3 1 12.9 0.187 3.99
d %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(ssei), SD = survey_sd(ssei))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 7.92 0.221 3.80
## 2 1 1 6.58 0.153 2.62
## 3 2 0 9.70 0.352 4.46
## 4 2 1 7.34 0.232 3.18
## 5 3 0 13.5 0.177 3.84
## 6 3 1 10.4 0.143 3.09
d %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(afqt), SD = survey_sd(afqt))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 89.7 0.681 11.5
## 2 1 1 90.4 0.608 10.5
## 3 2 0 96.4 1.23 14.8
## 4 2 1 94.2 0.946 12.6
## 5 3 0 108. 0.686 14.6
## 6 3 1 109. 0.636 13.6
d %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(efa), SD = survey_sd(efa))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 88.3 0.764 12.9
## 2 1 1 88.3 0.631 10.9
## 3 2 0 96.4 1.32 16.3
## 4 2 1 92.5 0.917 12.3
## 5 3 0 110. 0.615 13.3
## 6 3 1 106. 0.524 11.3
dk %>% group_by(bhw, sex) %>% summarise(mean=mean(age), sd=sd(age))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 -0.330 2.28
## 2 1 1 -0.273 2.23
## 3 2 0 -0.478 2.26
## 4 2 1 -0.377 2.28
## 5 3 0 -0.0275 2.37
## 6 3 1 0.0310 2.29
dk %>% group_by(bhw, sex) %>% summarise(mean=mean(ssgs), sd=sd(ssgs))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 11.4 4.70
## 2 1 1 10.8 4.03
## 3 2 0 12.7 5.46
## 4 2 1 11.4 4.77
## 5 3 0 17.2 4.88
## 6 3 1 15.6 4.21
dk %>% group_by(bhw, sex) %>% summarise(mean=mean(ssar), sd=sd(ssar))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 11.9 5.44
## 2 1 1 11.1 4.72
## 3 2 0 13.8 6.65
## 4 2 1 12.3 5.76
## 5 3 0 19.3 7.22
## 6 3 1 17.7 6.77
dk %>% group_by(bhw, sex) %>% summarise(mean=mean(sswk), sd=sd(sswk))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 17.9 8.38
## 2 1 1 18.6 7.67
## 3 2 0 20.4 8.63
## 4 2 1 20.0 8.31
## 5 3 0 26.7 7.44
## 6 3 1 27.1 6.74
dk %>% group_by(bhw, sex) %>% summarise(mean=mean(sspc), sd=sd(sspc))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 7.60 3.61
## 2 1 1 8.33 3.44
## 3 2 0 8.31 3.83
## 4 2 1 8.77 3.81
## 5 3 0 10.8 3.39
## 6 3 1 11.7 2.87
dk %>% group_by(bhw, sex) %>% summarise(mean=mean(ssno), sd=sd(ssno))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 -0.582 0.957
## 2 1 1 -0.342 0.984
## 3 2 0 -0.361 0.971
## 4 2 1 -0.175 1.01
## 5 3 0 0.182 0.928
## 6 3 1 0.421 0.853
dk %>% group_by(bhw, sex) %>% summarise(mean=mean(sscs), sd=sd(sscs))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 -0.691 0.879
## 2 1 1 -0.297 0.958
## 3 2 0 -0.376 0.920
## 4 2 1 -0.0522 1.02
## 5 3 0 0.0696 0.906
## 6 3 1 0.535 0.870
dk %>% group_by(bhw, sex) %>% summarise(mean=mean(ssasi), sd=sd(ssasi))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 10.4 4.41
## 2 1 1 7.76 2.87
## 3 2 0 12.8 5.63
## 4 2 1 8.38 3.76
## 5 3 0 17.6 4.99
## 6 3 1 11.8 3.62
dk %>% group_by(bhw, sex) %>% summarise(mean=mean(ssmk), sd=sd(ssmk))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 9.13 4.76
## 2 1 1 9.21 4.62
## 3 2 0 10.2 5.75
## 4 2 1 9.52 5.49
## 5 3 0 14.0 6.45
## 6 3 1 13.8 5.97
dk %>% group_by(bhw, sex) %>% summarise(mean=mean(ssmc), sd=sd(ssmc))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 10.2 4.26
## 2 1 1 8.49 2.93
## 3 2 0 12.3 5.33
## 4 2 1 9.17 3.75
## 5 3 0 16.5 5.10
## 6 3 1 12.7 4.23
dk %>% group_by(bhw, sex) %>% summarise(mean=mean(ssei), sd=sd(ssei))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 8.43 3.84
## 2 1 1 6.73 2.74
## 3 2 0 9.48 4.43
## 4 2 1 7.08 3.38
## 5 3 0 13.3 4.07
## 6 3 1 10.4 3.42
dk %>% group_by(bhw, sex) %>% summarise(mean=mean(afqt), sd=sd(afqt))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 90.7 11.5
## 2 1 1 90.9 10.8
## 3 2 0 94.7 13.4
## 4 2 1 93.6 12.9
## 5 3 0 106. 14.8
## 6 3 1 106. 13.8
dk %>% group_by(bhw, sex) %>% summarise(mean=mean(efa), sd=sd(efa))
## `summarise()` has grouped output by 'bhw'. You can override using the `.groups` argument.
## # A tibble: 6 Ă— 4
## # Groups: bhw [3]
## bhw sex mean sd
## <dbl> <dbl> <dbl> <dbl>
## 1 1 0 90.0 13.1
## 2 1 1 89.0 10.9
## 3 2 0 94.9 15.5
## 4 2 1 91.3 13.3
## 5 3 0 108. 14.3
## 6 3 1 105. 12.1
dk %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(age), SD = survey_sd(age))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 -0.371 0.0685 2.33
## 2 1 1 -0.271 0.0674 2.31
## 3 2 0 -0.448 0.0892 2.33
## 4 2 1 -0.287 0.0901 2.36
## 5 3 0 -0.214 0.0514 2.36
## 6 3 1 -0.219 0.0517 2.32
dk %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(ssgs), SD = survey_sd(ssgs))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 11.3 0.136 4.73
## 2 1 1 10.8 0.116 4.09
## 3 2 0 12.8 0.212 5.57
## 4 2 1 11.3 0.180 4.82
## 5 3 0 17.6 0.0970 4.62
## 6 3 1 15.8 0.0899 4.16
dk %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(ssar), SD = survey_sd(ssar))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 11.8 0.157 5.49
## 2 1 1 11.1 0.134 4.74
## 3 2 0 14.1 0.264 6.81
## 4 2 1 12.2 0.213 5.74
## 5 3 0 20.0 0.151 7.09
## 6 3 1 18.1 0.146 6.75
dk %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(sswk), SD = survey_sd(sswk))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 17.7 0.243 8.46
## 2 1 1 18.5 0.218 7.69
## 3 2 0 20.7 0.327 8.71
## 4 2 1 20.0 0.312 8.37
## 5 3 0 27.3 0.142 6.86
## 6 3 1 27.5 0.136 6.40
dk %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(sspc), SD = survey_sd(sspc))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 7.56 0.104 3.64
## 2 1 1 8.36 0.0970 3.45
## 3 2 0 8.47 0.146 3.87
## 4 2 1 8.74 0.142 3.84
## 5 3 0 11.1 0.0677 3.23
## 6 3 1 11.9 0.0588 2.77
dk %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(ssno), SD = survey_sd(ssno))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 -0.619 0.0270 0.955
## 2 1 1 -0.357 0.0274 0.981
## 3 2 0 -0.339 0.0384 0.993
## 4 2 1 -0.177 0.0388 1.03
## 5 3 0 0.253 0.0188 0.894
## 6 3 1 0.474 0.0178 0.830
dk %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(sscs), SD = survey_sd(sscs))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 -0.715 0.0243 0.868
## 2 1 1 -0.310 0.0267 0.954
## 3 2 0 -0.346 0.0356 0.932
## 4 2 1 -0.0577 0.0387 1.03
## 5 3 0 0.112 0.0190 0.886
## 6 3 1 0.555 0.0183 0.850
dk %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(ssasi), SD = survey_sd(ssasi))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 10.2 0.127 4.39
## 2 1 1 7.73 0.0816 2.87
## 3 2 0 12.9 0.217 5.73
## 4 2 1 8.39 0.143 3.79
## 5 3 0 17.8 0.102 4.80
## 6 3 1 11.8 0.0744 3.45
dk %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(ssmk), SD = survey_sd(ssmk))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 9.12 0.138 4.81
## 2 1 1 9.24 0.132 4.67
## 3 2 0 10.4 0.225 5.89
## 4 2 1 9.48 0.203 5.50
## 5 3 0 14.7 0.139 6.48
## 6 3 1 14.2 0.130 6.00
dk %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(ssmc), SD = survey_sd(ssmc))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 10.1 0.122 4.25
## 2 1 1 8.47 0.0824 2.92
## 3 2 0 12.5 0.204 5.39
## 4 2 1 9.07 0.138 3.72
## 5 3 0 16.9 0.104 4.92
## 6 3 1 12.7 0.0901 4.15
dk %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(ssei), SD = survey_sd(ssei))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 8.34 0.109 3.84
## 2 1 1 6.73 0.0779 2.74
## 3 2 0 9.62 0.174 4.52
## 4 2 1 7.08 0.130 3.42
## 5 3 0 13.6 0.0802 3.84
## 6 3 1 10.4 0.0722 3.34
dk %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(afqt), SD = survey_sd(afqt))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 90.7 0.334 11.6
## 2 1 1 91.0 0.315 11.0
## 3 2 0 95.4 0.530 13.8
## 4 2 1 93.5 0.469 12.8
## 5 3 0 107. 0.310 14.6
## 6 3 1 107. 0.298 13.8
dk %>% as_survey_design(ids = id, weights = sweight) %>% group_by(bhw, sex) %>% summarise(MEAN = survey_mean(efa), SD = survey_sd(efa))
## # A tibble: 6 Ă— 5
## # Groups: bhw [3]
## bhw sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 89.7 0.379 13.2
## 2 1 1 88.9 0.310 10.9
## 3 2 0 95.5 0.608 15.8
## 4 2 1 91.2 0.506 13.4
## 5 3 0 110. 0.282 13.5
## 6 3 1 106. 0.250 11.7
# full sibling sample
m<- subset(d, sex==0)
f<- subset(d, sex==1)
dm<- dplyr::select(m, starts_with("ss"), sweight)
df<- dplyr::select(f, starts_with("ss"), sweight)
ev <- eigen(cor(dm)) # get eigenvalues
ev$values
## [1] 7.5064649 0.8957738 0.6561243 0.4922016 0.3402431 0.2636506 0.2302194 0.1869160 0.1610041
## [10] 0.1439423 0.1234600
ev <- eigen(cor(df)) # get eigenvalues
ev$values
## [1] 6.9619283 0.8521744 0.6659142 0.5249446 0.4563668 0.3650880 0.3387081 0.2801558 0.2262488
## [10] 0.1783797 0.1500912
fa3<-fa(dm[,1:10], nfactors=3, rotate="promax", fm="minres")
fa3
## Factor Analysis using method = minres
## Call: fa(r = dm[, 1:10], nfactors = 3, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## ssgs 0.70 0.25 -0.01 0.83 0.17 1.3
## ssar 0.14 0.76 0.06 0.84 0.16 1.1
## sswk 0.63 0.16 0.19 0.83 0.17 1.3
## sspc 0.44 0.28 0.21 0.74 0.26 2.2
## ssno -0.06 0.08 0.87 0.78 0.22 1.0
## sscs 0.05 -0.05 0.82 0.68 0.32 1.0
## ssasi 1.04 -0.21 -0.01 0.77 0.23 1.1
## ssmk -0.07 0.96 0.02 0.85 0.15 1.0
## ssmc 0.76 0.13 0.00 0.74 0.26 1.1
## ssei 0.90 0.06 -0.04 0.84 0.16 1.0
##
## MR1 MR3 MR2
## SS loadings 3.98 2.15 1.77
## Proportion Var 0.40 0.22 0.18
## Cumulative Var 0.40 0.61 0.79
## Proportion Explained 0.50 0.27 0.22
## Cumulative Proportion 0.50 0.78 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.80 0.71
## MR3 0.80 1.00 0.78
## MR2 0.71 0.78 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 10.31 with Chi Square = 10948.52
## df of the model are 18 and the objective function was 0.24
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic n.obs is 1067 with the empirical chi square 24.37 with prob < 0.14
## The total n.obs was 1067 with Likelihood Chi Square = 252.42 with prob < 2.6e-43
##
## Tucker Lewis Index of factoring reliability = 0.946
## RMSEA index = 0.11 and the 90 % confidence intervals are 0.099 0.123
## BIC = 126.91
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.98 0.97 0.94
## Multiple R square of scores with factors 0.95 0.93 0.88
## Minimum correlation of possible factor scores 0.90 0.86 0.77
fa3<-fa(df[,1:10], nfactors=3, rotate="promax", fm="minres")
fa3
## Factor Analysis using method = minres
## Call: fa(r = df[, 1:10], nfactors = 3, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## ssgs 0.81 0.13 -0.03 0.80 0.20 1.1
## ssar 0.13 0.78 0.07 0.87 0.13 1.1
## sswk 0.84 -0.04 0.16 0.85 0.15 1.1
## sspc 0.65 -0.02 0.29 0.74 0.26 1.4
## ssno -0.12 0.21 0.80 0.74 0.26 1.2
## sscs 0.12 -0.09 0.77 0.64 0.36 1.1
## ssasi 0.68 0.08 0.00 0.56 0.44 1.0
## ssmk 0.14 0.69 0.09 0.76 0.24 1.1
## ssmc 0.45 0.40 -0.07 0.56 0.44 2.0
## ssei 0.74 0.12 -0.06 0.63 0.37 1.1
##
## MR1 MR3 MR2
## SS loadings 3.65 1.87 1.64
## Proportion Var 0.37 0.19 0.16
## Cumulative Var 0.37 0.55 0.72
## Proportion Explained 0.51 0.26 0.23
## Cumulative Proportion 0.51 0.77 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.78 0.69
## MR3 0.78 1.00 0.64
## MR2 0.69 0.64 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 8.14 with Chi Square = 8638.83
## df of the model are 18 and the objective function was 0.08
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.02
##
## The harmonic n.obs is 1067 with the empirical chi square 17.35 with prob < 0.5
## The total n.obs was 1067 with Likelihood Chi Square = 84.61 with prob < 1.3e-10
##
## Tucker Lewis Index of factoring reliability = 0.981
## RMSEA index = 0.059 and the 90 % confidence intervals are 0.047 0.072
## BIC = -40.89
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.97 0.95 0.92
## Multiple R square of scores with factors 0.94 0.90 0.85
## Minimum correlation of possible factor scores 0.87 0.80 0.70
fa4<-fa(dm[,1:10], nfactors=4, rotate="promax", fm="minres")
fa4
## Factor Analysis using method = minres
## Call: fa(r = dm[, 1:10], nfactors = 4, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR4 MR2 h2 u2 com
## ssgs 0.42 0.19 0.41 -0.05 0.83 0.166 2.4
## ssar 0.12 0.79 -0.01 0.06 0.86 0.143 1.1
## sswk 0.20 -0.03 0.76 0.07 0.93 0.072 1.2
## sspc 0.18 0.20 0.44 0.14 0.76 0.243 2.0
## ssno -0.05 0.14 0.07 0.73 0.74 0.262 1.1
## sscs 0.07 -0.05 -0.02 0.86 0.74 0.263 1.0
## ssasi 0.98 -0.15 0.00 0.03 0.81 0.192 1.1
## ssmk -0.05 0.93 -0.01 0.04 0.85 0.154 1.0
## ssmc 0.80 0.23 -0.16 0.05 0.80 0.202 1.3
## ssei 0.67 0.06 0.26 -0.04 0.83 0.173 1.3
##
## MR1 MR3 MR4 MR2
## SS loadings 2.91 2.07 1.58 1.58
## Proportion Var 0.29 0.21 0.16 0.16
## Cumulative Var 0.29 0.50 0.66 0.81
## Proportion Explained 0.36 0.25 0.19 0.19
## Cumulative Proportion 0.36 0.61 0.81 1.00
##
## With factor correlations of
## MR1 MR3 MR4 MR2
## MR1 1.00 0.75 0.79 0.64
## MR3 0.75 1.00 0.80 0.75
## MR4 0.79 0.80 1.00 0.71
## MR2 0.64 0.75 0.71 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 10.31 with Chi Square = 10948.52
## df of the model are 11 and the objective function was 0.04
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
##
## The harmonic n.obs is 1067 with the empirical chi square 2.58 with prob < 1
## The total n.obs was 1067 with Likelihood Chi Square = 39.88 with prob < 3.8e-05
##
## Tucker Lewis Index of factoring reliability = 0.989
## RMSEA index = 0.05 and the 90 % confidence intervals are 0.034 0.067
## BIC = -36.82
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR4 MR2
## Correlation of (regression) scores with factors 0.97 0.96 0.96 0.93
## Multiple R square of scores with factors 0.93 0.93 0.93 0.87
## Minimum correlation of possible factor scores 0.87 0.86 0.86 0.73
fa4<-fa(df[,1:10], nfactors=4, rotate="promax", fm="minres")
fa4
## Factor Analysis using method = minres
## Call: fa(r = df[, 1:10], nfactors = 4, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR4 MR2 h2 u2 com
## ssgs 0.60 0.15 0.27 -0.08 0.80 0.20 1.6
## ssar 0.02 0.72 0.19 0.04 0.84 0.16 1.2
## sswk 0.85 0.03 0.06 0.03 0.89 0.11 1.0
## sspc 0.61 0.06 0.07 0.20 0.75 0.25 1.3
## ssno 0.02 0.27 -0.08 0.67 0.68 0.32 1.3
## sscs 0.01 -0.13 0.09 0.88 0.73 0.27 1.1
## ssasi 0.17 -0.07 0.64 0.08 0.60 0.40 1.2
## ssmk 0.11 0.81 0.01 -0.01 0.81 0.19 1.0
## ssmc -0.09 0.27 0.63 0.01 0.62 0.38 1.4
## ssei 0.34 0.05 0.47 -0.02 0.64 0.36 1.9
##
## MR1 MR3 MR4 MR2
## SS loadings 2.26 1.83 1.81 1.46
## Proportion Var 0.23 0.18 0.18 0.15
## Cumulative Var 0.23 0.41 0.59 0.74
## Proportion Explained 0.31 0.25 0.25 0.20
## Cumulative Proportion 0.31 0.56 0.80 1.00
##
## With factor correlations of
## MR1 MR3 MR4 MR2
## MR1 1.00 0.75 0.81 0.71
## MR3 0.75 1.00 0.76 0.67
## MR4 0.81 0.76 1.00 0.59
## MR2 0.71 0.67 0.59 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 8.14 with Chi Square = 8638.83
## df of the model are 11 and the objective function was 0.01
##
## The root mean square of the residuals (RMSR) is 0
## The df corrected root mean square of the residuals is 0.01
##
## The harmonic n.obs is 1067 with the empirical chi square 1.29 with prob < 1
## The total n.obs was 1067 with Likelihood Chi Square = 9.36 with prob < 0.59
##
## Tucker Lewis Index of factoring reliability = 1.001
## RMSEA index = 0 and the 90 % confidence intervals are 0 0.028
## BIC = -67.34
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR4 MR2
## Correlation of (regression) scores with factors 0.96 0.95 0.92 0.92
## Multiple R square of scores with factors 0.93 0.90 0.85 0.85
## Minimum correlation of possible factor scores 0.86 0.80 0.70 0.70
fa3<-fa(dm[,1:10], nfactors=3, rotate="promax", fm="minres", weight=dm$sweight)
fa3
## Factor Analysis using method = minres
## Call: fa(r = dm[, 1:10], nfactors = 3, rotate = "promax", fm = "minres",
## weight = dm$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## ssgs 0.69 0.25 0.01 0.81 0.19 1.3
## ssar 0.13 0.72 0.10 0.83 0.17 1.1
## sswk 0.63 0.13 0.20 0.81 0.19 1.3
## sspc 0.44 0.23 0.26 0.72 0.28 2.2
## ssno -0.09 0.03 0.93 0.80 0.20 1.0
## sscs 0.04 -0.04 0.79 0.63 0.37 1.0
## ssasi 1.03 -0.21 -0.04 0.72 0.28 1.1
## ssmk -0.10 1.04 -0.02 0.90 0.10 1.0
## ssmc 0.78 0.14 -0.06 0.73 0.27 1.1
## ssei 0.93 0.00 -0.01 0.85 0.15 1.0
##
## MR1 MR3 MR2
## SS loadings 3.90 2.09 1.81
## Proportion Var 0.39 0.21 0.18
## Cumulative Var 0.39 0.60 0.78
## Proportion Explained 0.50 0.27 0.23
## Cumulative Proportion 0.50 0.77 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.77 0.70
## MR3 0.77 1.00 0.78
## MR2 0.70 0.78 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 9.88 with Chi Square = 10495.49
## df of the model are 18 and the objective function was 0.33
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic n.obs is 1067 with the empirical chi square 37.7 with prob < 0.0042
## The total n.obs was 1067 with Likelihood Chi Square = 345.11 with prob < 2.3e-62
##
## Tucker Lewis Index of factoring reliability = 0.922
## RMSEA index = 0.131 and the 90 % confidence intervals are 0.119 0.143
## BIC = 219.6
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.97 0.97 0.94
## Multiple R square of scores with factors 0.95 0.94 0.89
## Minimum correlation of possible factor scores 0.90 0.89 0.78
fa3<-fa(df[,1:10], nfactors=3, rotate="promax", fm="minres", weight=df$sweight)
fa3
## Factor Analysis using method = minres
## Call: fa(r = df[, 1:10], nfactors = 3, rotate = "promax", fm = "minres",
## weight = df$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## ssgs 0.82 0.14 -0.05 0.80 0.20 1.1
## ssar 0.12 0.80 0.05 0.88 0.12 1.1
## sswk 0.85 -0.05 0.16 0.85 0.15 1.1
## sspc 0.67 -0.01 0.26 0.72 0.28 1.3
## ssno -0.11 0.26 0.75 0.73 0.27 1.3
## sscs 0.09 -0.10 0.81 0.65 0.35 1.1
## ssasi 0.66 0.07 0.00 0.51 0.49 1.0
## ssmk 0.08 0.76 0.08 0.77 0.23 1.0
## ssmc 0.39 0.44 -0.07 0.54 0.46 2.0
## ssei 0.75 0.10 -0.07 0.62 0.38 1.1
##
## MR1 MR3 MR2
## SS loadings 3.53 2.01 1.54
## Proportion Var 0.35 0.20 0.15
## Cumulative Var 0.35 0.55 0.71
## Proportion Explained 0.50 0.28 0.22
## Cumulative Proportion 0.50 0.78 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.78 0.66
## MR3 0.78 1.00 0.63
## MR2 0.66 0.63 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 7.86 with Chi Square = 8346.61
## df of the model are 18 and the objective function was 0.08
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.02
##
## The harmonic n.obs is 1067 with the empirical chi square 18.11 with prob < 0.45
## The total n.obs was 1067 with Likelihood Chi Square = 86.2 with prob < 6.9e-11
##
## Tucker Lewis Index of factoring reliability = 0.979
## RMSEA index = 0.06 and the 90 % confidence intervals are 0.047 0.073
## BIC = -39.31
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.97 0.95 0.92
## Multiple R square of scores with factors 0.94 0.91 0.84
## Minimum correlation of possible factor scores 0.87 0.82 0.68
fa4<-fa(dm[,1:10], nfactors=4, rotate="promax", fm="minres", weight=dm$sweight)
fa4
## Factor Analysis using method = minres
## Call: fa(r = dm[, 1:10], nfactors = 4, rotate = "promax", fm = "minres",
## weight = dm$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR4 MR3 MR1 MR2 h2 u2 com
## ssgs 0.40 0.22 0.39 -0.05 0.82 0.1847 2.6
## ssar 0.12 0.77 -0.03 0.11 0.85 0.1517 1.1
## sswk 0.06 -0.06 0.98 0.02 1.00 0.0048 1.0
## sspc 0.15 0.19 0.43 0.17 0.73 0.2653 2.0
## ssno -0.05 0.04 -0.01 0.91 0.82 0.1792 1.0
## sscs 0.07 -0.01 0.01 0.74 0.63 0.3748 1.0
## ssasi 1.03 -0.18 -0.04 0.02 0.78 0.2248 1.1
## ssmk -0.10 1.01 -0.02 0.01 0.89 0.1138 1.0
## ssmc 0.82 0.22 -0.14 0.01 0.78 0.2194 1.2
## ssei 0.72 0.03 0.21 -0.01 0.83 0.1684 1.2
##
## MR4 MR3 MR1 MR2
## SS loadings 2.79 2.03 1.68 1.61
## Proportion Var 0.28 0.20 0.17 0.16
## Cumulative Var 0.28 0.48 0.65 0.81
## Proportion Explained 0.34 0.25 0.21 0.20
## Cumulative Proportion 0.34 0.59 0.80 1.00
##
## With factor correlations of
## MR4 MR3 MR1 MR2
## MR4 1.00 0.74 0.80 0.62
## MR3 0.74 1.00 0.79 0.75
## MR1 0.80 0.79 1.00 0.71
## MR2 0.62 0.75 0.71 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 9.88 with Chi Square = 10495.49
## df of the model are 11 and the objective function was 0.05
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
##
## The harmonic n.obs is 1067 with the empirical chi square 3.92 with prob < 0.97
## The total n.obs was 1067 with Likelihood Chi Square = 51.01 with prob < 4.1e-07
##
## Tucker Lewis Index of factoring reliability = 0.984
## RMSEA index = 0.058 and the 90 % confidence intervals are 0.043 0.075
## BIC = -25.69
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR4 MR3 MR1 MR2
## Correlation of (regression) scores with factors 0.97 0.97 1.00 0.94
## Multiple R square of scores with factors 0.93 0.94 1.00 0.89
## Minimum correlation of possible factor scores 0.87 0.88 0.99 0.77
fa4<-fa(df[,1:10], nfactors=4, rotate="promax", fm="minres", weight=df$sweight)
fa4
## Factor Analysis using method = minres
## Call: fa(r = df[, 1:10], nfactors = 4, rotate = "promax", fm = "minres",
## weight = df$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 MR4 h2 u2 com
## ssgs 0.80 0.18 -0.09 0.06 0.80 0.199 1.1
## ssar 0.12 0.79 0.03 0.06 0.86 0.143 1.1
## sswk 0.95 0.00 0.04 -0.10 0.91 0.085 1.0
## sspc 0.67 0.05 0.19 -0.02 0.72 0.278 1.2
## ssno -0.05 0.30 0.64 -0.03 0.68 0.324 1.4
## sscs 0.04 -0.13 0.92 0.06 0.74 0.256 1.1
## ssasi 0.59 -0.03 0.08 0.31 0.57 0.428 1.6
## ssmk 0.06 0.86 0.00 -0.04 0.81 0.192 1.0
## ssmc 0.29 0.39 -0.01 0.27 0.58 0.417 2.7
## ssei 0.69 0.08 -0.04 0.17 0.62 0.383 1.2
##
## MR1 MR3 MR2 MR4
## SS loadings 3.42 2.10 1.44 0.33
## Proportion Var 0.34 0.21 0.14 0.03
## Cumulative Var 0.34 0.55 0.70 0.73
## Proportion Explained 0.47 0.29 0.20 0.05
## Cumulative Proportion 0.47 0.76 0.95 1.00
##
## With factor correlations of
## MR1 MR3 MR2 MR4
## MR1 1.00 0.78 0.67 0.23
## MR3 0.78 1.00 0.64 0.29
## MR2 0.67 0.64 1.00 0.05
## MR4 0.23 0.29 0.05 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 7.86 with Chi Square = 8346.61
## df of the model are 11 and the objective function was 0.02
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
##
## The harmonic n.obs is 1067 with the empirical chi square 3.41 with prob < 0.98
## The total n.obs was 1067 with Likelihood Chi Square = 22.33 with prob < 0.022
##
## Tucker Lewis Index of factoring reliability = 0.994
## RMSEA index = 0.031 and the 90 % confidence intervals are 0.011 0.05
## BIC = -54.37
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2 MR4
## Correlation of (regression) scores with factors 0.98 0.96 0.92 0.66
## Multiple R square of scores with factors 0.95 0.92 0.85 0.43
## Minimum correlation of possible factor scores 0.90 0.83 0.70 -0.13
# white sibling sample
dw<- subset(d, bhw==3)
m<- subset(dw, sex==0)
f<- subset(dw, sex==1)
dm<- dplyr::select(m, starts_with("ss"), sweight)
df<- dplyr::select(f, starts_with("ss"), sweight)
ev <- eigen(cor(dm)) # get eigenvalues
ev$values
## [1] 6.6534982 1.1486107 0.8898470 0.5753375 0.4261700 0.3139847 0.2980345 0.2341430 0.1766542
## [10] 0.1516864 0.1320338
ev <- eigen(cor(df)) # get eigenvalues
ev$values
## [1] 6.0712643 1.0003917 0.9154149 0.6826670 0.5292353 0.4477126 0.4216869 0.3073626 0.2682701
## [10] 0.1850292 0.1709653
fa3<-fa(dm[,1:10], nfactors=3, rotate="promax", fm="minres")
fa3
## Factor Analysis using method = minres
## Call: fa(r = dm[, 1:10], nfactors = 3, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## ssgs 0.60 0.33 0.00 0.76 0.24 1.5
## ssar 0.06 0.79 0.09 0.81 0.19 1.0
## sswk 0.57 0.21 0.18 0.77 0.23 1.5
## sspc 0.38 0.27 0.27 0.68 0.32 2.7
## ssno -0.12 0.00 0.98 0.83 0.17 1.0
## sscs 0.05 -0.03 0.76 0.58 0.42 1.0
## ssasi 1.01 -0.24 -0.05 0.67 0.33 1.1
## ssmk -0.14 1.06 -0.03 0.88 0.12 1.0
## ssmc 0.75 0.16 -0.07 0.69 0.31 1.1
## ssei 0.93 -0.01 0.01 0.85 0.15 1.0
##
## MR1 MR3 MR2
## SS loadings 3.47 2.28 1.77
## Proportion Var 0.35 0.23 0.18
## Cumulative Var 0.35 0.57 0.75
## Proportion Explained 0.46 0.30 0.24
## Cumulative Proportion 0.46 0.76 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.75 0.63
## MR3 0.75 1.00 0.77
## MR2 0.63 0.77 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 8.8 with Chi Square = 4582.88
## df of the model are 18 and the objective function was 0.34
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.04
##
## The harmonic n.obs is 526 with the empirical chi square 25.05 with prob < 0.12
## The total n.obs was 526 with Likelihood Chi Square = 177.68 with prob < 2.8e-28
##
## Tucker Lewis Index of factoring reliability = 0.912
## RMSEA index = 0.13 and the 90 % confidence intervals are 0.113 0.148
## BIC = 64.9
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.97 0.97 0.95
## Multiple R square of scores with factors 0.94 0.94 0.90
## Minimum correlation of possible factor scores 0.88 0.88 0.80
fa3<-fa(df[,1:10], nfactors=3, rotate="promax", fm="minres")
fa3
## Factor Analysis using method = minres
## Call: fa(r = df[, 1:10], nfactors = 3, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## ssgs 0.79 0.16 -0.07 0.76 0.24 1.1
## ssar 0.07 0.83 0.08 0.88 0.12 1.0
## sswk 0.87 -0.07 0.15 0.83 0.17 1.1
## sspc 0.63 -0.01 0.25 0.65 0.35 1.3
## ssno -0.12 0.26 0.75 0.73 0.27 1.3
## sscs 0.09 -0.10 0.77 0.58 0.42 1.1
## ssasi 0.61 0.07 -0.01 0.42 0.58 1.0
## ssmk 0.06 0.76 0.10 0.76 0.24 1.0
## ssmc 0.32 0.49 -0.09 0.49 0.51 1.8
## ssei 0.72 0.07 -0.07 0.55 0.45 1.0
##
## MR1 MR3 MR2
## SS loadings 3.17 2.01 1.46
## Proportion Var 0.32 0.20 0.15
## Cumulative Var 0.32 0.52 0.66
## Proportion Explained 0.48 0.30 0.22
## Cumulative Proportion 0.48 0.78 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.76 0.6
## MR3 0.76 1.00 0.6
## MR2 0.60 0.60 1.0
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 6.74 with Chi Square = 3512.19
## df of the model are 18 and the objective function was 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
##
## The harmonic n.obs is 526 with the empirical chi square 14.12 with prob < 0.72
## The total n.obs was 526 with Likelihood Chi Square = 51.47 with prob < 4.5e-05
##
## Tucker Lewis Index of factoring reliability = 0.976
## RMSEA index = 0.059 and the 90 % confidence intervals are 0.041 0.079
## BIC = -61.3
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.96 0.96 0.91
## Multiple R square of scores with factors 0.92 0.91 0.82
## Minimum correlation of possible factor scores 0.84 0.83 0.64
fa4<-fa(dm[,1:10], nfactors=4, rotate="promax", fm="minres")
fa4
## Factor Analysis using method = minres
## Call: fa(r = dm[, 1:10], nfactors = 4, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR4 MR3 MR1 MR2 h2 u2 com
## ssgs 0.32 0.25 0.43 -0.06 0.77 0.2294 2.5
## ssar 0.08 0.80 -0.04 0.11 0.82 0.1752 1.1
## sswk 0.00 -0.07 1.05 0.00 1.00 0.0037 1.0
## sspc 0.15 0.19 0.39 0.20 0.69 0.3092 2.3
## ssno -0.07 0.01 -0.02 0.97 0.86 0.1438 1.0
## sscs 0.07 0.01 0.00 0.71 0.58 0.4239 1.0
## ssasi 1.01 -0.19 -0.05 0.01 0.72 0.2753 1.1
## ssmk -0.11 1.03 -0.02 0.00 0.88 0.1205 1.0
## ssmc 0.79 0.25 -0.14 -0.01 0.74 0.2590 1.3
## ssei 0.71 0.00 0.23 0.00 0.83 0.1744 1.2
##
## MR4 MR3 MR1 MR2
## SS loadings 2.49 2.05 1.73 1.61
## Proportion Var 0.25 0.21 0.17 0.16
## Cumulative Var 0.25 0.45 0.63 0.79
## Proportion Explained 0.32 0.26 0.22 0.20
## Cumulative Proportion 0.32 0.58 0.80 1.00
##
## With factor correlations of
## MR4 MR3 MR1 MR2
## MR4 1.00 0.70 0.78 0.54
## MR3 0.70 1.00 0.78 0.74
## MR1 0.78 0.78 1.00 0.68
## MR2 0.54 0.74 0.68 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 8.8 with Chi Square = 4582.88
## df of the model are 11 and the objective function was 0.07
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.02
##
## The harmonic n.obs is 526 with the empirical chi square 3.6 with prob < 0.98
## The total n.obs was 526 with Likelihood Chi Square = 36.51 with prob < 0.00014
##
## Tucker Lewis Index of factoring reliability = 0.977
## RMSEA index = 0.066 and the 90 % confidence intervals are 0.043 0.091
## BIC = -32.41
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR4 MR3 MR1 MR2
## Correlation of (regression) scores with factors 0.96 0.97 1.00 0.95
## Multiple R square of scores with factors 0.92 0.94 1.00 0.90
## Minimum correlation of possible factor scores 0.84 0.88 0.99 0.81
fa4<-fa(df[,1:10], nfactors=4, rotate="promax", fm="minres")
fa4
## Factor Analysis using method = minres
## Call: fa(r = df[, 1:10], nfactors = 4, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR3 MR1 MR4 MR2 h2 u2 com
## ssgs 0.16 0.47 0.37 -0.08 0.75 0.251 2.2
## ssar 0.89 0.08 0.00 -0.02 0.88 0.123 1.0
## sswk -0.05 0.18 0.89 -0.04 0.93 0.067 1.1
## sspc 0.09 0.14 0.55 0.11 0.65 0.346 1.3
## ssno 0.41 -0.13 0.10 0.48 0.62 0.380 2.2
## sscs -0.13 0.11 -0.05 0.97 0.83 0.168 1.1
## ssasi -0.04 0.69 -0.02 0.10 0.49 0.513 1.0
## ssmk 0.85 0.01 0.05 -0.02 0.77 0.230 1.0
## ssmc 0.45 0.46 -0.14 -0.03 0.52 0.480 2.2
## ssei 0.02 0.58 0.19 -0.01 0.56 0.442 1.2
##
## MR3 MR1 MR4 MR2
## SS loadings 2.22 1.88 1.68 1.23
## Proportion Var 0.22 0.19 0.17 0.12
## Cumulative Var 0.22 0.41 0.58 0.70
## Proportion Explained 0.32 0.27 0.24 0.17
## Cumulative Proportion 0.32 0.58 0.83 1.00
##
## With factor correlations of
## MR3 MR1 MR4 MR2
## MR3 1.00 0.72 0.74 0.59
## MR1 0.72 1.00 0.75 0.42
## MR4 0.74 0.75 1.00 0.60
## MR2 0.59 0.42 0.60 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 6.74 with Chi Square = 3512.19
## df of the model are 11 and the objective function was 0.02
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.02
##
## The harmonic n.obs is 526 with the empirical chi square 2.82 with prob < 0.99
## The total n.obs was 526 with Likelihood Chi Square = 12.37 with prob < 0.34
##
## Tucker Lewis Index of factoring reliability = 0.998
## RMSEA index = 0.015 and the 90 % confidence intervals are 0 0.05
## BIC = -56.55
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR3 MR1 MR4 MR2
## Correlation of (regression) scores with factors 0.96 0.91 0.97 0.93
## Multiple R square of scores with factors 0.92 0.84 0.94 0.87
## Minimum correlation of possible factor scores 0.85 0.67 0.87 0.74
fa3<-fa(dm[,1:10], nfactors=3, rotate="promax", fm="minres", weight=dm$sweight)
fa3
## Factor Analysis using method = minres
## Call: fa(r = dm[, 1:10], nfactors = 3, rotate = "promax", fm = "minres",
## weight = dm$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## ssgs 0.58 0.34 0.00 0.74 0.26 1.6
## ssar 0.04 0.78 0.11 0.80 0.20 1.0
## sswk 0.54 0.21 0.19 0.72 0.28 1.6
## sspc 0.36 0.27 0.27 0.65 0.35 2.8
## ssno -0.13 0.00 0.96 0.80 0.20 1.0
## sscs 0.03 -0.04 0.75 0.55 0.45 1.0
## ssasi 0.97 -0.25 -0.05 0.61 0.39 1.1
## ssmk -0.15 1.09 -0.05 0.89 0.11 1.0
## ssmc 0.74 0.17 -0.09 0.66 0.34 1.1
## ssei 0.93 -0.03 0.01 0.83 0.17 1.0
##
## MR1 MR3 MR2
## SS loadings 3.24 2.30 1.72
## Proportion Var 0.32 0.23 0.17
## Cumulative Var 0.32 0.55 0.73
## Proportion Explained 0.45 0.32 0.24
## Cumulative Proportion 0.45 0.76 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.74 0.60
## MR3 0.74 1.00 0.77
## MR2 0.60 0.77 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 8.08 with Chi Square = 4210.93
## df of the model are 18 and the objective function was 0.39
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.04
##
## The harmonic n.obs is 526 with the empirical chi square 36.57 with prob < 0.006
## The total n.obs was 526 with Likelihood Chi Square = 204.43 with prob < 1.3e-33
##
## Tucker Lewis Index of factoring reliability = 0.888
## RMSEA index = 0.14 and the 90 % confidence intervals are 0.123 0.158
## BIC = 91.65
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.96 0.97 0.94
## Multiple R square of scores with factors 0.93 0.94 0.89
## Minimum correlation of possible factor scores 0.86 0.89 0.77
fa3<-fa(df[,1:10], nfactors=3, rotate="promax", fm="minres", weight=df$sweight)
fa3
## Factor Analysis using method = minres
## Call: fa(r = df[, 1:10], nfactors = 3, rotate = "promax", fm = "minres",
## weight = df$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## ssgs 0.80 0.15 -0.07 0.76 0.24 1.1
## ssar 0.08 0.83 0.07 0.87 0.13 1.0
## sswk 0.89 -0.10 0.15 0.83 0.17 1.1
## sspc 0.64 -0.01 0.23 0.61 0.39 1.2
## ssno -0.11 0.27 0.73 0.71 0.29 1.3
## sscs 0.07 -0.10 0.77 0.57 0.43 1.1
## ssasi 0.56 0.09 -0.03 0.38 0.62 1.1
## ssmk 0.05 0.77 0.09 0.75 0.25 1.0
## ssmc 0.28 0.49 -0.09 0.47 0.53 1.7
## ssei 0.70 0.09 -0.08 0.53 0.47 1.1
##
## MR1 MR3 MR2
## SS loadings 3.07 2.01 1.38
## Proportion Var 0.31 0.20 0.14
## Cumulative Var 0.31 0.51 0.65
## Proportion Explained 0.48 0.31 0.21
## Cumulative Proportion 0.48 0.79 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.75 0.55
## MR3 0.75 1.00 0.56
## MR2 0.55 0.56 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 6.26 with Chi Square = 3261.83
## df of the model are 18 and the objective function was 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
##
## The harmonic n.obs is 526 with the empirical chi square 15.53 with prob < 0.63
## The total n.obs was 526 with Likelihood Chi Square = 49.72 with prob < 8.3e-05
##
## Tucker Lewis Index of factoring reliability = 0.975
## RMSEA index = 0.058 and the 90 % confidence intervals are 0.039 0.077
## BIC = -63.05
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.96 0.95 0.90
## Multiple R square of scores with factors 0.92 0.91 0.80
## Minimum correlation of possible factor scores 0.84 0.82 0.61
fa4<-fa(dm[,1:10], nfactors=4, rotate="promax", fm="minres", weight=dm$sweight)
fa4
## Factor Analysis using method = minres
## Call: fa(r = dm[, 1:10], nfactors = 4, rotate = "promax", fm = "minres",
## weight = dm$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR4 MR3 MR1 MR2 h2 u2 com
## ssgs 0.30 0.25 0.43 -0.06 0.74 0.2562 2.5
## ssar 0.06 0.81 -0.05 0.12 0.82 0.1758 1.1
## sswk -0.05 -0.09 1.12 -0.02 1.00 0.0009 1.0
## sspc 0.10 0.18 0.45 0.17 0.66 0.3372 1.8
## ssno -0.05 -0.01 -0.05 1.01 0.89 0.1058 1.0
## sscs 0.05 0.04 0.03 0.64 0.52 0.4811 1.0
## ssasi 0.99 -0.20 -0.07 0.02 0.68 0.3166 1.1
## ssmk -0.13 1.04 -0.01 -0.01 0.88 0.1151 1.0
## ssmc 0.77 0.27 -0.13 -0.04 0.72 0.2786 1.3
## ssei 0.70 -0.02 0.25 0.01 0.80 0.1979 1.2
##
## MR4 MR3 MR1 MR2
## SS loadings 2.29 2.06 1.83 1.55
## Proportion Var 0.23 0.21 0.18 0.15
## Cumulative Var 0.23 0.44 0.62 0.77
## Proportion Explained 0.30 0.27 0.24 0.20
## Cumulative Proportion 0.30 0.56 0.80 1.00
##
## With factor correlations of
## MR4 MR3 MR1 MR2
## MR4 1.00 0.68 0.76 0.49
## MR3 0.68 1.00 0.77 0.72
## MR1 0.76 0.77 1.00 0.65
## MR2 0.49 0.72 0.65 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 8.08 with Chi Square = 4210.93
## df of the model are 11 and the objective function was 0.07
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.02
##
## The harmonic n.obs is 526 with the empirical chi square 4.24 with prob < 0.96
## The total n.obs was 526 with Likelihood Chi Square = 35.72 with prob < 0.00019
##
## Tucker Lewis Index of factoring reliability = 0.976
## RMSEA index = 0.065 and the 90 % confidence intervals are 0.042 0.09
## BIC = -33.19
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR4 MR3 MR1 MR2
## Correlation of (regression) scores with factors 0.95 0.97 1 0.96
## Multiple R square of scores with factors 0.91 0.94 1 0.92
## Minimum correlation of possible factor scores 0.81 0.88 1 0.85
fa4<-fa(df[,1:10], nfactors=4, rotate="promax", fm="minres", weight=df$sweight)
fa4
## Factor Analysis using method = minres
## Call: fa(r = df[, 1:10], nfactors = 4, rotate = "promax", fm = "minres",
## weight = df$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR3 MR1 MR4 MR2 h2 u2 com
## ssgs 0.15 0.46 0.38 -0.09 0.74 0.26 2.2
## ssar 0.85 0.02 0.10 -0.02 0.86 0.14 1.0
## sswk -0.04 0.97 0.04 -0.02 0.93 0.07 1.0
## sspc 0.09 0.56 0.11 0.12 0.61 0.39 1.2
## ssno 0.39 0.06 -0.11 0.51 0.61 0.39 2.0
## sscs -0.15 -0.04 0.10 0.95 0.79 0.21 1.1
## ssasi -0.05 0.03 0.65 0.08 0.45 0.55 1.1
## ssmk 0.87 0.06 -0.02 -0.03 0.78 0.22 1.0
## ssmc 0.41 -0.14 0.49 -0.02 0.50 0.50 2.1
## ssei 0.02 0.28 0.49 -0.03 0.53 0.47 1.6
##
## MR3 MR1 MR4 MR2
## SS loadings 2.11 1.94 1.54 1.20
## Proportion Var 0.21 0.19 0.15 0.12
## Cumulative Var 0.21 0.41 0.56 0.68
## Proportion Explained 0.31 0.29 0.23 0.18
## Cumulative Proportion 0.31 0.60 0.82 1.00
##
## With factor correlations of
## MR3 MR1 MR4 MR2
## MR3 1.00 0.72 0.71 0.57
## MR1 0.72 1.00 0.76 0.56
## MR4 0.71 0.76 1.00 0.36
## MR2 0.57 0.56 0.36 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 6.26 with Chi Square = 3261.83
## df of the model are 11 and the objective function was 0.04
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.02
##
## The harmonic n.obs is 526 with the empirical chi square 4.65 with prob < 0.95
## The total n.obs was 526 with Likelihood Chi Square = 19.02 with prob < 0.061
##
## Tucker Lewis Index of factoring reliability = 0.99
## RMSEA index = 0.037 and the 90 % confidence intervals are 0 0.065
## BIC = -49.89
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR3 MR1 MR4 MR2
## Correlation of (regression) scores with factors 0.96 0.97 0.90 0.92
## Multiple R square of scores with factors 0.92 0.95 0.81 0.84
## Minimum correlation of possible factor scores 0.83 0.89 0.62 0.69
# full total sample
m<- subset(dk, sex==0)
f<- subset(dk, sex==1)
dm<- dplyr::select(m, starts_with("ss"), sweight)
df<- dplyr::select(f, starts_with("ss"), sweight)
ev <- eigen(cor(dm)) # get eigenvalues
ev$values
## [1] 7.3264300 0.9038625 0.7753772 0.4860249 0.3652766 0.2602612 0.2301454 0.1915608 0.1758508
## [10] 0.1569553 0.1282552
ev <- eigen(cor(df)) # get eigenvalues
ev$values
## [1] 6.7866452 0.8895363 0.8273077 0.5481897 0.4505542 0.3351343 0.3186843 0.2703994 0.2460046
## [10] 0.1771029 0.1504414
fa3<-fa(dm[,1:10], nfactors=3, rotate="promax", fm="minres")
fa3
## Factor Analysis using method = minres
## Call: fa(r = dm[, 1:10], nfactors = 3, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## ssgs 0.69 0.23 0.02 0.82 0.18 1.2
## ssar 0.19 0.66 0.10 0.81 0.19 1.2
## sswk 0.62 0.14 0.21 0.82 0.18 1.3
## sspc 0.45 0.24 0.23 0.72 0.28 2.1
## ssno -0.07 0.06 0.90 0.79 0.21 1.0
## sscs 0.07 -0.04 0.80 0.67 0.33 1.0
## ssasi 1.03 -0.21 0.01 0.77 0.23 1.1
## ssmk -0.09 0.99 0.01 0.87 0.13 1.0
## ssmc 0.79 0.12 -0.04 0.74 0.26 1.1
## ssei 0.91 0.04 -0.04 0.83 0.17 1.0
##
## MR1 MR3 MR2
## SS loadings 4.01 1.99 1.84
## Proportion Var 0.40 0.20 0.18
## Cumulative Var 0.40 0.60 0.78
## Proportion Explained 0.51 0.25 0.24
## Cumulative Proportion 0.51 0.76 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.79 0.73
## MR3 0.79 1.00 0.79
## MR2 0.73 0.79 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 10.06 with Chi Square = 54984.53
## df of the model are 18 and the objective function was 0.26
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic n.obs is 5469 with the empirical chi square 155.51 with prob < 6.3e-24
## The total n.obs was 5469 with Likelihood Chi Square = 1434.18 with prob < 6.5e-294
##
## Tucker Lewis Index of factoring reliability = 0.936
## RMSEA index = 0.12 and the 90 % confidence intervals are 0.115 0.125
## BIC = 1279.26
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.98 0.96 0.94
## Multiple R square of scores with factors 0.95 0.93 0.89
## Minimum correlation of possible factor scores 0.90 0.86 0.78
fa3<-fa(df[,1:10], nfactors=3, rotate="promax", fm="minres")
fa3
## Factor Analysis using method = minres
## Call: fa(r = df[, 1:10], nfactors = 3, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## ssgs 0.80 0.09 0.01 0.78 0.22 1.0
## ssar 0.15 0.75 0.07 0.84 0.16 1.1
## sswk 0.77 -0.04 0.22 0.82 0.18 1.2
## sspc 0.59 0.02 0.30 0.72 0.28 1.5
## ssno -0.12 0.13 0.88 0.80 0.20 1.1
## sscs 0.11 -0.04 0.73 0.62 0.38 1.0
## ssasi 0.80 -0.01 -0.03 0.59 0.41 1.0
## ssmk 0.06 0.77 0.10 0.79 0.21 1.0
## ssmc 0.53 0.35 -0.08 0.60 0.40 1.8
## ssei 0.81 0.08 -0.06 0.68 0.32 1.0
##
## MR1 MR3 MR2
## SS loadings 3.71 1.77 1.76
## Proportion Var 0.37 0.18 0.18
## Cumulative Var 0.37 0.55 0.72
## Proportion Explained 0.51 0.24 0.24
## Cumulative Proportion 0.51 0.76 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.78 0.70
## MR3 0.78 1.00 0.68
## MR2 0.70 0.68 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 8.25 with Chi Square = 44928.78
## df of the model are 18 and the objective function was 0.15
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic n.obs is 5449 with the empirical chi square 139.34 with prob < 8.6e-21
## The total n.obs was 5449 with Likelihood Chi Square = 811.49 with prob < 1.1e-160
##
## Tucker Lewis Index of factoring reliability = 0.956
## RMSEA index = 0.09 and the 90 % confidence intervals are 0.085 0.095
## BIC = 656.63
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.97 0.95 0.94
## Multiple R square of scores with factors 0.93 0.90 0.88
## Minimum correlation of possible factor scores 0.87 0.79 0.75
fa4<-fa(dm[,1:10], nfactors=4, rotate="promax", fm="minres")
fa4
## Factor Analysis using method = minres
## Call: fa(r = dm[, 1:10], nfactors = 4, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR4 MR3 MR1 MR2 h2 u2 com
## ssgs 0.37 0.18 0.45 -0.04 0.82 0.175 2.3
## ssar 0.17 0.71 -0.01 0.11 0.83 0.167 1.2
## sswk 0.12 -0.04 0.85 0.07 0.93 0.067 1.1
## sspc 0.11 0.16 0.53 0.13 0.75 0.248 1.4
## ssno -0.04 0.08 0.03 0.83 0.79 0.211 1.0
## sscs 0.08 -0.02 0.02 0.77 0.69 0.314 1.0
## ssasi 0.99 -0.17 -0.01 0.06 0.82 0.183 1.1
## ssmk -0.08 0.93 0.02 0.04 0.85 0.151 1.0
## ssmc 0.80 0.21 -0.11 0.01 0.79 0.212 1.2
## ssei 0.66 0.06 0.26 -0.04 0.81 0.186 1.3
##
## MR4 MR3 MR1 MR2
## SS loadings 2.78 1.87 1.82 1.61
## Proportion Var 0.28 0.19 0.18 0.16
## Cumulative Var 0.28 0.47 0.65 0.81
## Proportion Explained 0.34 0.23 0.23 0.20
## Cumulative Proportion 0.34 0.58 0.80 1.00
##
## With factor correlations of
## MR4 MR3 MR1 MR2
## MR4 1.00 0.75 0.81 0.65
## MR3 0.75 1.00 0.79 0.75
## MR1 0.81 0.79 1.00 0.73
## MR2 0.65 0.75 0.73 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 10.06 with Chi Square = 54984.53
## df of the model are 11 and the objective function was 0.02
##
## The root mean square of the residuals (RMSR) is 0
## The df corrected root mean square of the residuals is 0.01
##
## The harmonic n.obs is 5469 with the empirical chi square 7.79 with prob < 0.73
## The total n.obs was 5469 with Likelihood Chi Square = 112.34 with prob < 6.2e-19
##
## Tucker Lewis Index of factoring reliability = 0.992
## RMSEA index = 0.041 and the 90 % confidence intervals are 0.034 0.048
## BIC = 17.67
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR4 MR3 MR1 MR2
## Correlation of (regression) scores with factors 0.97 0.96 0.97 0.94
## Multiple R square of scores with factors 0.93 0.92 0.94 0.87
## Minimum correlation of possible factor scores 0.87 0.85 0.89 0.75
fa4<-fa(df[,1:10], nfactors=4, rotate="promax", fm="minres")
fa4
## Factor Analysis using method = minres
## Call: fa(r = df[, 1:10], nfactors = 4, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR4 MR2 h2 u2 com
## ssgs 0.42 0.13 0.44 -0.05 0.78 0.222 2.2
## ssar 0.21 0.68 -0.01 0.08 0.81 0.189 1.2
## sswk 0.14 0.00 0.83 0.02 0.92 0.079 1.1
## sspc 0.14 0.08 0.54 0.17 0.74 0.261 1.4
## ssno -0.10 0.17 0.05 0.76 0.74 0.265 1.1
## sscs 0.11 -0.10 -0.02 0.84 0.70 0.302 1.1
## ssasi 0.83 -0.12 0.03 0.06 0.65 0.354 1.1
## ssmk -0.05 0.91 0.06 0.00 0.85 0.151 1.0
## ssmc 0.66 0.29 -0.12 0.01 0.64 0.359 1.5
## ssei 0.66 0.05 0.18 -0.02 0.68 0.318 1.2
##
## MR1 MR3 MR4 MR2
## SS loadings 2.41 1.82 1.74 1.52
## Proportion Var 0.24 0.18 0.17 0.15
## Cumulative Var 0.24 0.42 0.60 0.75
## Proportion Explained 0.32 0.24 0.23 0.20
## Cumulative Proportion 0.32 0.56 0.80 1.00
##
## With factor correlations of
## MR1 MR3 MR4 MR2
## MR1 1.00 0.77 0.79 0.63
## MR3 0.77 1.00 0.74 0.69
## MR4 0.79 0.74 1.00 0.71
## MR2 0.63 0.69 0.71 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 8.25 with Chi Square = 44928.78
## df of the model are 11 and the objective function was 0.01
##
## The root mean square of the residuals (RMSR) is 0
## The df corrected root mean square of the residuals is 0.01
##
## The harmonic n.obs is 5449 with the empirical chi square 5.75 with prob < 0.89
## The total n.obs was 5449 with Likelihood Chi Square = 55.08 with prob < 7.5e-08
##
## Tucker Lewis Index of factoring reliability = 0.996
## RMSEA index = 0.027 and the 90 % confidence intervals are 0.02 0.034
## BIC = -39.56
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR4 MR2
## Correlation of (regression) scores with factors 0.94 0.96 0.96 0.93
## Multiple R square of scores with factors 0.89 0.91 0.93 0.86
## Minimum correlation of possible factor scores 0.78 0.83 0.86 0.71
fa3<-fa(dm[,1:10], nfactors=3, rotate="promax", fm="minres", weight=dm$sweight)
fa3
## Factor Analysis using method = minres
## Call: fa(r = dm[, 1:10], nfactors = 3, rotate = "promax", fm = "minres",
## weight = dm$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## ssgs 0.57 0.40 -0.03 0.80 0.20 1.8
## ssar 0.11 0.72 0.12 0.81 0.19 1.1
## sswk 0.51 0.31 0.14 0.79 0.21 1.8
## sspc 0.35 0.37 0.20 0.70 0.30 2.5
## ssno -0.05 0.04 0.90 0.81 0.19 1.0
## sscs 0.05 0.02 0.76 0.65 0.35 1.0
## ssasi 1.06 -0.29 0.03 0.76 0.24 1.1
## ssmk -0.16 1.00 0.04 0.84 0.16 1.1
## ssmc 0.76 0.14 -0.03 0.73 0.27 1.1
## ssei 0.85 0.10 -0.03 0.81 0.19 1.0
##
## MR1 MR3 MR2
## SS loadings 3.49 2.49 1.74
## Proportion Var 0.35 0.25 0.17
## Cumulative Var 0.35 0.60 0.77
## Proportion Explained 0.45 0.32 0.23
## Cumulative Proportion 0.45 0.77 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.78 0.67
## MR3 0.78 1.00 0.79
## MR2 0.67 0.79 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 9.56 with Chi Square = 52251.07
## df of the model are 18 and the objective function was 0.31
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic n.obs is 5469 with the empirical chi square 201.06 with prob < 6.2e-33
## The total n.obs was 5469 with Likelihood Chi Square = 1672.77 with prob < 0
##
## Tucker Lewis Index of factoring reliability = 0.921
## RMSEA index = 0.13 and the 90 % confidence intervals are 0.124 0.135
## BIC = 1517.85
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.97 0.97 0.94
## Multiple R square of scores with factors 0.94 0.93 0.89
## Minimum correlation of possible factor scores 0.88 0.87 0.77
fa3<-fa(df[,1:10], nfactors=3, rotate="promax", fm="minres", weight=df$sweight)
fa3
## Factor Analysis using method = minres
## Call: fa(r = df[, 1:10], nfactors = 3, rotate = "promax", fm = "minres",
## weight = df$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## ssgs 0.79 0.12 -0.01 0.76 0.24 1.0
## ssar 0.13 0.77 0.06 0.85 0.15 1.1
## sswk 0.79 -0.03 0.18 0.81 0.19 1.1
## sspc 0.61 0.04 0.25 0.69 0.31 1.3
## ssno -0.11 0.14 0.87 0.79 0.21 1.1
## sscs 0.09 -0.06 0.75 0.60 0.40 1.0
## ssasi 0.76 -0.03 -0.01 0.53 0.47 1.0
## ssmk 0.03 0.81 0.07 0.80 0.20 1.0
## ssmc 0.49 0.37 -0.08 0.58 0.42 1.9
## ssei 0.82 0.05 -0.08 0.65 0.35 1.0
##
## MR1 MR3 MR2
## SS loadings 3.57 1.85 1.64
## Proportion Var 0.36 0.18 0.16
## Cumulative Var 0.36 0.54 0.71
## Proportion Explained 0.51 0.26 0.23
## Cumulative Proportion 0.51 0.77 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.78 0.67
## MR3 0.78 1.00 0.66
## MR2 0.67 0.66 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 7.72 with Chi Square = 42014.1
## df of the model are 18 and the objective function was 0.15
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic n.obs is 5449 with the empirical chi square 166.95 with prob < 3.6e-26
## The total n.obs was 5449 with Likelihood Chi Square = 830.41 with prob < 1.1e-164
##
## Tucker Lewis Index of factoring reliability = 0.952
## RMSEA index = 0.091 and the 90 % confidence intervals are 0.086 0.096
## BIC = 675.55
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.96 0.95 0.93
## Multiple R square of scores with factors 0.93 0.91 0.87
## Minimum correlation of possible factor scores 0.85 0.81 0.73
fa4<-fa(dm[,1:10], nfactors=4, rotate="promax", fm="minres", weight=dm$sweight)
fa4
## Factor Analysis using method = minres
## Call: fa(r = dm[, 1:10], nfactors = 4, rotate = "promax", fm = "minres",
## weight = dm$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR4 MR3 MR1 MR2 h2 u2 com
## ssgs 0.33 0.22 0.46 -0.05 0.81 0.193 2.3
## ssar 0.15 0.70 -0.01 0.14 0.83 0.172 1.2
## sswk 0.07 -0.06 0.93 0.04 0.94 0.061 1.0
## sspc 0.08 0.14 0.55 0.15 0.73 0.266 1.3
## ssno -0.03 0.03 0.02 0.88 0.81 0.189 1.0
## sscs 0.06 0.03 0.02 0.73 0.65 0.352 1.0
## ssasi 1.01 -0.21 -0.01 0.05 0.79 0.208 1.1
## ssmk -0.12 0.97 0.02 0.05 0.87 0.126 1.0
## ssmc 0.80 0.23 -0.12 0.00 0.78 0.221 1.2
## ssei 0.67 0.06 0.24 -0.03 0.80 0.199 1.3
##
## MR4 MR3 MR1 MR2
## SS loadings 2.61 1.90 1.88 1.62
## Proportion Var 0.26 0.19 0.19 0.16
## Cumulative Var 0.26 0.45 0.64 0.80
## Proportion Explained 0.33 0.24 0.24 0.20
## Cumulative Proportion 0.33 0.56 0.80 1.00
##
## With factor correlations of
## MR4 MR3 MR1 MR2
## MR4 1.00 0.72 0.80 0.61
## MR3 0.72 1.00 0.80 0.75
## MR1 0.80 0.80 1.00 0.71
## MR2 0.61 0.75 0.71 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 9.56 with Chi Square = 52251.07
## df of the model are 11 and the objective function was 0.02
##
## The root mean square of the residuals (RMSR) is 0
## The df corrected root mean square of the residuals is 0.01
##
## The harmonic n.obs is 5469 with the empirical chi square 10.16 with prob < 0.52
## The total n.obs was 5469 with Likelihood Chi Square = 126.48 with prob < 9e-22
##
## Tucker Lewis Index of factoring reliability = 0.991
## RMSEA index = 0.044 and the 90 % confidence intervals are 0.037 0.051
## BIC = 31.8
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR4 MR3 MR1 MR2
## Correlation of (regression) scores with factors 0.96 0.96 0.98 0.94
## Multiple R square of scores with factors 0.93 0.93 0.95 0.88
## Minimum correlation of possible factor scores 0.86 0.86 0.90 0.76
fa4<-fa(df[,1:10], nfactors=4, rotate="promax", fm="minres", weight=df$sweight)
fa4
## Factor Analysis using method = minres
## Call: fa(r = df[, 1:10], nfactors = 4, rotate = "promax", fm = "minres",
## weight = df$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR4 MR3 MR1 MR2 h2 u2 com
## ssgs 0.35 0.17 0.46 -0.06 0.75 0.245 2.2
## ssar 0.13 0.75 0.01 0.07 0.83 0.174 1.1
## sswk 0.07 -0.02 0.90 0.03 0.92 0.076 1.0
## sspc 0.12 0.09 0.56 0.16 0.71 0.294 1.3
## ssno -0.08 0.17 0.02 0.78 0.75 0.252 1.1
## sscs 0.10 -0.08 0.01 0.80 0.65 0.346 1.1
## ssasi 0.83 -0.13 0.01 0.07 0.62 0.383 1.1
## ssmk -0.09 0.92 0.06 0.02 0.83 0.167 1.0
## ssmc 0.59 0.36 -0.12 0.00 0.62 0.377 1.7
## ssei 0.57 0.06 0.25 -0.06 0.65 0.355 1.4
##
## MR4 MR3 MR1 MR2
## SS loadings 2.02 1.97 1.88 1.46
## Proportion Var 0.20 0.20 0.19 0.15
## Cumulative Var 0.20 0.40 0.59 0.73
## Proportion Explained 0.28 0.27 0.26 0.20
## Cumulative Proportion 0.28 0.54 0.80 1.00
##
## With factor correlations of
## MR4 MR3 MR1 MR2
## MR4 1.00 0.75 0.80 0.59
## MR3 0.75 1.00 0.75 0.66
## MR1 0.80 0.75 1.00 0.67
## MR2 0.59 0.66 0.67 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 7.72 with Chi Square = 42014.1
## df of the model are 11 and the objective function was 0.02
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
##
## The harmonic n.obs is 5449 with the empirical chi square 14.42 with prob < 0.21
## The total n.obs was 5449 with Likelihood Chi Square = 109.9 with prob < 1.9e-18
##
## Tucker Lewis Index of factoring reliability = 0.99
## RMSEA index = 0.041 and the 90 % confidence intervals are 0.034 0.048
## BIC = 15.26
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR4 MR3 MR1 MR2
## Correlation of (regression) scores with factors 0.93 0.96 0.97 0.92
## Multiple R square of scores with factors 0.87 0.92 0.94 0.85
## Minimum correlation of possible factor scores 0.74 0.83 0.88 0.69
# white total sample
dw<- subset(dk, bhw==3)
m<- subset(dw, sex==0)
f<- subset(dw, sex==1)
dm<- dplyr::select(m, starts_with("ss"), sweight)
df<- dplyr::select(f, starts_with("ss"), sweight)
ev <- eigen(cor(dm)) # get eigenvalues
ev$values
## [1] 6.6655940 1.0517313 0.9716068 0.5476495 0.4282921 0.2910217 0.2820806 0.2330632 0.2079487
## [10] 0.1669759 0.1540363
ev <- eigen(cor(df)) # get eigenvalues
ev$values
## [1] 5.9806203 1.0788210 0.9591717 0.6436575 0.5636444 0.3987126 0.3752899 0.3182300 0.3019231
## [10] 0.1995904 0.1803392
fa3<-fa(dm[,1:10], nfactors=3, rotate="promax", fm="minres")
fa3
## Factor Analysis using method = minres
## Call: fa(r = dm[, 1:10], nfactors = 3, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR3 MR1 MR2 h2 u2 com
## ssgs 0.52 0.45 -0.04 0.78 0.22 2.0
## ssar 0.05 0.77 0.10 0.79 0.21 1.0
## sswk 0.47 0.37 0.11 0.77 0.23 2.0
## sspc 0.30 0.44 0.17 0.68 0.32 2.1
## ssno -0.06 0.06 0.88 0.80 0.20 1.0
## sscs 0.06 0.01 0.74 0.62 0.38 1.0
## ssasi 1.05 -0.30 0.03 0.74 0.26 1.2
## ssmk -0.18 1.00 0.04 0.81 0.19 1.1
## ssmc 0.71 0.17 -0.03 0.69 0.31 1.1
## ssei 0.80 0.13 -0.03 0.79 0.21 1.1
##
## MR3 MR1 MR2
## SS loadings 3.14 2.70 1.62
## Proportion Var 0.31 0.27 0.16
## Cumulative Var 0.31 0.58 0.75
## Proportion Explained 0.42 0.36 0.22
## Cumulative Proportion 0.42 0.78 1.00
##
## With factor correlations of
## MR3 MR1 MR2
## MR3 1.00 0.77 0.61
## MR1 0.77 1.00 0.77
## MR2 0.61 0.77 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 8.68 with Chi Square = 26819.03
## df of the model are 18 and the objective function was 0.29
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic n.obs is 3094 with the empirical chi square 130.44 with prob < 4.4e-19
## The total n.obs was 3094 with Likelihood Chi Square = 906.88 with prob < 5.3e-181
##
## Tucker Lewis Index of factoring reliability = 0.917
## RMSEA index = 0.126 and the 90 % confidence intervals are 0.119 0.133
## BIC = 762.21
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR3 MR1 MR2
## Correlation of (regression) scores with factors 0.96 0.96 0.94
## Multiple R square of scores with factors 0.93 0.93 0.87
## Minimum correlation of possible factor scores 0.86 0.86 0.75
fa3<-fa(df[,1:10], nfactors=3, rotate="promax", fm="minres")
fa3
## Factor Analysis using method = minres
## Call: fa(r = df[, 1:10], nfactors = 3, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## ssgs 0.77 0.12 -0.03 0.72 0.28 1.1
## ssar 0.11 0.76 0.09 0.82 0.18 1.1
## sswk 0.76 -0.02 0.18 0.76 0.24 1.1
## sspc 0.56 0.05 0.25 0.62 0.38 1.4
## ssno -0.12 0.14 0.84 0.75 0.25 1.1
## sscs 0.07 -0.07 0.75 0.56 0.44 1.0
## ssasi 0.77 -0.07 -0.04 0.48 0.52 1.0
## ssmk -0.01 0.88 0.05 0.81 0.19 1.0
## ssmc 0.48 0.37 -0.09 0.54 0.46 2.0
## ssei 0.81 0.02 -0.06 0.62 0.38 1.0
##
## MR1 MR3 MR2
## SS loadings 3.29 1.86 1.54
## Proportion Var 0.33 0.19 0.15
## Cumulative Var 0.33 0.52 0.67
## Proportion Explained 0.49 0.28 0.23
## Cumulative Proportion 0.49 0.77 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.76 0.62
## MR3 0.76 1.00 0.66
## MR2 0.62 0.66 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 6.73 with Chi Square = 20595.45
## df of the model are 18 and the objective function was 0.18
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.04
##
## The harmonic n.obs is 3067 with the empirical chi square 145.86 with prob < 4.7e-22
## The total n.obs was 3067 with Likelihood Chi Square = 540.78 with prob < 2.7e-103
##
## Tucker Lewis Index of factoring reliability = 0.936
## RMSEA index = 0.097 and the 90 % confidence intervals are 0.09 0.104
## BIC = 396.27
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.95 0.95 0.92
## Multiple R square of scores with factors 0.91 0.91 0.84
## Minimum correlation of possible factor scores 0.82 0.81 0.69
fa4<-fa(dm[,1:10], nfactors=4, rotate="promax", fm="minres")
fa4
## Factor Analysis using method = minres
## Call: fa(r = dm[, 1:10], nfactors = 4, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR2 MR4 MR1 MR3 h2 u2 com
## ssgs 0.29 0.50 0.21 -0.06 0.79 0.214 2.1
## ssar 0.11 0.00 0.73 0.13 0.81 0.190 1.1
## sswk 0.04 0.96 -0.07 0.04 0.93 0.072 1.0
## sspc 0.07 0.54 0.16 0.14 0.71 0.293 1.3
## ssno -0.04 0.03 0.05 0.86 0.80 0.205 1.0
## sscs 0.07 0.01 0.01 0.74 0.63 0.375 1.0
## ssasi 1.00 -0.02 -0.22 0.05 0.77 0.235 1.1
## ssmk -0.12 0.01 0.96 0.04 0.85 0.146 1.0
## ssmc 0.76 -0.12 0.27 -0.01 0.74 0.259 1.3
## ssei 0.64 0.26 0.06 -0.03 0.78 0.222 1.4
##
## MR2 MR4 MR1 MR3
## SS loadings 2.38 1.93 1.93 1.55
## Proportion Var 0.24 0.19 0.19 0.16
## Cumulative Var 0.24 0.43 0.62 0.78
## Proportion Explained 0.31 0.25 0.25 0.20
## Cumulative Proportion 0.31 0.55 0.80 1.00
##
## With factor correlations of
## MR2 MR4 MR1 MR3
## MR2 1.00 0.78 0.69 0.55
## MR4 0.78 1.00 0.80 0.69
## MR1 0.69 0.80 1.00 0.74
## MR3 0.55 0.69 0.74 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 8.68 with Chi Square = 26819.03
## df of the model are 11 and the objective function was 0.03
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
##
## The harmonic n.obs is 3094 with the empirical chi square 8.69 with prob < 0.65
## The total n.obs was 3094 with Likelihood Chi Square = 89.92 with prob < 1.7e-14
##
## Tucker Lewis Index of factoring reliability = 0.988
## RMSEA index = 0.048 and the 90 % confidence intervals are 0.039 0.058
## BIC = 1.51
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR2 MR4 MR1 MR3
## Correlation of (regression) scores with factors 0.96 0.97 0.96 0.93
## Multiple R square of scores with factors 0.91 0.95 0.92 0.87
## Minimum correlation of possible factor scores 0.83 0.90 0.85 0.74
fa4<-fa(df[,1:10], nfactors=4, rotate="promax", fm="minres")
fa4
## Factor Analysis using method = minres
## Call: fa(r = df[, 1:10], nfactors = 4, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR3 MR1 MR4 MR2 h2 u2 com
## ssgs 0.18 0.42 0.37 -0.07 0.71 0.292 2.4
## ssar 0.79 0.03 0.05 0.08 0.82 0.185 1.0
## sswk -0.05 0.97 0.03 -0.01 0.92 0.083 1.0
## sspc 0.10 0.61 0.05 0.12 0.65 0.350 1.1
## ssno 0.18 0.01 -0.08 0.76 0.72 0.281 1.1
## sscs -0.09 0.01 0.10 0.78 0.61 0.388 1.1
## ssasi -0.14 -0.03 0.86 0.06 0.59 0.405 1.1
## ssmk 0.94 0.03 -0.09 0.01 0.82 0.180 1.0
## ssmc 0.41 -0.12 0.53 -0.02 0.59 0.412 2.0
## ssei 0.06 0.21 0.58 -0.03 0.61 0.388 1.3
##
## MR3 MR1 MR4 MR2
## SS loadings 2.03 1.85 1.82 1.34
## Proportion Var 0.20 0.19 0.18 0.13
## Cumulative Var 0.20 0.39 0.57 0.70
## Proportion Explained 0.29 0.26 0.26 0.19
## Cumulative Proportion 0.29 0.55 0.81 1.00
##
## With factor correlations of
## MR3 MR1 MR4 MR2
## MR3 1.00 0.75 0.72 0.64
## MR1 0.75 1.00 0.77 0.63
## MR4 0.72 0.77 1.00 0.50
## MR2 0.64 0.63 0.50 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 6.73 with Chi Square = 20595.45
## df of the model are 11 and the objective function was 0.02
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
##
## The harmonic n.obs is 3067 with the empirical chi square 10.38 with prob < 0.5
## The total n.obs was 3067 with Likelihood Chi Square = 62.27 with prob < 3.5e-09
##
## Tucker Lewis Index of factoring reliability = 0.99
## RMSEA index = 0.039 and the 90 % confidence intervals are 0.03 0.049
## BIC = -26.04
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR3 MR1 MR4 MR2
## Correlation of (regression) scores with factors 0.96 0.97 0.92 0.91
## Multiple R square of scores with factors 0.92 0.94 0.85 0.82
## Minimum correlation of possible factor scores 0.83 0.88 0.70 0.64
fa3<-fa(dm[,1:10], nfactors=3, rotate="promax", fm="minres", weight=dm$sweight)
fa3
## Factor Analysis using method = minres
## Call: fa(r = dm[, 1:10], nfactors = 3, rotate = "promax", fm = "minres",
## weight = dm$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR2 MR3 h2 u2 com
## ssgs 0.77 0.23 -0.10 0.77 0.23 1.2
## ssar 0.72 -0.02 0.22 0.76 0.24 1.2
## sswk 0.73 0.18 0.01 0.76 0.24 1.1
## sspc 0.66 0.09 0.12 0.67 0.33 1.1
## ssno 0.08 0.00 0.81 0.76 0.24 1.0
## sscs 0.03 0.08 0.73 0.62 0.38 1.0
## ssasi -0.21 1.00 0.06 0.79 0.21 1.1
## ssmk 0.86 -0.21 0.18 0.75 0.25 1.2
## ssmc 0.30 0.57 0.02 0.67 0.33 1.5
## ssei 0.39 0.57 -0.05 0.75 0.25 1.8
##
## MR1 MR2 MR3
## SS loadings 3.63 2.06 1.60
## Proportion Var 0.36 0.21 0.16
## Cumulative Var 0.36 0.57 0.73
## Proportion Explained 0.50 0.28 0.22
## Cumulative Proportion 0.50 0.78 1.00
##
## With factor correlations of
## MR1 MR2 MR3
## MR1 1.0 0.70 0.70
## MR2 0.7 1.00 0.41
## MR3 0.7 0.41 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 8.06 with Chi Square = 24883.77
## df of the model are 18 and the objective function was 0.33
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.04
##
## The harmonic n.obs is 3094 with the empirical chi square 157.45 with prob < 2.6e-24
## The total n.obs was 3094 with Likelihood Chi Square = 1005.32 with prob < 5.1e-202
##
## Tucker Lewis Index of factoring reliability = 0.901
## RMSEA index = 0.133 and the 90 % confidence intervals are 0.126 0.14
## BIC = 860.65
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR2 MR3
## Correlation of (regression) scores with factors 0.97 0.95 0.92
## Multiple R square of scores with factors 0.94 0.89 0.85
## Minimum correlation of possible factor scores 0.87 0.79 0.70
fa3<-fa(df[,1:10], nfactors=3, rotate="promax", fm="minres", weight=df$sweight)
fa3
## Factor Analysis using method = minres
## Call: fa(r = df[, 1:10], nfactors = 3, rotate = "promax", fm = "minres",
## weight = df$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 h2 u2 com
## ssgs 0.76 0.14 -0.04 0.71 0.29 1.1
## ssar 0.11 0.78 0.06 0.83 0.17 1.1
## sswk 0.78 -0.01 0.15 0.75 0.25 1.1
## sspc 0.57 0.07 0.21 0.60 0.40 1.3
## ssno -0.11 0.15 0.83 0.75 0.25 1.1
## sscs 0.07 -0.08 0.75 0.55 0.45 1.0
## ssasi 0.72 -0.07 -0.02 0.43 0.57 1.0
## ssmk -0.01 0.87 0.04 0.80 0.20 1.0
## ssmc 0.45 0.37 -0.08 0.52 0.48 2.0
## ssei 0.81 0.00 -0.07 0.60 0.40 1.0
##
## MR1 MR3 MR2
## SS loadings 3.18 1.89 1.45
## Proportion Var 0.32 0.19 0.14
## Cumulative Var 0.32 0.51 0.65
## Proportion Explained 0.49 0.29 0.22
## Cumulative Proportion 0.49 0.78 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.76 0.59
## MR3 0.76 1.00 0.64
## MR2 0.59 0.64 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 6.35 with Chi Square = 19448.39
## df of the model are 18 and the objective function was 0.17
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.04
##
## The harmonic n.obs is 3067 with the empirical chi square 152.29 with prob < 2.7e-23
## The total n.obs was 3067 with Likelihood Chi Square = 506.64 with prob < 4.2e-96
##
## Tucker Lewis Index of factoring reliability = 0.937
## RMSEA index = 0.094 and the 90 % confidence intervals are 0.087 0.101
## BIC = 362.13
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.95 0.95 0.91
## Multiple R square of scores with factors 0.91 0.91 0.83
## Minimum correlation of possible factor scores 0.81 0.81 0.67
fa4<-fa(dm[,1:10], nfactors=4, rotate="promax", fm="minres", weight=dm$sweight)
fa4
## Factor Analysis using method = minres
## Call: fa(r = dm[, 1:10], nfactors = 4, rotate = "promax", fm = "minres",
## weight = dm$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR2 MR1 MR4 MR3 h2 u2 com
## ssgs 0.25 0.50 0.24 -0.07 0.76 0.243 2.0
## ssar 0.10 0.00 0.71 0.15 0.80 0.198 1.1
## sswk -0.01 1.02 -0.08 0.02 0.93 0.074 1.0
## sspc 0.05 0.56 0.13 0.16 0.68 0.317 1.3
## ssno -0.03 0.02 0.02 0.88 0.79 0.207 1.0
## sscs 0.05 0.00 0.04 0.72 0.60 0.400 1.0
## ssasi 0.99 -0.03 -0.24 0.05 0.73 0.273 1.1
## ssmk -0.15 0.01 0.98 0.05 0.87 0.127 1.1
## ssmc 0.75 -0.12 0.27 -0.02 0.73 0.271 1.3
## ssei 0.64 0.26 0.05 -0.03 0.75 0.246 1.3
##
## MR2 MR1 MR4 MR3
## SS loadings 2.21 1.98 1.91 1.54
## Proportion Var 0.22 0.20 0.19 0.15
## Cumulative Var 0.22 0.42 0.61 0.76
## Proportion Explained 0.29 0.26 0.25 0.20
## Cumulative Proportion 0.29 0.55 0.80 1.00
##
## With factor correlations of
## MR2 MR1 MR4 MR3
## MR2 1.00 0.75 0.67 0.50
## MR1 0.75 1.00 0.80 0.66
## MR4 0.67 0.80 1.00 0.73
## MR3 0.50 0.66 0.73 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 8.06 with Chi Square = 24883.77
## df of the model are 11 and the objective function was 0.03
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
##
## The harmonic n.obs is 3094 with the empirical chi square 10.43 with prob < 0.49
## The total n.obs was 3094 with Likelihood Chi Square = 92.13 with prob < 6.4e-15
##
## Tucker Lewis Index of factoring reliability = 0.987
## RMSEA index = 0.049 and the 90 % confidence intervals are 0.04 0.058
## BIC = 3.72
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR2 MR1 MR4 MR3
## Correlation of (regression) scores with factors 0.95 0.97 0.96 0.93
## Multiple R square of scores with factors 0.90 0.95 0.93 0.87
## Minimum correlation of possible factor scores 0.80 0.90 0.86 0.73
fa4<-fa(df[,1:10], nfactors=4, rotate="promax", fm="minres", weight=df$sweight)
fa4
## Factor Analysis using method = minres
## Call: fa(r = df[, 1:10], nfactors = 4, rotate = "promax", fm = "minres",
## weight = df$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR3 MR1 MR4 MR2 h2 u2 com
## ssgs 0.20 0.46 0.30 -0.08 0.69 0.308 2.2
## ssar 0.81 0.03 0.04 0.06 0.82 0.177 1.0
## sswk -0.06 1.01 -0.02 0.01 0.92 0.084 1.0
## sspc 0.11 0.58 0.05 0.12 0.62 0.382 1.2
## ssno 0.18 0.00 -0.07 0.76 0.72 0.280 1.1
## sscs -0.09 0.02 0.09 0.76 0.59 0.414 1.1
## ssasi -0.14 -0.03 0.83 0.07 0.56 0.440 1.1
## ssmk 0.94 0.04 -0.11 0.02 0.81 0.194 1.0
## ssmc 0.42 -0.12 0.51 -0.02 0.57 0.427 2.1
## ssei 0.06 0.29 0.50 -0.06 0.58 0.417 1.7
##
## MR3 MR1 MR4 MR2
## SS loadings 2.06 1.95 1.56 1.31
## Proportion Var 0.21 0.19 0.16 0.13
## Cumulative Var 0.21 0.40 0.56 0.69
## Proportion Explained 0.30 0.28 0.23 0.19
## Cumulative Proportion 0.30 0.58 0.81 1.00
##
## With factor correlations of
## MR3 MR1 MR4 MR2
## MR3 1.00 0.76 0.72 0.61
## MR1 0.76 1.00 0.77 0.58
## MR4 0.72 0.77 1.00 0.45
## MR2 0.61 0.58 0.45 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 6.35 with Chi Square = 19448.39
## df of the model are 11 and the objective function was 0.03
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.02
##
## The harmonic n.obs is 3067 with the empirical chi square 17.14 with prob < 0.1
## The total n.obs was 3067 with Likelihood Chi Square = 88 with prob < 4.1e-14
##
## Tucker Lewis Index of factoring reliability = 0.984
## RMSEA index = 0.048 and the 90 % confidence intervals are 0.039 0.057
## BIC = -0.31
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR3 MR1 MR4 MR2
## Correlation of (regression) scores with factors 0.96 0.97 0.91 0.90
## Multiple R square of scores with factors 0.92 0.94 0.83 0.81
## Minimum correlation of possible factor scores 0.83 0.88 0.65 0.62
# full sample black vs white
white<- subset(dk, bw==1)
black<- subset(dk, bw==0)
dw<- dplyr::select(white, starts_with("ss"), sweight)
db<- dplyr::select(black, starts_with("ss"), sweight)
ev <- eigen(cor(dm)) # get eigenvalues
ev$values
## [1] 6.6655940 1.0517313 0.9716068 0.5476495 0.4282921 0.2910217 0.2820806 0.2330632 0.2079487
## [10] 0.1669759 0.1540363
ev <- eigen(cor(df)) # get eigenvalues
ev$values
## [1] 5.9806203 1.0788210 0.9591717 0.6436575 0.5636444 0.3987126 0.3752899 0.3182300 0.3019231
## [10] 0.1995904 0.1803392
fa3<-fa(db[,1:10], nfactors=3, rotate="promax", fm="minres")
fa3
## Factor Analysis using method = minres
## Call: fa(r = db[, 1:10], nfactors = 3, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR2 MR3 h2 u2 com
## ssgs 0.64 0.18 0.07 0.69 0.31 1.2
## ssar 0.21 0.05 0.59 0.63 0.37 1.3
## sswk 0.50 0.42 0.04 0.76 0.24 2.0
## sspc 0.31 0.45 0.15 0.66 0.34 2.0
## ssno -0.09 0.82 0.08 0.68 0.32 1.0
## sscs -0.10 0.93 -0.11 0.63 0.37 1.1
## ssasi 0.86 -0.09 -0.08 0.56 0.44 1.0
## ssmk -0.10 -0.04 1.03 0.86 0.14 1.0
## ssmc 0.71 -0.09 0.08 0.50 0.50 1.1
## ssei 0.91 -0.05 -0.07 0.68 0.32 1.0
##
## MR1 MR2 MR3
## SS loadings 3.00 2.09 1.56
## Proportion Var 0.30 0.21 0.16
## Cumulative Var 0.30 0.51 0.66
## Proportion Explained 0.45 0.31 0.23
## Cumulative Proportion 0.45 0.77 1.00
##
## With factor correlations of
## MR1 MR2 MR3
## MR1 1.00 0.65 0.75
## MR2 0.65 1.00 0.74
## MR3 0.75 0.74 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 6.42 with Chi Square = 19202.44
## df of the model are 18 and the objective function was 0.22
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.04
##
## The harmonic n.obs is 2994 with the empirical chi square 162.14 with prob < 3.2e-25
## The total n.obs was 2994 with Likelihood Chi Square = 661.69 with prob < 7.6e-129
##
## Tucker Lewis Index of factoring reliability = 0.916
## RMSEA index = 0.109 and the 90 % confidence intervals are 0.102 0.117
## BIC = 517.61
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR2 MR3
## Correlation of (regression) scores with factors 0.95 0.94 0.96
## Multiple R square of scores with factors 0.90 0.88 0.91
## Minimum correlation of possible factor scores 0.80 0.75 0.83
fa3<-fa(dw[,1:10], nfactors=3, rotate="promax", fm="minres")
fa3
## Factor Analysis using method = minres
## Call: fa(r = dw[, 1:10], nfactors = 3, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR2 MR1 MR3 h2 u2 com
## ssgs 0.50 0.12 0.36 0.76 0.243 2.0
## ssar 0.41 0.66 -0.10 0.78 0.215 1.7
## sswk 0.12 0.15 0.76 0.90 0.099 1.1
## sspc 0.02 0.38 0.51 0.69 0.311 1.9
## ssno -0.13 0.86 0.03 0.67 0.332 1.0
## sscs -0.21 0.74 0.13 0.53 0.471 1.2
## ssasi 0.91 -0.22 0.03 0.68 0.318 1.1
## ssmk 0.27 0.70 -0.05 0.70 0.303 1.3
## ssmc 0.87 0.10 -0.12 0.74 0.256 1.1
## ssei 0.77 -0.06 0.20 0.75 0.245 1.1
##
## MR2 MR1 MR3
## SS loadings 2.99 2.76 1.45
## Proportion Var 0.30 0.28 0.15
## Cumulative Var 0.30 0.58 0.72
## Proportion Explained 0.42 0.38 0.20
## Cumulative Proportion 0.42 0.80 1.00
##
## With factor correlations of
## MR2 MR1 MR3
## MR2 1.00 0.56 0.62
## MR1 0.56 1.00 0.69
## MR3 0.62 0.69 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 7.84 with Chi Square = 48260.32
## df of the model are 18 and the objective function was 0.31
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.04
##
## The harmonic n.obs is 6161 with the empirical chi square 436.21 with prob < 2.5e-81
## The total n.obs was 6161 with Likelihood Chi Square = 1913.4 with prob < 0
##
## Tucker Lewis Index of factoring reliability = 0.902
## RMSEA index = 0.131 and the 90 % confidence intervals are 0.126 0.136
## BIC = 1756.33
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR2 MR1 MR3
## Correlation of (regression) scores with factors 0.96 0.95 0.95
## Multiple R square of scores with factors 0.92 0.90 0.90
## Minimum correlation of possible factor scores 0.83 0.80 0.79
fa4<-fa(db[,1:10], nfactors=4, rotate="promax", fm="minres")
fa4
## Factor Analysis using method = minres
## Call: fa(r = db[, 1:10], nfactors = 4, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR4 MR1 MR3 MR2 h2 u2 com
## ssgs 0.30 0.55 0.08 -0.03 0.71 0.289 1.6
## ssar 0.17 -0.03 0.70 0.03 0.67 0.330 1.1
## sswk 0.01 0.95 -0.04 0.04 0.91 0.086 1.0
## sspc 0.01 0.57 0.16 0.17 0.69 0.311 1.3
## ssno 0.00 0.00 0.13 0.74 0.70 0.303 1.1
## sscs 0.01 0.02 -0.10 0.87 0.69 0.313 1.0
## ssasi 0.83 -0.03 -0.07 0.02 0.61 0.394 1.0
## ssmk -0.08 0.05 0.91 -0.02 0.78 0.217 1.0
## ssmc 0.72 -0.11 0.11 0.03 0.55 0.448 1.1
## ssei 0.69 0.22 -0.04 -0.05 0.66 0.340 1.2
##
## MR4 MR1 MR3 MR2
## SS loadings 2.05 1.92 1.54 1.46
## Proportion Var 0.20 0.19 0.15 0.15
## Cumulative Var 0.20 0.40 0.55 0.70
## Proportion Explained 0.29 0.28 0.22 0.21
## Cumulative Proportion 0.29 0.57 0.79 1.00
##
## With factor correlations of
## MR4 MR1 MR3 MR2
## MR4 1.00 0.74 0.69 0.47
## MR1 0.74 1.00 0.76 0.68
## MR3 0.69 0.76 1.00 0.67
## MR2 0.47 0.68 0.67 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 6.42 with Chi Square = 19202.44
## df of the model are 11 and the objective function was 0.01
##
## The root mean square of the residuals (RMSR) is 0
## The df corrected root mean square of the residuals is 0.01
##
## The harmonic n.obs is 2994 with the empirical chi square 4.57 with prob < 0.95
## The total n.obs was 2994 with Likelihood Chi Square = 26.26 with prob < 0.0059
##
## Tucker Lewis Index of factoring reliability = 0.997
## RMSEA index = 0.022 and the 90 % confidence intervals are 0.011 0.032
## BIC = -61.79
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR4 MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.93 0.97 0.94 0.92
## Multiple R square of scores with factors 0.86 0.94 0.88 0.84
## Minimum correlation of possible factor scores 0.72 0.88 0.76 0.69
fa4<-fa(dw[,1:10], nfactors=4, rotate="promax", fm="minres")
fa4
## Factor Analysis using method = minres
## Call: fa(r = dw[, 1:10], nfactors = 4, rotate = "promax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR2 MR1 MR3 MR4 h2 u2 com
## ssgs 0.33 0.50 0.17 -0.06 0.76 0.241 2.0
## ssar 0.13 0.00 0.76 0.09 0.82 0.184 1.1
## sswk 0.01 0.99 -0.07 0.02 0.91 0.087 1.0
## sspc -0.06 0.67 0.10 0.17 0.69 0.314 1.2
## ssno 0.03 -0.03 0.13 0.78 0.73 0.267 1.1
## sscs 0.00 0.06 -0.07 0.81 0.65 0.347 1.0
## ssasi 1.05 -0.09 -0.20 0.04 0.80 0.202 1.1
## ssmk -0.10 0.02 0.95 0.01 0.83 0.166 1.0
## ssmc 0.73 -0.09 0.26 0.00 0.72 0.282 1.3
## ssei 0.69 0.23 0.02 -0.03 0.75 0.253 1.2
##
## MR2 MR1 MR3 MR4
## SS loadings 2.38 1.99 1.82 1.47
## Proportion Var 0.24 0.20 0.18 0.15
## Cumulative Var 0.24 0.44 0.62 0.77
## Proportion Explained 0.31 0.26 0.24 0.19
## Cumulative Proportion 0.31 0.57 0.81 1.00
##
## With factor correlations of
## MR2 MR1 MR3 MR4
## MR2 1.00 0.67 0.66 0.32
## MR1 0.67 1.00 0.78 0.65
## MR3 0.66 0.78 1.00 0.66
## MR4 0.32 0.65 0.66 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 7.84 with Chi Square = 48260.32
## df of the model are 11 and the objective function was 0.03
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
##
## The harmonic n.obs is 6161 with the empirical chi square 18.48 with prob < 0.071
## The total n.obs was 6161 with Likelihood Chi Square = 167.1 with prob < 4.7e-30
##
## Tucker Lewis Index of factoring reliability = 0.987
## RMSEA index = 0.048 and the 90 % confidence intervals are 0.042 0.055
## BIC = 71.11
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR2 MR1 MR3 MR4
## Correlation of (regression) scores with factors 0.96 0.97 0.96 0.92
## Multiple R square of scores with factors 0.92 0.94 0.92 0.84
## Minimum correlation of possible factor scores 0.83 0.88 0.84 0.69
fa3<-fa(db[,1:10], nfactors=3, rotate="promax", fm="minres", weight=db$sweight)
fa3
## Factor Analysis using method = minres
## Call: fa(r = db[, 1:10], nfactors = 3, rotate = "promax", fm = "minres",
## weight = db$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR2 MR3 h2 u2 com
## ssgs 0.63 0.19 0.08 0.69 0.31 1.2
## ssar 0.21 0.05 0.58 0.63 0.37 1.3
## sswk 0.49 0.43 0.05 0.77 0.23 2.0
## sspc 0.30 0.46 0.15 0.67 0.33 2.0
## ssno -0.10 0.82 0.08 0.67 0.33 1.0
## sscs -0.10 0.94 -0.11 0.64 0.36 1.1
## ssasi 0.85 -0.08 -0.08 0.55 0.45 1.0
## ssmk -0.10 -0.04 1.03 0.86 0.14 1.0
## ssmc 0.71 -0.10 0.08 0.50 0.50 1.1
## ssei 0.90 -0.05 -0.07 0.67 0.33 1.0
##
## MR1 MR2 MR3
## SS loadings 2.97 2.13 1.56
## Proportion Var 0.30 0.21 0.16
## Cumulative Var 0.30 0.51 0.67
## Proportion Explained 0.45 0.32 0.23
## Cumulative Proportion 0.45 0.77 1.00
##
## With factor correlations of
## MR1 MR2 MR3
## MR1 1.00 0.65 0.76
## MR2 0.65 1.00 0.74
## MR3 0.76 0.74 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 6.46 with Chi Square = 19318.85
## df of the model are 18 and the objective function was 0.21
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.04
##
## The harmonic n.obs is 2994 with the empirical chi square 152.92 with prob < 2e-23
## The total n.obs was 2994 with Likelihood Chi Square = 635.4 with prob < 2.8e-123
##
## Tucker Lewis Index of factoring reliability = 0.92
## RMSEA index = 0.107 and the 90 % confidence intervals are 0.1 0.114
## BIC = 491.33
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR2 MR3
## Correlation of (regression) scores with factors 0.95 0.94 0.96
## Multiple R square of scores with factors 0.90 0.88 0.91
## Minimum correlation of possible factor scores 0.80 0.76 0.83
fa3<-fa(dw[,1:10], nfactors=3, rotate="promax", fm="minres", weight=dw$sweight)
fa3
## Factor Analysis using method = minres
## Call: fa(r = dw[, 1:10], nfactors = 3, rotate = "promax", fm = "minres",
## weight = dw$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR2 MR3 MR1 h2 u2 com
## ssgs 0.42 0.02 0.50 0.74 0.26 1.9
## ssar 0.40 0.54 0.06 0.75 0.25 1.9
## sswk -0.03 -0.01 0.97 0.89 0.11 1.0
## sspc -0.07 0.26 0.65 0.66 0.34 1.3
## ssno -0.06 0.92 -0.08 0.70 0.30 1.0
## sscs -0.17 0.77 0.03 0.53 0.47 1.1
## ssasi 0.94 -0.16 -0.08 0.67 0.33 1.1
## ssmk 0.23 0.56 0.13 0.67 0.33 1.4
## ssmc 0.90 0.11 -0.14 0.74 0.26 1.1
## ssei 0.75 -0.09 0.21 0.74 0.26 1.2
##
## MR2 MR3 MR1
## SS loadings 2.78 2.34 1.97
## Proportion Var 0.28 0.23 0.20
## Cumulative Var 0.28 0.51 0.71
## Proportion Explained 0.39 0.33 0.28
## Cumulative Proportion 0.39 0.72 1.00
##
## With factor correlations of
## MR2 MR3 MR1
## MR2 1.00 0.49 0.70
## MR3 0.49 1.00 0.74
## MR1 0.70 0.74 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 3 factors are sufficient.
##
## df null model = 45 with the objective function = 7.43 with Chi Square = 45766.47
## df of the model are 18 and the objective function was 0.35
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.05
##
## The harmonic n.obs is 6161 with the empirical chi square 470.12 with prob < 2e-88
## The total n.obs was 6161 with Likelihood Chi Square = 2170.21 with prob < 0
##
## Tucker Lewis Index of factoring reliability = 0.882
## RMSEA index = 0.139 and the 90 % confidence intervals are 0.134 0.144
## BIC = 2013.15
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR2 MR3 MR1
## Correlation of (regression) scores with factors 0.96 0.94 0.96
## Multiple R square of scores with factors 0.91 0.88 0.93
## Minimum correlation of possible factor scores 0.82 0.77 0.86
fa4<-fa(db[,1:10], nfactors=4, rotate="promax", fm="minres", weight=db$sweight)
fa4
## Factor Analysis using method = minres
## Call: fa(r = db[, 1:10], nfactors = 4, rotate = "promax", fm = "minres",
## weight = db$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR4 MR1 MR3 MR2 h2 u2 com
## ssgs 0.30 0.55 0.08 -0.03 0.71 0.288 1.6
## ssar 0.17 -0.02 0.67 0.05 0.67 0.335 1.1
## sswk 0.03 0.91 -0.03 0.05 0.90 0.097 1.0
## sspc 0.00 0.59 0.15 0.16 0.70 0.301 1.3
## ssno 0.02 -0.04 0.10 0.80 0.73 0.270 1.0
## sscs -0.01 0.07 -0.09 0.82 0.65 0.349 1.0
## ssasi 0.82 -0.02 -0.07 0.03 0.59 0.405 1.0
## ssmk -0.07 0.07 0.90 -0.02 0.79 0.212 1.0
## ssmc 0.72 -0.10 0.11 0.03 0.55 0.451 1.1
## ssei 0.69 0.22 -0.04 -0.05 0.66 0.345 1.2
##
## MR4 MR1 MR3 MR2
## SS loadings 2.04 1.93 1.50 1.48
## Proportion Var 0.20 0.19 0.15 0.15
## Cumulative Var 0.20 0.40 0.55 0.69
## Proportion Explained 0.29 0.28 0.22 0.21
## Cumulative Proportion 0.29 0.57 0.79 1.00
##
## With factor correlations of
## MR4 MR1 MR3 MR2
## MR4 1.00 0.74 0.70 0.47
## MR1 0.74 1.00 0.76 0.69
## MR3 0.70 0.76 1.00 0.67
## MR2 0.47 0.69 0.67 1.00
##
## Mean item complexity = 1.1
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 6.46 with Chi Square = 19318.85
## df of the model are 11 and the objective function was 0.01
##
## The root mean square of the residuals (RMSR) is 0
## The df corrected root mean square of the residuals is 0.01
##
## The harmonic n.obs is 2994 with the empirical chi square 4.47 with prob < 0.95
## The total n.obs was 2994 with Likelihood Chi Square = 25.61 with prob < 0.0074
##
## Tucker Lewis Index of factoring reliability = 0.997
## RMSEA index = 0.021 and the 90 % confidence intervals are 0.01 0.032
## BIC = -62.44
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR4 MR1 MR3 MR2
## Correlation of (regression) scores with factors 0.93 0.96 0.94 0.92
## Multiple R square of scores with factors 0.86 0.93 0.88 0.85
## Minimum correlation of possible factor scores 0.72 0.86 0.75 0.69
fa4<-fa(dw[,1:10], nfactors=4, rotate="promax", fm="minres", weight=dw$sweight)
fa4
## Factor Analysis using method = minres
## Call: fa(r = dw[, 1:10], nfactors = 4, rotate = "promax", fm = "minres",
## weight = dw$sweight)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR2 MR1 MR4 MR3 h2 u2 com
## ssgs 0.31 0.49 0.20 -0.07 0.74 0.262 2.1
## ssar 0.12 0.00 0.77 0.09 0.82 0.182 1.1
## sswk 0.00 1.02 -0.09 0.01 0.91 0.087 1.0
## sspc -0.06 0.65 0.09 0.17 0.66 0.344 1.2
## ssno 0.03 -0.03 0.13 0.77 0.72 0.283 1.1
## sscs 0.00 0.06 -0.07 0.81 0.64 0.358 1.0
## ssasi 1.05 -0.09 -0.21 0.05 0.79 0.213 1.1
## ssmk -0.11 0.02 0.96 0.02 0.83 0.167 1.0
## ssmc 0.72 -0.09 0.26 0.00 0.71 0.287 1.3
## ssei 0.69 0.24 0.01 -0.04 0.73 0.266 1.2
##
## MR2 MR1 MR4 MR3
## SS loadings 2.32 1.96 1.84 1.43
## Proportion Var 0.23 0.20 0.18 0.14
## Cumulative Var 0.23 0.43 0.61 0.76
## Proportion Explained 0.31 0.26 0.24 0.19
## Cumulative Proportion 0.31 0.57 0.81 1.00
##
## With factor correlations of
## MR2 MR1 MR4 MR3
## MR2 1.00 0.64 0.64 0.25
## MR1 0.64 1.00 0.78 0.61
## MR4 0.64 0.78 1.00 0.64
## MR3 0.25 0.61 0.64 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 4 factors are sufficient.
##
## df null model = 45 with the objective function = 7.43 with Chi Square = 45766.47
## df of the model are 11 and the objective function was 0.03
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.01
##
## The harmonic n.obs is 6161 with the empirical chi square 24.5 with prob < 0.011
## The total n.obs was 6161 with Likelihood Chi Square = 194.17 with prob < 1.2e-35
##
## Tucker Lewis Index of factoring reliability = 0.984
## RMSEA index = 0.052 and the 90 % confidence intervals are 0.046 0.059
## BIC = 98.19
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR2 MR1 MR4 MR3
## Correlation of (regression) scores with factors 0.95 0.97 0.96 0.91
## Multiple R square of scores with factors 0.91 0.94 0.92 0.83
## Minimum correlation of possible factor scores 0.82 0.88 0.84 0.67
# MGCFA USING SIBLING DATA
# WHITE SAMPLE
dw<- filter(d, bhw==3)
nrow(dw)
## [1] 1052
dgroup<- dplyr::select(dw, id, starts_with("ss"), afqt, efa, educ2000, age, sex, agesex, age2, agesex2, age14:age22, sweight, weight2000, cweight, asvabweight)
fit<-lm(efa ~ sex + rcs(age, 3) + sex*rcs(age, 3), data=dgroup)
summary(fit)
##
## Call:
## lm(formula = efa ~ sex + rcs(age, 3) + sex * rcs(age, 3), data = dgroup)
##
## Residuals:
## Min 1Q Median 3Q Max
## -46.457 -8.287 1.416 10.253 25.160
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 109.08303 1.68241 64.837 <2e-16 ***
## sex -2.75632 2.35698 -1.169 0.242
## rcs(age, 3)age 0.99371 0.70449 1.411 0.159
## rcs(age, 3)age' -0.05216 0.97784 -0.053 0.957
## sex:rcs(age, 3)age 0.74893 0.99704 0.751 0.453
## sex:rcs(age, 3)age' -0.50551 1.38954 -0.364 0.716
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.96 on 1046 degrees of freedom
## Multiple R-squared: 0.05494, Adjusted R-squared: 0.05042
## F-statistic: 12.16 on 5 and 1046 DF, p-value: 1.787e-11
dgroup$pred1<-fitted(fit)
original_age_min <- 14
original_age_max <- 22
mean_centered_min <- min(dgroup$age)
mean_centered_max <- max(dgroup$age)
original_age_mean <- (original_age_min + original_age_max) / 2
mean_centered_age_mean <- (mean_centered_min + mean_centered_max) / 2
age_difference <- original_age_mean - mean_centered_age_mean
xyplot(dgroup$pred1 ~ dgroup$age, data=dgroup, groups=sex, pch=19, type=c("p"), col=c('red', 'blue'), grid=TRUE, ylab="Predicted IQ", xlab="age", key=list(text=list(c("White Male", "White Female")), points=list(pch=c(19,19), col=c("red", "blue")), columns=2))
xyplot(dgroup$pred1 ~ dgroup$age, data=dgroup, groups=sex, pch=19, type=c("p"), col=c('red', 'blue'), grid=TRUE, ylab="Predicted IQ", xlab="Age", key=list(text=list(c("White Male", "White Female")), points=list(pch=c(19,19), col=c("red", "blue")), columns=2), scales=list(x=list(at=seq(mean_centered_min, mean_centered_max), labels=seq(original_age_min, original_age_max))))
describeBy(dgroup$pred1, dgroup$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 526 108.53 2.06 108.07 108.49 2.81 105.11 112.77 7.66 0.1 -0.96 0.09
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 526 104.78 2.86 105.76 104.85 3.36 99.36 110.17 10.82 -0.24 -0.83 0.12
describeBy(dgroup$efa, dgroup$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 526 108.53 14.25 110.78 109.64 14.95 66.31 131.19 64.88 -0.62 -0.36 0.62
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 526 104.78 11.99 105.7 105.38 13.15 69.41 127.45 58.03 -0.39 -0.48 0.52
describeBy(dgroup$afqt, dgroup$sex)
##
## Descriptive statistics by group
## INDICES: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## V1 1 526 106.69 15.03 107.79 107.17 19.08 77.91 130.02 52.11 -0.21 -1.16 0.66
## --------------------------------------------------------------------------
## INDICES: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## V1 1 526 106.83 14.02 107.28 107.15 17.51 78.34 130.02 51.68 -0.15 -1.05 0.61
describeBy(dgroup$educ2000, dgroup$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 392 13.73 2.57 12 13.48 1.48 7 20 13 0.62 -0.1 0.13
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 393 14.07 2.42 14 13.89 2.97 7 20 13 0.35 -0.66 0.12
cor(dgroup$efa, dgroup$afqt, use="pairwise.complete.obs", method="pearson")
## [,1]
## [1,] 0.9181601
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(age, sex) %>% summarise(MEAN = survey_mean(pred1), SD = survey_sd(pred1))
## # A tibble: 18 Ă— 5
## # Groups: age [9]
## age sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -4 0 105. 1.19e-15 6.91e-15
## 2 -4 1 99.4 0 0
## 3 -3 0 106. 1.97e-16 1.68e-15
## 4 -3 1 101. 7.50e-16 5.12e-15
## 5 -2 0 107. 1.24e-15 9.55e-15
## 6 -2 1 103. 0 0
## 7 -1 0 108. 1.67e-16 1.55e-15
## 8 -1 1 104. 0 0
## 9 0 0 109. 8.80e-16 7.12e-15
## 10 0 1 106. 0 0
## 11 1 0 110. 7.05e-16 5.87e-15
## 12 1 1 107. 0 0
## 13 2 0 111. 1.42e-13 7.92e-13
## 14 2 1 108. 6.53e-16 4.41e-15
## 15 3 0 112. 0 0
## 16 3 1 109. 1.45e-15 8.63e-15
## 17 4 0 113. 3.74e-15 1.28e-14
## 18 4 1 110. 0 0
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(age, sex) %>% summarise(MEAN = survey_mean(efa), SD = survey_sd(efa))
## # A tibble: 18 Ă— 5
## # Groups: age [9]
## age sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -4 0 105. 2.24 13.1
## 2 -4 1 102. 2.05 11.7
## 3 -3 0 108. 1.55 13.0
## 4 -3 1 103. 1.29 9.87
## 5 -2 0 112. 1.65 13.0
## 6 -2 1 107. 1.30 10.2
## 7 -1 0 109. 1.31 11.8
## 8 -1 1 105. 1.30 11.6
## 9 0 0 111. 1.52 12.5
## 10 0 1 108. 1.16 10.6
## 11 1 0 110. 1.78 14.4
## 12 1 1 106. 1.55 12.9
## 13 2 0 114. 1.84 12.7
## 14 2 1 108. 1.79 11.9
## 15 3 0 113. 1.99 13.1
## 16 3 1 109. 1.76 10.6
## 17 4 0 108. 5.59 19.4
## 18 4 1 116. 0.785 2.61
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(age, sex) %>% summarise(MEAN = survey_mean(afqt), SD = survey_sd(afqt))
## # A tibble: 18 Ă— 5
## # Groups: age [9]
## age sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -4 0 108. 2.55 14.8
## 2 -4 1 108. 2.44 13.6
## 3 -3 0 109. 1.82 15.0
## 4 -3 1 110. 1.63 12.5
## 5 -2 0 112. 1.85 14.4
## 6 -2 1 110. 1.59 12.4
## 7 -1 0 108. 1.60 13.8
## 8 -1 1 106. 1.55 13.8
## 9 0 0 108. 1.74 14.2
## 10 0 1 110. 1.48 13.4
## 11 1 0 107. 1.96 15.4
## 12 1 1 108. 1.76 14.7
## 13 2 0 109. 2.04 14.1
## 14 2 1 108. 2.23 14.8
## 15 3 0 107. 2.24 14.6
## 16 3 1 107. 2.37 14.2
## 17 4 0 103. 5.22 17.6
## 18 4 1 118. 2.14 7.00
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(sex) %>% summarise(MEAN = survey_mean(pred1), SD = survey_sd(pred1))
## # A tibble: 2 Ă— 4
## sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl>
## 1 0 109. 0.101 2.12
## 2 1 105. 0.144 2.96
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(sex) %>% summarise(MEAN = survey_mean(efa), SD = survey_sd(efa))
## # A tibble: 2 Ă— 4
## sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl>
## 1 0 110. 0.615 13.3
## 2 1 106. 0.524 11.3
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(sex) %>% summarise(MEAN = survey_mean(afqt), SD = survey_sd(afqt))
## # A tibble: 2 Ă— 4
## sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl>
## 1 0 108. 0.686 14.6
## 2 1 109. 0.636 13.6
dgroup %>% as_survey_design(ids = id, weights = weight2000) %>% group_by(sex) %>% summarise(MEAN = survey_mean(educ2000, na.rm = TRUE), SD = survey_sd(educ2000, na.rm = TRUE))
## # A tibble: 2 Ă— 4
## sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl>
## 1 0 13.8 0.133 2.58
## 2 1 14.1 0.125 2.43
# CORRELATED FACTOR MODEL, INTERCEPT BIAS IN BOTH SSNO AND SSCS BUT FREEING BOTH CAUSES NONPOSITIVE MATRIX
cf.model<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
'
cf.lv<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
verbal~~1*verbal
math~~1*math
speed~~1*speed
'
cf.reduced<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
verbal~~1*verbal
math~~1*math
speed~~1*speed
math~0*1
'
baseline<-cfa(cf.model, data=dgroup, meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 369.321 27.000 0.000 0.956 0.110 0.045 48913.861 49102.282
Mc(baseline)
## [1] 0.8497145
configural<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 234.371 54.000 0.000 0.976 0.080 0.028 47841.441 48218.283
Mc(configural)
## [1] 0.9177692
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 52 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 76
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 234.371 201.180
## Degrees of freedom 54 54
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.165
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 177.916 152.720
## 1 56.455 48.460
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs 2.724 0.307 8.884 0.000 2.123 3.325 2.724 0.600
## sswk 6.154 0.286 21.552 0.000 5.595 6.714 6.154 0.916
## sspc 2.601 0.145 17.994 0.000 2.318 2.885 2.601 0.836
## math =~
## ssar 6.723 0.191 35.132 0.000 6.348 7.098 6.723 0.943
## ssmk 5.949 0.170 35.025 0.000 5.616 6.281 5.949 0.894
## ssmc 1.040 0.236 4.404 0.000 0.577 1.502 1.040 0.211
## electronic =~
## ssgs 1.392 0.307 4.530 0.000 0.790 1.994 1.392 0.307
## ssasi 3.537 0.208 16.974 0.000 3.129 3.946 3.537 0.746
## ssmc 3.197 0.239 13.397 0.000 2.729 3.664 3.197 0.648
## ssei 3.608 0.131 27.445 0.000 3.350 3.866 3.608 0.940
## speed =~
## ssno 0.775 0.037 20.810 0.000 0.702 0.848 0.775 0.876
## sscs 0.641 0.042 15.444 0.000 0.560 0.723 0.641 0.763
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.810 0.022 36.047 0.000 0.766 0.854 0.810 0.810
## electronic 0.822 0.024 33.823 0.000 0.775 0.870 0.822 0.822
## speed 0.699 0.039 18.047 0.000 0.623 0.774 0.699 0.699
## math ~~
## electronic 0.664 0.033 19.980 0.000 0.599 0.729 0.664 0.664
## speed 0.755 0.028 26.669 0.000 0.699 0.810 0.755 0.755
## electronic ~~
## speed 0.501 0.051 9.870 0.000 0.402 0.601 0.501 0.501
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 17.910 0.210 85.392 0.000 17.498 18.321 17.910 3.948
## .sswk 27.643 0.309 89.548 0.000 27.038 28.248 27.643 4.115
## .sspc 11.207 0.144 77.836 0.000 10.925 11.490 11.207 3.603
## .ssar 20.311 0.336 60.447 0.000 19.652 20.969 20.311 2.848
## .ssmk 15.277 0.316 48.361 0.000 14.658 15.896 15.277 2.296
## .ssmc 17.082 0.231 73.903 0.000 16.629 17.535 17.082 3.462
## .ssasi 17.796 0.221 80.523 0.000 17.363 18.230 17.796 3.756
## .ssei 13.530 0.177 76.269 0.000 13.182 13.877 13.530 3.524
## .ssno 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.275
## .sscs 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.091
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.985 0.426 11.711 0.000 4.151 5.819 4.985 0.242
## .sswk 7.240 0.938 7.722 0.000 5.403 9.078 7.240 0.160
## .sspc 2.911 0.247 11.770 0.000 2.426 3.396 2.911 0.301
## .ssar 5.652 0.984 5.745 0.000 3.723 7.580 5.652 0.111
## .ssmk 8.874 0.974 9.109 0.000 6.965 10.784 8.874 0.201
## .ssmc 8.630 0.701 12.308 0.000 7.256 10.004 8.630 0.355
## .ssasi 9.943 0.911 10.913 0.000 8.157 11.729 9.943 0.443
## .ssei 1.726 0.373 4.631 0.000 0.995 2.456 1.726 0.117
## .ssno 0.182 0.034 5.398 0.000 0.116 0.248 0.182 0.232
## .sscs 0.295 0.048 6.181 0.000 0.201 0.388 0.295 0.418
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs 0.633 0.655 0.966 0.334 -0.651 1.916 0.633 0.154
## sswk 5.819 0.261 22.299 0.000 5.308 6.331 5.819 0.933
## sspc 2.037 0.136 15.026 0.000 1.771 2.303 2.037 0.799
## math =~
## ssar 6.231 0.183 34.048 0.000 5.873 6.590 6.231 0.935
## ssmk 5.380 0.164 32.716 0.000 5.058 5.702 5.380 0.867
## ssmc 1.760 0.314 5.609 0.000 1.145 2.375 1.760 0.442
## electronic =~
## ssgs 3.039 0.649 4.680 0.000 1.766 4.312 3.039 0.742
## ssasi 2.111 0.151 13.952 0.000 1.814 2.407 2.111 0.619
## ssmc 1.030 0.315 3.269 0.001 0.412 1.647 1.030 0.258
## ssei 2.291 0.114 20.115 0.000 2.067 2.514 2.291 0.743
## speed =~
## ssno 0.779 0.039 20.147 0.000 0.703 0.854 0.779 0.921
## sscs 0.552 0.046 11.946 0.000 0.461 0.642 0.552 0.664
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.771 0.022 34.970 0.000 0.728 0.814 0.771 0.771
## electronic 0.896 0.030 29.890 0.000 0.837 0.954 0.896 0.896
## speed 0.613 0.050 12.174 0.000 0.515 0.712 0.613 0.613
## math ~~
## electronic 0.811 0.027 29.554 0.000 0.757 0.865 0.811 0.811
## speed 0.678 0.033 20.656 0.000 0.614 0.742 0.678 0.678
## electronic ~~
## speed 0.504 0.054 9.325 0.000 0.398 0.610 0.504 0.504
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 16.094 0.190 84.654 0.000 15.721 16.467 16.094 3.927
## .sswk 27.980 0.285 98.025 0.000 27.421 28.540 27.980 4.485
## .sspc 12.116 0.116 104.370 0.000 11.888 12.343 12.116 4.750
## .ssar 18.639 0.312 59.821 0.000 18.028 19.250 18.639 2.796
## .ssmk 14.968 0.291 51.396 0.000 14.397 15.539 14.968 2.413
## .ssmc 12.925 0.187 68.955 0.000 12.557 13.292 12.925 3.242
## .ssasi 11.745 0.159 73.710 0.000 11.433 12.058 11.745 3.447
## .ssei 10.387 0.143 72.446 0.000 10.106 10.668 10.387 3.370
## .ssno 0.511 0.039 13.006 0.000 0.434 0.588 0.511 0.604
## .sscs 0.629 0.039 16.289 0.000 0.554 0.705 0.629 0.758
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 3.718 0.486 7.646 0.000 2.765 4.671 3.718 0.221
## .sswk 5.067 0.996 5.086 0.000 3.114 7.019 5.067 0.130
## .sspc 2.357 0.198 11.929 0.000 1.970 2.744 2.357 0.362
## .ssar 5.606 0.972 5.765 0.000 3.700 7.512 5.606 0.126
## .ssmk 9.526 0.946 10.072 0.000 7.672 11.379 9.526 0.248
## .ssmc 8.795 0.593 14.822 0.000 7.632 9.957 8.795 0.553
## .ssasi 7.158 0.561 12.749 0.000 6.058 8.258 7.158 0.616
## .ssei 4.256 0.387 10.993 0.000 3.497 5.015 4.256 0.448
## .ssno 0.109 0.046 2.361 0.018 0.019 0.200 0.109 0.153
## .sscs 0.386 0.050 7.642 0.000 0.287 0.485 0.386 0.559
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
modificationIndices(configural, sort=T, maximum.number=30)
## lhs op rhs block group level mi epc sepc.lv sepc.all sepc.nox
## 97 verbal =~ ssei 1 1 1 47.864 2.698 2.698 0.703 0.703
## 101 math =~ sswk 1 1 1 46.052 -2.875 -2.875 -0.428 -0.428
## 156 ssmc ~~ ssasi 1 1 1 37.198 2.999 2.999 0.324 0.324
## 122 ssgs ~~ sspc 1 1 1 22.686 -1.069 -1.069 -0.281 -0.281
## 152 ssmk ~~ ssasi 1 1 1 22.628 -2.358 -2.358 -0.251 -0.251
## 96 verbal =~ ssasi 1 1 1 22.201 -1.801 -1.801 -0.380 -0.380
## 115 speed =~ sspc 1 1 1 21.820 0.700 0.700 0.225 0.225
## 157 ssmc ~~ ssei 1 1 1 20.305 -2.033 -2.033 -0.527 -0.527
## 120 speed =~ ssei 1 1 1 19.745 0.759 0.759 0.198 0.198
## 102 math =~ sspc 1 1 1 19.196 0.826 0.826 0.266 0.266
## 135 sswk ~~ ssei 1 1 1 16.753 1.386 1.386 0.392 0.392
## 114 speed =~ sswk 1 1 1 15.918 -1.320 -1.320 -0.196 -0.196
## 103 math =~ ssasi 1 1 1 15.799 -0.936 -0.936 -0.198 -0.198
## 124 ssgs ~~ ssmk 1 1 1 14.874 1.413 1.413 0.212 0.212
## 158 ssmc ~~ ssno 1 1 1 14.114 -0.297 -0.297 -0.237 -0.237
## 133 sswk ~~ ssmc 1 1 1 13.775 -1.720 -1.720 -0.218 -0.218
## 119 speed =~ ssasi 1 1 1 11.275 -0.673 -0.673 -0.142 -0.142
## 100 math =~ ssgs 1 1 1 10.956 0.783 0.783 0.172 0.172
## 145 ssar ~~ ssmk 1 1 1 10.247 -15.891 -15.891 -2.244 -2.244
## 107 electronic =~ sswk 1 1 1 9.877 1.615 1.615 0.240 0.240
## 108 electronic =~ sspc 1 1 1 9.877 -0.683 -0.683 -0.219 -0.219
## 171 verbal =~ ssno 2 2 1 8.669 -0.267 -0.267 -0.316 -0.316
## 172 verbal =~ sscs 2 2 1 8.669 0.190 0.190 0.228 0.228
## 131 sswk ~~ ssar 1 1 1 8.187 -1.584 -1.584 -0.248 -0.248
## 217 sspc ~~ sscs 2 2 1 8.140 0.137 0.137 0.144 0.144
## 95 verbal =~ ssmc 1 1 1 8.134 -1.274 -1.274 -0.258 -0.258
## 229 ssmc ~~ ssasi 2 2 1 7.712 1.057 1.057 0.133 0.133
## 179 math =~ sscs 2 2 1 7.574 -0.310 -0.310 -0.373 -0.373
## 178 math =~ ssno 2 2 1 7.574 0.437 0.437 0.517 0.517
## 121 ssgs ~~ sswk 1 1 1 7.338 1.350 1.350 0.225 0.225
metric<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 281.220 62.000 0.000 0.971 0.082 0.039 47872.289 48209.464
Mc(metric)
## [1] 0.9009631
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 59 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 80
## Number of equality constraints 12
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 281.220 242.359
## Degrees of freedom 62 62
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.160
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 188.061 162.074
## 1 93.159 80.286
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.686 0.257 10.471 0.000 2.183 3.189 2.686 0.578
## sswk (.p2.) 6.258 0.275 22.715 0.000 5.718 6.798 6.258 0.923
## sspc (.p3.) 2.431 0.130 18.627 0.000 2.175 2.686 2.431 0.813
## math =~
## ssar (.p4.) 6.755 0.179 37.681 0.000 6.403 7.106 6.755 0.945
## ssmk (.p5.) 5.906 0.161 36.681 0.000 5.591 6.222 5.906 0.891
## ssmc (.p6.) 1.163 0.191 6.088 0.000 0.788 1.537 1.163 0.239
## electronic =~
## ssgs (.p7.) 1.581 0.280 5.654 0.000 1.033 2.129 1.581 0.340
## ssasi (.p8.) 3.482 0.186 18.686 0.000 3.117 3.847 3.482 0.739
## ssmc (.p9.) 2.987 0.226 13.217 0.000 2.544 3.430 2.987 0.614
## ssei (.10.) 3.622 0.130 27.891 0.000 3.367 3.876 3.622 0.943
## speed =~
## ssno (.11.) 0.793 0.034 23.032 0.000 0.726 0.860 0.793 0.890
## sscs (.12.) 0.615 0.038 16.208 0.000 0.541 0.690 0.615 0.743
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.804 0.023 34.988 0.000 0.759 0.849 0.804 0.804
## electronic 0.818 0.025 33.174 0.000 0.769 0.866 0.818 0.818
## speed 0.688 0.040 17.297 0.000 0.610 0.766 0.688 0.688
## math ~~
## electronic 0.663 0.033 20.259 0.000 0.599 0.727 0.663 0.663
## speed 0.750 0.029 25.710 0.000 0.692 0.807 0.750 0.750
## electronic ~~
## speed 0.495 0.051 9.749 0.000 0.395 0.594 0.495 0.495
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 17.910 0.210 85.392 0.000 17.498 18.321 17.910 3.853
## .sswk 27.643 0.309 89.548 0.000 27.038 28.248 27.643 4.078
## .sspc 11.207 0.144 77.836 0.000 10.925 11.490 11.207 3.748
## .ssar 20.311 0.336 60.447 0.000 19.652 20.969 20.311 2.841
## .ssmk 15.277 0.316 48.361 0.000 14.658 15.896 15.277 2.306
## .ssmc 17.082 0.231 73.903 0.000 16.629 17.535 17.082 3.511
## .ssasi 17.796 0.221 80.523 0.000 17.363 18.230 17.796 3.779
## .ssei 13.530 0.177 76.269 0.000 13.182 13.877 13.530 3.522
## .ssno 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.274
## .sscs 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.092
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.949 0.415 11.940 0.000 4.137 5.762 4.949 0.229
## .sswk 6.786 0.958 7.081 0.000 4.908 8.665 6.786 0.148
## .sspc 3.034 0.254 11.956 0.000 2.537 3.532 3.034 0.339
## .ssar 5.477 0.921 5.947 0.000 3.672 7.282 5.477 0.107
## .ssmk 9.022 0.911 9.901 0.000 7.236 10.808 9.022 0.205
## .ssmc 8.794 0.691 12.723 0.000 7.439 10.148 8.794 0.371
## .ssasi 10.052 0.909 11.059 0.000 8.271 11.834 10.052 0.453
## .ssei 1.641 0.370 4.440 0.000 0.917 2.366 1.641 0.111
## .ssno 0.165 0.033 5.049 0.000 0.101 0.229 0.165 0.208
## .sscs 0.306 0.046 6.718 0.000 0.217 0.396 0.306 0.447
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.686 0.257 10.471 0.000 2.183 3.189 2.417 0.608
## sswk (.p2.) 6.258 0.275 22.715 0.000 5.718 6.798 5.632 0.912
## sspc (.p3.) 2.431 0.130 18.627 0.000 2.175 2.686 2.187 0.821
## math =~
## ssar (.p4.) 6.755 0.179 37.681 0.000 6.403 7.106 6.204 0.934
## ssmk (.p5.) 5.906 0.161 36.681 0.000 5.591 6.222 5.425 0.870
## ssmc (.p6.) 1.163 0.191 6.088 0.000 0.788 1.537 1.068 0.262
## electronic =~
## ssgs (.p7.) 1.581 0.280 5.654 0.000 1.033 2.129 1.014 0.255
## ssasi (.p8.) 3.482 0.186 18.686 0.000 3.117 3.847 2.234 0.650
## ssmc (.p9.) 2.987 0.226 13.217 0.000 2.544 3.430 1.916 0.471
## ssei (.10.) 3.622 0.130 27.891 0.000 3.367 3.876 2.324 0.756
## speed =~
## ssno (.11.) 0.793 0.034 23.032 0.000 0.726 0.860 0.756 0.900
## sscs (.12.) 0.615 0.038 16.208 0.000 0.541 0.690 0.586 0.693
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.656 0.060 10.860 0.000 0.538 0.775 0.794 0.794
## electronic 0.506 0.051 9.834 0.000 0.405 0.607 0.877 0.877
## speed 0.539 0.079 6.828 0.000 0.384 0.693 0.628 0.628
## math ~~
## electronic 0.469 0.041 11.405 0.000 0.388 0.549 0.795 0.795
## speed 0.602 0.060 10.016 0.000 0.484 0.720 0.688 0.688
## electronic ~~
## speed 0.300 0.045 6.588 0.000 0.211 0.389 0.490 0.490
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 16.094 0.190 84.654 0.000 15.721 16.467 16.094 4.050
## .sswk 27.980 0.285 98.025 0.000 27.421 28.540 27.980 4.533
## .sspc 12.116 0.116 104.370 0.000 11.888 12.343 12.116 4.548
## .ssar 18.639 0.312 59.821 0.000 18.028 19.250 18.639 2.805
## .ssmk 14.968 0.291 51.396 0.000 14.397 15.539 14.968 2.401
## .ssmc 12.925 0.187 68.955 0.000 12.557 13.292 12.925 3.175
## .ssasi 11.745 0.159 73.710 0.000 11.433 12.058 11.745 3.417
## .ssei 10.387 0.143 72.446 0.000 10.106 10.668 10.387 3.377
## .ssno 0.511 0.039 13.006 0.000 0.434 0.588 0.511 0.608
## .sscs 0.629 0.039 16.289 0.000 0.554 0.705 0.629 0.743
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.618 0.383 12.043 0.000 3.867 5.370 4.618 0.293
## .sswk 6.390 0.928 6.883 0.000 4.570 8.210 6.390 0.168
## .sspc 2.312 0.194 11.910 0.000 1.931 2.692 2.312 0.326
## .ssar 5.674 0.931 6.097 0.000 3.850 7.498 5.674 0.128
## .ssmk 9.428 0.903 10.446 0.000 7.659 11.197 9.428 0.243
## .ssmc 8.505 0.579 14.690 0.000 7.371 9.640 8.505 0.513
## .ssasi 6.821 0.533 12.801 0.000 5.776 7.865 6.821 0.577
## .ssei 4.060 0.384 10.563 0.000 3.307 4.814 4.060 0.429
## .ssno 0.135 0.037 3.615 0.000 0.062 0.208 0.135 0.191
## .sscs 0.373 0.047 7.963 0.000 0.281 0.465 0.373 0.520
## verbal 0.810 0.101 8.006 0.000 0.612 1.008 1.000 1.000
## math 0.844 0.060 14.136 0.000 0.727 0.961 1.000 1.000
## electronic 0.412 0.046 8.988 0.000 0.322 0.501 1.000 1.000
## speed 0.908 0.113 8.012 0.000 0.686 1.131 1.000 1.000
lavTestScore(metric, release = 1:12)
## 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 43.259 12 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p47. 4.694 1 0.030
## 2 .p2. == .p48. 2.600 1 0.107
## 3 .p3. == .p49. 12.500 1 0.000
## 4 .p4. == .p50. 0.342 1 0.558
## 5 .p5. == .p51. 0.252 1 0.616
## 6 .p6. == .p52. 0.113 1 0.736
## 7 .p7. == .p53. 12.758 1 0.000
## 8 .p8. == .p54. 0.377 1 0.539
## 9 .p9. == .p55. 3.540 1 0.060
## 10 .p10. == .p56. 0.036 1 0.851
## 11 .p11. == .p57. 3.048 1 0.081
## 12 .p12. == .p58. 3.048 1 0.081
metric2<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"), group.partial=c("electronic=~ssgs", "verbal=~sspc"))
fitMeasures(metric2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 259.500 60.000 0.000 0.973 0.080 0.032 47854.570 48201.661
Mc(metric2)
## [1] 0.9094553
scalar<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("electronic=~ssgs", "verbal=~sspc"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 529.426 66.000 0.000 0.938 0.116 0.068 48112.496 48429.837
Mc(scalar)
## [1] 0.8021423
summary(scalar, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 128 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 84
## Number of equality constraints 20
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 529.426 453.940
## Degrees of freedom 66 66
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.166
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 313.515 268.813
## 1 215.912 185.126
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.629 0.161 16.293 0.000 2.312 2.945 2.629 0.580
## sswk (.p2.) 6.135 0.277 22.118 0.000 5.592 6.679 6.135 0.912
## sspc 2.613 0.146 17.901 0.000 2.327 2.899 2.613 0.833
## math =~
## ssar (.p4.) 6.783 0.177 38.295 0.000 6.436 7.130 6.783 0.946
## ssmk (.p5.) 5.842 0.169 34.593 0.000 5.511 6.173 5.842 0.885
## ssmc (.p6.) 0.981 0.168 5.843 0.000 0.652 1.310 0.981 0.198
## electronic =~
## ssgs 1.500 0.172 8.742 0.000 1.164 1.837 1.500 0.331
## ssasi (.p8.) 4.186 0.155 26.967 0.000 3.882 4.490 4.186 0.796
## ssmc (.p9.) 3.335 0.181 18.395 0.000 2.980 3.690 3.335 0.674
## ssei (.10.) 3.301 0.142 23.253 0.000 3.023 3.579 3.301 0.897
## speed =~
## ssno (.11.) 0.754 0.037 20.471 0.000 0.682 0.826 0.754 0.857
## sscs (.12.) 0.660 0.037 17.843 0.000 0.587 0.732 0.660 0.769
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.810 0.022 36.134 0.000 0.766 0.854 0.810 0.810
## electronic 0.821 0.026 30.982 0.000 0.769 0.873 0.821 0.821
## speed 0.710 0.038 18.674 0.000 0.635 0.784 0.710 0.710
## math ~~
## electronic 0.667 0.034 19.753 0.000 0.601 0.734 0.667 0.667
## speed 0.761 0.028 27.179 0.000 0.706 0.816 0.761 0.761
## electronic ~~
## speed 0.500 0.053 9.452 0.000 0.396 0.604 0.500 0.500
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 18.077 0.221 81.802 0.000 17.644 18.510 18.077 3.988
## .sswk (.34.) 27.549 0.340 80.922 0.000 26.881 28.216 27.549 4.097
## .sspc (.35.) 11.600 0.139 83.358 0.000 11.327 11.873 11.600 3.700
## .ssar (.36.) 20.317 0.355 57.181 0.000 19.620 21.013 20.317 2.834
## .ssmk (.37.) 15.820 0.319 49.635 0.000 15.196 16.445 15.820 2.398
## .ssmc (.38.) 17.148 0.242 70.945 0.000 16.674 17.622 17.148 3.465
## .ssasi (.39.) 17.216 0.259 66.549 0.000 16.709 17.723 17.216 3.274
## .ssei (.40.) 13.854 0.178 77.677 0.000 13.505 14.204 13.854 3.763
## .ssno (.41.) 0.205 0.043 4.731 0.000 0.120 0.290 0.205 0.233
## .sscs (.42.) 0.188 0.042 4.498 0.000 0.106 0.270 0.188 0.219
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.916 0.407 12.070 0.000 4.118 5.715 4.916 0.239
## .sswk 7.569 0.996 7.597 0.000 5.617 9.522 7.569 0.167
## .sspc 3.005 0.261 11.524 0.000 2.494 3.516 3.005 0.306
## .ssar 5.368 0.966 5.559 0.000 3.476 7.261 5.368 0.104
## .ssmk 9.411 0.961 9.796 0.000 7.528 11.294 9.411 0.216
## .ssmc 8.036 0.673 11.949 0.000 6.718 9.354 8.036 0.328
## .ssasi 10.133 1.028 9.858 0.000 8.118 12.147 10.133 0.366
## .ssei 2.654 0.369 7.198 0.000 1.932 3.377 2.654 0.196
## .ssno 0.205 0.032 6.349 0.000 0.142 0.268 0.205 0.265
## .sscs 0.300 0.050 6.045 0.000 0.203 0.397 0.300 0.408
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.629 0.161 16.293 0.000 2.312 2.945 2.424 0.593
## sswk (.p2.) 6.135 0.277 22.118 0.000 5.592 6.679 5.658 0.911
## sspc 2.245 0.155 14.502 0.000 1.942 2.549 2.070 0.800
## math =~
## ssar (.p4.) 6.783 0.177 38.295 0.000 6.436 7.130 6.236 0.935
## ssmk (.p5.) 5.842 0.169 34.593 0.000 5.511 6.173 5.371 0.863
## ssmc (.p6.) 0.981 0.168 5.843 0.000 0.652 1.310 0.902 0.224
## electronic =~
## ssgs 1.959 0.169 11.580 0.000 1.628 2.291 1.172 0.287
## ssasi (.p8.) 4.186 0.155 26.967 0.000 3.882 4.490 2.505 0.685
## ssmc (.p9.) 3.335 0.181 18.395 0.000 2.980 3.690 1.996 0.496
## ssei (.10.) 3.301 0.142 23.253 0.000 3.023 3.579 1.976 0.671
## speed =~
## ssno (.11.) 0.754 0.037 20.471 0.000 0.682 0.826 0.712 0.857
## sscs (.12.) 0.660 0.037 17.843 0.000 0.587 0.732 0.623 0.713
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.673 0.063 10.620 0.000 0.549 0.797 0.794 0.794
## electronic 0.487 0.053 9.224 0.000 0.383 0.590 0.882 0.882
## speed 0.565 0.084 6.710 0.000 0.400 0.729 0.648 0.648
## math ~~
## electronic 0.449 0.039 11.365 0.000 0.371 0.526 0.816 0.816
## speed 0.608 0.062 9.738 0.000 0.485 0.730 0.700 0.700
## electronic ~~
## speed 0.287 0.045 6.346 0.000 0.199 0.376 0.508 0.508
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 18.077 0.221 81.802 0.000 17.644 18.510 18.077 4.422
## .sswk (.34.) 27.549 0.340 80.922 0.000 26.881 28.216 27.549 4.438
## .sspc (.35.) 11.600 0.139 83.358 0.000 11.327 11.873 11.600 4.480
## .ssar (.36.) 20.317 0.355 57.181 0.000 19.620 21.013 20.317 3.046
## .ssmk (.37.) 15.820 0.319 49.635 0.000 15.196 16.445 15.820 2.543
## .ssmc (.38.) 17.148 0.242 70.945 0.000 16.674 17.622 17.148 4.259
## .ssasi (.39.) 17.216 0.259 66.549 0.000 16.709 17.723 17.216 4.711
## .ssei (.40.) 13.854 0.178 77.677 0.000 13.505 14.204 13.854 4.706
## .ssno (.41.) 0.205 0.043 4.731 0.000 0.120 0.290 0.205 0.247
## .sscs (.42.) 0.188 0.042 4.498 0.000 0.106 0.270 0.188 0.215
## verbal 0.115 0.071 1.617 0.106 -0.024 0.255 0.125 0.125
## math -0.218 0.070 -3.097 0.002 -0.356 -0.080 -0.237 -0.237
## elctrnc -1.185 0.090 -13.183 0.000 -1.361 -1.009 -1.980 -1.980
## speed 0.477 0.084 5.695 0.000 0.313 0.642 0.505 0.505
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.444 0.388 11.462 0.000 3.684 5.204 4.444 0.266
## .sswk 6.528 0.973 6.707 0.000 4.620 8.435 6.528 0.169
## .sspc 2.418 0.207 11.703 0.000 2.013 2.823 2.418 0.361
## .ssar 5.597 0.956 5.857 0.000 3.724 7.470 5.597 0.126
## .ssmk 9.851 0.923 10.674 0.000 8.042 11.660 9.851 0.255
## .ssmc 8.479 0.580 14.627 0.000 7.343 9.615 8.479 0.523
## .ssasi 7.079 0.589 12.022 0.000 5.925 8.234 7.079 0.530
## .ssei 4.764 0.401 11.868 0.000 3.977 5.551 4.764 0.550
## .ssno 0.183 0.038 4.870 0.000 0.109 0.257 0.183 0.265
## .sscs 0.376 0.052 7.207 0.000 0.274 0.478 0.376 0.492
## verbal 0.850 0.113 7.505 0.000 0.628 1.072 1.000 1.000
## math 0.845 0.060 14.066 0.000 0.727 0.963 1.000 1.000
## electronic 0.358 0.041 8.755 0.000 0.278 0.438 1.000 1.000
## speed 0.892 0.118 7.553 0.000 0.661 1.124 1.000 1.000
lavTestScore(scalar, release = 11:20)
## 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 259.116 10 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p33. == .p79. 4.179 1 0.041
## 2 .p34. == .p80. 47.677 1 0.000
## 3 .p35. == .p81. 42.051 1 0.000
## 4 .p36. == .p82. 23.815 1 0.000
## 5 .p37. == .p83. 25.326 1 0.000
## 6 .p38. == .p84. 1.037 1 0.308
## 7 .p39. == .p85. 109.808 1 0.000
## 8 .p40. == .p86. 103.410 1 0.000
## 9 .p41. == .p87. 61.106 1 0.000
## 10 .p42. == .p88. 61.106 1 0.000
scalar2<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("electronic=~ssgs", "verbal=~sspc", "sswk~1", "ssar~1", "ssei~1", "sscs~1")) # no and cs biased but one needs to be constrained
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 269.709 62.000 0.000 0.972 0.080 0.034 47860.779 48197.954
Mc(scalar2)
## [1] 0.9059102
summary(scalar2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 105 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 84
## Number of equality constraints 16
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 269.709 231.884
## Degrees of freedom 62 62
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.163
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 188.400 161.978
## 1 81.309 69.906
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.665 0.157 16.933 0.000 2.357 2.974 2.665 0.589
## sswk (.p2.) 6.176 0.277 22.287 0.000 5.633 6.719 6.176 0.918
## sspc 2.603 0.144 18.136 0.000 2.321 2.884 2.603 0.837
## math =~
## ssar (.p4.) 6.752 0.179 37.671 0.000 6.401 7.104 6.752 0.945
## ssmk (.p5.) 5.907 0.161 36.736 0.000 5.592 6.222 5.907 0.891
## ssmc (.p6.) 1.412 0.157 9.002 0.000 1.105 1.720 1.412 0.294
## electronic =~
## ssgs 1.434 0.171 8.407 0.000 1.099 1.768 1.434 0.317
## ssasi (.p8.) 3.626 0.182 19.923 0.000 3.269 3.983 3.626 0.752
## ssmc (.p9.) 2.650 0.183 14.454 0.000 2.290 3.009 2.650 0.552
## ssei (.10.) 3.658 0.127 28.785 0.000 3.409 3.907 3.658 0.950
## speed =~
## ssno (.11.) 0.793 0.034 23.014 0.000 0.725 0.860 0.793 0.889
## sscs (.12.) 0.615 0.038 16.224 0.000 0.541 0.690 0.615 0.744
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.810 0.022 36.722 0.000 0.767 0.853 0.810 0.810
## electronic 0.817 0.024 33.709 0.000 0.770 0.865 0.817 0.817
## speed 0.692 0.040 17.482 0.000 0.615 0.770 0.692 0.692
## math ~~
## electronic 0.659 0.032 20.588 0.000 0.596 0.722 0.659 0.659
## speed 0.749 0.029 25.687 0.000 0.692 0.807 0.749 0.749
## electronic ~~
## speed 0.494 0.050 9.799 0.000 0.395 0.593 0.494 0.494
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 17.917 0.210 85.505 0.000 17.507 18.328 17.917 3.961
## .sswk 27.618 0.314 87.939 0.000 27.002 28.233 27.618 4.104
## .sspc (.35.) 11.180 0.147 76.150 0.000 10.892 11.468 11.180 3.594
## .ssar 20.289 0.339 59.860 0.000 19.624 20.953 20.289 2.838
## .ssmk (.37.) 15.235 0.318 47.921 0.000 14.611 15.858 15.235 2.299
## .ssmc (.38.) 17.165 0.227 75.668 0.000 16.721 17.610 17.165 3.576
## .ssasi (.39.) 17.677 0.227 77.957 0.000 17.233 18.122 17.677 3.665
## .ssei 13.515 0.180 74.935 0.000 13.161 13.868 13.515 3.510
## .ssno (.41.) 0.242 0.042 5.791 0.000 0.160 0.323 0.242 0.271
## .sscs 0.074 0.040 1.860 0.063 -0.004 0.153 0.074 0.090
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.056 0.413 12.246 0.000 4.247 5.865 5.056 0.247
## .sswk 7.137 0.932 7.659 0.000 5.311 8.964 7.137 0.158
## .sspc 2.905 0.243 11.977 0.000 2.429 3.380 2.905 0.300
## .ssar 5.515 0.911 6.054 0.000 3.729 7.300 5.515 0.108
## .ssmk 9.028 0.902 10.007 0.000 7.260 10.796 9.028 0.206
## .ssmc 9.096 0.686 13.254 0.000 7.751 10.441 9.096 0.395
## .ssasi 10.117 0.925 10.939 0.000 8.304 11.929 10.117 0.435
## .ssei 1.446 0.345 4.185 0.000 0.769 2.123 1.446 0.098
## .ssno 0.166 0.033 5.084 0.000 0.102 0.230 0.166 0.209
## .sscs 0.306 0.046 6.723 0.000 0.217 0.395 0.306 0.447
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.665 0.157 16.933 0.000 2.357 2.974 2.465 0.601
## sswk (.p2.) 6.176 0.277 22.287 0.000 5.633 6.719 5.712 0.917
## sspc 2.193 0.136 16.135 0.000 1.926 2.459 2.028 0.797
## math =~
## ssar (.p4.) 6.752 0.179 37.671 0.000 6.401 7.104 6.202 0.933
## ssmk (.p5.) 5.907 0.161 36.736 0.000 5.592 6.222 5.426 0.870
## ssmc (.p6.) 1.412 0.157 9.002 0.000 1.105 1.720 1.297 0.321
## electronic =~
## ssgs 1.858 0.168 11.049 0.000 1.528 2.187 1.160 0.283
## ssasi (.p8.) 3.626 0.182 19.923 0.000 3.269 3.983 2.265 0.656
## ssmc (.p9.) 2.650 0.183 14.454 0.000 2.290 3.009 1.655 0.409
## ssei (.10.) 3.658 0.127 28.785 0.000 3.409 3.907 2.285 0.751
## speed =~
## ssno (.11.) 0.793 0.034 23.014 0.000 0.725 0.860 0.756 0.900
## sscs (.12.) 0.615 0.038 16.224 0.000 0.541 0.690 0.587 0.693
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.673 0.061 10.945 0.000 0.552 0.793 0.792 0.792
## electronic 0.503 0.053 9.509 0.000 0.399 0.607 0.871 0.871
## speed 0.552 0.080 6.864 0.000 0.395 0.710 0.626 0.626
## math ~~
## electronic 0.452 0.039 11.597 0.000 0.375 0.528 0.787 0.787
## speed 0.602 0.060 10.004 0.000 0.484 0.720 0.688 0.688
## electronic ~~
## speed 0.287 0.045 6.410 0.000 0.199 0.374 0.481 0.481
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 17.917 0.210 85.505 0.000 17.507 18.328 17.917 4.368
## .sswk 25.303 0.505 50.109 0.000 24.313 26.292 25.303 4.063
## .sspc (.35.) 11.180 0.147 76.150 0.000 10.892 11.468 11.180 4.392
## .ssar 18.914 0.414 45.718 0.000 18.103 19.725 18.914 2.846
## .ssmk (.37.) 15.235 0.318 47.921 0.000 14.611 15.858 15.235 2.444
## .ssmc (.38.) 17.165 0.227 75.668 0.000 16.721 17.610 17.165 4.245
## .ssasi (.39.) 17.677 0.227 77.957 0.000 17.233 18.122 17.677 5.119
## .ssei 16.296 0.405 40.269 0.000 15.503 17.089 16.296 5.354
## .ssno (.41.) 0.242 0.042 5.791 0.000 0.160 0.323 0.242 0.288
## .sscs 0.420 0.047 8.864 0.000 0.327 0.513 0.420 0.496
## verbal 0.434 0.087 4.997 0.000 0.263 0.604 0.469 0.469
## math -0.041 0.073 -0.558 0.577 -0.184 0.102 -0.044 -0.044
## elctrnc -1.615 0.127 -12.724 0.000 -1.864 -1.367 -2.586 -2.586
## speed 0.340 0.071 4.764 0.000 0.200 0.480 0.356 0.356
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.419 0.387 11.414 0.000 3.660 5.178 4.419 0.263
## .sswk 6.156 0.927 6.641 0.000 4.339 7.973 6.156 0.159
## .sspc 2.367 0.193 12.239 0.000 1.988 2.746 2.367 0.365
## .ssar 5.686 0.919 6.184 0.000 3.884 7.488 5.686 0.129
## .ssmk 9.423 0.900 10.472 0.000 7.659 11.186 9.423 0.242
## .ssmc 8.549 0.578 14.783 0.000 7.416 9.682 8.549 0.523
## .ssasi 6.795 0.535 12.693 0.000 5.746 7.844 6.795 0.570
## .ssei 4.044 0.384 10.523 0.000 3.290 4.797 4.044 0.437
## .ssno 0.135 0.037 3.620 0.000 0.062 0.207 0.135 0.191
## .sscs 0.373 0.047 7.958 0.000 0.281 0.465 0.373 0.520
## verbal 0.855 0.107 7.987 0.000 0.645 1.065 1.000 1.000
## math 0.844 0.060 14.139 0.000 0.727 0.961 1.000 1.000
## electronic 0.390 0.043 8.985 0.000 0.305 0.475 1.000 1.000
## speed 0.909 0.114 8.006 0.000 0.686 1.132 1.000 1.000
strict<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("electronic=~ssgs", "verbal=~sspc", "sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 326.652 72.000 0.000 0.966 0.082 0.041 47897.722 48185.312
Mc(strict)
## [1] 0.8859032
cf.cov<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("electronic=~ssgs", "verbal=~sspc", "sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(cf.cov, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 299.664 68.000 0.000 0.969 0.080 0.091 47878.734 48186.157
Mc(cf.cov)
## [1] 0.895645
summary(cf.cov, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 106 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 84
## Number of equality constraints 22
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 299.664 256.547
## Degrees of freedom 68 68
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.168
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 205.549 175.974
## 1 94.115 80.573
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.443 0.125 19.492 0.000 2.197 2.688 2.443 0.573
## sswk (.p2.) 5.791 0.202 28.702 0.000 5.395 6.186 5.791 0.904
## sspc 2.470 0.115 21.555 0.000 2.246 2.695 2.470 0.827
## math =~
## ssar (.p4.) 6.575 0.152 43.238 0.000 6.277 6.873 6.575 0.941
## ssmk (.p5.) 5.759 0.136 42.237 0.000 5.492 6.026 5.759 0.887
## ssmc (.p6.) 1.380 0.150 9.174 0.000 1.085 1.675 1.380 0.304
## electronic =~
## ssgs 1.408 0.149 9.473 0.000 1.117 1.700 1.408 0.330
## ssasi (.p8.) 3.240 0.140 23.069 0.000 2.964 3.515 3.240 0.714
## ssmc (.p9.) 2.367 0.152 15.576 0.000 2.069 2.665 2.367 0.521
## ssei (.10.) 3.335 0.092 36.448 0.000 3.156 3.514 3.335 0.940
## speed =~
## ssno (.11.) 0.767 0.029 26.462 0.000 0.710 0.824 0.767 0.884
## sscs (.12.) 0.593 0.033 18.165 0.000 0.529 0.657 0.593 0.731
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.27.) 0.813 0.020 41.389 0.000 0.775 0.852 0.813 0.813
## elctrnc (.28.) 0.752 0.027 28.348 0.000 0.700 0.804 0.752 0.752
## speed (.29.) 0.686 0.034 19.986 0.000 0.619 0.753 0.686 0.686
## math ~~
## elctrnc (.30.) 0.612 0.026 23.741 0.000 0.562 0.663 0.612 0.612
## speed (.31.) 0.720 0.026 27.214 0.000 0.668 0.772 0.720 0.720
## electronic ~~
## speed (.32.) 0.429 0.035 12.124 0.000 0.360 0.498 0.429 0.429
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 17.919 0.209 85.760 0.000 17.510 18.329 17.919 4.202
## .sswk 27.628 0.312 88.685 0.000 27.017 28.238 27.628 4.315
## .sspc (.35.) 11.188 0.145 77.004 0.000 10.903 11.473 11.188 3.744
## .ssar 20.297 0.338 60.085 0.000 19.635 20.959 20.297 2.905
## .ssmk (.37.) 15.241 0.317 48.076 0.000 14.620 15.863 15.241 2.348
## .ssmc (.38.) 17.174 0.226 75.973 0.000 16.731 17.617 17.174 3.781
## .ssasi (.39.) 17.688 0.225 78.604 0.000 17.247 18.129 17.688 3.898
## .ssei 13.522 0.179 75.574 0.000 13.171 13.872 13.522 3.813
## .ssno (.41.) 0.242 0.042 5.831 0.000 0.161 0.324 0.242 0.279
## .sscs 0.075 0.040 1.880 0.060 -0.003 0.153 0.075 0.093
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.065 0.413 12.278 0.000 4.256 5.873 5.065 0.278
## .sswk 7.466 0.957 7.802 0.000 5.590 9.341 7.466 0.182
## .sspc 2.830 0.237 11.932 0.000 2.365 3.294 2.830 0.317
## .ssar 5.588 0.903 6.185 0.000 3.817 7.358 5.588 0.114
## .ssmk 8.979 0.900 9.979 0.000 7.216 10.743 8.979 0.213
## .ssmc 9.129 0.688 13.275 0.000 7.781 10.476 9.129 0.442
## .ssasi 10.097 0.923 10.935 0.000 8.287 11.907 10.097 0.490
## .ssei 1.455 0.367 3.969 0.000 0.736 2.174 1.455 0.116
## .ssno 0.164 0.033 4.974 0.000 0.100 0.229 0.164 0.218
## .sscs 0.307 0.045 6.753 0.000 0.218 0.396 0.307 0.466
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.443 0.125 19.492 0.000 2.197 2.688 2.577 0.595
## sswk (.p2.) 5.791 0.202 28.702 0.000 5.395 6.186 6.110 0.928
## sspc 2.044 0.120 17.052 0.000 1.809 2.278 2.156 0.813
## math =~
## ssar (.p4.) 6.575 0.152 43.238 0.000 6.277 6.873 6.404 0.937
## ssmk (.p5.) 5.759 0.136 42.237 0.000 5.492 6.026 5.610 0.878
## ssmc (.p6.) 1.380 0.150 9.174 0.000 1.085 1.675 1.344 0.318
## electronic =~
## ssgs 1.636 0.132 12.373 0.000 1.377 1.896 1.286 0.297
## ssasi (.p8.) 3.240 0.140 23.069 0.000 2.964 3.515 2.545 0.698
## ssmc (.p9.) 2.367 0.152 15.576 0.000 2.069 2.665 1.859 0.440
## ssei (.10.) 3.335 0.092 36.448 0.000 3.156 3.514 2.620 0.795
## speed =~
## ssno (.11.) 0.767 0.029 26.462 0.000 0.710 0.824 0.788 0.910
## sscs (.12.) 0.593 0.033 18.165 0.000 0.529 0.657 0.609 0.705
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.27.) 0.813 0.020 41.389 0.000 0.775 0.852 0.791 0.791
## elctrnc (.28.) 0.752 0.027 28.348 0.000 0.700 0.804 0.907 0.907
## speed (.29.) 0.686 0.034 19.986 0.000 0.619 0.753 0.633 0.633
## math ~~
## elctrnc (.30.) 0.612 0.026 23.741 0.000 0.562 0.663 0.800 0.800
## speed (.31.) 0.720 0.026 27.214 0.000 0.668 0.772 0.720 0.720
## electronic ~~
## speed (.32.) 0.429 0.035 12.124 0.000 0.360 0.498 0.532 0.532
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 17.919 0.209 85.760 0.000 17.510 18.329 17.919 4.140
## .sswk 25.319 0.507 49.918 0.000 24.325 26.313 25.319 3.844
## .sspc (.35.) 11.188 0.145 77.004 0.000 10.903 11.473 11.188 4.217
## .ssar 18.921 0.412 45.890 0.000 18.113 19.730 18.921 2.767
## .ssmk (.37.) 15.241 0.317 48.076 0.000 14.620 15.863 15.241 2.384
## .ssmc (.38.) 17.174 0.226 75.973 0.000 16.731 17.617 17.174 4.062
## .ssasi (.39.) 17.688 0.225 78.604 0.000 17.247 18.129 17.688 4.849
## .ssei 16.432 0.411 39.996 0.000 15.627 17.237 16.432 4.988
## .ssno (.41.) 0.242 0.042 5.831 0.000 0.161 0.324 0.242 0.280
## .sscs 0.422 0.047 8.917 0.000 0.329 0.514 0.422 0.488
## verbal 0.460 0.099 4.661 0.000 0.266 0.653 0.436 0.436
## math -0.043 0.075 -0.575 0.566 -0.189 0.104 -0.044 -0.044
## elctrnc -1.812 0.129 -14.098 0.000 -2.064 -1.560 -2.307 -2.307
## speed 0.350 0.076 4.606 0.000 0.201 0.499 0.341 0.341
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.430 0.387 11.443 0.000 3.672 5.189 4.430 0.236
## .sswk 6.055 0.933 6.492 0.000 4.227 7.884 6.055 0.140
## .sspc 2.389 0.194 12.297 0.000 2.008 2.770 2.389 0.339
## .ssar 5.742 0.934 6.147 0.000 3.911 7.573 5.742 0.123
## .ssmk 9.387 0.899 10.441 0.000 7.625 11.149 9.387 0.230
## .ssmc 8.611 0.582 14.805 0.000 7.471 9.751 8.611 0.482
## .ssasi 6.829 0.536 12.732 0.000 5.778 7.880 6.829 0.513
## .ssei 3.987 0.384 10.371 0.000 3.233 4.740 3.987 0.367
## .ssno 0.129 0.037 3.540 0.000 0.058 0.201 0.129 0.172
## .sscs 0.376 0.047 8.010 0.000 0.284 0.468 0.376 0.503
## verbal 1.113 0.052 21.499 0.000 1.012 1.215 1.000 1.000
## math 0.949 0.036 26.646 0.000 0.879 1.019 1.000 1.000
## electronic 0.617 0.042 14.554 0.000 0.534 0.700 1.000 1.000
## speed 1.055 0.075 14.085 0.000 0.908 1.202 1.000 1.000
cf.vcov<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances", "lv.variances"), group.partial=c("electronic=~ssgs", "verbal=~sspc", "sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(cf.vcov, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 373.254 72.000 0.000 0.960 0.089 0.117 47944.324 48231.914
Mc(cf.vcov)
## [1] 0.8664786
cf.cov2<-cfa(cf.lv, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("electronic=~ssgs", "verbal=~sspc", "sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(cf.cov2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 307.970 71.000 0.000 0.968 0.080 0.091 47881.040 48173.588
Mc(cf.cov2)
## [1] 0.8933871
summary(cf.cov2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 101 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 81
## Number of equality constraints 22
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 307.970 265.087
## Degrees of freedom 71 71
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.162
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 211.417 181.979
## 1 96.552 83.108
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.529 0.122 20.652 0.000 2.289 2.769 2.529 0.590
## sswk (.p2.) 5.946 0.196 30.336 0.000 5.562 6.330 5.946 0.915
## sspc 2.487 0.116 21.477 0.000 2.260 2.714 2.487 0.827
## math =~
## ssar (.p4.) 6.488 0.132 49.024 0.000 6.229 6.748 6.488 0.938
## ssmk (.p5.) 5.679 0.119 47.613 0.000 5.445 5.913 5.679 0.884
## ssmc (.p6.) 1.374 0.149 9.221 0.000 1.082 1.666 1.374 0.303
## electronic =~
## ssgs 1.369 0.151 9.097 0.000 1.074 1.664 1.369 0.319
## ssasi (.p8.) 3.209 0.143 22.510 0.000 2.930 3.489 3.209 0.710
## ssmc (.p9.) 2.337 0.154 15.151 0.000 2.034 2.639 2.337 0.516
## ssei (.10.) 3.319 0.092 36.111 0.000 3.139 3.500 3.319 0.941
## speed =~
## ssno (.11.) 0.774 0.027 28.916 0.000 0.722 0.827 0.774 0.889
## sscs (.12.) 0.601 0.031 19.281 0.000 0.540 0.663 0.601 0.736
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.27.) 0.803 0.015 51.959 0.000 0.773 0.833 0.803 0.803
## elctrnc (.28.) 0.731 0.026 28.596 0.000 0.681 0.781 0.731 0.731
## speed (.29.) 0.662 0.031 21.677 0.000 0.603 0.722 0.662 0.662
## math ~~
## elctrnc (.30.) 0.626 0.025 25.463 0.000 0.578 0.675 0.626 0.626
## speed (.31.) 0.721 0.022 33.119 0.000 0.678 0.763 0.721 0.721
## electronic ~~
## speed (.32.) 0.428 0.034 12.557 0.000 0.361 0.495 0.428 0.428
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 17.922 0.209 85.743 0.000 17.512 18.332 17.922 4.181
## .sswk 27.627 0.312 88.672 0.000 27.016 28.237 27.627 4.252
## .sspc (.35.) 11.185 0.145 77.019 0.000 10.901 11.470 11.185 3.719
## .ssar 20.297 0.338 60.068 0.000 19.634 20.959 20.297 2.936
## .ssmk (.37.) 15.242 0.317 48.083 0.000 14.621 15.864 15.242 2.373
## .ssmc (.38.) 17.168 0.226 75.902 0.000 16.724 17.611 17.168 3.791
## .ssasi (.39.) 17.689 0.225 78.560 0.000 17.248 18.131 17.689 3.915
## .ssei 13.521 0.179 75.575 0.000 13.171 13.872 13.521 3.832
## .ssno (.41.) 0.242 0.042 5.829 0.000 0.161 0.324 0.242 0.278
## .sscs 0.075 0.040 1.880 0.060 -0.003 0.153 0.075 0.092
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssgs 5.040 0.412 12.219 0.000 4.231 5.848 5.040 0.274
## .sswk 6.857 0.905 7.574 0.000 5.083 8.631 6.857 0.162
## .sspc 2.860 0.241 11.865 0.000 2.388 3.332 2.860 0.316
## .ssar 5.703 0.869 6.566 0.000 4.001 7.406 5.703 0.119
## .ssmk 9.010 0.884 10.195 0.000 7.278 10.742 9.010 0.218
## .ssmc 9.143 0.697 13.110 0.000 7.776 10.510 9.143 0.446
## .ssasi 10.115 0.922 10.971 0.000 8.308 11.922 10.115 0.496
## .ssei 1.429 0.384 3.726 0.000 0.678 2.181 1.429 0.115
## .ssno 0.160 0.032 5.009 0.000 0.097 0.222 0.160 0.211
## .sscs 0.307 0.046 6.677 0.000 0.217 0.397 0.307 0.459
## electronic 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.529 0.122 20.652 0.000 2.289 2.769 2.529 0.589
## sswk (.p2.) 5.946 0.196 30.336 0.000 5.562 6.330 5.946 0.917
## sspc 2.138 0.125 17.153 0.000 1.894 2.382 2.138 0.810
## math =~
## ssar (.p4.) 6.488 0.132 49.024 0.000 6.229 6.748 6.488 0.940
## ssmk (.p5.) 5.679 0.119 47.613 0.000 5.445 5.913 5.679 0.880
## ssmc (.p6.) 1.374 0.149 9.221 0.000 1.082 1.666 1.374 0.324
## electronic =~
## ssgs 1.620 0.132 12.281 0.000 1.362 1.879 1.289 0.300
## ssasi (.p8.) 3.209 0.143 22.510 0.000 2.930 3.489 2.553 0.698
## ssmc (.p9.) 2.337 0.154 15.151 0.000 2.034 2.639 1.859 0.438
## ssei (.10.) 3.319 0.092 36.111 0.000 3.139 3.500 2.640 0.798
## speed =~
## ssno (.11.) 0.774 0.027 28.916 0.000 0.722 0.827 0.774 0.900
## sscs (.12.) 0.601 0.031 19.281 0.000 0.540 0.663 0.601 0.702
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.27.) 0.803 0.015 51.959 0.000 0.773 0.833 0.803 0.803
## elctrnc (.28.) 0.731 0.026 28.596 0.000 0.681 0.781 0.919 0.919
## speed (.29.) 0.662 0.031 21.677 0.000 0.603 0.722 0.662 0.662
## math ~~
## elctrnc (.30.) 0.626 0.025 25.463 0.000 0.578 0.675 0.787 0.787
## speed (.31.) 0.721 0.022 33.119 0.000 0.678 0.763 0.721 0.721
## electronic ~~
## speed (.32.) 0.428 0.034 12.557 0.000 0.361 0.495 0.538 0.538
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 17.922 0.209 85.743 0.000 17.512 18.332 17.922 4.175
## .sswk 25.355 0.499 50.807 0.000 24.377 26.333 25.355 3.912
## .sspc (.35.) 11.185 0.145 77.019 0.000 10.901 11.470 11.185 4.236
## .ssar 18.924 0.413 45.865 0.000 18.115 19.733 18.924 2.741
## .ssmk (.37.) 15.242 0.317 48.083 0.000 14.621 15.864 15.242 2.362
## .ssmc (.38.) 17.168 0.226 75.902 0.000 16.724 17.611 17.168 4.044
## .ssasi (.39.) 17.689 0.225 78.560 0.000 17.248 18.131 17.689 4.840
## .ssei 16.463 0.421 39.064 0.000 15.637 17.289 16.463 4.974
## .ssno (.41.) 0.242 0.042 5.829 0.000 0.161 0.324 0.242 0.282
## .sscs 0.421 0.047 8.889 0.000 0.328 0.514 0.421 0.491
## verbal 0.441 0.095 4.634 0.000 0.255 0.628 0.441 0.441
## math -0.044 0.076 -0.580 0.562 -0.193 0.105 -0.044 -0.044
## elctrnc -1.830 0.132 -13.824 0.000 -2.090 -1.571 -2.301 -2.301
## speed 0.347 0.075 4.609 0.000 0.199 0.494 0.347 0.347
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssgs 4.381 0.384 11.401 0.000 3.628 5.135 4.381 0.238
## .sswk 6.661 0.913 7.295 0.000 4.871 8.451 6.661 0.159
## .sspc 2.401 0.198 12.147 0.000 2.013 2.788 2.401 0.344
## .ssar 5.554 0.921 6.030 0.000 3.749 7.359 5.554 0.117
## .ssmk 9.407 0.916 10.265 0.000 7.611 11.203 9.407 0.226
## .ssmc 8.659 0.583 14.846 0.000 7.516 9.802 8.659 0.480
## .ssasi 6.844 0.536 12.773 0.000 5.793 7.894 6.844 0.512
## .ssei 3.981 0.388 10.250 0.000 3.220 4.742 3.981 0.363
## .ssno 0.141 0.034 4.183 0.000 0.075 0.207 0.141 0.190
## .sscs 0.372 0.047 7.985 0.000 0.281 0.464 0.372 0.507
## electronic 0.633 0.045 14.165 0.000 0.545 0.720 1.000 1.000
reduced<-cfa(cf.reduced, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("electronic=~ssgs", "verbal=~sspc", "sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(reduced, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 308.366 72.000 0.000 0.968 0.079 0.092 47879.436 48167.026
Mc(reduced)
## [1] 0.8936438
summary(reduced, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 96 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 80
## Number of equality constraints 22
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 308.366 265.366
## Degrees of freedom 72 72
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.162
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 211.559 182.058
## 1 96.807 83.308
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.528 0.123 20.634 0.000 2.288 2.768 2.528 0.590
## sswk (.p2.) 5.946 0.196 30.355 0.000 5.562 6.330 5.946 0.915
## sspc 2.488 0.116 21.517 0.000 2.261 2.715 2.488 0.827
## math =~
## ssar (.p4.) 6.490 0.132 49.190 0.000 6.231 6.748 6.490 0.938
## ssmk (.p5.) 5.680 0.119 47.570 0.000 5.446 5.914 5.680 0.884
## ssmc (.p6.) 1.372 0.149 9.207 0.000 1.080 1.664 1.372 0.303
## electronic =~
## ssgs 1.371 0.150 9.111 0.000 1.076 1.665 1.371 0.320
## ssasi (.p8.) 3.208 0.143 22.493 0.000 2.929 3.488 3.208 0.710
## ssmc (.p9.) 2.341 0.154 15.218 0.000 2.039 2.642 2.341 0.517
## ssei (.10.) 3.319 0.092 36.116 0.000 3.139 3.499 3.319 0.941
## speed =~
## ssno (.11.) 0.774 0.027 28.919 0.000 0.722 0.827 0.774 0.889
## sscs (.12.) 0.601 0.031 19.283 0.000 0.540 0.663 0.601 0.736
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.28.) 0.803 0.015 51.971 0.000 0.773 0.833 0.803 0.803
## elctrnc (.29.) 0.731 0.026 28.600 0.000 0.681 0.781 0.731 0.731
## speed (.30.) 0.663 0.031 21.687 0.000 0.603 0.722 0.663 0.663
## math ~~
## elctrnc (.31.) 0.626 0.025 25.466 0.000 0.578 0.675 0.626 0.626
## speed (.32.) 0.721 0.022 33.139 0.000 0.678 0.764 0.721 0.721
## electronic ~~
## speed (.33.) 0.428 0.034 12.564 0.000 0.362 0.495 0.428 0.428
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.34.) 17.874 0.183 97.516 0.000 17.514 18.233 17.874 4.170
## .sswk 27.547 0.276 99.654 0.000 27.005 28.089 27.547 4.240
## .sspc (.36.) 11.152 0.129 86.524 0.000 10.900 11.405 11.152 3.707
## .ssar 20.188 0.265 76.080 0.000 19.668 20.708 20.188 2.919
## .ssmk (.38.) 15.121 0.216 70.117 0.000 14.699 15.544 15.121 2.354
## .ssmc (.39.) 17.119 0.203 84.336 0.000 16.721 17.516 17.119 3.779
## .ssasi (.40.) 17.657 0.219 80.486 0.000 17.227 18.087 17.657 3.909
## .ssei 13.487 0.164 82.322 0.000 13.165 13.808 13.487 3.822
## .ssno (.42.) 0.233 0.038 6.204 0.000 0.159 0.307 0.233 0.267
## .sscs 0.068 0.037 1.824 0.068 -0.005 0.141 0.068 0.083
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssgs 5.040 0.412 12.220 0.000 4.232 5.848 5.040 0.274
## .sswk 6.857 0.905 7.572 0.000 5.082 8.631 6.857 0.162
## .sspc 2.860 0.241 11.858 0.000 2.387 3.332 2.860 0.316
## .ssar 5.701 0.869 6.560 0.000 3.998 7.404 5.701 0.119
## .ssmk 9.014 0.884 10.195 0.000 7.281 10.747 9.014 0.218
## .ssmc 9.138 0.698 13.094 0.000 7.770 10.506 9.138 0.445
## .ssasi 10.113 0.922 10.969 0.000 8.306 11.920 10.113 0.496
## .ssei 1.432 0.383 3.737 0.000 0.681 2.183 1.432 0.115
## .ssno 0.160 0.032 5.009 0.000 0.097 0.222 0.160 0.210
## .sscs 0.307 0.046 6.677 0.000 0.217 0.397 0.307 0.459
## electronic 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.528 0.123 20.634 0.000 2.288 2.768 2.528 0.589
## sswk (.p2.) 5.946 0.196 30.355 0.000 5.562 6.330 5.946 0.917
## sspc 2.138 0.125 17.150 0.000 1.894 2.382 2.138 0.810
## math =~
## ssar (.p4.) 6.490 0.132 49.190 0.000 6.231 6.748 6.490 0.940
## ssmk (.p5.) 5.680 0.119 47.570 0.000 5.446 5.914 5.680 0.880
## ssmc (.p6.) 1.372 0.149 9.207 0.000 1.080 1.664 1.372 0.323
## electronic =~
## ssgs 1.623 0.132 12.276 0.000 1.364 1.882 1.291 0.301
## ssasi (.p8.) 3.208 0.143 22.493 0.000 2.929 3.488 2.552 0.698
## ssmc (.p9.) 2.341 0.154 15.218 0.000 2.039 2.642 1.862 0.438
## ssei (.10.) 3.319 0.092 36.116 0.000 3.139 3.499 2.640 0.798
## speed =~
## ssno (.11.) 0.774 0.027 28.919 0.000 0.722 0.827 0.774 0.900
## sscs (.12.) 0.601 0.031 19.283 0.000 0.540 0.663 0.601 0.702
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.28.) 0.803 0.015 51.971 0.000 0.773 0.833 0.803 0.803
## elctrnc (.29.) 0.731 0.026 28.600 0.000 0.681 0.781 0.919 0.919
## speed (.30.) 0.663 0.031 21.687 0.000 0.603 0.722 0.663 0.663
## math ~~
## elctrnc (.31.) 0.626 0.025 25.466 0.000 0.578 0.675 0.787 0.787
## speed (.32.) 0.721 0.022 33.139 0.000 0.678 0.764 0.721 0.721
## electronic ~~
## speed (.33.) 0.428 0.034 12.564 0.000 0.362 0.495 0.539 0.539
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.34.) 17.874 0.183 97.516 0.000 17.514 18.233 17.874 4.163
## .sswk 25.263 0.454 55.601 0.000 24.372 26.153 25.263 3.897
## .sspc (.36.) 11.152 0.129 86.524 0.000 10.900 11.405 11.152 4.224
## .ssar 18.753 0.262 71.632 0.000 18.240 19.266 18.753 2.716
## .ssmk (.38.) 15.121 0.216 70.117 0.000 14.699 15.544 15.121 2.342
## .ssmc (.39.) 17.119 0.203 84.336 0.000 16.721 17.516 17.119 4.031
## .ssasi (.40.) 17.657 0.219 80.486 0.000 17.227 18.087 17.657 4.831
## .ssei 16.431 0.418 39.351 0.000 15.613 17.250 16.431 4.965
## .ssno (.42.) 0.233 0.038 6.204 0.000 0.159 0.307 0.233 0.271
## .sscs 0.414 0.045 9.247 0.000 0.326 0.501 0.414 0.483
## verbal 0.471 0.077 6.100 0.000 0.320 0.623 0.471 0.471
## elctrnc -1.810 0.127 -14.205 0.000 -2.060 -1.560 -2.275 -2.275
## speed 0.371 0.062 5.967 0.000 0.249 0.493 0.371 0.371
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssgs 4.381 0.384 11.401 0.000 3.628 5.134 4.381 0.238
## .sswk 6.660 0.913 7.295 0.000 4.871 8.449 6.660 0.158
## .sspc 2.401 0.198 12.148 0.000 2.013 2.788 2.401 0.344
## .ssar 5.552 0.921 6.028 0.000 3.747 7.357 5.552 0.116
## .ssmk 9.412 0.918 10.258 0.000 7.614 11.210 9.412 0.226
## .ssmc 8.659 0.583 14.843 0.000 7.515 9.802 8.659 0.480
## .ssasi 6.844 0.536 12.775 0.000 5.794 7.894 6.844 0.512
## .ssei 3.982 0.388 10.253 0.000 3.221 4.743 3.982 0.364
## .ssno 0.141 0.034 4.183 0.000 0.075 0.207 0.141 0.190
## .sscs 0.372 0.047 7.985 0.000 0.281 0.464 0.372 0.507
## electronic 0.633 0.045 14.170 0.000 0.545 0.720 1.000 1.000
tests<-lavTestLRT(configural, metric2, scalar2, cf.cov, cf.cov2, reduced)
Td=tests[2:6,"Chisq diff"]
Td
## [1] 21.4160944 9.4329700 24.5698454 8.1511306 0.3352272
dfd=tests[2:6,"Df diff"]
dfd
## [1] 6 2 6 3 1
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-526 + 526 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
## Warning in sqrt((ld) * G/(N - G)): NaNs produced
RMSEAD
## [1] 0.06995712 0.08413691 0.07678013 0.05718880 NaN
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.03943611 0.10306430
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.03575879 0.14133825
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.04677058 0.10946959
RMSEA.CI(T=Td[4],df=dfd[4],N=N,G=2)
## [1] 0.009106328 0.105998965
RMSEA.CI(T=Td[5],df=dfd[5],N=N,G=2)
## [1] NA 0.09587373
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
## 0.998 0.998 0.871 0.734 0.339 0.070
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
## 0.991 0.989 0.889 0.821 0.617 0.371
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 0.999 0.931 0.836 0.474 0.129
round(pvals(T=Td[4],df=dfd[4],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 0.957 0.949 0.670 0.532 0.255 0.079
round(pvals(T=Td[5],df=dfd[5],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 0.437 0.427 0.243 0.188 0.097 0.041
tests<-lavTestLRT(configural, metric2, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 21.41609 9.43297 40.00921
dfd=tests[2:4,"Df diff"]
dfd
## [1] 6 2 10
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-526 + 526 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.06995712 0.08413691 0.07560449
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.03943611 0.10306430
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.03575879 0.14133825
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.05197196 0.10078747
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
## 0.998 0.998 0.871 0.734 0.339 0.070
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
## 0.991 0.989 0.889 0.821 0.617 0.371
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 0.962 0.869 0.414 0.056
tests<-lavTestLRT(configural, metric2, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 21.41609 230.49948
dfd=tests[2:3,"Df diff"]
dfd
## [1] 6 6
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-526 + 526 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.06995712 0.26696381
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.03943611 0.10306430
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.2379598 0.2968726
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
## 0.998 0.998 0.871 0.734 0.339 0.070
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)
Td=tests[2,"Chisq diff"]
Td
## [1] 41.49454
dfd=tests[2,"Df diff"]
dfd
## [1] 8
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-526 + 526 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.08930225
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.06355752 0.11697473
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 0.993 0.968 0.742 0.280
# ONE FACTOR, just for checking if gap direction aligns with HOF
fmodel<-'
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
'
configural<-cfa(fmodel, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1345.119 70.000 0.000 0.830 0.186 0.069 48920.189 49217.696
Mc(configural)
## [1] 0.5451895
metric<-cfa(fmodel, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1397.059 79.000 0.000 0.824 0.178 0.084 48954.128 49207.009
Mc(metric)
## [1] 0.5341654
scalar<-cfa(fmodel, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 3026.630 88.000 0.000 0.607 0.252 0.175 50565.700 50773.955
Mc(scalar)
## [1] 0.2470866
summary(scalar, standardized=T, ci=T) # -0.326 Std.all
## lavaan 0.6-18 ended normally after 97 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 62
## Number of equality constraints 20
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3026.630 2562.854
## Degrees of freedom 88 88
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.181
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 1860.432 1575.355
## 1 1166.198 987.500
##
## 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 ci.upper Std.lv Std.all
## g =~
## ssgs (.p1.) 4.008 0.150 26.756 0.000 3.714 4.302 4.008 0.864
## ssar (.p2.) 6.290 0.205 30.616 0.000 5.887 6.692 6.290 0.855
## sswk (.p3.) 5.761 0.274 21.042 0.000 5.224 6.298 5.761 0.848
## sspc (.p4.) 2.255 0.136 16.563 0.000 1.988 2.522 2.255 0.740
## ssno (.p5.) 0.547 0.041 13.439 0.000 0.467 0.627 0.547 0.610
## sscs (.p6.) 0.425 0.044 9.598 0.000 0.338 0.512 0.425 0.496
## ssasi (.p7.) 2.810 0.202 13.921 0.000 2.414 3.205 2.810 0.449
## ssmk (.p8.) 5.490 0.199 27.572 0.000 5.100 5.880 5.490 0.815
## ssmc (.p9.) 3.616 0.176 20.543 0.000 3.271 3.961 3.616 0.693
## ssei (.10.) 3.002 0.147 20.400 0.000 2.714 3.291 3.002 0.756
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.22.) 17.558 0.239 73.558 0.000 17.090 18.025 17.558 3.783
## .ssar (.23.) 20.353 0.358 56.810 0.000 19.650 21.055 20.353 2.766
## .sswk (.24.) 28.610 0.301 94.948 0.000 28.019 29.200 28.610 4.211
## .sspc (.25.) 12.049 0.136 88.580 0.000 11.782 12.316 12.049 3.952
## .ssno (.26.) 0.449 0.038 11.764 0.000 0.374 0.524 0.449 0.501
## .sscs (.27.) 0.367 0.046 8.011 0.000 0.277 0.456 0.367 0.428
## .ssasi (.28.) 13.778 0.373 36.923 0.000 13.047 14.509 13.778 2.204
## .ssmk (.29.) 15.890 0.326 48.711 0.000 15.250 16.529 15.890 2.360
## .ssmc (.30.) 15.378 0.309 49.742 0.000 14.772 15.984 15.378 2.948
## .ssei (.31.) 12.379 0.255 48.519 0.000 11.879 12.879 12.379 3.115
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.477 0.572 9.581 0.000 4.357 6.598 5.477 0.254
## .ssar 14.589 1.404 10.387 0.000 11.836 17.341 14.589 0.269
## .sswk 12.969 1.364 9.507 0.000 10.295 15.643 12.969 0.281
## .sspc 4.211 0.383 10.988 0.000 3.460 4.962 4.211 0.453
## .ssno 0.504 0.037 13.725 0.000 0.432 0.576 0.504 0.627
## .sscs 0.553 0.061 9.119 0.000 0.434 0.672 0.553 0.754
## .ssasi 31.190 3.421 9.118 0.000 24.486 37.895 31.190 0.798
## .ssmk 15.186 1.420 10.694 0.000 12.403 17.970 15.186 0.335
## .ssmc 14.127 1.307 10.806 0.000 11.565 16.689 14.127 0.519
## .ssei 6.776 0.823 8.235 0.000 5.164 8.389 6.776 0.429
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g =~
## ssgs (.p1.) 4.008 0.150 26.756 0.000 3.714 4.302 3.425 0.834
## ssar (.p2.) 6.290 0.205 30.616 0.000 5.887 6.692 5.374 0.836
## sswk (.p3.) 5.761 0.274 21.042 0.000 5.224 6.298 4.922 0.813
## sspc (.p4.) 2.255 0.136 16.563 0.000 1.988 2.522 1.927 0.728
## ssno (.p5.) 0.547 0.041 13.439 0.000 0.467 0.627 0.467 0.551
## sscs (.p6.) 0.425 0.044 9.598 0.000 0.338 0.512 0.363 0.401
## ssasi (.p7.) 2.810 0.202 13.921 0.000 2.414 3.205 2.401 0.620
## ssmk (.p8.) 5.490 0.199 27.572 0.000 5.100 5.880 4.691 0.779
## ssmc (.p9.) 3.616 0.176 20.543 0.000 3.271 3.961 3.090 0.675
## ssei (.10.) 3.002 0.147 20.400 0.000 2.714 3.291 2.565 0.710
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.22.) 17.558 0.239 73.558 0.000 17.090 18.025 17.558 4.275
## .ssar (.23.) 20.353 0.358 56.810 0.000 19.650 21.055 20.353 3.165
## .sswk (.24.) 28.610 0.301 94.948 0.000 28.019 29.200 28.610 4.726
## .sspc (.25.) 12.049 0.136 88.580 0.000 11.782 12.316 12.049 4.549
## .ssno (.26.) 0.449 0.038 11.764 0.000 0.374 0.524 0.449 0.530
## .sscs (.27.) 0.367 0.046 8.011 0.000 0.277 0.456 0.367 0.405
## .ssasi (.28.) 13.778 0.373 36.923 0.000 13.047 14.509 13.778 3.560
## .ssmk (.29.) 15.890 0.326 48.711 0.000 15.250 16.529 15.890 2.637
## .ssmc (.30.) 15.378 0.309 49.742 0.000 14.772 15.984 15.378 3.361
## .ssei (.31.) 12.379 0.255 48.519 0.000 11.879 12.879 12.379 3.427
## g -0.278 0.084 -3.318 0.001 -0.443 -0.114 -0.326 -0.326
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.137 0.482 10.655 0.000 4.192 6.082 5.137 0.305
## .ssar 12.463 1.085 11.492 0.000 10.337 14.589 12.463 0.301
## .sswk 12.415 1.197 10.374 0.000 10.070 14.761 12.415 0.339
## .sspc 3.301 0.314 10.528 0.000 2.687 3.916 3.301 0.471
## .ssno 0.500 0.035 14.188 0.000 0.431 0.569 0.500 0.696
## .sscs 0.689 0.064 10.807 0.000 0.564 0.814 0.689 0.839
## .ssasi 9.220 1.034 8.917 0.000 7.194 11.247 9.220 0.615
## .ssmk 14.294 1.073 13.323 0.000 12.191 16.397 14.294 0.394
## .ssmc 11.385 1.003 11.348 0.000 9.418 13.351 11.385 0.544
## .ssei 6.468 0.597 10.826 0.000 5.297 7.639 6.468 0.496
## g 0.730 0.067 10.821 0.000 0.598 0.862 1.000 1.000
# HIGH ORDER FACTOR
hof.model<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
'
hof.lv<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal # yes, verbal variance among females is greater, but non-significant and no fit decrement
math~~1*math
speed~~1*speed
g~~1*g
'
hof.weak<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
g~~1*g
math~0*1
'
baseline<-cfa(hof.model, data=dgroup, meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 519.597 29.000 0.000 0.936 0.127 0.066 49060.137 49238.641
Mc(baseline)
## [1] 0.7918404
configural<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 353.773 58.000 0.000 0.960 0.098 0.038 47952.843 48309.851
Mc(configural)
## [1] 0.8687409
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 91 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 72
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 353.773 301.959
## Degrees of freedom 58 58
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.172
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 241.478 206.110
## 1 112.296 95.848
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs 0.614 0.222 2.764 0.006 0.179 1.049 2.569 0.567
## sswk 1.462 0.550 2.659 0.008 0.384 2.540 6.120 0.911
## sspc 0.627 0.234 2.684 0.007 0.169 1.085 2.625 0.844
## math =~
## ssar 3.512 0.259 13.579 0.000 3.005 4.019 6.711 0.941
## ssmk 3.117 0.227 13.749 0.000 2.673 3.562 5.956 0.895
## ssmc 0.546 0.141 3.886 0.000 0.271 0.822 1.043 0.211
## electronic =~
## ssgs 0.924 0.166 5.570 0.000 0.599 1.249 1.577 0.348
## ssasi 2.069 0.160 12.938 0.000 1.755 2.382 3.533 0.746
## ssmc 1.865 0.166 11.222 0.000 1.539 2.191 3.185 0.644
## ssei 2.115 0.125 16.975 0.000 1.871 2.360 3.613 0.941
## speed =~
## ssno 0.501 0.033 15.246 0.000 0.437 0.565 0.756 0.854
## sscs 0.436 0.033 13.121 0.000 0.371 0.501 0.658 0.783
## g =~
## verbal 4.065 1.625 2.502 0.012 0.880 7.250 0.971 0.971
## math 1.628 0.157 10.343 0.000 1.320 1.937 0.852 0.852
## electronic 1.384 0.129 10.703 0.000 1.131 1.638 0.811 0.811
## speed 1.129 0.124 9.143 0.000 0.887 1.372 0.749 0.749
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 17.910 0.210 85.392 0.000 17.498 18.321 17.910 3.954
## .sswk 27.643 0.309 89.548 0.000 27.038 28.248 27.643 4.115
## .sspc 11.207 0.144 77.836 0.000 10.925 11.490 11.207 3.603
## .ssar 20.311 0.336 60.447 0.000 19.652 20.969 20.311 2.848
## .ssmk 15.277 0.316 48.361 0.000 14.658 15.896 15.277 2.296
## .ssmc 17.082 0.231 73.903 0.000 16.629 17.535 17.082 3.455
## .ssasi 17.796 0.221 80.523 0.000 17.363 18.230 17.796 3.756
## .ssei 13.530 0.177 76.269 0.000 13.182 13.877 13.530 3.524
## .ssno 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.275
## .sscs 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.091
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.042 0.420 12.004 0.000 4.219 5.866 5.042 0.246
## .sswk 7.665 0.986 7.775 0.000 5.733 9.597 7.665 0.170
## .sspc 2.786 0.241 11.558 0.000 2.313 3.258 2.786 0.288
## .ssar 5.815 1.054 5.517 0.000 3.750 7.881 5.815 0.114
## .ssmk 8.786 1.006 8.736 0.000 6.815 10.757 8.786 0.199
## .ssmc 8.624 0.719 12.000 0.000 7.215 10.032 8.624 0.353
## .ssasi 9.975 0.910 10.959 0.000 8.191 11.759 9.975 0.444
## .ssei 1.691 0.395 4.279 0.000 0.916 2.466 1.691 0.115
## .ssno 0.212 0.035 6.063 0.000 0.143 0.280 0.212 0.270
## .sscs 0.273 0.048 5.667 0.000 0.179 0.368 0.273 0.387
## .verbal 1.000 1.000 1.000 0.057 0.057
## .math 1.000 1.000 1.000 0.274 0.274
## .electronic 1.000 1.000 1.000 0.343 0.343
## .speed 1.000 1.000 1.000 0.439 0.439
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs 0.640 0.182 3.528 0.000 0.285 0.996 1.578 0.386
## sswk 2.349 0.308 7.636 0.000 1.746 2.952 5.791 0.928
## sspc 0.831 0.111 7.476 0.000 0.613 1.049 2.048 0.803
## math =~
## ssar 2.992 0.251 11.916 0.000 2.500 3.484 6.234 0.935
## ssmk 2.579 0.218 11.845 0.000 2.152 3.006 5.375 0.867
## ssmc 0.843 0.180 4.688 0.000 0.491 1.196 1.757 0.441
## electronic =~
## ssgs 0.920 0.155 5.954 0.000 0.617 1.223 2.125 0.519
## ssasi 0.942 0.139 6.764 0.000 0.669 1.215 2.175 0.638
## ssmc 0.463 0.166 2.794 0.005 0.138 0.787 1.068 0.268
## ssei 1.018 0.152 6.699 0.000 0.720 1.316 2.351 0.763
## speed =~
## ssno 0.558 0.039 14.251 0.000 0.482 0.635 0.761 0.900
## sscs 0.414 0.031 13.518 0.000 0.354 0.474 0.564 0.679
## g =~
## verbal 2.253 0.345 6.539 0.000 1.578 2.928 0.914 0.914
## math 1.828 0.200 9.125 0.000 1.435 2.221 0.877 0.877
## electronic 2.081 0.346 6.014 0.000 1.403 2.760 0.901 0.901
## speed 0.927 0.101 9.166 0.000 0.729 1.125 0.680 0.680
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 16.094 0.190 84.654 0.000 15.721 16.467 16.094 3.933
## .sswk 27.980 0.285 98.025 0.000 27.421 28.540 27.980 4.485
## .sspc 12.116 0.116 104.370 0.000 11.888 12.343 12.116 4.750
## .ssar 18.639 0.312 59.821 0.000 18.028 19.250 18.639 2.796
## .ssmk 14.968 0.291 51.396 0.000 14.397 15.539 14.968 2.413
## .ssmc 12.925 0.187 68.955 0.000 12.557 13.292 12.925 3.242
## .ssasi 11.745 0.159 73.710 0.000 11.433 12.058 11.745 3.447
## .ssei 10.387 0.143 72.446 0.000 10.106 10.668 10.387 3.370
## .ssno 0.511 0.039 13.006 0.000 0.434 0.588 0.511 0.604
## .sscs 0.629 0.039 16.289 0.000 0.554 0.705 0.629 0.758
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.210 0.435 9.679 0.000 3.358 5.063 4.210 0.251
## .sswk 5.396 0.995 5.422 0.000 3.445 7.347 5.396 0.139
## .sspc 2.312 0.193 11.959 0.000 1.933 2.691 2.312 0.355
## .ssar 5.572 0.994 5.608 0.000 3.625 7.520 5.572 0.125
## .ssmk 9.583 0.977 9.809 0.000 7.668 11.498 9.583 0.249
## .ssmc 8.697 0.581 14.974 0.000 7.559 9.835 8.697 0.547
## .ssasi 6.884 0.555 12.404 0.000 5.796 7.972 6.884 0.593
## .ssei 3.975 0.376 10.565 0.000 3.238 4.713 3.975 0.418
## .ssno 0.136 0.050 2.705 0.007 0.037 0.234 0.136 0.190
## .sscs 0.372 0.056 6.697 0.000 0.263 0.481 0.372 0.539
## .verbal 1.000 1.000 1.000 0.165 0.165
## .math 1.000 1.000 1.000 0.230 0.230
## .electronic 1.000 1.000 1.000 0.188 0.188
## .speed 1.000 1.000 1.000 0.538 0.538
## g 1.000 1.000 1.000 1.000 1.000
#modificationIndices(configural, sort=T, maximum.number=30)
metric<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 404.583 69.000 0.000 0.955 0.096 0.053 47981.653 48284.118
Mc(metric)
## [1] 0.8524427
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 80 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 77
## Number of equality constraints 16
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 404.583 346.383
## Degrees of freedom 69 69
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.168
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 259.666 222.313
## 1 144.917 124.070
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.724 0.188 3.848 0.000 0.355 1.093 2.584 0.568
## sswk (.p2.) 1.756 0.467 3.759 0.000 0.841 2.672 6.268 0.917
## sspc (.p3.) 0.691 0.182 3.794 0.000 0.334 1.048 2.467 0.823
## math =~
## ssar (.p4.) 3.388 0.256 13.257 0.000 2.887 3.889 6.916 0.945
## ssmk (.p5.) 2.967 0.223 13.299 0.000 2.530 3.405 6.058 0.897
## ssmc (.p6.) 0.592 0.114 5.173 0.000 0.367 0.816 1.208 0.254
## electronic =~
## ssgs (.p7.) 1.058 0.149 7.111 0.000 0.766 1.349 1.655 0.364
## ssasi (.p8.) 2.104 0.152 13.872 0.000 1.807 2.402 3.292 0.720
## ssmc (.p9.) 1.792 0.169 10.576 0.000 1.460 2.124 2.803 0.589
## ssei (.10.) 2.216 0.121 18.305 0.000 1.979 2.453 3.466 0.939
## speed =~
## ssno (.11.) 0.507 0.032 15.812 0.000 0.444 0.570 0.774 0.869
## sscs (.12.) 0.416 0.029 14.212 0.000 0.359 0.474 0.635 0.765
## g =~
## verbal (.13.) 3.426 0.982 3.488 0.000 1.501 5.350 0.960 0.960
## math (.14.) 1.780 0.158 11.241 0.000 1.469 2.090 0.872 0.872
## elctrnc (.15.) 1.203 0.110 10.899 0.000 0.986 1.419 0.769 0.769
## speed (.16.) 1.153 0.109 10.553 0.000 0.939 1.367 0.755 0.755
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 17.910 0.210 85.392 0.000 17.498 18.321 17.910 3.936
## .sswk 27.643 0.309 89.548 0.000 27.038 28.248 27.643 4.045
## .sspc 11.207 0.144 77.836 0.000 10.925 11.490 11.207 3.740
## .ssar 20.311 0.336 60.447 0.000 19.652 20.969 20.311 2.776
## .ssmk 15.277 0.316 48.361 0.000 14.658 15.896 15.277 2.262
## .ssmc 17.082 0.231 73.903 0.000 16.629 17.535 17.082 3.589
## .ssasi 17.796 0.221 80.523 0.000 17.363 18.230 17.796 3.893
## .ssei 13.530 0.177 76.269 0.000 13.182 13.877 13.530 3.667
## .ssno 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.274
## .sscs 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.092
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.974 0.410 12.123 0.000 4.170 5.778 4.974 0.240
## .sswk 7.429 0.996 7.457 0.000 5.476 9.381 7.429 0.159
## .sspc 2.895 0.244 11.844 0.000 2.416 3.374 2.895 0.322
## .ssar 5.681 0.960 5.920 0.000 3.800 7.562 5.681 0.106
## .ssmk 8.910 0.927 9.614 0.000 7.094 10.727 8.910 0.195
## .ssmc 8.807 0.718 12.261 0.000 7.399 10.215 8.807 0.389
## .ssasi 10.067 0.912 11.036 0.000 8.279 11.855 10.067 0.482
## .ssei 1.602 0.410 3.906 0.000 0.798 2.406 1.602 0.118
## .ssno 0.194 0.033 5.879 0.000 0.129 0.259 0.194 0.244
## .sscs 0.287 0.046 6.296 0.000 0.197 0.376 0.287 0.415
## .verbal 1.000 1.000 1.000 0.079 0.079
## .math 1.000 1.000 1.000 0.240 0.240
## .electronic 1.000 1.000 1.000 0.409 0.409
## .speed 1.000 1.000 1.000 0.429 0.429
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.724 0.188 3.848 0.000 0.355 1.093 2.294 0.574
## sswk (.p2.) 1.756 0.467 3.759 0.000 0.841 2.672 5.565 0.910
## sspc (.p3.) 0.691 0.182 3.794 0.000 0.334 1.048 2.190 0.824
## math =~
## ssar (.p4.) 3.388 0.256 13.257 0.000 2.887 3.889 6.023 0.930
## ssmk (.p5.) 2.967 0.223 13.299 0.000 2.530 3.405 5.276 0.864
## ssmc (.p6.) 0.592 0.114 5.173 0.000 0.367 0.816 1.052 0.255
## electronic =~
## ssgs (.p7.) 1.058 0.149 7.111 0.000 0.766 1.349 1.182 0.296
## ssasi (.p8.) 2.104 0.152 13.872 0.000 1.807 2.402 2.352 0.671
## ssmc (.p9.) 1.792 0.169 10.576 0.000 1.460 2.124 2.002 0.486
## ssei (.10.) 2.216 0.121 18.305 0.000 1.979 2.453 2.476 0.778
## speed =~
## ssno (.11.) 0.507 0.032 15.812 0.000 0.444 0.570 0.731 0.870
## sscs (.12.) 0.416 0.029 14.212 0.000 0.359 0.474 0.600 0.711
## g =~
## verbal (.13.) 3.426 0.982 3.488 0.000 1.501 5.350 0.927 0.927
## math (.14.) 1.780 0.158 11.241 0.000 1.469 2.090 0.858 0.858
## elctrnc (.15.) 1.203 0.110 10.899 0.000 0.986 1.419 0.923 0.923
## speed (.16.) 1.153 0.109 10.553 0.000 0.939 1.367 0.686 0.686
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 16.094 0.190 84.654 0.000 15.721 16.467 16.094 4.026
## .sswk 27.980 0.285 98.025 0.000 27.421 28.540 27.980 4.576
## .sspc 12.116 0.116 104.370 0.000 11.888 12.343 12.116 4.558
## .ssar 18.639 0.312 59.821 0.000 18.028 19.250 18.639 2.878
## .ssmk 14.968 0.291 51.396 0.000 14.397 15.539 14.968 2.451
## .ssmc 12.925 0.187 68.955 0.000 12.557 13.292 12.925 3.136
## .ssasi 11.745 0.159 73.710 0.000 11.433 12.058 11.745 3.354
## .ssei 10.387 0.143 72.446 0.000 10.106 10.668 10.387 3.262
## .ssno 0.511 0.039 13.006 0.000 0.434 0.588 0.511 0.608
## .sscs 0.629 0.039 16.289 0.000 0.554 0.705 0.629 0.747
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.682 0.383 12.228 0.000 3.932 5.433 4.682 0.293
## .sswk 6.430 0.926 6.946 0.000 4.616 8.245 6.430 0.172
## .sspc 2.270 0.191 11.877 0.000 1.896 2.645 2.270 0.321
## .ssar 5.666 0.945 5.994 0.000 3.813 7.518 5.666 0.135
## .ssmk 9.451 0.928 10.189 0.000 7.633 11.269 9.451 0.253
## .ssmc 8.531 0.580 14.720 0.000 7.395 9.667 8.531 0.502
## .ssasi 6.737 0.540 12.484 0.000 5.679 7.794 6.737 0.549
## .ssei 4.009 0.377 10.625 0.000 3.270 4.749 4.009 0.395
## .ssno 0.172 0.039 4.385 0.000 0.095 0.249 0.172 0.244
## .sscs 0.351 0.050 7.056 0.000 0.254 0.449 0.351 0.494
## .verbal 1.411 0.731 1.930 0.054 -0.022 2.843 0.141 0.141
## .math 0.832 0.140 5.939 0.000 0.557 1.106 0.263 0.263
## .electronic 0.185 0.060 3.105 0.002 0.068 0.302 0.148 0.148
## .speed 1.098 0.170 6.451 0.000 0.764 1.432 0.529 0.529
## g 0.735 0.079 9.270 0.000 0.580 0.891 1.000 1.000
lavTestScore(metric, release = 1:16)
## 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 49.933 16 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p47. 3.094 1 0.079
## 2 .p2. == .p48. 4.994 1 0.025
## 3 .p3. == .p49. 12.186 1 0.000
## 4 .p4. == .p50. 3.524 1 0.060
## 5 .p5. == .p51. 0.002 1 0.968
## 6 .p6. == .p52. 0.809 1 0.369
## 7 .p7. == .p53. 7.057 1 0.008
## 8 .p8. == .p54. 2.073 1 0.150
## 9 .p9. == .p55. 6.218 1 0.013
## 10 .p10. == .p56. 2.785 1 0.095
## 11 .p11. == .p57. 1.185 1 0.276
## 12 .p12. == .p58. 1.924 1 0.165
## 13 .p13. == .p59. 0.431 1 0.511
## 14 .p14. == .p60. 5.205 1 0.023
## 15 .p15. == .p61. 11.685 1 0.001
## 16 .p16. == .p62. 0.000 1 0.993
metric2<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"), group.partial=c("g=~electronic"))
fitMeasures(metric2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 392.935 68.000 0.000 0.957 0.095 0.048 47972.005 48279.429
Mc(metric2)
## [1] 0.8567718
scalar<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= 2.577983e-13) 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 aic bic
## 649.510 73.000 0.000 0.923 0.123 0.078 48218.580 48501.212
Mc(scalar)
## [1] 0.7601287
summary(scalar, standardized=T, ci=T) # -.153
## lavaan 0.6-18 ended normally after 148 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 25
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 649.510 547.578
## Degrees of freedom 73 73
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.186
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 382.628 322.580
## 1 266.882 224.998
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.776 0.176 4.405 0.000 0.431 1.121 2.533 0.546
## sswk (.p2.) 1.885 0.421 4.478 0.000 1.060 2.711 6.155 0.914
## sspc (.p3.) 0.750 0.165 4.537 0.000 0.426 1.074 2.448 0.815
## math =~
## ssar (.p4.) 3.394 0.256 13.252 0.000 2.892 3.896 6.867 0.946
## ssmk (.p5.) 2.925 0.216 13.510 0.000 2.500 3.349 5.918 0.889
## ssmc (.p6.) 0.489 0.097 5.067 0.000 0.300 0.678 0.990 0.201
## electronic =~
## ssgs (.p7.) 1.071 0.092 11.674 0.000 0.891 1.251 1.802 0.389
## ssasi (.p8.) 2.468 0.170 14.550 0.000 2.135 2.800 4.152 0.796
## ssmc (.p9.) 1.963 0.148 13.230 0.000 1.672 2.253 3.302 0.669
## ssei (.10.) 1.929 0.120 16.082 0.000 1.694 2.164 3.245 0.888
## speed =~
## ssno (.11.) 0.469 0.030 15.415 0.000 0.409 0.529 0.720 0.826
## sscs (.12.) 0.440 0.032 13.660 0.000 0.377 0.503 0.675 0.793
## g =~
## verbal (.13.) 3.108 0.756 4.110 0.000 1.625 4.590 0.952 0.952
## math (.14.) 1.759 0.162 10.863 0.000 1.442 2.076 0.869 0.869
## elctrnc 1.353 0.142 9.505 0.000 1.074 1.632 0.804 0.804
## speed (.16.) 1.165 0.113 10.349 0.000 0.945 1.386 0.759 0.759
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 17.888 0.207 86.229 0.000 17.481 18.294 17.888 3.857
## .sswk (.33.) 27.357 0.316 86.599 0.000 26.738 27.976 27.357 4.062
## .sspc (.34.) 11.513 0.135 85.600 0.000 11.250 11.777 11.513 3.831
## .ssar (.35.) 20.122 0.342 58.884 0.000 19.452 20.791 20.122 2.773
## .ssmk (.36.) 15.654 0.307 51.069 0.000 15.053 16.255 15.654 2.350
## .ssmc (.37.) 17.056 0.231 73.882 0.000 16.604 17.509 17.056 3.456
## .ssasi (.38.) 17.142 0.247 69.417 0.000 16.658 17.626 17.142 3.287
## .ssei (.39.) 13.785 0.168 82.197 0.000 13.456 14.113 13.785 3.771
## .ssno (.40.) 0.178 0.042 4.232 0.000 0.096 0.261 0.178 0.204
## .sscs (.41.) 0.154 0.041 3.736 0.000 0.073 0.234 0.154 0.180
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.848 0.403 12.017 0.000 4.058 5.639 4.848 0.225
## .sswk 7.487 1.054 7.103 0.000 5.421 9.553 7.487 0.165
## .sspc 3.039 0.267 11.366 0.000 2.515 3.563 3.039 0.337
## .ssar 5.516 1.015 5.434 0.000 3.526 7.505 5.516 0.105
## .ssmk 9.339 0.981 9.517 0.000 7.416 11.262 9.339 0.211
## .ssmc 7.908 0.686 11.523 0.000 6.563 9.253 7.908 0.325
## .ssasi 9.955 1.017 9.785 0.000 7.961 11.949 9.955 0.366
## .ssei 2.835 0.401 7.066 0.000 2.049 3.621 2.835 0.212
## .ssno 0.242 0.034 7.180 0.000 0.176 0.308 0.242 0.318
## .sscs 0.269 0.049 5.452 0.000 0.172 0.365 0.269 0.371
## .verbal 1.000 1.000 1.000 0.094 0.094
## .math 1.000 1.000 1.000 0.244 0.244
## .electronic 1.000 1.000 1.000 0.353 0.353
## .speed 1.000 1.000 1.000 0.424 0.424
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.776 0.176 4.405 0.000 0.431 1.121 2.319 0.584
## sswk (.p2.) 1.885 0.421 4.478 0.000 1.060 2.711 5.633 0.909
## sspc (.p3.) 0.750 0.165 4.537 0.000 0.426 1.074 2.240 0.826
## math =~
## ssar (.p4.) 3.394 0.256 13.252 0.000 2.892 3.896 6.147 0.934
## ssmk (.p5.) 2.925 0.216 13.510 0.000 2.500 3.349 5.297 0.860
## ssmc (.p6.) 0.489 0.097 5.067 0.000 0.300 0.678 0.886 0.220
## electronic =~
## ssgs (.p7.) 1.071 0.092 11.674 0.000 0.891 1.251 1.112 0.280
## ssasi (.p8.) 2.468 0.170 14.550 0.000 2.135 2.800 2.561 0.700
## ssmc (.p9.) 1.963 0.148 13.230 0.000 1.672 2.253 2.037 0.505
## ssei (.10.) 1.929 0.120 16.082 0.000 1.694 2.164 2.002 0.675
## speed =~
## ssno (.11.) 0.469 0.030 15.415 0.000 0.409 0.529 0.688 0.825
## sscs (.12.) 0.440 0.032 13.660 0.000 0.377 0.503 0.645 0.739
## g =~
## verbal (.13.) 3.108 0.756 4.110 0.000 1.625 4.590 0.931 0.931
## math (.14.) 1.759 0.162 10.863 0.000 1.442 2.076 0.870 0.870
## elctrnc 1.062 0.102 10.429 0.000 0.862 1.261 0.916 0.916
## speed (.16.) 1.165 0.113 10.349 0.000 0.945 1.386 0.712 0.712
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 17.888 0.207 86.229 0.000 17.481 18.294 17.888 4.504
## .sswk (.33.) 27.357 0.316 86.599 0.000 26.738 27.976 27.357 4.413
## .sspc (.34.) 11.513 0.135 85.600 0.000 11.250 11.777 11.513 4.244
## .ssar (.35.) 20.122 0.342 58.884 0.000 19.452 20.791 20.122 3.058
## .ssmk (.36.) 15.654 0.307 51.069 0.000 15.053 16.255 15.654 2.541
## .ssmc (.37.) 17.056 0.231 73.882 0.000 16.604 17.509 17.056 4.231
## .ssasi (.38.) 17.142 0.247 69.417 0.000 16.658 17.626 17.142 4.687
## .ssei (.39.) 13.785 0.168 82.197 0.000 13.456 14.113 13.785 4.650
## .ssno (.40.) 0.178 0.042 4.232 0.000 0.096 0.261 0.178 0.214
## .sscs (.41.) 0.154 0.041 3.736 0.000 0.073 0.234 0.154 0.176
## .verbal 0.898 0.112 7.986 0.000 0.678 1.119 0.301 0.301
## .math -0.137 0.104 -1.320 0.187 -0.341 0.067 -0.076 -0.076
## .elctrnc -1.851 0.149 -12.402 0.000 -2.143 -1.558 -1.783 -1.783
## .speed 1.003 0.127 7.913 0.000 0.755 1.252 0.684 0.684
## g -0.137 0.074 -1.856 0.063 -0.281 0.008 -0.153 -0.153
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.761 0.390 12.220 0.000 3.997 5.525 4.761 0.302
## .sswk 6.688 0.958 6.981 0.000 4.811 8.566 6.688 0.174
## .sspc 2.339 0.202 11.571 0.000 1.943 2.735 2.339 0.318
## .ssar 5.524 0.974 5.671 0.000 3.615 7.433 5.524 0.128
## .ssmk 9.891 0.954 10.367 0.000 8.021 11.761 9.891 0.261
## .ssmc 8.443 0.577 14.629 0.000 7.312 9.575 8.443 0.519
## .ssasi 6.813 0.586 11.626 0.000 5.665 7.962 6.813 0.509
## .ssei 4.779 0.400 11.962 0.000 3.996 5.562 4.779 0.544
## .ssno 0.223 0.040 5.557 0.000 0.144 0.301 0.223 0.320
## .sscs 0.345 0.056 6.177 0.000 0.235 0.454 0.345 0.453
## .verbal 1.182 0.544 2.174 0.030 0.117 2.248 0.132 0.132
## .math 0.799 0.140 5.719 0.000 0.525 1.073 0.244 0.244
## .electronic 0.173 0.059 2.940 0.003 0.058 0.288 0.161 0.161
## .speed 1.060 0.175 6.048 0.000 0.717 1.404 0.493 0.493
## g 0.802 0.088 9.132 0.000 0.630 0.974 1.000 1.000
lavTestScore(scalar, release = 16:25)
## 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 243.406 10 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p32. == .p78. 0.523 1 0.470
## 2 .p33. == .p79. 35.927 1 0.000
## 3 .p34. == .p80. 42.231 1 0.000
## 4 .p35. == .p81. 24.201 1 0.000
## 5 .p36. == .p82. 25.049 1 0.000
## 6 .p37. == .p83. 0.288 1 0.591
## 7 .p38. == .p84. 101.181 1 0.000
## 8 .p39. == .p85. 105.628 1 0.000
## 9 .p40. == .p86. 54.688 1 0.000
## 10 .p41. == .p87. 54.688 1 0.000
scalar2<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "sswk~1", "ssar~1", "ssei~1", "sscs~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 (= 2.669465e-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 aic bic
## 398.423 69.000 0.000 0.956 0.095 0.049 47975.493 48277.959
Mc(scalar2)
## [1] 0.8549443
summary(scalar2, standardized=T, ci=T) # -.103
## lavaan 0.6-18 ended normally after 155 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 21
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 398.423 335.430
## Degrees of freedom 69 69
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.188
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 260.642 219.433
## 1 137.781 115.997
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.727 0.179 4.058 0.000 0.376 1.077 2.618 0.566
## sswk (.p2.) 1.720 0.426 4.039 0.000 0.885 2.554 6.196 0.917
## sspc (.p3.) 0.674 0.165 4.084 0.000 0.351 0.998 2.429 0.817
## math =~
## ssar (.p4.) 3.450 0.237 14.579 0.000 2.986 3.914 6.836 0.944
## ssmk (.p5.) 3.023 0.206 14.703 0.000 2.620 3.426 5.990 0.895
## ssmc (.p6.) 0.742 0.096 7.718 0.000 0.554 0.931 1.471 0.305
## electronic =~
## ssgs (.p7.) 0.992 0.085 11.628 0.000 0.825 1.160 1.670 0.361
## ssasi (.p8.) 2.119 0.147 14.387 0.000 1.831 2.408 3.566 0.745
## ssmc (.p9.) 1.532 0.128 11.931 0.000 1.280 1.784 2.578 0.535
## ssei (.10.) 2.173 0.125 17.429 0.000 1.929 2.418 3.657 0.952
## speed =~
## ssno (.11.) 0.513 0.032 16.293 0.000 0.452 0.575 0.769 0.867
## sscs (.12.) 0.422 0.029 14.577 0.000 0.365 0.479 0.633 0.764
## g =~
## verbal (.13.) 3.462 0.921 3.758 0.000 1.656 5.267 0.961 0.961
## math (.14.) 1.711 0.146 11.750 0.000 1.425 1.996 0.863 0.863
## elctrnc 1.353 0.125 10.821 0.000 1.108 1.598 0.804 0.804
## speed (.16.) 1.117 0.105 10.682 0.000 0.912 1.321 0.745 0.745
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 17.904 0.208 85.988 0.000 17.496 18.312 17.904 3.870
## .sswk 27.643 0.309 89.548 0.000 27.038 28.248 27.643 4.092
## .sspc (.34.) 11.211 0.142 78.734 0.000 10.932 11.490 11.211 3.770
## .ssar 20.311 0.336 60.447 0.000 19.652 20.969 20.311 2.804
## .ssmk (.36.) 15.254 0.315 48.359 0.000 14.636 15.872 15.254 2.278
## .ssmc (.37.) 17.179 0.225 76.396 0.000 16.738 17.620 17.179 3.565
## .ssasi (.38.) 17.724 0.220 80.426 0.000 17.292 18.156 17.724 3.703
## .ssei 13.530 0.177 76.269 0.000 13.182 13.877 13.530 3.522
## .ssno (.40.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.275
## .sscs 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.092
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.005 0.411 12.166 0.000 4.198 5.811 5.005 0.234
## .sswk 7.245 0.989 7.322 0.000 5.305 9.184 7.245 0.159
## .sspc 2.941 0.247 11.932 0.000 2.458 3.425 2.941 0.333
## .ssar 5.726 0.958 5.978 0.000 3.849 7.603 5.726 0.109
## .ssmk 8.946 0.915 9.774 0.000 7.152 10.739 8.946 0.200
## .ssmc 9.138 0.691 13.220 0.000 7.783 10.493 9.138 0.394
## .ssasi 10.191 0.923 11.039 0.000 8.382 12.000 10.191 0.445
## .ssei 1.384 0.363 3.814 0.000 0.673 2.094 1.384 0.094
## .ssno 0.195 0.033 5.879 0.000 0.130 0.260 0.195 0.248
## .sscs 0.286 0.046 6.270 0.000 0.197 0.375 0.286 0.417
## .verbal 1.000 1.000 1.000 0.077 0.077
## .math 1.000 1.000 1.000 0.255 0.255
## .electronic 1.000 1.000 1.000 0.353 0.353
## .speed 1.000 1.000 1.000 0.445 0.445
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.727 0.179 4.058 0.000 0.376 1.077 2.393 0.601
## sswk (.p2.) 1.720 0.426 4.039 0.000 0.885 2.554 5.665 0.913
## sspc (.p3.) 0.674 0.165 4.084 0.000 0.351 0.998 2.221 0.827
## math =~
## ssar (.p4.) 3.450 0.237 14.579 0.000 2.986 3.914 6.105 0.932
## ssmk (.p5.) 3.023 0.206 14.703 0.000 2.620 3.426 5.349 0.867
## ssmc (.p6.) 0.742 0.096 7.718 0.000 0.554 0.931 1.314 0.325
## electronic =~
## ssgs (.p7.) 0.992 0.085 11.628 0.000 0.825 1.160 1.071 0.269
## ssasi (.p8.) 2.119 0.147 14.387 0.000 1.831 2.408 2.287 0.663
## ssmc (.p9.) 1.532 0.128 11.931 0.000 1.280 1.784 1.653 0.409
## ssei (.10.) 2.173 0.125 17.429 0.000 1.929 2.418 2.345 0.762
## speed =~
## ssno (.11.) 0.513 0.032 16.293 0.000 0.452 0.575 0.735 0.870
## sscs (.12.) 0.422 0.029 14.577 0.000 0.365 0.479 0.604 0.714
## g =~
## verbal (.13.) 3.462 0.921 3.758 0.000 1.656 5.267 0.938 0.938
## math (.14.) 1.711 0.146 11.750 0.000 1.425 1.996 0.863 0.863
## elctrnc 1.084 0.096 11.289 0.000 0.896 1.272 0.896 0.896
## speed (.16.) 1.117 0.105 10.682 0.000 0.912 1.321 0.696 0.696
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 17.904 0.208 85.988 0.000 17.496 18.312 17.904 4.492
## .sswk 25.680 0.411 62.443 0.000 24.874 26.486 25.680 4.137
## .sspc (.34.) 11.211 0.142 78.734 0.000 10.932 11.490 11.211 4.176
## .ssar 18.936 0.410 46.155 0.000 18.132 19.740 18.936 2.889
## .ssmk (.36.) 15.254 0.315 48.359 0.000 14.636 15.872 15.254 2.473
## .ssmc (.37.) 17.179 0.225 76.396 0.000 16.738 17.620 17.179 4.246
## .ssasi (.38.) 17.724 0.220 80.426 0.000 17.292 18.156 17.724 5.139
## .ssei 16.467 0.412 39.941 0.000 15.659 17.275 16.467 5.354
## .ssno (.40.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.289
## .sscs 0.410 0.048 8.507 0.000 0.315 0.504 0.410 0.484
## .verbal 1.657 0.174 9.531 0.000 1.316 1.997 0.503 0.503
## .math 0.072 0.159 0.450 0.652 -0.240 0.383 0.040 0.040
## .elctrnc -2.697 0.253 -10.654 0.000 -3.194 -2.201 -2.500 -2.500
## .speed 0.623 0.132 4.729 0.000 0.365 0.882 0.436 0.436
## g -0.092 0.096 -0.957 0.338 -0.281 0.097 -0.103 -0.103
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.703 0.385 12.231 0.000 3.949 5.457 4.703 0.296
## .sswk 6.441 0.903 7.129 0.000 4.670 8.211 6.441 0.167
## .sspc 2.273 0.191 11.906 0.000 1.899 2.647 2.273 0.315
## .ssar 5.676 0.925 6.133 0.000 3.862 7.490 5.676 0.132
## .ssmk 9.438 0.924 10.213 0.000 7.627 11.249 9.438 0.248
## .ssmc 8.549 0.576 14.841 0.000 7.420 9.678 8.549 0.522
## .ssasi 6.667 0.541 12.325 0.000 5.606 7.727 6.667 0.560
## .ssei 3.959 0.381 10.388 0.000 3.212 4.706 3.959 0.419
## .ssno 0.173 0.039 4.435 0.000 0.096 0.249 0.173 0.242
## .sscs 0.351 0.050 7.067 0.000 0.253 0.448 0.351 0.490
## .verbal 1.311 0.664 1.975 0.048 0.010 2.612 0.121 0.121
## .math 0.802 0.132 6.060 0.000 0.542 1.061 0.256 0.256
## .electronic 0.229 0.066 3.479 0.001 0.100 0.357 0.196 0.196
## .speed 1.055 0.162 6.516 0.000 0.738 1.373 0.515 0.515
## g 0.796 0.087 9.107 0.000 0.625 0.968 1.000 1.000
strict<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("g=~electronic", "sswk~1", "ssar~1", "ssei~1", "sscs~1"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= 4.537227e-13) 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 aic bic
## 454.384 79.000 0.000 0.950 0.095 0.055 48011.454 48264.335
Mc(strict)
## [1] 0.8364536
summary(strict, standardized=T, ci=T) # -.040, lv variance of verbal now almost group equal
## lavaan 0.6-18 ended normally after 116 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 31
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 454.384 372.230
## Degrees of freedom 79 79
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.221
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 291.042 238.421
## 1 163.342 133.810
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.805 0.170 4.738 0.000 0.472 1.138 2.594 0.563
## sswk (.p2.) 1.932 0.412 4.685 0.000 1.124 2.740 6.226 0.921
## sspc (.p3.) 0.766 0.161 4.749 0.000 0.450 1.082 2.470 0.838
## math =~
## ssar (.p4.) 3.367 0.243 13.852 0.000 2.891 3.844 6.814 0.944
## ssmk (.p5.) 2.949 0.211 14.006 0.000 2.536 3.361 5.967 0.891
## ssmc (.p6.) 0.686 0.095 7.221 0.000 0.500 0.872 1.388 0.291
## electronic =~
## ssgs (.p7.) 1.036 0.095 10.909 0.000 0.850 1.223 1.716 0.373
## ssasi (.p8.) 2.197 0.173 12.710 0.000 1.858 2.536 3.638 0.789
## ssmc (.p9.) 1.616 0.148 10.915 0.000 1.326 1.906 2.676 0.560
## ssei (.10.) 2.137 0.126 16.990 0.000 1.890 2.383 3.538 0.896
## speed =~
## ssno (.11.) 0.512 0.033 15.529 0.000 0.447 0.577 0.770 0.874
## sscs (.12.) 0.419 0.027 15.552 0.000 0.366 0.472 0.630 0.745
## g =~
## verbal (.13.) 3.064 0.714 4.292 0.000 1.665 4.464 0.951 0.951
## math (.14.) 1.759 0.158 11.148 0.000 1.450 2.069 0.869 0.869
## elctrnc 1.320 0.135 9.753 0.000 1.054 1.585 0.797 0.797
## speed (.16.) 1.123 0.106 10.552 0.000 0.915 1.332 0.747 0.747
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 17.912 0.208 86.034 0.000 17.504 18.320 17.912 3.890
## .sswk 27.643 0.309 89.548 0.000 27.038 28.248 27.643 4.090
## .sspc (.34.) 11.206 0.143 78.565 0.000 10.926 11.486 11.206 3.801
## .ssar 20.311 0.336 60.447 0.000 19.652 20.969 20.311 2.814
## .ssmk (.36.) 15.249 0.316 48.316 0.000 14.630 15.868 15.249 2.278
## .ssmc (.37.) 17.195 0.224 76.742 0.000 16.756 17.634 17.195 3.601
## .ssasi (.38.) 17.717 0.219 80.740 0.000 17.287 18.147 17.717 3.842
## .ssei 13.530 0.177 76.269 0.000 13.182 13.877 13.530 3.426
## .ssno (.40.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.277
## .sscs 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.090
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.17.) 4.775 0.285 16.737 0.000 4.216 5.335 4.775 0.225
## .sswk (.18.) 6.901 0.685 10.081 0.000 5.559 8.242 6.901 0.151
## .sspc (.19.) 2.593 0.155 16.679 0.000 2.289 2.898 2.593 0.298
## .ssar (.20.) 5.675 0.718 7.907 0.000 4.268 7.081 5.675 0.109
## .ssmk (.21.) 9.200 0.697 13.199 0.000 7.834 10.566 9.200 0.205
## .ssmc (.22.) 8.558 0.457 18.730 0.000 7.663 9.454 8.558 0.375
## .ssasi (.23.) 8.026 0.544 14.744 0.000 6.959 9.093 8.026 0.378
## .ssei (.24.) 3.079 0.301 10.237 0.000 2.489 3.668 3.079 0.197
## .ssno (.25.) 0.183 0.029 6.300 0.000 0.126 0.240 0.183 0.236
## .sscs (.26.) 0.318 0.037 8.704 0.000 0.247 0.390 0.318 0.445
## .verbal 1.000 1.000 1.000 0.096 0.096
## .math 1.000 1.000 1.000 0.244 0.244
## .elctrnc 1.000 1.000 1.000 0.365 0.365
## .speed 1.000 1.000 1.000 0.442 0.442
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.805 0.170 4.738 0.000 0.472 1.138 2.336 0.585
## sswk (.p2.) 1.932 0.412 4.685 0.000 1.124 2.740 5.607 0.906
## sspc (.p3.) 0.766 0.161 4.749 0.000 0.450 1.082 2.224 0.810
## math =~
## ssar (.p4.) 3.367 0.243 13.852 0.000 2.891 3.844 6.128 0.932
## ssmk (.p5.) 2.949 0.211 14.006 0.000 2.536 3.361 5.366 0.871
## ssmc (.p6.) 0.686 0.095 7.221 0.000 0.500 0.872 1.249 0.306
## electronic =~
## ssgs (.p7.) 1.036 0.095 10.909 0.000 0.850 1.223 1.141 0.286
## ssasi (.p8.) 2.197 0.173 12.710 0.000 1.858 2.536 2.418 0.649
## ssmc (.p9.) 1.616 0.148 10.915 0.000 1.326 1.906 1.779 0.436
## ssei (.10.) 2.137 0.126 16.990 0.000 1.890 2.383 2.351 0.801
## speed =~
## ssno (.11.) 0.512 0.033 15.529 0.000 0.447 0.577 0.735 0.865
## sscs (.12.) 0.419 0.027 15.552 0.000 0.366 0.472 0.602 0.729
## g =~
## verbal (.13.) 3.064 0.714 4.292 0.000 1.665 4.464 0.942 0.942
## math (.14.) 1.759 0.158 11.148 0.000 1.450 2.069 0.863 0.863
## elctrnc 1.086 0.100 10.842 0.000 0.889 1.282 0.880 0.880
## speed (.16.) 1.123 0.106 10.552 0.000 0.915 1.332 0.698 0.698
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 17.912 0.208 86.034 0.000 17.504 18.320 17.912 4.484
## .sswk 25.683 0.403 63.666 0.000 24.892 26.474 25.683 4.148
## .sspc (.34.) 11.206 0.143 78.565 0.000 10.926 11.486 11.206 4.081
## .ssar 18.926 0.411 46.059 0.000 18.121 19.731 18.926 2.879
## .ssmk (.36.) 15.249 0.316 48.316 0.000 14.630 15.868 15.249 2.474
## .ssmc (.37.) 17.195 0.224 76.742 0.000 16.756 17.634 17.195 4.214
## .ssasi (.38.) 17.717 0.219 80.740 0.000 17.287 18.147 17.717 4.757
## .ssei 16.112 0.380 42.370 0.000 15.367 16.858 16.112 5.492
## .ssno (.40.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.287
## .sscs 0.411 0.048 8.601 0.000 0.317 0.504 0.411 0.498
## .verbal 1.298 0.154 8.406 0.000 0.995 1.601 0.447 0.447
## .math -0.023 0.123 -0.186 0.852 -0.263 0.218 -0.013 -0.013
## .elctrnc -2.641 0.256 -10.320 0.000 -3.143 -2.139 -2.400 -2.400
## .speed 0.562 0.110 5.094 0.000 0.346 0.778 0.391 0.391
## g -0.035 0.076 -0.466 0.641 -0.185 0.114 -0.040 -0.040
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.17.) 4.775 0.285 16.737 0.000 4.216 5.335 4.775 0.299
## .sswk (.18.) 6.901 0.685 10.081 0.000 5.559 8.242 6.901 0.180
## .sspc (.19.) 2.593 0.155 16.679 0.000 2.289 2.898 2.593 0.344
## .ssar (.20.) 5.675 0.718 7.907 0.000 4.268 7.081 5.675 0.131
## .ssmk (.21.) 9.200 0.697 13.199 0.000 7.834 10.566 9.200 0.242
## .ssmc (.22.) 8.558 0.457 18.730 0.000 7.663 9.454 8.558 0.514
## .ssasi (.23.) 8.026 0.544 14.744 0.000 6.959 9.093 8.026 0.579
## .ssei (.24.) 3.079 0.301 10.237 0.000 2.489 3.668 3.079 0.358
## .ssno (.25.) 0.183 0.029 6.300 0.000 0.126 0.240 0.183 0.253
## .sscs (.26.) 0.318 0.037 8.704 0.000 0.247 0.390 0.318 0.468
## .verbal 0.947 0.411 2.304 0.021 0.142 1.753 0.112 0.112
## .math 0.847 0.134 6.338 0.000 0.585 1.109 0.256 0.256
## .elctrnc 0.272 0.078 3.495 0.000 0.120 0.425 0.225 0.225
## .speed 1.058 0.146 7.226 0.000 0.771 1.345 0.513 0.513
## g 0.796 0.087 9.152 0.000 0.626 0.967 1.000 1.000
latent<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("g=~electronic", "sswk~1", "ssar~1", "ssei~1", "sscs~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 (= 1.322148e-14) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(latent, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 457.700 74.000 0.000 0.949 0.099 0.078 48024.770 48302.443
Mc(latent)
## [1] 0.8331508
summary(latent, standardized=T, ci=T) # g -.073 Std.all
## lavaan 0.6-18 ended normally after 126 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 77
## Number of equality constraints 21
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 457.700 386.995
## Degrees of freedom 74 74
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.183
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 286.252 242.032
## 1 171.449 144.963
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.772 0.122 6.326 0.000 0.533 1.012 2.508 0.560
## sswk (.p2.) 1.833 0.290 6.318 0.000 1.264 2.401 5.951 0.914
## sspc (.p3.) 0.715 0.112 6.376 0.000 0.495 0.934 2.320 0.801
## math =~
## ssar (.p4.) 3.348 0.177 18.917 0.000 3.001 3.695 6.484 0.936
## ssmk (.p5.) 2.931 0.153 19.189 0.000 2.632 3.230 5.677 0.884
## ssmc (.p6.) 0.737 0.087 8.474 0.000 0.567 0.908 1.428 0.306
## electronic =~
## ssgs (.p7.) 0.783 0.063 12.353 0.000 0.659 0.907 1.554 0.347
## ssasi (.p8.) 1.644 0.106 15.450 0.000 1.435 1.852 3.263 0.712
## ssmc (.p9.) 1.185 0.094 12.647 0.000 1.001 1.369 2.353 0.504
## ssei (.10.) 1.717 0.104 16.505 0.000 1.513 1.921 3.410 0.932
## speed =~
## ssno (.11.) 0.521 0.024 21.756 0.000 0.474 0.568 0.751 0.860
## sscs (.12.) 0.430 0.023 19.092 0.000 0.386 0.474 0.620 0.758
## g =~
## verbal (.13.) 3.089 0.541 5.706 0.000 2.028 4.151 0.951 0.951
## math (.14.) 1.659 0.115 14.447 0.000 1.434 1.884 0.856 0.856
## elctrnc 1.715 0.152 11.295 0.000 1.418 2.013 0.864 0.864
## speed (.16.) 1.039 0.078 13.256 0.000 0.886 1.193 0.721 0.721
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 17.916 0.208 86.036 0.000 17.508 18.324 17.916 4.001
## .sswk 27.643 0.309 89.548 0.000 27.038 28.248 27.643 4.247
## .sspc (.34.) 11.203 0.142 78.679 0.000 10.924 11.482 11.203 3.865
## .ssar 20.311 0.336 60.447 0.000 19.652 20.969 20.311 2.931
## .ssmk (.36.) 15.255 0.315 48.356 0.000 14.637 15.874 15.255 2.375
## .ssmc (.37.) 17.172 0.225 76.364 0.000 16.731 17.613 17.172 3.681
## .ssasi (.38.) 17.717 0.222 79.981 0.000 17.283 18.152 17.717 3.868
## .ssei 13.530 0.177 76.269 0.000 13.182 13.877 13.530 3.698
## .ssno (.40.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.279
## .sscs 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.093
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.930 0.407 12.109 0.000 4.132 5.728 4.930 0.246
## .sswk 6.951 0.904 7.688 0.000 5.179 8.722 6.951 0.164
## .sspc 3.016 0.251 12.017 0.000 2.524 3.508 3.016 0.359
## .ssar 5.988 0.924 6.483 0.000 4.177 7.798 5.988 0.125
## .ssmk 9.020 0.880 10.247 0.000 7.295 10.745 9.020 0.219
## .ssmc 9.213 0.674 13.673 0.000 7.892 10.533 9.213 0.423
## .ssasi 10.336 0.923 11.198 0.000 8.527 12.145 10.336 0.493
## .ssei 1.763 0.338 5.220 0.000 1.101 2.425 1.763 0.132
## .ssno 0.199 0.033 6.110 0.000 0.135 0.262 0.199 0.260
## .sscs 0.284 0.045 6.246 0.000 0.195 0.373 0.284 0.425
## .verbal 1.000 1.000 1.000 0.095 0.095
## .math 1.000 1.000 1.000 0.267 0.267
## .electronic 1.000 1.000 1.000 0.254 0.254
## .speed 1.000 1.000 1.000 0.481 0.481
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.772 0.122 6.326 0.000 0.533 1.012 2.508 0.608
## sswk (.p2.) 1.833 0.290 6.318 0.000 1.264 2.401 5.951 0.920
## sspc (.p3.) 0.715 0.112 6.376 0.000 0.495 0.934 2.320 0.841
## math =~
## ssar (.p4.) 3.348 0.177 18.917 0.000 3.001 3.695 6.484 0.942
## ssmk (.p5.) 2.931 0.153 19.189 0.000 2.632 3.230 5.677 0.879
## ssmc (.p6.) 0.737 0.087 8.474 0.000 0.567 0.908 1.428 0.341
## electronic =~
## ssgs (.p7.) 0.783 0.063 12.353 0.000 0.659 0.907 1.236 0.300
## ssasi (.p8.) 1.644 0.106 15.450 0.000 1.435 1.852 2.596 0.712
## ssmc (.p9.) 1.185 0.094 12.647 0.000 1.001 1.369 1.872 0.446
## ssei (.10.) 1.717 0.104 16.505 0.000 1.513 1.921 2.712 0.824
## speed =~
## ssno (.11.) 0.521 0.024 21.756 0.000 0.474 0.568 0.751 0.874
## sscs (.12.) 0.430 0.023 19.092 0.000 0.386 0.474 0.620 0.724
## g =~
## verbal (.13.) 3.089 0.541 5.706 0.000 2.028 4.151 0.951 0.951
## math (.14.) 1.659 0.115 14.447 0.000 1.434 1.884 0.856 0.856
## elctrnc 1.223 0.098 12.491 0.000 1.031 1.414 0.774 0.774
## speed (.16.) 1.039 0.078 13.256 0.000 0.886 1.193 0.721 0.721
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 17.916 0.208 86.036 0.000 17.508 18.324 17.916 4.342
## .sswk 25.630 0.415 61.698 0.000 24.816 26.445 25.630 3.962
## .sspc (.34.) 11.203 0.142 78.679 0.000 10.924 11.482 11.203 4.059
## .ssar 18.939 0.411 46.129 0.000 18.135 19.744 18.939 2.751
## .ssmk (.36.) 15.255 0.315 48.356 0.000 14.637 15.874 15.255 2.363
## .ssmc (.37.) 17.172 0.225 76.364 0.000 16.731 17.613 17.172 4.096
## .ssasi (.38.) 17.717 0.222 79.981 0.000 17.283 18.152 17.717 4.859
## .ssei 16.572 0.418 39.689 0.000 15.753 17.390 16.572 5.036
## .ssno (.40.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.284
## .sscs 0.409 0.048 8.450 0.000 0.314 0.503 0.409 0.477
## .verbal 1.509 0.144 10.455 0.000 1.226 1.792 0.465 0.465
## .math 0.032 0.119 0.270 0.787 -0.201 0.265 0.017 0.017
## .elctrnc -3.512 0.274 -12.793 0.000 -4.050 -2.974 -2.223 -2.223
## .speed 0.590 0.102 5.764 0.000 0.389 0.790 0.409 0.409
## g -0.073 0.084 -0.872 0.383 -0.239 0.092 -0.073 -0.073
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.637 0.378 12.282 0.000 3.897 5.377 4.637 0.272
## .sswk 6.424 0.892 7.201 0.000 4.675 8.172 6.424 0.154
## .sspc 2.235 0.189 11.845 0.000 1.865 2.605 2.235 0.293
## .ssar 5.369 0.941 5.706 0.000 3.525 7.213 5.369 0.113
## .ssmk 9.460 0.968 9.768 0.000 7.561 11.358 9.460 0.227
## .ssmc 8.486 0.581 14.603 0.000 7.347 9.625 8.486 0.483
## .ssasi 6.557 0.547 11.981 0.000 5.485 7.630 6.557 0.493
## .ssei 3.474 0.401 8.668 0.000 2.688 4.259 3.474 0.321
## .ssno 0.174 0.037 4.768 0.000 0.103 0.246 0.174 0.236
## .sscs 0.349 0.049 7.093 0.000 0.253 0.445 0.349 0.476
## .verbal 1.000 1.000 1.000 0.095 0.095
## .math 1.000 1.000 1.000 0.267 0.267
## .electronic 1.000 1.000 1.000 0.401 0.401
## .speed 1.000 1.000 1.000 0.481 0.481
## g 1.000 1.000 1.000 1.000 1.000
latent2<-cfa(hof.lv, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "sswk~1", "ssar~1", "ssei~1", "sscs~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 (= 7.604739e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(latent2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 405.518 73.000 0.000 0.956 0.093 0.074 47974.588 48257.220
Mc(latent2)
## [1] 0.8536864
summary(latent2, standardized=T, ci=T) # g -.149 Std.all
## lavaan 0.6-18 ended normally after 119 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 78
## Number of equality constraints 21
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 405.518 342.961
## Degrees of freedom 73 73
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.182
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 264.203 223.445
## 1 141.315 119.515
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.786 0.118 6.675 0.000 0.555 1.017 2.509 0.560
## sswk (.p2.) 1.861 0.278 6.683 0.000 1.315 2.407 5.940 0.911
## sspc (.p3.) 0.729 0.108 6.723 0.000 0.516 0.941 2.327 0.805
## math =~
## ssar (.p4.) 3.269 0.180 18.171 0.000 2.917 3.622 6.485 0.936
## ssmk (.p5.) 2.863 0.155 18.432 0.000 2.559 3.168 5.679 0.885
## ssmc (.p6.) 0.706 0.088 7.996 0.000 0.533 0.879 1.400 0.297
## electronic =~
## ssgs (.p7.) 0.997 0.086 11.538 0.000 0.828 1.167 1.631 0.364
## ssasi (.p8.) 2.127 0.150 14.191 0.000 1.833 2.421 3.479 0.737
## ssmc (.p9.) 1.535 0.130 11.786 0.000 1.280 1.791 2.511 0.533
## ssei (.10.) 2.179 0.126 17.259 0.000 1.932 2.427 3.565 0.949
## speed =~
## ssno (.11.) 0.519 0.024 21.486 0.000 0.471 0.566 0.752 0.864
## sscs (.12.) 0.427 0.022 19.277 0.000 0.384 0.471 0.619 0.757
## g =~
## verbal (.13.) 3.031 0.505 6.004 0.000 2.042 4.021 0.950 0.950
## math (.14.) 1.713 0.122 14.027 0.000 1.474 1.952 0.864 0.864
## elctrnc 1.294 0.117 11.094 0.000 1.066 1.523 0.791 0.791
## speed (.16.) 1.049 0.079 13.282 0.000 0.894 1.204 0.724 0.724
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 17.905 0.208 86.030 0.000 17.497 18.313 17.905 3.994
## .sswk 27.643 0.309 89.547 0.000 27.038 28.248 27.643 4.240
## .sspc (.34.) 11.210 0.142 78.719 0.000 10.931 11.489 11.210 3.876
## .ssar 20.311 0.336 60.447 0.000 19.652 20.969 20.311 2.933
## .ssmk (.36.) 15.254 0.315 48.362 0.000 14.636 15.873 15.254 2.376
## .ssmc (.37.) 17.177 0.225 76.429 0.000 16.736 17.617 17.177 3.646
## .ssasi (.38.) 17.725 0.221 80.376 0.000 17.293 18.157 17.725 3.755
## .ssei 13.530 0.177 76.269 0.000 13.182 13.877 13.530 3.603
## .ssno (.40.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.280
## .sscs 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.093
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.098 0.098
## .math 1.000 1.000 1.000 0.254 0.254
## .speed 1.000 1.000 1.000 0.476 0.476
## g 1.000 1.000 1.000 1.000 1.000
## .ssgs 4.990 0.410 12.169 0.000 4.187 5.794 4.990 0.248
## .sswk 7.222 0.943 7.661 0.000 5.374 9.070 7.222 0.170
## .sspc 2.949 0.247 11.946 0.000 2.465 3.433 2.949 0.353
## .ssar 5.904 0.920 6.417 0.000 4.101 7.707 5.904 0.123
## .ssmk 8.953 0.895 10.005 0.000 7.199 10.707 8.953 0.217
## .ssmc 9.127 0.693 13.172 0.000 7.769 10.486 9.127 0.411
## .ssasi 10.183 0.921 11.052 0.000 8.377 11.989 10.183 0.457
## .ssei 1.394 0.368 3.793 0.000 0.674 2.115 1.394 0.099
## .ssno 0.192 0.033 5.866 0.000 0.128 0.256 0.192 0.253
## .sscs 0.286 0.046 6.238 0.000 0.196 0.376 0.286 0.427
## .electronic 1.000 1.000 1.000 0.374 0.374
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.786 0.118 6.675 0.000 0.555 1.017 2.509 0.608
## sswk (.p2.) 1.861 0.278 6.683 0.000 1.315 2.407 5.940 0.920
## sspc (.p3.) 0.729 0.108 6.723 0.000 0.516 0.941 2.327 0.839
## math =~
## ssar (.p4.) 3.269 0.180 18.171 0.000 2.917 3.622 6.485 0.941
## ssmk (.p5.) 2.863 0.155 18.432 0.000 2.559 3.168 5.679 0.879
## ssmc (.p6.) 0.706 0.088 7.996 0.000 0.533 0.879 1.400 0.338
## electronic =~
## ssgs (.p7.) 0.997 0.086 11.538 0.000 0.828 1.167 1.112 0.270
## ssasi (.p8.) 2.127 0.150 14.191 0.000 1.833 2.421 2.372 0.677
## ssmc (.p9.) 1.535 0.130 11.786 0.000 1.280 1.791 1.712 0.413
## ssei (.10.) 2.179 0.126 17.259 0.000 1.932 2.427 2.430 0.774
## speed =~
## ssno (.11.) 0.519 0.024 21.486 0.000 0.471 0.566 0.752 0.872
## sscs (.12.) 0.427 0.022 19.277 0.000 0.384 0.471 0.619 0.723
## g =~
## verbal (.13.) 3.031 0.505 6.004 0.000 2.042 4.021 0.950 0.950
## math (.14.) 1.713 0.122 14.027 0.000 1.474 1.952 0.864 0.864
## elctrnc 1.007 0.077 13.089 0.000 0.856 1.157 0.903 0.903
## speed (.16.) 1.049 0.079 13.282 0.000 0.894 1.204 0.724 0.724
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 17.905 0.208 86.030 0.000 17.497 18.313 17.905 4.340
## .sswk 25.675 0.413 62.166 0.000 24.865 26.484 25.675 3.975
## .sspc (.34.) 11.210 0.142 78.719 0.000 10.931 11.489 11.210 4.042
## .ssar 18.937 0.410 46.139 0.000 18.133 19.741 18.937 2.748
## .ssmk (.36.) 15.254 0.315 48.362 0.000 14.636 15.873 15.254 2.361
## .ssmc (.37.) 17.177 0.225 76.429 0.000 16.736 17.617 17.177 4.143
## .ssasi (.38.) 17.725 0.221 80.376 0.000 17.293 18.157 17.725 5.057
## .ssei 16.463 0.414 39.813 0.000 15.653 17.274 16.463 5.244
## .ssno (.40.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.283
## .sscs 0.409 0.048 8.491 0.000 0.315 0.504 0.409 0.478
## .verbal 1.689 0.145 11.683 0.000 1.406 1.973 0.529 0.529
## .math 0.163 0.126 1.295 0.195 -0.084 0.410 0.082 0.082
## .elctrnc -2.638 0.239 -11.047 0.000 -3.107 -2.170 -2.366 -2.366
## .speed 0.671 0.105 6.370 0.000 0.464 0.877 0.463 0.463
## g -0.149 0.085 -1.754 0.079 -0.314 0.017 -0.149 -0.149
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.098 0.098
## .math 1.000 1.000 1.000 0.254 0.254
## .speed 1.000 1.000 1.000 0.476 0.476
## g 1.000 1.000 1.000 1.000 1.000
## .ssgs 4.700 0.384 12.234 0.000 3.947 5.453 4.700 0.276
## .sswk 6.444 0.873 7.381 0.000 4.733 8.155 6.444 0.154
## .sspc 2.279 0.191 11.908 0.000 1.904 2.654 2.279 0.296
## .ssar 5.439 0.930 5.849 0.000 3.616 7.261 5.439 0.115
## .ssmk 9.483 0.951 9.971 0.000 7.619 11.347 9.483 0.227
## .ssmc 8.563 0.575 14.882 0.000 7.435 9.691 8.563 0.498
## .ssasi 6.662 0.540 12.332 0.000 5.603 7.720 6.662 0.542
## .ssei 3.949 0.381 10.364 0.000 3.202 4.696 3.949 0.401
## .ssno 0.178 0.036 4.881 0.000 0.106 0.249 0.178 0.239
## .sscs 0.350 0.049 7.093 0.000 0.253 0.446 0.350 0.477
## .electronic 0.230 0.065 3.516 0.000 0.102 0.358 0.185 0.185
weak<-cfa(hof.weak, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(weak, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 405.518 74.000 0.000 0.956 0.092 0.074 47972.588 48250.261
Mc(weak)
## [1] 0.8540926
summary(weak, standardized=T, ci=T) # -0.053 Std.all
## lavaan 0.6-18 ended normally after 127 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 77
## Number of equality constraints 21
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 405.518 347.659
## Degrees of freedom 74 74
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.166
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 264.203 226.506
## 1 141.315 121.152
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.786 0.118 6.675 0.000 0.555 1.017 2.509 0.560
## sswk (.p2.) 1.861 0.278 6.683 0.000 1.315 2.407 5.940 0.911
## sspc (.p3.) 0.729 0.108 6.723 0.000 0.516 0.941 2.327 0.805
## math =~
## ssar (.p4.) 3.269 0.180 18.170 0.000 2.917 3.622 6.485 0.936
## ssmk (.p5.) 2.863 0.155 18.432 0.000 2.559 3.168 5.679 0.885
## ssmc (.p6.) 0.706 0.088 7.996 0.000 0.533 0.879 1.400 0.297
## electronic =~
## ssgs (.p7.) 0.997 0.086 11.538 0.000 0.828 1.167 1.631 0.364
## ssasi (.p8.) 2.127 0.150 14.191 0.000 1.833 2.421 3.479 0.737
## ssmc (.p9.) 1.535 0.130 11.786 0.000 1.280 1.791 2.511 0.533
## ssei (.10.) 2.179 0.126 17.259 0.000 1.932 2.427 3.565 0.949
## speed =~
## ssno (.11.) 0.519 0.024 21.486 0.000 0.471 0.566 0.752 0.864
## sscs (.12.) 0.427 0.022 19.277 0.000 0.384 0.471 0.619 0.757
## g =~
## verbal (.13.) 3.031 0.505 6.004 0.000 2.042 4.021 0.950 0.950
## math (.14.) 1.713 0.122 14.027 0.000 1.474 1.952 0.864 0.864
## elctrnc 1.294 0.117 11.094 0.000 1.066 1.523 0.791 0.791
## speed (.16.) 1.049 0.079 13.282 0.000 0.894 1.204 0.724 0.724
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.33.) 17.905 0.208 86.030 0.000 17.497 18.313 17.905 3.994
## .sswk 27.643 0.309 89.547 0.000 27.038 28.248 27.643 4.240
## .sspc (.35.) 11.210 0.142 78.719 0.000 10.931 11.489 11.210 3.876
## .ssar 20.311 0.336 60.447 0.000 19.652 20.969 20.311 2.933
## .ssmk (.37.) 15.254 0.315 48.362 0.000 14.636 15.873 15.254 2.376
## .ssmc (.38.) 17.177 0.225 76.429 0.000 16.736 17.617 17.177 3.646
## .ssasi (.39.) 17.725 0.221 80.376 0.000 17.293 18.157 17.725 3.755
## .ssei 13.530 0.177 76.269 0.000 13.182 13.877 13.530 3.603
## .ssno (.41.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.280
## .sscs 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.093
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.098 0.098
## .math 1.000 1.000 1.000 0.254 0.254
## .speed 1.000 1.000 1.000 0.476 0.476
## g 1.000 1.000 1.000 1.000 1.000
## .ssgs 4.990 0.410 12.169 0.000 4.187 5.794 4.990 0.248
## .sswk 7.222 0.943 7.661 0.000 5.374 9.070 7.222 0.170
## .sspc 2.949 0.247 11.946 0.000 2.465 3.433 2.949 0.353
## .ssar 5.904 0.920 6.417 0.000 4.101 7.707 5.904 0.123
## .ssmk 8.953 0.895 10.005 0.000 7.199 10.707 8.953 0.217
## .ssmc 9.127 0.693 13.172 0.000 7.769 10.486 9.127 0.411
## .ssasi 10.183 0.921 11.052 0.000 8.377 11.989 10.183 0.457
## .ssei 1.394 0.368 3.793 0.000 0.674 2.115 1.394 0.099
## .ssno 0.192 0.033 5.866 0.000 0.128 0.256 0.192 0.253
## .sscs 0.286 0.046 6.238 0.000 0.196 0.376 0.286 0.427
## .electronic 1.000 1.000 1.000 0.374 0.374
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.786 0.118 6.675 0.000 0.555 1.017 2.509 0.608
## sswk (.p2.) 1.861 0.278 6.683 0.000 1.315 2.407 5.940 0.920
## sspc (.p3.) 0.729 0.108 6.723 0.000 0.516 0.941 2.327 0.839
## math =~
## ssar (.p4.) 3.269 0.180 18.170 0.000 2.917 3.622 6.485 0.941
## ssmk (.p5.) 2.863 0.155 18.432 0.000 2.559 3.168 5.679 0.879
## ssmc (.p6.) 0.706 0.088 7.996 0.000 0.533 0.879 1.400 0.338
## electronic =~
## ssgs (.p7.) 0.997 0.086 11.538 0.000 0.828 1.167 1.112 0.270
## ssasi (.p8.) 2.127 0.150 14.191 0.000 1.833 2.421 2.372 0.677
## ssmc (.p9.) 1.535 0.130 11.786 0.000 1.280 1.791 1.712 0.413
## ssei (.10.) 2.179 0.126 17.259 0.000 1.932 2.427 2.430 0.774
## speed =~
## ssno (.11.) 0.519 0.024 21.486 0.000 0.471 0.566 0.752 0.872
## sscs (.12.) 0.427 0.022 19.277 0.000 0.384 0.471 0.619 0.723
## g =~
## verbal (.13.) 3.031 0.505 6.004 0.000 2.042 4.021 0.950 0.950
## math (.14.) 1.713 0.122 14.027 0.000 1.474 1.952 0.864 0.864
## elctrnc 1.007 0.077 13.089 0.000 0.856 1.157 0.903 0.903
## speed (.16.) 1.049 0.079 13.282 0.000 0.894 1.204 0.724 0.724
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.33.) 17.905 0.208 86.030 0.000 17.497 18.313 17.905 4.340
## .sswk 25.675 0.413 62.166 0.000 24.865 26.484 25.675 3.975
## .sspc (.35.) 11.210 0.142 78.719 0.000 10.931 11.489 11.210 4.042
## .ssar 18.937 0.410 46.139 0.000 18.133 19.741 18.937 2.748
## .ssmk (.37.) 15.254 0.315 48.362 0.000 14.636 15.873 15.254 2.361
## .ssmc (.38.) 17.177 0.225 76.429 0.000 16.736 17.617 17.177 4.143
## .ssasi (.39.) 17.725 0.221 80.376 0.000 17.293 18.157 17.725 5.057
## .ssei 16.463 0.414 39.813 0.000 15.653 17.274 16.463 5.244
## .ssno (.41.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.283
## .sscs 0.409 0.048 8.491 0.000 0.315 0.504 0.409 0.478
## .verbal 1.400 0.303 4.617 0.000 0.806 1.995 0.439 0.439
## .elctrnc -2.734 0.243 -11.240 0.000 -3.211 -2.258 -2.452 -2.452
## .speed 0.571 0.100 5.729 0.000 0.376 0.766 0.394 0.394
## g -0.053 0.087 -0.609 0.542 -0.224 0.118 -0.053 -0.053
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.098 0.098
## .math 1.000 1.000 1.000 0.254 0.254
## .speed 1.000 1.000 1.000 0.476 0.476
## g 1.000 1.000 1.000 1.000 1.000
## .ssgs 4.700 0.384 12.234 0.000 3.947 5.453 4.700 0.276
## .sswk 6.444 0.873 7.381 0.000 4.733 8.155 6.444 0.154
## .sspc 2.279 0.191 11.908 0.000 1.904 2.654 2.279 0.296
## .ssar 5.439 0.930 5.850 0.000 3.616 7.261 5.439 0.115
## .ssmk 9.483 0.951 9.971 0.000 7.619 11.347 9.483 0.227
## .ssmc 8.563 0.575 14.882 0.000 7.435 9.691 8.563 0.498
## .ssasi 6.662 0.540 12.332 0.000 5.603 7.720 6.662 0.542
## .ssei 3.949 0.381 10.364 0.000 3.202 4.696 3.949 0.401
## .ssno 0.178 0.036 4.881 0.000 0.106 0.249 0.178 0.239
## .sscs 0.350 0.049 7.093 0.000 0.253 0.446 0.350 0.477
## .electronic 0.230 0.065 3.516 0.000 0.102 0.358 0.185 0.185
lvstrict<-cfa(hof.lv, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("g=~electronic", "sswk~1", "ssar~1", "ssei~1", "sscs~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 (= 3.808067e-13) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(lvstrict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 461.342 83.000 0.000 0.949 0.093 0.082 48010.412 48243.459
Mc(lvstrict)
## [1] 0.8352775
summary(lvstrict, standardized=T, ci=T) # -.028
## lavaan 0.6-18 ended normally after 101 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 78
## Number of equality constraints 31
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 461.342 379.776
## Degrees of freedom 83 83
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.215
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 294.418 242.364
## 1 166.924 137.412
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.799 0.121 6.616 0.000 0.562 1.036 2.473 0.555
## sswk (.p2.) 1.918 0.289 6.626 0.000 1.351 2.485 5.935 0.915
## sspc (.p3.) 0.760 0.113 6.714 0.000 0.538 0.982 2.352 0.825
## math =~
## ssar (.p4.) 3.232 0.185 17.445 0.000 2.869 3.596 6.484 0.939
## ssmk (.p5.) 2.831 0.160 17.729 0.000 2.518 3.144 5.679 0.882
## ssmc (.p6.) 0.660 0.087 7.557 0.000 0.489 0.831 1.324 0.284
## electronic =~
## ssgs (.p7.) 1.039 0.094 11.067 0.000 0.855 1.223 1.675 0.376
## ssasi (.p8.) 2.199 0.172 12.810 0.000 1.863 2.536 3.546 0.781
## ssmc (.p9.) 1.617 0.147 10.989 0.000 1.329 1.905 2.607 0.558
## ssei (.10.) 2.139 0.125 17.182 0.000 1.895 2.384 3.449 0.891
## speed =~
## ssno (.11.) 0.520 0.024 21.391 0.000 0.472 0.567 0.754 0.870
## sscs (.12.) 0.425 0.022 19.227 0.000 0.381 0.468 0.616 0.737
## g =~
## verbal (.13.) 2.928 0.494 5.928 0.000 1.960 3.897 0.946 0.946
## math (.14.) 1.739 0.128 13.552 0.000 1.487 1.990 0.867 0.867
## elctrnc 1.265 0.124 10.216 0.000 1.022 1.507 0.784 0.784
## speed (.16.) 1.051 0.079 13.238 0.000 0.895 1.206 0.724 0.724
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 17.912 0.208 86.039 0.000 17.504 18.320 17.912 4.022
## .sswk 27.643 0.309 89.548 0.000 27.038 28.248 27.643 4.260
## .sspc (.34.) 11.206 0.143 78.594 0.000 10.926 11.485 11.206 3.930
## .ssar 20.311 0.336 60.447 0.000 19.652 20.969 20.311 2.940
## .ssmk (.36.) 15.249 0.316 48.320 0.000 14.631 15.868 15.249 2.369
## .ssmc (.37.) 17.194 0.224 76.767 0.000 16.755 17.633 17.194 3.682
## .ssasi (.38.) 17.717 0.219 80.721 0.000 17.287 18.147 17.717 3.903
## .ssei 13.530 0.177 76.269 0.000 13.182 13.877 13.530 3.496
## .ssno (.40.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.281
## .sscs 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.091
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.104 0.104
## .math 1.000 1.000 1.000 0.249 0.249
## .speed 1.000 1.000 1.000 0.475 0.475
## g 1.000 1.000 1.000 1.000 1.000
## .ssgs (.21.) 4.769 0.284 16.764 0.000 4.211 5.326 4.769 0.240
## .sswk (.22.) 6.880 0.680 10.111 0.000 5.547 8.214 6.880 0.163
## .sspc (.23.) 2.601 0.155 16.777 0.000 2.297 2.905 2.601 0.320
## .ssar (.24.) 5.679 0.720 7.893 0.000 4.269 7.090 5.679 0.119
## .ssmk (.25.) 9.200 0.698 13.177 0.000 7.831 10.568 9.200 0.222
## .ssmc (.26.) 8.558 0.456 18.747 0.000 7.663 9.452 8.558 0.392
## .ssasi (.27.) 8.028 0.544 14.762 0.000 6.962 9.094 8.028 0.390
## .ssei (.28.) 3.076 0.300 10.251 0.000 2.488 3.664 3.076 0.205
## .ssno (.29.) 0.182 0.029 6.294 0.000 0.125 0.238 0.182 0.242
## .sscs (.30.) 0.319 0.037 8.735 0.000 0.247 0.391 0.319 0.457
## .elctrnc 1.000 1.000 1.000 0.385 0.385
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.799 0.121 6.616 0.000 0.562 1.036 2.473 0.596
## sswk (.p2.) 1.918 0.289 6.626 0.000 1.351 2.485 5.935 0.915
## sspc (.p3.) 0.760 0.113 6.714 0.000 0.538 0.982 2.352 0.825
## math =~
## ssar (.p4.) 3.232 0.185 17.445 0.000 2.869 3.596 6.484 0.939
## ssmk (.p5.) 2.831 0.160 17.729 0.000 2.518 3.144 5.679 0.882
## ssmc (.p6.) 0.660 0.087 7.557 0.000 0.489 0.831 1.324 0.317
## electronic =~
## ssgs (.p7.) 1.039 0.094 11.067 0.000 0.855 1.223 1.183 0.285
## ssasi (.p8.) 2.199 0.172 12.810 0.000 1.863 2.536 2.506 0.663
## ssmc (.p9.) 1.617 0.147 10.989 0.000 1.329 1.905 1.842 0.441
## ssei (.10.) 2.139 0.125 17.182 0.000 1.895 2.384 2.438 0.812
## speed =~
## ssno (.11.) 0.520 0.024 21.391 0.000 0.472 0.567 0.754 0.870
## sscs (.12.) 0.425 0.022 19.227 0.000 0.381 0.468 0.616 0.737
## g =~
## verbal (.13.) 2.928 0.494 5.928 0.000 1.960 3.897 0.946 0.946
## math (.14.) 1.739 0.128 13.552 0.000 1.487 1.990 0.867 0.867
## elctrnc 1.013 0.080 12.583 0.000 0.855 1.171 0.889 0.889
## speed (.16.) 1.051 0.079 13.238 0.000 0.895 1.206 0.724 0.724
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 17.912 0.208 86.039 0.000 17.504 18.320 17.912 4.318
## .sswk 25.679 0.404 63.494 0.000 24.886 26.472 25.679 3.958
## .sspc (.34.) 11.206 0.143 78.594 0.000 10.926 11.485 11.206 3.930
## .ssar 18.926 0.411 46.062 0.000 18.121 19.732 18.926 2.740
## .ssmk (.36.) 15.249 0.316 48.320 0.000 14.631 15.868 15.249 2.369
## .ssmc (.37.) 17.194 0.224 76.767 0.000 16.755 17.633 17.194 4.114
## .ssasi (.38.) 17.717 0.219 80.721 0.000 17.287 18.147 17.717 4.684
## .ssei 16.115 0.380 42.444 0.000 15.371 16.859 16.115 5.366
## .ssno (.40.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.281
## .sscs 0.411 0.048 8.635 0.000 0.318 0.504 0.411 0.492
## .verbal 1.283 0.130 9.879 0.000 1.028 1.537 0.415 0.415
## .math -0.040 0.108 -0.365 0.715 -0.252 0.173 -0.020 -0.020
## .elctrnc -2.648 0.247 -10.737 0.000 -3.132 -2.165 -2.324 -2.324
## .speed 0.544 0.097 5.634 0.000 0.355 0.733 0.375 0.375
## g -0.028 0.078 -0.364 0.716 -0.181 0.124 -0.028 -0.028
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.104 0.104
## .math 1.000 1.000 1.000 0.249 0.249
## .speed 1.000 1.000 1.000 0.475 0.475
## g 1.000 1.000 1.000 1.000 1.000
## .ssgs (.21.) 4.769 0.284 16.764 0.000 4.211 5.326 4.769 0.277
## .sswk (.22.) 6.880 0.680 10.111 0.000 5.547 8.214 6.880 0.163
## .sspc (.23.) 2.601 0.155 16.777 0.000 2.297 2.905 2.601 0.320
## .ssar (.24.) 5.679 0.720 7.893 0.000 4.269 7.090 5.679 0.119
## .ssmk (.25.) 9.200 0.698 13.177 0.000 7.831 10.568 9.200 0.222
## .ssmc (.26.) 8.558 0.456 18.747 0.000 7.663 9.452 8.558 0.490
## .ssasi (.27.) 8.028 0.544 14.762 0.000 6.962 9.094 8.028 0.561
## .ssei (.28.) 3.076 0.300 10.251 0.000 2.488 3.664 3.076 0.341
## .ssno (.29.) 0.182 0.029 6.294 0.000 0.125 0.238 0.182 0.242
## .sscs (.30.) 0.319 0.037 8.735 0.000 0.247 0.391 0.319 0.457
## .elctrnc 0.272 0.078 3.514 0.000 0.120 0.424 0.210 0.210
tests<-lavTestLRT(configural, metric2, scalar2, latent2, weak)
## Warning: lavaan->lav_test_diff_SatorraBentler2001():
## scaling factor is negative
Td=tests[2:5,"Chisq diff"]
Td
## [1] 33.389792 2.410328 6.512958 NA
dfd=tests[2:5,"Df diff"]
dfd
## [1] 10 1 4 1
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-526 + 526 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.06674727 0.05182990 0.03459258 NA
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04255477 0.09238715
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] NA 0.1394781
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] NA 0.08074373
RMSEA.CI(T=Td[4],df=dfd[4],N=N,G=2)
## [1] NA NA
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.881 0.703 0.212 0.015
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
## 0.879 0.870 0.654 0.569 0.389 0.230
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
## 0.836 0.814 0.354 0.218 0.054 0.007
round(pvals(T=Td[4],df=dfd[4],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## NA NA NA NA NA NA
tests<-lavTestLRT(configural, metric2, scalar2, latent)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 33.389792 2.410328 53.288094
dfd=tests[2:4,"Df diff"]
dfd
## [1] 10 1 5
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-526 + 526 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.06674727 0.05182990 0.13562988
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] NA 0.1394781
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.1040732 0.1695945
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
## 0.879 0.870 0.654 0.569 0.389 0.230
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 1.000 0.998 0.968
tests<-lavTestLRT(configural, metric2, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 33.389792 2.410328 38.653246
dfd=tests[2:4,"Df diff"]
dfd
## [1] 10 1 10
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-526 + 526 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.06674727 0.05182990 0.07387666
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04255477 0.09238715
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] NA 0.1394781
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.05015608 0.09913933
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 0.881 0.703 0.212 0.015
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
## 0.879 0.870 0.654 0.569 0.389 0.230
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 0.951 0.843 0.370 0.044
tests<-lavTestLRT(configural, metric2, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 33.38979 185.71070
dfd=tests[2:3,"Df diff"]
dfd
## [1] 10 5
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-526 + 526 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.06674727 0.26237792
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04255477 0.09238715
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.2306935 0.2952273
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 0.881 0.703 0.212 0.015
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)
Td=tests[2,"Chisq diff"]
Td
## [1] 44.21409
dfd=tests[2,"Df diff"]
dfd
## [1] 11
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-526 + 526 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.07583771
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.05326756 0.09980853
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 0.969 0.882 0.413 0.049
hof.age<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
g~~1*g
math~0*1
g ~ age
'
hof.ageq<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
g~~1*g
math~0*1
g ~ c(a,a)*age
'
hof.age2<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
g~~1*g
math~0*1
g ~ age + age2
'
hof.age2q<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
g~~1*g
math~0*1
g ~ c(a,a)*age + c(b,b)*age2
'
sem.age<-sem(hof.age, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(sem.age, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 513.448 92.000 0.000 0.945 0.093 0.077 0.598 47946.484 48234.074
Mc(sem.age)
## [1] 0.8183227
summary(sem.age, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 156 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 79
## Number of equality constraints 21
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 513.448 429.698
## Degrees of freedom 92 92
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.195
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 315.355 263.916
## 1 198.093 165.781
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.761 0.117 6.498 0.000 0.531 0.990 2.493 0.558
## sswk (.p2.) 1.803 0.279 6.453 0.000 1.256 2.351 5.910 0.911
## sspc (.p3.) 0.704 0.109 6.467 0.000 0.491 0.917 2.307 0.801
## math =~
## ssar (.p4.) 3.339 0.173 19.276 0.000 2.999 3.678 6.458 0.937
## ssmk (.p5.) 2.917 0.150 19.459 0.000 2.623 3.211 5.642 0.883
## ssmc (.p6.) 0.723 0.089 8.139 0.000 0.549 0.897 1.398 0.298
## electronic =~
## ssgs (.p7.) 0.985 0.085 11.576 0.000 0.818 1.151 1.620 0.363
## ssasi (.p8.) 2.104 0.148 14.191 0.000 1.813 2.394 3.460 0.735
## ssmc (.p9.) 1.517 0.128 11.821 0.000 1.266 1.769 2.496 0.531
## ssei (.10.) 2.161 0.125 17.257 0.000 1.915 2.406 3.555 0.950
## speed =~
## ssno (.11.) 0.520 0.024 21.551 0.000 0.472 0.567 0.747 0.862
## sscs (.12.) 0.430 0.022 19.391 0.000 0.386 0.473 0.618 0.757
## g =~
## verbal (.13.) 3.094 0.524 5.905 0.000 2.067 4.121 0.952 0.952
## math (.14.) 1.641 0.114 14.367 0.000 1.417 1.865 0.856 0.856
## elctrnc 1.295 0.115 11.278 0.000 1.070 1.520 0.794 0.794
## speed (.16.) 1.024 0.079 13.003 0.000 0.870 1.179 0.719 0.719
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.060 0.026 2.309 0.021 0.009 0.111 0.060 0.132
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.35.) 17.956 0.213 84.234 0.000 17.538 18.374 17.956 4.019
## .sswk 27.723 0.314 88.360 0.000 27.108 28.338 27.723 4.274
## .sspc (.37.) 11.243 0.144 77.995 0.000 10.960 11.525 11.243 3.905
## .ssar 20.390 0.341 59.863 0.000 19.722 21.058 20.390 2.958
## .ssmk (.39.) 15.324 0.321 47.770 0.000 14.695 15.952 15.324 2.397
## .ssmc (.40.) 17.221 0.227 75.738 0.000 16.776 17.667 17.221 3.666
## .ssasi (.41.) 17.766 0.220 80.676 0.000 17.335 18.198 17.766 3.773
## .ssei 13.570 0.178 76.340 0.000 13.222 13.918 13.570 3.625
## .ssno (.43.) 0.251 0.042 6.022 0.000 0.170 0.333 0.251 0.290
## .sscs 0.082 0.040 2.053 0.040 0.004 0.161 0.082 0.101
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.093 0.093
## .math 1.000 1.000 1.000 0.267 0.267
## .speed 1.000 1.000 1.000 0.484 0.484
## .g 1.000 1.000 1.000 0.983 0.983
## .ssgs 5.014 0.412 12.159 0.000 4.206 5.822 5.014 0.251
## .sswk 7.136 0.939 7.598 0.000 5.295 8.977 7.136 0.170
## .sspc 2.967 0.248 11.965 0.000 2.481 3.453 2.967 0.358
## .ssar 5.799 0.924 6.279 0.000 3.989 7.609 5.799 0.122
## .ssmk 9.021 0.899 10.036 0.000 7.259 10.783 9.021 0.221
## .ssmc 9.149 0.692 13.226 0.000 7.793 10.504 9.149 0.415
## .ssasi 10.198 0.923 11.044 0.000 8.388 12.008 10.198 0.460
## .ssei 1.375 0.362 3.796 0.000 0.665 2.085 1.375 0.098
## .ssno 0.194 0.033 5.932 0.000 0.130 0.258 0.194 0.257
## .sscs 0.285 0.046 6.206 0.000 0.195 0.375 0.285 0.427
## .electronic 1.000 1.000 1.000 0.370 0.370
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.761 0.117 6.498 0.000 0.531 0.990 2.527 0.610
## sswk (.p2.) 1.803 0.279 6.453 0.000 1.256 2.351 5.991 0.922
## sspc (.p3.) 0.704 0.109 6.467 0.000 0.491 0.917 2.338 0.839
## math =~
## ssar (.p4.) 3.339 0.173 19.276 0.000 2.999 3.678 6.530 0.943
## ssmk (.p5.) 2.917 0.150 19.459 0.000 2.623 3.211 5.704 0.879
## ssmc (.p6.) 0.723 0.089 8.139 0.000 0.549 0.897 1.413 0.340
## electronic =~
## ssgs (.p7.) 0.985 0.085 11.576 0.000 0.818 1.151 1.113 0.269
## ssasi (.p8.) 2.104 0.148 14.191 0.000 1.813 2.394 2.378 0.677
## ssmc (.p9.) 1.517 0.128 11.821 0.000 1.266 1.769 1.715 0.412
## ssei (.10.) 2.161 0.125 17.257 0.000 1.915 2.406 2.443 0.777
## speed =~
## ssno (.11.) 0.520 0.024 21.551 0.000 0.472 0.567 0.753 0.871
## sscs (.12.) 0.430 0.022 19.391 0.000 0.386 0.473 0.623 0.726
## g =~
## verbal (.13.) 3.094 0.524 5.905 0.000 2.067 4.121 0.954 0.954
## math (.14.) 1.641 0.114 14.367 0.000 1.417 1.865 0.859 0.859
## elctrnc 1.000 0.076 13.167 0.000 0.851 1.149 0.906 0.906
## speed (.16.) 1.024 0.079 13.003 0.000 0.870 1.179 0.724 0.724
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.102 0.022 4.678 0.000 0.059 0.145 0.100 0.215
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.35.) 17.956 0.213 84.234 0.000 17.538 18.374 17.956 4.332
## .sswk 25.752 0.419 61.510 0.000 24.931 26.572 25.752 3.965
## .sspc (.37.) 11.243 0.144 77.995 0.000 10.960 11.525 11.243 4.034
## .ssar 19.017 0.417 45.658 0.000 18.200 19.833 19.017 2.746
## .ssmk (.39.) 15.324 0.321 47.770 0.000 14.695 15.952 15.324 2.361
## .ssmc (.40.) 17.221 0.227 75.738 0.000 16.776 17.667 17.221 4.142
## .ssasi (.41.) 17.766 0.220 80.676 0.000 17.335 18.198 17.766 5.058
## .ssei 16.523 0.418 39.540 0.000 15.704 17.342 16.523 5.252
## .ssno (.43.) 0.251 0.042 6.022 0.000 0.170 0.333 0.251 0.291
## .sscs 0.415 0.048 8.568 0.000 0.320 0.510 0.415 0.484
## .verbal 1.449 0.319 4.543 0.000 0.824 2.074 0.436 0.436
## .elctrnc -2.770 0.247 -11.209 0.000 -3.255 -2.286 -2.451 -2.451
## .speed 0.570 0.099 5.732 0.000 0.375 0.765 0.393 0.393
## .g -0.036 0.091 -0.400 0.689 -0.215 0.142 -0.036 -0.036
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.091 0.091
## .math 1.000 1.000 1.000 0.261 0.261
## .speed 1.000 1.000 1.000 0.476 0.476
## .g 1.000 1.000 1.000 0.954 0.954
## .ssgs 4.692 0.382 12.279 0.000 3.943 5.441 4.692 0.273
## .sswk 6.299 0.863 7.302 0.000 4.608 7.989 6.299 0.149
## .sspc 2.300 0.193 11.942 0.000 1.922 2.677 2.300 0.296
## .ssar 5.330 0.934 5.708 0.000 3.500 7.160 5.330 0.111
## .ssmk 9.579 0.957 10.007 0.000 7.703 11.455 9.579 0.227
## .ssmc 8.576 0.576 14.892 0.000 7.447 9.705 8.576 0.496
## .ssasi 6.683 0.540 12.375 0.000 5.624 7.741 6.683 0.542
## .ssei 3.928 0.381 10.298 0.000 3.180 4.676 3.928 0.397
## .ssno 0.181 0.037 4.941 0.000 0.109 0.252 0.181 0.242
## .sscs 0.348 0.049 7.031 0.000 0.251 0.445 0.348 0.473
## .electronic 0.229 0.066 3.456 0.001 0.099 0.359 0.179 0.179
sem.ageq<-sem(hof.ageq, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(sem.ageq, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 515.412 93.000 0.000 0.944 0.093 0.072 0.598 47946.448 48229.079
Mc(sem.ageq)
## [1] 0.8179475
summary(sem.ageq, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 139 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 79
## Number of equality constraints 22
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 515.412 431.187
## Degrees of freedom 93 93
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.195
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 316.259 264.579
## 1 199.153 166.609
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.769 0.115 6.673 0.000 0.543 0.995 2.510 0.559
## sswk (.p2.) 1.825 0.274 6.651 0.000 1.287 2.362 5.952 0.913
## sspc (.p3.) 0.712 0.107 6.672 0.000 0.503 0.922 2.324 0.803
## math =~
## ssar (.p4.) 3.330 0.173 19.266 0.000 2.991 3.669 6.495 0.938
## ssmk (.p5.) 2.909 0.150 19.429 0.000 2.616 3.203 5.674 0.884
## ssmc (.p6.) 0.720 0.088 8.137 0.000 0.547 0.893 1.404 0.298
## electronic =~
## ssgs (.p7.) 0.984 0.085 11.567 0.000 0.817 1.151 1.628 0.362
## ssasi (.p8.) 2.102 0.148 14.179 0.000 1.811 2.392 3.476 0.736
## ssmc (.p9.) 1.516 0.128 11.807 0.000 1.264 1.767 2.507 0.532
## ssei (.10.) 2.158 0.125 17.239 0.000 1.913 2.403 3.570 0.950
## speed =~
## ssno (.11.) 0.519 0.024 21.528 0.000 0.472 0.567 0.751 0.863
## sscs (.12.) 0.429 0.022 19.401 0.000 0.386 0.473 0.620 0.758
## g =~
## verbal (.13.) 3.057 0.503 6.074 0.000 2.071 4.044 0.952 0.952
## math (.14.) 1.649 0.114 14.426 0.000 1.425 1.873 0.859 0.859
## elctrnc 1.297 0.115 11.255 0.000 1.071 1.523 0.797 0.797
## speed (.16.) 1.027 0.079 13.031 0.000 0.873 1.182 0.722 0.722
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.080 0.018 4.552 0.000 0.046 0.115 0.079 0.174
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.35.) 17.974 0.211 85.249 0.000 17.560 18.387 17.974 4.003
## .sswk 27.750 0.310 89.573 0.000 27.143 28.357 27.750 4.255
## .sspc (.37.) 11.253 0.143 78.501 0.000 10.972 11.534 11.253 3.890
## .ssar 20.416 0.338 60.403 0.000 19.754 21.079 20.416 2.948
## .ssmk (.39.) 15.347 0.320 47.978 0.000 14.720 15.974 15.347 2.390
## .ssmc (.40.) 17.237 0.225 76.483 0.000 16.795 17.678 17.237 3.656
## .ssasi (.41.) 17.779 0.218 81.622 0.000 17.352 18.206 17.779 3.767
## .ssei 13.583 0.176 77.318 0.000 13.239 13.928 13.583 3.615
## .ssno (.43.) 0.254 0.041 6.120 0.000 0.173 0.335 0.254 0.292
## .sscs 0.085 0.040 2.119 0.034 0.006 0.163 0.085 0.103
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.094 0.094
## .math 1.000 1.000 1.000 0.263 0.263
## .speed 1.000 1.000 1.000 0.479 0.479
## .g 1.000 1.000 1.000 0.970 0.970
## .ssgs 5.019 0.413 12.167 0.000 4.211 5.828 5.019 0.249
## .sswk 7.108 0.937 7.584 0.000 5.271 8.945 7.108 0.167
## .sspc 2.969 0.248 11.971 0.000 2.483 3.455 2.969 0.355
## .ssar 5.789 0.922 6.281 0.000 3.982 7.595 5.789 0.121
## .ssmk 9.036 0.899 10.053 0.000 7.274 10.797 9.036 0.219
## .ssmc 9.149 0.692 13.221 0.000 7.792 10.505 9.149 0.412
## .ssasi 10.196 0.924 11.039 0.000 8.386 12.006 10.196 0.458
## .ssei 1.376 0.362 3.804 0.000 0.667 2.085 1.376 0.097
## .ssno 0.194 0.033 5.934 0.000 0.130 0.258 0.194 0.256
## .sscs 0.285 0.046 6.207 0.000 0.195 0.375 0.285 0.425
## .electronic 1.000 1.000 1.000 0.366 0.366
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.769 0.115 6.673 0.000 0.543 0.995 2.508 0.608
## sswk (.p2.) 1.825 0.274 6.651 0.000 1.287 2.362 5.948 0.921
## sspc (.p3.) 0.712 0.107 6.672 0.000 0.503 0.922 2.322 0.838
## math =~
## ssar (.p4.) 3.330 0.173 19.266 0.000 2.991 3.669 6.491 0.942
## ssmk (.p5.) 2.909 0.150 19.429 0.000 2.616 3.203 5.671 0.878
## ssmc (.p6.) 0.720 0.088 8.137 0.000 0.547 0.893 1.403 0.339
## electronic =~
## ssgs (.p7.) 0.984 0.085 11.567 0.000 0.817 1.151 1.108 0.269
## ssasi (.p8.) 2.102 0.148 14.179 0.000 1.811 2.392 2.366 0.675
## ssmc (.p9.) 1.516 0.128 11.807 0.000 1.264 1.767 1.706 0.412
## ssei (.10.) 2.158 0.125 17.239 0.000 1.913 2.403 2.429 0.775
## speed =~
## ssno (.11.) 0.519 0.024 21.528 0.000 0.472 0.567 0.750 0.870
## sscs (.12.) 0.429 0.022 19.401 0.000 0.386 0.473 0.620 0.724
## g =~
## verbal (.13.) 3.057 0.503 6.074 0.000 2.071 4.044 0.952 0.952
## math (.14.) 1.649 0.114 14.426 0.000 1.425 1.873 0.858 0.858
## elctrnc 1.003 0.076 13.169 0.000 0.854 1.153 0.905 0.905
## speed (.16.) 1.027 0.079 13.031 0.000 0.873 1.182 0.722 0.722
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.080 0.018 4.552 0.000 0.046 0.115 0.079 0.170
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.35.) 17.974 0.211 85.249 0.000 17.560 18.387 17.974 4.360
## .sswk 25.778 0.417 61.821 0.000 24.960 26.595 25.778 3.992
## .sspc (.37.) 11.253 0.143 78.501 0.000 10.972 11.534 11.253 4.059
## .ssar 19.043 0.416 45.752 0.000 18.227 19.859 19.043 2.764
## .ssmk (.39.) 15.347 0.320 47.978 0.000 14.720 15.974 15.347 2.376
## .ssmc (.40.) 17.237 0.225 76.483 0.000 16.795 17.678 17.237 4.159
## .ssasi (.41.) 17.779 0.218 81.622 0.000 17.352 18.206 17.779 5.075
## .ssei 16.534 0.417 39.655 0.000 15.716 17.351 16.534 5.273
## .ssno (.43.) 0.254 0.041 6.120 0.000 0.173 0.335 0.254 0.295
## .sscs 0.417 0.048 8.653 0.000 0.323 0.512 0.417 0.487
## .verbal 1.432 0.310 4.617 0.000 0.824 2.040 0.439 0.439
## .elctrnc -2.774 0.247 -11.210 0.000 -3.259 -2.289 -2.465 -2.465
## .speed 0.570 0.099 5.732 0.000 0.375 0.765 0.395 0.395
## .g -0.048 0.090 -0.535 0.593 -0.225 0.128 -0.047 -0.047
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.094 0.094
## .math 1.000 1.000 1.000 0.263 0.263
## .speed 1.000 1.000 1.000 0.479 0.479
## .g 1.000 1.000 1.000 0.971 0.971
## .ssgs 4.695 0.382 12.277 0.000 3.946 5.445 4.695 0.276
## .sswk 6.314 0.864 7.307 0.000 4.620 8.008 6.314 0.151
## .sspc 2.295 0.192 11.944 0.000 1.918 2.671 2.295 0.299
## .ssar 5.337 0.934 5.716 0.000 3.507 7.167 5.337 0.112
## .ssmk 9.567 0.957 9.999 0.000 7.691 11.442 9.567 0.229
## .ssmc 8.573 0.576 14.890 0.000 7.445 9.702 8.573 0.499
## .ssasi 6.678 0.540 12.364 0.000 5.620 7.737 6.678 0.544
## .ssei 3.932 0.381 10.313 0.000 3.185 4.679 3.932 0.400
## .ssno 0.180 0.037 4.933 0.000 0.109 0.252 0.180 0.242
## .sscs 0.348 0.049 7.043 0.000 0.251 0.445 0.348 0.475
## .electronic 0.230 0.067 3.461 0.001 0.100 0.361 0.182 0.182
sem.age2<-sem(hof.age2, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(sem.age2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 544.735 110.000 0.000 0.943 0.087 0.072 0.632 47947.667 48245.174
Mc(sem.age2)
## [1] 0.8131662
summary(sem.age2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 148 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 81
## Number of equality constraints 21
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 544.735 457.467
## Degrees of freedom 110 110
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.191
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 332.055 278.858
## 1 212.681 178.609
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.760 0.117 6.501 0.000 0.531 0.990 2.496 0.558
## sswk (.p2.) 1.804 0.279 6.463 0.000 1.257 2.351 5.919 0.912
## sspc (.p3.) 0.704 0.109 6.479 0.000 0.491 0.917 2.310 0.802
## math =~
## ssar (.p4.) 3.342 0.173 19.316 0.000 3.003 3.681 6.465 0.937
## ssmk (.p5.) 2.920 0.150 19.530 0.000 2.627 3.213 5.648 0.883
## ssmc (.p6.) 0.724 0.089 8.140 0.000 0.549 0.898 1.400 0.298
## electronic =~
## ssgs (.p7.) 0.983 0.085 11.570 0.000 0.816 1.149 1.620 0.362
## ssasi (.p8.) 2.100 0.148 14.183 0.000 1.810 2.390 3.462 0.735
## ssmc (.p9.) 1.514 0.128 11.811 0.000 1.263 1.765 2.496 0.531
## ssei (.10.) 2.158 0.125 17.232 0.000 1.913 2.404 3.558 0.950
## speed =~
## ssno (.11.) 0.520 0.024 21.580 0.000 0.473 0.567 0.748 0.862
## sscs (.12.) 0.430 0.022 19.414 0.000 0.386 0.473 0.618 0.757
## g =~
## verbal (.13.) 3.089 0.523 5.912 0.000 2.065 4.113 0.952 0.952
## math (.14.) 1.637 0.114 14.399 0.000 1.414 1.859 0.856 0.856
## elctrnc 1.295 0.114 11.325 0.000 1.071 1.519 0.795 0.795
## speed (.16.) 1.022 0.078 13.055 0.000 0.869 1.175 0.719 0.719
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.054 0.027 1.992 0.046 0.001 0.107 0.053 0.118
## age2 -0.016 0.012 -1.312 0.190 -0.040 0.008 -0.016 -0.077
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.38.) 18.236 0.281 64.932 0.000 17.686 18.787 18.236 4.078
## .sswk 28.155 0.411 68.487 0.000 27.349 28.960 28.155 4.337
## .sspc (.40.) 11.411 0.176 64.710 0.000 11.065 11.757 11.411 3.960
## .ssar 20.813 0.446 46.669 0.000 19.939 21.687 20.813 3.017
## .ssmk (.42.) 15.693 0.412 38.069 0.000 14.885 16.501 15.693 2.453
## .ssmc (.43.) 17.465 0.280 62.339 0.000 16.916 18.014 17.465 3.715
## .ssasi (.44.) 17.977 0.255 70.540 0.000 17.477 18.476 17.977 3.816
## .ssei 13.786 0.225 61.275 0.000 13.345 14.227 13.786 3.681
## .ssno (.46.) 0.293 0.048 6.150 0.000 0.199 0.386 0.293 0.337
## .sscs 0.116 0.043 2.692 0.007 0.032 0.201 0.116 0.143
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.093 0.093
## .math 1.000 1.000 1.000 0.267 0.267
## .speed 1.000 1.000 1.000 0.483 0.483
## .g 1.000 1.000 1.000 0.977 0.977
## .ssgs 5.025 0.414 12.132 0.000 4.213 5.836 5.025 0.251
## .sswk 7.113 0.934 7.612 0.000 5.281 8.944 7.113 0.169
## .sspc 2.967 0.248 11.941 0.000 2.480 3.453 2.967 0.357
## .ssar 5.801 0.924 6.281 0.000 3.990 7.611 5.801 0.122
## .ssmk 9.020 0.899 10.028 0.000 7.257 10.783 9.020 0.220
## .ssmc 9.156 0.692 13.238 0.000 7.801 10.512 9.156 0.414
## .ssasi 10.204 0.925 11.036 0.000 8.392 12.017 10.204 0.460
## .ssei 1.367 0.360 3.794 0.000 0.661 2.073 1.367 0.097
## .ssno 0.194 0.033 5.931 0.000 0.130 0.258 0.194 0.257
## .sscs 0.285 0.046 6.202 0.000 0.195 0.375 0.285 0.427
## .electronic 1.000 1.000 1.000 0.368 0.368
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.760 0.117 6.501 0.000 0.531 0.990 2.523 0.609
## sswk (.p2.) 1.804 0.279 6.463 0.000 1.257 2.351 5.984 0.922
## sspc (.p3.) 0.704 0.109 6.479 0.000 0.491 0.917 2.336 0.839
## math =~
## ssar (.p4.) 3.342 0.173 19.316 0.000 3.003 3.681 6.523 0.943
## ssmk (.p5.) 2.920 0.150 19.530 0.000 2.627 3.213 5.698 0.879
## ssmc (.p6.) 0.724 0.089 8.140 0.000 0.549 0.898 1.412 0.340
## electronic =~
## ssgs (.p7.) 0.983 0.085 11.570 0.000 0.816 1.149 1.112 0.269
## ssasi (.p8.) 2.100 0.148 14.183 0.000 1.810 2.390 2.376 0.677
## ssmc (.p9.) 1.514 0.128 11.811 0.000 1.263 1.765 1.713 0.412
## ssei (.10.) 2.158 0.125 17.232 0.000 1.913 2.404 2.442 0.776
## speed =~
## ssno (.11.) 0.520 0.024 21.580 0.000 0.473 0.567 0.753 0.871
## sscs (.12.) 0.430 0.022 19.414 0.000 0.386 0.473 0.622 0.726
## g =~
## verbal (.13.) 3.089 0.523 5.912 0.000 2.065 4.113 0.953 0.953
## math (.14.) 1.637 0.114 14.399 0.000 1.414 1.859 0.859 0.859
## elctrnc 1.001 0.076 13.188 0.000 0.852 1.149 0.906 0.906
## speed (.16.) 1.022 0.078 13.055 0.000 0.869 1.175 0.723 0.723
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.102 0.022 4.753 0.000 0.060 0.145 0.100 0.215
## age2 -0.000 0.009 -0.019 0.985 -0.018 0.017 -0.000 -0.001
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.38.) 18.236 0.281 64.932 0.000 17.686 18.787 18.236 4.405
## .sswk 26.182 0.498 52.567 0.000 25.206 27.159 26.182 4.035
## .sspc (.40.) 11.411 0.176 64.710 0.000 11.065 11.757 11.411 4.098
## .ssar 19.440 0.511 38.050 0.000 18.439 20.442 19.440 2.810
## .ssmk (.42.) 15.693 0.412 38.069 0.000 14.885 16.501 15.693 2.420
## .ssmc (.43.) 17.465 0.280 62.339 0.000 16.916 18.014 17.465 4.203
## .ssasi (.44.) 17.977 0.255 70.540 0.000 17.477 18.476 17.977 5.120
## .ssei 16.743 0.428 39.111 0.000 15.904 17.582 16.743 5.324
## .ssno (.46.) 0.293 0.048 6.150 0.000 0.199 0.386 0.293 0.338
## .sscs 0.449 0.052 8.692 0.000 0.348 0.550 0.449 0.524
## .verbal 1.449 0.319 4.539 0.000 0.824 2.075 0.437 0.437
## .elctrnc -2.798 0.250 -11.185 0.000 -3.288 -2.308 -2.474 -2.474
## .speed 0.570 0.099 5.734 0.000 0.375 0.764 0.394 0.394
## .g -0.113 0.114 -0.993 0.321 -0.337 0.110 -0.111 -0.111
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.091 0.091
## .math 1.000 1.000 1.000 0.263 0.263
## .speed 1.000 1.000 1.000 0.477 0.477
## .g 1.000 1.000 1.000 0.954 0.954
## .ssgs 4.693 0.382 12.277 0.000 3.944 5.442 4.693 0.274
## .sswk 6.295 0.863 7.298 0.000 4.604 7.985 6.295 0.150
## .sspc 2.300 0.193 11.940 0.000 1.922 2.677 2.300 0.297
## .ssar 5.327 0.934 5.704 0.000 3.497 7.158 5.327 0.111
## .ssmk 9.579 0.958 10.000 0.000 7.702 11.457 9.579 0.228
## .ssmc 8.576 0.576 14.888 0.000 7.447 9.705 8.576 0.497
## .ssasi 6.683 0.540 12.366 0.000 5.624 7.743 6.683 0.542
## .ssei 3.927 0.382 10.291 0.000 3.179 4.675 3.927 0.397
## .ssno 0.181 0.037 4.937 0.000 0.109 0.252 0.181 0.242
## .sscs 0.348 0.049 7.029 0.000 0.251 0.445 0.348 0.473
## .electronic 0.230 0.067 3.453 0.001 0.099 0.360 0.180 0.180
sem.age2q<-sem(hof.age2q, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(sem.age2q, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 547.948 112.000 0.000 0.943 0.086 0.069 0.631 47946.880 48234.471
Mc(sem.age2q)
## [1] 0.812697
summary(sem.age2q, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 130 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 81
## Number of equality constraints 23
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 547.948 460.110
## Degrees of freedom 112 112
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.191
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 333.443 279.991
## 1 214.505 180.119
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.770 0.115 6.687 0.000 0.544 0.995 2.508 0.559
## sswk (.p2.) 1.826 0.274 6.671 0.000 1.290 2.363 5.952 0.913
## sspc (.p3.) 0.713 0.107 6.692 0.000 0.504 0.922 2.323 0.803
## math =~
## ssar (.p4.) 3.333 0.173 19.288 0.000 2.994 3.671 6.494 0.938
## ssmk (.p5.) 2.911 0.150 19.471 0.000 2.618 3.204 5.672 0.884
## ssmc (.p6.) 0.720 0.089 8.139 0.000 0.547 0.894 1.404 0.298
## electronic =~
## ssgs (.p7.) 0.983 0.085 11.567 0.000 0.816 1.150 1.627 0.362
## ssasi (.p8.) 2.100 0.148 14.174 0.000 1.810 2.390 3.475 0.736
## ssmc (.p9.) 1.515 0.128 11.803 0.000 1.263 1.766 2.507 0.532
## ssei (.10.) 2.156 0.125 17.218 0.000 1.911 2.402 3.569 0.950
## speed =~
## ssno (.11.) 0.519 0.024 21.546 0.000 0.472 0.567 0.750 0.863
## sscs (.12.) 0.429 0.022 19.408 0.000 0.386 0.473 0.620 0.758
## g =~
## verbal (.13.) 3.053 0.501 6.092 0.000 2.071 4.035 0.952 0.952
## math (.14.) 1.646 0.114 14.434 0.000 1.422 1.869 0.858 0.858
## elctrnc 1.298 0.115 11.278 0.000 1.072 1.523 0.797 0.797
## speed (.16.) 1.026 0.079 13.043 0.000 0.872 1.180 0.722 0.722
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.076 0.018 4.176 0.000 0.040 0.112 0.075 0.166
## age2 (b) -0.008 0.008 -1.089 0.276 -0.024 0.007 -0.008 -0.041
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.38.) 18.122 0.237 76.305 0.000 17.656 18.587 18.122 4.037
## .sswk 27.978 0.347 80.650 0.000 27.298 28.658 27.978 4.291
## .sspc (.40.) 11.342 0.155 73.226 0.000 11.038 11.645 11.342 3.921
## .ssar 20.640 0.381 54.123 0.000 19.893 21.388 20.640 2.980
## .ssmk (.42.) 15.542 0.358 43.437 0.000 14.841 16.244 15.542 2.421
## .ssmc (.43.) 17.365 0.247 70.411 0.000 16.882 17.849 17.365 3.684
## .ssasi (.44.) 17.890 0.231 77.606 0.000 17.439 18.342 17.890 3.790
## .ssei 13.698 0.194 70.546 0.000 13.317 14.078 13.698 3.646
## .ssno (.46.) 0.276 0.043 6.365 0.000 0.191 0.361 0.276 0.317
## .sscs 0.103 0.041 2.522 0.012 0.023 0.182 0.103 0.125
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.094 0.094
## .math 1.000 1.000 1.000 0.263 0.263
## .speed 1.000 1.000 1.000 0.479 0.479
## .g 1.000 1.000 1.000 0.968 0.968
## .ssgs 5.025 0.413 12.155 0.000 4.214 5.835 5.025 0.249
## .sswk 7.094 0.935 7.589 0.000 5.262 8.926 7.094 0.167
## .sspc 2.968 0.248 11.958 0.000 2.482 3.455 2.968 0.355
## .ssar 5.787 0.922 6.276 0.000 3.980 7.594 5.787 0.121
## .ssmk 9.036 0.899 10.049 0.000 7.274 10.799 9.036 0.219
## .ssmc 9.152 0.692 13.226 0.000 7.795 10.508 9.152 0.412
## .ssasi 10.198 0.924 11.036 0.000 8.387 12.010 10.198 0.458
## .ssei 1.373 0.361 3.805 0.000 0.666 2.081 1.373 0.097
## .ssno 0.194 0.033 5.936 0.000 0.130 0.258 0.194 0.256
## .sscs 0.285 0.046 6.205 0.000 0.195 0.375 0.285 0.426
## .electronic 1.000 1.000 1.000 0.365 0.365
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.770 0.115 6.687 0.000 0.544 0.995 2.508 0.608
## sswk (.p2.) 1.826 0.274 6.671 0.000 1.290 2.363 5.950 0.921
## sspc (.p3.) 0.713 0.107 6.692 0.000 0.504 0.922 2.323 0.838
## math =~
## ssar (.p4.) 3.333 0.173 19.288 0.000 2.994 3.671 6.493 0.942
## ssmk (.p5.) 2.911 0.150 19.471 0.000 2.618 3.204 5.671 0.878
## ssmc (.p6.) 0.720 0.089 8.139 0.000 0.547 0.894 1.404 0.339
## electronic =~
## ssgs (.p7.) 0.983 0.085 11.567 0.000 0.816 1.150 1.108 0.269
## ssasi (.p8.) 2.100 0.148 14.174 0.000 1.810 2.390 2.366 0.675
## ssmc (.p9.) 1.515 0.128 11.803 0.000 1.263 1.766 1.707 0.412
## ssei (.10.) 2.156 0.125 17.218 0.000 1.911 2.402 2.430 0.775
## speed =~
## ssno (.11.) 0.519 0.024 21.546 0.000 0.472 0.567 0.750 0.870
## sscs (.12.) 0.429 0.022 19.408 0.000 0.386 0.473 0.620 0.725
## g =~
## verbal (.13.) 3.053 0.501 6.092 0.000 2.071 4.035 0.952 0.952
## math (.14.) 1.646 0.114 14.434 0.000 1.422 1.869 0.858 0.858
## elctrnc 1.004 0.076 13.180 0.000 0.855 1.153 0.905 0.905
## speed (.16.) 1.026 0.079 13.043 0.000 0.872 1.180 0.722 0.722
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.076 0.018 4.176 0.000 0.040 0.112 0.075 0.162
## age2 (b) -0.008 0.008 -1.089 0.276 -0.024 0.007 -0.008 -0.042
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.38.) 18.122 0.237 76.305 0.000 17.656 18.587 18.122 4.395
## .sswk 26.005 0.442 58.794 0.000 25.138 26.872 26.005 4.026
## .sspc (.40.) 11.342 0.155 73.226 0.000 11.038 11.645 11.342 4.090
## .ssar 19.267 0.457 42.194 0.000 18.372 20.162 19.267 2.796
## .ssmk (.42.) 15.542 0.358 43.437 0.000 14.841 16.244 15.542 2.406
## .ssmc (.43.) 17.365 0.247 70.411 0.000 16.882 17.849 17.365 4.190
## .ssasi (.44.) 17.890 0.231 77.606 0.000 17.439 18.342 17.890 5.106
## .ssei 16.648 0.417 39.923 0.000 15.831 17.465 16.648 5.307
## .ssno (.46.) 0.276 0.043 6.365 0.000 0.191 0.361 0.276 0.320
## .sscs 0.435 0.049 8.877 0.000 0.339 0.531 0.435 0.508
## .verbal 1.431 0.310 4.617 0.000 0.824 2.039 0.439 0.439
## .elctrnc -2.788 0.249 -11.206 0.000 -3.276 -2.301 -2.474 -2.474
## .speed 0.570 0.099 5.732 0.000 0.375 0.765 0.395 0.395
## .g -0.050 0.090 -0.557 0.577 -0.227 0.126 -0.049 -0.049
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.094 0.094
## .math 1.000 1.000 1.000 0.263 0.263
## .speed 1.000 1.000 1.000 0.479 0.479
## .g 1.000 1.000 1.000 0.969 0.969
## .ssgs 4.699 0.383 12.275 0.000 3.948 5.449 4.699 0.276
## .sswk 6.313 0.864 7.305 0.000 4.619 8.007 6.313 0.151
## .sspc 2.294 0.192 11.935 0.000 1.918 2.671 2.294 0.298
## .ssar 5.329 0.934 5.705 0.000 3.498 7.159 5.329 0.112
## .ssmk 9.574 0.958 9.996 0.000 7.697 11.451 9.574 0.229
## .ssmc 8.571 0.575 14.895 0.000 7.443 9.699 8.571 0.499
## .ssasi 6.675 0.540 12.364 0.000 5.617 7.733 6.675 0.544
## .ssei 3.935 0.381 10.318 0.000 3.188 4.683 3.935 0.400
## .ssno 0.180 0.036 4.941 0.000 0.109 0.252 0.180 0.243
## .sscs 0.348 0.049 7.042 0.000 0.251 0.445 0.348 0.475
## .electronic 0.230 0.067 3.454 0.001 0.099 0.360 0.181 0.181
# BIFACTOR (model with verbal =~ gs + pc shows that gs loading is negative, even without cross loading on electronic)
bf.notworking<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
'
baseline<-cfa(bf.notworking, data=dgroup, meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 357.029 23.000 0.000 0.957 0.117 0.055 48909.569 49117.824
Mc(baseline)
## [1] 0.8530731
summary(baseline, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 77 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 42
##
## Number of observations 1052
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 357.029 297.203
## Degrees of freedom 23 23
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.201
## Yuan-Bentler correction (Mplus variant)
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs 0.301 0.402 0.748 0.455 -0.487 1.088 0.301 0.068
## sswk 7.745 8.809 0.879 0.379 -9.520 25.009 7.745 1.193
## sspc 0.333 0.424 0.785 0.432 -0.498 1.163 0.333 0.115
## math =~
## ssar 2.857 0.322 8.868 0.000 2.226 3.489 2.857 0.411
## ssmk 2.430 0.265 9.162 0.000 1.910 2.950 2.430 0.377
## ssmc 1.263 0.165 7.660 0.000 0.940 1.586 1.263 0.257
## electronic =~
## ssgs 1.251 0.099 12.644 0.000 1.057 1.445 1.251 0.285
## ssasi 3.766 0.144 26.230 0.000 3.485 4.048 3.766 0.734
## ssmc 2.857 0.130 22.051 0.000 2.603 3.111 2.857 0.581
## ssei 2.200 0.101 21.687 0.000 2.001 2.399 2.200 0.575
## speed =~
## ssno 0.490 0.018 27.119 0.000 0.454 0.525 0.490 0.559
## sscs 0.533 0.020 26.767 0.000 0.494 0.572 0.533 0.605
## g =~
## ssgs 3.541 0.134 26.449 0.000 3.279 3.804 3.541 0.807
## ssar 5.809 0.172 33.720 0.000 5.472 6.147 5.809 0.835
## sswk 5.321 0.247 21.570 0.000 4.837 5.804 5.321 0.820
## sspc 2.172 0.117 18.615 0.000 1.944 2.401 2.172 0.752
## ssno 0.560 0.032 17.742 0.000 0.498 0.621 0.560 0.639
## sscs 0.430 0.035 12.290 0.000 0.361 0.498 0.430 0.488
## ssasi 2.131 0.184 11.575 0.000 1.770 2.492 2.131 0.415
## ssmk 5.158 0.148 34.742 0.000 4.867 5.449 5.158 0.801
## ssmc 2.756 0.149 18.492 0.000 2.464 3.048 2.756 0.560
## ssei 2.514 0.117 21.561 0.000 2.286 2.743 2.514 0.657
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.000 0.000 0.000 0.000 0.000
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 17.025 0.145 117.394 0.000 16.741 17.309 17.025 3.879
## .sswk 27.807 0.211 131.932 0.000 27.394 28.220 27.807 4.284
## .sspc 11.650 0.094 123.594 0.000 11.465 11.835 11.650 4.034
## .ssar 19.496 0.231 84.266 0.000 19.043 19.950 19.496 2.802
## .ssmk 15.127 0.215 70.219 0.000 14.704 15.549 15.127 2.349
## .ssmc 15.057 0.165 91.221 0.000 14.733 15.380 15.057 3.059
## .ssasi 14.849 0.172 86.576 0.000 14.512 15.185 14.849 2.894
## .ssei 11.999 0.126 95.165 0.000 11.752 12.246 11.999 3.134
## .ssno 0.374 0.029 12.900 0.000 0.317 0.431 0.374 0.427
## .sscs 0.346 0.029 11.791 0.000 0.288 0.403 0.346 0.393
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.072 0.337 15.051 0.000 4.411 5.732 5.072 0.263
## .sswk -46.159 137.201 -0.336 0.737 -315.067 222.750 -46.159 -1.096
## .sspc 3.509 0.262 13.413 0.000 2.996 4.022 3.509 0.421
## .ssar 6.511 1.117 5.832 0.000 4.323 8.699 6.511 0.134
## .ssmk 8.957 0.927 9.666 0.000 7.141 10.774 8.957 0.216
## .ssmc 6.868 0.598 11.479 0.000 5.695 8.041 6.868 0.284
## .ssasi 7.593 0.702 10.813 0.000 6.217 8.969 7.593 0.288
## .ssei 3.495 0.272 12.828 0.000 2.961 4.028 3.495 0.238
## .ssno 0.215 0.021 10.436 0.000 0.175 0.256 0.215 0.280
## .sscs 0.306 0.032 9.469 0.000 0.243 0.370 0.306 0.395
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
bf.model<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
'
bf.lv<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
'
bf.reduced<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
math~0*1
g~0*1
'
baseline<-cfa(bf.model, data=dgroup, meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= -1.702479e-07) is smaller than zero. This may
## be a symptom that the model is not identified.
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 432.106 26.000 0.000 0.947 0.122 0.057 48978.646 49172.025
Mc(baseline)
## [1] 0.8243173
summary(baseline, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 29 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 39
##
## Number of observations 1052
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 432.106 356.059
## Degrees of freedom 26 26
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.214
## Yuan-Bentler correction (Mplus variant)
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar 3.656 0.251 14.567 0.000 3.164 4.148 3.656 0.525
## ssmk 3.092 0.220 14.080 0.000 2.661 3.522 3.092 0.480
## ssmc 1.185 0.126 9.414 0.000 0.938 1.431 1.185 0.243
## electronic =~
## ssgs 1.350 0.097 13.892 0.000 1.159 1.540 1.350 0.305
## ssasi 3.812 0.136 27.932 0.000 3.545 4.080 3.812 0.743
## ssmc 2.814 0.125 22.461 0.000 2.568 3.060 2.814 0.577
## ssei 2.216 0.092 24.162 0.000 2.036 2.396 2.216 0.579
## speed =~
## ssno 0.443 0.011 39.363 0.000 0.421 0.465 0.443 0.506
## sscs 0.611 0.027 22.336 0.000 0.558 0.665 0.611 0.694
## g =~
## ssgs 3.616 0.113 32.080 0.000 3.395 3.837 3.616 0.818
## ssar 5.360 0.156 34.295 0.000 5.053 5.666 5.360 0.770
## sswk 5.870 0.202 29.087 0.000 5.474 6.265 5.870 0.904
## sspc 2.328 0.105 22.258 0.000 2.123 2.533 2.328 0.806
## ssno 0.530 0.032 16.702 0.000 0.468 0.592 0.530 0.605
## sscs 0.434 0.034 12.841 0.000 0.368 0.501 0.434 0.493
## ssasi 2.088 0.175 11.951 0.000 1.745 2.430 2.088 0.407
## ssmk 4.777 0.136 35.058 0.000 4.510 5.044 4.777 0.742
## ssmc 2.676 0.141 18.989 0.000 2.400 2.952 2.676 0.549
## ssei 2.506 0.104 24.181 0.000 2.303 2.709 2.506 0.655
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 19.496 0.231 84.266 0.000 19.043 19.950 19.496 2.802
## .ssmk 15.127 0.215 70.219 0.000 14.704 15.549 15.127 2.349
## .ssmc 15.057 0.165 91.221 0.000 14.733 15.380 15.057 3.087
## .ssgs 17.025 0.145 117.394 0.000 16.741 17.309 17.025 3.850
## .ssasi 14.849 0.172 86.576 0.000 14.512 15.185 14.849 2.894
## .ssei 11.999 0.126 95.165 0.000 11.752 12.246 11.999 3.134
## .ssno 0.374 0.029 12.900 0.000 0.317 0.431 0.374 0.427
## .sscs 0.346 0.029 11.791 0.000 0.288 0.403 0.346 0.393
## .sswk 27.807 0.211 131.932 0.000 27.394 28.220 27.807 4.284
## .sspc 11.650 0.094 123.594 0.000 11.465 11.835 11.650 4.034
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.334 1.464 4.326 0.000 3.464 9.204 6.334 0.131
## .ssmk 9.084 1.151 7.892 0.000 6.828 11.340 9.084 0.219
## .ssmc 7.305 0.512 14.275 0.000 6.302 8.308 7.305 0.307
## .ssgs 4.666 0.288 16.186 0.000 4.101 5.231 4.666 0.239
## .ssasi 7.428 0.685 10.845 0.000 6.085 8.770 7.428 0.282
## .ssei 3.466 0.268 12.943 0.000 2.941 3.991 3.466 0.236
## .ssno 0.290 0.020 14.585 0.000 0.251 0.329 0.290 0.378
## .sscs 0.213 0.037 5.795 0.000 0.141 0.284 0.213 0.274
## .sswk 7.677 0.699 10.983 0.000 6.307 9.047 7.677 0.182
## .sspc 2.918 0.176 16.592 0.000 2.573 3.263 2.918 0.350
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
configural<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 326.036 52.000 0.000 0.963 0.100 0.037 47937.106 48323.865
Mc(configural)
## [1] 0.8777714
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 42 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 78
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 326.036 274.630
## Degrees of freedom 52 52
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.187
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 199.242 167.828
## 1 126.794 106.803
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar 3.709 0.378 9.800 0.000 2.968 4.451 3.709 0.520
## ssmk 3.250 0.329 9.884 0.000 2.606 3.895 3.250 0.489
## ssmc 0.958 0.178 5.392 0.000 0.610 1.307 0.958 0.194
## electronic =~
## ssgs 0.849 0.163 5.217 0.000 0.530 1.168 0.849 0.187
## ssasi 2.939 0.208 14.153 0.000 2.532 3.346 2.939 0.620
## ssmc 2.424 0.190 12.741 0.000 2.052 2.797 2.424 0.490
## ssei 1.715 0.149 11.485 0.000 1.422 2.007 1.715 0.447
## speed =~
## ssno 0.449 0.030 14.873 0.000 0.390 0.508 0.449 0.507
## sscs 0.517 0.022 23.546 0.000 0.474 0.560 0.517 0.615
## g =~
## ssgs 3.861 0.166 23.257 0.000 3.535 4.186 3.861 0.851
## ssar 5.566 0.215 25.845 0.000 5.144 5.988 5.566 0.781
## sswk 6.099 0.290 21.052 0.000 5.531 6.666 6.099 0.908
## sspc 2.599 0.144 18.031 0.000 2.317 2.882 2.599 0.836
## ssno 0.553 0.045 12.414 0.000 0.465 0.640 0.553 0.625
## sscs 0.480 0.042 11.290 0.000 0.396 0.563 0.480 0.571
## ssasi 2.539 0.251 10.125 0.000 2.048 3.031 2.539 0.536
## ssmk 5.008 0.195 25.720 0.000 4.627 5.390 5.008 0.753
## ssmc 3.276 0.199 16.504 0.000 2.887 3.665 3.276 0.662
## ssei 3.010 0.154 19.562 0.000 2.709 3.312 3.010 0.784
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 20.311 0.336 60.447 0.000 19.652 20.969 20.311 2.848
## .ssmk 15.277 0.316 48.361 0.000 14.658 15.896 15.277 2.296
## .ssmc 17.082 0.231 73.903 0.000 16.629 17.535 17.082 3.450
## .ssgs 17.910 0.210 85.392 0.000 17.498 18.321 17.910 3.948
## .ssasi 17.796 0.221 80.523 0.000 17.363 18.230 17.796 3.756
## .ssei 13.530 0.177 76.269 0.000 13.182 13.877 13.530 3.524
## .ssno 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.275
## .sscs 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.091
## .sswk 27.643 0.309 89.548 0.000 27.038 28.248 27.643 4.115
## .sspc 11.207 0.144 77.836 0.000 10.925 11.490 11.207 3.603
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.114 2.384 2.564 0.010 1.441 10.786 6.114 0.120
## .ssmk 8.611 1.914 4.499 0.000 4.859 12.362 8.611 0.195
## .ssmc 6.982 0.784 8.907 0.000 5.445 8.518 6.982 0.285
## .ssgs 4.953 0.420 11.797 0.000 4.130 5.776 4.953 0.241
## .ssasi 7.368 1.048 7.029 0.000 5.314 9.423 7.368 0.328
## .ssei 2.741 0.310 8.837 0.000 2.133 3.349 2.741 0.186
## .ssno 0.276 0.028 10.002 0.000 0.222 0.330 0.276 0.352
## .sscs 0.209 0.041 5.083 0.000 0.128 0.289 0.209 0.296
## .sswk 7.925 0.912 8.685 0.000 6.136 9.713 7.925 0.176
## .sspc 2.921 0.243 12.031 0.000 2.445 3.397 2.921 0.302
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar 3.396 0.325 10.459 0.000 2.759 4.032 3.396 0.509
## ssmk 3.031 0.295 10.276 0.000 2.453 3.609 3.031 0.489
## ssmc 1.277 0.178 7.172 0.000 0.928 1.626 1.277 0.322
## electronic =~
## ssgs 0.878 0.299 2.934 0.003 0.291 1.464 0.878 0.214
## ssasi 1.000 0.351 2.848 0.004 0.312 1.688 1.000 0.293
## ssmc 1.032 0.425 2.425 0.015 0.198 1.866 1.032 0.260
## ssei 0.979 0.323 3.032 0.002 0.346 1.612 0.979 0.318
## speed =~
## ssno 0.511 0.040 12.631 0.000 0.432 0.590 0.511 0.604
## sscs 0.471 0.085 5.547 0.000 0.305 0.637 0.471 0.567
## g =~
## ssgs 3.436 0.134 25.573 0.000 3.173 3.700 3.436 0.838
## ssar 5.176 0.214 24.141 0.000 4.756 5.597 5.176 0.777
## sswk 5.642 0.265 21.296 0.000 5.123 6.161 5.642 0.904
## sspc 2.031 0.137 14.841 0.000 1.763 2.299 2.031 0.796
## ssno 0.494 0.043 11.510 0.000 0.410 0.578 0.494 0.584
## sscs 0.383 0.047 8.154 0.000 0.291 0.475 0.383 0.461
## ssasi 1.947 0.153 12.700 0.000 1.646 2.247 1.947 0.571
## ssmk 4.475 0.184 24.375 0.000 4.115 4.834 4.475 0.721
## ssmc 2.263 0.148 15.248 0.000 1.972 2.554 2.263 0.570
## ssei 2.105 0.109 19.331 0.000 1.891 2.318 2.105 0.683
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 18.639 0.312 59.821 0.000 18.028 19.250 18.639 2.796
## .ssmk 14.968 0.291 51.396 0.000 14.397 15.539 14.968 2.413
## .ssmc 12.925 0.187 68.955 0.000 12.557 13.292 12.925 3.254
## .ssgs 16.094 0.190 84.654 0.000 15.721 16.467 16.094 3.927
## .ssasi 11.745 0.159 73.710 0.000 11.433 12.058 11.745 3.447
## .ssei 10.387 0.143 72.446 0.000 10.106 10.668 10.387 3.370
## .ssno 0.511 0.039 13.006 0.000 0.434 0.588 0.511 0.604
## .sscs 0.629 0.039 16.289 0.000 0.554 0.705 0.629 0.758
## .sswk 27.980 0.285 98.025 0.000 27.421 28.540 27.980 4.485
## .sspc 12.116 0.116 104.370 0.000 11.888 12.343 12.116 4.750
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.108 1.739 3.512 0.000 2.700 9.517 6.108 0.137
## .ssmk 9.263 1.507 6.148 0.000 6.310 12.216 9.263 0.241
## .ssmc 7.962 0.911 8.738 0.000 6.176 9.748 7.962 0.505
## .ssgs 4.218 0.479 8.800 0.000 3.279 5.158 4.218 0.251
## .ssasi 6.823 0.657 10.383 0.000 5.535 8.111 6.823 0.588
## .ssei 4.115 0.591 6.960 0.000 2.956 5.274 4.115 0.433
## .ssno 0.211 0.063 3.341 0.001 0.087 0.335 0.211 0.295
## .sscs 0.322 0.076 4.250 0.000 0.173 0.470 0.322 0.466
## .sswk 7.096 0.897 7.911 0.000 5.338 8.854 7.096 0.182
## .sspc 2.380 0.195 12.213 0.000 1.998 2.762 2.380 0.366
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
#modificationIndices(configural, sort=T, maximum.number=30)
metric<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 365.050 67.000 0.000 0.960 0.092 0.052 47946.120 48258.502
Mc(metric)
## [1] 0.8678004
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 52 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 19
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 365.050 307.938
## Degrees of freedom 67 67
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.185
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 215.340 181.651
## 1 149.710 126.288
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.628 0.294 12.356 0.000 3.053 4.204 3.628 0.501
## ssmk (.p2.) 3.230 0.254 12.705 0.000 2.732 3.729 3.230 0.483
## ssmc (.p3.) 1.132 0.132 8.596 0.000 0.874 1.390 1.132 0.237
## electronic =~
## ssgs (.p4.) 0.937 0.149 6.288 0.000 0.645 1.229 0.937 0.206
## ssasi (.p5.) 2.927 0.199 14.726 0.000 2.538 3.317 2.927 0.633
## ssmc (.p6.) 2.544 0.177 14.386 0.000 2.198 2.891 2.544 0.532
## ssei (.p7.) 1.776 0.143 12.412 0.000 1.496 2.057 1.776 0.486
## speed =~
## ssno (.p8.) 0.473 0.049 9.659 0.000 0.377 0.569 0.473 0.534
## sscs (.p9.) 0.488 0.029 17.067 0.000 0.432 0.544 0.488 0.587
## g =~
## ssgs (.10.) 3.873 0.155 25.008 0.000 3.570 4.177 3.873 0.850
## ssar (.11.) 5.740 0.213 26.890 0.000 5.322 6.159 5.740 0.792
## sswk (.12.) 6.245 0.269 23.210 0.000 5.718 6.772 6.245 0.912
## sspc (.13.) 2.465 0.128 19.218 0.000 2.214 2.717 2.465 0.818
## ssno (.14.) 0.559 0.036 15.377 0.000 0.487 0.630 0.559 0.630
## sscs (.15.) 0.464 0.036 12.825 0.000 0.393 0.534 0.464 0.557
## ssasi (.16.) 2.291 0.173 13.260 0.000 1.952 2.629 2.291 0.495
## ssmk (.17.) 5.079 0.187 27.131 0.000 4.712 5.446 5.079 0.760
## ssmc (.18.) 2.901 0.170 17.077 0.000 2.568 3.234 2.901 0.606
## ssei (.19.) 2.733 0.143 19.163 0.000 2.453 3.012 2.733 0.747
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 20.311 0.336 60.447 0.000 19.652 20.969 20.311 2.802
## .ssmk 15.277 0.316 48.361 0.000 14.658 15.896 15.277 2.285
## .ssmc 17.082 0.231 73.903 0.000 16.629 17.535 17.082 3.569
## .ssgs 17.910 0.210 85.392 0.000 17.498 18.321 17.910 3.932
## .ssasi 17.796 0.221 80.523 0.000 17.363 18.230 17.796 3.847
## .ssei 13.530 0.177 76.269 0.000 13.182 13.877 13.530 3.700
## .ssno 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.275
## .sscs 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.092
## .sswk 27.643 0.309 89.548 0.000 27.038 28.248 27.643 4.038
## .sspc 11.207 0.144 77.836 0.000 10.925 11.490 11.207 3.718
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.435 1.641 3.921 0.000 3.218 9.651 6.435 0.122
## .ssmk 8.456 1.392 6.075 0.000 5.728 11.185 8.456 0.189
## .ssmc 6.740 0.784 8.600 0.000 5.204 8.277 6.740 0.294
## .ssgs 4.867 0.408 11.917 0.000 4.067 5.668 4.867 0.235
## .ssasi 7.579 1.007 7.530 0.000 5.607 9.552 7.579 0.354
## .ssei 2.750 0.314 8.758 0.000 2.135 3.366 2.750 0.206
## .ssno 0.250 0.042 5.977 0.000 0.168 0.332 0.250 0.318
## .sscs 0.239 0.048 4.946 0.000 0.144 0.334 0.239 0.345
## .sswk 7.859 0.907 8.664 0.000 6.081 9.637 7.859 0.168
## .sspc 3.007 0.246 12.215 0.000 2.525 3.490 3.007 0.331
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.628 0.294 12.356 0.000 3.053 4.204 3.429 0.524
## ssmk (.p2.) 3.230 0.254 12.705 0.000 2.732 3.729 3.053 0.495
## ssmc (.p3.) 1.132 0.132 8.596 0.000 0.874 1.390 1.070 0.262
## electronic =~
## ssgs (.p4.) 0.937 0.149 6.288 0.000 0.645 1.229 0.399 0.099
## ssasi (.p5.) 2.927 0.199 14.726 0.000 2.538 3.317 1.245 0.363
## ssmc (.p6.) 2.544 0.177 14.386 0.000 2.198 2.891 1.082 0.265
## ssei (.p7.) 1.776 0.143 12.412 0.000 1.496 2.057 0.755 0.232
## speed =~
## ssno (.p8.) 0.473 0.049 9.603 0.000 0.377 0.570 0.485 0.575
## sscs (.p9.) 0.488 0.029 17.104 0.000 0.432 0.544 0.500 0.595
## g =~
## ssgs (.10.) 3.873 0.155 25.008 0.000 3.570 4.177 3.374 0.840
## ssar (.11.) 5.740 0.213 26.890 0.000 5.322 6.159 5.000 0.764
## sswk (.12.) 6.245 0.269 23.210 0.000 5.718 6.772 5.439 0.892
## sspc (.13.) 2.465 0.128 19.218 0.000 2.214 2.717 2.147 0.812
## ssno (.14.) 0.559 0.036 15.377 0.000 0.487 0.630 0.487 0.576
## sscs (.15.) 0.464 0.036 12.825 0.000 0.393 0.534 0.404 0.480
## ssasi (.16.) 2.291 0.173 13.260 0.000 1.952 2.629 1.995 0.581
## ssmk (.17.) 5.079 0.187 27.131 0.000 4.712 5.446 4.424 0.717
## ssmc (.18.) 2.901 0.170 17.077 0.000 2.568 3.234 2.527 0.620
## ssei (.19.) 2.733 0.143 19.163 0.000 2.453 3.012 2.380 0.731
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 18.639 0.312 59.821 0.000 18.028 19.250 18.639 2.849
## .ssmk 14.968 0.291 51.396 0.000 14.397 15.539 14.968 2.425
## .ssmc 12.925 0.187 68.955 0.000 12.557 13.292 12.925 3.169
## .ssgs 16.094 0.190 84.654 0.000 15.721 16.467 16.094 4.006
## .ssasi 11.745 0.159 73.710 0.000 11.433 12.058 11.745 3.423
## .ssei 10.387 0.143 72.446 0.000 10.106 10.668 10.387 3.191
## .ssno 0.511 0.039 13.006 0.000 0.434 0.588 0.511 0.605
## .sscs 0.629 0.039 16.289 0.000 0.554 0.705 0.629 0.748
## .sswk 27.980 0.285 98.025 0.000 27.421 28.540 27.980 4.590
## .sspc 12.116 0.116 104.370 0.000 11.888 12.343 12.116 4.579
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.042 1.431 4.221 0.000 3.237 8.848 6.042 0.141
## .ssmk 9.219 1.283 7.183 0.000 6.703 11.734 9.219 0.242
## .ssmc 7.932 0.599 13.252 0.000 6.759 9.105 7.932 0.477
## .ssgs 4.602 0.388 11.875 0.000 3.842 5.361 4.602 0.285
## .ssasi 6.243 0.523 11.943 0.000 5.219 7.268 6.243 0.530
## .ssei 4.359 0.348 12.530 0.000 3.677 5.040 4.359 0.411
## .ssno 0.241 0.037 6.484 0.000 0.168 0.313 0.241 0.338
## .sscs 0.295 0.059 5.008 0.000 0.179 0.410 0.295 0.416
## .sswk 7.574 0.866 8.741 0.000 5.876 9.272 7.574 0.204
## .sspc 2.390 0.198 12.047 0.000 2.001 2.778 2.390 0.341
## math 0.893 0.121 7.361 0.000 0.655 1.131 1.000 1.000
## electronic 0.181 0.048 3.732 0.000 0.086 0.276 1.000 1.000
## speed 1.051 0.153 6.866 0.000 0.751 1.351 1.000 1.000
## g 0.759 0.084 9.069 0.000 0.595 0.923 1.000 1.000
lavTestScore(metric, release = 1:19)
## 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 39.188 19 0.004
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p54. 0.346 1 0.556
## 2 .p2. == .p55. 0.276 1 0.599
## 3 .p3. == .p56. 1.611 1 0.204
## 4 .p4. == .p57. 3.004 1 0.083
## 5 .p5. == .p58. 0.774 1 0.379
## 6 .p6. == .p59. 0.015 1 0.903
## 7 .p7. == .p60. 0.208 1 0.649
## 8 .p8. == .p61. 0.000 1 1.000
## 9 .p9. == .p62. 0.000 1 1.000
## 10 .p10. == .p63. 3.051 1 0.081
## 11 .p11. == .p64. 2.793 1 0.095
## 12 .p12. == .p65. 5.919 1 0.015
## 13 .p13. == .p66. 7.369 1 0.007
## 14 .p14. == .p67. 0.413 1 0.520
## 15 .p15. == .p68. 1.152 1 0.283
## 16 .p16. == .p69. 0.164 1 0.686
## 17 .p17. == .p70. 0.043 1 0.835
## 18 .p18. == .p71. 4.378 1 0.036
## 19 .p19. == .p72. 8.833 1 0.003
metric2<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings"), group.partial=c("g=~sspc", "g=~ssei"))
fitMeasures(metric2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 347.287 65.000 0.000 0.962 0.091 0.046 47932.357 48254.656
Mc(metric2)
## [1] 0.8743324
scalar<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 431.037 73.000 0.000 0.952 0.097 0.055 48000.107 48282.738
Mc(scalar)
## [1] 0.8433852
summary(scalar, standardized=T, ci=T) # +.178
## lavaan 0.6-18 ended normally after 128 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 29
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 431.037 369.651
## Degrees of freedom 73 73
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.166
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 248.252 212.898
## 1 182.785 156.754
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.296 0.341 12.582 0.000 3.627 4.966 4.296 0.592
## ssmk (.p2.) 2.601 0.255 10.207 0.000 2.101 3.100 2.601 0.389
## ssmc (.p3.) 0.858 0.150 5.734 0.000 0.565 1.151 0.858 0.183
## electronic =~
## ssgs (.p4.) 1.130 0.083 13.670 0.000 0.968 1.292 1.130 0.246
## ssasi (.p5.) 3.123 0.155 20.118 0.000 2.819 3.428 3.123 0.665
## ssmc (.p6.) 2.136 0.130 16.389 0.000 1.881 2.392 2.136 0.455
## ssei (.p7.) 1.776 0.100 17.807 0.000 1.580 1.971 1.776 0.485
## speed =~
## ssno (.p8.) 0.292 0.038 7.718 0.000 0.218 0.366 0.292 0.329
## sscs (.p9.) 0.779 0.100 7.760 0.000 0.583 0.976 0.779 0.937
## g =~
## ssgs (.10.) 3.859 0.150 25.809 0.000 3.566 4.152 3.859 0.841
## ssar (.11.) 5.771 0.215 26.865 0.000 5.350 6.192 5.771 0.795
## sswk (.12.) 6.195 0.265 23.418 0.000 5.677 6.714 6.195 0.907
## sspc (.13.) 2.495 0.133 18.760 0.000 2.234 2.755 2.495 0.819
## ssno (.14.) 0.562 0.036 15.428 0.000 0.490 0.633 0.562 0.634
## sscs (.15.) 0.466 0.036 12.867 0.000 0.395 0.537 0.466 0.561
## ssasi (.16.) 2.271 0.173 13.131 0.000 1.932 2.610 2.271 0.484
## ssmk (.17.) 5.143 0.190 27.134 0.000 4.771 5.514 5.143 0.769
## ssmc (.18.) 2.981 0.170 17.516 0.000 2.647 3.314 2.981 0.635
## ssei (.19.) 2.738 0.140 19.528 0.000 2.463 3.012 2.738 0.747
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 20.298 0.342 59.432 0.000 19.628 20.967 20.298 2.795
## .ssmk (.41.) 15.482 0.300 51.535 0.000 14.893 16.071 15.482 2.316
## .ssmc (.42.) 17.180 0.224 76.655 0.000 16.741 17.619 17.180 3.661
## .ssgs (.43.) 17.846 0.207 86.367 0.000 17.441 18.251 17.846 3.889
## .ssasi (.44.) 17.754 0.223 79.679 0.000 17.317 18.190 17.754 3.782
## .ssei (.45.) 13.540 0.176 77.050 0.000 13.196 13.884 13.540 3.697
## .ssno (.46.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.275
## .sscs (.47.) 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.092
## .sswk (.48.) 27.335 0.316 86.613 0.000 26.716 27.953 27.335 4.001
## .sspc (.49.) 11.490 0.134 85.537 0.000 11.226 11.753 11.490 3.773
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 0.987 2.681 0.368 0.713 -4.268 6.243 0.987 0.019
## .ssmk 11.468 1.344 8.533 0.000 8.834 14.102 11.468 0.257
## .ssmc 7.834 0.685 11.441 0.000 6.492 9.176 7.834 0.356
## .ssgs 4.892 0.405 12.087 0.000 4.099 5.686 4.892 0.232
## .ssasi 7.120 0.935 7.611 0.000 5.287 8.954 7.120 0.323
## .ssei 2.766 0.289 9.555 0.000 2.199 3.333 2.766 0.206
## .ssno 0.385 0.033 11.834 0.000 0.322 0.449 0.385 0.490
## .sscs -0.134 0.151 -0.888 0.374 -0.429 0.161 -0.134 -0.193
## .sswk 8.295 0.971 8.544 0.000 6.392 10.198 8.295 0.178
## .sspc 3.049 0.258 11.818 0.000 2.544 3.555 3.049 0.329
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.296 0.341 12.582 0.000 3.627 4.966 4.044 0.619
## ssmk (.p2.) 2.601 0.255 10.207 0.000 2.101 3.100 2.448 0.397
## ssmc (.p3.) 0.858 0.150 5.734 0.000 0.565 1.151 0.808 0.197
## electronic =~
## ssgs (.p4.) 1.130 0.083 13.670 0.000 0.968 1.292 0.473 0.118
## ssasi (.p5.) 3.123 0.155 20.118 0.000 2.819 3.428 1.308 0.382
## ssmc (.p6.) 2.136 0.130 16.389 0.000 1.881 2.392 0.895 0.219
## ssei (.p7.) 1.776 0.100 17.807 0.000 1.580 1.971 0.744 0.229
## speed =~
## ssno (.p8.) 0.292 0.038 7.718 0.000 0.218 0.366 0.301 0.357
## sscs (.p9.) 0.779 0.100 7.760 0.000 0.583 0.976 0.803 0.954
## g =~
## ssgs (.10.) 3.859 0.150 25.809 0.000 3.566 4.152 3.352 0.837
## ssar (.11.) 5.771 0.215 26.865 0.000 5.350 6.192 5.013 0.768
## sswk (.12.) 6.195 0.265 23.418 0.000 5.677 6.714 5.382 0.885
## sspc (.13.) 2.495 0.133 18.760 0.000 2.234 2.755 2.167 0.810
## ssno (.14.) 0.562 0.036 15.428 0.000 0.490 0.633 0.488 0.578
## sscs (.15.) 0.466 0.036 12.867 0.000 0.395 0.537 0.405 0.481
## ssasi (.16.) 2.271 0.173 13.131 0.000 1.932 2.610 1.973 0.576
## ssmk (.17.) 5.143 0.190 27.134 0.000 4.771 5.514 4.467 0.725
## ssmc (.18.) 2.981 0.170 17.516 0.000 2.647 3.314 2.589 0.633
## ssei (.19.) 2.738 0.140 19.528 0.000 2.463 3.012 2.378 0.731
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 20.298 0.342 59.432 0.000 19.628 20.967 20.298 3.108
## .ssmk (.41.) 15.482 0.300 51.535 0.000 14.893 16.071 15.482 2.514
## .ssmc (.42.) 17.180 0.224 76.655 0.000 16.741 17.619 17.180 4.200
## .ssgs (.43.) 17.846 0.207 86.367 0.000 17.441 18.251 17.846 4.455
## .ssasi (.44.) 17.754 0.223 79.679 0.000 17.317 18.190 17.754 5.183
## .ssei (.45.) 13.540 0.176 77.050 0.000 13.196 13.884 13.540 4.163
## .ssno (.46.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.289
## .sscs (.47.) 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.090
## .sswk (.48.) 27.335 0.316 86.613 0.000 26.716 27.953 27.335 4.497
## .sspc (.49.) 11.490 0.134 85.537 0.000 11.226 11.753 11.490 4.293
## math -0.590 0.089 -6.637 0.000 -0.764 -0.416 -0.627 -0.627
## elctrnc -2.024 0.129 -15.682 0.000 -2.276 -1.771 -4.831 -4.831
## speed 0.617 0.110 5.627 0.000 0.402 0.832 0.599 0.599
## g 0.155 0.064 2.408 0.016 0.029 0.280 0.178 0.178
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 1.180 2.333 0.506 0.613 -3.393 5.752 1.180 0.028
## .ssmk 11.978 1.138 10.527 0.000 9.748 14.208 11.978 0.316
## .ssmc 8.577 0.589 14.552 0.000 7.422 9.732 8.577 0.513
## .ssgs 4.585 0.389 11.789 0.000 3.823 5.348 4.585 0.286
## .ssasi 6.128 0.529 11.579 0.000 5.090 7.165 6.128 0.522
## .ssei 4.371 0.344 12.698 0.000 3.696 5.046 4.371 0.413
## .ssno 0.384 0.040 9.569 0.000 0.305 0.462 0.384 0.538
## .sscs -0.100 0.171 -0.586 0.558 -0.436 0.235 -0.100 -0.141
## .sswk 7.980 0.912 8.746 0.000 6.192 9.768 7.980 0.216
## .sspc 2.466 0.209 11.786 0.000 2.056 2.877 2.466 0.344
## math 0.886 0.121 7.304 0.000 0.648 1.124 1.000 1.000
## electronic 0.175 0.048 3.658 0.000 0.081 0.269 1.000 1.000
## speed 1.061 0.156 6.819 0.000 0.756 1.366 1.000 1.000
## g 0.755 0.083 9.095 0.000 0.592 0.917 1.000 1.000
lavTestScore(scalar, release = 20:29)
## 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 64.634 10 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p40. == .p93. 15.331 1 0.000
## 2 .p41. == .p94. 9.954 1 0.002
## 3 .p42. == .p95. 8.053 1 0.005
## 4 .p43. == .p96. 4.270 1 0.039
## 5 .p44. == .p97. 3.075 1 0.080
## 6 .p45. == .p98. 0.355 1 0.551
## 7 .p46. == .p99. 0.000 1 1.000
## 8 .p47. == .p100. 0.000 1 1.000
## 9 .p48. == .p101. 33.992 1 0.000
## 10 .p49. == .p102. 37.747 1 0.000
scalar2<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1", "ssar~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 373.078 71.000 0.000 0.960 0.090 0.053 47946.148 48238.696
Mc(scalar2)
## [1] 0.8661391
summary(scalar2, standardized=T, ci=T) # +.053
## lavaan 0.6-18 ended normally after 132 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 27
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 373.078 318.183
## Degrees of freedom 71 71
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.173
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 220.104 187.718
## 1 152.974 130.465
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.639 0.305 11.915 0.000 3.040 4.237 3.639 0.502
## ssmk (.p2.) 3.221 0.257 12.528 0.000 2.717 3.725 3.221 0.482
## ssmc (.p3.) 1.076 0.128 8.409 0.000 0.825 1.326 1.076 0.228
## electronic =~
## ssgs (.p4.) 1.011 0.084 12.001 0.000 0.846 1.176 1.011 0.221
## ssasi (.p5.) 3.173 0.151 21.016 0.000 2.877 3.469 3.173 0.675
## ssmc (.p6.) 2.258 0.130 17.319 0.000 2.002 2.513 2.258 0.479
## ssei (.p7.) 1.732 0.098 17.626 0.000 1.540 1.925 1.732 0.474
## speed =~
## ssno (.p8.) 0.323 0.033 9.704 0.000 0.258 0.389 0.323 0.365
## sscs (.p9.) 0.713 0.074 9.674 0.000 0.568 0.857 0.713 0.857
## g =~
## ssgs (.10.) 3.871 0.150 25.752 0.000 3.576 4.165 3.871 0.847
## ssar (.11.) 5.743 0.214 26.883 0.000 5.324 6.162 5.743 0.792
## sswk (.12.) 6.247 0.269 23.209 0.000 5.720 6.775 6.247 0.912
## sspc (.13.) 2.469 0.129 19.203 0.000 2.217 2.722 2.469 0.819
## ssno (.14.) 0.559 0.036 15.378 0.000 0.488 0.630 0.559 0.630
## sscs (.15.) 0.464 0.036 12.834 0.000 0.393 0.535 0.464 0.558
## ssasi (.16.) 2.273 0.171 13.276 0.000 1.938 2.609 2.273 0.484
## ssmk (.17.) 5.083 0.187 27.241 0.000 4.718 5.449 5.083 0.760
## ssmc (.18.) 2.942 0.169 17.417 0.000 2.611 3.273 2.942 0.624
## ssei (.19.) 2.741 0.140 19.597 0.000 2.467 3.015 2.741 0.750
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 20.311 0.336 60.447 0.000 19.652 20.969 20.311 2.801
## .ssmk (.41.) 15.247 0.315 48.342 0.000 14.629 15.865 15.247 2.280
## .ssmc (.42.) 17.161 0.225 76.423 0.000 16.721 17.602 17.161 3.637
## .ssgs (.43.) 17.876 0.206 86.699 0.000 17.472 18.280 17.876 3.910
## .ssasi (.44.) 17.742 0.223 79.413 0.000 17.304 18.180 17.742 3.776
## .ssei (.45.) 13.542 0.175 77.256 0.000 13.199 13.886 13.542 3.707
## .ssno (.46.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.275
## .sscs (.47.) 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.092
## .sswk (.48.) 27.667 0.309 89.626 0.000 27.062 28.272 27.667 4.039
## .sspc 11.207 0.144 77.836 0.000 10.925 11.490 11.207 3.718
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.372 1.716 3.714 0.000 3.009 9.734 6.372 0.121
## .ssmk 8.508 1.419 5.996 0.000 5.727 11.289 8.508 0.190
## .ssmc 7.351 0.678 10.845 0.000 6.023 8.680 7.351 0.330
## .ssgs 4.895 0.407 12.032 0.000 4.098 5.692 4.895 0.234
## .ssasi 6.843 0.924 7.405 0.000 5.032 8.654 6.843 0.310
## .ssei 2.829 0.286 9.889 0.000 2.268 3.389 2.829 0.212
## .ssno 0.369 0.032 11.681 0.000 0.307 0.431 0.369 0.470
## .sscs -0.032 0.101 -0.317 0.751 -0.229 0.165 -0.032 -0.046
## .sswk 7.882 0.910 8.664 0.000 6.099 9.665 7.882 0.168
## .sspc 2.990 0.246 12.157 0.000 2.508 3.472 2.990 0.329
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.639 0.305 11.915 0.000 3.040 4.237 3.441 0.526
## ssmk (.p2.) 3.221 0.257 12.528 0.000 2.717 3.725 3.046 0.493
## ssmc (.p3.) 1.076 0.128 8.409 0.000 0.825 1.326 1.017 0.249
## electronic =~
## ssgs (.p4.) 1.011 0.084 12.001 0.000 0.846 1.176 0.428 0.107
## ssasi (.p5.) 3.173 0.151 21.016 0.000 2.877 3.469 1.343 0.392
## ssmc (.p6.) 2.258 0.130 17.319 0.000 2.002 2.513 0.956 0.234
## ssei (.p7.) 1.732 0.098 17.626 0.000 1.540 1.925 0.733 0.225
## speed =~
## ssno (.p8.) 0.323 0.033 9.704 0.000 0.258 0.389 0.332 0.393
## sscs (.p9.) 0.713 0.074 9.674 0.000 0.568 0.857 0.731 0.869
## g =~
## ssgs (.10.) 3.871 0.150 25.752 0.000 3.576 4.165 3.367 0.839
## ssar (.11.) 5.743 0.214 26.883 0.000 5.324 6.162 4.996 0.764
## sswk (.12.) 6.247 0.269 23.209 0.000 5.720 6.775 5.435 0.892
## sspc (.13.) 2.469 0.129 19.203 0.000 2.217 2.722 2.148 0.812
## ssno (.14.) 0.559 0.036 15.378 0.000 0.488 0.630 0.486 0.576
## sscs (.15.) 0.464 0.036 12.834 0.000 0.393 0.535 0.404 0.480
## ssasi (.16.) 2.273 0.171 13.276 0.000 1.938 2.609 1.978 0.577
## ssmk (.17.) 5.083 0.187 27.241 0.000 4.718 5.449 4.422 0.716
## ssmc (.18.) 2.942 0.169 17.417 0.000 2.611 3.273 2.559 0.627
## ssei (.19.) 2.741 0.140 19.597 0.000 2.467 3.015 2.384 0.732
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 18.914 0.403 46.903 0.000 18.124 19.704 18.914 2.893
## .ssmk (.41.) 15.247 0.315 48.342 0.000 14.629 15.865 15.247 2.470
## .ssmc (.42.) 17.161 0.225 76.423 0.000 16.721 17.602 17.161 4.202
## .ssgs (.43.) 17.876 0.206 86.699 0.000 17.472 18.280 17.876 4.452
## .ssasi (.44.) 17.742 0.223 79.413 0.000 17.304 18.180 17.742 5.175
## .ssei (.45.) 13.542 0.175 77.256 0.000 13.199 13.886 13.542 4.156
## .ssno (.46.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.289
## .sscs (.47.) 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.090
## .sswk (.48.) 27.667 0.309 89.626 0.000 27.062 28.272 27.667 4.541
## .sspc 12.001 0.149 80.568 0.000 11.709 12.293 12.001 4.536
## math -0.149 0.105 -1.417 0.156 -0.354 0.057 -0.157 -0.157
## elctrnc -1.907 0.119 -15.993 0.000 -2.141 -1.673 -4.506 -4.506
## speed 0.746 0.111 6.741 0.000 0.529 0.963 0.727 0.727
## g 0.046 0.066 0.699 0.485 -0.084 0.176 0.053 0.053
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 5.962 1.498 3.981 0.000 3.026 8.897 5.962 0.139
## .ssmk 9.266 1.321 7.014 0.000 6.677 11.856 9.266 0.243
## .ssmc 8.185 0.575 14.225 0.000 7.058 9.313 8.185 0.491
## .ssgs 4.602 0.387 11.880 0.000 3.843 5.361 4.602 0.285
## .ssasi 6.040 0.523 11.541 0.000 5.014 7.065 6.040 0.514
## .ssei 4.392 0.344 12.757 0.000 3.718 5.067 4.392 0.414
## .ssno 0.366 0.039 9.416 0.000 0.290 0.442 0.366 0.514
## .sscs 0.010 0.117 0.086 0.932 -0.220 0.240 0.010 0.014
## .sswk 7.591 0.870 8.726 0.000 5.886 9.296 7.591 0.204
## .sspc 2.387 0.198 12.027 0.000 1.998 2.776 2.387 0.341
## math 0.894 0.122 7.308 0.000 0.654 1.134 1.000 1.000
## electronic 0.179 0.048 3.754 0.000 0.086 0.273 1.000 1.000
## speed 1.052 0.154 6.854 0.000 0.751 1.353 1.000 1.000
## g 0.757 0.083 9.113 0.000 0.594 0.919 1.000 1.000
lavTestScore(scalar2, release = 20:27)
## 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 8.424 8 0.393
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p41. == .p94. 5.350 1 0.021
## 2 .p42. == .p95. 5.350 1 0.021
## 3 .p43. == .p96. 1.112 1 0.292
## 4 .p44. == .p97. 4.764 1 0.029
## 5 .p45. == .p98. 0.438 1 0.508
## 6 .p46. == .p99. 0.000 1 1.000
## 7 .p47. == .p100. 0.000 1 1.000
## 8 .p48. == .p101. 0.831 1 0.362
strict<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("sspc~1", "ssar~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 395.577 81.000 0.000 0.958 0.086 0.052 47948.647 48191.611
Mc(strict)
## [1] 0.8610041
summary(strict, standardized=T, ci=T) # +.051
## lavaan 0.6-18 ended normally after 70 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 37
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 395.577 330.908
## Degrees of freedom 81 81
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.195
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 232.977 194.890
## 1 162.600 136.018
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.630 0.313 11.605 0.000 3.017 4.243 3.630 0.501
## ssmk (.p2.) 3.217 0.245 13.128 0.000 2.737 3.698 3.217 0.479
## ssmc (.p3.) 1.068 0.127 8.432 0.000 0.820 1.317 1.068 0.224
## electronic =~
## ssgs (.p4.) 1.005 0.084 11.982 0.000 0.840 1.169 1.005 0.220
## ssasi (.p5.) 3.188 0.148 21.589 0.000 2.898 3.477 3.188 0.686
## ssmc (.p6.) 2.238 0.125 17.958 0.000 1.993 2.482 2.238 0.470
## ssei (.p7.) 1.705 0.093 18.292 0.000 1.522 1.888 1.705 0.456
## speed =~
## ssno (.p8.) 0.314 0.029 10.659 0.000 0.257 0.372 0.314 0.355
## sscs (.p9.) 0.704 0.073 9.622 0.000 0.561 0.848 0.704 0.848
## g =~
## ssgs (.10.) 3.874 0.150 25.857 0.000 3.580 4.167 3.874 0.850
## ssar (.11.) 5.754 0.214 26.945 0.000 5.335 6.172 5.754 0.794
## sswk (.12.) 6.243 0.269 23.213 0.000 5.716 6.770 6.243 0.912
## sspc (.13.) 2.489 0.130 19.176 0.000 2.234 2.743 2.489 0.835
## ssno (.14.) 0.560 0.036 15.400 0.000 0.489 0.632 0.560 0.633
## sscs (.15.) 0.464 0.036 12.832 0.000 0.394 0.535 0.464 0.559
## ssasi (.16.) 2.281 0.172 13.293 0.000 1.944 2.617 2.281 0.491
## ssmk (.17.) 5.093 0.187 27.275 0.000 4.727 5.459 5.093 0.758
## ssmc (.18.) 2.950 0.167 17.630 0.000 2.622 3.278 2.950 0.620
## ssei (.19.) 2.717 0.140 19.342 0.000 2.441 2.992 2.717 0.727
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 20.311 0.336 60.447 0.000 19.652 20.969 20.311 2.804
## .ssmk (.41.) 15.250 0.315 48.405 0.000 14.632 15.867 15.250 2.269
## .ssmc (.42.) 17.156 0.225 76.196 0.000 16.714 17.597 17.156 3.604
## .ssgs (.43.) 17.877 0.207 86.537 0.000 17.472 18.282 17.877 3.922
## .ssasi (.44.) 17.770 0.219 81.212 0.000 17.341 18.199 17.770 3.826
## .ssei (.45.) 13.529 0.175 77.089 0.000 13.185 13.873 13.529 3.620
## .ssno (.46.) 0.246 0.041 5.940 0.000 0.165 0.327 0.246 0.278
## .sscs (.47.) 0.076 0.040 1.908 0.056 -0.002 0.154 0.076 0.092
## .sswk (.48.) 27.672 0.309 89.439 0.000 27.065 28.278 27.672 4.045
## .sspc 11.207 0.144 77.836 0.000 10.925 11.490 11.207 3.761
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.20.) 6.182 1.486 4.160 0.000 3.269 9.094 6.182 0.118
## .ssmk (.21.) 8.870 1.227 7.230 0.000 6.465 11.274 8.870 0.196
## .ssmc (.22.) 7.813 0.443 17.633 0.000 6.944 8.681 7.813 0.345
## .ssgs (.23.) 4.761 0.290 16.401 0.000 4.192 5.329 4.761 0.229
## .ssasi (.24.) 6.212 0.480 12.942 0.000 5.271 7.153 6.212 0.288
## .ssei (.25.) 3.677 0.230 16.007 0.000 3.227 4.128 3.677 0.263
## .ssno (.26.) 0.369 0.029 12.804 0.000 0.313 0.426 0.369 0.472
## .sscs (.27.) -0.021 0.102 -0.210 0.834 -0.220 0.178 -0.021 -0.031
## .sswk (.28.) 7.834 0.637 12.303 0.000 6.586 9.082 7.834 0.167
## .sspc (.29.) 2.684 0.158 16.986 0.000 2.374 2.994 2.684 0.302
## math 1.000 1.000 1.000 1.000 1.000
## elctrnc 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.630 0.313 11.605 0.000 3.017 4.243 3.427 0.524
## ssmk (.p2.) 3.217 0.245 13.128 0.000 2.737 3.698 3.037 0.495
## ssmc (.p3.) 1.068 0.127 8.432 0.000 0.820 1.317 1.009 0.250
## electronic =~
## ssgs (.p4.) 1.005 0.084 11.982 0.000 0.840 1.169 0.431 0.107
## ssasi (.p5.) 3.188 0.148 21.589 0.000 2.898 3.477 1.367 0.395
## ssmc (.p6.) 2.238 0.125 17.958 0.000 1.993 2.482 0.960 0.238
## ssei (.p7.) 1.705 0.093 18.292 0.000 1.522 1.888 0.731 0.234
## speed =~
## ssno (.p8.) 0.314 0.029 10.659 0.000 0.257 0.372 0.336 0.397
## sscs (.p9.) 0.704 0.073 9.622 0.000 0.561 0.848 0.754 0.895
## g =~
## ssgs (.10.) 3.874 0.150 25.857 0.000 3.580 4.167 3.361 0.834
## ssar (.11.) 5.754 0.214 26.945 0.000 5.335 6.172 4.992 0.763
## sswk (.12.) 6.243 0.269 23.213 0.000 5.716 6.770 5.416 0.888
## sspc (.13.) 2.489 0.130 19.176 0.000 2.234 2.743 2.159 0.797
## ssno (.14.) 0.560 0.036 15.400 0.000 0.489 0.632 0.486 0.573
## sscs (.15.) 0.464 0.036 12.832 0.000 0.394 0.535 0.403 0.479
## ssasi (.16.) 2.281 0.172 13.293 0.000 1.944 2.617 1.979 0.571
## ssmk (.17.) 5.093 0.187 27.275 0.000 4.727 5.459 4.419 0.720
## ssmc (.18.) 2.950 0.167 17.630 0.000 2.622 3.278 2.559 0.634
## ssei (.19.) 2.717 0.140 19.342 0.000 2.441 2.992 2.357 0.754
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 18.924 0.402 47.074 0.000 18.136 19.712 18.924 2.891
## .ssmk (.41.) 15.250 0.315 48.405 0.000 14.632 15.867 15.250 2.486
## .ssmc (.42.) 17.156 0.225 76.196 0.000 16.714 17.597 17.156 4.249
## .ssgs (.43.) 17.877 0.207 86.537 0.000 17.472 18.282 17.877 4.436
## .ssasi (.44.) 17.770 0.219 81.212 0.000 17.341 18.199 17.770 5.130
## .ssei (.45.) 13.529 0.175 77.089 0.000 13.185 13.873 13.529 4.329
## .ssno (.46.) 0.246 0.041 5.940 0.000 0.165 0.327 0.246 0.290
## .sscs (.47.) 0.076 0.040 1.908 0.056 -0.002 0.154 0.076 0.090
## .sswk (.48.) 27.672 0.309 89.439 0.000 27.065 28.278 27.672 4.539
## .sspc 12.005 0.150 79.771 0.000 11.710 12.300 12.005 4.429
## math -0.149 0.105 -1.422 0.155 -0.355 0.056 -0.158 -0.158
## elctrnc -1.913 0.119 -16.142 0.000 -2.145 -1.681 -4.461 -4.461
## speed 0.756 0.114 6.647 0.000 0.533 0.979 0.707 0.707
## g 0.045 0.067 0.669 0.504 -0.086 0.175 0.051 0.051
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.20.) 6.182 1.486 4.160 0.000 3.269 9.094 6.182 0.144
## .ssmk (.21.) 8.870 1.227 7.230 0.000 6.465 11.274 8.870 0.236
## .ssmc (.22.) 7.813 0.443 17.633 0.000 6.944 8.681 7.813 0.479
## .ssgs (.23.) 4.761 0.290 16.401 0.000 4.192 5.329 4.761 0.293
## .ssasi (.24.) 6.212 0.480 12.942 0.000 5.271 7.153 6.212 0.518
## .ssei (.25.) 3.677 0.230 16.007 0.000 3.227 4.128 3.677 0.376
## .ssno (.26.) 0.369 0.029 12.804 0.000 0.313 0.426 0.369 0.514
## .sscs (.27.) -0.021 0.102 -0.210 0.834 -0.220 0.178 -0.021 -0.030
## .sswk (.28.) 7.834 0.637 12.303 0.000 6.586 9.082 7.834 0.211
## .sspc (.29.) 2.684 0.158 16.986 0.000 2.374 2.994 2.684 0.365
## math 0.891 0.116 7.701 0.000 0.664 1.118 1.000 1.000
## elctrnc 0.184 0.047 3.928 0.000 0.092 0.276 1.000 1.000
## speed 1.145 0.145 7.918 0.000 0.861 1.428 1.000 1.000
## g 0.753 0.083 9.083 0.000 0.590 0.915 1.000 1.000
latent<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("sspc~1", "ssar~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(latent, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 471.793 75.000 0.000 0.947 0.100 0.126 48036.863 48309.577
Mc(latent)
## [1] 0.8279776
summary(latent, standardized=T, ci=T) # +.055 Std.all
## lavaan 0.6-18 ended normally after 131 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 27
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 471.793 404.258
## Degrees of freedom 75 75
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.167
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 254.955 218.459
## 1 216.838 185.799
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.589 0.266 13.499 0.000 3.068 4.110 3.589 0.518
## ssmk (.p2.) 3.163 0.229 13.836 0.000 2.715 3.611 3.163 0.493
## ssmc (.p3.) 1.016 0.125 8.152 0.000 0.772 1.260 1.016 0.228
## electronic =~
## ssgs (.p4.) 0.783 0.065 12.114 0.000 0.656 0.909 0.783 0.180
## ssasi (.p5.) 2.399 0.124 19.324 0.000 2.155 2.642 2.399 0.557
## ssmc (.p6.) 1.705 0.109 15.699 0.000 1.492 1.917 1.705 0.383
## ssei (.p7.) 1.324 0.078 16.885 0.000 1.170 1.478 1.324 0.387
## speed =~
## ssno (.p8.) 0.327 0.031 10.532 0.000 0.266 0.388 0.327 0.376
## sscs (.p9.) 0.725 0.071 10.257 0.000 0.587 0.864 0.725 0.886
## g =~
## ssgs (.10.) 3.666 0.107 34.295 0.000 3.456 3.875 3.666 0.843
## ssar (.11.) 5.365 0.152 35.316 0.000 5.067 5.662 5.365 0.775
## sswk (.12.) 5.887 0.197 29.812 0.000 5.500 6.274 5.887 0.903
## sspc (.13.) 2.318 0.101 22.863 0.000 2.119 2.516 2.318 0.799
## ssno (.14.) 0.523 0.031 16.821 0.000 0.462 0.584 0.523 0.601
## sscs (.15.) 0.436 0.031 13.871 0.000 0.375 0.498 0.436 0.533
## ssasi (.16.) 2.259 0.147 15.354 0.000 1.971 2.547 2.259 0.524
## ssmk (.17.) 4.743 0.135 35.167 0.000 4.479 5.008 4.743 0.739
## ssmc (.18.) 2.841 0.130 21.836 0.000 2.586 3.096 2.841 0.638
## ssei (.19.) 2.640 0.100 26.410 0.000 2.444 2.836 2.640 0.772
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 20.311 0.336 60.447 0.000 19.652 20.969 20.311 2.933
## .ssmk (.41.) 15.251 0.316 48.326 0.000 14.632 15.869 15.251 2.376
## .ssmc (.42.) 17.156 0.226 76.059 0.000 16.714 17.599 17.156 3.852
## .ssgs (.43.) 17.889 0.206 86.634 0.000 17.484 18.293 17.889 4.114
## .ssasi (.44.) 17.725 0.226 78.413 0.000 17.282 18.168 17.725 4.114
## .ssei (.45.) 13.551 0.175 77.268 0.000 13.207 13.894 13.551 3.964
## .ssno (.46.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.280
## .sscs (.47.) 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.093
## .sswk (.48.) 27.650 0.309 89.478 0.000 27.044 28.255 27.650 4.241
## .sspc 11.207 0.144 77.836 0.000 10.925 11.490 11.207 3.866
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.293 1.726 3.646 0.000 2.911 9.676 6.293 0.131
## .ssmk 8.700 1.404 6.197 0.000 5.948 11.452 8.700 0.211
## .ssmc 7.827 0.684 11.441 0.000 6.486 9.168 7.827 0.395
## .ssgs 4.860 0.403 12.050 0.000 4.069 5.650 4.860 0.257
## .ssasi 7.708 0.945 8.157 0.000 5.856 9.561 7.708 0.415
## .ssei 2.962 0.292 10.133 0.000 2.389 3.535 2.962 0.253
## .ssno 0.376 0.032 11.767 0.000 0.313 0.439 0.376 0.497
## .sscs -0.046 0.101 -0.453 0.650 -0.244 0.152 -0.046 -0.068
## .sswk 7.854 0.874 8.985 0.000 6.141 9.567 7.854 0.185
## .sspc 3.032 0.248 12.219 0.000 2.546 3.518 3.032 0.361
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.589 0.266 13.499 0.000 3.068 4.110 3.589 0.521
## ssmk (.p2.) 3.163 0.229 13.836 0.000 2.715 3.611 3.163 0.490
## ssmc (.p3.) 1.016 0.125 8.152 0.000 0.772 1.260 1.016 0.227
## electronic =~
## ssgs (.p4.) 0.783 0.065 12.114 0.000 0.656 0.909 0.783 0.181
## ssasi (.p5.) 2.399 0.124 19.324 0.000 2.155 2.642 2.399 0.601
## ssmc (.p6.) 1.705 0.109 15.699 0.000 1.492 1.917 1.705 0.381
## ssei (.p7.) 1.324 0.078 16.885 0.000 1.170 1.478 1.324 0.366
## speed =~
## ssno (.p8.) 0.327 0.031 10.532 0.000 0.266 0.388 0.327 0.379
## sscs (.p9.) 0.725 0.071 10.257 0.000 0.587 0.864 0.725 0.849
## g =~
## ssgs (.10.) 3.666 0.107 34.295 0.000 3.456 3.875 3.666 0.849
## ssar (.11.) 5.365 0.152 35.316 0.000 5.067 5.662 5.365 0.778
## sswk (.12.) 5.887 0.197 29.812 0.000 5.500 6.274 5.887 0.910
## sspc (.13.) 2.318 0.101 22.863 0.000 2.119 2.516 2.318 0.836
## ssno (.14.) 0.523 0.031 16.821 0.000 0.462 0.584 0.523 0.606
## sscs (.15.) 0.436 0.031 13.871 0.000 0.375 0.498 0.436 0.511
## ssasi (.16.) 2.259 0.147 15.354 0.000 1.971 2.547 2.259 0.566
## ssmk (.17.) 4.743 0.135 35.167 0.000 4.479 5.008 4.743 0.734
## ssmc (.18.) 2.841 0.130 21.836 0.000 2.586 3.096 2.841 0.636
## ssei (.19.) 2.640 0.100 26.410 0.000 2.444 2.836 2.640 0.729
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 18.927 0.406 46.642 0.000 18.132 19.723 18.927 2.746
## .ssmk (.41.) 15.251 0.316 48.326 0.000 14.632 15.869 15.251 2.361
## .ssmc (.42.) 17.156 0.226 76.059 0.000 16.714 17.599 17.156 3.838
## .ssgs (.43.) 17.889 0.206 86.634 0.000 17.484 18.293 17.889 4.141
## .ssasi (.44.) 17.725 0.226 78.413 0.000 17.282 18.168 17.725 4.440
## .ssei (.45.) 13.551 0.175 77.268 0.000 13.207 13.894 13.551 3.741
## .ssno (.46.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.283
## .sscs (.47.) 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.089
## .sswk (.48.) 27.650 0.309 89.478 0.000 27.044 28.255 27.650 4.276
## .sspc 11.988 0.148 80.901 0.000 11.698 12.279 11.988 4.324
## math -0.162 0.106 -1.531 0.126 -0.370 0.046 -0.162 -0.162
## elctrnc -2.524 0.160 -15.777 0.000 -2.838 -2.210 -2.524 -2.524
## speed 0.730 0.105 6.955 0.000 0.524 0.935 0.730 0.730
## g 0.055 0.071 0.776 0.438 -0.084 0.194 0.055 0.055
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 5.861 1.645 3.562 0.000 2.636 9.085 5.861 0.123
## .ssmk 9.225 1.428 6.461 0.000 6.427 12.024 9.225 0.221
## .ssmc 7.974 0.594 13.431 0.000 6.811 9.138 7.974 0.399
## .ssgs 4.611 0.382 12.068 0.000 3.862 5.360 4.611 0.247
## .ssasi 5.082 0.533 9.531 0.000 4.037 6.127 5.082 0.319
## .ssei 4.393 0.371 11.855 0.000 3.666 5.119 4.393 0.335
## .ssno 0.364 0.038 9.468 0.000 0.289 0.439 0.364 0.489
## .sscs 0.014 0.114 0.119 0.905 -0.209 0.236 0.014 0.019
## .sswk 7.164 0.878 8.161 0.000 5.444 8.885 7.164 0.171
## .sspc 2.316 0.193 12.009 0.000 1.938 2.694 2.316 0.301
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
latent2<-cfa(bf.lv, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1", "ssar~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(latent2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 373.865 73.000 0.000 0.960 0.089 0.053 47942.935 48225.567
Mc(latent2)
## [1] 0.866639
summary(latent2, standardized=T, ci=T) # +.053 Std.all
## lavaan 0.6-18 ended normally after 131 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 84
## Number of equality constraints 27
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 373.865 320.596
## Degrees of freedom 73 73
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.166
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 220.631 189.195
## 1 153.235 131.401
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.535 0.255 13.842 0.000 3.035 4.036 3.535 0.490
## ssmk (.p2.) 3.137 0.224 14.019 0.000 2.698 3.575 3.137 0.472
## ssmc (.p3.) 1.054 0.123 8.547 0.000 0.812 1.296 1.054 0.224
## electronic =~
## ssgs (.p4.) 1.012 0.084 12.032 0.000 0.847 1.177 1.012 0.221
## ssasi (.p5.) 3.176 0.151 20.975 0.000 2.879 3.472 3.176 0.676
## ssmc (.p6.) 2.259 0.131 17.300 0.000 2.003 2.515 2.259 0.479
## ssei (.p7.) 1.734 0.098 17.601 0.000 1.541 1.927 1.734 0.475
## speed =~
## ssno (.p8.) 0.327 0.031 10.633 0.000 0.267 0.388 0.327 0.368
## sscs (.p9.) 0.721 0.070 10.346 0.000 0.584 0.858 0.721 0.864
## g =~
## ssgs (.10.) 3.870 0.150 25.731 0.000 3.576 4.165 3.870 0.847
## ssar (.11.) 5.743 0.212 27.100 0.000 5.327 6.158 5.743 0.797
## sswk (.12.) 6.247 0.269 23.205 0.000 5.720 6.775 6.247 0.911
## sspc (.13.) 2.470 0.128 19.226 0.000 2.218 2.722 2.470 0.819
## ssno (.14.) 0.559 0.036 15.434 0.000 0.488 0.630 0.559 0.629
## sscs (.15.) 0.465 0.036 12.860 0.000 0.394 0.535 0.465 0.557
## ssasi (.16.) 2.272 0.171 13.268 0.000 1.936 2.608 2.272 0.483
## ssmk (.17.) 5.082 0.185 27.416 0.000 4.718 5.445 5.082 0.765
## ssmc (.18.) 2.939 0.168 17.463 0.000 2.610 3.269 2.939 0.624
## ssei (.19.) 2.740 0.140 19.578 0.000 2.466 3.014 2.740 0.750
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 20.311 0.336 60.447 0.000 19.652 20.969 20.311 2.817
## .ssmk (.41.) 15.247 0.315 48.351 0.000 14.628 15.865 15.247 2.294
## .ssmc (.42.) 17.161 0.225 76.411 0.000 16.721 17.602 17.161 3.642
## .ssgs (.43.) 17.876 0.206 86.719 0.000 17.472 18.280 17.876 3.911
## .ssasi (.44.) 17.742 0.223 79.407 0.000 17.304 18.180 17.742 3.775
## .ssei (.45.) 13.543 0.175 77.256 0.000 13.199 13.886 13.543 3.707
## .ssno (.46.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.274
## .sscs (.47.) 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.091
## .sswk (.48.) 27.667 0.309 89.621 0.000 27.062 28.272 27.667 4.035
## .sspc 11.207 0.144 77.836 0.000 10.925 11.490 11.207 3.717
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 6.504 1.639 3.968 0.000 3.292 9.717 6.504 0.125
## .ssmk 8.497 1.376 6.174 0.000 5.800 11.195 8.497 0.192
## .ssmc 7.348 0.678 10.839 0.000 6.019 8.677 7.348 0.331
## .ssgs 4.890 0.406 12.047 0.000 4.095 5.686 4.890 0.234
## .ssasi 6.838 0.924 7.404 0.000 5.028 8.648 6.838 0.310
## .ssei 2.831 0.287 9.877 0.000 2.269 3.393 2.831 0.212
## .ssno 0.371 0.032 11.679 0.000 0.309 0.433 0.371 0.469
## .sscs -0.039 0.099 -0.397 0.691 -0.233 0.155 -0.039 -0.056
## .sswk 7.980 0.899 8.877 0.000 6.218 9.742 7.980 0.170
## .sspc 2.989 0.245 12.188 0.000 2.508 3.469 2.989 0.329
## electronic 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.535 0.255 13.842 0.000 3.035 4.036 3.535 0.537
## ssmk (.p2.) 3.137 0.224 14.019 0.000 2.698 3.575 3.137 0.505
## ssmc (.p3.) 1.054 0.123 8.547 0.000 0.812 1.296 1.054 0.258
## electronic =~
## ssgs (.p4.) 1.012 0.084 12.032 0.000 0.847 1.177 0.429 0.107
## ssasi (.p5.) 3.176 0.151 20.975 0.000 2.879 3.472 1.347 0.393
## ssmc (.p6.) 2.259 0.131 17.300 0.000 2.003 2.515 0.958 0.234
## ssei (.p7.) 1.734 0.098 17.601 0.000 1.541 1.927 0.735 0.226
## speed =~
## ssno (.p8.) 0.327 0.031 10.633 0.000 0.267 0.388 0.327 0.389
## sscs (.p9.) 0.721 0.070 10.346 0.000 0.584 0.858 0.721 0.860
## g =~
## ssgs (.10.) 3.870 0.150 25.731 0.000 3.576 4.165 3.366 0.838
## ssar (.11.) 5.743 0.212 27.100 0.000 5.327 6.158 4.995 0.759
## sswk (.12.) 6.247 0.269 23.205 0.000 5.720 6.775 5.434 0.893
## sspc (.13.) 2.470 0.128 19.226 0.000 2.218 2.722 2.149 0.812
## ssno (.14.) 0.559 0.036 15.434 0.000 0.488 0.630 0.486 0.578
## sscs (.15.) 0.465 0.036 12.860 0.000 0.394 0.535 0.404 0.482
## ssasi (.16.) 2.272 0.171 13.268 0.000 1.936 2.608 1.976 0.576
## ssmk (.17.) 5.082 0.185 27.416 0.000 4.718 5.445 4.420 0.711
## ssmc (.18.) 2.939 0.168 17.463 0.000 2.610 3.269 2.557 0.625
## ssei (.19.) 2.740 0.140 19.578 0.000 2.466 3.014 2.383 0.732
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 18.912 0.403 46.936 0.000 18.123 19.702 18.912 2.873
## .ssmk (.41.) 15.247 0.315 48.351 0.000 14.628 15.865 15.247 2.453
## .ssmc (.42.) 17.161 0.225 76.411 0.000 16.721 17.602 17.161 4.194
## .ssgs (.43.) 17.876 0.206 86.719 0.000 17.472 18.280 17.876 4.452
## .ssasi (.44.) 17.742 0.223 79.407 0.000 17.304 18.180 17.742 5.175
## .ssei (.45.) 13.543 0.175 77.256 0.000 13.199 13.886 13.543 4.157
## .ssno (.46.) 0.244 0.041 5.880 0.000 0.162 0.325 0.244 0.290
## .sscs (.47.) 0.076 0.040 1.909 0.056 -0.002 0.154 0.076 0.091
## .sswk (.48.) 27.667 0.309 89.621 0.000 27.062 28.272 27.667 4.545
## .sspc 12.001 0.149 80.550 0.000 11.709 12.293 12.001 4.537
## math -0.153 0.107 -1.430 0.153 -0.362 0.057 -0.153 -0.153
## elctrnc -1.905 0.119 -15.967 0.000 -2.139 -1.672 -4.493 -4.493
## speed 0.737 0.105 7.011 0.000 0.531 0.944 0.737 0.737
## g 0.046 0.066 0.699 0.485 -0.084 0.176 0.053 0.053
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 5.874 1.550 3.790 0.000 2.836 8.911 5.874 0.136
## .ssmk 9.254 1.362 6.793 0.000 6.584 11.924 9.254 0.240
## .ssmc 8.176 0.575 14.228 0.000 7.050 9.302 8.176 0.488
## .ssgs 4.608 0.388 11.891 0.000 3.849 5.368 4.608 0.286
## .ssasi 6.035 0.523 11.541 0.000 5.010 7.060 6.035 0.513
## .ssei 4.391 0.345 12.738 0.000 3.715 5.066 4.391 0.414
## .ssno 0.365 0.038 9.486 0.000 0.289 0.440 0.365 0.515
## .sscs 0.019 0.112 0.170 0.865 -0.200 0.238 0.019 0.027
## .sswk 7.533 0.864 8.720 0.000 5.840 9.226 7.533 0.203
## .sspc 2.382 0.198 12.023 0.000 1.993 2.770 2.382 0.340
## electronic 0.180 0.048 3.774 0.000 0.086 0.273 1.000 1.000
## g 0.757 0.083 9.107 0.000 0.594 0.919 1.000 1.000
reduced<-cfa(bf.reduced, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1", "ssar~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(reduced, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 376.670 75.000 0.000 0.960 0.087 0.053 47941.740 48214.455
Mc(reduced)
## [1] 0.8663071
tests<-lavTestLRT(configural, metric, scalar2, latent2, reduced)
Td=tests[2:5,"Chisq diff"]
Td
## [1] 33.0764975 8.3990024 0.8375065 2.3604963
dfd=tests[2:5,"Df diff"]
dfd
## [1] 15 4 2 2
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-526 + 526 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
## Warning in sqrt((ld) * G/(N - G)): NaNs produced
RMSEAD
## [1] 0.04791063 0.04576858 NaN 0.01852916
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.02558663 0.07007865
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] NA 0.08949844
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] NA 0.06691625
RMSEA.CI(T=Td[4],df=dfd[4],N=N,G=2)
## [1] NA 0.09067041
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
## 0.995 0.992 0.473 0.200 0.007 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
## 0.922 0.908 0.505 0.347 0.108 0.018
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
## 0.342 0.328 0.118 0.073 0.022 0.004
round(pvals(T=Td[4],df=dfd[4],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 0.693 0.674 0.334 0.236 0.094 0.027
tests<-lavTestLRT(configural, metric, scalar2, latent)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 33.076498 8.399002 92.255559
dfd=tests[2:4,"Df diff"]
dfd
## [1] 15 4 4
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-526 + 526 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04791063 0.04576858 0.20500355
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] NA 0.08949844
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.1698375 0.2422042
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
## 0.922 0.908 0.505 0.347 0.108 0.018
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 1 1 1 1
tests<-lavTestLRT(configural, metric, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 33.076498 8.399002 16.567297
dfd=tests[2:4,"Df diff"]
dfd
## [1] 15 4 10
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-526 + 526 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04791063 0.04576858 0.03536826
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.02558663 0.07007865
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] NA 0.08949844
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] NA 0.06450968
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
## 0.995 0.992 0.473 0.200 0.007 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
## 0.922 0.908 0.505 0.347 0.108 0.018
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
## 0.915 0.893 0.232 0.088 0.004 0.000
tests<-lavTestLRT(configural, metric, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 33.07650 69.50205
dfd=tests[2:3,"Df diff"]
dfd
## [1] 15 6
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-526 + 526 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04791063 0.14198373
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.02558663 0.07007865
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.1130598 0.1728060
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
## 0.995 0.992 0.473 0.200 0.007 0.000
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 1.000 1.000 0.991
bf.age<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
g ~ age
'
bf.ageq<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
g ~ c(a,a)*age
'
bf.age2<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
g ~ age + age2
'
bf.age2q<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
g ~ c(a,a)*age + c(b,b)*age2
'
sem.age<-sem(bf.age, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1", "ssar~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(sem.age, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 477.725 91.000 0.000 0.949 0.090 0.055 0.566 47912.761 48205.309
Mc(sem.age)
## [1] 0.8319528
summary(sem.age, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 113 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 27
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 477.725 400.398
## Degrees of freedom 91 91
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.193
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 272.627 228.498
## 1 205.098 171.900
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.554 0.254 13.988 0.000 3.056 4.052 3.554 0.493
## ssmk (.p2.) 3.166 0.222 14.229 0.000 2.730 3.602 3.166 0.477
## ssmc (.p3.) 1.060 0.123 8.611 0.000 0.819 1.301 1.060 0.225
## electronic =~
## ssgs (.p4.) 1.007 0.084 12.024 0.000 0.843 1.171 1.007 0.220
## ssasi (.p5.) 3.167 0.152 20.893 0.000 2.869 3.464 3.167 0.674
## ssmc (.p6.) 2.255 0.131 17.263 0.000 1.999 2.511 2.255 0.479
## ssei (.p7.) 1.727 0.098 17.562 0.000 1.534 1.920 1.727 0.473
## speed =~
## ssno (.p8.) 0.328 0.031 10.647 0.000 0.267 0.388 0.328 0.369
## sscs (.p9.) 0.722 0.070 10.365 0.000 0.585 0.858 0.722 0.865
## g =~
## ssgs (.10.) 3.846 0.157 24.471 0.000 3.538 4.154 3.870 0.847
## ssar (.11.) 5.693 0.217 26.236 0.000 5.267 6.118 5.729 0.795
## sswk (.12.) 6.221 0.277 22.424 0.000 5.678 6.765 6.260 0.912
## sspc (.13.) 2.451 0.131 18.656 0.000 2.193 2.708 2.466 0.818
## ssno (.14.) 0.554 0.036 15.184 0.000 0.482 0.625 0.557 0.627
## sscs (.15.) 0.461 0.036 12.733 0.000 0.390 0.532 0.464 0.556
## ssasi (.16.) 2.260 0.172 13.123 0.000 1.922 2.598 2.274 0.484
## ssmk (.17.) 5.028 0.188 26.695 0.000 4.659 5.397 5.060 0.762
## ssmc (.18.) 2.918 0.171 17.071 0.000 2.583 3.252 2.936 0.623
## ssei (.19.) 2.727 0.142 19.256 0.000 2.449 3.005 2.744 0.751
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.051 0.025 2.072 0.038 0.003 0.099 0.051 0.112
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 20.380 0.340 59.910 0.000 19.714 21.047 20.380 2.828
## .ssmk (.40.) 15.307 0.320 47.824 0.000 14.680 15.935 15.307 2.305
## .ssmc (.41.) 17.198 0.227 75.872 0.000 16.754 17.643 17.198 3.652
## .ssgs (.42.) 17.922 0.211 84.898 0.000 17.508 18.336 17.922 3.920
## .ssasi (.43.) 17.770 0.223 79.808 0.000 17.333 18.206 17.770 3.784
## .ssei (.44.) 13.575 0.176 77.261 0.000 13.231 13.919 13.575 3.717
## .ssno (.45.) 0.250 0.042 6.007 0.000 0.169 0.332 0.250 0.282
## .sscs (.46.) 0.082 0.040 2.037 0.042 0.003 0.160 0.082 0.098
## .sswk (.47.) 27.744 0.314 88.354 0.000 27.128 28.359 27.744 4.044
## .sspc 11.237 0.146 77.084 0.000 10.952 11.523 11.237 3.729
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 6.499 1.635 3.975 0.000 3.294 9.703 6.499 0.125
## .ssmk 8.489 1.380 6.150 0.000 5.784 11.194 8.489 0.192
## .ssmc 7.346 0.678 10.842 0.000 6.018 8.675 7.346 0.331
## .ssgs 4.909 0.408 12.034 0.000 4.109 5.709 4.909 0.235
## .ssasi 6.852 0.922 7.430 0.000 5.045 8.660 6.852 0.311
## .ssei 2.823 0.285 9.896 0.000 2.264 3.382 2.823 0.212
## .ssno 0.371 0.032 11.692 0.000 0.309 0.434 0.371 0.471
## .sscs -0.040 0.099 -0.404 0.686 -0.234 0.154 -0.040 -0.057
## .sswk 7.885 0.894 8.822 0.000 6.133 9.636 7.885 0.167
## .sspc 3.000 0.246 12.212 0.000 2.518 3.481 3.000 0.330
## electronic 1.000 1.000 1.000 1.000 1.000
## .g 1.000 1.000 1.000 0.988 0.988
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.554 0.254 13.988 0.000 3.056 4.052 3.554 0.540
## ssmk (.p2.) 3.166 0.222 14.229 0.000 2.730 3.602 3.166 0.509
## ssmc (.p3.) 1.060 0.123 8.611 0.000 0.819 1.301 1.060 0.259
## electronic =~
## ssgs (.p4.) 1.007 0.084 12.024 0.000 0.843 1.171 0.427 0.106
## ssasi (.p5.) 3.167 0.152 20.893 0.000 2.869 3.464 1.342 0.391
## ssmc (.p6.) 2.255 0.131 17.263 0.000 1.999 2.511 0.956 0.234
## ssei (.p7.) 1.727 0.098 17.562 0.000 1.534 1.920 0.732 0.225
## speed =~
## ssno (.p8.) 0.328 0.031 10.647 0.000 0.267 0.388 0.328 0.389
## sscs (.p9.) 0.722 0.070 10.365 0.000 0.585 0.858 0.722 0.861
## g =~
## ssgs (.10.) 3.846 0.157 24.471 0.000 3.538 4.154 3.368 0.839
## ssar (.11.) 5.693 0.217 26.236 0.000 5.267 6.118 4.986 0.757
## sswk (.12.) 6.221 0.277 22.424 0.000 5.678 6.765 5.449 0.895
## sspc (.13.) 2.451 0.131 18.656 0.000 2.193 2.708 2.146 0.811
## ssno (.14.) 0.554 0.036 15.184 0.000 0.482 0.625 0.485 0.576
## sscs (.15.) 0.461 0.036 12.733 0.000 0.390 0.532 0.404 0.482
## ssasi (.16.) 2.260 0.172 13.123 0.000 1.922 2.598 1.979 0.577
## ssmk (.17.) 5.028 0.188 26.695 0.000 4.659 5.397 4.404 0.708
## ssmc (.18.) 2.918 0.171 17.071 0.000 2.583 3.252 2.555 0.624
## ssei (.19.) 2.727 0.142 19.256 0.000 2.449 3.005 2.388 0.733
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.098 0.019 5.127 0.000 0.060 0.135 0.112 0.241
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 18.978 0.407 46.643 0.000 18.181 19.776 18.978 2.882
## .ssmk (.40.) 15.307 0.320 47.824 0.000 14.680 15.935 15.307 2.461
## .ssmc (.41.) 17.198 0.227 75.872 0.000 16.754 17.643 17.198 4.203
## .ssgs (.42.) 17.922 0.211 84.898 0.000 17.508 18.336 17.922 4.463
## .ssasi (.43.) 17.770 0.223 79.808 0.000 17.333 18.206 17.770 5.180
## .ssei (.44.) 13.575 0.176 77.261 0.000 13.231 13.919 13.575 4.167
## .ssno (.45.) 0.250 0.042 6.007 0.000 0.169 0.332 0.250 0.298
## .sscs (.46.) 0.082 0.040 2.037 0.042 0.003 0.160 0.082 0.098
## .sswk (.47.) 27.744 0.314 88.354 0.000 27.128 28.359 27.744 4.560
## .sspc 12.032 0.150 80.168 0.000 11.738 12.326 12.032 4.545
## math -0.150 0.106 -1.420 0.156 -0.357 0.057 -0.150 -0.150
## elctrnc -1.911 0.120 -15.908 0.000 -2.146 -1.675 -4.507 -4.507
## speed 0.737 0.105 7.024 0.000 0.531 0.943 0.737 0.737
## .g 0.065 0.066 0.987 0.324 -0.064 0.195 0.074 0.074
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 5.866 1.546 3.795 0.000 2.837 8.896 5.866 0.135
## .ssmk 9.272 1.369 6.773 0.000 6.589 11.956 9.272 0.240
## .ssmc 8.176 0.574 14.244 0.000 7.051 9.301 8.176 0.488
## .ssgs 4.596 0.384 11.976 0.000 3.844 5.348 4.596 0.285
## .ssasi 6.049 0.524 11.553 0.000 5.023 7.075 6.049 0.514
## .ssei 4.373 0.345 12.676 0.000 3.697 5.049 4.373 0.412
## .ssno 0.366 0.039 9.478 0.000 0.290 0.442 0.366 0.516
## .sscs 0.018 0.112 0.160 0.873 -0.202 0.237 0.018 0.025
## .sswk 7.335 0.857 8.561 0.000 5.656 9.015 7.335 0.198
## .sspc 2.402 0.200 12.027 0.000 2.010 2.793 2.402 0.343
## electronic 0.180 0.048 3.729 0.000 0.085 0.274 1.000 1.000
## .g 0.723 0.084 8.563 0.000 0.557 0.888 0.942 0.942
sem.ageq<-sem(bf.ageq, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1", "ssar~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(sem.ageq, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 480.695 92.000 0.000 0.949 0.090 0.053 0.567 47913.731 48201.321
Mc(sem.ageq)
## [1] 0.8311735
summary(sem.ageq, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 130 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 28
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 480.695 402.742
## Degrees of freedom 92 92
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.194
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 274.129 229.675
## 1 206.566 173.068
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.553 0.254 13.971 0.000 3.054 4.051 3.553 0.490
## ssmk (.p2.) 3.164 0.222 14.221 0.000 2.728 3.600 3.164 0.474
## ssmc (.p3.) 1.060 0.123 8.610 0.000 0.818 1.301 1.060 0.224
## electronic =~
## ssgs (.p4.) 1.005 0.084 12.007 0.000 0.841 1.170 1.005 0.218
## ssasi (.p5.) 3.162 0.151 20.904 0.000 2.865 3.458 3.162 0.672
## ssmc (.p6.) 2.252 0.131 17.249 0.000 1.996 2.508 2.252 0.477
## ssei (.p7.) 1.725 0.098 17.574 0.000 1.532 1.917 1.725 0.470
## speed =~
## ssno (.p8.) 0.328 0.031 10.646 0.000 0.267 0.388 0.328 0.367
## sscs (.p9.) 0.721 0.070 10.365 0.000 0.585 0.858 0.721 0.862
## g =~
## ssgs (.10.) 3.852 0.160 24.101 0.000 3.539 4.165 3.907 0.849
## ssar (.11.) 5.704 0.219 25.989 0.000 5.274 6.134 5.785 0.798
## sswk (.12.) 6.230 0.281 22.174 0.000 5.679 6.780 6.319 0.914
## sspc (.13.) 2.455 0.132 18.542 0.000 2.196 2.715 2.490 0.821
## ssno (.14.) 0.555 0.037 15.157 0.000 0.483 0.627 0.563 0.631
## sscs (.15.) 0.462 0.036 12.710 0.000 0.391 0.534 0.469 0.560
## ssasi (.16.) 2.268 0.173 13.103 0.000 1.929 2.607 2.300 0.489
## ssmk (.17.) 5.038 0.190 26.521 0.000 4.665 5.410 5.109 0.765
## ssmc (.18.) 2.924 0.172 16.963 0.000 2.586 3.262 2.966 0.628
## ssei (.19.) 2.733 0.143 19.113 0.000 2.453 3.014 2.772 0.755
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.077 0.016 4.899 0.000 0.046 0.107 0.076 0.167
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 20.416 0.337 60.558 0.000 19.755 21.077 20.416 2.816
## .ssmk (.40.) 15.339 0.319 48.045 0.000 14.713 15.964 15.339 2.296
## .ssmc (.41.) 17.217 0.224 76.725 0.000 16.777 17.657 17.217 3.643
## .ssgs (.42.) 17.946 0.208 86.190 0.000 17.538 18.354 17.946 3.898
## .ssasi (.43.) 17.784 0.220 80.755 0.000 17.352 18.215 17.784 3.779
## .ssei (.44.) 13.592 0.173 78.460 0.000 13.252 13.931 13.592 3.702
## .ssno (.45.) 0.254 0.041 6.134 0.000 0.173 0.335 0.254 0.285
## .sscs (.46.) 0.085 0.040 2.124 0.034 0.007 0.163 0.085 0.101
## .sswk (.47.) 27.783 0.309 89.963 0.000 27.177 28.388 27.783 4.019
## .sspc 11.253 0.145 77.834 0.000 10.969 11.536 11.253 3.709
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 6.485 1.635 3.966 0.000 3.281 9.690 6.485 0.123
## .ssmk 8.504 1.381 6.160 0.000 5.798 11.210 8.504 0.191
## .ssmc 7.346 0.677 10.844 0.000 6.018 8.674 7.346 0.329
## .ssgs 4.919 0.408 12.058 0.000 4.120 5.719 4.919 0.232
## .ssasi 6.861 0.922 7.445 0.000 5.054 8.667 6.861 0.310
## .ssei 2.820 0.285 9.901 0.000 2.262 3.378 2.820 0.209
## .ssno 0.371 0.032 11.693 0.000 0.309 0.434 0.371 0.467
## .sscs -0.040 0.099 -0.402 0.687 -0.233 0.154 -0.040 -0.057
## .sswk 7.875 0.892 8.828 0.000 6.127 9.624 7.875 0.165
## .sspc 3.002 0.245 12.229 0.000 2.521 3.483 3.002 0.326
## electronic 1.000 1.000 1.000 1.000 1.000
## .g 1.000 1.000 1.000 0.972 0.972
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.553 0.254 13.971 0.000 3.054 4.051 3.553 0.543
## ssmk (.p2.) 3.164 0.222 14.221 0.000 2.728 3.600 3.164 0.511
## ssmc (.p3.) 1.060 0.123 8.610 0.000 0.818 1.301 1.060 0.260
## electronic =~
## ssgs (.p4.) 1.005 0.084 12.007 0.000 0.841 1.170 0.427 0.107
## ssasi (.p5.) 3.162 0.151 20.904 0.000 2.865 3.458 1.343 0.392
## ssmc (.p6.) 2.252 0.131 17.249 0.000 1.996 2.508 0.956 0.235
## ssei (.p7.) 1.725 0.098 17.574 0.000 1.532 1.917 0.732 0.226
## speed =~
## ssno (.p8.) 0.328 0.031 10.646 0.000 0.267 0.388 0.328 0.391
## sscs (.p9.) 0.721 0.070 10.365 0.000 0.585 0.858 0.721 0.863
## g =~
## ssgs (.10.) 3.852 0.160 24.101 0.000 3.539 4.165 3.334 0.836
## ssar (.11.) 5.704 0.219 25.989 0.000 5.274 6.134 4.937 0.754
## sswk (.12.) 6.230 0.281 22.174 0.000 5.679 6.780 5.392 0.893
## sspc (.13.) 2.455 0.132 18.542 0.000 2.196 2.715 2.125 0.808
## ssno (.14.) 0.555 0.037 15.157 0.000 0.483 0.627 0.480 0.573
## sscs (.15.) 0.462 0.036 12.710 0.000 0.391 0.534 0.400 0.479
## ssasi (.16.) 2.268 0.173 13.103 0.000 1.929 2.607 1.963 0.574
## ssmk (.17.) 5.038 0.190 26.521 0.000 4.665 5.410 4.360 0.705
## ssmc (.18.) 2.924 0.172 16.963 0.000 2.586 3.262 2.531 0.621
## ssei (.19.) 2.733 0.143 19.113 0.000 2.453 3.014 2.366 0.730
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.077 0.016 4.899 0.000 0.046 0.107 0.089 0.191
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 19.013 0.407 46.728 0.000 18.216 19.811 19.013 2.904
## .ssmk (.40.) 15.339 0.319 48.045 0.000 14.713 15.964 15.339 2.479
## .ssmc (.41.) 17.217 0.224 76.725 0.000 16.777 17.657 17.217 4.223
## .ssgs (.42.) 17.946 0.208 86.190 0.000 17.538 18.354 17.946 4.501
## .ssasi (.43.) 17.784 0.220 80.755 0.000 17.352 18.215 17.784 5.199
## .ssei (.44.) 13.592 0.173 78.460 0.000 13.252 13.931 13.592 4.193
## .ssno (.45.) 0.254 0.041 6.134 0.000 0.173 0.335 0.254 0.303
## .sscs (.46.) 0.085 0.040 2.124 0.034 0.007 0.163 0.085 0.101
## .sswk (.47.) 27.783 0.309 89.963 0.000 27.177 28.388 27.783 4.601
## .sspc 12.048 0.148 81.157 0.000 11.757 12.339 12.048 4.582
## math -0.150 0.106 -1.416 0.157 -0.357 0.058 -0.150 -0.150
## elctrnc -1.914 0.120 -15.907 0.000 -2.149 -1.678 -4.507 -4.507
## speed 0.737 0.105 7.025 0.000 0.532 0.943 0.737 0.737
## .g 0.052 0.065 0.800 0.424 -0.076 0.180 0.060 0.060
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 5.870 1.546 3.797 0.000 2.840 8.900 5.870 0.137
## .ssmk 9.265 1.368 6.773 0.000 6.584 11.946 9.265 0.242
## .ssmc 8.176 0.574 14.241 0.000 7.050 9.301 8.176 0.492
## .ssgs 4.600 0.385 11.961 0.000 3.847 5.354 4.600 0.289
## .ssasi 6.046 0.523 11.552 0.000 5.020 7.072 6.046 0.517
## .ssei 4.377 0.345 12.691 0.000 3.701 5.053 4.377 0.416
## .ssno 0.366 0.039 9.482 0.000 0.290 0.441 0.366 0.520
## .sscs 0.018 0.112 0.163 0.870 -0.201 0.238 0.018 0.026
## .sswk 7.379 0.858 8.605 0.000 5.698 9.060 7.379 0.202
## .sspc 2.397 0.199 12.029 0.000 2.006 2.787 2.397 0.347
## electronic 0.180 0.048 3.734 0.000 0.086 0.275 1.000 1.000
## .g 0.722 0.085 8.524 0.000 0.556 0.888 0.964 0.964
sem.age2<-sem(bf.age2, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1", "ssar~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(sem.age2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 509.262 109.000 0.000 0.947 0.084 0.053 0.600 47914.194 48216.660
Mc(sem.age2)
## [1] 0.8266122
summary(sem.age2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 119 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 88
## Number of equality constraints 27
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 509.262 427.993
## Degrees of freedom 109 109
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.190
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 289.412 243.227
## 1 219.850 184.766
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.555 0.254 14.004 0.000 3.058 4.053 3.555 0.493
## ssmk (.p2.) 3.167 0.222 14.249 0.000 2.731 3.603 3.167 0.477
## ssmc (.p3.) 1.061 0.123 8.620 0.000 0.820 1.303 1.061 0.225
## electronic =~
## ssgs (.p4.) 1.007 0.084 12.019 0.000 0.843 1.171 1.007 0.220
## ssasi (.p5.) 3.165 0.151 20.899 0.000 2.868 3.462 3.165 0.674
## ssmc (.p6.) 2.255 0.131 17.251 0.000 1.998 2.511 2.255 0.479
## ssei (.p7.) 1.726 0.098 17.573 0.000 1.534 1.919 1.726 0.473
## speed =~
## ssno (.p8.) 0.328 0.031 10.648 0.000 0.267 0.388 0.328 0.369
## sscs (.p9.) 0.722 0.070 10.366 0.000 0.585 0.858 0.722 0.865
## g =~
## ssgs (.10.) 3.835 0.155 24.668 0.000 3.530 4.140 3.869 0.846
## ssar (.11.) 5.677 0.214 26.534 0.000 5.258 6.097 5.728 0.795
## sswk (.12.) 6.206 0.273 22.728 0.000 5.671 6.741 6.261 0.913
## sspc (.13.) 2.445 0.129 18.918 0.000 2.191 2.698 2.466 0.818
## ssno (.14.) 0.552 0.036 15.318 0.000 0.482 0.623 0.557 0.627
## sscs (.15.) 0.460 0.036 12.816 0.000 0.390 0.531 0.464 0.556
## ssasi (.16.) 2.255 0.171 13.220 0.000 1.921 2.589 2.275 0.484
## ssmk (.17.) 5.014 0.187 26.837 0.000 4.648 5.381 5.059 0.762
## ssmc (.18.) 2.909 0.169 17.190 0.000 2.577 3.241 2.935 0.623
## ssei (.19.) 2.721 0.140 19.454 0.000 2.447 2.995 2.745 0.752
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.045 0.025 1.771 0.077 -0.005 0.095 0.045 0.099
## age2 -0.015 0.011 -1.320 0.187 -0.037 0.007 -0.015 -0.072
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 20.791 0.439 47.317 0.000 19.930 21.653 20.791 2.885
## .ssmk (.43.) 15.670 0.408 38.422 0.000 14.871 16.470 15.670 2.359
## .ssmc (.44.) 17.409 0.266 65.445 0.000 16.888 17.931 17.409 3.698
## .ssgs (.45.) 18.200 0.279 65.210 0.000 17.653 18.747 18.200 3.981
## .ssasi (.46.) 17.933 0.243 73.754 0.000 17.456 18.409 17.933 3.819
## .ssei (.47.) 13.772 0.211 65.188 0.000 13.358 14.186 13.772 3.771
## .ssno (.48.) 0.290 0.047 6.172 0.000 0.198 0.383 0.290 0.327
## .sscs (.49.) 0.115 0.043 2.672 0.008 0.031 0.199 0.115 0.138
## .sswk (.50.) 28.193 0.420 67.201 0.000 27.371 29.015 28.193 4.109
## .sspc 11.414 0.181 63.114 0.000 11.060 11.769 11.414 3.788
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 6.500 1.634 3.978 0.000 3.298 9.702 6.500 0.125
## .ssmk 8.489 1.380 6.153 0.000 5.785 11.193 8.489 0.192
## .ssmc 7.345 0.678 10.836 0.000 6.016 8.673 7.345 0.331
## .ssgs 4.920 0.410 12.011 0.000 4.117 5.723 4.920 0.235
## .ssasi 6.856 0.922 7.434 0.000 5.048 8.664 6.856 0.311
## .ssei 2.819 0.284 9.912 0.000 2.261 3.376 2.819 0.211
## .ssno 0.372 0.032 11.697 0.000 0.309 0.434 0.372 0.471
## .sscs -0.040 0.099 -0.405 0.686 -0.234 0.154 -0.040 -0.057
## .sswk 7.870 0.889 8.849 0.000 6.127 9.613 7.870 0.167
## .sspc 2.998 0.246 12.185 0.000 2.516 3.480 2.998 0.330
## electronic 1.000 1.000 1.000 1.000 1.000
## .g 1.000 1.000 1.000 0.982 0.982
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.555 0.254 14.004 0.000 3.058 4.053 3.555 0.540
## ssmk (.p2.) 3.167 0.222 14.249 0.000 2.731 3.603 3.167 0.509
## ssmc (.p3.) 1.061 0.123 8.620 0.000 0.820 1.303 1.061 0.259
## electronic =~
## ssgs (.p4.) 1.007 0.084 12.019 0.000 0.843 1.171 0.427 0.106
## ssasi (.p5.) 3.165 0.151 20.899 0.000 2.868 3.462 1.343 0.391
## ssmc (.p6.) 2.255 0.131 17.251 0.000 1.998 2.511 0.956 0.234
## ssei (.p7.) 1.726 0.098 17.573 0.000 1.534 1.919 0.732 0.225
## speed =~
## ssno (.p8.) 0.328 0.031 10.648 0.000 0.267 0.388 0.328 0.389
## sscs (.p9.) 0.722 0.070 10.366 0.000 0.585 0.858 0.722 0.861
## g =~
## ssgs (.10.) 3.835 0.155 24.668 0.000 3.530 4.140 3.367 0.839
## ssar (.11.) 5.677 0.214 26.534 0.000 5.258 6.097 4.985 0.757
## sswk (.12.) 6.206 0.273 22.728 0.000 5.671 6.741 5.449 0.896
## sspc (.13.) 2.445 0.129 18.918 0.000 2.191 2.698 2.146 0.811
## ssno (.14.) 0.552 0.036 15.318 0.000 0.482 0.623 0.485 0.576
## sscs (.15.) 0.460 0.036 12.816 0.000 0.390 0.531 0.404 0.482
## ssasi (.16.) 2.255 0.171 13.220 0.000 1.921 2.589 1.980 0.577
## ssmk (.17.) 5.014 0.187 26.837 0.000 4.648 5.381 4.403 0.708
## ssmc (.18.) 2.909 0.169 17.190 0.000 2.577 3.241 2.554 0.624
## ssei (.19.) 2.721 0.140 19.454 0.000 2.447 2.995 2.389 0.733
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.099 0.019 5.261 0.000 0.062 0.135 0.112 0.242
## age2 0.001 0.008 0.089 0.929 -0.015 0.016 0.001 0.004
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 19.389 0.496 39.096 0.000 18.417 20.361 19.389 2.945
## .ssmk (.43.) 15.670 0.408 38.422 0.000 14.871 16.470 15.670 2.519
## .ssmc (.44.) 17.409 0.266 65.445 0.000 16.888 17.931 17.409 4.255
## .ssgs (.45.) 18.200 0.279 65.210 0.000 17.653 18.747 18.200 4.533
## .ssasi (.46.) 17.933 0.243 73.754 0.000 17.456 18.409 17.933 5.227
## .ssei (.47.) 13.772 0.211 65.188 0.000 13.358 14.186 13.772 4.226
## .ssno (.48.) 0.290 0.047 6.172 0.000 0.198 0.383 0.290 0.345
## .sscs (.49.) 0.115 0.043 2.672 0.008 0.031 0.199 0.115 0.137
## .sswk (.50.) 28.193 0.420 67.201 0.000 27.371 29.015 28.193 4.633
## .sspc 12.209 0.186 65.693 0.000 11.845 12.573 12.209 4.612
## math -0.150 0.106 -1.419 0.156 -0.357 0.057 -0.150 -0.150
## elctrnc -1.912 0.120 -15.913 0.000 -2.147 -1.676 -4.506 -4.506
## speed 0.737 0.105 7.025 0.000 0.531 0.942 0.737 0.737
## .g -0.010 0.091 -0.114 0.910 -0.188 0.167 -0.012 -0.012
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 5.866 1.544 3.799 0.000 2.840 8.893 5.866 0.135
## .ssmk 9.272 1.368 6.778 0.000 6.591 11.953 9.272 0.240
## .ssmc 8.175 0.574 14.244 0.000 7.050 9.299 8.175 0.488
## .ssgs 4.596 0.384 11.969 0.000 3.844 5.349 4.596 0.285
## .ssasi 6.049 0.523 11.555 0.000 5.023 7.075 6.049 0.514
## .ssei 4.373 0.345 12.672 0.000 3.697 5.050 4.373 0.412
## .ssno 0.366 0.039 9.477 0.000 0.290 0.442 0.366 0.516
## .sscs 0.018 0.112 0.159 0.874 -0.202 0.237 0.018 0.025
## .sswk 7.333 0.857 8.561 0.000 5.654 9.011 7.333 0.198
## .sspc 2.402 0.200 12.024 0.000 2.010 2.793 2.402 0.343
## electronic 0.180 0.048 3.729 0.000 0.085 0.275 1.000 1.000
## .g 0.726 0.084 8.631 0.000 0.561 0.891 0.942 0.942
sem.age2q<-sem(bf.age2q, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1", "ssar~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(sem.age2q, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 513.716 111.000 0.000 0.947 0.083 0.052 0.600 47914.648 48207.197
Mc(sem.age2q)
## [1] 0.8256478
summary(sem.age2q, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 136 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 88
## Number of equality constraints 29
##
## Number of observations per group:
## 0 526
## 1 526
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 513.716 431.704
## Degrees of freedom 111 111
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.190
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 291.675 245.111
## 1 222.041 186.593
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.553 0.254 13.974 0.000 3.055 4.051 3.553 0.490
## ssmk (.p2.) 3.165 0.222 14.226 0.000 2.729 3.601 3.165 0.474
## ssmc (.p3.) 1.060 0.123 8.608 0.000 0.818 1.301 1.060 0.224
## electronic =~
## ssgs (.p4.) 1.005 0.084 12.003 0.000 0.841 1.170 1.005 0.219
## ssasi (.p5.) 3.161 0.151 20.904 0.000 2.865 3.458 3.161 0.672
## ssmc (.p6.) 2.252 0.131 17.244 0.000 1.996 2.508 2.252 0.477
## ssei (.p7.) 1.724 0.098 17.578 0.000 1.532 1.916 1.724 0.470
## speed =~
## ssno (.p8.) 0.328 0.031 10.646 0.000 0.267 0.388 0.328 0.368
## sscs (.p9.) 0.721 0.070 10.366 0.000 0.585 0.858 0.721 0.862
## g =~
## ssgs (.10.) 3.845 0.158 24.263 0.000 3.534 4.155 3.900 0.848
## ssar (.11.) 5.694 0.217 26.214 0.000 5.268 6.119 5.776 0.797
## sswk (.12.) 6.219 0.278 22.394 0.000 5.675 6.763 6.309 0.914
## sspc (.13.) 2.451 0.131 18.727 0.000 2.195 2.708 2.487 0.821
## ssno (.14.) 0.554 0.036 15.236 0.000 0.483 0.625 0.562 0.630
## sscs (.15.) 0.462 0.036 12.771 0.000 0.391 0.532 0.468 0.560
## ssasi (.16.) 2.265 0.172 13.186 0.000 1.928 2.601 2.298 0.488
## ssmk (.17.) 5.028 0.189 26.639 0.000 4.658 5.398 5.101 0.764
## ssmc (.18.) 2.919 0.171 17.070 0.000 2.584 3.254 2.962 0.627
## ssei (.19.) 2.729 0.142 19.267 0.000 2.451 3.006 2.769 0.755
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.074 0.016 4.571 0.000 0.042 0.105 0.073 0.161
## age2 (b) -0.006 0.007 -0.935 0.350 -0.020 0.007 -0.006 -0.031
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 20.591 0.376 54.709 0.000 19.853 21.329 20.591 2.842
## .ssmk (.43.) 15.493 0.354 43.799 0.000 14.800 16.186 15.493 2.322
## .ssmc (.44.) 17.307 0.240 72.173 0.000 16.837 17.777 17.307 3.664
## .ssgs (.45.) 18.064 0.235 76.798 0.000 17.603 18.525 18.064 3.928
## .ssasi (.46.) 17.853 0.228 78.166 0.000 17.406 18.301 17.853 3.795
## .ssei (.47.) 13.676 0.187 73.138 0.000 13.309 14.042 13.676 3.728
## .ssno (.48.) 0.271 0.043 6.265 0.000 0.186 0.356 0.271 0.304
## .sscs (.49.) 0.099 0.041 2.424 0.015 0.019 0.179 0.099 0.118
## .sswk (.50.) 27.974 0.351 79.625 0.000 27.285 28.662 27.974 4.051
## .sspc 11.328 0.158 71.710 0.000 11.018 11.638 11.328 3.738
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 6.487 1.635 3.968 0.000 3.283 9.691 6.487 0.124
## .ssmk 8.502 1.381 6.157 0.000 5.796 11.209 8.502 0.191
## .ssmc 7.345 0.677 10.842 0.000 6.017 8.673 7.345 0.329
## .ssgs 4.924 0.409 12.049 0.000 4.123 5.725 4.924 0.233
## .ssasi 6.862 0.922 7.447 0.000 5.056 8.668 6.862 0.310
## .ssei 2.818 0.284 9.906 0.000 2.261 3.376 2.818 0.209
## .ssno 0.371 0.032 11.696 0.000 0.309 0.434 0.371 0.467
## .sscs -0.040 0.099 -0.403 0.687 -0.233 0.154 -0.040 -0.057
## .sswk 7.868 0.890 8.838 0.000 6.123 9.613 7.868 0.165
## .sspc 3.001 0.246 12.217 0.000 2.520 3.482 3.001 0.327
## electronic 1.000 1.000 1.000 1.000 1.000
## .g 1.000 1.000 1.000 0.972 0.972
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.553 0.254 13.974 0.000 3.055 4.051 3.553 0.542
## ssmk (.p2.) 3.165 0.222 14.226 0.000 2.729 3.601 3.165 0.511
## ssmc (.p3.) 1.060 0.123 8.608 0.000 0.818 1.301 1.060 0.260
## electronic =~
## ssgs (.p4.) 1.005 0.084 12.003 0.000 0.841 1.170 0.426 0.107
## ssasi (.p5.) 3.161 0.151 20.904 0.000 2.865 3.458 1.340 0.392
## ssmc (.p6.) 2.252 0.131 17.244 0.000 1.996 2.508 0.955 0.234
## ssei (.p7.) 1.724 0.098 17.578 0.000 1.532 1.916 0.731 0.225
## speed =~
## ssno (.p8.) 0.328 0.031 10.646 0.000 0.267 0.388 0.328 0.390
## sscs (.p9.) 0.721 0.070 10.366 0.000 0.585 0.858 0.721 0.863
## g =~
## ssgs (.10.) 3.845 0.158 24.263 0.000 3.534 4.155 3.339 0.836
## ssar (.11.) 5.694 0.217 26.214 0.000 5.268 6.119 4.944 0.755
## sswk (.12.) 6.219 0.278 22.394 0.000 5.675 6.763 5.401 0.893
## sspc (.13.) 2.451 0.131 18.727 0.000 2.195 2.708 2.129 0.809
## ssno (.14.) 0.554 0.036 15.236 0.000 0.483 0.625 0.481 0.573
## sscs (.15.) 0.462 0.036 12.771 0.000 0.391 0.532 0.401 0.479
## ssasi (.16.) 2.265 0.172 13.186 0.000 1.928 2.601 1.967 0.575
## ssmk (.17.) 5.028 0.189 26.639 0.000 4.658 5.398 4.366 0.705
## ssmc (.18.) 2.919 0.171 17.070 0.000 2.584 3.254 2.535 0.622
## ssei (.19.) 2.729 0.142 19.267 0.000 2.451 3.006 2.370 0.730
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.074 0.016 4.571 0.000 0.042 0.105 0.085 0.183
## age2 (b) -0.006 0.007 -0.935 0.350 -0.020 0.007 -0.007 -0.037
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 19.188 0.443 43.308 0.000 18.320 20.056 19.188 2.928
## .ssmk (.43.) 15.493 0.354 43.799 0.000 14.800 16.186 15.493 2.502
## .ssmc (.44.) 17.307 0.240 72.173 0.000 16.837 17.777 17.307 4.243
## .ssgs (.45.) 18.064 0.235 76.798 0.000 17.603 18.525 18.064 4.526
## .ssasi (.46.) 17.853 0.228 78.166 0.000 17.406 18.301 17.853 5.217
## .ssei (.47.) 13.676 0.187 73.138 0.000 13.309 14.042 13.676 4.215
## .ssno (.48.) 0.271 0.043 6.265 0.000 0.186 0.356 0.271 0.323
## .sscs (.49.) 0.099 0.041 2.424 0.015 0.019 0.179 0.099 0.118
## .sswk (.50.) 27.974 0.351 79.625 0.000 27.285 28.662 27.974 4.627
## .sspc 12.123 0.164 73.889 0.000 11.801 12.445 12.123 4.606
## math -0.150 0.106 -1.416 0.157 -0.357 0.058 -0.150 -0.150
## elctrnc -1.914 0.120 -15.908 0.000 -2.150 -1.678 -4.514 -4.514
## speed 0.737 0.105 7.025 0.000 0.532 0.943 0.737 0.737
## .g 0.051 0.065 0.778 0.437 -0.077 0.178 0.058 0.058
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 5.868 1.546 3.796 0.000 2.839 8.898 5.868 0.137
## .ssmk 9.267 1.368 6.772 0.000 6.584 11.949 9.267 0.242
## .ssmc 8.176 0.574 14.242 0.000 7.051 9.301 8.176 0.491
## .ssgs 4.604 0.385 11.956 0.000 3.849 5.359 4.604 0.289
## .ssasi 6.047 0.523 11.553 0.000 5.021 7.073 6.047 0.516
## .ssei 4.379 0.345 12.692 0.000 3.703 5.055 4.379 0.416
## .ssno 0.366 0.039 9.486 0.000 0.290 0.441 0.366 0.519
## .sscs 0.018 0.112 0.163 0.871 -0.201 0.237 0.018 0.026
## .sswk 7.379 0.858 8.603 0.000 5.698 9.060 7.379 0.202
## .sspc 2.396 0.199 12.015 0.000 2.005 2.787 2.396 0.346
## electronic 0.180 0.048 3.728 0.000 0.085 0.274 1.000 1.000
## .g 0.726 0.085 8.584 0.000 0.560 0.891 0.962 0.962
# FULL SAMPLE
dgroup<- dplyr::select(d, id, starts_with("ss"), afqt, efa, educ2000, age, age2, sex, agesex, bhw, sweight, weight2000, cweight, asvabweight)
nrow(dgroup) # 2134
## [1] 2134
fit<-lm(efa ~ sex + rcs(age, 3) + sex*rcs(age, 3), data=dgroup)
summary(fit)
##
## Call:
## lm(formula = efa ~ sex + rcs(age, 3) + sex * rcs(age, 3), data = dgroup)
##
## Residuals:
## Min 1Q Median 3Q Max
## -43.274 -12.212 -0.343 12.264 33.116
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 99.5352 1.3754 72.369 <2e-16 ***
## sex -0.6783 1.9623 -0.346 0.730
## rcs(age, 3)age 0.7117 0.5861 1.214 0.225
## rcs(age, 3)age' 0.4539 0.8200 0.554 0.580
## sex:rcs(age, 3)age 0.9025 0.8380 1.077 0.282
## sex:rcs(age, 3)age' -1.2220 1.1710 -1.044 0.297
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.22 on 2128 degrees of freedom
## Multiple R-squared: 0.02776, Adjusted R-squared: 0.02548
## F-statistic: 12.15 on 5 and 2128 DF, p-value: 1.245e-11
dgroup$pred1<-fitted(fit)
original_age_min <- 14
original_age_max <- 22
mean_centered_min <- min(dgroup$age)
mean_centered_max <- max(dgroup$age)
original_age_mean <- (original_age_min + original_age_max) / 2
mean_centered_age_mean <- (mean_centered_min + mean_centered_max) / 2
age_difference <- original_age_mean - mean_centered_age_mean
xyplot(dgroup$pred1 ~ dgroup$age, data=dgroup, groups=sex, pch=19, type=c("p"), col=c('red', 'blue'), grid=TRUE, ylab="Predicted IQ", xlab="age", key=list(text=list(c("Male", "Female")), points=list(pch=c(19,19), col=c("red", "blue")), columns=2))
xyplot(dgroup$pred1 ~ dgroup$age, data=dgroup, groups=sex, pch=19, type=c("p"), col=c('red', 'blue'), grid=TRUE, ylab="Predicted IQ", xlab="Age", key=list(text=list(c("Male", "Female")), points=list(pch=c(19,19), col=c("red", "blue")), columns=2), scales=list(x=list(at=seq(mean_centered_min, mean_centered_max), labels=seq(original_age_min, original_age_max))))
describeBy(dgroup$pred1, dgroup$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1067 99.71 2.11 98.97 99.56 2.33 96.69 104.92 8.24 0.53 -0.6 0.06
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1067 97.11 2.32 97 97.23 2.84 92.4 101.01 8.61 -0.44 -0.8 0.07
describeBy(dgroup$efa, dgroup$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1067 99.71 16.73 99.84 99.77 21.42 54.86 131.19 76.34 -0.03 -1.11 0.51
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1067 97.11 13.88 96.96 96.88 15.79 54.86 127.45 72.59 0.11 -0.87 0.42
describeBy(dgroup$afqt, dgroup$sex)
##
## Descriptive statistics by group
## INDICES: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## V1 1 1067 99.2 15.74 96.1 98.28 18.93 77.91 130.02 52.11 0.38 -1.16 0.48
## --------------------------------------------------------------------------
## INDICES: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## V1 1 1067 99.12 14.77 96.71 98.19 17.46 77.91 130.02 52.11 0.43 -0.98 0.45
describeBy(dgroup$educ2000, dgroup$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 838 13.04 2.4 12 12.92 1.48 4 20 16 0.64 0.86 0.08
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 866 13.49 2.34 13 13.37 1.48 6 20 14 0.4 0.07 0.08
cor(dgroup$efa, dgroup$afqt, use="pairwise.complete.obs", method="pearson")
## [,1]
## [1,] 0.9404975
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(age, sex) %>% summarise(MEAN = survey_mean(pred1), SD = survey_sd(pred1))
## # A tibble: 18 Ă— 5
## # Groups: age [9]
## age sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -4 0 96.7 0 0
## 2 -4 1 92.4 0 0
## 3 -3 0 97.4 5.97e-16 5.98e-15
## 4 -3 1 94.0 5.83e-15 4.42e-14
## 5 -2 0 98.1 3.24e-16 3.42e-15
## 6 -2 1 95.6 0 0
## 7 -1 0 99.0 8.57e-16 9.20e-15
## 8 -1 1 97.0 6.71e-16 7.06e-15
## 9 0 0 100. 8.52e-16 9.37e-15
## 10 0 1 98.1 0 0
## 11 1 0 101. 3.57e-15 3.28e-14
## 12 1 1 98.9 0 0
## 13 2 0 102. 1.55e-14 9.69e-14
## 14 2 1 99.6 0 0
## 15 3 0 104. 0 0
## 16 3 1 100. 9.71e-16 7.05e-15
## 17 4 0 105. 1.75e-15 6.73e-15
## 18 4 1 101. 3.09e-15 1.12e-14
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(age, sex) %>% summarise(MEAN = survey_mean(efa), SD = survey_sd(efa))
## # A tibble: 18 Ă— 5
## # Groups: age [9]
## age sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -4 0 100. 1.94 15.1
## 2 -4 1 97.7 1.83 12.9
## 3 -3 0 105. 1.42 15.0
## 4 -3 1 99.2 1.20 12.1
## 5 -2 0 105. 1.53 16.9
## 6 -2 1 102. 1.20 12.8
## 7 -1 0 105. 1.24 14.8
## 8 -1 1 102. 1.13 12.6
## 9 0 0 106. 1.37 15.9
## 10 0 1 104. 1.10 13.5
## 11 1 0 107. 1.56 15.7
## 12 1 1 103. 1.37 14.7
## 13 2 0 110. 1.72 15.9
## 14 2 1 104. 1.53 13.7
## 15 3 0 109. 1.93 16.0
## 16 3 1 105. 1.59 13.4
## 17 4 0 105. 4.81 19.7
## 18 4 1 113. 1.67 9.28
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(age, sex) %>% summarise(MEAN = survey_mean(afqt), SD = survey_sd(afqt))
## # A tibble: 18 Ă— 5
## # Groups: age [9]
## age sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -4 0 104. 2.11 15.8
## 2 -4 1 104. 2.11 14.7
## 3 -3 0 106. 1.59 16.1
## 4 -3 1 105. 1.46 14.5
## 5 -2 0 106. 1.58 16.7
## 6 -2 1 105. 1.39 14.5
## 7 -1 0 104. 1.38 15.4
## 8 -1 1 103. 1.32 14.3
## 9 0 0 104. 1.43 15.7
## 10 0 1 106. 1.30 15.1
## 11 1 0 104. 1.65 15.8
## 12 1 1 104. 1.51 15.8
## 13 2 0 105. 1.80 15.6
## 14 2 1 103. 1.83 15.7
## 15 3 0 104. 2.03 15.7
## 16 3 1 104. 1.95 15.2
## 17 4 0 101. 4.42 17.3
## 18 4 1 115. 2.61 12.1
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(sex) %>% summarise(MEAN = survey_mean(pred1), SD = survey_sd(pred1))
## # A tibble: 2 Ă— 4
## sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl>
## 1 0 100. 0.0892 2.26
## 2 1 97.2 0.0934 2.40
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(sex) %>% summarise(MEAN = survey_mean(efa), SD = survey_sd(efa))
## # A tibble: 2 Ă— 4
## sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl>
## 1 0 106. 0.558 15.9
## 2 1 103. 0.472 13.4
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(sex) %>% summarise(MEAN = survey_mean(afqt), SD = survey_sd(afqt))
## # A tibble: 2 Ă— 4
## sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl>
## 1 0 105. 0.586 15.9
## 2 1 105. 0.548 15.0
dgroup %>% as_survey_design(ids = id, weights = weight2000) %>% group_by(sex) %>% summarise(MEAN = survey_mean(educ2000, na.rm = TRUE), SD = survey_sd(educ2000, na.rm = TRUE))
## # A tibble: 2 Ă— 4
## sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl>
## 1 0 13.5 0.107 2.51
## 2 1 13.9 0.100 2.42
# CORRELATED FACTOR MODEL
cf.model<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
'
cf.lv<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
verbal~~1*verbal
math~~1*math
speed~~1*speed
'
baseline<-cfa(cf.model, data=dgroup, meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 588.264 27.000 0.000 0.970 0.099 0.031 100014.979 100230.278
Mc(baseline)
## [1] 0.8767208
configural<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 393.626 54.000 0.000 0.982 0.077 0.020 98110.280 98540.878
Mc(configural)
## [1] 0.9234743
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 56 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 76
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 393.626 265.158
## Degrees of freedom 54 54
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.484
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 277.111 186.670
## 1 116.515 78.488
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs 3.173 0.306 10.383 0.000 2.574 3.771 3.173 0.583
## sswk 7.780 0.184 42.197 0.000 7.418 8.141 7.780 0.941
## sspc 3.132 0.087 36.061 0.000 2.962 3.302 3.132 0.873
## math =~
## ssar 7.318 0.139 52.742 0.000 7.046 7.590 7.318 0.954
## ssmk 6.113 0.142 43.144 0.000 5.836 6.391 6.113 0.895
## ssmc 1.125 0.220 5.118 0.000 0.694 1.556 1.125 0.202
## electronic =~
## ssgs 1.912 0.305 6.264 0.000 1.314 2.510 1.912 0.351
## ssasi 4.629 0.139 33.298 0.000 4.357 4.902 4.629 0.830
## ssmc 3.849 0.211 18.230 0.000 3.435 4.263 3.849 0.692
## ssei 4.176 0.089 46.791 0.000 4.001 4.351 4.176 0.940
## speed =~
## ssno 0.855 0.028 31.066 0.000 0.801 0.909 0.855 0.888
## sscs 0.724 0.031 23.418 0.000 0.663 0.784 0.724 0.803
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.846 0.015 57.597 0.000 0.818 0.875 0.846 0.846
## electronic 0.883 0.013 67.131 0.000 0.857 0.908 0.883 0.883
## speed 0.772 0.022 35.709 0.000 0.729 0.814 0.772 0.772
## math ~~
## electronic 0.759 0.021 36.211 0.000 0.718 0.800 0.759 0.759
## speed 0.791 0.019 41.778 0.000 0.754 0.828 0.791 0.791
## electronic ~~
## speed 0.633 0.029 21.752 0.000 0.576 0.690 0.633 0.633
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 16.396 0.190 86.372 0.000 16.024 16.768 16.396 3.013
## .sswk 25.438 0.284 89.414 0.000 24.881 25.996 25.438 3.078
## .sspc 10.375 0.126 82.229 0.000 10.127 10.622 10.375 2.892
## .ssar 18.495 0.286 64.662 0.000 17.934 19.056 18.495 2.411
## .ssmk 13.973 0.261 53.474 0.000 13.461 14.486 13.973 2.047
## .ssmc 15.637 0.201 77.759 0.000 15.243 16.031 15.637 2.811
## .ssasi 16.211 0.198 81.891 0.000 15.823 16.599 16.211 2.907
## .ssei 12.364 0.157 78.687 0.000 12.056 12.672 12.364 2.783
## .ssno 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.061
## .sscs -0.083 0.033 -2.497 0.013 -0.149 -0.018 -0.083 -0.092
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.190 0.343 15.145 0.000 4.518 5.862 5.190 0.175
## .sswk 7.801 0.790 9.872 0.000 6.252 9.349 7.801 0.114
## .sspc 3.060 0.202 15.115 0.000 2.663 3.457 3.060 0.238
## .ssar 5.286 0.767 6.889 0.000 3.782 6.791 5.286 0.090
## .ssmk 9.237 0.722 12.791 0.000 7.821 10.652 9.237 0.198
## .ssmc 8.282 0.532 15.564 0.000 7.239 9.325 8.282 0.268
## .ssasi 9.676 0.740 13.073 0.000 8.226 11.127 9.676 0.311
## .ssei 2.305 0.271 8.520 0.000 1.775 2.835 2.305 0.117
## .ssno 0.196 0.026 7.522 0.000 0.145 0.247 0.196 0.212
## .sscs 0.289 0.037 7.775 0.000 0.216 0.362 0.289 0.355
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs 0.915 0.667 1.371 0.170 -0.393 2.222 0.915 0.196
## sswk 7.240 0.167 43.365 0.000 6.913 7.567 7.240 0.943
## sspc 2.735 0.083 32.782 0.000 2.572 2.899 2.735 0.860
## math =~
## ssar 6.579 0.149 44.027 0.000 6.286 6.872 6.579 0.938
## ssmk 5.599 0.138 40.616 0.000 5.329 5.869 5.599 0.879
## ssmc 1.794 0.297 6.044 0.000 1.212 2.376 1.794 0.427
## electronic =~
## ssgs 3.345 0.659 5.080 0.000 2.054 4.636 3.345 0.718
## ssasi 2.671 0.117 22.867 0.000 2.442 2.900 2.671 0.715
## ssmc 1.383 0.282 4.901 0.000 0.830 1.936 1.383 0.329
## ssei 2.682 0.091 29.624 0.000 2.505 2.860 2.682 0.794
## speed =~
## ssno 0.835 0.027 30.390 0.000 0.781 0.888 0.835 0.885
## sscs 0.706 0.033 21.485 0.000 0.641 0.770 0.706 0.757
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.822 0.014 60.166 0.000 0.795 0.849 0.822 0.822
## electronic 0.931 0.019 48.089 0.000 0.893 0.969 0.931 0.931
## speed 0.748 0.025 29.466 0.000 0.698 0.797 0.748 0.748
## math ~~
## electronic 0.857 0.018 48.383 0.000 0.823 0.892 0.857 0.857
## speed 0.741 0.021 35.662 0.000 0.700 0.782 0.741 0.741
## electronic ~~
## speed 0.648 0.031 20.769 0.000 0.587 0.709 0.648 0.648
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 14.908 0.166 89.625 0.000 14.582 15.234 14.908 3.201
## .sswk 25.835 0.262 98.598 0.000 25.322 26.349 25.835 3.365
## .sspc 11.246 0.107 105.151 0.000 11.036 11.455 11.246 3.538
## .ssar 16.999 0.262 64.966 0.000 16.486 17.512 16.999 2.424
## .ssmk 13.732 0.240 57.183 0.000 13.262 14.203 13.732 2.157
## .ssmc 11.961 0.157 76.345 0.000 11.654 12.268 11.961 2.846
## .ssasi 10.841 0.136 79.844 0.000 10.575 11.107 10.841 2.902
## .ssei 9.562 0.123 77.895 0.000 9.322 9.803 9.562 2.831
## .ssno 0.328 0.034 9.769 0.000 0.262 0.394 0.328 0.347
## .sscs 0.432 0.033 13.004 0.000 0.367 0.497 0.432 0.463
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 3.965 0.370 10.705 0.000 3.239 4.691 3.965 0.183
## .sswk 6.516 0.801 8.134 0.000 4.946 8.086 6.516 0.111
## .sspc 2.623 0.168 15.571 0.000 2.293 2.953 2.623 0.260
## .ssar 5.909 0.749 7.889 0.000 4.441 7.378 5.909 0.120
## .ssmk 9.186 0.722 12.714 0.000 7.769 10.602 9.186 0.227
## .ssmc 8.282 0.474 17.460 0.000 7.353 9.212 8.282 0.469
## .ssasi 6.821 0.453 15.065 0.000 5.934 7.708 6.821 0.489
## .ssei 4.213 0.319 13.221 0.000 3.588 4.837 4.213 0.369
## .ssno 0.193 0.031 6.173 0.000 0.132 0.255 0.193 0.217
## .sscs 0.372 0.041 9.041 0.000 0.291 0.453 0.372 0.428
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
modificationIndices(configural, sort=T, maximum.number=30)
## lhs op rhs block group level mi epc sepc.lv sepc.all sepc.nox
## 101 math =~ sswk 1 1 1 78.950 -3.071 -3.071 -0.371 -0.371
## 156 ssmc ~~ ssasi 1 1 1 67.709 2.830 2.830 0.316 0.316
## 97 verbal =~ ssei 1 1 1 64.385 2.512 2.512 0.565 0.565
## 152 ssmk ~~ ssasi 1 1 1 51.909 -2.520 -2.520 -0.267 -0.267
## 102 math =~ sspc 1 1 1 38.993 0.926 0.926 0.258 0.258
## 115 speed =~ sspc 1 1 1 32.040 0.691 0.691 0.193 0.193
## 122 ssgs ~~ sspc 1 1 1 31.245 -0.921 -0.921 -0.231 -0.231
## 178 math =~ ssno 2 2 1 26.582 0.460 0.460 0.487 0.487
## 179 math =~ sscs 2 2 1 26.582 -0.389 -0.389 -0.417 -0.417
## 103 math =~ ssasi 1 1 1 24.568 -0.998 -0.998 -0.179 -0.179
## 172 verbal =~ sscs 2 2 1 24.263 0.357 0.357 0.383 0.383
## 171 verbal =~ ssno 2 2 1 24.263 -0.422 -0.422 -0.447 -0.447
## 157 ssmc ~~ ssei 1 1 1 24.101 -1.389 -1.389 -0.318 -0.318
## 96 verbal =~ ssasi 1 1 1 22.449 -1.656 -1.656 -0.297 -0.297
## 124 ssgs ~~ ssmk 1 1 1 21.950 1.227 1.227 0.177 0.177
## 133 sswk ~~ ssmc 1 1 1 19.278 -1.499 -1.499 -0.187 -0.187
## 120 speed =~ ssei 1 1 1 19.119 0.566 0.566 0.127 0.127
## 114 speed =~ sswk 1 1 1 18.882 -1.230 -1.230 -0.149 -0.149
## 135 sswk ~~ ssei 1 1 1 18.435 1.083 1.083 0.255 0.255
## 188 speed =~ sspc 2 2 1 18.310 0.486 0.486 0.153 0.153
## 217 sspc ~~ sscs 2 2 1 17.669 0.159 0.159 0.161 0.161
## 95 verbal =~ ssmc 1 1 1 17.369 -1.510 -1.510 -0.271 -0.271
## 187 speed =~ sswk 2 2 1 16.196 -1.202 -1.202 -0.157 -0.157
## 229 ssmc ~~ ssasi 2 2 1 15.688 1.021 1.021 0.136 0.136
## 107 electronic =~ sswk 1 1 1 15.579 1.976 1.976 0.239 0.239
## 108 electronic =~ sspc 1 1 1 15.579 -0.795 -0.795 -0.222 -0.222
## 100 math =~ ssgs 1 1 1 15.383 0.717 0.717 0.132 0.132
## 121 ssgs ~~ sswk 1 1 1 14.796 1.463 1.463 0.230 0.230
## 131 sswk ~~ ssar 1 1 1 13.261 -1.508 -1.508 -0.235 -0.235
## 158 ssmc ~~ ssno 1 1 1 12.040 -0.194 -0.194 -0.152 -0.152
metric<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 448.741 62.000 0.000 0.980 0.076 0.026 98149.396 98534.667
Mc(metric)
## [1] 0.9133312
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 59 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 80
## Number of equality constraints 12
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 448.741 305.642
## Degrees of freedom 62 62
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.468
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 284.896 194.045
## 1 163.846 111.597
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 3.032 0.213 14.233 0.000 2.614 3.449 3.032 0.550
## sswk (.p2.) 7.823 0.178 44.061 0.000 7.475 8.171 7.823 0.944
## sspc (.p3.) 3.059 0.079 38.754 0.000 2.904 3.214 3.059 0.867
## math =~
## ssar (.p4.) 7.305 0.136 53.672 0.000 7.038 7.572 7.305 0.953
## ssmk (.p5.) 6.146 0.128 48.156 0.000 5.896 6.396 6.146 0.897
## ssmc (.p6.) 1.201 0.174 6.894 0.000 0.860 1.543 1.201 0.219
## electronic =~
## ssgs (.p7.) 2.145 0.239 8.987 0.000 1.677 2.612 2.145 0.389
## ssasi (.p8.) 4.531 0.132 34.291 0.000 4.272 4.790 4.531 0.822
## ssmc (.p9.) 3.659 0.193 18.943 0.000 3.281 4.038 3.659 0.668
## ssei (.10.) 4.211 0.087 48.280 0.000 4.040 4.382 4.211 0.943
## speed =~
## ssno (.11.) 0.856 0.026 32.707 0.000 0.805 0.907 0.856 0.889
## sscs (.12.) 0.722 0.027 26.577 0.000 0.669 0.775 0.722 0.802
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.845 0.015 57.772 0.000 0.816 0.874 0.845 0.845
## electronic 0.881 0.013 66.532 0.000 0.855 0.907 0.881 0.881
## speed 0.771 0.022 35.775 0.000 0.728 0.813 0.771 0.771
## math ~~
## electronic 0.760 0.021 37.014 0.000 0.720 0.801 0.760 0.760
## speed 0.791 0.019 41.958 0.000 0.754 0.828 0.791 0.791
## electronic ~~
## speed 0.633 0.029 22.023 0.000 0.577 0.689 0.633 0.633
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 16.396 0.190 86.372 0.000 16.024 16.768 16.396 2.973
## .sswk 25.438 0.284 89.414 0.000 24.881 25.996 25.438 3.068
## .sspc 10.375 0.126 82.229 0.000 10.127 10.622 10.375 2.940
## .ssar 18.495 0.286 64.662 0.000 17.934 19.056 18.495 2.413
## .ssmk 13.973 0.261 53.474 0.000 13.461 14.486 13.973 2.039
## .ssmc 15.637 0.201 77.759 0.000 15.243 16.031 15.637 2.856
## .ssasi 16.211 0.198 81.891 0.000 15.823 16.599 16.211 2.941
## .ssei 12.364 0.157 78.687 0.000 12.056 12.672 12.364 2.768
## .ssno 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.061
## .sscs -0.083 0.033 -2.497 0.013 -0.149 -0.018 -0.083 -0.093
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.177 0.334 15.488 0.000 4.522 5.833 5.177 0.170
## .sswk 7.539 0.781 9.654 0.000 6.009 9.070 7.539 0.110
## .sspc 3.093 0.203 15.250 0.000 2.695 3.490 3.093 0.248
## .ssar 5.383 0.735 7.325 0.000 3.943 6.824 5.383 0.092
## .ssmk 9.178 0.687 13.368 0.000 7.832 10.523 9.178 0.195
## .ssmc 8.451 0.531 15.925 0.000 7.411 9.491 8.451 0.282
## .ssasi 9.847 0.738 13.337 0.000 8.400 11.294 9.847 0.324
## .ssei 2.219 0.264 8.411 0.000 1.702 2.737 2.219 0.111
## .ssno 0.195 0.024 7.981 0.000 0.147 0.243 0.195 0.210
## .sscs 0.289 0.035 8.199 0.000 0.220 0.359 0.289 0.357
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 3.032 0.213 14.233 0.000 2.614 3.449 2.779 0.607
## sswk (.p2.) 7.823 0.178 44.061 0.000 7.475 8.171 7.169 0.937
## sspc (.p3.) 3.059 0.079 38.754 0.000 2.904 3.214 2.803 0.866
## math =~
## ssar (.p4.) 7.305 0.136 53.672 0.000 7.038 7.572 6.605 0.941
## ssmk (.p5.) 6.146 0.128 48.156 0.000 5.896 6.396 5.557 0.877
## ssmc (.p6.) 1.201 0.174 6.894 0.000 0.860 1.543 1.086 0.252
## electronic =~
## ssgs (.p7.) 2.145 0.239 8.987 0.000 1.677 2.612 1.340 0.293
## ssasi (.p8.) 4.531 0.132 34.291 0.000 4.272 4.790 2.832 0.745
## ssmc (.p9.) 3.659 0.193 18.943 0.000 3.281 4.038 2.287 0.530
## ssei (.10.) 4.211 0.087 48.280 0.000 4.040 4.382 2.632 0.794
## speed =~
## ssno (.11.) 0.856 0.026 32.707 0.000 0.805 0.907 0.837 0.887
## sscs (.12.) 0.722 0.027 26.577 0.000 0.669 0.775 0.706 0.755
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.689 0.038 18.086 0.000 0.614 0.763 0.831 0.831
## electronic 0.522 0.030 17.290 0.000 0.463 0.581 0.911 0.911
## speed 0.664 0.051 12.974 0.000 0.564 0.765 0.742 0.742
## math ~~
## electronic 0.479 0.029 16.725 0.000 0.423 0.535 0.847 0.847
## speed 0.654 0.043 15.163 0.000 0.570 0.739 0.740 0.740
## electronic ~~
## speed 0.387 0.032 12.224 0.000 0.325 0.449 0.634 0.634
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 14.908 0.166 89.625 0.000 14.582 15.234 14.908 3.258
## .sswk 25.835 0.262 98.598 0.000 25.322 26.349 25.835 3.377
## .sspc 11.246 0.107 105.151 0.000 11.036 11.455 11.246 3.475
## .ssar 16.999 0.262 64.966 0.000 16.486 17.512 16.999 2.421
## .ssmk 13.732 0.240 57.183 0.000 13.262 14.203 13.732 2.167
## .ssmc 11.961 0.157 76.345 0.000 11.654 12.268 11.961 2.771
## .ssasi 10.841 0.136 79.844 0.000 10.575 11.107 10.841 2.851
## .ssei 9.562 0.123 77.895 0.000 9.322 9.803 9.562 2.883
## .ssno 0.328 0.034 9.769 0.000 0.262 0.394 0.328 0.348
## .sscs 0.432 0.033 13.004 0.000 0.367 0.497 0.432 0.462
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.630 0.301 15.393 0.000 4.040 5.219 4.630 0.221
## .sswk 7.133 0.757 9.426 0.000 5.650 8.616 7.133 0.122
## .sspc 2.616 0.165 15.870 0.000 2.293 2.939 2.616 0.250
## .ssar 5.668 0.729 7.776 0.000 4.239 7.096 5.668 0.115
## .ssmk 9.293 0.701 13.253 0.000 7.919 10.667 9.293 0.231
## .ssmc 8.016 0.464 17.269 0.000 7.106 8.926 8.016 0.430
## .ssasi 6.438 0.424 15.188 0.000 5.607 7.269 6.438 0.445
## .ssei 4.074 0.296 13.747 0.000 3.493 4.655 4.074 0.370
## .ssno 0.189 0.028 6.649 0.000 0.133 0.245 0.189 0.213
## .sscs 0.375 0.038 9.781 0.000 0.300 0.451 0.375 0.430
## verbal 0.840 0.053 15.802 0.000 0.736 0.944 1.000 1.000
## math 0.818 0.045 18.172 0.000 0.729 0.906 1.000 1.000
## electronic 0.391 0.028 13.954 0.000 0.336 0.446 1.000 1.000
## speed 0.955 0.078 12.195 0.000 0.801 1.108 1.000 1.000
scalar<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 832.653 68.000 0.000 0.960 0.103 0.049 98521.307 98872.584
Mc(scalar)
## [1] 0.8359023
summary(scalar, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 120 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 84
## Number of equality constraints 22
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 832.653 569.629
## Degrees of freedom 68 68
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.462
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 464.581 317.826
## 1 368.072 251.803
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 3.047 0.123 24.694 0.000 2.805 3.289 3.047 0.552
## sswk (.p2.) 7.784 0.175 44.388 0.000 7.441 8.128 7.784 0.941
## sspc (.p3.) 3.072 0.081 37.705 0.000 2.912 3.231 3.072 0.865
## math =~
## ssar (.p4.) 7.323 0.137 53.573 0.000 7.055 7.591 7.323 0.954
## ssmk (.p5.) 6.098 0.129 47.325 0.000 5.846 6.351 6.098 0.893
## ssmc (.p6.) 1.037 0.161 6.451 0.000 0.722 1.352 1.037 0.187
## electronic =~
## ssgs (.p7.) 2.141 0.131 16.313 0.000 1.884 2.399 2.141 0.388
## ssasi (.p8.) 4.965 0.115 43.232 0.000 4.740 5.191 4.965 0.844
## ssmc (.p9.) 3.917 0.168 23.260 0.000 3.587 4.247 3.917 0.707
## ssei (.10.) 3.999 0.091 44.034 0.000 3.821 4.177 3.999 0.923
## speed =~
## ssno (.11.) 0.829 0.028 30.109 0.000 0.775 0.883 0.829 0.870
## sscs (.12.) 0.749 0.026 28.398 0.000 0.697 0.800 0.749 0.814
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.846 0.015 58.136 0.000 0.817 0.874 0.846 0.846
## electronic 0.883 0.014 64.792 0.000 0.856 0.910 0.883 0.883
## speed 0.778 0.021 36.635 0.000 0.736 0.820 0.778 0.778
## math ~~
## electronic 0.764 0.020 37.253 0.000 0.723 0.804 0.764 0.764
## speed 0.796 0.019 42.245 0.000 0.759 0.833 0.796 0.796
## electronic ~~
## speed 0.639 0.029 22.089 0.000 0.583 0.696 0.639 0.639
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 16.397 0.188 87.263 0.000 16.029 16.765 16.397 2.969
## .sswk (.34.) 25.175 0.289 87.204 0.000 24.609 25.741 25.175 3.043
## .sspc (.35.) 10.643 0.117 91.033 0.000 10.414 10.873 10.643 2.997
## .ssar (.36.) 18.336 0.290 63.161 0.000 17.767 18.905 18.336 2.388
## .ssmk (.37.) 14.324 0.251 56.998 0.000 13.832 14.817 14.324 2.098
## .ssmc (.38.) 15.575 0.200 77.784 0.000 15.183 15.967 15.575 2.811
## .ssasi (.39.) 15.579 0.213 73.161 0.000 15.161 15.996 15.579 2.648
## .ssei (.40.) 12.605 0.150 83.964 0.000 12.311 12.899 12.605 2.908
## .ssno (.41.) 0.007 0.036 0.208 0.835 -0.062 0.077 0.007 0.008
## .sscs (.42.) -0.009 0.033 -0.274 0.784 -0.073 0.055 -0.009 -0.010
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.103 0.332 15.360 0.000 4.452 5.754 5.103 0.167
## .sswk 7.867 0.802 9.805 0.000 6.295 9.440 7.867 0.115
## .sspc 3.177 0.215 14.809 0.000 2.757 3.597 3.177 0.252
## .ssar 5.323 0.764 6.967 0.000 3.825 6.820 5.323 0.090
## .ssmk 9.446 0.721 13.109 0.000 8.033 10.858 9.446 0.203
## .ssmc 8.071 0.527 15.304 0.000 7.037 9.104 8.071 0.263
## .ssasi 9.950 0.805 12.356 0.000 8.372 11.528 9.950 0.288
## .ssei 2.793 0.270 10.328 0.000 2.263 3.323 2.793 0.149
## .ssno 0.220 0.025 8.861 0.000 0.171 0.269 0.220 0.242
## .sscs 0.286 0.037 7.640 0.000 0.213 0.360 0.286 0.338
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 3.047 0.123 24.694 0.000 2.805 3.289 2.796 0.612
## sswk (.p2.) 7.784 0.175 44.388 0.000 7.441 8.128 7.143 0.934
## sspc (.p3.) 3.072 0.081 37.705 0.000 2.912 3.231 2.819 0.865
## math =~
## ssar (.p4.) 7.323 0.137 53.573 0.000 7.055 7.591 6.626 0.941
## ssmk (.p5.) 6.098 0.129 47.325 0.000 5.846 6.351 5.518 0.872
## ssmc (.p6.) 1.037 0.161 6.451 0.000 0.722 1.352 0.938 0.219
## electronic =~
## ssgs (.p7.) 2.141 0.131 16.313 0.000 1.884 2.399 1.302 0.285
## ssasi (.p8.) 4.965 0.115 43.232 0.000 4.740 5.191 3.018 0.759
## ssmc (.p9.) 3.917 0.168 23.260 0.000 3.587 4.247 2.381 0.555
## ssei (.10.) 3.999 0.091 44.034 0.000 3.821 4.177 2.431 0.751
## speed =~
## ssno (.11.) 0.829 0.028 30.109 0.000 0.775 0.883 0.810 0.866
## sscs (.12.) 0.749 0.026 28.398 0.000 0.697 0.800 0.731 0.766
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.691 0.038 18.061 0.000 0.616 0.766 0.833 0.833
## electronic 0.512 0.029 17.642 0.000 0.455 0.569 0.919 0.919
## speed 0.675 0.052 13.026 0.000 0.574 0.777 0.754 0.754
## math ~~
## electronic 0.472 0.028 17.003 0.000 0.417 0.526 0.858 0.858
## speed 0.659 0.044 14.966 0.000 0.573 0.745 0.746 0.746
## electronic ~~
## speed 0.385 0.031 12.267 0.000 0.324 0.447 0.649 0.649
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 16.397 0.188 87.263 0.000 16.029 16.765 16.397 3.591
## .sswk (.34.) 25.175 0.289 87.204 0.000 24.609 25.741 25.175 3.293
## .sspc (.35.) 10.643 0.117 91.033 0.000 10.414 10.873 10.643 3.265
## .ssar (.36.) 18.336 0.290 63.161 0.000 17.767 18.905 18.336 2.605
## .ssmk (.37.) 14.324 0.251 56.998 0.000 13.832 14.817 14.324 2.263
## .ssmc (.38.) 15.575 0.200 77.784 0.000 15.183 15.967 15.575 3.632
## .ssasi (.39.) 15.579 0.213 73.161 0.000 15.161 15.996 15.579 3.920
## .ssei (.40.) 12.605 0.150 83.964 0.000 12.311 12.899 12.605 3.896
## .ssno (.41.) 0.007 0.036 0.208 0.835 -0.062 0.077 0.007 0.008
## .sscs (.42.) -0.009 0.033 -0.274 0.784 -0.073 0.055 -0.009 -0.009
## verbal 0.118 0.048 2.456 0.014 0.024 0.213 0.129 0.129
## math -0.158 0.053 -2.998 0.003 -0.262 -0.055 -0.175 -0.175
## elctrnc -0.864 0.051 -17.025 0.000 -0.964 -0.765 -1.422 -1.422
## speed 0.452 0.061 7.453 0.000 0.333 0.570 0.462 0.462
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.646 0.303 15.329 0.000 4.052 5.240 4.646 0.223
## .sswk 7.428 0.769 9.663 0.000 5.921 8.934 7.428 0.127
## .sspc 2.682 0.174 15.458 0.000 2.342 3.022 2.682 0.252
## .ssar 5.634 0.749 7.519 0.000 4.166 7.103 5.634 0.114
## .ssmk 9.601 0.712 13.485 0.000 8.206 10.997 9.601 0.240
## .ssmc 8.010 0.466 17.200 0.000 7.097 8.922 8.010 0.435
## .ssasi 6.684 0.462 14.478 0.000 5.779 7.588 6.684 0.423
## .ssei 4.557 0.321 14.214 0.000 3.929 5.185 4.557 0.435
## .ssno 0.219 0.029 7.594 0.000 0.163 0.276 0.219 0.250
## .sscs 0.376 0.041 9.148 0.000 0.296 0.457 0.376 0.413
## verbal 0.842 0.053 15.864 0.000 0.738 0.946 1.000 1.000
## math 0.819 0.045 18.156 0.000 0.730 0.907 1.000 1.000
## electronic 0.369 0.026 14.100 0.000 0.318 0.421 1.000 1.000
## speed 0.954 0.081 11.808 0.000 0.796 1.112 1.000 1.000
lavTestScore(scalar, release = 13:22)
## 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 371.935 10 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p33. == .p79. 0.002 1 0.968
## 2 .p34. == .p80. 61.151 1 0.000
## 3 .p35. == .p81. 65.305 1 0.000
## 4 .p36. == .p82. 38.297 1 0.000
## 5 .p37. == .p83. 41.527 1 0.000
## 6 .p38. == .p84. 2.340 1 0.126
## 7 .p39. == .p85. 148.996 1 0.000
## 8 .p40. == .p86. 157.655 1 0.000
## 9 .p41. == .p87. 83.836 1 0.000
## 10 .p42. == .p88. 83.836 1 0.000
scalar2<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("sswk~1", "ssei~1", "sscs~1"))
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 503.099 65.000 0.000 0.977 0.079 0.029 98197.753 98566.027
Mc(scalar2)
## [1] 0.9024017
summary(scalar2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 100 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 84
## Number of equality constraints 19
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 503.099 343.396
## Degrees of freedom 65 65
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.465
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 317.584 216.771
## 1 185.514 126.625
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 3.074 0.115 26.666 0.000 2.848 3.300 3.074 0.557
## sswk (.p2.) 7.822 0.177 44.091 0.000 7.474 8.169 7.822 0.943
## sspc (.p3.) 3.059 0.079 38.757 0.000 2.904 3.214 3.059 0.867
## math =~
## ssar (.p4.) 7.322 0.136 53.725 0.000 7.055 7.589 7.322 0.953
## ssmk (.p5.) 6.110 0.129 47.519 0.000 5.858 6.362 6.110 0.894
## ssmc (.p6.) 1.474 0.152 9.691 0.000 1.176 1.772 1.474 0.274
## electronic =~
## ssgs (.p7.) 2.100 0.122 17.248 0.000 1.861 2.338 2.100 0.381
## ssasi (.p8.) 4.616 0.126 36.619 0.000 4.369 4.863 4.616 0.827
## ssmc (.p9.) 3.286 0.166 19.760 0.000 2.960 3.612 3.286 0.610
## ssei (.10.) 4.226 0.086 49.134 0.000 4.058 4.395 4.226 0.946
## speed =~
## ssno (.11.) 0.856 0.026 32.700 0.000 0.805 0.907 0.856 0.888
## sscs (.12.) 0.722 0.027 26.576 0.000 0.669 0.775 0.722 0.802
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.847 0.014 58.524 0.000 0.818 0.875 0.847 0.847
## electronic 0.880 0.013 66.098 0.000 0.853 0.906 0.880 0.880
## speed 0.771 0.022 35.820 0.000 0.729 0.813 0.771 0.771
## math ~~
## electronic 0.758 0.020 37.530 0.000 0.719 0.798 0.758 0.758
## speed 0.792 0.019 41.934 0.000 0.755 0.829 0.792 0.792
## electronic ~~
## speed 0.631 0.029 21.919 0.000 0.574 0.687 0.631 0.631
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 16.396 0.189 86.927 0.000 16.027 16.766 16.396 2.974
## .sswk 25.438 0.284 89.414 0.000 24.881 25.996 25.438 3.068
## .sspc (.35.) 10.375 0.125 82.937 0.000 10.129 10.620 10.375 2.940
## .ssar (.36.) 18.317 0.291 63.022 0.000 17.747 18.886 18.317 2.383
## .ssmk (.37.) 14.309 0.251 56.901 0.000 13.816 14.802 14.309 2.093
## .ssmc (.38.) 15.763 0.196 80.490 0.000 15.380 16.147 15.763 2.925
## .ssasi (.39.) 16.108 0.198 81.329 0.000 15.720 16.497 16.108 2.885
## .ssei 12.364 0.157 78.688 0.000 12.056 12.672 12.364 2.767
## .ssno (.41.) 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.061
## .sscs -0.083 0.033 -2.497 0.013 -0.149 -0.018 -0.083 -0.093
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.192 0.335 15.498 0.000 4.535 5.848 5.192 0.171
## .sswk 7.559 0.770 9.815 0.000 6.050 9.069 7.559 0.110
## .sspc 3.095 0.202 15.303 0.000 2.699 3.492 3.095 0.249
## .ssar 5.448 0.754 7.225 0.000 3.970 6.926 5.448 0.092
## .ssmk 9.404 0.712 13.204 0.000 8.008 10.800 9.404 0.201
## .ssmc 8.720 0.534 16.345 0.000 7.675 9.766 8.720 0.300
## .ssasi 9.868 0.745 13.249 0.000 8.408 11.328 9.868 0.317
## .ssei 2.110 0.253 8.329 0.000 1.614 2.607 2.110 0.106
## .ssno 0.196 0.024 7.997 0.000 0.148 0.244 0.196 0.211
## .sscs 0.289 0.035 8.192 0.000 0.220 0.358 0.289 0.357
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 3.074 0.115 26.666 0.000 2.848 3.300 2.816 0.615
## sswk (.p2.) 7.822 0.177 44.091 0.000 7.474 8.169 7.166 0.937
## sspc (.p3.) 3.059 0.079 38.757 0.000 2.904 3.214 2.802 0.866
## math =~
## ssar (.p4.) 7.322 0.136 53.725 0.000 7.055 7.589 6.612 0.940
## ssmk (.p5.) 6.110 0.129 47.519 0.000 5.858 6.362 5.518 0.873
## ssmc (.p6.) 1.474 0.152 9.691 0.000 1.176 1.772 1.331 0.309
## electronic =~
## ssgs (.p7.) 2.100 0.122 17.248 0.000 1.861 2.338 1.306 0.285
## ssasi (.p8.) 4.616 0.126 36.619 0.000 4.369 4.863 2.870 0.750
## ssmc (.p9.) 3.286 0.166 19.760 0.000 2.960 3.612 2.043 0.474
## ssei (.10.) 4.226 0.086 49.134 0.000 4.058 4.395 2.628 0.794
## speed =~
## ssno (.11.) 0.856 0.026 32.700 0.000 0.805 0.907 0.836 0.887
## sscs (.12.) 0.722 0.027 26.576 0.000 0.669 0.775 0.706 0.755
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.689 0.038 18.073 0.000 0.614 0.763 0.832 0.832
## electronic 0.519 0.029 17.609 0.000 0.461 0.577 0.911 0.911
## speed 0.664 0.051 13.032 0.000 0.564 0.764 0.742 0.742
## math ~~
## electronic 0.473 0.028 17.186 0.000 0.419 0.527 0.842 0.842
## speed 0.654 0.043 15.139 0.000 0.569 0.738 0.741 0.741
## electronic ~~
## speed 0.384 0.031 12.265 0.000 0.322 0.445 0.631 0.631
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 16.396 0.189 86.927 0.000 16.027 16.766 16.396 3.582
## .sswk 23.608 0.359 65.775 0.000 22.904 24.311 23.608 3.086
## .sspc (.35.) 10.375 0.125 82.937 0.000 10.129 10.620 10.375 3.206
## .ssar (.36.) 18.317 0.291 63.022 0.000 17.747 18.886 18.317 2.604
## .ssmk (.37.) 14.309 0.251 56.901 0.000 13.816 14.802 14.309 2.263
## .ssmc (.38.) 15.763 0.196 80.490 0.000 15.380 16.147 15.763 3.657
## .ssasi (.39.) 16.108 0.198 81.329 0.000 15.720 16.497 16.108 4.210
## .ssei 14.320 0.244 58.789 0.000 13.843 14.798 14.320 4.327
## .ssno (.41.) 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.063
## .sscs 0.205 0.040 5.121 0.000 0.127 0.284 0.205 0.219
## verbal 0.285 0.052 5.500 0.000 0.183 0.386 0.311 0.311
## math -0.153 0.053 -2.892 0.004 -0.257 -0.049 -0.169 -0.169
## elctrnc -1.126 0.061 -18.322 0.000 -1.246 -1.005 -1.811 -1.811
## speed 0.314 0.057 5.524 0.000 0.203 0.426 0.322 0.322
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.625 0.301 15.378 0.000 4.035 5.214 4.625 0.221
## .sswk 7.172 0.741 9.672 0.000 5.718 8.625 7.172 0.123
## .sspc 2.620 0.165 15.893 0.000 2.297 2.943 2.620 0.250
## .ssar 5.743 0.740 7.757 0.000 4.292 7.194 5.743 0.116
## .ssmk 9.526 0.708 13.462 0.000 8.139 10.913 9.526 0.238
## .ssmc 8.055 0.464 17.366 0.000 7.146 8.964 8.055 0.433
## .ssasi 6.402 0.425 15.049 0.000 5.568 7.236 6.402 0.437
## .ssei 4.049 0.299 13.563 0.000 3.464 4.634 4.049 0.370
## .ssno 0.189 0.028 6.659 0.000 0.134 0.245 0.189 0.213
## .sscs 0.375 0.038 9.763 0.000 0.300 0.451 0.375 0.430
## verbal 0.839 0.053 15.946 0.000 0.736 0.942 1.000 1.000
## math 0.816 0.045 18.161 0.000 0.728 0.904 1.000 1.000
## electronic 0.387 0.027 14.324 0.000 0.334 0.440 1.000 1.000
## speed 0.955 0.078 12.191 0.000 0.801 1.108 1.000 1.000
strict<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("sswk~1", "ssei~1", "sscs~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 592.684 75.000 0.000 0.973 0.080 0.036 98267.338 98578.954
Mc(strict)
## [1] 0.885723
cf.cov<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("sswk~1", "ssei~1", "sscs~1"))
fitMeasures(cf.cov, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 612.730 71.000 0.000 0.971 0.085 0.120 98295.385 98629.664
Mc(cf.cov)
## [1] 0.8807443
summary(cf.cov, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 100 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 84
## Number of equality constraints 25
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 612.730 421.253
## Degrees of freedom 71 71
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.455
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 381.839 262.515
## 1 230.892 158.738
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.869 0.107 26.752 0.000 2.659 3.080 2.869 0.569
## sswk (.p2.) 7.341 0.134 54.588 0.000 7.078 7.605 7.341 0.934
## sspc (.p3.) 2.880 0.062 46.162 0.000 2.758 3.002 2.880 0.856
## math =~
## ssar (.p4.) 7.061 0.114 62.148 0.000 6.839 7.284 7.061 0.949
## ssmk (.p5.) 5.896 0.114 51.853 0.000 5.673 6.119 5.896 0.888
## ssmc (.p6.) 1.433 0.146 9.819 0.000 1.147 1.719 1.433 0.289
## electronic =~
## ssgs (.p7.) 1.843 0.102 17.986 0.000 1.642 2.043 1.843 0.365
## ssasi (.p8.) 3.977 0.097 41.146 0.000 3.787 4.166 3.977 0.784
## ssmc (.p9.) 2.833 0.139 20.365 0.000 2.561 3.106 2.833 0.572
## ssei (.10.) 3.715 0.063 59.382 0.000 3.592 3.837 3.715 0.932
## speed =~
## ssno (.11.) 0.839 0.021 39.065 0.000 0.797 0.881 0.839 0.884
## sscs (.12.) 0.704 0.024 29.229 0.000 0.657 0.751 0.704 0.795
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.27.) 0.848 0.013 65.536 0.000 0.823 0.873 0.848 0.848
## elctrnc (.28.) 0.815 0.017 47.251 0.000 0.781 0.849 0.815 0.815
## speed (.29.) 0.776 0.019 41.753 0.000 0.740 0.813 0.776 0.776
## math ~~
## elctrnc (.30.) 0.699 0.019 37.385 0.000 0.663 0.736 0.699 0.699
## speed (.31.) 0.768 0.018 43.566 0.000 0.734 0.803 0.768 0.768
## electronic ~~
## speed (.32.) 0.563 0.023 24.976 0.000 0.519 0.607 0.563 0.563
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 16.411 0.188 87.334 0.000 16.043 16.779 16.411 3.253
## .sswk 25.438 0.284 89.414 0.000 24.881 25.996 25.438 3.235
## .sspc (.35.) 10.366 0.126 82.546 0.000 10.120 10.612 10.366 3.082
## .ssar (.36.) 18.316 0.291 63.040 0.000 17.746 18.885 18.316 2.462
## .ssmk (.37.) 14.308 0.251 56.895 0.000 13.815 14.801 14.308 2.154
## .ssmc (.38.) 15.760 0.196 80.269 0.000 15.375 16.144 15.760 3.182
## .ssasi (.39.) 16.099 0.199 81.028 0.000 15.710 16.488 16.099 3.175
## .ssei 12.364 0.157 78.687 0.000 12.056 12.672 12.364 3.104
## .ssno (.41.) 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.062
## .sscs -0.083 0.033 -2.497 0.013 -0.149 -0.018 -0.083 -0.094
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.209 0.335 15.551 0.000 4.552 5.865 5.209 0.205
## .sswk 7.946 0.783 10.145 0.000 6.411 9.482 7.946 0.128
## .sspc 3.018 0.197 15.306 0.000 2.632 3.405 3.018 0.267
## .ssar 5.489 0.748 7.337 0.000 4.022 6.955 5.489 0.099
## .ssmk 9.369 0.713 13.144 0.000 7.972 10.766 9.369 0.212
## .ssmc 8.779 0.539 16.301 0.000 7.723 9.834 8.779 0.358
## .ssasi 9.889 0.750 13.191 0.000 8.420 11.359 9.889 0.385
## .ssei 2.070 0.273 7.578 0.000 1.535 2.606 2.070 0.130
## .ssno 0.196 0.025 7.969 0.000 0.148 0.244 0.196 0.218
## .sscs 0.289 0.035 8.205 0.000 0.220 0.358 0.289 0.368
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.869 0.107 26.752 0.000 2.659 3.080 2.986 0.604
## sswk (.p2.) 7.341 0.134 54.588 0.000 7.078 7.605 7.639 0.944
## sspc (.p3.) 2.880 0.062 46.162 0.000 2.758 3.002 2.997 0.879
## math =~
## ssar (.p4.) 7.061 0.114 62.148 0.000 6.839 7.284 6.911 0.945
## ssmk (.p5.) 5.896 0.114 51.853 0.000 5.673 6.119 5.771 0.882
## ssmc (.p6.) 1.433 0.146 9.819 0.000 1.147 1.719 1.402 0.303
## electronic =~
## ssgs (.p7.) 1.843 0.102 17.986 0.000 1.642 2.043 1.542 0.312
## ssasi (.p8.) 3.977 0.097 41.146 0.000 3.787 4.166 3.328 0.794
## ssmc (.p9.) 2.833 0.139 20.365 0.000 2.561 3.106 2.371 0.513
## ssei (.10.) 3.715 0.063 59.382 0.000 3.592 3.837 3.108 0.841
## speed =~
## ssno (.11.) 0.839 0.021 39.065 0.000 0.797 0.881 0.860 0.897
## sscs (.12.) 0.704 0.024 29.229 0.000 0.657 0.751 0.722 0.760
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.27.) 0.848 0.013 65.536 0.000 0.823 0.873 0.833 0.833
## elctrnc (.28.) 0.815 0.017 47.251 0.000 0.781 0.849 0.936 0.936
## speed (.29.) 0.776 0.019 41.753 0.000 0.740 0.813 0.728 0.728
## math ~~
## elctrnc (.30.) 0.699 0.019 37.385 0.000 0.663 0.736 0.854 0.854
## speed (.31.) 0.768 0.018 43.566 0.000 0.734 0.803 0.766 0.766
## electronic ~~
## speed (.32.) 0.563 0.023 24.976 0.000 0.519 0.607 0.657 0.657
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 16.411 0.188 87.334 0.000 16.043 16.779 16.411 3.318
## .sswk 23.573 0.359 65.600 0.000 22.869 24.278 23.573 2.912
## .sspc (.35.) 10.366 0.126 82.546 0.000 10.120 10.612 10.366 3.040
## .ssar (.36.) 18.316 0.291 63.040 0.000 17.746 18.885 18.316 2.504
## .ssmk (.37.) 14.308 0.251 56.895 0.000 13.815 14.801 14.308 2.186
## .ssmc (.38.) 15.760 0.196 80.269 0.000 15.375 16.144 15.760 3.407
## .ssasi (.39.) 16.099 0.199 81.028 0.000 15.710 16.488 16.099 3.842
## .ssei 14.402 0.254 56.754 0.000 13.904 14.899 14.402 3.898
## .ssno (.41.) 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.061
## .sscs 0.206 0.040 5.161 0.000 0.128 0.285 0.206 0.217
## verbal 0.308 0.057 5.441 0.000 0.197 0.419 0.296 0.296
## math -0.158 0.055 -2.863 0.004 -0.267 -0.050 -0.162 -0.162
## elctrnc -1.303 0.070 -18.707 0.000 -1.439 -1.166 -1.557 -1.557
## speed 0.321 0.059 5.454 0.000 0.205 0.436 0.313 0.313
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.557 0.299 15.240 0.000 3.971 5.143 4.557 0.186
## .sswk 7.179 0.749 9.585 0.000 5.711 8.647 7.179 0.110
## .sspc 2.647 0.166 15.908 0.000 2.321 2.973 2.647 0.228
## .ssar 5.756 0.751 7.666 0.000 4.285 7.228 5.756 0.108
## .ssmk 9.534 0.707 13.494 0.000 8.149 10.919 9.534 0.223
## .ssmc 8.126 0.469 17.341 0.000 7.208 9.045 8.126 0.380
## .ssasi 6.482 0.430 15.068 0.000 5.639 7.325 6.482 0.369
## .ssei 3.987 0.297 13.405 0.000 3.404 4.570 3.987 0.292
## .ssno 0.180 0.028 6.396 0.000 0.125 0.236 0.180 0.196
## .sscs 0.381 0.038 9.978 0.000 0.307 0.456 0.381 0.423
## verbal 1.083 0.028 38.263 0.000 1.027 1.138 1.000 1.000
## math 0.958 0.026 36.529 0.000 0.907 1.009 1.000 1.000
## electronic 0.700 0.030 23.736 0.000 0.642 0.758 1.000 1.000
## speed 1.051 0.048 21.891 0.000 0.957 1.145 1.000 1.000
cf.vcov<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances", "lv.variances"), group.partial=c("sswk~1", "ssei~1", "sscs~1"))
fitMeasures(cf.vcov, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 760.524 75.000 0.000 0.964 0.093 0.145 98435.178 98746.795
Mc(cf.vcov)
## [1] 0.851552
cf.cov2<-cfa(cf.lv, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("sswk~1", "ssei~1", "sscs~1"))
fitMeasures(cf.cov2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 630.869 74.000 0.000 0.971 0.084 0.119 98307.524 98624.806
Mc(cf.cov2)
## [1] 0.8776243
summary(cf.cov2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 108 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 81
## Number of equality constraints 25
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 630.869 434.667
## Degrees of freedom 74 74
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.451
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 397.736 274.039
## 1 233.133 160.628
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.931 0.108 27.097 0.000 2.719 3.143 2.931 0.578
## sswk (.p2.) 7.495 0.126 59.426 0.000 7.248 7.742 7.495 0.941
## sspc (.p3.) 2.942 0.061 48.382 0.000 2.823 3.062 2.942 0.861
## math =~
## ssar (.p4.) 6.984 0.100 69.552 0.000 6.787 7.181 6.984 0.947
## ssmk (.p5.) 5.829 0.103 56.732 0.000 5.627 6.030 5.829 0.885
## ssmc (.p6.) 1.428 0.145 9.831 0.000 1.143 1.712 1.428 0.289
## electronic =~
## ssgs (.p7.) 1.837 0.103 17.879 0.000 1.636 2.039 1.837 0.362
## ssasi (.p8.) 3.950 0.098 40.415 0.000 3.758 4.141 3.950 0.782
## ssmc (.p9.) 2.807 0.141 19.876 0.000 2.530 3.083 2.807 0.568
## ssei (.10.) 3.700 0.063 58.900 0.000 3.576 3.823 3.700 0.932
## speed =~
## ssno (.11.) 0.846 0.020 43.269 0.000 0.808 0.884 0.846 0.888
## sscs (.12.) 0.713 0.022 31.733 0.000 0.669 0.757 0.713 0.799
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.27.) 0.841 0.010 83.665 0.000 0.821 0.861 0.841 0.841
## elctrnc (.28.) 0.797 0.017 48.004 0.000 0.764 0.829 0.797 0.797
## speed (.29.) 0.758 0.016 46.494 0.000 0.726 0.790 0.758 0.758
## math ~~
## elctrnc (.30.) 0.714 0.017 41.425 0.000 0.680 0.748 0.714 0.714
## speed (.31.) 0.768 0.014 54.115 0.000 0.740 0.796 0.768 0.768
## electronic ~~
## speed (.32.) 0.563 0.021 26.357 0.000 0.521 0.605 0.563 0.563
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 16.414 0.188 87.327 0.000 16.046 16.783 16.414 3.235
## .sswk 25.438 0.284 89.414 0.000 24.881 25.996 25.438 3.192
## .sspc (.35.) 10.364 0.126 82.538 0.000 10.118 10.610 10.364 3.033
## .ssar (.36.) 18.311 0.291 62.964 0.000 17.741 18.881 18.311 2.482
## .ssmk (.37.) 14.310 0.251 56.906 0.000 13.817 14.802 14.310 2.173
## .ssmc (.38.) 15.756 0.196 80.257 0.000 15.371 16.140 15.756 3.189
## .ssasi (.39.) 16.099 0.199 81.001 0.000 15.710 16.489 16.099 3.188
## .ssei 12.364 0.157 78.687 0.000 12.056 12.672 12.364 3.116
## .ssno (.41.) 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.062
## .sscs -0.083 0.033 -2.497 0.013 -0.149 -0.018 -0.083 -0.093
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssgs 5.202 0.335 15.549 0.000 4.546 5.858 5.202 0.202
## .sswk 7.325 0.749 9.782 0.000 5.857 8.793 7.325 0.115
## .sspc 3.022 0.200 15.133 0.000 2.631 3.414 3.022 0.259
## .ssar 5.630 0.714 7.886 0.000 4.231 7.030 5.630 0.103
## .ssmk 9.397 0.704 13.340 0.000 8.016 10.778 9.397 0.217
## .ssmc 8.769 0.545 16.085 0.000 7.700 9.837 8.769 0.359
## .ssasi 9.909 0.749 13.229 0.000 8.441 11.377 9.909 0.388
## .ssei 2.061 0.285 7.228 0.000 1.502 2.619 2.061 0.131
## .ssno 0.191 0.024 7.954 0.000 0.144 0.238 0.191 0.211
## .sscs 0.288 0.036 8.086 0.000 0.218 0.358 0.288 0.361
## electronic 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.931 0.108 27.097 0.000 2.719 3.143 2.931 0.597
## sswk (.p2.) 7.495 0.126 59.426 0.000 7.248 7.742 7.495 0.938
## sspc (.p3.) 2.942 0.061 48.382 0.000 2.823 3.062 2.942 0.875
## math =~
## ssar (.p4.) 6.984 0.100 69.552 0.000 6.787 7.181 6.984 0.947
## ssmk (.p5.) 5.829 0.103 56.732 0.000 5.627 6.030 5.829 0.884
## ssmc (.p6.) 1.428 0.145 9.831 0.000 1.143 1.712 1.428 0.308
## electronic =~
## ssgs (.p7.) 1.837 0.103 17.879 0.000 1.636 2.039 1.552 0.316
## ssasi (.p8.) 3.950 0.098 40.415 0.000 3.758 4.141 3.336 0.795
## ssmc (.p9.) 2.807 0.141 19.876 0.000 2.530 3.083 2.371 0.511
## ssei (.10.) 3.700 0.063 58.900 0.000 3.576 3.823 3.125 0.843
## speed =~
## ssno (.11.) 0.846 0.020 43.269 0.000 0.808 0.884 0.846 0.886
## sscs (.12.) 0.713 0.022 31.733 0.000 0.669 0.757 0.713 0.758
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.27.) 0.841 0.010 83.665 0.000 0.821 0.861 0.841 0.841
## elctrnc (.28.) 0.797 0.017 48.004 0.000 0.764 0.829 0.944 0.944
## speed (.29.) 0.758 0.016 46.494 0.000 0.726 0.790 0.758 0.758
## math ~~
## elctrnc (.30.) 0.714 0.017 41.425 0.000 0.680 0.748 0.845 0.845
## speed (.31.) 0.768 0.014 54.115 0.000 0.740 0.796 0.768 0.768
## electronic ~~
## speed (.32.) 0.563 0.021 26.357 0.000 0.521 0.605 0.667 0.667
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 16.414 0.188 87.327 0.000 16.046 16.783 16.414 3.342
## .sswk 23.566 0.359 65.628 0.000 22.862 24.269 23.566 2.948
## .sspc (.35.) 10.364 0.126 82.538 0.000 10.118 10.610 10.364 3.081
## .ssar (.36.) 18.311 0.291 62.964 0.000 17.741 18.881 18.311 2.484
## .ssmk (.37.) 14.310 0.251 56.906 0.000 13.817 14.802 14.310 2.169
## .ssmc (.38.) 15.756 0.196 80.257 0.000 15.371 16.140 15.756 3.394
## .ssasi (.39.) 16.099 0.199 81.001 0.000 15.710 16.489 16.099 3.835
## .ssei 14.415 0.258 55.934 0.000 13.910 14.921 14.415 3.888
## .ssno (.41.) 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.062
## .sscs 0.205 0.040 5.123 0.000 0.127 0.284 0.205 0.218
## verbal 0.303 0.056 5.439 0.000 0.194 0.412 0.303 0.303
## math -0.161 0.056 -2.871 0.004 -0.270 -0.051 -0.161 -0.161
## elctrnc -1.312 0.071 -18.474 0.000 -1.451 -1.173 -1.553 -1.553
## speed 0.318 0.058 5.471 0.000 0.204 0.432 0.318 0.318
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssgs 4.539 0.299 15.180 0.000 3.953 5.125 4.539 0.188
## .sswk 7.724 0.745 10.374 0.000 6.264 9.183 7.724 0.121
## .sspc 2.658 0.167 15.886 0.000 2.330 2.986 2.658 0.235
## .ssar 5.570 0.731 7.619 0.000 4.137 7.003 5.570 0.102
## .ssmk 9.539 0.718 13.294 0.000 8.133 10.945 9.539 0.219
## .ssmc 8.172 0.470 17.380 0.000 7.250 9.093 8.172 0.379
## .ssasi 6.496 0.430 15.121 0.000 5.654 7.338 6.496 0.369
## .ssei 3.983 0.300 13.294 0.000 3.395 4.570 3.983 0.290
## .ssno 0.195 0.026 7.447 0.000 0.144 0.246 0.195 0.214
## .sscs 0.377 0.038 10.000 0.000 0.303 0.451 0.377 0.426
## electronic 0.713 0.031 22.988 0.000 0.653 0.774 1.000 1.000
tests<-lavTestLRT(configural, metric, scalar2, cf.cov, cf.cov2)
Td=tests[2:5,"Chisq diff"]
Td
## [1] 40.58216 38.81275 81.78372 13.17603
dfd=tests[2:5,"Df diff"]
dfd
## [1] 8 3 6 3
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-1067+ 1067 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.06181108 0.10582288 0.10885133 0.05640921
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04373078 0.08128093
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.07768007 0.13666784
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.0885868 0.1303928
RMSEA.CI(T=Td[4],df=dfd[4],N=N,G=2)
## [1] 0.02772545 0.08909604
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 0.866 0.594 0.063 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 0.999 0.996 0.935 0.658
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 1.000 0.990 0.774
round(pvals(T=Td[4],df=dfd[4],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 0.996 0.993 0.687 0.479 0.126 0.012
tests<-lavTestLRT(configural, metric, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 40.58216 38.81275 50.49976
dfd=tests[2:4,"Df diff"]
dfd
## [1] 8 3 10
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-1067+ 1067 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.06181108 0.10582288 0.06163787
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04373078 0.08128093
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.07768007 0.13666784
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.04537321 0.07900369
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 0.866 0.594 0.063 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 0.999 0.996 0.935 0.658
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 0.885 0.592 0.041 0.000
tests<-lavTestLRT(configural, metric, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 40.58216 275.17904
dfd=tests[2:3,"Df diff"]
dfd
## [1] 8 6
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-1067+ 1067 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.06181108 0.20514758
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04373078 0.08128093
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.1848146 0.2261304
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 0.866 0.594 0.063 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
# ONE FACTOR, just for checking if gap direction aligns with HOF
fmodel<-'
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
'
configural<-cfa(fmodel, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2442.129 70.000 0.000 0.874 0.178 0.054 100126.783 100466.729
Mc(configural)
## [1] 0.5734671
metric<-cfa(fmodel, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2642.482 79.000 0.000 0.864 0.174 0.084 100309.136 100598.089
Mc(metric)
## [1] 0.5483125
scalar<-cfa(fmodel, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 5404.556 88.000 0.000 0.719 0.238 0.140 103053.210 103291.172
Mc(scalar)
## [1] 0.2875776
summary(scalar, standardized=T, ci=T) # -0.239
## lavaan 0.6-18 ended normally after 100 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 62
## Number of equality constraints 20
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 5404.556 3647.096
## Degrees of freedom 88 88
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.482
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 3213.430 2168.483
## 1 2191.126 1478.613
##
## 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 ci.upper Std.lv Std.all
## g =~
## ssgs (.p1.) 4.932 0.113 43.724 0.000 4.711 5.153 4.932 0.901
## ssar (.p2.) 6.862 0.142 48.304 0.000 6.583 7.140 6.862 0.870
## sswk (.p3.) 7.629 0.180 42.425 0.000 7.277 7.982 7.629 0.903
## sspc (.p4.) 3.006 0.084 35.788 0.000 2.842 3.171 3.006 0.832
## ssno (.p5.) 0.682 0.027 25.519 0.000 0.630 0.734 0.682 0.692
## sscs (.p6.) 0.576 0.029 19.681 0.000 0.518 0.633 0.576 0.619
## ssasi (.p7.) 3.635 0.164 22.184 0.000 3.314 3.956 3.635 0.573
## ssmk (.p8.) 5.782 0.136 42.565 0.000 5.516 6.048 5.782 0.826
## ssmc (.p9.) 4.241 0.142 29.792 0.000 3.962 4.520 4.241 0.759
## ssei (.10.) 3.621 0.111 32.654 0.000 3.404 3.838 3.621 0.819
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.22.) 16.134 0.207 77.934 0.000 15.728 16.540 16.134 2.949
## .ssar (.23.) 18.431 0.289 63.726 0.000 17.864 18.998 18.431 2.337
## .sswk (.24.) 26.366 0.281 93.963 0.000 25.816 26.916 26.366 3.120
## .sspc (.25.) 11.117 0.118 94.393 0.000 10.886 11.348 11.117 3.077
## .ssno (.26.) 0.250 0.032 7.796 0.000 0.187 0.312 0.250 0.253
## .sscs (.27.) 0.179 0.035 5.064 0.000 0.109 0.248 0.179 0.192
## .ssasi (.28.) 12.742 0.298 42.752 0.000 12.158 13.326 12.742 2.008
## .ssmk (.29.) 14.442 0.255 56.695 0.000 13.943 14.941 14.442 2.064
## .ssmc (.30.) 14.099 0.248 56.867 0.000 13.613 14.585 14.099 2.522
## .ssei (.31.) 11.315 0.205 55.247 0.000 10.913 11.716 11.315 2.559
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.617 0.426 13.180 0.000 4.782 6.452 5.617 0.188
## .ssar 15.090 1.009 14.960 0.000 13.113 17.067 15.090 0.243
## .sswk 13.208 1.016 12.998 0.000 11.217 15.200 13.208 0.185
## .sspc 4.012 0.272 14.729 0.000 3.478 4.546 4.012 0.307
## .ssno 0.506 0.029 17.636 0.000 0.449 0.562 0.506 0.521
## .sscs 0.532 0.045 11.946 0.000 0.445 0.619 0.532 0.616
## .ssasi 27.062 2.433 11.121 0.000 22.293 31.832 27.062 0.672
## .ssmk 15.525 0.970 16.009 0.000 13.624 17.426 15.525 0.317
## .ssmc 13.268 0.943 14.077 0.000 11.420 15.115 13.268 0.425
## .ssei 6.438 0.570 11.289 0.000 5.320 7.556 6.438 0.329
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g =~
## ssgs (.p1.) 4.932 0.113 43.724 0.000 4.711 5.153 4.138 0.882
## ssar (.p2.) 6.862 0.142 48.304 0.000 6.583 7.140 5.757 0.846
## sswk (.p3.) 7.629 0.180 42.425 0.000 7.277 7.982 6.401 0.867
## sspc (.p4.) 3.006 0.084 35.788 0.000 2.842 3.171 2.522 0.793
## ssno (.p5.) 0.682 0.027 25.519 0.000 0.630 0.734 0.572 0.614
## sscs (.p6.) 0.576 0.029 19.681 0.000 0.518 0.633 0.483 0.497
## ssasi (.p7.) 3.635 0.164 22.184 0.000 3.314 3.956 3.050 0.719
## ssmk (.p8.) 5.782 0.136 42.565 0.000 5.516 6.048 4.851 0.791
## ssmc (.p9.) 4.241 0.142 29.792 0.000 3.962 4.520 3.558 0.738
## ssei (.10.) 3.621 0.111 32.654 0.000 3.404 3.838 3.038 0.779
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.22.) 16.134 0.207 77.934 0.000 15.728 16.540 16.134 3.441
## .ssar (.23.) 18.431 0.289 63.726 0.000 17.864 18.998 18.431 2.709
## .sswk (.24.) 26.366 0.281 93.963 0.000 25.816 26.916 26.366 3.572
## .sspc (.25.) 11.117 0.118 94.393 0.000 10.886 11.348 11.117 3.494
## .ssno (.26.) 0.250 0.032 7.796 0.000 0.187 0.312 0.250 0.268
## .sscs (.27.) 0.179 0.035 5.064 0.000 0.109 0.248 0.179 0.184
## .ssasi (.28.) 12.742 0.298 42.752 0.000 12.158 13.326 12.742 3.003
## .ssmk (.29.) 14.442 0.255 56.695 0.000 13.943 14.941 14.442 2.353
## .ssmc (.30.) 14.099 0.248 56.867 0.000 13.613 14.585 14.099 2.925
## .ssei (.31.) 11.315 0.205 55.247 0.000 10.913 11.716 11.315 2.900
## g -0.200 0.057 -3.526 0.000 -0.312 -0.089 -0.239 -0.239
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.867 0.352 13.816 0.000 4.176 5.557 4.867 0.221
## .ssar 13.157 0.818 16.075 0.000 11.553 14.761 13.157 0.284
## .sswk 13.510 1.045 12.928 0.000 11.462 15.559 13.510 0.248
## .sspc 3.759 0.275 13.682 0.000 3.220 4.297 3.759 0.371
## .ssno 0.542 0.029 18.418 0.000 0.484 0.599 0.542 0.623
## .sscs 0.713 0.050 14.238 0.000 0.615 0.811 0.713 0.753
## .ssasi 8.704 0.784 11.102 0.000 7.167 10.241 8.704 0.483
## .ssmk 14.126 0.790 17.888 0.000 12.578 15.674 14.126 0.375
## .ssmc 10.581 0.740 14.298 0.000 9.131 12.032 10.581 0.455
## .ssei 5.993 0.426 14.073 0.000 5.158 6.828 5.993 0.394
## g 0.704 0.041 17.352 0.000 0.624 0.783 1.000 1.000
# HIGH ORDER FACTOR
hof.model<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
'
hof.lv<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
g~~1*g
'
hof.weak<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
g~~1*g
math~0*1
'
baseline<-cfa(hof.model, data=dgroup, meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 864.295 29.000 0.000 0.956 0.116 0.048 100287.011 100490.978
Mc(baseline)
## [1] 0.8221743
configural<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 580.702 58.000 0.000 0.972 0.092 0.028 98289.356 98697.290
Mc(configural)
## [1] 0.8846817
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 103 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 72
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 580.702 387.013
## Degrees of freedom 58 58
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.500
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 379.776 253.104
## 1 200.926 133.909
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs 0.587 0.174 3.369 0.001 0.245 0.928 3.057 0.562
## sswk 1.488 0.455 3.274 0.001 0.597 2.379 7.756 0.938
## sspc 0.604 0.183 3.307 0.001 0.246 0.962 3.147 0.877
## math =~
## ssar 3.544 0.185 19.151 0.000 3.181 3.907 7.324 0.955
## ssmk 2.955 0.152 19.458 0.000 2.658 3.253 6.107 0.895
## ssmc 0.532 0.117 4.533 0.000 0.302 0.761 1.098 0.197
## electronic =~
## ssgs 0.966 0.131 7.396 0.000 0.710 1.222 2.045 0.376
## ssasi 2.187 0.124 17.675 0.000 1.944 2.429 4.630 0.830
## ssmc 1.829 0.126 14.513 0.000 1.582 2.076 3.873 0.696
## ssei 1.972 0.100 19.771 0.000 1.777 2.168 4.176 0.940
## speed =~
## ssno 0.506 0.025 20.141 0.000 0.457 0.555 0.842 0.875
## sscs 0.442 0.024 18.362 0.000 0.394 0.489 0.735 0.815
## g =~
## verbal 5.114 1.613 3.171 0.002 1.953 8.275 0.981 0.981
## math 1.809 0.117 15.401 0.000 1.578 2.039 0.875 0.875
## electronic 1.866 0.126 14.841 0.000 1.620 2.113 0.881 0.881
## speed 1.331 0.094 14.219 0.000 1.147 1.514 0.799 0.799
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 16.396 0.190 86.372 0.000 16.024 16.768 16.396 3.015
## .sswk 25.438 0.284 89.414 0.000 24.881 25.996 25.438 3.078
## .sspc 10.375 0.126 82.229 0.000 10.127 10.622 10.375 2.892
## .ssar 18.495 0.286 64.662 0.000 17.934 19.056 18.495 2.411
## .ssmk 13.973 0.261 53.474 0.000 13.461 14.486 13.973 2.047
## .ssmc 15.637 0.201 77.759 0.000 15.243 16.031 15.637 2.808
## .ssasi 16.211 0.198 81.891 0.000 15.823 16.599 16.211 2.907
## .ssei 12.364 0.157 78.687 0.000 12.056 12.672 12.364 2.783
## .ssno 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.061
## .sscs -0.083 0.033 -2.497 0.013 -0.149 -0.018 -0.083 -0.092
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.234 0.341 15.329 0.000 4.564 5.903 5.234 0.177
## .sswk 8.170 0.813 10.051 0.000 6.577 9.763 8.170 0.120
## .sspc 2.965 0.198 15.006 0.000 2.578 3.352 2.965 0.230
## .ssar 5.200 0.814 6.388 0.000 3.605 6.795 5.200 0.088
## .ssmk 9.308 0.739 12.594 0.000 7.860 10.757 9.308 0.200
## .ssmc 8.232 0.542 15.174 0.000 7.169 9.295 8.232 0.266
## .ssasi 9.665 0.741 13.035 0.000 8.212 11.119 9.665 0.311
## .ssei 2.309 0.280 8.254 0.000 1.760 2.857 2.309 0.117
## .ssno 0.218 0.027 8.143 0.000 0.165 0.270 0.218 0.235
## .sscs 0.273 0.037 7.406 0.000 0.200 0.345 0.273 0.335
## .verbal 1.000 1.000 1.000 0.037 0.037
## .math 1.000 1.000 1.000 0.234 0.234
## .electronic 1.000 1.000 1.000 0.223 0.223
## .speed 1.000 1.000 1.000 0.361 0.361
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs 0.626 0.135 4.631 0.000 0.361 0.891 2.039 0.438
## sswk 2.222 0.262 8.474 0.000 1.708 2.736 7.235 0.942
## sspc 0.840 0.098 8.597 0.000 0.649 1.032 2.736 0.861
## math =~
## ssar 3.031 0.166 18.293 0.000 2.706 3.356 6.578 0.938
## ssmk 2.581 0.141 18.326 0.000 2.305 2.857 5.601 0.880
## ssmc 0.824 0.144 5.719 0.000 0.541 1.106 1.787 0.425
## electronic =~
## ssgs 0.779 0.125 6.231 0.000 0.534 1.024 2.228 0.479
## ssasi 0.956 0.122 7.865 0.000 0.718 1.195 2.735 0.732
## ssmc 0.498 0.121 4.101 0.000 0.260 0.736 1.425 0.339
## ssei 0.956 0.122 7.834 0.000 0.717 1.195 2.735 0.810
## speed =~
## ssno 0.524 0.026 20.131 0.000 0.473 0.575 0.823 0.872
## sscs 0.456 0.023 19.937 0.000 0.411 0.501 0.716 0.767
## g =~
## verbal 3.098 0.397 7.810 0.000 2.321 3.876 0.952 0.952
## math 1.926 0.134 14.426 0.000 1.664 2.188 0.888 0.888
## electronic 2.680 0.362 7.401 0.000 1.970 3.390 0.937 0.937
## speed 1.211 0.083 14.567 0.000 1.048 1.374 0.771 0.771
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 14.908 0.166 89.625 0.000 14.582 15.234 14.908 3.203
## .sswk 25.835 0.262 98.598 0.000 25.322 26.349 25.835 3.365
## .sspc 11.246 0.107 105.151 0.000 11.036 11.455 11.246 3.538
## .ssar 16.999 0.262 64.966 0.000 16.486 17.512 16.999 2.424
## .ssmk 13.732 0.240 57.183 0.000 13.262 14.203 13.732 2.157
## .ssmc 11.961 0.157 76.345 0.000 11.654 12.268 11.961 2.847
## .ssasi 10.841 0.136 79.844 0.000 10.575 11.107 10.841 2.902
## .ssei 9.562 0.123 77.895 0.000 9.322 9.803 9.562 2.831
## .ssno 0.328 0.034 9.769 0.000 0.262 0.394 0.328 0.347
## .sscs 0.432 0.033 13.004 0.000 0.367 0.497 0.432 0.463
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.441 0.332 13.378 0.000 3.790 5.092 4.441 0.205
## .sswk 6.586 0.807 8.157 0.000 5.004 8.169 6.586 0.112
## .sspc 2.622 0.166 15.797 0.000 2.297 2.947 2.622 0.259
## .ssar 5.921 0.755 7.845 0.000 4.442 7.400 5.921 0.120
## .ssmk 9.162 0.735 12.474 0.000 7.723 10.602 9.162 0.226
## .ssmc 8.194 0.465 17.619 0.000 7.282 9.105 8.194 0.464
## .ssasi 6.472 0.438 14.764 0.000 5.613 7.331 6.472 0.464
## .ssei 3.926 0.297 13.211 0.000 3.343 4.508 3.926 0.344
## .ssno 0.213 0.034 6.330 0.000 0.147 0.279 0.213 0.239
## .sscs 0.358 0.044 8.164 0.000 0.272 0.444 0.358 0.411
## .verbal 1.000 1.000 1.000 0.094 0.094
## .math 1.000 1.000 1.000 0.212 0.212
## .electronic 1.000 1.000 1.000 0.122 0.122
## .speed 1.000 1.000 1.000 0.406 0.406
## g 1.000 1.000 1.000 1.000 1.000
#modificationIndices(configural, sort=T, maximum.number=30)
metric<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 697.933 69.000 0.000 0.967 0.092 0.059 98384.587 98730.198
Mc(metric)
## [1] 0.8629235
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 90 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 77
## Number of equality constraints 16
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 697.933 475.579
## Degrees of freedom 69 69
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.468
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 435.771 296.939
## 1 262.162 178.640
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.576 0.170 3.377 0.001 0.242 0.910 3.001 0.562
## sswk (.p2.) 1.517 0.451 3.363 0.001 0.633 2.402 7.910 0.940
## sspc (.p3.) 0.598 0.177 3.381 0.001 0.251 0.945 3.118 0.876
## math =~
## ssar (.p4.) 3.453 0.186 18.569 0.000 3.089 3.818 7.489 0.955
## ssmk (.p5.) 2.904 0.156 18.632 0.000 2.598 3.209 6.297 0.901
## ssmc (.p6.) 0.575 0.093 6.161 0.000 0.392 0.758 1.248 0.239
## electronic =~
## ssgs (.p7.) 1.138 0.113 10.091 0.000 0.917 1.359 2.054 0.385
## ssasi (.p8.) 2.283 0.120 19.100 0.000 2.048 2.517 4.120 0.795
## ssmc (.p9.) 1.843 0.127 14.493 0.000 1.594 2.092 3.327 0.638
## ssei (.10.) 2.159 0.095 22.653 0.000 1.973 2.346 3.898 0.936
## speed =~
## ssno (.11.) 0.499 0.025 20.230 0.000 0.450 0.547 0.863 0.881
## sscs (.12.) 0.433 0.023 19.013 0.000 0.388 0.477 0.749 0.819
## g =~
## verbal (.13.) 5.116 1.561 3.278 0.001 2.057 8.176 0.981 0.981
## math (.14.) 1.924 0.120 16.070 0.000 1.690 2.159 0.887 0.887
## elctrnc (.15.) 1.503 0.100 15.055 0.000 1.307 1.698 0.833 0.833
## speed (.16.) 1.412 0.089 15.917 0.000 1.238 1.586 0.816 0.816
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 16.396 0.190 86.372 0.000 16.024 16.768 16.396 3.070
## .sswk 25.438 0.284 89.414 0.000 24.881 25.996 25.438 3.022
## .sspc 10.375 0.126 82.229 0.000 10.127 10.622 10.375 2.915
## .ssar 18.495 0.286 64.662 0.000 17.934 19.056 18.495 2.359
## .ssmk 13.973 0.261 53.474 0.000 13.461 14.486 13.973 1.999
## .ssmc 15.637 0.201 77.759 0.000 15.243 16.031 15.637 2.997
## .ssasi 16.211 0.198 81.891 0.000 15.823 16.599 16.211 3.129
## .ssei 12.364 0.157 78.687 0.000 12.056 12.672 12.364 2.967
## .ssno 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.060
## .sscs -0.083 0.033 -2.497 0.013 -0.149 -0.018 -0.083 -0.091
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.224 0.336 15.564 0.000 4.566 5.882 5.224 0.183
## .sswk 8.289 0.827 10.020 0.000 6.668 9.911 8.289 0.117
## .sspc 2.943 0.195 15.129 0.000 2.562 3.324 2.943 0.232
## .ssar 5.383 0.759 7.092 0.000 3.895 6.870 5.383 0.088
## .ssmk 9.185 0.698 13.153 0.000 7.817 10.554 9.185 0.188
## .ssmc 8.465 0.551 15.355 0.000 7.385 9.546 8.465 0.311
## .ssasi 9.868 0.745 13.240 0.000 8.408 11.329 9.868 0.368
## .ssei 2.166 0.293 7.398 0.000 1.592 2.740 2.166 0.125
## .ssno 0.215 0.025 8.649 0.000 0.166 0.264 0.215 0.224
## .sscs 0.275 0.035 7.884 0.000 0.206 0.343 0.275 0.329
## .verbal 1.000 1.000 1.000 0.037 0.037
## .math 1.000 1.000 1.000 0.213 0.213
## .electronic 1.000 1.000 1.000 0.307 0.307
## .speed 1.000 1.000 1.000 0.334 0.334
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.576 0.170 3.377 0.001 0.242 0.910 2.649 0.575
## sswk (.p2.) 1.517 0.451 3.363 0.001 0.633 2.402 6.983 0.934
## sspc (.p3.) 0.598 0.177 3.381 0.001 0.251 0.945 2.752 0.862
## math =~
## ssar (.p4.) 3.453 0.186 18.569 0.000 3.089 3.818 6.420 0.938
## ssmk (.p5.) 2.904 0.156 18.632 0.000 2.598 3.209 5.398 0.870
## ssmc (.p6.) 0.575 0.093 6.161 0.000 0.392 0.758 1.069 0.241
## electronic =~
## ssgs (.p7.) 1.138 0.113 10.091 0.000 0.917 1.359 1.517 0.329
## ssasi (.p8.) 2.283 0.120 19.100 0.000 2.048 2.517 3.043 0.770
## ssmc (.p9.) 1.843 0.127 14.493 0.000 1.594 2.092 2.457 0.554
## ssei (.10.) 2.159 0.095 22.653 0.000 1.973 2.346 2.879 0.821
## speed =~
## ssno (.11.) 0.499 0.025 20.230 0.000 0.450 0.547 0.801 0.867
## sscs (.12.) 0.433 0.023 19.013 0.000 0.388 0.477 0.695 0.758
## g =~
## verbal (.13.) 5.116 1.561 3.278 0.001 2.057 8.176 0.943 0.943
## math (.14.) 1.924 0.120 16.070 0.000 1.690 2.159 0.878 0.878
## elctrnc (.15.) 1.503 0.100 15.055 0.000 1.307 1.698 0.956 0.956
## speed (.16.) 1.412 0.089 15.917 0.000 1.238 1.586 0.746 0.746
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 14.908 0.166 89.625 0.000 14.582 15.234 14.908 3.235
## .sswk 25.835 0.262 98.598 0.000 25.322 26.349 25.835 3.455
## .sspc 11.246 0.107 105.151 0.000 11.036 11.455 11.246 3.524
## .ssar 16.999 0.262 64.966 0.000 16.486 17.512 16.999 2.484
## .ssmk 13.732 0.240 57.183 0.000 13.262 14.203 13.732 2.214
## .ssmc 11.961 0.157 76.345 0.000 11.654 12.268 11.961 2.697
## .ssasi 10.841 0.136 79.844 0.000 10.575 11.107 10.841 2.743
## .ssei 9.562 0.123 77.895 0.000 9.322 9.803 9.562 2.727
## .ssno 0.328 0.034 9.769 0.000 0.262 0.394 0.328 0.355
## .sscs 0.432 0.033 13.004 0.000 0.367 0.497 0.432 0.471
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.664 0.302 15.448 0.000 4.072 5.255 4.664 0.220
## .sswk 7.151 0.770 9.282 0.000 5.641 8.661 7.151 0.128
## .sspc 2.610 0.164 15.899 0.000 2.288 2.932 2.610 0.256
## .ssar 5.616 0.740 7.585 0.000 4.165 7.067 5.616 0.120
## .ssmk 9.338 0.712 13.112 0.000 7.942 10.733 9.338 0.243
## .ssmc 8.076 0.469 17.230 0.000 7.158 8.995 8.076 0.411
## .ssasi 6.363 0.430 14.798 0.000 5.520 7.206 6.363 0.407
## .ssei 4.009 0.290 13.828 0.000 3.441 4.577 4.009 0.326
## .ssno 0.212 0.030 7.042 0.000 0.153 0.271 0.212 0.248
## .sscs 0.359 0.040 9.011 0.000 0.281 0.437 0.359 0.426
## .verbal 2.330 1.359 1.715 0.086 -0.332 4.993 0.110 0.110
## .math 0.789 0.108 7.340 0.000 0.579 1.000 0.228 0.228
## .electronic 0.151 0.046 3.283 0.001 0.061 0.242 0.085 0.085
## .speed 1.144 0.142 8.043 0.000 0.865 1.422 0.443 0.443
## g 0.720 0.045 16.119 0.000 0.633 0.808 1.000 1.000
lavTestScore(metric, release = 1:16)
## 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 117.464 16 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p47. 0.948 1 0.330
## 2 .p2. == .p48. 10.826 1 0.001
## 3 .p3. == .p49. 2.300 1 0.129
## 4 .p4. == .p50. 3.038 1 0.081
## 5 .p5. == .p51. 2.307 1 0.129
## 6 .p6. == .p52. 9.161 1 0.002
## 7 .p7. == .p53. 2.814 1 0.093
## 8 .p8. == .p54. 19.180 1 0.000
## 9 .p9. == .p55. 22.567 1 0.000
## 10 .p10. == .p56. 5.768 1 0.016
## 11 .p11. == .p57. 1.857 1 0.173
## 12 .p12. == .p58. 0.566 1 0.452
## 13 .p13. == .p59. 10.877 1 0.001
## 14 .p14. == .p60. 9.241 1 0.002
## 15 .p15. == .p61. 78.620 1 0.000
## 16 .p16. == .p62. 4.630 1 0.031
metric2<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"), group.partial=c("g=~electronic"))
fitMeasures(metric2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 619.358 68.000 0.000 0.971 0.087 0.033 98308.013 98659.289
Mc(metric2)
## [1] 0.8787588
scalar<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= 1.395560e-13) 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 aic bic
## 995.766 73.000 0.000 0.951 0.109 0.054 98674.421 98997.369
Mc(scalar)
## [1] 0.8054879
summary(scalar, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 127 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 25
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 995.766 671.281
## Degrees of freedom 73 73
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.483
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 565.336 381.113
## 1 430.430 290.168
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.643 0.154 4.165 0.000 0.341 0.946 3.055 0.555
## sswk (.p2.) 1.629 0.390 4.173 0.000 0.864 2.395 7.738 0.938
## sspc (.p3.) 0.646 0.153 4.209 0.000 0.345 0.946 3.066 0.867
## math =~
## ssar (.p4.) 3.500 0.177 19.738 0.000 3.152 3.847 7.352 0.955
## ssmk (.p5.) 2.911 0.146 19.940 0.000 2.625 3.197 6.115 0.893
## ssmc (.p6.) 0.504 0.084 5.967 0.000 0.338 0.669 1.058 0.191
## electronic =~
## ssgs (.p7.) 1.005 0.075 13.419 0.000 0.858 1.152 2.133 0.388
## ssasi (.p8.) 2.350 0.131 17.989 0.000 2.094 2.606 4.987 0.846
## ssmc (.p9.) 1.842 0.115 15.985 0.000 1.616 2.068 3.910 0.704
## ssei (.10.) 1.883 0.098 19.260 0.000 1.691 2.075 3.997 0.922
## speed =~
## ssno (.11.) 0.481 0.024 20.121 0.000 0.434 0.528 0.822 0.857
## sscs (.12.) 0.450 0.023 19.167 0.000 0.404 0.496 0.768 0.830
## g =~
## verbal (.13.) 4.642 1.153 4.027 0.000 2.383 6.902 0.978 0.978
## math (.14.) 1.847 0.112 16.482 0.000 1.628 2.067 0.879 0.879
## elctrnc 1.872 0.131 14.302 0.000 1.616 2.129 0.882 0.882
## speed (.16.) 1.385 0.087 15.969 0.000 1.215 1.555 0.811 0.811
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 16.392 0.188 87.339 0.000 16.024 16.759 16.392 2.979
## .sswk (.33.) 25.164 0.289 87.142 0.000 24.598 25.730 25.164 3.049
## .sspc (.34.) 10.637 0.117 90.643 0.000 10.407 10.867 10.637 3.009
## .ssar (.35.) 18.339 0.290 63.128 0.000 17.769 18.908 18.339 2.381
## .ssmk (.36.) 14.326 0.251 57.011 0.000 13.834 14.819 14.326 2.092
## .ssmc (.37.) 15.577 0.201 77.533 0.000 15.183 15.971 15.577 2.806
## .ssasi (.38.) 15.588 0.212 73.535 0.000 15.173 16.004 15.588 2.645
## .ssei (.39.) 12.607 0.150 84.215 0.000 12.314 12.901 12.607 2.909
## .ssno (.40.) 0.003 0.035 0.086 0.931 -0.066 0.072 0.003 0.003
## .sscs (.41.) -0.018 0.033 -0.553 0.580 -0.082 0.046 -0.018 -0.019
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.145 0.334 15.404 0.000 4.491 5.800 5.145 0.170
## .sswk 8.245 0.839 9.828 0.000 6.601 9.890 8.245 0.121
## .sspc 3.100 0.210 14.761 0.000 2.689 3.512 3.100 0.248
## .ssar 5.248 0.799 6.571 0.000 3.683 6.813 5.248 0.089
## .ssmk 9.510 0.733 12.981 0.000 8.074 10.946 9.510 0.203
## .ssmc 7.984 0.537 14.880 0.000 6.932 9.035 7.984 0.259
## .ssasi 9.857 0.805 12.240 0.000 8.279 11.435 9.857 0.284
## .ssei 2.809 0.282 9.967 0.000 2.257 3.361 2.809 0.150
## .ssno 0.244 0.026 9.535 0.000 0.194 0.294 0.244 0.266
## .sscs 0.266 0.037 7.233 0.000 0.194 0.338 0.266 0.311
## .verbal 1.000 1.000 1.000 0.044 0.044
## .math 1.000 1.000 1.000 0.227 0.227
## .electronic 1.000 1.000 1.000 0.222 0.222
## .speed 1.000 1.000 1.000 0.343 0.343
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.643 0.154 4.165 0.000 0.341 0.946 2.831 0.617
## sswk (.p2.) 1.629 0.390 4.173 0.000 0.864 2.395 7.172 0.934
## sspc (.p3.) 0.646 0.153 4.209 0.000 0.345 0.946 2.842 0.867
## math =~
## ssar (.p4.) 3.500 0.177 19.738 0.000 3.152 3.847 6.607 0.942
## ssmk (.p5.) 2.911 0.146 19.940 0.000 2.625 3.197 5.496 0.871
## ssmc (.p6.) 0.504 0.084 5.967 0.000 0.338 0.669 0.951 0.222
## electronic =~
## ssgs (.p7.) 1.005 0.075 13.419 0.000 0.858 1.152 1.294 0.282
## ssasi (.p8.) 2.350 0.131 17.989 0.000 2.094 2.606 3.024 0.765
## ssmc (.p9.) 1.842 0.115 15.985 0.000 1.616 2.068 2.371 0.554
## ssei (.10.) 1.883 0.098 19.260 0.000 1.691 2.075 2.424 0.750
## speed =~
## ssno (.11.) 0.481 0.024 20.121 0.000 0.434 0.528 0.784 0.846
## sscs (.12.) 0.450 0.023 19.167 0.000 0.404 0.496 0.733 0.776
## g =~
## verbal (.13.) 4.642 1.153 4.027 0.000 2.383 6.902 0.956 0.956
## math (.14.) 1.847 0.112 16.482 0.000 1.628 2.067 0.887 0.887
## elctrnc 1.342 0.090 14.896 0.000 1.166 1.519 0.945 0.945
## speed (.16.) 1.385 0.087 15.969 0.000 1.215 1.555 0.771 0.771
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 16.392 0.188 87.339 0.000 16.024 16.759 16.392 3.574
## .sswk (.33.) 25.164 0.289 87.142 0.000 24.598 25.730 25.164 3.279
## .sspc (.34.) 10.637 0.117 90.643 0.000 10.407 10.867 10.637 3.244
## .ssar (.35.) 18.339 0.290 63.128 0.000 17.769 18.908 18.339 2.614
## .ssmk (.36.) 14.326 0.251 57.011 0.000 13.834 14.819 14.326 2.270
## .ssmc (.37.) 15.577 0.201 77.533 0.000 15.183 15.971 15.577 3.639
## .ssasi (.38.) 15.588 0.212 73.535 0.000 15.173 16.004 15.588 3.945
## .ssei (.39.) 12.607 0.150 84.215 0.000 12.314 12.901 12.607 3.901
## .ssno (.40.) 0.003 0.035 0.086 0.931 -0.066 0.072 0.003 0.003
## .sscs (.41.) -0.018 0.033 -0.553 0.580 -0.082 0.046 -0.018 -0.019
## .verbal 0.839 0.075 11.215 0.000 0.693 0.986 0.191 0.191
## .math -0.227 0.091 -2.494 0.013 -0.405 -0.049 -0.120 -0.120
## .elctrnc -1.761 0.117 -15.058 0.000 -1.990 -1.532 -1.368 -1.368
## .speed 0.877 0.100 8.779 0.000 0.681 1.073 0.538 0.538
## g -0.058 0.057 -1.010 0.312 -0.169 0.054 -0.063 -0.063
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.719 0.307 15.388 0.000 4.118 5.320 4.719 0.224
## .sswk 7.470 0.776 9.628 0.000 5.950 8.991 7.470 0.127
## .sspc 2.679 0.172 15.563 0.000 2.341 3.016 2.679 0.249
## .ssar 5.577 0.755 7.386 0.000 4.097 7.057 5.577 0.113
## .ssmk 9.609 0.725 13.245 0.000 8.187 11.031 9.609 0.241
## .ssmc 8.017 0.467 17.173 0.000 7.102 8.931 8.017 0.437
## .ssasi 6.464 0.459 14.096 0.000 5.565 7.363 6.464 0.414
## .ssei 4.571 0.319 14.315 0.000 3.945 5.196 4.571 0.438
## .ssno 0.245 0.030 8.029 0.000 0.185 0.304 0.245 0.285
## .sscs 0.355 0.043 8.316 0.000 0.271 0.438 0.355 0.398
## .verbal 1.655 0.806 2.054 0.040 0.076 3.233 0.085 0.085
## .math 0.758 0.103 7.394 0.000 0.557 0.959 0.213 0.213
## .electronic 0.176 0.052 3.389 0.001 0.074 0.277 0.106 0.106
## .speed 1.079 0.138 7.812 0.000 0.808 1.349 0.406 0.406
## g 0.822 0.050 16.325 0.000 0.723 0.921 1.000 1.000
lavTestScore(scalar, release = 16:25)
## 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 364.145 10 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p32. == .p78. 0.036 1 0.850
## 2 .p33. == .p79. 59.558 1 0.000
## 3 .p34. == .p80. 65.444 1 0.000
## 4 .p35. == .p81. 38.236 1 0.000
## 5 .p36. == .p82. 41.463 1 0.000
## 6 .p37. == .p83. 2.262 1 0.133
## 7 .p38. == .p84. 146.664 1 0.000
## 8 .p39. == .p85. 158.496 1 0.000
## 9 .p40. == .p86. 77.533 1 0.000
## 10 .p41. == .p87. 77.533 1 0.000
scalar2<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "sspc~1", "ssei~1", "sscs~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 (= 3.733194e-13) 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 aic bic
## 681.516 70.000 0.000 0.968 0.090 0.036 98366.170 98706.115
Mc(scalar2)
## [1] 0.8664539
summary(scalar2, standardized=T, ci=T) # g -0.093 Std.all
## lavaan 0.6-18 ended normally after 132 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 22
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 681.516 458.594
## Degrees of freedom 70 70
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.486
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 422.569 284.348
## 1 258.946 174.246
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.645 0.180 3.593 0.000 0.293 0.997 3.440 0.633
## sswk (.p2.) 1.459 0.410 3.558 0.000 0.655 2.263 7.778 0.939
## sspc (.p3.) 0.574 0.160 3.578 0.000 0.259 0.888 3.057 0.868
## math =~
## ssar (.p4.) 3.529 0.174 20.293 0.000 3.188 3.870 7.352 0.953
## ssmk (.p5.) 2.942 0.145 20.350 0.000 2.659 3.226 6.130 0.894
## ssmc (.p6.) 0.717 0.082 8.713 0.000 0.556 0.879 1.495 0.276
## electronic =~
## ssgs (.p7.) 0.786 0.068 11.571 0.000 0.653 0.919 1.649 0.303
## ssasi (.p8.) 2.223 0.118 18.806 0.000 1.992 2.455 4.667 0.830
## ssmc (.p9.) 1.573 0.106 14.821 0.000 1.365 1.781 3.302 0.609
## ssei (.10.) 2.021 0.098 20.591 0.000 1.829 2.214 4.243 0.949
## speed =~
## ssno (.11.) 0.508 0.024 21.116 0.000 0.461 0.555 0.852 0.877
## sscs (.12.) 0.443 0.022 19.796 0.000 0.399 0.486 0.743 0.818
## g =~
## verbal (.13.) 5.235 1.516 3.452 0.001 2.263 8.208 0.982 0.982
## math (.14.) 1.828 0.108 16.881 0.000 1.616 2.040 0.877 0.877
## elctrnc 1.846 0.121 15.310 0.000 1.609 2.082 0.879 0.879
## speed (.16.) 1.348 0.082 16.399 0.000 1.187 1.509 0.803 0.803
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 16.459 0.188 87.711 0.000 16.091 16.827 16.459 3.027
## .sswk (.33.) 25.395 0.285 89.250 0.000 24.837 25.953 25.395 3.066
## .sspc 10.375 0.126 82.229 0.000 10.127 10.622 10.375 2.946
## .ssar (.35.) 18.320 0.291 63.004 0.000 17.750 18.890 18.320 2.375
## .ssmk (.36.) 14.312 0.251 56.912 0.000 13.820 14.805 14.312 2.087
## .ssmc (.37.) 15.740 0.197 79.986 0.000 15.355 16.126 15.740 2.901
## .ssasi (.38.) 16.085 0.199 81.005 0.000 15.696 16.475 16.085 2.860
## .ssei 12.364 0.157 78.688 0.000 12.056 12.672 12.364 2.765
## .ssno (.40.) 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.061
## .sscs -0.083 0.033 -2.497 0.013 -0.149 -0.018 -0.083 -0.092
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.220 0.341 15.298 0.000 4.551 5.888 5.220 0.177
## .sswk 8.110 0.780 10.402 0.000 6.582 9.638 8.110 0.118
## .sspc 3.053 0.199 15.308 0.000 2.662 3.444 3.053 0.246
## .ssar 5.422 0.792 6.845 0.000 3.870 6.975 5.422 0.091
## .ssmk 9.451 0.722 13.086 0.000 8.035 10.866 9.451 0.201
## .ssmc 8.680 0.544 15.959 0.000 7.614 9.746 8.680 0.295
## .ssasi 9.850 0.758 12.991 0.000 8.364 11.336 9.850 0.311
## .ssei 1.991 0.265 7.519 0.000 1.472 2.510 1.991 0.100
## .ssno 0.218 0.025 8.672 0.000 0.168 0.267 0.218 0.231
## .sscs 0.273 0.035 7.820 0.000 0.204 0.341 0.273 0.331
## .verbal 1.000 1.000 1.000 0.035 0.035
## .math 1.000 1.000 1.000 0.230 0.230
## .electronic 1.000 1.000 1.000 0.227 0.227
## .speed 1.000 1.000 1.000 0.355 0.355
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.645 0.180 3.593 0.000 0.293 0.997 3.167 0.683
## sswk (.p2.) 1.459 0.410 3.558 0.000 0.655 2.263 7.160 0.934
## sspc (.p3.) 0.574 0.160 3.578 0.000 0.259 0.888 2.814 0.866
## math =~
## ssar (.p4.) 3.529 0.174 20.293 0.000 3.188 3.870 6.588 0.940
## ssmk (.p5.) 2.942 0.145 20.350 0.000 2.659 3.226 5.493 0.872
## ssmc (.p6.) 0.717 0.082 8.713 0.000 0.556 0.879 1.339 0.312
## electronic =~
## ssgs (.p7.) 0.786 0.068 11.571 0.000 0.653 0.919 1.015 0.219
## ssasi (.p8.) 2.223 0.118 18.806 0.000 1.992 2.455 2.872 0.755
## ssmc (.p9.) 1.573 0.106 14.821 0.000 1.365 1.781 2.032 0.473
## ssei (.10.) 2.021 0.098 20.591 0.000 1.829 2.214 2.611 0.792
## speed =~
## ssno (.11.) 0.508 0.024 21.116 0.000 0.461 0.555 0.810 0.868
## sscs (.12.) 0.443 0.022 19.796 0.000 0.399 0.486 0.707 0.764
## g =~
## verbal (.13.) 5.235 1.516 3.452 0.001 2.263 8.208 0.962 0.962
## math (.14.) 1.828 0.108 16.881 0.000 1.616 2.040 0.883 0.883
## elctrnc 1.340 0.084 15.889 0.000 1.175 1.505 0.935 0.935
## speed (.16.) 1.348 0.082 16.399 0.000 1.187 1.509 0.762 0.762
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 16.459 0.188 87.711 0.000 16.091 16.827 16.459 3.547
## .sswk (.33.) 25.395 0.285 89.250 0.000 24.837 25.953 25.395 3.313
## .sspc 11.056 0.131 84.478 0.000 10.799 11.313 11.056 3.404
## .ssar (.35.) 18.320 0.291 63.004 0.000 17.750 18.890 18.320 2.615
## .ssmk (.36.) 14.312 0.251 56.912 0.000 13.820 14.805 14.312 2.271
## .ssmc (.37.) 15.740 0.197 79.986 0.000 15.355 16.126 15.740 3.662
## .ssasi (.38.) 16.085 0.199 81.005 0.000 15.696 16.475 16.085 4.227
## .ssei 14.255 0.246 57.845 0.000 13.772 14.738 14.255 4.323
## .ssno (.40.) 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.063
## .sscs 0.198 0.041 4.864 0.000 0.118 0.277 0.198 0.214
## .verbal 0.768 0.071 10.785 0.000 0.628 0.907 0.156 0.156
## .math -0.167 0.092 -1.815 0.069 -0.347 0.013 -0.089 -0.089
## .elctrnc -2.209 0.152 -14.564 0.000 -2.507 -1.912 -1.710 -1.710
## .speed 0.642 0.094 6.856 0.000 0.459 0.826 0.402 0.402
## g -0.083 0.057 -1.476 0.140 -0.194 0.027 -0.093 -0.093
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 4.686 0.307 15.252 0.000 4.084 5.288 4.686 0.218
## .sswk 7.489 0.746 10.039 0.000 6.027 8.951 7.489 0.127
## .sspc 2.629 0.164 16.023 0.000 2.308 2.951 2.629 0.249
## .ssar 5.686 0.743 7.654 0.000 4.230 7.143 5.686 0.116
## .ssmk 9.541 0.720 13.242 0.000 8.129 10.953 9.541 0.240
## .ssmc 8.059 0.463 17.403 0.000 7.151 8.966 8.059 0.436
## .ssasi 6.236 0.427 14.601 0.000 5.399 7.073 6.236 0.431
## .ssei 4.052 0.297 13.648 0.000 3.470 4.634 4.052 0.373
## .ssno 0.215 0.030 7.210 0.000 0.156 0.273 0.215 0.246
## .sscs 0.357 0.040 8.991 0.000 0.279 0.434 0.357 0.417
## .verbal 1.785 1.008 1.770 0.077 -0.192 3.761 0.074 0.074
## .math 0.769 0.101 7.588 0.000 0.570 0.967 0.221 0.221
## .electronic 0.209 0.055 3.805 0.000 0.101 0.317 0.125 0.125
## .speed 1.070 0.130 8.204 0.000 0.815 1.326 0.420 0.420
## g 0.813 0.050 16.404 0.000 0.716 0.910 1.000 1.000
strict<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("g=~electronic", "sspc~1", "ssei~1", "sscs~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 (= 7.984848e-13) 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 aic bic
## 771.478 80.000 0.000 0.963 0.090 0.042 98436.133 98719.420
Mc(strict)
## [1] 0.8503642
summary(strict, standardized=T, ci=T) # lv variances similar to scalar2, g -0.132 Std.all
## lavaan 0.6-18 ended normally after 116 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 32
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 771.478 506.021
## Degrees of freedom 80 80
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.525
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 470.949 308.901
## 1 300.529 197.121
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.708 0.166 4.268 0.000 0.383 1.034 3.419 0.631
## sswk (.p2.) 1.615 0.385 4.196 0.000 0.860 2.369 7.796 0.941
## sspc (.p3.) 0.636 0.151 4.226 0.000 0.341 0.931 3.072 0.877
## math =~
## ssar (.p4.) 3.491 0.169 20.697 0.000 3.160 3.821 7.338 0.952
## ssmk (.p5.) 2.911 0.141 20.639 0.000 2.634 3.187 6.119 0.893
## ssmc (.p6.) 0.675 0.081 8.340 0.000 0.516 0.833 1.418 0.263
## electronic =~
## ssgs (.p7.) 0.818 0.072 11.392 0.000 0.677 0.959 1.685 0.311
## ssasi (.p8.) 2.298 0.129 17.819 0.000 2.045 2.551 4.736 0.864
## ssmc (.p9.) 1.652 0.114 14.510 0.000 1.429 1.876 3.405 0.631
## ssei (.10.) 2.034 0.099 20.559 0.000 1.840 2.228 4.191 0.916
## speed =~
## ssno (.11.) 0.498 0.025 20.097 0.000 0.450 0.547 0.847 0.876
## sscs (.12.) 0.436 0.021 20.289 0.000 0.394 0.478 0.740 0.798
## g =~
## verbal (.13.) 4.723 1.168 4.045 0.000 2.435 7.011 0.978 0.978
## math (.14.) 1.849 0.109 16.934 0.000 1.635 2.063 0.880 0.880
## elctrnc 1.802 0.123 14.659 0.000 1.561 2.043 0.874 0.874
## speed (.16.) 1.374 0.085 16.075 0.000 1.206 1.541 0.808 0.808
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 16.459 0.188 87.625 0.000 16.090 16.827 16.459 3.039
## .sswk (.33.) 25.395 0.284 89.322 0.000 24.838 25.952 25.395 3.067
## .sspc 10.375 0.126 82.229 0.000 10.127 10.622 10.375 2.961
## .ssar (.35.) 18.314 0.289 63.398 0.000 17.748 18.880 18.314 2.376
## .ssmk (.36.) 14.313 0.250 57.277 0.000 13.823 14.803 14.313 2.089
## .ssmc (.37.) 15.752 0.196 80.223 0.000 15.368 16.137 15.752 2.917
## .ssasi (.38.) 16.099 0.197 81.541 0.000 15.712 16.486 16.099 2.938
## .ssei 12.364 0.157 78.687 0.000 12.056 12.672 12.364 2.704
## .ssno (.40.) 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.061
## .sscs -0.083 0.033 -2.497 0.013 -0.149 -0.018 -0.083 -0.090
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.17.) 4.935 0.233 21.210 0.000 4.479 5.391 4.935 0.168
## .sswk (.18.) 7.807 0.551 14.180 0.000 6.728 8.886 7.807 0.114
## .sspc (.19.) 2.840 0.131 21.749 0.000 2.584 3.096 2.840 0.231
## .ssar (.20.) 5.550 0.571 9.713 0.000 4.430 6.669 5.550 0.093
## .ssmk (.21.) 9.487 0.540 17.569 0.000 8.429 10.545 9.487 0.202
## .ssmc (.22.) 8.128 0.358 22.699 0.000 7.426 8.829 8.128 0.279
## .ssasi (.23.) 7.597 0.433 17.538 0.000 6.748 8.446 7.597 0.253
## .ssei (.24.) 3.348 0.221 15.153 0.000 2.915 3.782 3.348 0.160
## .ssno (.25.) 0.218 0.021 10.280 0.000 0.176 0.259 0.218 0.233
## .sscs (.26.) 0.312 0.028 10.998 0.000 0.257 0.368 0.312 0.363
## .verbal 1.000 1.000 1.000 0.043 0.043
## .math 1.000 1.000 1.000 0.226 0.226
## .elctrnc 1.000 1.000 1.000 0.235 0.235
## .speed 1.000 1.000 1.000 0.346 0.346
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.708 0.166 4.268 0.000 0.383 1.034 3.128 0.671
## sswk (.p2.) 1.615 0.385 4.196 0.000 0.860 2.369 7.132 0.931
## sspc (.p3.) 0.636 0.151 4.226 0.000 0.341 0.931 2.810 0.858
## math =~
## ssar (.p4.) 3.491 0.169 20.697 0.000 3.160 3.821 6.603 0.942
## ssmk (.p5.) 2.911 0.141 20.639 0.000 2.634 3.187 5.506 0.873
## ssmc (.p6.) 0.675 0.081 8.340 0.000 0.516 0.833 1.276 0.295
## electronic =~
## ssgs (.p7.) 0.818 0.072 11.392 0.000 0.677 0.959 1.051 0.225
## ssasi (.p8.) 2.298 0.129 17.819 0.000 2.045 2.551 2.954 0.731
## ssmc (.p9.) 1.652 0.114 14.510 0.000 1.429 1.876 2.124 0.491
## ssei (.10.) 2.034 0.099 20.559 0.000 1.840 2.228 2.614 0.819
## speed =~
## ssno (.11.) 0.498 0.025 20.097 0.000 0.450 0.547 0.814 0.868
## sscs (.12.) 0.436 0.021 20.289 0.000 0.394 0.478 0.712 0.786
## g =~
## verbal (.13.) 4.723 1.168 4.045 0.000 2.435 7.011 0.965 0.965
## math (.14.) 1.849 0.109 16.934 0.000 1.635 2.063 0.882 0.882
## elctrnc 1.326 0.085 15.548 0.000 1.159 1.493 0.931 0.931
## speed (.16.) 1.374 0.085 16.075 0.000 1.206 1.541 0.759 0.759
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 16.459 0.188 87.625 0.000 16.090 16.827 16.459 3.531
## .sswk (.33.) 25.395 0.284 89.322 0.000 24.838 25.952 25.395 3.315
## .sspc 11.054 0.131 84.193 0.000 10.797 11.311 11.054 3.374
## .ssar (.35.) 18.314 0.289 63.398 0.000 17.748 18.880 18.314 2.612
## .ssmk (.36.) 14.313 0.250 57.277 0.000 13.823 14.803 14.313 2.269
## .ssmc (.37.) 15.752 0.196 80.223 0.000 15.368 16.137 15.752 3.641
## .ssasi (.38.) 16.099 0.197 81.541 0.000 15.712 16.486 16.099 3.985
## .ssei 14.110 0.237 59.454 0.000 13.645 14.576 14.110 4.423
## .ssno (.40.) 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.063
## .sscs 0.197 0.041 4.831 0.000 0.117 0.277 0.197 0.218
## .verbal 0.865 0.080 10.877 0.000 0.709 1.021 0.196 0.196
## .math -0.101 0.091 -1.111 0.266 -0.280 0.077 -0.054 -0.054
## .elctrnc -2.078 0.150 -13.812 0.000 -2.373 -1.783 -1.617 -1.617
## .speed 0.704 0.095 7.407 0.000 0.518 0.890 0.431 0.431
## g -0.120 0.055 -2.170 0.030 -0.227 -0.012 -0.132 -0.132
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.17.) 4.935 0.233 21.210 0.000 4.479 5.391 4.935 0.227
## .sswk (.18.) 7.807 0.551 14.180 0.000 6.728 8.886 7.807 0.133
## .sspc (.19.) 2.840 0.131 21.749 0.000 2.584 3.096 2.840 0.265
## .ssar (.20.) 5.550 0.571 9.713 0.000 4.430 6.669 5.550 0.113
## .ssmk (.21.) 9.487 0.540 17.569 0.000 8.429 10.545 9.487 0.238
## .ssmc (.22.) 8.128 0.358 22.699 0.000 7.426 8.829 8.128 0.434
## .ssasi (.23.) 7.597 0.433 17.538 0.000 6.748 8.446 7.597 0.465
## .ssei (.24.) 3.348 0.221 15.153 0.000 2.915 3.782 3.348 0.329
## .ssno (.25.) 0.218 0.021 10.280 0.000 0.176 0.259 0.218 0.247
## .sscs (.26.) 0.312 0.028 10.998 0.000 0.257 0.368 0.312 0.381
## .verbal 1.354 0.641 2.113 0.035 0.098 2.610 0.069 0.069
## .math 0.796 0.096 8.295 0.000 0.608 0.984 0.222 0.222
## .elctrnc 0.221 0.057 3.865 0.000 0.109 0.332 0.134 0.134
## .speed 1.133 0.128 8.870 0.000 0.882 1.383 0.424 0.424
## g 0.814 0.050 16.398 0.000 0.717 0.911 1.000 1.000
latent<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("g=~electronic", "sspc~1", "ssei~1", "sscs~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 (= 9.286555e-14) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(latent, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 795.399 75.000 0.000 0.962 0.095 0.067 98470.054 98781.670
Mc(latent)
## [1] 0.8446187
latent2<-cfa(hof.lv, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "sspc~1", "ssei~1", "sscs~1"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= 4.531887e-14) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(latent2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 696.995 74.000 0.000 0.967 0.089 0.065 98373.649 98690.931
Mc(latent2)
## [1] 0.8641255
summary(latent2, standardized=T, ci=T) # g -0.151 Std.all
## lavaan 0.6-18 ended normally after 109 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 78
## Number of equality constraints 22
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 696.995 473.788
## Degrees of freedom 74 74
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.471
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 430.468 292.614
## 1 266.527 181.174
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.756 0.107 7.048 0.000 0.546 0.966 3.305 0.628
## sswk (.p2.) 1.711 0.249 6.868 0.000 1.223 2.199 7.478 0.935
## sspc (.p3.) 0.673 0.097 6.917 0.000 0.482 0.863 2.940 0.860
## math =~
## ssar (.p4.) 3.325 0.126 26.307 0.000 3.077 3.572 6.986 0.946
## ssmk (.p5.) 2.772 0.104 26.723 0.000 2.569 2.976 5.826 0.885
## ssmc (.p6.) 0.681 0.076 8.955 0.000 0.532 0.830 1.431 0.271
## electronic =~
## ssgs (.p7.) 0.788 0.069 11.495 0.000 0.654 0.922 1.606 0.305
## ssasi (.p8.) 2.223 0.121 18.418 0.000 1.987 2.460 4.533 0.822
## ssmc (.p9.) 1.569 0.108 14.571 0.000 1.358 1.780 3.198 0.605
## ssei (.10.) 2.021 0.100 20.184 0.000 1.825 2.218 4.121 0.946
## speed =~
## ssno (.11.) 0.513 0.018 28.904 0.000 0.479 0.548 0.831 0.873
## sscs (.12.) 0.449 0.017 26.950 0.000 0.416 0.481 0.726 0.812
## g =~
## verbal (.13.) 4.255 0.651 6.539 0.000 2.979 5.530 0.973 0.973
## math (.14.) 1.848 0.087 21.140 0.000 1.677 2.020 0.880 0.880
## elctrnc 1.776 0.115 15.395 0.000 1.550 2.003 0.871 0.871
## speed (.16.) 1.273 0.062 20.509 0.000 1.151 1.395 0.786 0.786
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 16.461 0.187 87.841 0.000 16.094 16.829 16.461 3.127
## .sswk (.33.) 25.394 0.285 89.182 0.000 24.836 25.952 25.394 3.176
## .sspc 10.375 0.126 82.229 0.000 10.127 10.622 10.375 3.034
## .ssar (.35.) 18.311 0.291 62.890 0.000 17.740 18.882 18.311 2.480
## .ssmk (.36.) 14.312 0.252 56.897 0.000 13.819 14.805 14.312 2.173
## .ssmc (.37.) 15.737 0.197 80.017 0.000 15.352 16.122 15.737 2.976
## .ssasi (.38.) 16.087 0.199 80.911 0.000 15.697 16.476 16.087 2.918
## .ssei 12.364 0.157 78.687 0.000 12.056 12.672 12.364 2.839
## .ssno (.40.) 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.062
## .sscs -0.083 0.033 -2.497 0.013 -0.149 -0.018 -0.083 -0.093
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.052 0.052
## .math 1.000 1.000 1.000 0.226 0.226
## .speed 1.000 1.000 1.000 0.382 0.382
## g 1.000 1.000 1.000 1.000 1.000
## .ssgs 5.211 0.341 15.298 0.000 4.544 5.879 5.211 0.188
## .sswk 8.015 0.746 10.738 0.000 6.552 9.478 8.015 0.125
## .sspc 3.052 0.199 15.319 0.000 2.662 3.443 3.052 0.261
## .ssar 5.696 0.756 7.537 0.000 4.214 7.177 5.696 0.104
## .ssmk 9.436 0.709 13.313 0.000 8.047 10.825 9.436 0.218
## .ssmc 8.670 0.546 15.888 0.000 7.600 9.739 8.670 0.310
## .ssasi 9.851 0.757 13.008 0.000 8.367 11.335 9.851 0.324
## .ssei 1.994 0.269 7.419 0.000 1.467 2.521 1.994 0.105
## .ssno 0.215 0.025 8.708 0.000 0.167 0.263 0.215 0.237
## .sscs 0.272 0.035 7.770 0.000 0.203 0.341 0.272 0.340
## .electronic 1.000 1.000 1.000 0.241 0.241
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.756 0.107 7.048 0.000 0.546 0.966 3.305 0.688
## sswk (.p2.) 1.711 0.249 6.868 0.000 1.223 2.199 7.478 0.938
## sspc (.p3.) 0.673 0.097 6.917 0.000 0.482 0.863 2.940 0.876
## math =~
## ssar (.p4.) 3.325 0.126 26.307 0.000 3.077 3.572 6.986 0.949
## ssmk (.p5.) 2.772 0.104 26.723 0.000 2.569 2.976 5.826 0.883
## ssmc (.p6.) 0.681 0.076 8.955 0.000 0.532 0.830 1.431 0.324
## electronic =~
## ssgs (.p7.) 0.788 0.069 11.495 0.000 0.654 0.922 1.057 0.220
## ssasi (.p8.) 2.223 0.121 18.418 0.000 1.987 2.460 2.982 0.767
## ssmc (.p9.) 1.569 0.108 14.571 0.000 1.358 1.780 2.104 0.476
## ssei (.10.) 2.021 0.100 20.184 0.000 1.825 2.218 2.711 0.803
## speed =~
## ssno (.11.) 0.513 0.018 28.904 0.000 0.479 0.548 0.831 0.870
## sscs (.12.) 0.449 0.017 26.950 0.000 0.416 0.481 0.726 0.773
## g =~
## verbal (.13.) 4.255 0.651 6.539 0.000 2.979 5.530 0.973 0.973
## math (.14.) 1.848 0.087 21.140 0.000 1.677 2.020 0.880 0.880
## elctrnc 1.258 0.074 16.956 0.000 1.112 1.403 0.938 0.938
## speed (.16.) 1.273 0.062 20.509 0.000 1.151 1.395 0.786 0.786
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 16.461 0.187 87.841 0.000 16.094 16.829 16.461 3.425
## .sswk (.33.) 25.394 0.285 89.182 0.000 24.836 25.952 25.394 3.186
## .sspc 11.055 0.131 84.443 0.000 10.798 11.311 11.055 3.293
## .ssar (.35.) 18.311 0.291 62.890 0.000 17.740 18.882 18.311 2.487
## .ssmk (.36.) 14.312 0.252 56.897 0.000 13.819 14.805 14.312 2.170
## .ssmc (.37.) 15.737 0.197 80.017 0.000 15.352 16.122 15.737 3.561
## .ssasi (.38.) 16.087 0.199 80.911 0.000 15.697 16.476 16.087 4.137
## .ssei 14.256 0.248 57.595 0.000 13.771 14.741 14.256 4.224
## .ssno (.40.) 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.062
## .sscs 0.197 0.041 4.841 0.000 0.117 0.277 0.197 0.210
## .verbal 0.925 0.069 13.447 0.000 0.790 1.059 0.212 0.212
## .math -0.061 0.079 -0.774 0.439 -0.216 0.093 -0.029 -0.029
## .elctrnc -2.133 0.147 -14.485 0.000 -2.421 -1.844 -1.590 -1.590
## .speed 0.716 0.080 8.913 0.000 0.558 0.873 0.442 0.442
## g -0.151 0.054 -2.784 0.005 -0.257 -0.045 -0.151 -0.151
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.052 0.052
## .math 1.000 1.000 1.000 0.226 0.226
## .speed 1.000 1.000 1.000 0.382 0.382
## g 1.000 1.000 1.000 1.000 1.000
## .ssgs 4.689 0.307 15.272 0.000 4.087 5.291 4.689 0.203
## .sswk 7.586 0.725 10.459 0.000 6.164 9.007 7.586 0.119
## .sspc 2.631 0.164 16.003 0.000 2.309 2.953 2.631 0.233
## .ssar 5.407 0.738 7.331 0.000 3.961 6.853 5.407 0.100
## .ssmk 9.567 0.741 12.912 0.000 8.115 11.019 9.567 0.220
## .ssmc 8.082 0.463 17.449 0.000 7.175 8.990 8.082 0.414
## .ssasi 6.228 0.426 14.628 0.000 5.394 7.063 6.228 0.412
## .ssei 4.042 0.297 13.615 0.000 3.460 4.624 4.042 0.355
## .ssno 0.222 0.028 7.895 0.000 0.167 0.277 0.222 0.243
## .sscs 0.355 0.039 9.034 0.000 0.278 0.432 0.355 0.402
## .electronic 0.218 0.055 3.927 0.000 0.109 0.326 0.121 0.121
weak<-cfa(hof.weak, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "sspc~1", "ssei~1", "sscs~1"))
fitMeasures(weak, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 696.995 75.000 0.000 0.967 0.088 0.065 98371.649 98683.266
Mc(weak)
## [1] 0.8643281
summary(weak, standardized=T, ci=T) # -0.184
## lavaan 0.6-18 ended normally after 113 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 77
## Number of equality constraints 22
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 696.995 480.191
## Degrees of freedom 75 75
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.451
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 430.468 296.568
## 1 266.527 183.623
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.756 0.107 7.048 0.000 0.546 0.966 3.305 0.628
## sswk (.p2.) 1.711 0.249 6.868 0.000 1.223 2.199 7.478 0.935
## sspc (.p3.) 0.673 0.097 6.917 0.000 0.482 0.863 2.940 0.860
## math =~
## ssar (.p4.) 3.325 0.126 26.307 0.000 3.077 3.572 6.986 0.946
## ssmk (.p5.) 2.772 0.104 26.723 0.000 2.569 2.976 5.826 0.885
## ssmc (.p6.) 0.681 0.076 8.955 0.000 0.532 0.830 1.431 0.271
## electronic =~
## ssgs (.p7.) 0.788 0.069 11.495 0.000 0.654 0.922 1.606 0.305
## ssasi (.p8.) 2.223 0.121 18.418 0.000 1.987 2.460 4.533 0.822
## ssmc (.p9.) 1.569 0.108 14.571 0.000 1.358 1.780 3.198 0.605
## ssei (.10.) 2.021 0.100 20.184 0.000 1.825 2.218 4.121 0.946
## speed =~
## ssno (.11.) 0.513 0.018 28.904 0.000 0.479 0.548 0.831 0.873
## sscs (.12.) 0.449 0.017 26.950 0.000 0.416 0.481 0.726 0.812
## g =~
## verbal (.13.) 4.255 0.651 6.539 0.000 2.979 5.530 0.973 0.973
## math (.14.) 1.848 0.087 21.140 0.000 1.677 2.020 0.880 0.880
## elctrnc 1.776 0.115 15.395 0.000 1.550 2.003 0.871 0.871
## speed (.16.) 1.273 0.062 20.509 0.000 1.151 1.395 0.786 0.786
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.33.) 16.461 0.187 87.841 0.000 16.094 16.829 16.461 3.127
## .sswk (.34.) 25.394 0.285 89.182 0.000 24.836 25.952 25.394 3.176
## .sspc 10.375 0.126 82.229 0.000 10.127 10.622 10.375 3.034
## .ssar (.36.) 18.311 0.291 62.890 0.000 17.740 18.882 18.311 2.480
## .ssmk (.37.) 14.312 0.252 56.897 0.000 13.819 14.805 14.312 2.173
## .ssmc (.38.) 15.737 0.197 80.017 0.000 15.352 16.122 15.737 2.976
## .ssasi (.39.) 16.087 0.199 80.911 0.000 15.697 16.476 16.087 2.918
## .ssei 12.364 0.157 78.687 0.000 12.056 12.672 12.364 2.839
## .ssno (.41.) 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.062
## .sscs -0.083 0.033 -2.497 0.013 -0.149 -0.018 -0.083 -0.093
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.052 0.052
## .math 1.000 1.000 1.000 0.226 0.226
## .speed 1.000 1.000 1.000 0.382 0.382
## g 1.000 1.000 1.000 1.000 1.000
## .ssgs 5.211 0.341 15.298 0.000 4.544 5.879 5.211 0.188
## .sswk 8.015 0.746 10.738 0.000 6.552 9.478 8.015 0.125
## .sspc 3.052 0.199 15.319 0.000 2.662 3.443 3.052 0.261
## .ssar 5.696 0.756 7.537 0.000 4.214 7.177 5.696 0.104
## .ssmk 9.436 0.709 13.313 0.000 8.047 10.825 9.436 0.218
## .ssmc 8.670 0.546 15.888 0.000 7.600 9.739 8.670 0.310
## .ssasi 9.851 0.757 13.008 0.000 8.367 11.335 9.851 0.324
## .ssei 1.994 0.269 7.419 0.000 1.467 2.521 1.994 0.105
## .ssno 0.215 0.025 8.708 0.000 0.167 0.263 0.215 0.237
## .sscs 0.272 0.035 7.770 0.000 0.203 0.341 0.272 0.340
## .electronic 1.000 1.000 1.000 0.241 0.241
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.756 0.107 7.048 0.000 0.546 0.966 3.305 0.688
## sswk (.p2.) 1.711 0.249 6.868 0.000 1.223 2.199 7.478 0.938
## sspc (.p3.) 0.673 0.097 6.917 0.000 0.482 0.863 2.940 0.876
## math =~
## ssar (.p4.) 3.325 0.126 26.307 0.000 3.077 3.572 6.986 0.949
## ssmk (.p5.) 2.772 0.104 26.723 0.000 2.569 2.976 5.826 0.883
## ssmc (.p6.) 0.681 0.076 8.955 0.000 0.532 0.830 1.431 0.324
## electronic =~
## ssgs (.p7.) 0.788 0.069 11.495 0.000 0.654 0.922 1.057 0.220
## ssasi (.p8.) 2.223 0.121 18.418 0.000 1.987 2.460 2.982 0.767
## ssmc (.p9.) 1.569 0.108 14.571 0.000 1.358 1.780 2.104 0.476
## ssei (.10.) 2.021 0.100 20.184 0.000 1.825 2.218 2.711 0.803
## speed =~
## ssno (.11.) 0.513 0.018 28.904 0.000 0.479 0.548 0.831 0.870
## sscs (.12.) 0.449 0.017 26.950 0.000 0.416 0.481 0.726 0.773
## g =~
## verbal (.13.) 4.255 0.651 6.539 0.000 2.979 5.530 0.973 0.973
## math (.14.) 1.848 0.087 21.140 0.000 1.677 2.020 0.880 0.880
## elctrnc 1.258 0.074 16.956 0.000 1.112 1.403 0.938 0.938
## speed (.16.) 1.273 0.062 20.509 0.000 1.151 1.395 0.786 0.786
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.33.) 16.461 0.187 87.841 0.000 16.094 16.829 16.461 3.425
## .sswk (.34.) 25.394 0.285 89.182 0.000 24.836 25.952 25.394 3.186
## .sspc 11.055 0.131 84.443 0.000 10.798 11.311 11.055 3.293
## .ssar (.36.) 18.311 0.291 62.890 0.000 17.740 18.882 18.311 2.487
## .ssmk (.37.) 14.312 0.252 56.897 0.000 13.819 14.805 14.312 2.170
## .ssmc (.38.) 15.737 0.197 80.017 0.000 15.352 16.122 15.737 3.561
## .ssasi (.39.) 16.087 0.199 80.911 0.000 15.697 16.476 16.087 4.137
## .ssei 14.256 0.248 57.595 0.000 13.771 14.741 14.256 4.224
## .ssno (.41.) 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.062
## .sscs 0.197 0.041 4.841 0.000 0.117 0.277 0.197 0.210
## .verbal 1.065 0.249 4.277 0.000 0.577 1.553 0.244 0.244
## .elctrnc -2.091 0.152 -13.733 0.000 -2.390 -1.793 -1.559 -1.559
## .speed 0.758 0.080 9.440 0.000 0.600 0.915 0.468 0.468
## g -0.184 0.064 -2.877 0.004 -0.309 -0.059 -0.184 -0.184
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.052 0.052
## .math 1.000 1.000 1.000 0.226 0.226
## .speed 1.000 1.000 1.000 0.382 0.382
## g 1.000 1.000 1.000 1.000 1.000
## .ssgs 4.689 0.307 15.272 0.000 4.087 5.291 4.689 0.203
## .sswk 7.586 0.725 10.459 0.000 6.164 9.007 7.586 0.119
## .sspc 2.631 0.164 16.003 0.000 2.309 2.953 2.631 0.233
## .ssar 5.407 0.738 7.331 0.000 3.961 6.853 5.407 0.100
## .ssmk 9.567 0.741 12.912 0.000 8.115 11.019 9.567 0.220
## .ssmc 8.082 0.463 17.449 0.000 7.174 8.990 8.082 0.414
## .ssasi 6.228 0.426 14.628 0.000 5.394 7.063 6.228 0.412
## .ssei 4.042 0.297 13.615 0.000 3.460 4.624 4.042 0.355
## .ssno 0.222 0.028 7.895 0.000 0.167 0.277 0.222 0.243
## .sscs 0.355 0.039 9.034 0.000 0.278 0.432 0.355 0.402
## .electronic 0.218 0.055 3.927 0.000 0.109 0.326 0.121 0.121
lvstrict<-cfa(hof.lv, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("g=~electronic", "sspc~1", "ssei~1", "sscs~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 (= 1.672352e-13) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(lvstrict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 786.869 84.000 0.000 0.963 0.089 0.071 98443.524 98704.148
Mc(lvstrict)
## [1] 0.8480966
summary(lvstrict, standardized=T, ci=T) # -0.126
## lavaan 0.6-18 ended normally after 97 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 78
## Number of equality constraints 32
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 786.869 521.353
## Degrees of freedom 84 84
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.509
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 478.250 316.872
## 1 308.620 204.481
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.766 0.108 7.090 0.000 0.554 0.977 3.276 0.626
## sswk (.p2.) 1.748 0.253 6.895 0.000 1.251 2.244 7.478 0.937
## sspc (.p3.) 0.689 0.099 6.954 0.000 0.495 0.883 2.946 0.868
## math =~
## ssar (.p4.) 3.312 0.127 26.127 0.000 3.064 3.561 6.988 0.948
## ssmk (.p5.) 2.762 0.104 26.518 0.000 2.558 2.966 5.827 0.884
## ssmc (.p6.) 0.644 0.075 8.572 0.000 0.497 0.791 1.358 0.258
## electronic =~
## ssgs (.p7.) 0.820 0.072 11.399 0.000 0.679 0.961 1.642 0.313
## ssasi (.p8.) 2.298 0.131 17.594 0.000 2.042 2.554 4.600 0.858
## ssmc (.p9.) 1.649 0.115 14.387 0.000 1.425 1.874 3.301 0.627
## ssei (.10.) 2.034 0.100 20.291 0.000 1.837 2.230 4.070 0.912
## speed =~
## ssno (.11.) 0.513 0.018 28.919 0.000 0.478 0.548 0.832 0.872
## sscs (.12.) 0.449 0.017 27.035 0.000 0.416 0.481 0.727 0.793
## g =~
## verbal (.13.) 4.160 0.635 6.555 0.000 2.916 5.404 0.972 0.972
## math (.14.) 1.857 0.088 21.009 0.000 1.684 2.031 0.881 0.881
## elctrnc 1.734 0.117 14.825 0.000 1.504 1.963 0.866 0.866
## speed (.16.) 1.275 0.062 20.497 0.000 1.153 1.397 0.787 0.787
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 16.461 0.188 87.723 0.000 16.093 16.829 16.461 3.143
## .sswk (.33.) 25.393 0.284 89.284 0.000 24.836 25.951 25.393 3.181
## .sspc 10.375 0.126 82.229 0.000 10.127 10.622 10.375 3.057
## .ssar (.35.) 18.314 0.289 63.348 0.000 17.748 18.881 18.314 2.484
## .ssmk (.36.) 14.313 0.250 57.247 0.000 13.823 14.803 14.313 2.172
## .ssmc (.37.) 15.750 0.196 80.241 0.000 15.365 16.135 15.750 2.992
## .ssasi (.38.) 16.099 0.198 81.490 0.000 15.712 16.486 16.099 3.003
## .ssei 12.364 0.157 78.688 0.000 12.056 12.672 12.364 2.771
## .ssno (.40.) 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.062
## .sscs -0.083 0.033 -2.497 0.013 -0.149 -0.018 -0.083 -0.091
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.055 0.055
## .math 1.000 1.000 1.000 0.225 0.225
## .speed 1.000 1.000 1.000 0.381 0.381
## g 1.000 1.000 1.000 1.000 1.000
## .ssgs (.21.) 4.937 0.233 21.222 0.000 4.481 5.393 4.937 0.180
## .sswk (.22.) 7.808 0.551 14.184 0.000 6.729 8.887 7.808 0.123
## .sspc (.23.) 2.839 0.130 21.780 0.000 2.584 3.095 2.839 0.246
## .ssar (.24.) 5.547 0.574 9.662 0.000 4.421 6.672 5.547 0.102
## .ssmk (.25.) 9.492 0.541 17.550 0.000 8.432 10.552 9.492 0.218
## .ssmc (.26.) 8.130 0.358 22.724 0.000 7.429 8.832 8.130 0.293
## .ssasi (.27.) 7.594 0.433 17.548 0.000 6.745 8.442 7.594 0.264
## .ssei (.28.) 3.346 0.222 15.101 0.000 2.912 3.781 3.346 0.168
## .ssno (.29.) 0.217 0.021 10.296 0.000 0.176 0.259 0.217 0.239
## .sscs (.30.) 0.313 0.028 11.033 0.000 0.257 0.368 0.313 0.372
## .elctrnc 1.000 1.000 1.000 0.250 0.250
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.766 0.108 7.090 0.000 0.554 0.977 3.276 0.678
## sswk (.p2.) 1.748 0.253 6.895 0.000 1.251 2.244 7.478 0.937
## sspc (.p3.) 0.689 0.099 6.954 0.000 0.495 0.883 2.946 0.868
## math =~
## ssar (.p4.) 3.312 0.127 26.127 0.000 3.064 3.561 6.988 0.948
## ssmk (.p5.) 2.762 0.104 26.518 0.000 2.558 2.966 5.827 0.884
## ssmc (.p6.) 0.644 0.075 8.572 0.000 0.497 0.791 1.358 0.306
## electronic =~
## ssgs (.p7.) 0.820 0.072 11.399 0.000 0.679 0.961 1.095 0.226
## ssasi (.p8.) 2.298 0.131 17.594 0.000 2.042 2.554 3.068 0.744
## ssmc (.p9.) 1.649 0.115 14.387 0.000 1.425 1.874 2.202 0.496
## ssei (.10.) 2.034 0.100 20.291 0.000 1.837 2.230 2.715 0.829
## speed =~
## ssno (.11.) 0.513 0.018 28.919 0.000 0.478 0.548 0.832 0.872
## sscs (.12.) 0.449 0.017 27.035 0.000 0.416 0.481 0.727 0.793
## g =~
## verbal (.13.) 4.160 0.635 6.555 0.000 2.916 5.404 0.972 0.972
## math (.14.) 1.857 0.088 21.009 0.000 1.684 2.031 0.881 0.881
## elctrnc 1.247 0.075 16.726 0.000 1.101 1.393 0.934 0.934
## speed (.16.) 1.275 0.062 20.497 0.000 1.153 1.397 0.787 0.787
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 16.461 0.188 87.723 0.000 16.093 16.829 16.461 3.404
## .sswk (.33.) 25.393 0.284 89.284 0.000 24.836 25.951 25.393 3.181
## .sspc 11.053 0.131 84.153 0.000 10.795 11.310 11.053 3.256
## .ssar (.35.) 18.314 0.289 63.348 0.000 17.748 18.881 18.314 2.484
## .ssmk (.36.) 14.313 0.250 57.247 0.000 13.823 14.803 14.313 2.172
## .ssmc (.37.) 15.750 0.196 80.241 0.000 15.365 16.135 15.750 3.545
## .ssasi (.38.) 16.099 0.198 81.490 0.000 15.712 16.486 16.099 3.904
## .ssei 14.112 0.238 59.415 0.000 13.646 14.577 14.112 4.311
## .ssno (.40.) 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.062
## .sscs 0.197 0.041 4.851 0.000 0.117 0.277 0.197 0.215
## .verbal 0.803 0.067 12.031 0.000 0.672 0.934 0.188 0.188
## .math -0.106 0.075 -1.407 0.159 -0.254 0.042 -0.050 -0.050
## .elctrnc -2.080 0.145 -14.317 0.000 -2.365 -1.795 -1.558 -1.558
## .speed 0.684 0.078 8.740 0.000 0.531 0.838 0.422 0.422
## g -0.126 0.053 -2.358 0.018 -0.230 -0.021 -0.126 -0.126
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.055 0.055
## .math 1.000 1.000 1.000 0.225 0.225
## .speed 1.000 1.000 1.000 0.381 0.381
## g 1.000 1.000 1.000 1.000 1.000
## .ssgs (.21.) 4.937 0.233 21.222 0.000 4.481 5.393 4.937 0.211
## .sswk (.22.) 7.808 0.551 14.184 0.000 6.729 8.887 7.808 0.123
## .sspc (.23.) 2.839 0.130 21.780 0.000 2.584 3.095 2.839 0.246
## .ssar (.24.) 5.547 0.574 9.662 0.000 4.421 6.672 5.547 0.102
## .ssmk (.25.) 9.492 0.541 17.550 0.000 8.432 10.552 9.492 0.218
## .ssmc (.26.) 8.130 0.358 22.724 0.000 7.429 8.832 8.130 0.412
## .ssasi (.27.) 7.594 0.433 17.548 0.000 6.745 8.442 7.594 0.447
## .ssei (.28.) 3.346 0.222 15.101 0.000 2.912 3.781 3.346 0.312
## .ssno (.29.) 0.217 0.021 10.296 0.000 0.176 0.259 0.217 0.239
## .sscs (.30.) 0.313 0.028 11.033 0.000 0.257 0.368 0.313 0.372
## .elctrnc 0.227 0.058 3.939 0.000 0.114 0.340 0.128 0.128
tests<-lavTestLRT(configural, metric2, scalar2, latent2, weak)
## Warning: lavaan->lav_test_diff_SatorraBentler2001():
## scaling factor is negative
Td=tests[2:5,"Chisq diff"]
Td
## [1] 29.53607 31.78043 12.80516 NA
dfd=tests[2:5,"Df diff"]
dfd
## [1] 10 2 4 1
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-1067+ 1067 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04280949 0.11818759 0.04544228 NA
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.02543736 0.06108027
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.0841313 0.1559762
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.01899893 0.07442759
RMSEA.CI(T=Td[4],df=dfd[4],N=N,G=2)
## [1] NA NA
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 0.999 0.997 0.281 0.062 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 0.999 0.997 0.967 0.822
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
## 0.988 0.980 0.448 0.228 0.023 0.001
round(pvals(T=Td[4],df=dfd[4],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## NA NA NA NA NA NA
tests<-lavTestLRT(configural, metric2, scalar2, latent)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 29.53607 31.78043 88.31230
dfd=tests[2:4,"Df diff"]
dfd
## [1] 10 2 5
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-1067+ 1067 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04280949 0.11818759 0.12502330
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.0841313 0.1559762
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.1029061 0.1484995
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 0.999 0.997 0.967 0.822
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 1.000 0.999 0.968
tests<-lavTestLRT(configural, metric2, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 29.53607 31.78043 50.14412
dfd=tests[2:4,"Df diff"]
dfd
## [1] 10 2 10
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-1067+ 1067 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04280949 0.11818759 0.06136664
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.02543736 0.06108027
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.0841313 0.1559762
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.04509472 0.07874115
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
## 0.999 0.997 0.281 0.062 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 0.999 0.997 0.967 0.822
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 0.880 0.581 0.039 0.000
tests<-lavTestLRT(configural, metric2, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 29.53607 230.31043
dfd=tests[2:3,"Df diff"]
dfd
## [1] 10 5
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-1067+ 1067 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04280949 0.20560186
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.02543736 0.06108027
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.1833756 0.2286256
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
## 0.999 0.997 0.281 0.062 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)
Td=tests[2,"Chisq diff"]
Td
## [1] 90.60087
dfd=tests[2,"Df diff"]
dfd
## [1] 11
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-1067+ 1067 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.08239179
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.06715467 0.09847901
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 0.992 0.620 0.036
hof.age<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
g~~1*g
math~0*1
g ~ age
'
hof.ageq<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
g~~1*g
math~0*1
g ~ c(a,a)*age
'
hof.age2<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
g~~1*g
math~0*1
g ~ age + age2
'
hof.age2q<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
g~~1*g
math~0*1
g ~ c(a,a)*age+c(b,b)*age2
'
sem.age<-sem(hof.age, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "sspc~1", "ssei~1", "sscs~1"))
fitMeasures(sem.age, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 840.405 93.000 0.000 0.961 0.087 0.066 0.447 98327.198 98650.146
Mc(sem.age)
## [1] 0.8392889
summary(sem.age, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 99 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 79
## Number of equality constraints 22
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 840.405 566.370
## Degrees of freedom 93 93
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.484
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 499.286 336.482
## 1 341.118 229.888
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.744 0.108 6.912 0.000 0.533 0.955 3.295 0.627
## sswk (.p2.) 1.684 0.250 6.729 0.000 1.194 2.175 7.456 0.935
## sspc (.p3.) 0.661 0.098 6.773 0.000 0.470 0.853 2.928 0.858
## math =~
## ssar (.p4.) 3.352 0.126 26.656 0.000 3.105 3.598 6.971 0.947
## ssmk (.p5.) 2.792 0.103 27.039 0.000 2.589 2.994 5.806 0.884
## ssmc (.p6.) 0.688 0.076 8.999 0.000 0.538 0.837 1.430 0.271
## electronic =~
## ssgs (.p7.) 0.782 0.068 11.494 0.000 0.648 0.915 1.599 0.304
## ssasi (.p8.) 2.210 0.120 18.402 0.000 1.975 2.446 4.520 0.821
## ssmc (.p9.) 1.558 0.107 14.576 0.000 1.349 1.768 3.187 0.604
## ssei (.10.) 2.011 0.100 20.136 0.000 1.815 2.207 4.112 0.946
## speed =~
## ssno (.11.) 0.514 0.018 28.934 0.000 0.479 0.549 0.828 0.872
## sscs (.12.) 0.450 0.017 27.020 0.000 0.417 0.482 0.725 0.812
## g =~
## verbal (.13.) 4.275 0.665 6.432 0.000 2.972 5.578 0.974 0.974
## math (.14.) 1.808 0.086 21.123 0.000 1.640 1.976 0.877 0.877
## elctrnc 1.769 0.115 15.421 0.000 1.544 1.993 0.872 0.872
## speed (.16.) 1.254 0.062 20.364 0.000 1.134 1.375 0.785 0.785
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.060 0.019 3.200 0.001 0.023 0.097 0.060 0.130
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.35.) 16.539 0.192 86.067 0.000 16.163 16.916 16.539 3.149
## .sswk (.36.) 25.519 0.291 87.743 0.000 24.949 26.089 25.519 3.200
## .sspc 10.424 0.128 81.403 0.000 10.173 10.675 10.424 3.056
## .ssar (.38.) 18.418 0.296 62.227 0.000 17.838 18.998 18.418 2.501
## .ssmk (.39.) 14.400 0.256 56.308 0.000 13.899 14.902 14.400 2.191
## .ssmc (.40.) 15.806 0.200 79.046 0.000 15.414 16.198 15.806 2.995
## .ssasi (.41.) 16.155 0.200 80.750 0.000 15.763 16.547 16.155 2.936
## .ssei 12.426 0.159 78.278 0.000 12.115 12.737 12.426 2.858
## .ssno (.43.) 0.070 0.035 1.977 0.048 0.001 0.140 0.070 0.074
## .sscs -0.074 0.034 -2.176 0.030 -0.140 -0.007 -0.074 -0.082
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.051 0.051
## .math 1.000 1.000 1.000 0.231 0.231
## .speed 1.000 1.000 1.000 0.385 0.385
## .g 1.000 1.000 1.000 0.983 0.983
## .ssgs 5.224 0.342 15.291 0.000 4.554 5.893 5.224 0.189
## .sswk 7.989 0.745 10.722 0.000 6.529 9.450 7.989 0.126
## .sspc 3.060 0.200 15.332 0.000 2.669 3.451 3.060 0.263
## .ssar 5.637 0.757 7.450 0.000 4.154 7.120 5.637 0.104
## .ssmk 9.469 0.711 13.318 0.000 8.075 10.862 9.469 0.219
## .ssmc 8.683 0.545 15.917 0.000 7.613 9.752 8.683 0.312
## .ssasi 9.854 0.758 12.995 0.000 8.368 11.340 9.854 0.325
## .ssei 1.987 0.267 7.453 0.000 1.465 2.510 1.987 0.105
## .ssno 0.216 0.025 8.734 0.000 0.167 0.264 0.216 0.239
## .sscs 0.272 0.035 7.752 0.000 0.203 0.340 0.272 0.341
## .electronic 1.000 1.000 1.000 0.239 0.239
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.744 0.108 6.912 0.000 0.533 0.955 3.318 0.689
## sswk (.p2.) 1.684 0.250 6.729 0.000 1.194 2.175 7.509 0.939
## sspc (.p3.) 0.661 0.098 6.773 0.000 0.470 0.853 2.948 0.876
## math =~
## ssar (.p4.) 3.352 0.126 26.656 0.000 3.105 3.598 7.011 0.950
## ssmk (.p5.) 2.792 0.103 27.039 0.000 2.589 2.994 5.840 0.883
## ssmc (.p6.) 0.688 0.076 8.999 0.000 0.538 0.837 1.438 0.325
## electronic =~
## ssgs (.p7.) 0.782 0.068 11.494 0.000 0.648 0.915 1.057 0.219
## ssasi (.p8.) 2.210 0.120 18.402 0.000 1.975 2.446 2.989 0.767
## ssmc (.p9.) 1.558 0.107 14.576 0.000 1.349 1.768 2.107 0.476
## ssei (.10.) 2.011 0.100 20.136 0.000 1.815 2.207 2.719 0.804
## speed =~
## ssno (.11.) 0.514 0.018 28.934 0.000 0.479 0.549 0.832 0.870
## sscs (.12.) 0.450 0.017 27.020 0.000 0.417 0.482 0.728 0.775
## g =~
## verbal (.13.) 4.275 0.665 6.432 0.000 2.972 5.578 0.975 0.975
## math (.14.) 1.808 0.086 21.123 0.000 1.640 1.976 0.878 0.878
## elctrnc 1.248 0.074 16.914 0.000 1.104 1.393 0.938 0.938
## speed (.16.) 1.254 0.062 20.364 0.000 1.134 1.375 0.787 0.787
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.084 0.016 5.191 0.000 0.052 0.116 0.083 0.178
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.35.) 16.539 0.192 86.067 0.000 16.163 16.916 16.539 3.432
## .sswk (.36.) 25.519 0.291 87.743 0.000 24.949 26.089 25.519 3.193
## .sspc 11.105 0.133 83.601 0.000 10.844 11.365 11.105 3.298
## .ssar (.38.) 18.418 0.296 62.227 0.000 17.838 18.998 18.418 2.495
## .ssmk (.39.) 14.400 0.256 56.308 0.000 13.899 14.902 14.400 2.178
## .ssmc (.40.) 15.806 0.200 79.046 0.000 15.414 16.198 15.806 3.571
## .ssasi (.41.) 16.155 0.200 80.750 0.000 15.763 16.547 16.155 4.147
## .ssei 14.322 0.250 57.387 0.000 13.833 14.812 14.322 4.237
## .ssno (.43.) 0.070 0.035 1.977 0.048 0.001 0.140 0.070 0.073
## .sscs 0.206 0.041 5.038 0.000 0.126 0.287 0.206 0.219
## .verbal 1.086 0.255 4.260 0.000 0.586 1.586 0.244 0.244
## .elctrnc -2.112 0.154 -13.694 0.000 -2.414 -1.810 -1.562 -1.562
## .speed 0.758 0.080 9.456 0.000 0.601 0.915 0.468 0.468
## .g -0.176 0.066 -2.688 0.007 -0.305 -0.048 -0.174 -0.174
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.050 0.050
## .math 1.000 1.000 1.000 0.229 0.229
## .speed 1.000 1.000 1.000 0.381 0.381
## .g 1.000 1.000 1.000 0.968 0.968
## .ssgs 4.682 0.306 15.303 0.000 4.082 5.282 4.682 0.202
## .sswk 7.502 0.721 10.399 0.000 6.088 8.917 7.502 0.117
## .sspc 2.643 0.165 16.013 0.000 2.320 2.967 2.643 0.233
## .ssar 5.353 0.739 7.243 0.000 3.904 6.801 5.353 0.098
## .ssmk 9.611 0.743 12.934 0.000 8.155 11.068 9.611 0.220
## .ssmc 8.089 0.463 17.459 0.000 7.181 8.997 8.089 0.413
## .ssasi 6.241 0.426 14.660 0.000 5.407 7.075 6.241 0.411
## .ssei 4.031 0.297 13.566 0.000 3.448 4.613 4.031 0.353
## .ssno 0.223 0.028 7.916 0.000 0.168 0.279 0.223 0.244
## .sscs 0.354 0.039 8.994 0.000 0.277 0.431 0.354 0.400
## .electronic 0.219 0.056 3.909 0.000 0.109 0.329 0.120 0.120
sem.ageq<-sem(hof.ageq, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "sspc~1", "ssei~1", "sscs~1"))
fitMeasures(sem.ageq, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 841.716 94.000 0.000 0.961 0.086 0.063 0.447 98326.509 98643.791
Mc(sem.ageq)
## [1] 0.8392277
summary(sem.ageq, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 107 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 79
## Number of equality constraints 23
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 841.716 567.621
## Degrees of freedom 94 94
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.483
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 499.940 337.140
## 1 341.776 230.480
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.749 0.107 7.013 0.000 0.539 0.958 3.306 0.628
## sswk (.p2.) 1.694 0.248 6.833 0.000 1.208 2.180 7.483 0.936
## sspc (.p3.) 0.665 0.097 6.880 0.000 0.476 0.855 2.938 0.859
## math =~
## ssar (.p4.) 3.349 0.126 26.661 0.000 3.103 3.595 6.991 0.947
## ssmk (.p5.) 2.790 0.103 27.042 0.000 2.587 2.992 5.823 0.884
## ssmc (.p6.) 0.687 0.076 8.997 0.000 0.537 0.836 1.434 0.271
## electronic =~
## ssgs (.p7.) 0.781 0.068 11.488 0.000 0.648 0.915 1.603 0.304
## ssasi (.p8.) 2.209 0.120 18.391 0.000 1.973 2.444 4.532 0.822
## ssmc (.p9.) 1.558 0.107 14.566 0.000 1.348 1.767 3.196 0.604
## ssei (.10.) 2.009 0.100 20.130 0.000 1.814 2.205 4.123 0.946
## speed =~
## ssno (.11.) 0.514 0.018 28.926 0.000 0.479 0.548 0.830 0.873
## sscs (.12.) 0.449 0.017 27.021 0.000 0.417 0.482 0.727 0.813
## g =~
## verbal (.13.) 4.251 0.651 6.527 0.000 2.975 5.528 0.974 0.974
## math (.14.) 1.810 0.086 21.160 0.000 1.643 1.978 0.878 0.878
## elctrnc 1.770 0.115 15.414 0.000 1.545 1.995 0.873 0.873
## speed (.16.) 1.255 0.062 20.378 0.000 1.135 1.376 0.786 0.786
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.072 0.013 5.655 0.000 0.047 0.096 0.071 0.154
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.35.) 16.554 0.189 87.364 0.000 16.183 16.926 16.554 3.143
## .sswk (.36.) 25.543 0.286 89.208 0.000 24.982 26.104 25.543 3.193
## .sspc 10.433 0.127 82.214 0.000 10.184 10.682 10.433 3.051
## .ssar (.38.) 18.438 0.293 62.882 0.000 17.863 19.013 18.438 2.497
## .ssmk (.39.) 14.417 0.254 56.846 0.000 13.920 14.914 14.417 2.189
## .ssmc (.40.) 15.819 0.198 80.034 0.000 15.432 16.207 15.819 2.991
## .ssasi (.41.) 16.168 0.197 81.932 0.000 15.781 16.555 16.168 2.933
## .ssei 12.437 0.156 79.507 0.000 12.131 12.744 12.437 2.854
## .ssno (.43.) 0.072 0.035 2.054 0.040 0.003 0.141 0.072 0.076
## .sscs -0.072 0.033 -2.141 0.032 -0.137 -0.006 -0.072 -0.080
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.051 0.051
## .math 1.000 1.000 1.000 0.229 0.229
## .speed 1.000 1.000 1.000 0.383 0.383
## .g 1.000 1.000 1.000 0.976 0.976
## .ssgs 5.226 0.342 15.293 0.000 4.556 5.895 5.226 0.188
## .sswk 7.979 0.744 10.720 0.000 6.520 9.438 7.979 0.125
## .sspc 3.061 0.200 15.333 0.000 2.669 3.452 3.061 0.262
## .ssar 5.634 0.756 7.451 0.000 4.152 7.116 5.634 0.103
## .ssmk 9.473 0.711 13.325 0.000 8.080 10.867 9.473 0.218
## .ssmc 8.683 0.546 15.915 0.000 7.614 9.752 8.683 0.310
## .ssasi 9.853 0.758 12.993 0.000 8.367 11.340 9.853 0.324
## .ssei 1.988 0.267 7.456 0.000 1.465 2.510 1.988 0.105
## .ssno 0.216 0.025 8.735 0.000 0.167 0.264 0.216 0.238
## .sscs 0.272 0.035 7.752 0.000 0.203 0.340 0.272 0.340
## .electronic 1.000 1.000 1.000 0.237 0.237
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.749 0.107 7.013 0.000 0.539 0.958 3.305 0.688
## sswk (.p2.) 1.694 0.248 6.833 0.000 1.208 2.180 7.481 0.939
## sspc (.p3.) 0.665 0.097 6.880 0.000 0.476 0.855 2.937 0.875
## math =~
## ssar (.p4.) 3.349 0.126 26.661 0.000 3.103 3.595 6.989 0.949
## ssmk (.p5.) 2.790 0.103 27.042 0.000 2.587 2.992 5.822 0.883
## ssmc (.p6.) 0.687 0.076 8.997 0.000 0.537 0.836 1.433 0.324
## electronic =~
## ssgs (.p7.) 0.781 0.068 11.488 0.000 0.648 0.915 1.054 0.219
## ssasi (.p8.) 2.209 0.120 18.391 0.000 1.973 2.444 2.979 0.766
## ssmc (.p9.) 1.558 0.107 14.566 0.000 1.348 1.767 2.101 0.476
## ssei (.10.) 2.009 0.100 20.130 0.000 1.814 2.205 2.710 0.804
## speed =~
## ssno (.11.) 0.514 0.018 28.926 0.000 0.479 0.548 0.830 0.869
## sscs (.12.) 0.449 0.017 27.021 0.000 0.417 0.482 0.727 0.774
## g =~
## verbal (.13.) 4.251 0.651 6.527 0.000 2.975 5.528 0.974 0.974
## math (.14.) 1.810 0.086 21.160 0.000 1.643 1.978 0.878 0.878
## elctrnc 1.250 0.074 16.919 0.000 1.105 1.395 0.938 0.938
## speed (.16.) 1.255 0.062 20.378 0.000 1.135 1.376 0.786 0.786
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.072 0.013 5.655 0.000 0.047 0.096 0.071 0.152
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.35.) 16.554 0.189 87.364 0.000 16.183 16.926 16.554 3.446
## .sswk (.36.) 25.543 0.286 89.208 0.000 24.982 26.104 25.543 3.206
## .sspc 11.114 0.131 84.767 0.000 10.857 11.371 11.114 3.311
## .ssar (.38.) 18.438 0.293 62.882 0.000 17.863 19.013 18.438 2.504
## .ssmk (.39.) 14.417 0.254 56.846 0.000 13.920 14.914 14.417 2.186
## .ssmc (.40.) 15.819 0.198 80.034 0.000 15.432 16.207 15.819 3.581
## .ssasi (.41.) 16.168 0.197 81.932 0.000 15.781 16.555 16.168 4.159
## .ssei 14.334 0.249 57.652 0.000 13.846 14.821 14.334 4.249
## .ssno (.43.) 0.072 0.035 2.054 0.040 0.003 0.141 0.072 0.076
## .sscs 0.208 0.041 5.111 0.000 0.128 0.288 0.208 0.222
## .verbal 1.080 0.252 4.290 0.000 0.586 1.573 0.244 0.244
## .elctrnc -2.115 0.154 -13.702 0.000 -2.418 -1.813 -1.568 -1.568
## .speed 0.758 0.080 9.457 0.000 0.601 0.915 0.469 0.469
## .g -0.184 0.065 -2.847 0.004 -0.310 -0.057 -0.181 -0.181
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.051 0.051
## .math 1.000 1.000 1.000 0.230 0.230
## .speed 1.000 1.000 1.000 0.383 0.383
## .g 1.000 1.000 1.000 0.977 0.977
## .ssgs 4.683 0.306 15.301 0.000 4.084 5.283 4.683 0.203
## .sswk 7.509 0.722 10.404 0.000 6.094 8.923 7.509 0.118
## .sspc 2.641 0.165 16.016 0.000 2.318 2.964 2.641 0.234
## .ssar 5.355 0.739 7.245 0.000 3.906 6.803 5.355 0.099
## .ssmk 9.608 0.743 12.928 0.000 8.151 11.065 9.608 0.221
## .ssmc 8.088 0.463 17.456 0.000 7.180 8.996 8.088 0.414
## .ssasi 6.239 0.426 14.655 0.000 5.405 7.074 6.239 0.413
## .ssei 4.032 0.297 13.576 0.000 3.450 4.614 4.032 0.354
## .ssno 0.223 0.028 7.914 0.000 0.168 0.278 0.223 0.245
## .sscs 0.354 0.039 8.999 0.000 0.277 0.431 0.354 0.401
## .electronic 0.219 0.056 3.907 0.000 0.109 0.329 0.120 0.120
sem.age2<-sem(hof.age2, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "sspc~1", "ssei~1", "sscs~1"))
fitMeasures(sem.age2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 889.409 111.000 0.000 0.959 0.081 0.061 0.472 98329.553 98663.833
Mc(sem.age2)
## [1] 0.8332113
summary(sem.age2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 105 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 81
## Number of equality constraints 22
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 889.409 595.690
## Degrees of freedom 111 111
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.493
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 527.699 353.431
## 1 361.710 242.259
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.745 0.108 6.913 0.000 0.533 0.956 3.296 0.627
## sswk (.p2.) 1.685 0.250 6.733 0.000 1.195 2.176 7.459 0.935
## sspc (.p3.) 0.662 0.098 6.777 0.000 0.470 0.853 2.929 0.859
## math =~
## ssar (.p4.) 3.352 0.126 26.663 0.000 3.106 3.599 6.972 0.947
## ssmk (.p5.) 2.792 0.103 27.051 0.000 2.590 2.995 5.808 0.884
## ssmc (.p6.) 0.688 0.076 8.999 0.000 0.538 0.838 1.431 0.271
## electronic =~
## ssgs (.p7.) 0.781 0.068 11.489 0.000 0.648 0.915 1.599 0.304
## ssasi (.p8.) 2.209 0.120 18.395 0.000 1.974 2.445 4.521 0.821
## ssmc (.p9.) 1.558 0.107 14.567 0.000 1.348 1.767 3.187 0.604
## ssei (.10.) 2.010 0.100 20.135 0.000 1.815 2.206 4.113 0.946
## speed =~
## ssno (.11.) 0.514 0.018 28.944 0.000 0.479 0.549 0.829 0.872
## sscs (.12.) 0.450 0.017 27.030 0.000 0.417 0.482 0.725 0.812
## g =~
## verbal (.13.) 4.272 0.664 6.434 0.000 2.970 5.573 0.974 0.974
## math (.14.) 1.807 0.085 21.137 0.000 1.639 1.974 0.877 0.877
## elctrnc 1.769 0.115 15.437 0.000 1.544 1.993 0.872 0.872
## speed (.16.) 1.254 0.062 20.373 0.000 1.133 1.374 0.785 0.785
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.057 0.020 2.834 0.005 0.017 0.096 0.056 0.122
## age2 -0.008 0.009 -0.950 0.342 -0.025 0.009 -0.008 -0.040
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.38.) 16.716 0.249 67.221 0.000 16.229 17.203 16.716 3.182
## .sswk (.39.) 25.798 0.380 67.956 0.000 25.054 26.542 25.798 3.234
## .sspc 10.533 0.159 66.081 0.000 10.221 10.845 10.533 3.088
## .ssar (.41.) 18.652 0.367 50.838 0.000 17.933 19.371 18.652 2.532
## .ssmk (.42.) 14.596 0.315 46.408 0.000 13.979 15.212 14.596 2.221
## .ssmc (.43.) 15.961 0.246 64.968 0.000 15.479 16.442 15.961 3.023
## .ssasi (.44.) 16.307 0.243 67.135 0.000 15.830 16.783 16.307 2.963
## .ssei 12.563 0.202 62.216 0.000 12.168 12.959 12.563 2.890
## .ssno (.46.) 0.095 0.041 2.336 0.019 0.015 0.175 0.095 0.100
## .sscs -0.052 0.037 -1.390 0.165 -0.125 0.021 -0.052 -0.058
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.051 0.051
## .math 1.000 1.000 1.000 0.231 0.231
## .speed 1.000 1.000 1.000 0.384 0.384
## .g 1.000 1.000 1.000 0.982 0.982
## .ssgs 5.228 0.342 15.275 0.000 4.557 5.898 5.228 0.189
## .sswk 7.982 0.743 10.738 0.000 6.525 9.439 7.982 0.125
## .sspc 3.060 0.200 15.319 0.000 2.668 3.451 3.060 0.263
## .ssar 5.639 0.757 7.452 0.000 4.156 7.122 5.639 0.104
## .ssmk 9.467 0.711 13.315 0.000 8.074 10.861 9.467 0.219
## .ssmc 8.686 0.546 15.919 0.000 7.616 9.755 8.686 0.312
## .ssasi 9.857 0.759 12.989 0.000 8.370 11.345 9.857 0.325
## .ssei 1.984 0.266 7.455 0.000 1.463 2.506 1.984 0.105
## .ssno 0.216 0.025 8.734 0.000 0.167 0.264 0.216 0.239
## .sscs 0.272 0.035 7.749 0.000 0.203 0.340 0.272 0.340
## .electronic 1.000 1.000 1.000 0.239 0.239
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.745 0.108 6.913 0.000 0.533 0.956 3.317 0.688
## sswk (.p2.) 1.685 0.250 6.733 0.000 1.195 2.176 7.507 0.939
## sspc (.p3.) 0.662 0.098 6.777 0.000 0.470 0.853 2.948 0.876
## math =~
## ssar (.p4.) 3.352 0.126 26.663 0.000 3.106 3.599 7.009 0.950
## ssmk (.p5.) 2.792 0.103 27.051 0.000 2.590 2.995 5.838 0.883
## ssmc (.p6.) 0.688 0.076 8.999 0.000 0.538 0.838 1.438 0.325
## electronic =~
## ssgs (.p7.) 0.781 0.068 11.489 0.000 0.648 0.915 1.057 0.219
## ssasi (.p8.) 2.209 0.120 18.395 0.000 1.974 2.445 2.988 0.767
## ssmc (.p9.) 1.558 0.107 14.567 0.000 1.348 1.767 2.106 0.476
## ssei (.10.) 2.010 0.100 20.135 0.000 1.815 2.206 2.719 0.804
## speed =~
## ssno (.11.) 0.514 0.018 28.944 0.000 0.479 0.549 0.832 0.870
## sscs (.12.) 0.450 0.017 27.030 0.000 0.417 0.482 0.728 0.774
## g =~
## verbal (.13.) 4.272 0.664 6.434 0.000 2.970 5.573 0.974 0.974
## math (.14.) 1.807 0.085 21.137 0.000 1.639 1.974 0.878 0.878
## elctrnc 1.249 0.074 16.924 0.000 1.104 1.393 0.938 0.938
## speed (.16.) 1.254 0.062 20.373 0.000 1.133 1.374 0.787 0.787
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.083 0.017 5.007 0.000 0.050 0.115 0.081 0.175
## age2 -0.002 0.007 -0.274 0.784 -0.016 0.012 -0.002 -0.010
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.38.) 16.716 0.249 67.221 0.000 16.229 17.203 16.716 3.470
## .sswk (.39.) 25.798 0.380 67.956 0.000 25.054 26.542 25.798 3.228
## .sspc 11.214 0.164 68.488 0.000 10.893 11.535 11.214 3.331
## .ssar (.41.) 18.652 0.367 50.838 0.000 17.933 19.371 18.652 2.527
## .ssmk (.42.) 14.596 0.315 46.408 0.000 13.979 15.212 14.596 2.208
## .ssmc (.43.) 15.961 0.246 64.968 0.000 15.479 16.442 15.961 3.606
## .ssasi (.44.) 16.307 0.243 67.135 0.000 15.830 16.783 16.307 4.187
## .ssei 14.461 0.279 51.823 0.000 13.914 15.008 14.461 4.279
## .ssno (.46.) 0.095 0.041 2.336 0.019 0.015 0.175 0.095 0.099
## .sscs 0.228 0.045 5.117 0.000 0.141 0.316 0.228 0.243
## .verbal 1.086 0.255 4.259 0.000 0.586 1.585 0.244 0.244
## .elctrnc -2.133 0.158 -13.537 0.000 -2.442 -1.825 -1.578 -1.578
## .speed 0.758 0.080 9.457 0.000 0.601 0.915 0.468 0.468
## .g -0.206 0.081 -2.541 0.011 -0.365 -0.047 -0.203 -0.203
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.050 0.050
## .math 1.000 1.000 1.000 0.229 0.229
## .speed 1.000 1.000 1.000 0.381 0.381
## .g 1.000 1.000 1.000 0.968 0.968
## .ssgs 4.683 0.306 15.299 0.000 4.083 5.282 4.683 0.202
## .sswk 7.501 0.721 10.397 0.000 6.087 8.915 7.501 0.117
## .sspc 2.643 0.165 16.011 0.000 2.319 2.966 2.643 0.233
## .ssar 5.351 0.739 7.241 0.000 3.903 6.799 5.351 0.098
## .ssmk 9.612 0.743 12.933 0.000 8.156 11.069 9.612 0.220
## .ssmc 8.089 0.463 17.455 0.000 7.181 8.997 8.089 0.413
## .ssasi 6.241 0.426 14.654 0.000 5.406 7.075 6.241 0.411
## .ssei 4.031 0.297 13.563 0.000 3.448 4.613 4.031 0.353
## .ssno 0.223 0.028 7.916 0.000 0.168 0.279 0.223 0.244
## .sscs 0.354 0.039 8.994 0.000 0.277 0.431 0.354 0.400
## .electronic 0.219 0.056 3.908 0.000 0.109 0.329 0.120 0.120
sem.age2q<-sem(hof.age2q, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "sspc~1", "ssei~1", "sscs~1"))
fitMeasures(sem.age2q, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 891.076 113.000 0.000 0.959 0.080 0.059 0.471 98327.221 98650.169
Mc(sem.age2q)
## [1] 0.8332763
summary(sem.age2q, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 109 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 81
## Number of equality constraints 24
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 891.076 597.539
## Degrees of freedom 113 113
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.491
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 528.469 354.382
## 1 362.607 243.158
##
## 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 ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.749 0.107 7.020 0.000 0.540 0.958 3.306 0.628
## sswk (.p2.) 1.695 0.248 6.842 0.000 1.210 2.181 7.483 0.936
## sspc (.p3.) 0.666 0.097 6.888 0.000 0.476 0.855 2.938 0.859
## math =~
## ssar (.p4.) 3.350 0.126 26.662 0.000 3.103 3.596 6.991 0.947
## ssmk (.p5.) 2.790 0.103 27.046 0.000 2.588 2.992 5.823 0.884
## ssmc (.p6.) 0.687 0.076 8.996 0.000 0.537 0.836 1.433 0.271
## electronic =~
## ssgs (.p7.) 0.781 0.068 11.487 0.000 0.648 0.914 1.603 0.304
## ssasi (.p8.) 2.208 0.120 18.388 0.000 1.973 2.443 4.532 0.822
## ssmc (.p9.) 1.557 0.107 14.561 0.000 1.347 1.767 3.196 0.604
## ssei (.10.) 2.009 0.100 20.128 0.000 1.813 2.204 4.123 0.946
## speed =~
## ssno (.11.) 0.514 0.018 28.934 0.000 0.479 0.548 0.830 0.873
## sscs (.12.) 0.450 0.017 27.024 0.000 0.417 0.482 0.727 0.813
## g =~
## verbal (.13.) 4.247 0.650 6.535 0.000 2.973 5.521 0.974 0.974
## math (.14.) 1.809 0.086 21.158 0.000 1.642 1.977 0.878 0.878
## elctrnc 1.770 0.115 15.425 0.000 1.545 1.995 0.873 0.873
## speed (.16.) 1.255 0.062 20.376 0.000 1.134 1.375 0.786 0.786
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.069 0.013 5.145 0.000 0.043 0.095 0.068 0.149
## age2 (b) -0.005 0.006 -0.933 0.351 -0.016 0.006 -0.005 -0.026
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.38.) 16.669 0.215 77.477 0.000 16.247 17.091 16.669 3.165
## .sswk (.39.) 25.724 0.327 78.780 0.000 25.084 26.363 25.724 3.216
## .sspc 10.504 0.141 74.660 0.000 10.228 10.780 10.504 3.072
## .ssar (.41.) 18.590 0.326 56.988 0.000 17.951 19.229 18.590 2.518
## .ssmk (.42.) 14.544 0.280 52.034 0.000 13.996 15.092 14.544 2.208
## .ssmc (.43.) 15.920 0.218 72.926 0.000 15.492 16.347 15.920 3.010
## .ssasi (.44.) 16.266 0.217 74.910 0.000 15.841 16.692 16.266 2.951
## .ssei 12.527 0.176 71.084 0.000 12.181 12.872 12.527 2.875
## .ssno (.46.) 0.088 0.037 2.370 0.018 0.015 0.161 0.088 0.093
## .sscs -0.058 0.035 -1.653 0.098 -0.126 0.011 -0.058 -0.064
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.051 0.051
## .math 1.000 1.000 1.000 0.230 0.230
## .speed 1.000 1.000 1.000 0.383 0.383
## .g 1.000 1.000 1.000 0.976 0.976
## .ssgs 5.228 0.342 15.285 0.000 4.558 5.899 5.228 0.188
## .sswk 7.973 0.743 10.729 0.000 6.517 9.430 7.973 0.125
## .sspc 3.060 0.200 15.324 0.000 2.669 3.452 3.060 0.262
## .ssar 5.634 0.756 7.451 0.000 4.152 7.116 5.634 0.103
## .ssmk 9.473 0.711 13.323 0.000 8.079 10.866 9.473 0.218
## .ssmc 8.685 0.546 15.916 0.000 7.615 9.754 8.685 0.310
## .ssasi 9.855 0.759 12.989 0.000 8.368 11.342 9.855 0.324
## .ssei 1.986 0.266 7.458 0.000 1.464 2.508 1.986 0.105
## .ssno 0.216 0.025 8.735 0.000 0.167 0.264 0.216 0.238
## .sscs 0.272 0.035 7.750 0.000 0.203 0.340 0.272 0.340
## .electronic 1.000 1.000 1.000 0.237 0.237
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.749 0.107 7.020 0.000 0.540 0.958 3.306 0.688
## sswk (.p2.) 1.695 0.248 6.842 0.000 1.210 2.181 7.482 0.939
## sspc (.p3.) 0.666 0.097 6.888 0.000 0.476 0.855 2.938 0.875
## math =~
## ssar (.p4.) 3.350 0.126 26.662 0.000 3.103 3.596 6.990 0.949
## ssmk (.p5.) 2.790 0.103 27.046 0.000 2.588 2.992 5.822 0.883
## ssmc (.p6.) 0.687 0.076 8.996 0.000 0.537 0.836 1.433 0.324
## electronic =~
## ssgs (.p7.) 0.781 0.068 11.487 0.000 0.648 0.914 1.054 0.219
## ssasi (.p8.) 2.208 0.120 18.388 0.000 1.973 2.443 2.980 0.766
## ssmc (.p9.) 1.557 0.107 14.561 0.000 1.347 1.767 2.101 0.476
## ssei (.10.) 2.009 0.100 20.128 0.000 1.813 2.204 2.711 0.804
## speed =~
## ssno (.11.) 0.514 0.018 28.934 0.000 0.479 0.548 0.830 0.869
## sscs (.12.) 0.450 0.017 27.024 0.000 0.417 0.482 0.727 0.774
## g =~
## verbal (.13.) 4.247 0.650 6.535 0.000 2.973 5.521 0.974 0.974
## math (.14.) 1.809 0.086 21.158 0.000 1.642 1.977 0.878 0.878
## elctrnc 1.250 0.074 16.927 0.000 1.106 1.395 0.938 0.938
## speed (.16.) 1.255 0.062 20.376 0.000 1.134 1.375 0.786 0.786
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.069 0.013 5.145 0.000 0.043 0.095 0.068 0.146
## age2 (b) -0.005 0.006 -0.933 0.351 -0.016 0.006 -0.005 -0.026
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.38.) 16.669 0.215 77.477 0.000 16.247 17.091 16.669 3.469
## .sswk (.39.) 25.724 0.327 78.780 0.000 25.084 26.363 25.724 3.228
## .sspc 11.185 0.146 76.501 0.000 10.898 11.471 11.185 3.331
## .ssar (.41.) 18.590 0.326 56.988 0.000 17.951 19.229 18.590 2.525
## .ssmk (.42.) 14.544 0.280 52.034 0.000 13.996 15.092 14.544 2.205
## .ssmc (.43.) 15.920 0.218 72.926 0.000 15.492 16.347 15.920 3.604
## .ssasi (.44.) 16.266 0.217 74.910 0.000 15.841 16.692 16.266 4.184
## .ssei 14.423 0.259 55.641 0.000 13.915 14.931 14.423 4.275
## .ssno (.46.) 0.088 0.037 2.370 0.018 0.015 0.161 0.088 0.093
## .sscs 0.222 0.042 5.280 0.000 0.140 0.305 0.222 0.237
## .verbal 1.079 0.251 4.291 0.000 0.586 1.572 0.244 0.244
## .elctrnc -2.129 0.156 -13.650 0.000 -2.435 -1.823 -1.578 -1.578
## .speed 0.758 0.080 9.458 0.000 0.601 0.915 0.469 0.469
## .g -0.184 0.065 -2.859 0.004 -0.311 -0.058 -0.182 -0.182
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.051 0.051
## .math 1.000 1.000 1.000 0.230 0.230
## .speed 1.000 1.000 1.000 0.383 0.383
## .g 1.000 1.000 1.000 0.976 0.976
## .ssgs 4.685 0.306 15.300 0.000 4.085 5.285 4.685 0.203
## .sswk 7.507 0.722 10.402 0.000 6.093 8.922 7.507 0.118
## .sspc 2.641 0.165 16.011 0.000 2.318 2.964 2.641 0.234
## .ssar 5.351 0.739 7.242 0.000 3.903 6.799 5.351 0.099
## .ssmk 9.611 0.743 12.928 0.000 8.154 11.068 9.611 0.221
## .ssmc 8.087 0.463 17.458 0.000 7.179 8.995 8.087 0.414
## .ssasi 6.238 0.426 14.654 0.000 5.403 7.072 6.238 0.413
## .ssei 4.034 0.297 13.578 0.000 3.451 4.616 4.034 0.354
## .ssno 0.223 0.028 7.919 0.000 0.168 0.278 0.223 0.245
## .sscs 0.354 0.039 8.999 0.000 0.277 0.431 0.354 0.401
## .electronic 0.219 0.056 3.905 0.000 0.109 0.329 0.120 0.120
# BIFACTOR
bf.notworking<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
'
baseline<-cfa(bf.notworking, data=dgroup, meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= -1.310254e-05) is smaller than zero. This may
## be a symptom that the model is not identified.
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 611.291 23.000 0.000 0.969 0.109 0.040 100046.007 100283.969
Mc(baseline)
## [1] 0.8711838
summary(baseline, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 4370 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 42
##
## Number of observations 2134
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 611.291 377.042
## Degrees of freedom 23 23
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.621
## Yuan-Bentler correction (Mplus variant)
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs 0.033 0.006 5.921 0.000 0.022 0.045 0.033 0.007
## sswk 59.233 0.161 367.222 0.000 58.916 59.549 59.233 7.416
## sspc 0.036 0.006 6.575 0.000 0.026 0.047 0.036 0.011
## math =~
## ssar 3.039 0.222 13.667 0.000 2.603 3.475 3.039 0.411
## ssmk 2.552 0.187 13.671 0.000 2.187 2.918 2.552 0.386
## ssmc 1.105 0.115 9.608 0.000 0.879 1.330 1.105 0.210
## electronic =~
## ssgs 1.139 0.086 13.266 0.000 0.971 1.307 1.139 0.223
## ssasi 3.585 0.126 28.417 0.000 3.338 3.832 3.585 0.655
## ssmc 2.692 0.111 24.355 0.000 2.476 2.909 2.692 0.513
## ssei 2.016 0.085 23.717 0.000 1.849 2.182 2.016 0.480
## speed =~
## ssno 0.804 NA NA NA 0.804 0.835
## sscs 0.332 0.019 17.618 0.000 0.295 0.369 0.332 0.349
## g =~
## ssgs 4.427 0.092 47.930 0.000 4.246 4.608 4.427 0.866
## ssar 6.251 0.117 53.242 0.000 6.021 6.481 6.251 0.845
## sswk 7.073 0.143 49.359 0.000 6.793 7.354 7.073 0.886
## sspc 2.843 0.067 42.682 0.000 2.712 2.973 2.843 0.831
## ssno 0.662 0.022 30.000 0.000 0.619 0.706 0.662 0.688
## sscs 0.562 0.025 22.816 0.000 0.513 0.610 0.562 0.590
## ssasi 3.155 0.127 24.893 0.000 2.906 3.403 3.155 0.577
## ssmk 5.308 0.110 48.304 0.000 5.092 5.523 5.308 0.803
## ssmc 3.498 0.109 32.017 0.000 3.284 3.713 3.498 0.666
## ssei 3.148 0.081 38.745 0.000 2.989 3.307 3.148 0.749
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.000 0.000 0.000 0.000 0.000
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 15.671 0.129 121.787 0.000 15.419 15.923 15.671 3.067
## .sswk 25.632 0.194 132.206 0.000 25.252 26.012 25.632 3.209
## .sspc 10.799 0.084 128.729 0.000 10.635 10.964 10.799 3.156
## .ssar 17.766 0.196 90.837 0.000 17.382 18.149 17.766 2.402
## .ssmk 13.856 0.178 77.872 0.000 13.507 14.205 13.856 2.097
## .ssmc 13.845 0.139 99.554 0.000 13.572 14.117 13.845 2.636
## .ssasi 13.593 0.145 93.926 0.000 13.309 13.877 13.593 2.484
## .ssei 10.998 0.108 101.610 0.000 10.786 11.210 10.998 2.618
## .ssno 0.190 0.025 7.731 0.000 0.142 0.238 0.190 0.197
## .sscs 0.168 0.025 6.818 0.000 0.120 0.216 0.168 0.176
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.211 0.282 18.502 0.000 4.659 5.763 5.211 0.200
## .sswk -3494.744 19.232 -181.719 0.000 -3532.437 -3457.050 -3494.744 -54.788
## .sspc 3.629 0.187 19.359 0.000 3.261 3.996 3.629 0.310
## .ssar 6.386 1.062 6.014 0.000 4.305 8.467 6.386 0.117
## .ssmk 8.974 0.827 10.850 0.000 7.353 10.596 8.974 0.206
## .ssmc 6.870 0.435 15.787 0.000 6.017 7.723 6.870 0.249
## .ssasi 7.141 0.552 12.936 0.000 6.059 8.223 7.141 0.238
## .ssei 3.670 0.214 17.141 0.000 3.250 4.090 3.670 0.208
## .ssno -0.157 0.017 -9.436 0.000 -0.190 -0.125 -0.157 -0.170
## .sscs 0.481 0.026 18.853 0.000 0.431 0.531 0.481 0.531
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
bf.model<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
'
bf.lv<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
'
baseline<-cfa(bf.model, data=dgroup, meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= -1.860489e-06) is smaller than zero. This may
## be a symptom that the model is not identified.
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 713.177 26.000 0.000 0.964 0.111 0.042 100141.893 100362.857
Mc(baseline)
## [1] 0.851222
summary(baseline, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 32 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 39
##
## Number of observations 2134
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 713.177 456.111
## Degrees of freedom 26 26
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.564
## Yuan-Bentler correction (Mplus variant)
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar 3.548 0.208 17.076 0.000 3.140 3.955 3.548 0.480
## ssmk 2.945 0.179 16.443 0.000 2.594 3.296 2.945 0.446
## ssmc 1.105 0.102 10.790 0.000 0.905 1.306 1.105 0.212
## electronic =~
## ssgs 1.248 0.083 15.070 0.000 1.086 1.411 1.248 0.243
## ssasi 3.618 0.120 30.194 0.000 3.383 3.853 3.618 0.661
## ssmc 2.686 0.107 25.006 0.000 2.475 2.897 2.686 0.515
## ssei 2.068 0.079 26.332 0.000 1.914 2.222 2.068 0.492
## speed =~
## ssno 0.492 0.026 18.605 0.000 0.440 0.544 0.492 0.511
## sscs 0.555 0.001 401.072 0.000 0.552 0.558 0.555 0.583
## g =~
## ssgs 4.461 0.086 52.130 0.000 4.294 4.629 4.461 0.870
## ssar 5.983 0.116 51.364 0.000 5.754 6.211 5.983 0.809
## sswk 7.446 0.128 58.189 0.000 7.195 7.697 7.446 0.932
## sspc 2.939 0.063 46.909 0.000 2.816 3.062 2.939 0.859
## ssno 0.647 0.022 29.663 0.000 0.604 0.690 0.647 0.672
## sscs 0.565 0.024 24.045 0.000 0.519 0.611 0.565 0.594
## ssasi 3.116 0.120 25.867 0.000 2.880 3.352 3.116 0.569
## ssmk 5.096 0.108 47.155 0.000 4.884 5.308 5.096 0.771
## ssmc 3.425 0.105 32.571 0.000 3.219 3.631 3.425 0.657
## ssei 3.113 0.076 40.858 0.000 2.964 3.262 3.113 0.741
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 17.766 0.196 90.837 0.000 17.382 18.149 17.766 2.402
## .ssmk 13.856 0.178 77.872 0.000 13.507 14.205 13.856 2.097
## .ssmc 13.845 0.139 99.554 0.000 13.572 14.117 13.845 2.654
## .ssgs 15.671 0.129 121.787 0.000 15.419 15.923 15.671 3.055
## .ssasi 13.593 0.145 93.926 0.000 13.309 13.877 13.593 2.484
## .ssei 10.998 0.108 101.610 0.000 10.786 11.210 10.998 2.618
## .ssno 0.190 0.025 7.731 0.000 0.142 0.238 0.190 0.197
## .sscs 0.168 0.025 6.818 0.000 0.120 0.216 0.168 0.176
## .sswk 25.632 0.194 132.206 0.000 25.252 26.012 25.632 3.209
## .sspc 10.799 0.084 128.729 0.000 10.635 10.964 10.799 3.156
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.318 1.232 5.127 0.000 3.903 8.734 6.318 0.116
## .ssmk 9.019 0.922 9.779 0.000 7.212 10.827 9.019 0.207
## .ssmc 7.042 0.409 17.237 0.000 6.241 7.843 7.042 0.259
## .ssgs 4.845 0.232 20.894 0.000 4.390 5.299 4.845 0.184
## .ssasi 7.147 0.539 13.258 0.000 6.091 8.204 7.147 0.239
## .ssei 3.674 0.216 17.020 0.000 3.251 4.097 3.674 0.208
## .ssno 0.266 0.023 11.719 0.000 0.222 0.311 0.266 0.287
## .sscs 0.280 0.027 10.371 0.000 0.227 0.332 0.280 0.308
## .sswk 8.342 0.557 14.984 0.000 7.251 9.434 8.342 0.131
## .sspc 3.073 0.143 21.452 0.000 2.792 3.353 3.073 0.262
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
configural<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= -2.755071e-06) is smaller than zero. This may
## be a symptom that the model is not identified.
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 531.787 52.000 0.000 0.975 0.093 0.027 98252.442 98694.370
Mc(configural)
## [1] 0.8936262
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 39 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 78
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 531.787 350.466
## Degrees of freedom 52 52
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.517
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 314.519 207.279
## 1 217.268 143.187
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar 3.593 0.307 11.711 0.000 2.992 4.195 3.593 0.468
## ssmk 3.108 0.262 11.864 0.000 2.595 3.622 3.108 0.455
## ssmc 0.943 0.145 6.523 0.000 0.660 1.226 0.943 0.169
## electronic =~
## ssgs 0.886 0.137 6.445 0.000 0.616 1.155 0.886 0.163
## ssasi 2.929 0.177 16.509 0.000 2.582 3.277 2.929 0.525
## ssmc 2.385 0.159 15.026 0.000 2.074 2.696 2.385 0.428
## ssei 1.583 0.124 12.811 0.000 1.341 1.825 1.583 0.356
## speed =~
## ssno 0.483 0.025 19.604 0.000 0.434 0.531 0.483 0.501
## sscs 0.485 0.018 27.201 0.000 0.450 0.520 0.485 0.538
## g =~
## ssgs 4.861 0.124 39.219 0.000 4.618 5.104 4.861 0.893
## ssar 6.313 0.157 40.211 0.000 6.006 6.621 6.313 0.823
## sswk 7.727 0.185 41.744 0.000 7.364 8.089 7.727 0.935
## sspc 3.133 0.087 36.175 0.000 2.964 3.303 3.133 0.873
## ssno 0.664 0.030 21.797 0.000 0.605 0.724 0.664 0.690
## sscs 0.579 0.031 18.970 0.000 0.519 0.639 0.579 0.642
## ssasi 3.885 0.163 23.808 0.000 3.565 4.205 3.885 0.697
## ssmk 5.310 0.154 34.489 0.000 5.009 5.612 5.310 0.778
## ssmc 4.208 0.140 29.970 0.000 3.933 4.483 4.208 0.755
## ssei 3.750 0.104 36.212 0.000 3.547 3.953 3.750 0.844
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 18.495 0.286 64.662 0.000 17.934 19.056 18.495 2.411
## .ssmk 13.973 0.261 53.474 0.000 13.461 14.486 13.973 2.047
## .ssmc 15.637 0.201 77.759 0.000 15.243 16.031 15.637 2.805
## .ssgs 16.396 0.190 86.372 0.000 16.024 16.768 16.396 3.013
## .ssasi 16.211 0.198 81.891 0.000 15.823 16.599 16.211 2.907
## .ssei 12.364 0.157 78.687 0.000 12.056 12.672 12.364 2.783
## .ssno 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.061
## .sscs -0.083 0.033 -2.497 0.013 -0.149 -0.018 -0.083 -0.092
## .sswk 25.438 0.284 89.414 0.000 24.881 25.996 25.438 3.078
## .sspc 10.375 0.126 82.229 0.000 10.127 10.622 10.375 2.892
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.069 1.899 3.196 0.001 2.347 9.791 6.069 0.103
## .ssmk 8.748 1.482 5.903 0.000 5.843 11.653 8.748 0.188
## .ssmc 6.789 0.626 10.848 0.000 5.563 8.016 6.789 0.219
## .ssgs 5.202 0.344 15.124 0.000 4.528 5.876 5.202 0.176
## .ssasi 7.430 0.842 8.825 0.000 5.780 9.080 7.430 0.239
## .ssei 3.176 0.250 12.705 0.000 2.686 3.666 3.176 0.161
## .ssno 0.252 0.023 10.976 0.000 0.207 0.297 0.252 0.272
## .sscs 0.242 0.032 7.560 0.000 0.179 0.305 0.242 0.298
## .sswk 8.623 0.743 11.607 0.000 7.167 10.079 8.623 0.126
## .sspc 3.050 0.198 15.427 0.000 2.662 3.437 3.050 0.237
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar 3.302 0.275 12.021 0.000 2.764 3.841 3.302 0.471
## ssmk 2.860 0.245 11.652 0.000 2.379 3.341 2.860 0.449
## ssmc 1.165 0.146 7.993 0.000 0.879 1.451 1.165 0.278
## electronic =~
## ssgs 0.730 0.248 2.944 0.003 0.244 1.215 0.730 0.157
## ssasi 1.058 0.271 3.899 0.000 0.526 1.590 1.058 0.283
## ssmc 1.113 0.335 3.322 0.001 0.456 1.769 1.113 0.266
## ssei 0.920 0.277 3.323 0.001 0.377 1.462 0.920 0.272
## speed =~
## ssno 0.509 0.051 9.918 0.000 0.408 0.610 0.509 0.540
## sscs 0.483 0.009 53.796 0.000 0.465 0.501 0.483 0.518
## g =~
## ssgs 4.085 0.106 38.492 0.000 3.877 4.292 4.085 0.877
## ssar 5.656 0.166 34.100 0.000 5.331 5.981 5.656 0.806
## sswk 7.133 0.168 42.341 0.000 6.803 7.463 7.133 0.929
## sspc 2.726 0.084 32.535 0.000 2.561 2.890 2.726 0.857
## ssno 0.621 0.030 20.853 0.000 0.563 0.680 0.621 0.658
## sscs 0.552 0.033 16.791 0.000 0.488 0.617 0.552 0.592
## ssasi 2.539 0.112 22.649 0.000 2.319 2.758 2.539 0.680
## ssmk 4.836 0.149 32.426 0.000 4.544 5.128 4.836 0.760
## ssmc 2.745 0.117 23.431 0.000 2.516 2.975 2.745 0.656
## ssei 2.535 0.086 29.585 0.000 2.367 2.703 2.535 0.751
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 16.999 0.262 64.966 0.000 16.486 17.512 16.999 2.424
## .ssmk 13.732 0.240 57.183 0.000 13.262 14.203 13.732 2.157
## .ssmc 11.961 0.157 76.345 0.000 11.654 12.268 11.961 2.856
## .ssgs 14.908 0.166 89.625 0.000 14.582 15.234 14.908 3.201
## .ssasi 10.841 0.136 79.844 0.000 10.575 11.107 10.841 2.902
## .ssei 9.562 0.123 77.895 0.000 9.322 9.803 9.562 2.831
## .ssno 0.328 0.034 9.769 0.000 0.262 0.394 0.328 0.347
## .sscs 0.432 0.033 13.004 0.000 0.367 0.497 0.432 0.463
## .sswk 25.835 0.262 98.598 0.000 25.322 26.349 25.835 3.365
## .sspc 11.246 0.107 105.151 0.000 11.036 11.455 11.246 3.538
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.297 1.499 4.202 0.000 3.360 9.235 6.297 0.128
## .ssmk 8.965 1.203 7.449 0.000 6.606 11.324 8.965 0.221
## .ssmc 7.408 0.757 9.780 0.000 5.923 8.892 7.408 0.422
## .ssgs 4.474 0.354 12.638 0.000 3.780 5.167 4.474 0.206
## .ssasi 6.390 0.531 12.027 0.000 5.348 7.431 6.390 0.458
## .ssei 4.133 0.472 8.754 0.000 3.208 5.059 4.133 0.362
## .ssno 0.245 0.047 5.178 0.000 0.152 0.338 0.245 0.275
## .sscs 0.332 0.044 7.505 0.000 0.245 0.418 0.332 0.381
## .sswk 8.050 0.738 10.909 0.000 6.604 9.497 8.050 0.137
## .sspc 2.676 0.168 15.916 0.000 2.346 3.005 2.676 0.265
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
#modificationIndices(configural, sort=T, maximum.number=30)
metric<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 635.554 67.000 0.000 0.970 0.089 0.061 98326.209 98683.151
Mc(metric)
## [1] 0.8752237
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 53 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 19
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 635.554 427.045
## Degrees of freedom 67 67
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.488
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 373.339 250.856
## 1 262.215 176.189
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.537 0.243 14.583 0.000 3.062 4.013 3.537 0.458
## ssmk (.p2.) 3.069 0.209 14.711 0.000 2.660 3.478 3.069 0.445
## ssmc (.p3.) 1.075 0.108 9.944 0.000 0.863 1.286 1.075 0.207
## electronic =~
## ssgs (.p4.) 1.026 0.123 8.364 0.000 0.786 1.267 1.026 0.193
## ssasi (.p5.) 3.042 0.163 18.610 0.000 2.722 3.362 3.042 0.586
## ssmc (.p6.) 2.573 0.142 18.150 0.000 2.295 2.851 2.573 0.495
## ssei (.p7.) 1.739 0.117 14.919 0.000 1.511 1.968 1.739 0.423
## speed =~
## ssno (.p8.) 0.398 0.024 16.847 0.000 0.352 0.445 0.398 0.409
## sscs (.p9.) 0.578 0.018 32.342 0.000 0.543 0.613 0.578 0.633
## g =~
## ssgs (.10.) 4.702 0.116 40.561 0.000 4.474 4.929 4.702 0.883
## ssar (.11.) 6.401 0.149 42.927 0.000 6.109 6.694 6.401 0.828
## sswk (.12.) 7.893 0.175 45.033 0.000 7.549 8.236 7.893 0.937
## sspc (.13.) 3.126 0.078 39.839 0.000 2.972 3.280 3.126 0.874
## ssno (.14.) 0.684 0.025 27.915 0.000 0.636 0.733 0.684 0.703
## sscs (.15.) 0.599 0.025 23.829 0.000 0.550 0.648 0.599 0.656
## ssasi (.16.) 3.182 0.126 25.212 0.000 2.935 3.430 3.182 0.613
## ssmk (.17.) 5.423 0.134 40.456 0.000 5.161 5.686 5.423 0.787
## ssmc (.18.) 3.548 0.126 28.260 0.000 3.302 3.794 3.548 0.683
## ssei (.19.) 3.272 0.101 32.320 0.000 3.073 3.470 3.272 0.796
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 18.495 0.286 64.662 0.000 17.934 19.056 18.495 2.393
## .ssmk 13.973 0.261 53.474 0.000 13.461 14.486 13.973 2.027
## .ssmc 15.637 0.201 77.759 0.000 15.243 16.031 15.637 3.010
## .ssgs 16.396 0.190 86.372 0.000 16.024 16.768 16.396 3.080
## .ssasi 16.211 0.198 81.891 0.000 15.823 16.599 16.211 3.121
## .ssei 12.364 0.157 78.687 0.000 12.056 12.672 12.364 3.007
## .ssno 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.061
## .sscs -0.083 0.033 -2.497 0.013 -0.149 -0.018 -0.083 -0.091
## .sswk 25.438 0.284 89.414 0.000 24.881 25.996 25.438 3.021
## .sspc 10.375 0.126 82.229 0.000 10.127 10.622 10.375 2.900
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.254 1.379 4.534 0.000 3.551 8.958 6.254 0.105
## .ssmk 8.678 1.115 7.784 0.000 6.493 10.863 8.678 0.183
## .ssmc 6.625 0.614 10.790 0.000 5.422 7.829 6.625 0.246
## .ssgs 5.181 0.337 15.373 0.000 4.521 5.842 5.181 0.183
## .ssasi 7.592 0.805 9.434 0.000 6.015 9.170 7.592 0.281
## .ssei 3.178 0.255 12.442 0.000 2.677 3.679 3.178 0.188
## .ssno 0.321 0.022 14.806 0.000 0.278 0.363 0.321 0.338
## .sscs 0.141 0.033 4.293 0.000 0.077 0.206 0.141 0.169
## .sswk 8.609 0.752 11.444 0.000 7.134 10.083 8.609 0.121
## .sspc 3.023 0.195 15.508 0.000 2.641 3.405 3.023 0.236
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.537 0.243 14.583 0.000 3.062 4.013 3.303 0.475
## ssmk (.p2.) 3.069 0.209 14.711 0.000 2.660 3.478 2.866 0.455
## ssmc (.p3.) 1.075 0.108 9.944 0.000 0.863 1.286 1.004 0.229
## electronic =~
## ssgs (.p4.) 1.026 0.123 8.364 0.000 0.786 1.267 0.427 0.092
## ssasi (.p5.) 3.042 0.163 18.610 0.000 2.722 3.362 1.267 0.325
## ssmc (.p6.) 2.573 0.142 18.150 0.000 2.295 2.851 1.072 0.244
## ssei (.p7.) 1.739 0.117 14.919 0.000 1.511 1.968 0.725 0.201
## speed =~
## ssno (.p8.) 0.398 0.024 16.844 0.000 0.352 0.445 0.416 0.447
## sscs (.p9.) 0.578 0.018 32.408 0.000 0.543 0.613 0.604 0.657
## g =~
## ssgs (.10.) 4.702 0.116 40.561 0.000 4.474 4.929 4.105 0.883
## ssar (.11.) 6.401 0.149 42.927 0.000 6.109 6.694 5.589 0.804
## sswk (.12.) 7.893 0.175 45.033 0.000 7.549 8.236 6.891 0.919
## sspc (.13.) 3.126 0.078 39.839 0.000 2.972 3.280 2.730 0.856
## ssno (.14.) 0.684 0.025 27.915 0.000 0.636 0.733 0.598 0.642
## sscs (.15.) 0.599 0.025 23.829 0.000 0.550 0.648 0.523 0.569
## ssasi (.16.) 3.182 0.126 25.212 0.000 2.935 3.430 2.779 0.713
## ssmk (.17.) 5.423 0.134 40.456 0.000 5.161 5.686 4.735 0.752
## ssmc (.18.) 3.548 0.126 28.260 0.000 3.302 3.794 3.098 0.705
## ssei (.19.) 3.272 0.101 32.320 0.000 3.073 3.470 2.857 0.792
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 16.999 0.262 64.966 0.000 16.486 17.512 16.999 2.446
## .ssmk 13.732 0.240 57.183 0.000 13.262 14.203 13.732 2.182
## .ssmc 11.961 0.157 76.345 0.000 11.654 12.268 11.961 2.723
## .ssgs 14.908 0.166 89.625 0.000 14.582 15.234 14.908 3.205
## .ssasi 10.841 0.136 79.844 0.000 10.575 11.107 10.841 2.780
## .ssei 9.562 0.123 77.895 0.000 9.322 9.803 9.562 2.650
## .ssno 0.328 0.034 9.769 0.000 0.262 0.394 0.328 0.352
## .sscs 0.432 0.033 13.004 0.000 0.367 0.497 0.432 0.470
## .sswk 25.835 0.262 98.598 0.000 25.322 26.349 25.835 3.447
## .sspc 11.246 0.107 105.151 0.000 11.036 11.455 11.246 3.526
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.167 1.183 5.212 0.000 3.848 8.487 6.167 0.128
## .ssmk 8.982 0.996 9.021 0.000 7.030 10.934 8.982 0.227
## .ssmc 7.539 0.480 15.693 0.000 6.597 8.480 7.539 0.391
## .ssgs 4.598 0.306 15.026 0.000 3.999 5.198 4.598 0.213
## .ssasi 5.880 0.417 14.108 0.000 5.063 6.697 5.880 0.387
## .ssei 4.332 0.276 15.666 0.000 3.790 4.873 4.332 0.333
## .ssno 0.336 0.025 13.669 0.000 0.288 0.384 0.336 0.388
## .sscs 0.206 0.043 4.844 0.000 0.123 0.290 0.206 0.244
## .sswk 8.697 0.724 12.006 0.000 7.277 10.116 8.697 0.155
## .sspc 2.722 0.170 16.056 0.000 2.390 3.054 2.722 0.268
## math 0.872 0.100 8.708 0.000 0.676 1.068 1.000 1.000
## electronic 0.174 0.039 4.476 0.000 0.098 0.249 1.000 1.000
## speed 1.092 0.129 8.480 0.000 0.839 1.344 1.000 1.000
## g 0.762 0.046 16.536 0.000 0.672 0.853 1.000 1.000
lavTestScore(metric, release = 1:19)
## 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 102.079 19 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p54. 0.307 1 0.579
## 2 .p2. == .p55. 0.397 1 0.528
## 3 .p3. == .p56. 1.735 1 0.188
## 4 .p4. == .p57. 0.587 1 0.444
## 5 .p5. == .p58. 1.708 1 0.191
## 6 .p6. == .p59. 0.370 1 0.543
## 7 .p7. == .p60. 0.004 1 0.948
## 8 .p8. == .p61. 0.000 1 1.000
## 9 .p9. == .p62. 0.000 1 1.000
## 10 .p10. == .p63. 0.955 1 0.328
## 11 .p11. == .p64. 0.931 1 0.335
## 12 .p12. == .p65. 14.720 1 0.000
## 13 .p13. == .p66. 0.139 1 0.709
## 14 .p14. == .p67. 0.372 1 0.542
## 15 .p15. == .p68. 0.921 1 0.337
## 16 .p16. == .p69. 5.558 1 0.018
## 17 .p17. == .p70. 1.281 1 0.258
## 18 .p18. == .p71. 14.354 1 0.000
## 19 .p19. == .p72. 23.369 1 0.000
metric2<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings"), group.partial=c("g=~ssei", "g=~ssmc"))
fitMeasures(metric2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 587.893 65.000 0.000 0.972 0.087 0.045 98282.547 98650.821
Mc(metric2)
## [1] 0.884642
summary(metric2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 58 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 17
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 587.893 393.015
## Degrees of freedom 65 65
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.496
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 344.577 230.355
## 1 243.316 162.660
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.543 0.242 14.630 0.000 3.069 4.018 3.543 0.460
## ssmk (.p2.) 3.072 0.207 14.811 0.000 2.665 3.478 3.072 0.447
## ssmc (.p3.) 1.077 0.107 10.076 0.000 0.868 1.286 1.077 0.199
## electronic =~
## ssgs (.p4.) 0.999 0.125 8.014 0.000 0.754 1.243 0.999 0.187
## ssasi (.p5.) 3.015 0.170 17.688 0.000 2.681 3.349 3.015 0.578
## ssmc (.p6.) 2.470 0.149 16.574 0.000 2.178 2.762 2.470 0.457
## ssei (.p7.) 1.652 0.120 13.813 0.000 1.418 1.887 1.652 0.384
## speed =~
## ssno (.p8.) 0.496 0.021 23.248 0.000 0.454 0.538 0.496 0.511
## sscs (.p9.) 0.466 0.022 21.653 0.000 0.424 0.508 0.466 0.511
## g =~
## ssgs (.10.) 4.710 0.115 41.043 0.000 4.485 4.934 4.710 0.884
## ssar (.11.) 6.363 0.149 42.591 0.000 6.071 6.656 6.363 0.826
## sswk (.12.) 7.858 0.174 45.033 0.000 7.516 8.200 7.858 0.937
## sspc (.13.) 3.108 0.078 39.774 0.000 2.955 3.261 3.108 0.872
## ssno (.14.) 0.680 0.024 27.856 0.000 0.633 0.728 0.680 0.700
## sscs (.15.) 0.596 0.025 23.850 0.000 0.547 0.645 0.596 0.654
## ssasi (.16.) 3.252 0.126 25.771 0.000 3.005 3.499 3.252 0.623
## ssmk (.17.) 5.392 0.134 40.319 0.000 5.130 5.654 5.392 0.785
## ssmc 3.914 0.143 27.405 0.000 3.634 4.194 3.914 0.724
## ssei 3.551 0.106 33.351 0.000 3.342 3.760 3.551 0.826
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 18.495 0.286 64.662 0.000 17.934 19.056 18.495 2.401
## .ssmk 13.973 0.261 53.474 0.000 13.461 14.486 13.973 2.034
## .ssmc 15.637 0.201 77.759 0.000 15.243 16.031 15.637 2.891
## .ssgs 16.396 0.190 86.372 0.000 16.024 16.768 16.396 3.078
## .ssasi 16.211 0.198 81.891 0.000 15.823 16.599 16.211 3.106
## .ssei 12.364 0.157 78.687 0.000 12.056 12.672 12.364 2.876
## .ssno 0.059 0.035 1.682 0.093 -0.010 0.128 0.059 0.061
## .sscs -0.083 0.033 -2.497 0.013 -0.149 -0.018 -0.083 -0.091
## .sswk 25.438 0.284 89.414 0.000 24.881 25.996 25.438 3.033
## .sspc 10.375 0.126 82.229 0.000 10.127 10.622 10.375 2.911
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.266 1.369 4.579 0.000 3.584 8.949 6.266 0.106
## .ssmk 8.691 1.099 7.906 0.000 6.536 10.845 8.691 0.184
## .ssmc 6.682 0.609 10.981 0.000 5.490 7.875 6.682 0.228
## .ssgs 5.208 0.337 15.472 0.000 4.548 5.867 5.208 0.183
## .ssasi 7.573 0.837 9.054 0.000 5.934 9.213 7.573 0.278
## .ssei 3.148 0.248 12.697 0.000 2.662 3.633 3.148 0.170
## .ssno 0.235 0.022 10.520 0.000 0.191 0.279 0.235 0.249
## .sscs 0.258 0.033 7.916 0.000 0.194 0.322 0.258 0.311
## .sswk 8.585 0.744 11.539 0.000 7.127 10.044 8.585 0.122
## .sspc 3.041 0.196 15.535 0.000 2.657 3.425 3.041 0.239
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.543 0.242 14.630 0.000 3.069 4.018 3.313 0.475
## ssmk (.p2.) 3.072 0.207 14.811 0.000 2.665 3.478 2.872 0.454
## ssmc (.p3.) 1.077 0.107 10.076 0.000 0.868 1.286 1.007 0.240
## electronic =~
## ssgs (.p4.) 0.999 0.125 8.014 0.000 0.754 1.243 0.427 0.091
## ssasi (.p5.) 3.015 0.170 17.688 0.000 2.681 3.349 1.288 0.324
## ssmc (.p6.) 2.470 0.149 16.574 0.000 2.178 2.762 1.056 0.251
## ssei (.p7.) 1.652 0.120 13.813 0.000 1.418 1.887 0.706 0.207
## speed =~
## ssno (.p8.) 0.496 0.021 23.248 0.000 0.454 0.538 0.516 0.553
## sscs (.p9.) 0.466 0.022 21.654 0.000 0.424 0.508 0.485 0.527
## g =~
## ssgs (.10.) 4.710 0.115 41.043 0.000 4.485 4.934 4.163 0.886
## ssar (.11.) 6.363 0.149 42.591 0.000 6.071 6.656 5.625 0.806
## sswk (.12.) 7.858 0.174 45.033 0.000 7.516 8.200 6.947 0.922
## sspc (.13.) 3.108 0.078 39.774 0.000 2.955 3.261 2.748 0.858
## ssno (.14.) 0.680 0.024 27.856 0.000 0.633 0.728 0.602 0.645
## sscs (.15.) 0.596 0.025 23.850 0.000 0.547 0.645 0.527 0.572
## ssasi (.16.) 3.252 0.126 25.771 0.000 3.005 3.499 2.875 0.723
## ssmk (.17.) 5.392 0.134 40.319 0.000 5.130 5.654 4.767 0.754
## ssmc 3.200 0.135 23.657 0.000 2.935 3.465 2.829 0.673
## ssei 2.940 0.113 26.017 0.000 2.718 3.161 2.599 0.763
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 16.999 0.262 64.966 0.000 16.486 17.512 16.999 2.434
## .ssmk 13.732 0.240 57.183 0.000 13.262 14.203 13.732 2.172
## .ssmc 11.961 0.157 76.345 0.000 11.654 12.268 11.961 2.847
## .ssgs 14.908 0.166 89.625 0.000 14.582 15.234 14.908 3.172
## .ssasi 10.841 0.136 79.844 0.000 10.575 11.107 10.841 2.728
## .ssei 9.562 0.123 77.895 0.000 9.322 9.803 9.562 2.807
## .ssno 0.328 0.034 9.769 0.000 0.262 0.394 0.328 0.351
## .sscs 0.432 0.033 13.004 0.000 0.367 0.497 0.432 0.469
## .sswk 25.835 0.262 98.598 0.000 25.322 26.349 25.835 3.427
## .sspc 11.246 0.107 105.151 0.000 11.036 11.455 11.246 3.511
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.133 1.187 5.165 0.000 3.805 8.460 6.133 0.126
## .ssmk 8.983 1.002 8.963 0.000 7.019 10.947 8.983 0.225
## .ssmc 7.517 0.475 15.813 0.000 6.585 8.448 7.517 0.426
## .ssgs 4.574 0.306 14.933 0.000 3.974 5.174 4.574 0.207
## .ssasi 5.869 0.425 13.797 0.000 5.035 6.703 5.869 0.372
## .ssei 4.351 0.274 15.884 0.000 3.814 4.888 4.351 0.375
## .ssno 0.242 0.025 9.693 0.000 0.193 0.291 0.242 0.278
## .sscs 0.335 0.037 9.072 0.000 0.262 0.407 0.335 0.395
## .sswk 8.566 0.718 11.928 0.000 7.159 9.974 8.566 0.151
## .sspc 2.709 0.168 16.078 0.000 2.379 3.039 2.709 0.264
## math 0.874 0.100 8.745 0.000 0.678 1.070 1.000 1.000
## electronic 0.183 0.040 4.540 0.000 0.104 0.261 1.000 1.000
## speed 1.083 0.128 8.489 0.000 0.833 1.333 1.000 1.000
## g 0.782 0.047 16.612 0.000 0.689 0.874 1.000 1.000
lavTestScore(metric2, release = 1:17)
## 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 55.664 17 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p54. 0.536 1 0.464
## 2 .p2. == .p55. 0.684 1 0.408
## 3 .p3. == .p56. 3.024 1 0.082
## 4 .p4. == .p57. 1.189 1 0.275
## 5 .p5. == .p58. 2.995 1 0.083
## 6 .p6. == .p59. 0.467 1 0.494
## 7 .p7. == .p60. 0.020 1 0.887
## 8 .p8. == .p61. 0.000 1 1.000
## 9 .p9. == .p62. 0.000 1 1.000
## 10 .p10. == .p63. 0.482 1 0.487
## 11 .p11. == .p64. 0.003 1 0.957
## 12 .p12. == .p65. 9.070 1 0.003
## 13 .p13. == .p66. 0.748 1 0.387
## 14 .p14. == .p67. 0.233 1 0.629
## 15 .p15. == .p68. 0.721 1 0.396
## 16 .p16. == .p69. 35.220 1 0.000
## 17 .p17. == .p70. 0.366 1 0.545
scalar<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("g=~ssei", "g=~ssmc"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 691.055 71.000 0.000 0.967 0.090 0.046 98373.709 98707.989
Mc(scalar)
## [1] 0.8647212
summary(scalar, standardized=T, ci=T) # +.134
## lavaan 0.6-18 ended normally after 164 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 27
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 691.055 470.366
## Degrees of freedom 71 71
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.469
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 397.886 270.821
## 1 293.169 199.545
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.197 0.283 14.832 0.000 3.642 4.751 4.197 0.545
## ssmk (.p2.) 2.490 0.210 11.864 0.000 2.079 2.902 2.490 0.363
## ssmc (.p3.) 0.839 0.122 6.869 0.000 0.600 1.079 0.839 0.157
## electronic =~
## ssgs (.p4.) 1.104 0.074 14.953 0.000 0.960 1.249 1.104 0.207
## ssasi (.p5.) 3.135 0.137 22.941 0.000 2.867 3.403 3.135 0.597
## ssmc (.p6.) 2.097 0.112 18.662 0.000 1.877 2.317 2.097 0.392
## ssei (.p7.) 1.723 0.082 20.929 0.000 1.562 1.885 1.723 0.401
## speed =~
## ssno (.p8.) 0.309 0.031 9.814 0.000 0.247 0.370 0.309 0.318
## sscs (.p9.) 0.741 0.076 9.729 0.000 0.592 0.891 0.741 0.814
## g =~
## ssgs (.10.) 4.695 0.112 42.083 0.000 4.476 4.913 4.695 0.880
## ssar (.11.) 6.374 0.149 42.635 0.000 6.081 6.667 6.374 0.827
## sswk (.12.) 7.817 0.173 45.269 0.000 7.478 8.155 7.817 0.934
## sspc (.13.) 3.125 0.080 38.869 0.000 2.967 3.282 3.125 0.872
## ssno (.14.) 0.682 0.024 27.887 0.000 0.634 0.730 0.682 0.702
## sscs (.15.) 0.597 0.025 23.866 0.000 0.548 0.646 0.597 0.656
## ssasi (.16.) 3.232 0.125 25.757 0.000 2.986 3.477 3.232 0.615
## ssmk (.17.) 5.427 0.134 40.499 0.000 5.165 5.690 5.427 0.791
## ssmc 3.983 0.138 28.863 0.000 3.712 4.253 3.983 0.744
## ssei 3.532 0.103 34.185 0.000 3.330 3.735 3.532 0.821
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.523 0.292 63.399 0.000 17.951 19.096 18.523 2.404
## .ssmk (.41.) 14.214 0.248 57.377 0.000 13.728 14.699 14.214 2.072
## .ssmc (.42.) 15.755 0.194 81.130 0.000 15.375 16.136 15.755 2.944
## .ssgs (.43.) 16.396 0.187 87.456 0.000 16.028 16.763 16.396 3.073
## .ssasi (.44.) 16.205 0.198 81.667 0.000 15.816 16.594 16.205 3.085
## .ssei (.45.) 12.377 0.156 79.383 0.000 12.071 12.682 12.377 2.877
## .ssno (.46.) 0.064 0.035 1.803 0.071 -0.006 0.133 0.064 0.065
## .sscs (.47.) -0.079 0.033 -2.369 0.018 -0.145 -0.014 -0.079 -0.087
## .sswk (.48.) 25.204 0.290 86.808 0.000 24.635 25.773 25.204 3.011
## .sspc (.49.) 10.641 0.118 89.998 0.000 10.410 10.873 10.641 2.969
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 1.133 2.229 0.508 0.611 -3.237 5.502 1.133 0.019
## .ssmk 11.411 1.054 10.828 0.000 9.345 13.476 11.411 0.242
## .ssmc 7.683 0.541 14.200 0.000 6.622 8.743 7.683 0.268
## .ssgs 5.201 0.335 15.533 0.000 4.545 5.857 5.201 0.183
## .ssasi 7.326 0.745 9.830 0.000 5.865 8.786 7.326 0.265
## .ssei 3.066 0.236 12.987 0.000 2.603 3.529 3.066 0.166
## .ssno 0.384 0.028 13.932 0.000 0.330 0.438 0.384 0.407
## .sscs -0.077 0.108 -0.709 0.478 -0.288 0.135 -0.077 -0.092
## .sswk 8.966 0.790 11.343 0.000 7.417 10.515 8.966 0.128
## .sspc 3.081 0.204 15.105 0.000 2.681 3.481 3.081 0.240
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.197 0.283 14.832 0.000 3.642 4.751 3.918 0.561
## ssmk (.p2.) 2.490 0.210 11.864 0.000 2.079 2.902 2.325 0.368
## ssmc (.p3.) 0.839 0.122 6.869 0.000 0.600 1.079 0.784 0.187
## electronic =~
## ssgs (.p4.) 1.104 0.074 14.953 0.000 0.960 1.249 0.462 0.099
## ssasi (.p5.) 3.135 0.137 22.941 0.000 2.867 3.403 1.313 0.331
## ssmc (.p6.) 2.097 0.112 18.662 0.000 1.877 2.317 0.878 0.209
## ssei (.p7.) 1.723 0.082 20.929 0.000 1.562 1.885 0.721 0.212
## speed =~
## ssno (.p8.) 0.309 0.031 9.814 0.000 0.247 0.370 0.322 0.346
## sscs (.p9.) 0.741 0.076 9.729 0.000 0.592 0.891 0.775 0.841
## g =~
## ssgs (.10.) 4.695 0.112 42.083 0.000 4.476 4.913 4.154 0.885
## ssar (.11.) 6.374 0.149 42.635 0.000 6.081 6.667 5.639 0.808
## sswk (.12.) 7.817 0.173 45.269 0.000 7.478 8.155 6.916 0.918
## sspc (.13.) 3.125 0.080 38.869 0.000 2.967 3.282 2.764 0.856
## ssno (.14.) 0.682 0.024 27.887 0.000 0.634 0.730 0.603 0.646
## sscs (.15.) 0.597 0.025 23.866 0.000 0.548 0.646 0.529 0.574
## ssasi (.16.) 3.232 0.125 25.757 0.000 2.986 3.477 2.859 0.721
## ssmk (.17.) 5.427 0.134 40.499 0.000 5.165 5.690 4.802 0.760
## ssmc 3.235 0.140 23.116 0.000 2.960 3.509 2.862 0.681
## ssei 2.934 0.112 26.163 0.000 2.714 3.154 2.596 0.762
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.523 0.292 63.399 0.000 17.951 19.096 18.523 2.653
## .ssmk (.41.) 14.214 0.248 57.377 0.000 13.728 14.699 14.214 2.250
## .ssmc (.42.) 15.755 0.194 81.130 0.000 15.375 16.136 15.755 3.751
## .ssgs (.43.) 16.396 0.187 87.456 0.000 16.028 16.763 16.396 3.494
## .ssasi (.44.) 16.205 0.198 81.667 0.000 15.816 16.594 16.205 4.088
## .ssei (.45.) 12.377 0.156 79.383 0.000 12.071 12.682 12.377 3.635
## .ssno (.46.) 0.064 0.035 1.803 0.071 -0.006 0.133 0.064 0.068
## .sscs (.47.) -0.079 0.033 -2.369 0.018 -0.145 -0.014 -0.079 -0.086
## .sswk (.48.) 25.204 0.290 86.808 0.000 24.635 25.773 25.204 3.347
## .sspc (.49.) 10.641 0.118 89.998 0.000 10.410 10.873 10.641 3.296
## math -0.538 0.070 -7.669 0.000 -0.676 -0.401 -0.577 -0.577
## elctrnc -1.826 0.095 -19.306 0.000 -2.011 -1.640 -4.361 -4.361
## speed 0.594 0.086 6.882 0.000 0.425 0.763 0.568 0.568
## g 0.119 0.048 2.470 0.014 0.025 0.213 0.134 0.134
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 1.607 1.933 0.831 0.406 -2.182 5.395 1.607 0.033
## .ssmk 11.427 0.885 12.912 0.000 9.692 13.162 11.427 0.286
## .ssmc 8.068 0.474 17.004 0.000 7.138 8.998 8.068 0.457
## .ssgs 4.558 0.307 14.868 0.000 3.957 5.159 4.558 0.207
## .ssasi 5.819 0.426 13.645 0.000 4.983 6.654 5.819 0.370
## .ssei 4.334 0.273 15.873 0.000 3.799 4.869 4.334 0.374
## .ssno 0.403 0.033 12.055 0.000 0.338 0.469 0.403 0.463
## .sscs -0.030 0.125 -0.242 0.809 -0.276 0.215 -0.030 -0.036
## .sswk 8.873 0.742 11.960 0.000 7.419 10.328 8.873 0.156
## .sspc 2.780 0.177 15.726 0.000 2.433 3.126 2.780 0.267
## math 0.872 0.099 8.773 0.000 0.677 1.067 1.000 1.000
## electronic 0.175 0.040 4.374 0.000 0.097 0.254 1.000 1.000
## speed 1.092 0.129 8.444 0.000 0.838 1.345 1.000 1.000
## g 0.783 0.047 16.666 0.000 0.691 0.875 1.000 1.000
lavTestScore(scalar, release = 18:27)
## 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 99.812 10 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p40. == .p93. 27.382 1 0.000
## 2 .p41. == .p94. 18.051 1 0.000
## 3 .p42. == .p95. 13.162 1 0.000
## 4 .p43. == .p96. 1.804 1 0.179
## 5 .p44. == .p97. 2.365 1 0.124
## 6 .p45. == .p98. 0.626 1 0.429
## 7 .p46. == .p99. 0.000 1 1.000
## 8 .p47. == .p100. 0.000 1 1.000
## 9 .p48. == .p101. 55.180 1 0.000
## 10 .p49. == .p102. 60.308 1 0.000
scalar2<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("g=~ssei", "g=~ssmc", "sspc~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 629.972 70.000 0.000 0.970 0.087 0.046 98314.626 98654.571
Mc(scalar2)
## [1] 0.8769864
summary(scalar2, standardized=T, ci=T) # +.059
## lavaan 0.6-18 ended normally after 158 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 26
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 629.972 428.988
## Degrees of freedom 70 70
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.469
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 366.514 249.583
## 1 263.458 179.405
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.161 0.312 13.353 0.000 3.551 4.772 4.161 0.540
## ssmk (.p2.) 2.533 0.240 10.533 0.000 2.062 3.004 2.533 0.369
## ssmc (.p3.) 0.867 0.135 6.408 0.000 0.602 1.132 0.867 0.162
## electronic =~
## ssgs (.p4.) 1.012 0.075 13.453 0.000 0.865 1.159 1.012 0.190
## ssasi (.p5.) 3.168 0.137 23.205 0.000 2.900 3.435 3.168 0.602
## ssmc (.p6.) 2.120 0.112 18.857 0.000 1.900 2.340 2.120 0.396
## ssei (.p7.) 1.700 0.082 20.643 0.000 1.538 1.861 1.700 0.395
## speed =~
## ssno (.p8.) 0.332 0.028 11.642 0.000 0.276 0.387 0.332 0.341
## sscs (.p9.) 0.695 0.060 11.526 0.000 0.577 0.813 0.695 0.762
## g =~
## ssgs (.10.) 4.706 0.112 42.002 0.000 4.486 4.925 4.706 0.883
## ssar (.11.) 6.365 0.149 42.622 0.000 6.073 6.658 6.365 0.826
## sswk (.12.) 7.849 0.174 45.057 0.000 7.507 8.190 7.849 0.936
## sspc (.13.) 3.109 0.078 39.728 0.000 2.955 3.262 3.109 0.873
## ssno (.14.) 0.681 0.024 27.867 0.000 0.633 0.728 0.681 0.700
## sscs (.15.) 0.597 0.025 23.862 0.000 0.548 0.646 0.597 0.655
## ssasi (.16.) 3.235 0.125 25.845 0.000 2.990 3.481 3.235 0.615
## ssmk (.17.) 5.413 0.135 40.098 0.000 5.149 5.678 5.413 0.790
## ssmc 3.979 0.138 28.909 0.000 3.709 4.249 3.979 0.743
## ssei 3.538 0.103 34.377 0.000 3.336 3.740 3.538 0.822
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.508 0.298 62.113 0.000 17.924 19.092 18.508 2.402
## .ssmk (.41.) 14.271 0.244 58.433 0.000 13.793 14.750 14.271 2.081
## .ssmc (.42.) 15.748 0.194 81.279 0.000 15.368 16.127 15.748 2.940
## .ssgs (.43.) 16.421 0.187 87.752 0.000 16.055 16.788 16.421 3.083
## .ssasi (.44.) 16.193 0.199 81.441 0.000 15.804 16.583 16.193 3.079
## .ssei (.45.) 12.374 0.156 79.518 0.000 12.069 12.678 12.374 2.876
## .ssno (.46.) 0.063 0.035 1.792 0.073 -0.006 0.132 0.063 0.065
## .sscs (.47.) -0.080 0.033 -2.380 0.017 -0.145 -0.014 -0.080 -0.087
## .sswk (.48.) 25.458 0.287 88.569 0.000 24.895 26.021 25.458 3.036
## .sspc 10.394 0.126 82.311 0.000 10.146 10.641 10.394 2.918
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 1.563 2.534 0.617 0.537 -3.403 6.529 1.563 0.026
## .ssmk 11.291 1.176 9.599 0.000 8.986 13.597 11.291 0.240
## .ssmc 7.610 0.549 13.862 0.000 6.534 8.686 7.610 0.265
## .ssgs 5.205 0.335 15.515 0.000 4.548 5.863 5.205 0.183
## .ssasi 7.152 0.748 9.562 0.000 5.686 8.618 7.152 0.259
## .ssei 3.097 0.235 13.155 0.000 2.636 3.559 3.097 0.167
## .ssno 0.371 0.027 13.897 0.000 0.319 0.423 0.371 0.393
## .sscs -0.008 0.080 -0.105 0.917 -0.165 0.148 -0.008 -0.010
## .sswk 8.709 0.753 11.568 0.000 7.234 10.185 8.709 0.124
## .sspc 3.025 0.196 15.440 0.000 2.641 3.409 3.025 0.238
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.161 0.312 13.353 0.000 3.551 4.772 3.885 0.556
## ssmk (.p2.) 2.533 0.240 10.533 0.000 2.062 3.004 2.365 0.375
## ssmc (.p3.) 0.867 0.135 6.408 0.000 0.602 1.132 0.810 0.193
## electronic =~
## ssgs (.p4.) 1.012 0.075 13.453 0.000 0.865 1.159 0.426 0.091
## ssasi (.p5.) 3.168 0.137 23.205 0.000 2.900 3.435 1.334 0.336
## ssmc (.p6.) 2.120 0.112 18.857 0.000 1.900 2.340 0.893 0.213
## ssei (.p7.) 1.700 0.082 20.643 0.000 1.538 1.861 0.716 0.210
## speed =~
## ssno (.p8.) 0.332 0.028 11.642 0.000 0.276 0.387 0.346 0.370
## sscs (.p9.) 0.695 0.060 11.526 0.000 0.577 0.813 0.724 0.786
## g =~
## ssgs (.10.) 4.706 0.112 42.002 0.000 4.486 4.925 4.163 0.886
## ssar (.11.) 6.365 0.149 42.622 0.000 6.073 6.658 5.631 0.806
## sswk (.12.) 7.849 0.174 45.057 0.000 7.507 8.190 6.943 0.921
## sspc (.13.) 3.109 0.078 39.728 0.000 2.955 3.262 2.750 0.858
## ssno (.14.) 0.681 0.024 27.867 0.000 0.633 0.728 0.602 0.645
## sscs (.15.) 0.597 0.025 23.862 0.000 0.548 0.646 0.528 0.573
## ssasi (.16.) 3.235 0.125 25.845 0.000 2.990 3.481 2.862 0.721
## ssmk (.17.) 5.413 0.135 40.098 0.000 5.149 5.678 4.789 0.759
## ssmc 3.223 0.139 23.213 0.000 2.951 3.495 2.851 0.679
## ssei 2.937 0.112 26.199 0.000 2.717 3.156 2.598 0.763
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.508 0.298 62.113 0.000 17.924 19.092 18.508 2.650
## .ssmk (.41.) 14.271 0.244 58.433 0.000 13.793 14.750 14.271 2.260
## .ssmc (.42.) 15.748 0.194 81.279 0.000 15.368 16.127 15.748 3.753
## .ssgs (.43.) 16.421 0.187 87.752 0.000 16.055 16.788 16.421 3.494
## .ssasi (.44.) 16.193 0.199 81.441 0.000 15.804 16.583 16.193 4.082
## .ssei (.45.) 12.374 0.156 79.518 0.000 12.069 12.678 12.374 3.632
## .ssno (.46.) 0.063 0.035 1.792 0.073 -0.006 0.132 0.063 0.068
## .sscs (.47.) -0.080 0.033 -2.380 0.017 -0.145 -0.014 -0.080 -0.086
## .sswk (.48.) 25.458 0.287 88.569 0.000 24.895 26.021 25.458 3.377
## .sspc 11.085 0.134 82.900 0.000 10.822 11.347 11.085 3.458
## math -0.434 0.071 -6.083 0.000 -0.573 -0.294 -0.464 -0.464
## elctrnc -1.733 0.091 -19.053 0.000 -1.911 -1.554 -4.114 -4.114
## speed 0.692 0.088 7.883 0.000 0.520 0.864 0.664 0.664
## g 0.052 0.049 1.053 0.292 -0.045 0.148 0.059 0.059
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 1.966 2.204 0.892 0.372 -2.354 6.287 1.966 0.040
## .ssmk 11.334 0.986 11.494 0.000 9.401 13.266 11.334 0.284
## .ssmc 8.026 0.478 16.801 0.000 7.089 8.962 8.026 0.456
## .ssgs 4.577 0.306 14.937 0.000 3.976 5.177 4.577 0.207
## .ssasi 5.764 0.427 13.490 0.000 4.927 6.602 5.764 0.366
## .ssei 4.346 0.273 15.928 0.000 3.811 4.881 4.346 0.374
## .ssno 0.389 0.032 11.981 0.000 0.325 0.452 0.389 0.446
## .sscs 0.046 0.094 0.482 0.630 -0.140 0.231 0.046 0.054
## .sswk 8.631 0.720 11.996 0.000 7.221 10.042 8.631 0.152
## .sspc 2.711 0.168 16.093 0.000 2.381 3.041 2.711 0.264
## math 0.872 0.099 8.826 0.000 0.678 1.065 1.000 1.000
## electronic 0.177 0.040 4.407 0.000 0.099 0.256 1.000 1.000
## speed 1.086 0.128 8.469 0.000 0.835 1.337 1.000 1.000
## g 0.783 0.047 16.700 0.000 0.691 0.874 1.000 1.000
lavTestScore(scalar2, release = 18:26)
## 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 40.856 9 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p40. == .p93. 33.702 1 0.000
## 2 .p41. == .p94. 25.036 1 0.000
## 3 .p42. == .p95. 10.909 1 0.001
## 4 .p43. == .p96. 0.024 1 0.878
## 5 .p44. == .p97. 4.207 1 0.040
## 6 .p45. == .p98. 0.680 1 0.410
## 7 .p46. == .p99. 0.000 1 1.000
## 8 .p47. == .p100. 0.000 1 1.000
## 9 .p48. == .p101. 1.924 1 0.165
strict<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("g=~ssei", "g=~ssmc", "sspc~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 661.697 80.000 0.000 0.969 0.083 0.046 98326.351 98609.639
Mc(strict)
## [1] 0.8725315
summary(strict, standardized=T, ci=T) # +.061
## lavaan 0.6-18 ended normally after 116 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 36
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 661.697 443.579
## Degrees of freedom 80 80
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.492
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 383.844 257.316
## 1 277.853 186.263
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.102 0.270 15.170 0.000 3.572 4.632 4.102 0.532
## ssmk (.p2.) 2.536 0.244 10.406 0.000 2.058 3.013 2.536 0.370
## ssmc (.p3.) 0.871 0.135 6.442 0.000 0.606 1.136 0.871 0.162
## electronic =~
## ssgs (.p4.) 1.013 0.076 13.419 0.000 0.865 1.161 1.013 0.191
## ssasi (.p5.) 3.233 0.132 24.507 0.000 2.975 3.492 3.233 0.620
## ssmc (.p6.) 2.125 0.107 19.859 0.000 1.915 2.335 2.125 0.395
## ssei (.p7.) 1.692 0.078 21.678 0.000 1.539 1.845 1.692 0.388
## speed =~
## ssno (.p8.) 0.318 0.026 12.201 0.000 0.267 0.369 0.318 0.326
## sscs (.p9.) 0.691 0.062 11.112 0.000 0.569 0.813 0.691 0.758
## g =~
## ssgs (.10.) 4.710 0.111 42.294 0.000 4.492 4.928 4.710 0.888
## ssar (.11.) 6.374 0.149 42.882 0.000 6.082 6.665 6.374 0.826
## sswk (.12.) 7.850 0.174 45.108 0.000 7.509 8.191 7.850 0.936
## sspc (.13.) 3.113 0.078 39.805 0.000 2.960 3.266 3.113 0.878
## ssno (.14.) 0.681 0.024 27.846 0.000 0.633 0.729 0.681 0.699
## sscs (.15.) 0.597 0.025 23.844 0.000 0.548 0.646 0.597 0.655
## ssasi (.16.) 3.253 0.125 26.018 0.000 3.008 3.498 3.253 0.624
## ssmk (.17.) 5.422 0.135 40.192 0.000 5.158 5.687 5.422 0.791
## ssmc 3.977 0.137 29.059 0.000 3.708 4.245 3.977 0.739
## ssei 3.521 0.102 34.479 0.000 3.320 3.721 3.521 0.806
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.475 0.298 62.072 0.000 17.891 19.058 18.475 2.395
## .ssmk (.41.) 14.257 0.244 58.383 0.000 13.778 14.735 14.257 2.079
## .ssmc (.42.) 15.723 0.195 80.726 0.000 15.342 16.105 15.723 2.924
## .ssgs (.43.) 16.398 0.188 87.376 0.000 16.030 16.766 16.398 3.093
## .ssasi (.44.) 16.211 0.197 82.177 0.000 15.824 16.598 16.211 3.110
## .ssei (.45.) 12.338 0.156 78.912 0.000 12.031 12.644 12.338 2.825
## .ssno (.46.) 0.065 0.035 1.830 0.067 -0.005 0.135 0.065 0.067
## .sscs (.47.) -0.082 0.034 -2.436 0.015 -0.148 -0.016 -0.082 -0.090
## .sswk (.48.) 25.434 0.289 88.094 0.000 24.868 26.000 25.434 3.032
## .sspc 10.382 0.127 81.974 0.000 10.134 10.630 10.382 2.929
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.20.) 2.052 2.168 0.947 0.344 -2.197 6.301 2.052 0.034
## .ssmk (.21.) 11.199 0.954 11.741 0.000 9.330 13.069 11.199 0.238
## .ssmc (.22.) 7.835 0.374 20.928 0.000 7.101 8.568 7.835 0.271
## .ssgs (.23.) 4.905 0.232 21.108 0.000 4.450 5.361 4.905 0.174
## .ssasi (.24.) 6.127 0.392 15.615 0.000 5.358 6.896 6.127 0.226
## .ssei (.25.) 3.811 0.186 20.432 0.000 3.445 4.176 3.811 0.200
## .ssno (.26.) 0.384 0.025 15.461 0.000 0.336 0.433 0.384 0.405
## .sscs (.27.) -0.004 0.088 -0.043 0.966 -0.176 0.168 -0.004 -0.005
## .sswk (.28.) 8.730 0.527 16.559 0.000 7.697 9.764 8.730 0.124
## .sspc (.29.) 2.872 0.130 22.026 0.000 2.616 3.128 2.872 0.229
## math 1.000 1.000 1.000 1.000 1.000
## elctrnc 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.102 0.270 15.170 0.000 3.572 4.632 3.867 0.554
## ssmk (.p2.) 2.536 0.244 10.406 0.000 2.058 3.013 2.390 0.379
## ssmc (.p3.) 0.871 0.135 6.442 0.000 0.606 1.136 0.821 0.197
## electronic =~
## ssgs (.p4.) 1.013 0.076 13.419 0.000 0.865 1.161 0.417 0.088
## ssasi (.p5.) 3.233 0.132 24.507 0.000 2.975 3.492 1.331 0.331
## ssmc (.p6.) 2.125 0.107 19.859 0.000 1.915 2.335 0.875 0.210
## ssei (.p7.) 1.692 0.078 21.678 0.000 1.539 1.845 0.697 0.209
## speed =~
## ssno (.p8.) 0.318 0.026 12.201 0.000 0.267 0.369 0.348 0.374
## sscs (.p9.) 0.691 0.062 11.112 0.000 0.569 0.813 0.758 0.823
## g =~
## ssgs (.10.) 4.710 0.111 42.294 0.000 4.492 4.928 4.159 0.879
## ssar (.11.) 6.374 0.149 42.882 0.000 6.082 6.665 5.628 0.807
## sswk (.12.) 7.850 0.174 45.108 0.000 7.509 8.191 6.931 0.920
## sspc (.13.) 3.113 0.078 39.805 0.000 2.960 3.266 2.749 0.851
## ssno (.14.) 0.681 0.024 27.846 0.000 0.633 0.729 0.601 0.646
## sscs (.15.) 0.597 0.025 23.844 0.000 0.548 0.646 0.527 0.572
## ssasi (.16.) 3.253 0.125 26.018 0.000 3.008 3.498 2.872 0.715
## ssmk (.17.) 5.422 0.135 40.192 0.000 5.158 5.687 4.787 0.759
## ssmc 3.230 0.139 23.250 0.000 2.958 3.503 2.852 0.684
## ssei 2.961 0.113 26.293 0.000 2.741 3.182 2.615 0.784
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.475 0.298 62.072 0.000 17.891 19.058 18.475 2.648
## .ssmk (.41.) 14.257 0.244 58.383 0.000 13.778 14.735 14.257 2.259
## .ssmc (.42.) 15.723 0.195 80.726 0.000 15.342 16.105 15.723 3.768
## .ssgs (.43.) 16.398 0.188 87.376 0.000 16.030 16.766 16.398 3.467
## .ssasi (.44.) 16.211 0.197 82.177 0.000 15.824 16.598 16.211 4.034
## .ssei (.45.) 12.338 0.156 78.912 0.000 12.031 12.644 12.338 3.698
## .ssno (.46.) 0.065 0.035 1.830 0.067 -0.005 0.135 0.065 0.070
## .sscs (.47.) -0.082 0.034 -2.436 0.015 -0.148 -0.016 -0.082 -0.089
## .sswk (.48.) 25.434 0.289 88.094 0.000 24.868 26.000 25.434 3.376
## .sspc 11.077 0.135 82.055 0.000 10.813 11.342 11.077 3.431
## math -0.435 0.073 -5.953 0.000 -0.578 -0.292 -0.461 -0.461
## elctrnc -1.713 0.087 -19.608 0.000 -1.884 -1.542 -4.160 -4.160
## speed 0.697 0.095 7.354 0.000 0.511 0.883 0.635 0.635
## g 0.054 0.049 1.093 0.274 -0.043 0.151 0.061 0.061
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.20.) 2.052 2.168 0.947 0.344 -2.197 6.301 2.052 0.042
## .ssmk (.21.) 11.199 0.954 11.741 0.000 9.330 13.069 11.199 0.281
## .ssmc (.22.) 7.835 0.374 20.928 0.000 7.101 8.568 7.835 0.450
## .ssgs (.23.) 4.905 0.232 21.108 0.000 4.450 5.361 4.905 0.219
## .ssasi (.24.) 6.127 0.392 15.615 0.000 5.358 6.896 6.127 0.379
## .ssei (.25.) 3.811 0.186 20.432 0.000 3.445 4.176 3.811 0.342
## .ssno (.26.) 0.384 0.025 15.461 0.000 0.336 0.433 0.384 0.443
## .sscs (.27.) -0.004 0.088 -0.043 0.966 -0.176 0.168 -0.004 -0.004
## .sswk (.28.) 8.730 0.527 16.559 0.000 7.697 9.764 8.730 0.154
## .sspc (.29.) 2.872 0.130 22.026 0.000 2.616 3.128 2.872 0.275
## math 0.889 0.084 10.619 0.000 0.725 1.053 1.000 1.000
## elctrnc 0.170 0.038 4.460 0.000 0.095 0.244 1.000 1.000
## speed 1.204 0.120 10.015 0.000 0.969 1.440 1.000 1.000
## g 0.780 0.046 16.793 0.000 0.689 0.871 1.000 1.000
latent<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("g=~ssei", "g=~ssmc", "sspc~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(latent, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 811.267 74.000 0.000 0.961 0.097 0.115 98487.922 98805.204
Mc(latent)
## [1] 0.8412856
summary(latent, standardized=T, ci=T) # +.056 Std.all
## lavaan 0.6-18 ended normally after 139 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 26
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 811.267 556.163
## Degrees of freedom 74 74
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.459
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 434.160 297.638
## 1 377.107 258.525
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.126 0.295 13.980 0.000 3.548 4.704 4.126 0.560
## ssmk (.p2.) 2.450 0.216 11.325 0.000 2.026 2.874 2.450 0.372
## ssmc (.p3.) 0.798 0.131 6.114 0.000 0.542 1.054 0.798 0.155
## electronic =~
## ssgs (.p4.) 0.753 0.056 13.375 0.000 0.643 0.863 0.753 0.148
## ssasi (.p5.) 2.313 0.110 20.938 0.000 2.097 2.530 2.313 0.474
## ssmc (.p6.) 1.556 0.093 16.694 0.000 1.373 1.739 1.556 0.302
## ssei (.p7.) 1.266 0.067 19.019 0.000 1.136 1.397 1.266 0.308
## speed =~
## ssno (.p8.) 0.338 0.027 12.499 0.000 0.285 0.391 0.338 0.355
## sscs (.p9.) 0.711 0.058 12.344 0.000 0.598 0.824 0.711 0.795
## g =~
## ssgs (.10.) 4.499 0.082 55.132 0.000 4.339 4.659 4.499 0.883
## ssar (.11.) 5.996 0.114 52.595 0.000 5.772 6.219 5.996 0.814
## sswk (.12.) 7.440 0.126 58.830 0.000 7.192 7.688 7.440 0.929
## sspc (.13.) 2.938 0.061 48.353 0.000 2.819 3.057 2.938 0.858
## ssno (.14.) 0.642 0.021 30.048 0.000 0.600 0.684 0.642 0.675
## sscs (.15.) 0.565 0.022 25.436 0.000 0.521 0.608 0.565 0.631
## ssasi (.16.) 3.188 0.103 30.987 0.000 2.986 3.389 3.188 0.652
## ssmk (.17.) 5.094 0.108 47.344 0.000 4.883 5.305 5.094 0.773
## ssmc 3.930 0.114 34.370 0.000 3.706 4.154 3.930 0.763
## ssei 3.475 0.083 41.959 0.000 3.313 3.638 3.475 0.846
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.527 0.295 62.742 0.000 17.948 19.105 18.527 2.514
## .ssmk (.41.) 14.272 0.244 58.414 0.000 13.793 14.751 14.272 2.166
## .ssmc (.42.) 15.748 0.195 80.737 0.000 15.366 16.131 15.748 3.056
## .ssgs (.43.) 16.438 0.188 87.582 0.000 16.070 16.805 16.438 3.225
## .ssasi (.44.) 16.178 0.200 80.815 0.000 15.785 16.570 16.178 3.311
## .ssei (.45.) 12.397 0.155 79.762 0.000 12.093 12.702 12.397 3.020
## .ssno (.46.) 0.064 0.035 1.835 0.067 -0.004 0.133 0.064 0.068
## .sscs (.47.) -0.078 0.033 -2.349 0.019 -0.144 -0.013 -0.078 -0.088
## .sswk (.48.) 25.461 0.287 88.755 0.000 24.898 26.023 25.461 3.179
## .sspc 10.400 0.126 82.526 0.000 10.153 10.647 10.400 3.036
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 1.317 2.541 0.519 0.604 -3.662 6.297 1.317 0.024
## .ssmk 11.466 1.126 10.183 0.000 9.259 13.673 11.466 0.264
## .ssmc 8.055 0.549 14.665 0.000 6.978 9.131 8.055 0.303
## .ssgs 5.175 0.334 15.470 0.000 4.519 5.830 5.175 0.199
## .ssasi 8.354 0.780 10.711 0.000 6.825 9.882 8.354 0.350
## .ssei 3.175 0.235 13.536 0.000 2.715 3.635 3.175 0.188
## .ssno 0.378 0.027 13.923 0.000 0.325 0.432 0.378 0.418
## .sscs -0.024 0.080 -0.303 0.762 -0.182 0.133 -0.024 -0.030
## .sswk 8.801 0.724 12.153 0.000 7.382 10.221 8.801 0.137
## .sspc 3.104 0.199 15.614 0.000 2.715 3.494 3.104 0.264
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.126 0.295 13.980 0.000 3.548 4.704 4.126 0.561
## ssmk (.p2.) 2.450 0.216 11.325 0.000 2.026 2.874 2.450 0.371
## ssmc (.p3.) 0.798 0.131 6.114 0.000 0.542 1.054 0.798 0.176
## electronic =~
## ssgs (.p4.) 0.753 0.056 13.375 0.000 0.643 0.863 0.753 0.149
## ssasi (.p5.) 2.313 0.110 20.938 0.000 2.097 2.530 2.313 0.511
## ssmc (.p6.) 1.556 0.093 16.694 0.000 1.373 1.739 1.556 0.343
## ssei (.p7.) 1.266 0.067 19.019 0.000 1.136 1.397 1.266 0.340
## speed =~
## ssno (.p8.) 0.338 0.027 12.499 0.000 0.285 0.391 0.338 0.354
## sscs (.p9.) 0.711 0.058 12.344 0.000 0.598 0.824 0.711 0.758
## g =~
## ssgs (.10.) 4.499 0.082 55.132 0.000 4.339 4.659 4.499 0.892
## ssar (.11.) 5.996 0.114 52.595 0.000 5.772 6.219 5.996 0.816
## sswk (.12.) 7.440 0.126 58.830 0.000 7.192 7.688 7.440 0.934
## sspc (.13.) 2.938 0.061 48.353 0.000 2.819 3.057 2.938 0.876
## ssno (.14.) 0.642 0.021 30.048 0.000 0.600 0.684 0.642 0.672
## sscs (.15.) 0.565 0.022 25.436 0.000 0.521 0.608 0.565 0.602
## ssasi (.16.) 3.188 0.103 30.987 0.000 2.986 3.389 3.188 0.705
## ssmk (.17.) 5.094 0.108 47.344 0.000 4.883 5.305 5.094 0.771
## ssmc 3.109 0.120 26.013 0.000 2.874 3.343 3.109 0.686
## ssei 2.827 0.091 31.237 0.000 2.650 3.005 2.827 0.759
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.527 0.295 62.742 0.000 17.948 19.105 18.527 2.521
## .ssmk (.41.) 14.272 0.244 58.414 0.000 13.793 14.751 14.272 2.161
## .ssmc (.42.) 15.748 0.195 80.737 0.000 15.366 16.131 15.748 3.474
## .ssgs (.43.) 16.438 0.188 87.582 0.000 16.070 16.805 16.438 3.259
## .ssasi (.44.) 16.178 0.200 80.815 0.000 15.785 16.570 16.178 3.576
## .ssei (.45.) 12.397 0.155 79.762 0.000 12.093 12.702 12.397 3.326
## .ssno (.46.) 0.064 0.035 1.835 0.067 -0.004 0.133 0.064 0.067
## .sscs (.47.) -0.078 0.033 -2.349 0.019 -0.144 -0.013 -0.078 -0.084
## .sswk (.48.) 25.461 0.287 88.755 0.000 24.898 26.023 25.461 3.197
## .sspc 11.082 0.133 83.509 0.000 10.822 11.342 11.082 3.302
## math -0.447 0.067 -6.688 0.000 -0.578 -0.316 -0.447 -0.447
## elctrnc -2.367 0.132 -17.986 0.000 -2.625 -2.109 -2.367 -2.367
## speed 0.673 0.082 8.230 0.000 0.513 0.834 0.673 0.673
## g 0.056 0.052 1.069 0.285 -0.046 0.158 0.056 0.056
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 1.038 2.495 0.416 0.677 -3.852 5.929 1.038 0.019
## .ssmk 11.663 1.069 10.911 0.000 9.568 13.758 11.663 0.267
## .ssmc 7.830 0.491 15.942 0.000 6.868 8.793 7.830 0.381
## .ssgs 4.628 0.306 15.130 0.000 4.029 5.228 4.628 0.182
## .ssasi 4.954 0.443 11.185 0.000 4.086 5.822 4.954 0.242
## .ssei 4.293 0.290 14.816 0.000 3.725 4.861 4.293 0.309
## .ssno 0.386 0.032 12.103 0.000 0.323 0.448 0.386 0.423
## .sscs 0.055 0.091 0.605 0.545 -0.123 0.233 0.055 0.062
## .sswk 8.084 0.715 11.306 0.000 6.683 9.486 8.084 0.127
## .sspc 2.627 0.164 16.016 0.000 2.306 2.949 2.627 0.233
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
latent2<-cfa(bf.lv, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("g=~ssei", "g=~ssmc", "sspc~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(latent2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 632.692 72.000 0.000 0.970 0.085 0.046 98313.346 98641.960
Mc(latent2)
## [1] 0.8768384
summary(latent2, standardized=T, ci=T) # +.058 Std.all
## lavaan 0.6-18 ended normally after 140 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 84
## Number of equality constraints 26
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 632.692 432.332
## Degrees of freedom 72 72
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.463
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 368.218 251.612
## 1 264.473 180.720
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.017 0.278 14.433 0.000 3.471 4.562 4.017 0.524
## ssmk (.p2.) 2.454 0.217 11.325 0.000 2.029 2.879 2.454 0.360
## ssmc (.p3.) 0.845 0.130 6.518 0.000 0.591 1.100 0.845 0.158
## electronic =~
## ssgs (.p4.) 1.013 0.075 13.480 0.000 0.866 1.160 1.013 0.190
## ssasi (.p5.) 3.171 0.137 23.173 0.000 2.903 3.440 3.171 0.603
## ssmc (.p6.) 2.121 0.113 18.846 0.000 1.900 2.341 2.121 0.396
## ssei (.p7.) 1.701 0.082 20.622 0.000 1.539 1.863 1.701 0.395
## speed =~
## ssno (.p8.) 0.338 0.027 12.571 0.000 0.285 0.391 0.338 0.346
## sscs (.p9.) 0.708 0.057 12.398 0.000 0.596 0.820 0.708 0.773
## g =~
## ssgs (.10.) 4.705 0.112 41.952 0.000 4.485 4.925 4.705 0.883
## ssar (.11.) 6.364 0.149 42.846 0.000 6.073 6.655 6.364 0.831
## sswk (.12.) 7.849 0.174 45.051 0.000 7.507 8.190 7.849 0.935
## sspc (.13.) 3.110 0.078 39.792 0.000 2.957 3.263 3.110 0.873
## ssno (.14.) 0.681 0.024 27.936 0.000 0.633 0.729 0.681 0.698
## sscs (.15.) 0.597 0.025 23.932 0.000 0.549 0.646 0.597 0.652
## ssasi (.16.) 3.234 0.125 25.816 0.000 2.988 3.479 3.234 0.615
## ssmk (.17.) 5.413 0.134 40.262 0.000 5.149 5.676 5.413 0.794
## ssmc 3.979 0.137 28.950 0.000 3.710 4.248 3.979 0.744
## ssei 3.537 0.103 34.325 0.000 3.335 3.739 3.537 0.822
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.500 0.299 61.885 0.000 17.914 19.086 18.500 2.415
## .ssmk (.41.) 14.269 0.244 58.386 0.000 13.790 14.748 14.269 2.094
## .ssmc (.42.) 15.748 0.194 81.271 0.000 15.368 16.128 15.748 2.943
## .ssgs (.43.) 16.422 0.187 87.761 0.000 16.055 16.788 16.422 3.083
## .ssasi (.44.) 16.194 0.199 81.445 0.000 15.804 16.583 16.194 3.080
## .ssei (.45.) 12.373 0.156 79.513 0.000 12.068 12.678 12.373 2.876
## .ssno (.46.) 0.063 0.035 1.792 0.073 -0.006 0.132 0.063 0.065
## .sscs (.47.) -0.080 0.033 -2.379 0.017 -0.145 -0.014 -0.080 -0.087
## .sswk (.48.) 25.458 0.287 88.555 0.000 24.895 26.022 25.458 3.034
## .sspc 10.394 0.126 82.307 0.000 10.146 10.641 10.394 2.917
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 2.047 2.364 0.866 0.387 -2.587 6.681 2.047 0.035
## .ssmk 11.135 1.128 9.876 0.000 8.925 13.345 11.135 0.240
## .ssmc 7.587 0.547 13.875 0.000 6.516 8.659 7.587 0.265
## .ssgs 5.201 0.335 15.525 0.000 4.545 5.858 5.201 0.183
## .ssasi 7.136 0.747 9.555 0.000 5.673 8.600 7.136 0.258
## .ssei 3.100 0.236 13.138 0.000 2.638 3.562 3.100 0.168
## .ssno 0.374 0.027 13.835 0.000 0.321 0.427 0.374 0.393
## .sscs -0.019 0.079 -0.245 0.806 -0.175 0.136 -0.019 -0.023
## .sswk 8.828 0.748 11.800 0.000 7.361 10.294 8.828 0.125
## .sspc 3.023 0.195 15.479 0.000 2.640 3.405 3.023 0.238
## electronic 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.017 0.278 14.433 0.000 3.471 4.562 4.017 0.571
## ssmk (.p2.) 2.454 0.217 11.325 0.000 2.029 2.879 2.454 0.386
## ssmc (.p3.) 0.845 0.130 6.518 0.000 0.591 1.100 0.845 0.201
## electronic =~
## ssgs (.p4.) 1.013 0.075 13.480 0.000 0.866 1.160 0.428 0.091
## ssasi (.p5.) 3.171 0.137 23.173 0.000 2.903 3.440 1.340 0.338
## ssmc (.p6.) 2.121 0.113 18.846 0.000 1.900 2.341 0.896 0.213
## ssei (.p7.) 1.701 0.082 20.622 0.000 1.539 1.863 0.719 0.211
## speed =~
## ssno (.p8.) 0.338 0.027 12.571 0.000 0.285 0.391 0.338 0.364
## sscs (.p9.) 0.708 0.057 12.398 0.000 0.596 0.820 0.708 0.772
## g =~
## ssgs (.10.) 4.705 0.112 41.952 0.000 4.485 4.925 4.162 0.885
## ssar (.11.) 6.364 0.149 42.846 0.000 6.073 6.655 5.630 0.801
## sswk (.12.) 7.849 0.174 45.051 0.000 7.507 8.190 6.943 0.922
## sspc (.13.) 3.110 0.078 39.792 0.000 2.957 3.263 2.751 0.858
## ssno (.14.) 0.681 0.024 27.936 0.000 0.633 0.729 0.603 0.648
## sscs (.15.) 0.597 0.025 23.932 0.000 0.549 0.646 0.529 0.577
## ssasi (.16.) 3.234 0.125 25.816 0.000 2.988 3.479 2.861 0.721
## ssmk (.17.) 5.413 0.134 40.262 0.000 5.149 5.676 4.788 0.753
## ssmc 3.219 0.139 23.225 0.000 2.947 3.490 2.847 0.677
## ssei 2.936 0.112 26.177 0.000 2.716 3.156 2.597 0.762
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.500 0.299 61.885 0.000 17.914 19.086 18.500 2.631
## .ssmk (.41.) 14.269 0.244 58.386 0.000 13.790 14.748 14.269 2.245
## .ssmc (.42.) 15.748 0.194 81.271 0.000 15.368 16.128 15.748 3.747
## .ssgs (.43.) 16.422 0.187 87.761 0.000 16.055 16.788 16.422 3.494
## .ssasi (.44.) 16.194 0.199 81.445 0.000 15.804 16.583 16.194 4.082
## .ssei (.45.) 12.373 0.156 79.513 0.000 12.068 12.678 12.373 3.632
## .ssno (.46.) 0.063 0.035 1.792 0.073 -0.006 0.132 0.063 0.068
## .sscs (.47.) -0.080 0.033 -2.379 0.017 -0.145 -0.014 -0.080 -0.087
## .sswk (.48.) 25.458 0.287 88.555 0.000 24.895 26.022 25.458 3.379
## .sspc 11.085 0.134 82.867 0.000 10.823 11.347 11.085 3.459
## math -0.449 0.070 -6.408 0.000 -0.586 -0.311 -0.449 -0.449
## elctrnc -1.731 0.091 -19.033 0.000 -1.909 -1.552 -4.096 -4.096
## speed 0.679 0.082 8.255 0.000 0.518 0.840 0.679 0.679
## g 0.052 0.049 1.051 0.293 -0.045 0.148 0.058 0.058
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.608 2.304 0.698 0.485 -2.907 6.123 1.608 0.033
## .ssmk 11.458 1.037 11.050 0.000 9.425 13.490 11.458 0.284
## .ssmc 8.038 0.481 16.725 0.000 7.096 8.980 8.038 0.455
## .ssgs 4.587 0.307 14.966 0.000 3.987 5.188 4.587 0.208
## .ssasi 5.756 0.427 13.475 0.000 4.918 6.593 5.756 0.366
## .ssei 4.347 0.273 15.916 0.000 3.812 4.883 4.347 0.374
## .ssno 0.386 0.032 12.117 0.000 0.324 0.449 0.386 0.447
## .sscs 0.060 0.090 0.664 0.507 -0.116 0.236 0.060 0.071
## .sswk 8.552 0.714 11.980 0.000 7.153 9.951 8.552 0.151
## .sspc 2.702 0.168 16.084 0.000 2.373 3.031 2.702 0.263
## electronic 0.179 0.040 4.442 0.000 0.100 0.257 1.000 1.000
## g 0.783 0.047 16.694 0.000 0.691 0.874 1.000 1.000
tests<-lavTestLRT(configural, metric2, scalar2, latent2)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 39.797396 37.807121 2.114885
dfd=tests[2:4,"Df diff"]
dfd
## [1] 13 5 2
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-1067+ 1067 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04397400 0.07845497 0.00734070
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.02879291 0.05988172
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.05623577 0.10268384
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] NA 0.06161349
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 0.999 0.286 0.049 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 0.981 0.917 0.489 0.073
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
## 0.653 0.614 0.127 0.058 0.007 0.000
tests<-lavTestLRT(configural, metric2, scalar2, latent)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 39.79740 37.80712 140.88244
dfd=tests[2:4,"Df diff"]
dfd
## [1] 13 5 4
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-1067+ 1067 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04397400 0.07845497 0.17916999
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.05623577 0.10268384
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.1544436 0.2050877
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 0.981 0.917 0.489 0.073
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 1 1 1 1
tests<-lavTestLRT(configural, metric2, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 39.79740 37.80712 19.17827
dfd=tests[2:4,"Df diff"]
dfd
## [1] 13 5 10
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-1067+ 1067 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04397400 0.07845497 0.02934281
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.02879291 0.05988172
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.05623577 0.10268384
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.006721022 0.049020983
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 0.999 0.286 0.049 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 0.981 0.917 0.489 0.073
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
## 0.962 0.933 0.041 0.004 0.000 0.000
tests<-lavTestLRT(configural, metric2, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 39.79740 87.40567
dfd=tests[2:3,"Df diff"]
dfd
## [1] 13 6
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-1067+ 1067 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.0439740 0.1128166
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.02879291 0.05988172
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.09255516 0.13431386
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 0.999 0.286 0.049 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 0.996 0.856
tests<-lavTestLRT(configural, metric)
Td=tests[2,"Chisq diff"]
Td
## [1] 74.79517
dfd=tests[2,"Df diff"]
dfd
## [1] 15
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-1067+ 1067 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.06115174
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04775237 0.07527233
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 0.917 0.578 0.013 0.000
bf.age<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
g ~ age
'
bf.ageq<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
g ~ c(a,a)*age
'
bf.age2<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
g ~ age + age2
'
bf.age2q<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
g ~ c(a,a)*age+c(b,b)*age2
'
sem.age<-sem(bf.age, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("g=~ssei", "g=~ssmc", "sspc~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(sem.age, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 773.573 90.000 0.000 0.964 0.084 0.047 0.419 98266.366 98606.311
Mc(sem.age)
## [1] 0.8519416
summary(sem.age, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 112 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 26
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 773.573 517.809
## Degrees of freedom 90 90
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.494
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 438.322 293.401
## 1 335.250 224.408
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.021 0.278 14.488 0.000 3.477 4.565 4.021 0.525
## ssmk (.p2.) 2.470 0.217 11.366 0.000 2.044 2.896 2.470 0.362
## ssmc (.p3.) 0.851 0.130 6.545 0.000 0.596 1.105 0.851 0.159
## electronic =~
## ssgs (.p4.) 1.009 0.075 13.458 0.000 0.862 1.156 1.009 0.189
## ssasi (.p5.) 3.160 0.137 23.073 0.000 2.892 3.428 3.160 0.601
## ssmc (.p6.) 2.119 0.112 18.847 0.000 1.899 2.340 2.119 0.396
## ssei (.p7.) 1.698 0.082 20.661 0.000 1.537 1.859 1.698 0.395
## speed =~
## ssno (.p8.) 0.338 0.027 12.581 0.000 0.286 0.391 0.338 0.347
## sscs (.p9.) 0.708 0.057 12.416 0.000 0.596 0.820 0.708 0.773
## g =~
## ssgs (.10.) 4.674 0.115 40.489 0.000 4.448 4.900 4.706 0.883
## ssar (.11.) 6.316 0.151 41.882 0.000 6.020 6.612 6.359 0.830
## sswk (.12.) 7.803 0.180 43.360 0.000 7.450 8.155 7.856 0.936
## sspc (.13.) 3.087 0.080 38.419 0.000 2.930 3.245 3.108 0.873
## ssno (.14.) 0.676 0.025 27.578 0.000 0.628 0.724 0.680 0.698
## sscs (.15.) 0.593 0.025 23.766 0.000 0.544 0.642 0.597 0.652
## ssasi (.16.) 3.214 0.126 25.555 0.000 2.968 3.461 3.236 0.616
## ssmk (.17.) 5.368 0.136 39.460 0.000 5.101 5.634 5.404 0.793
## ssmc 3.952 0.138 28.674 0.000 3.682 4.223 3.979 0.744
## ssei 3.516 0.103 34.022 0.000 3.313 3.718 3.540 0.823
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.053 0.018 2.990 0.003 0.018 0.088 0.053 0.116
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.39.) 18.595 0.303 61.298 0.000 18.000 19.189 18.595 2.428
## .ssmk (.40.) 14.353 0.248 57.783 0.000 13.867 14.840 14.353 2.106
## .ssmc (.41.) 15.809 0.196 80.466 0.000 15.423 16.194 15.809 2.954
## .ssgs (.42.) 16.493 0.192 86.070 0.000 16.117 16.868 16.493 3.096
## .ssasi (.43.) 16.243 0.199 81.616 0.000 15.853 16.633 16.243 3.091
## .ssei (.44.) 12.426 0.157 79.225 0.000 12.118 12.733 12.426 2.889
## .ssno (.45.) 0.073 0.036 2.063 0.039 0.004 0.143 0.073 0.075
## .sscs (.46.) -0.071 0.034 -2.086 0.037 -0.137 -0.004 -0.071 -0.077
## .sswk (.47.) 25.578 0.293 87.228 0.000 25.003 26.153 25.578 3.046
## .sspc 10.441 0.128 81.479 0.000 10.190 10.692 10.441 2.931
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 2.071 2.361 0.877 0.380 -2.557 6.700 2.071 0.035
## .ssmk 11.135 1.135 9.814 0.000 8.911 13.359 11.135 0.240
## .ssmc 7.582 0.547 13.850 0.000 6.509 8.655 7.582 0.265
## .ssgs 5.212 0.336 15.521 0.000 4.554 5.870 5.212 0.184
## .ssasi 7.164 0.746 9.598 0.000 5.701 8.626 7.164 0.259
## .ssei 3.092 0.235 13.143 0.000 2.631 3.553 3.092 0.167
## .ssno 0.374 0.027 13.840 0.000 0.321 0.427 0.374 0.393
## .sscs -0.020 0.079 -0.247 0.805 -0.175 0.136 -0.020 -0.023
## .sswk 8.779 0.745 11.786 0.000 7.319 10.239 8.779 0.125
## .sspc 3.028 0.195 15.494 0.000 2.645 3.411 3.028 0.239
## electronic 1.000 1.000 1.000 1.000 1.000
## .g 1.000 1.000 1.000 0.987 0.987
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.021 0.278 14.488 0.000 3.477 4.565 4.021 0.572
## ssmk (.p2.) 2.470 0.217 11.366 0.000 2.044 2.896 2.470 0.388
## ssmc (.p3.) 0.851 0.130 6.545 0.000 0.596 1.105 0.851 0.202
## electronic =~
## ssgs (.p4.) 1.009 0.075 13.458 0.000 0.862 1.156 0.427 0.091
## ssasi (.p5.) 3.160 0.137 23.073 0.000 2.892 3.428 1.339 0.337
## ssmc (.p6.) 2.119 0.112 18.847 0.000 1.899 2.340 0.898 0.214
## ssei (.p7.) 1.698 0.082 20.661 0.000 1.537 1.859 0.719 0.211
## speed =~
## ssno (.p8.) 0.338 0.027 12.581 0.000 0.286 0.391 0.338 0.364
## sscs (.p9.) 0.708 0.057 12.416 0.000 0.596 0.820 0.708 0.773
## g =~
## ssgs (.10.) 4.674 0.115 40.489 0.000 4.448 4.900 4.163 0.886
## ssar (.11.) 6.316 0.151 41.882 0.000 6.020 6.612 5.626 0.800
## sswk (.12.) 7.803 0.180 43.360 0.000 7.450 8.155 6.950 0.923
## sspc (.13.) 3.087 0.080 38.419 0.000 2.930 3.245 2.750 0.858
## ssno (.14.) 0.676 0.025 27.578 0.000 0.628 0.724 0.602 0.648
## sscs (.15.) 0.593 0.025 23.766 0.000 0.544 0.642 0.529 0.577
## ssasi (.16.) 3.214 0.126 25.555 0.000 2.968 3.461 2.863 0.721
## ssmk (.17.) 5.368 0.136 39.460 0.000 5.101 5.634 4.781 0.752
## ssmc 3.193 0.139 22.996 0.000 2.921 3.465 2.844 0.677
## ssei 2.919 0.113 25.848 0.000 2.698 3.140 2.600 0.763
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.080 0.015 5.471 0.000 0.051 0.108 0.089 0.193
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.39.) 18.595 0.303 61.298 0.000 18.000 19.189 18.595 2.644
## .ssmk (.40.) 14.353 0.248 57.783 0.000 13.867 14.840 14.353 2.257
## .ssmc (.41.) 15.809 0.196 80.466 0.000 15.423 16.194 15.809 3.762
## .ssgs (.42.) 16.493 0.192 86.070 0.000 16.117 16.868 16.493 3.509
## .ssasi (.43.) 16.243 0.199 81.616 0.000 15.853 16.633 16.243 4.092
## .ssei (.44.) 12.426 0.157 79.225 0.000 12.118 12.733 12.426 3.646
## .ssno (.45.) 0.073 0.036 2.063 0.039 0.004 0.143 0.073 0.079
## .sscs (.46.) -0.071 0.034 -2.086 0.037 -0.137 -0.004 -0.071 -0.077
## .sswk (.47.) 25.578 0.293 87.228 0.000 25.003 26.153 25.578 3.396
## .sspc 11.133 0.135 82.181 0.000 10.867 11.398 11.133 3.473
## math -0.447 0.070 -6.372 0.000 -0.584 -0.309 -0.447 -0.447
## elctrnc -1.737 0.092 -18.959 0.000 -1.916 -1.557 -4.100 -4.100
## speed 0.679 0.082 8.266 0.000 0.518 0.840 0.679 0.679
## .g 0.063 0.050 1.267 0.205 -0.034 0.160 0.071 0.071
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.637 2.300 0.712 0.477 -2.871 6.145 1.637 0.033
## .ssmk 11.471 1.045 10.978 0.000 9.423 13.518 11.471 0.284
## .ssmc 8.035 0.481 16.717 0.000 7.093 8.977 8.035 0.455
## .ssgs 4.576 0.305 15.019 0.000 3.979 5.173 4.576 0.207
## .ssasi 5.768 0.428 13.492 0.000 4.930 6.606 5.768 0.366
## .ssei 4.337 0.273 15.868 0.000 3.801 4.872 4.337 0.373
## .ssno 0.387 0.032 12.109 0.000 0.325 0.450 0.387 0.448
## .sscs 0.059 0.090 0.659 0.510 -0.117 0.235 0.059 0.070
## .sswk 8.433 0.711 11.857 0.000 7.039 9.827 8.433 0.149
## .sspc 2.715 0.169 16.074 0.000 2.384 3.046 2.715 0.264
## electronic 0.179 0.041 4.425 0.000 0.100 0.259 1.000 1.000
## .g 0.764 0.048 15.908 0.000 0.670 0.858 0.963 0.963
sem.ageq<-sem(bf.ageq, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("g=~ssei", "g=~ssmc", "sspc~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(sem.ageq, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 775.430 91.000 0.000 0.964 0.084 0.045 0.419 98266.223 98600.503
Mc(sem.ageq)
## [1] 0.8517703
summary(sem.ageq, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 143 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 27
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 775.430 519.441
## Degrees of freedom 91 91
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.493
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 439.205 294.213
## 1 336.225 225.229
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.020 0.278 14.484 0.000 3.476 4.564 4.020 0.523
## ssmk (.p2.) 2.469 0.217 11.365 0.000 2.043 2.895 2.469 0.361
## ssmc (.p3.) 0.851 0.130 6.546 0.000 0.596 1.106 0.851 0.159
## electronic =~
## ssgs (.p4.) 1.007 0.075 13.446 0.000 0.861 1.154 1.007 0.188
## ssasi (.p5.) 3.157 0.137 23.084 0.000 2.889 3.425 3.157 0.600
## ssmc (.p6.) 2.119 0.112 18.848 0.000 1.899 2.339 2.119 0.395
## ssei (.p7.) 1.698 0.082 20.674 0.000 1.537 1.859 1.698 0.393
## speed =~
## ssno (.p8.) 0.338 0.027 12.581 0.000 0.285 0.391 0.338 0.346
## sscs (.p9.) 0.708 0.057 12.417 0.000 0.596 0.820 0.708 0.772
## g =~
## ssgs (.10.) 4.677 0.116 40.173 0.000 4.448 4.905 4.727 0.884
## ssar (.11.) 6.320 0.152 41.658 0.000 6.023 6.617 6.389 0.831
## sswk (.12.) 7.806 0.181 43.022 0.000 7.451 8.162 7.891 0.936
## sspc (.13.) 3.089 0.081 38.204 0.000 2.931 3.247 3.123 0.873
## ssno (.14.) 0.676 0.025 27.532 0.000 0.628 0.724 0.684 0.699
## sscs (.15.) 0.594 0.025 23.740 0.000 0.545 0.643 0.600 0.654
## ssasi (.16.) 3.218 0.126 25.537 0.000 2.971 3.465 3.253 0.618
## ssmk (.17.) 5.371 0.137 39.328 0.000 5.103 5.638 5.429 0.794
## ssmc 3.955 0.138 28.625 0.000 3.684 4.226 3.998 0.745
## ssei 3.518 0.104 33.947 0.000 3.315 3.721 3.556 0.824
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.068 0.012 5.859 0.000 0.045 0.090 0.067 0.146
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.39.) 18.621 0.300 62.072 0.000 18.033 19.209 18.621 2.423
## .ssmk (.40.) 14.375 0.246 58.371 0.000 13.893 14.858 14.375 2.103
## .ssmc (.41.) 15.825 0.194 81.542 0.000 15.444 16.205 15.825 2.950
## .ssgs (.42.) 16.512 0.189 87.532 0.000 16.142 16.882 16.512 3.089
## .ssasi (.43.) 16.256 0.196 82.730 0.000 15.871 16.641 16.256 3.088
## .ssei (.44.) 12.440 0.154 80.563 0.000 12.137 12.743 12.440 2.883
## .ssno (.45.) 0.076 0.035 2.161 0.031 0.007 0.145 0.076 0.078
## .sscs (.46.) -0.068 0.034 -2.033 0.042 -0.134 -0.002 -0.068 -0.074
## .sswk (.47.) 25.610 0.288 88.829 0.000 25.045 26.175 25.610 3.038
## .sspc 10.453 0.127 82.442 0.000 10.205 10.702 10.453 2.924
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 2.067 2.361 0.875 0.381 -2.561 6.695 2.067 0.035
## .ssmk 11.140 1.134 9.819 0.000 8.916 13.363 11.140 0.238
## .ssmc 7.582 0.548 13.845 0.000 6.508 8.655 7.582 0.263
## .ssgs 5.215 0.336 15.526 0.000 4.557 5.874 5.215 0.182
## .ssasi 7.171 0.746 9.615 0.000 5.709 8.633 7.171 0.259
## .ssei 3.090 0.235 13.146 0.000 2.629 3.550 3.090 0.166
## .ssno 0.374 0.027 13.842 0.000 0.321 0.427 0.374 0.391
## .sscs -0.020 0.079 -0.246 0.806 -0.175 0.136 -0.020 -0.023
## .sswk 8.777 0.744 11.792 0.000 7.318 10.235 8.777 0.124
## .sspc 3.029 0.195 15.499 0.000 2.646 3.412 3.029 0.237
## electronic 1.000 1.000 1.000 1.000 1.000
## .g 1.000 1.000 1.000 0.979 0.979
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.020 0.278 14.484 0.000 3.476 4.564 4.020 0.573
## ssmk (.p2.) 2.469 0.217 11.365 0.000 2.043 2.895 2.469 0.389
## ssmc (.p3.) 0.851 0.130 6.546 0.000 0.596 1.106 0.851 0.203
## electronic =~
## ssgs (.p4.) 1.007 0.075 13.446 0.000 0.861 1.154 0.427 0.091
## ssasi (.p5.) 3.157 0.137 23.084 0.000 2.889 3.425 1.338 0.338
## ssmc (.p6.) 2.119 0.112 18.848 0.000 1.899 2.339 0.898 0.214
## ssei (.p7.) 1.698 0.082 20.674 0.000 1.537 1.859 0.719 0.212
## speed =~
## ssno (.p8.) 0.338 0.027 12.581 0.000 0.285 0.391 0.338 0.365
## sscs (.p9.) 0.708 0.057 12.417 0.000 0.596 0.820 0.708 0.774
## g =~
## ssgs (.10.) 4.677 0.116 40.173 0.000 4.448 4.905 4.143 0.885
## ssar (.11.) 6.320 0.152 41.658 0.000 6.023 6.617 5.599 0.799
## sswk (.12.) 7.806 0.181 43.022 0.000 7.451 8.162 6.916 0.922
## sspc (.13.) 3.089 0.081 38.204 0.000 2.931 3.247 2.737 0.857
## ssno (.14.) 0.676 0.025 27.532 0.000 0.628 0.724 0.599 0.646
## sscs (.15.) 0.594 0.025 23.740 0.000 0.545 0.643 0.526 0.575
## ssasi (.16.) 3.218 0.126 25.537 0.000 2.971 3.465 2.851 0.720
## ssmk (.17.) 5.371 0.137 39.328 0.000 5.103 5.638 4.758 0.750
## ssmc 3.195 0.139 22.950 0.000 2.922 3.468 2.831 0.675
## ssei 2.921 0.114 25.713 0.000 2.699 3.144 2.588 0.761
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.068 0.012 5.859 0.000 0.045 0.090 0.076 0.164
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.39.) 18.621 0.300 62.072 0.000 18.033 19.209 18.621 2.656
## .ssmk (.40.) 14.375 0.246 58.371 0.000 13.893 14.858 14.375 2.267
## .ssmc (.41.) 15.825 0.194 81.542 0.000 15.444 16.205 15.825 3.775
## .ssgs (.42.) 16.512 0.189 87.532 0.000 16.142 16.882 16.512 3.526
## .ssasi (.43.) 16.256 0.196 82.730 0.000 15.871 16.641 16.256 4.105
## .ssei (.44.) 12.440 0.154 80.563 0.000 12.137 12.743 12.440 3.660
## .ssno (.45.) 0.076 0.035 2.161 0.031 0.007 0.145 0.076 0.082
## .sscs (.46.) -0.068 0.034 -2.033 0.042 -0.134 -0.002 -0.068 -0.074
## .sswk (.47.) 25.610 0.288 88.829 0.000 25.045 26.175 25.610 3.414
## .sspc 11.146 0.134 83.361 0.000 10.884 11.408 11.146 3.490
## math -0.447 0.070 -6.372 0.000 -0.584 -0.309 -0.447 -0.447
## elctrnc -1.739 0.092 -18.979 0.000 -1.918 -1.559 -4.103 -4.103
## speed 0.679 0.082 8.267 0.000 0.518 0.840 0.679 0.679
## .g 0.055 0.049 1.127 0.260 -0.041 0.150 0.062 0.062
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.639 2.300 0.713 0.476 -2.869 6.147 1.639 0.033
## .ssmk 11.467 1.045 10.976 0.000 9.419 13.514 11.467 0.285
## .ssmc 8.034 0.481 16.714 0.000 7.092 8.976 8.034 0.457
## .ssgs 4.578 0.305 15.012 0.000 3.980 5.175 4.578 0.209
## .ssasi 5.769 0.427 13.495 0.000 4.931 6.606 5.769 0.368
## .ssei 4.338 0.273 15.873 0.000 3.802 4.873 4.338 0.375
## .ssno 0.387 0.032 12.112 0.000 0.324 0.450 0.387 0.450
## .sscs 0.059 0.090 0.661 0.509 -0.117 0.235 0.059 0.071
## .sswk 8.452 0.711 11.892 0.000 7.059 9.845 8.452 0.150
## .sspc 2.713 0.169 16.076 0.000 2.382 3.043 2.713 0.266
## electronic 0.180 0.041 4.425 0.000 0.100 0.259 1.000 1.000
## .g 0.764 0.048 15.866 0.000 0.669 0.858 0.973 0.973
sem.age2<-sem(bf.age2, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("g=~ssei", "g=~ssmc", "sspc~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(sem.age2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 822.052 108.000 0.000 0.963 0.079 0.044 0.443 98268.197 98619.473
Mc(sem.age2)
## [1] 0.8458764
summary(sem.age2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 103 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 88
## Number of equality constraints 26
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 822.052 547.072
## Degrees of freedom 108 108
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.503
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 466.174 310.237
## 1 355.878 236.835
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.018 0.276 14.552 0.000 3.477 4.560 4.018 0.524
## ssmk (.p2.) 2.472 0.217 11.410 0.000 2.048 2.897 2.472 0.363
## ssmc (.p3.) 0.854 0.130 6.577 0.000 0.599 1.108 0.854 0.159
## electronic =~
## ssgs (.p4.) 1.006 0.075 13.448 0.000 0.860 1.153 1.006 0.189
## ssasi (.p5.) 3.149 0.138 22.899 0.000 2.879 3.418 3.149 0.599
## ssmc (.p6.) 2.126 0.113 18.893 0.000 1.905 2.347 2.126 0.397
## ssei (.p7.) 1.704 0.082 20.809 0.000 1.543 1.864 1.704 0.396
## speed =~
## ssno (.p8.) 0.338 0.027 12.580 0.000 0.286 0.391 0.338 0.347
## sscs (.p9.) 0.708 0.057 12.414 0.000 0.596 0.820 0.708 0.773
## g =~
## ssgs (.10.) 4.671 0.115 40.633 0.000 4.445 4.896 4.707 0.883
## ssar (.11.) 6.311 0.150 42.128 0.000 6.017 6.604 6.360 0.830
## sswk (.12.) 7.797 0.178 43.698 0.000 7.447 8.147 7.858 0.936
## sspc (.13.) 3.085 0.080 38.794 0.000 2.929 3.241 3.109 0.873
## ssno (.14.) 0.675 0.024 27.667 0.000 0.628 0.723 0.681 0.698
## sscs (.15.) 0.593 0.025 23.806 0.000 0.544 0.642 0.598 0.652
## ssasi (.16.) 3.213 0.125 25.624 0.000 2.967 3.459 3.238 0.616
## ssmk (.17.) 5.363 0.135 39.594 0.000 5.098 5.629 5.405 0.793
## ssmc 3.953 0.137 28.828 0.000 3.684 4.221 3.983 0.744
## ssei 3.513 0.102 34.348 0.000 3.312 3.713 3.540 0.823
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.049 0.019 2.606 0.009 0.012 0.086 0.049 0.107
## age2 -0.009 0.008 -1.165 0.244 -0.025 0.006 -0.009 -0.046
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.42.) 18.873 0.369 51.185 0.000 18.150 19.595 18.873 2.463
## .ssmk (.43.) 14.590 0.308 47.373 0.000 13.987 15.194 14.590 2.141
## .ssmc (.44.) 15.980 0.234 68.264 0.000 15.522 16.439 15.980 2.984
## .ssgs (.45.) 16.700 0.245 68.266 0.000 16.221 17.180 16.700 3.135
## .ssasi (.46.) 16.387 0.224 73.027 0.000 15.947 16.827 16.387 3.119
## .ssei (.47.) 12.579 0.191 65.870 0.000 12.205 12.953 12.579 2.923
## .ssno (.48.) 0.103 0.041 2.537 0.011 0.023 0.183 0.103 0.106
## .sscs (.49.) -0.044 0.037 -1.195 0.232 -0.117 0.028 -0.044 -0.049
## .sswk (.50.) 25.921 0.383 67.764 0.000 25.171 26.671 25.921 3.087
## .sspc 10.577 0.160 66.111 0.000 10.263 10.890 10.577 2.969
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 2.098 2.348 0.894 0.372 -2.504 6.699 2.098 0.036
## .ssmk 11.126 1.132 9.828 0.000 8.907 13.344 11.126 0.239
## .ssmc 7.569 0.548 13.805 0.000 6.494 8.643 7.569 0.264
## .ssgs 5.216 0.336 15.507 0.000 4.557 5.875 5.216 0.184
## .ssasi 7.206 0.748 9.628 0.000 5.739 8.673 7.206 0.261
## .ssei 3.081 0.235 13.128 0.000 2.621 3.541 3.081 0.166
## .ssno 0.374 0.027 13.842 0.000 0.321 0.427 0.374 0.393
## .sscs -0.020 0.079 -0.248 0.804 -0.175 0.136 -0.020 -0.023
## .sswk 8.770 0.743 11.805 0.000 7.314 10.227 8.770 0.124
## .sspc 3.027 0.196 15.475 0.000 2.644 3.411 3.027 0.238
## electronic 1.000 1.000 1.000 1.000 1.000
## .g 1.000 1.000 1.000 0.985 0.985
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.018 0.276 14.552 0.000 3.477 4.560 4.018 0.571
## ssmk (.p2.) 2.472 0.217 11.410 0.000 2.048 2.897 2.472 0.389
## ssmc (.p3.) 0.854 0.130 6.577 0.000 0.599 1.108 0.854 0.203
## electronic =~
## ssgs (.p4.) 1.006 0.075 13.448 0.000 0.860 1.153 0.427 0.091
## ssasi (.p5.) 3.149 0.138 22.899 0.000 2.879 3.418 1.334 0.336
## ssmc (.p6.) 2.126 0.113 18.893 0.000 1.905 2.347 0.901 0.215
## ssei (.p7.) 1.704 0.082 20.809 0.000 1.543 1.864 0.722 0.212
## speed =~
## ssno (.p8.) 0.338 0.027 12.580 0.000 0.286 0.391 0.338 0.364
## sscs (.p9.) 0.708 0.057 12.414 0.000 0.596 0.820 0.708 0.773
## g =~
## ssgs (.10.) 4.671 0.115 40.633 0.000 4.445 4.896 4.163 0.886
## ssar (.11.) 6.311 0.150 42.128 0.000 6.017 6.604 5.625 0.800
## sswk (.12.) 7.797 0.178 43.698 0.000 7.447 8.147 6.950 0.923
## sspc (.13.) 3.085 0.080 38.794 0.000 2.929 3.241 2.750 0.858
## ssno (.14.) 0.675 0.024 27.667 0.000 0.628 0.723 0.602 0.648
## sscs (.15.) 0.593 0.025 23.806 0.000 0.544 0.642 0.528 0.577
## ssasi (.16.) 3.213 0.125 25.624 0.000 2.967 3.459 2.864 0.721
## ssmk (.17.) 5.363 0.135 39.594 0.000 5.098 5.629 4.780 0.752
## ssmc 3.185 0.138 23.111 0.000 2.915 3.455 2.839 0.676
## ssei 2.918 0.113 25.932 0.000 2.697 3.139 2.601 0.763
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.079 0.015 5.323 0.000 0.050 0.108 0.089 0.191
## age2 -0.001 0.007 -0.193 0.847 -0.014 0.012 -0.001 -0.007
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.42.) 18.873 0.369 51.185 0.000 18.150 19.595 18.873 2.684
## .ssmk (.43.) 14.590 0.308 47.373 0.000 13.987 15.194 14.590 2.295
## .ssmc (.44.) 15.980 0.234 68.264 0.000 15.522 16.439 15.980 3.806
## .ssgs (.45.) 16.700 0.245 68.266 0.000 16.221 17.180 16.700 3.553
## .ssasi (.46.) 16.387 0.224 73.027 0.000 15.947 16.827 16.387 4.128
## .ssei (.47.) 12.579 0.191 65.870 0.000 12.205 12.953 12.579 3.690
## .ssno (.48.) 0.103 0.041 2.537 0.011 0.023 0.183 0.103 0.111
## .sscs (.49.) -0.044 0.037 -1.195 0.232 -0.117 0.028 -0.044 -0.049
## .sswk (.50.) 25.921 0.383 67.764 0.000 25.171 26.671 25.921 3.441
## .sspc 11.269 0.167 67.624 0.000 10.942 11.595 11.269 3.515
## math -0.447 0.070 -6.367 0.000 -0.585 -0.310 -0.447 -0.447
## elctrnc -1.744 0.092 -18.885 0.000 -1.925 -1.563 -4.116 -4.116
## speed 0.679 0.082 8.266 0.000 0.518 0.840 0.679 0.679
## .g 0.025 0.066 0.374 0.708 -0.105 0.154 0.028 0.028
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.663 2.286 0.727 0.467 -2.818 6.143 1.663 0.034
## .ssmk 11.461 1.043 10.991 0.000 9.417 13.505 11.461 0.284
## .ssmc 8.028 0.481 16.701 0.000 7.086 8.970 8.028 0.455
## .ssgs 4.576 0.305 15.015 0.000 3.979 5.174 4.576 0.207
## .ssasi 5.778 0.427 13.522 0.000 4.941 6.616 5.778 0.367
## .ssei 4.334 0.273 15.849 0.000 3.798 4.870 4.334 0.373
## .ssno 0.387 0.032 12.110 0.000 0.325 0.450 0.387 0.448
## .sscs 0.059 0.090 0.657 0.511 -0.117 0.235 0.059 0.070
## .sswk 8.432 0.711 11.855 0.000 7.038 9.826 8.432 0.149
## .sspc 2.714 0.169 16.070 0.000 2.383 3.045 2.714 0.264
## electronic 0.180 0.041 4.426 0.000 0.100 0.259 1.000 1.000
## .g 0.765 0.048 15.965 0.000 0.671 0.859 0.963 0.963
sem.age2q<-sem(bf.age2q, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("g=~ssei", "g=~ssmc", "sspc~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(sem.age2q, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 824.683 110.000 0.000 0.963 0.078 0.043 0.443 98266.828 98606.773
Mc(sem.age2q)
## [1] 0.8457513
summary(sem.age2q, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 155 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 88
## Number of equality constraints 28
##
## Number of observations per group:
## 0 1067
## 1 1067
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 824.683 549.699
## Degrees of freedom 110 110
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.500
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 0 467.376 311.533
## 1 357.306 238.165
##
## 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 ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.019 0.277 14.515 0.000 3.477 4.562 4.019 0.523
## ssmk (.p2.) 2.471 0.217 11.385 0.000 2.045 2.896 2.471 0.362
## ssmc (.p3.) 0.852 0.130 6.557 0.000 0.597 1.107 0.852 0.159
## electronic =~
## ssgs (.p4.) 1.006 0.075 13.442 0.000 0.860 1.153 1.006 0.188
## ssasi (.p5.) 3.151 0.137 22.984 0.000 2.882 3.419 3.151 0.599
## ssmc (.p6.) 2.122 0.112 18.882 0.000 1.902 2.343 2.122 0.396
## ssei (.p7.) 1.701 0.082 20.743 0.000 1.540 1.861 1.701 0.394
## speed =~
## ssno (.p8.) 0.338 0.027 12.579 0.000 0.285 0.391 0.338 0.346
## sscs (.p9.) 0.708 0.057 12.415 0.000 0.596 0.820 0.708 0.772
## g =~
## ssgs (.10.) 4.673 0.116 40.316 0.000 4.446 4.900 4.725 0.884
## ssar (.11.) 6.315 0.151 41.876 0.000 6.020 6.611 6.385 0.831
## sswk (.12.) 7.801 0.180 43.322 0.000 7.448 8.154 7.887 0.936
## sspc (.13.) 3.087 0.080 38.530 0.000 2.930 3.244 3.121 0.873
## ssno (.14.) 0.676 0.024 27.603 0.000 0.628 0.724 0.683 0.699
## sscs (.15.) 0.593 0.025 23.782 0.000 0.544 0.642 0.600 0.654
## ssasi (.16.) 3.216 0.126 25.615 0.000 2.970 3.462 3.252 0.618
## ssmk (.17.) 5.367 0.136 39.443 0.000 5.100 5.633 5.426 0.794
## ssmc 3.954 0.138 28.745 0.000 3.685 4.224 3.998 0.745
## ssei 3.516 0.103 34.188 0.000 3.314 3.717 3.554 0.824
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.065 0.012 5.352 0.000 0.041 0.089 0.064 0.141
## age2 (b) -0.005 0.005 -0.988 0.323 -0.015 0.005 -0.005 -0.025
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.42.) 18.772 0.328 57.189 0.000 18.128 19.415 18.772 2.444
## .ssmk (.43.) 14.504 0.272 53.260 0.000 13.970 15.038 14.504 2.123
## .ssmc (.44.) 15.918 0.211 75.490 0.000 15.505 16.331 15.918 2.967
## .ssgs (.45.) 16.624 0.213 78.232 0.000 16.208 17.041 16.624 3.111
## .ssasi (.46.) 16.334 0.208 78.532 0.000 15.927 16.742 16.334 3.104
## .ssei (.47.) 12.523 0.170 73.871 0.000 12.191 12.855 12.523 2.903
## .ssno (.48.) 0.092 0.037 2.468 0.014 0.019 0.166 0.092 0.094
## .sscs (.49.) -0.054 0.035 -1.545 0.122 -0.122 0.014 -0.054 -0.059
## .sswk (.50.) 25.796 0.329 78.367 0.000 25.151 26.441 25.796 3.062
## .sspc 10.527 0.141 74.732 0.000 10.251 10.803 10.527 2.946
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 2.080 2.355 0.883 0.377 -2.535 6.695 2.080 0.035
## .ssmk 11.135 1.133 9.825 0.000 8.914 13.356 11.135 0.239
## .ssmc 7.574 0.548 13.821 0.000 6.500 8.648 7.574 0.263
## .ssgs 5.217 0.336 15.519 0.000 4.558 5.876 5.217 0.183
## .ssasi 7.194 0.747 9.632 0.000 5.730 8.658 7.194 0.260
## .ssei 3.084 0.235 13.133 0.000 2.624 3.544 3.084 0.166
## .ssno 0.374 0.027 13.843 0.000 0.321 0.427 0.374 0.391
## .sscs -0.020 0.079 -0.247 0.805 -0.175 0.136 -0.020 -0.023
## .sswk 8.772 0.743 11.801 0.000 7.315 10.229 8.772 0.124
## .sspc 3.028 0.196 15.488 0.000 2.645 3.412 3.028 0.237
## electronic 1.000 1.000 1.000 1.000 1.000
## .g 1.000 1.000 1.000 0.978 0.978
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.019 0.277 14.515 0.000 3.477 4.562 4.019 0.573
## ssmk (.p2.) 2.471 0.217 11.385 0.000 2.045 2.896 2.471 0.390
## ssmc (.p3.) 0.852 0.130 6.557 0.000 0.597 1.107 0.852 0.203
## electronic =~
## ssgs (.p4.) 1.006 0.075 13.442 0.000 0.860 1.153 0.426 0.091
## ssasi (.p5.) 3.151 0.137 22.984 0.000 2.882 3.419 1.335 0.337
## ssmc (.p6.) 2.122 0.112 18.882 0.000 1.902 2.343 0.899 0.215
## ssei (.p7.) 1.701 0.082 20.743 0.000 1.540 1.861 0.721 0.212
## speed =~
## ssno (.p8.) 0.338 0.027 12.579 0.000 0.285 0.391 0.338 0.364
## sscs (.p9.) 0.708 0.057 12.415 0.000 0.596 0.820 0.708 0.774
## g =~
## ssgs (.10.) 4.673 0.116 40.316 0.000 4.446 4.900 4.146 0.885
## ssar (.11.) 6.315 0.151 41.876 0.000 6.020 6.611 5.603 0.799
## sswk (.12.) 7.801 0.180 43.322 0.000 7.448 8.154 6.921 0.922
## sspc (.13.) 3.087 0.080 38.530 0.000 2.930 3.244 2.739 0.857
## ssno (.14.) 0.676 0.024 27.603 0.000 0.628 0.724 0.600 0.646
## sscs (.15.) 0.593 0.025 23.782 0.000 0.544 0.642 0.526 0.575
## ssasi (.16.) 3.216 0.126 25.615 0.000 2.970 3.462 2.853 0.720
## ssmk (.17.) 5.367 0.136 39.443 0.000 5.100 5.633 4.761 0.751
## ssmc 3.190 0.138 23.051 0.000 2.919 3.461 2.830 0.675
## ssei 2.920 0.113 25.794 0.000 2.698 3.142 2.590 0.762
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.065 0.012 5.352 0.000 0.041 0.089 0.073 0.158
## age2 (b) -0.005 0.005 -0.988 0.323 -0.015 0.005 -0.006 -0.029
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.42.) 18.772 0.328 57.189 0.000 18.128 19.415 18.772 2.676
## .ssmk (.43.) 14.504 0.272 53.260 0.000 13.970 15.038 14.504 2.287
## .ssmc (.44.) 15.918 0.211 75.490 0.000 15.505 16.331 15.918 3.797
## .ssgs (.45.) 16.624 0.213 78.232 0.000 16.208 17.041 16.624 3.548
## .ssasi (.46.) 16.334 0.208 78.532 0.000 15.927 16.742 16.334 4.123
## .ssei (.47.) 12.523 0.170 73.871 0.000 12.191 12.855 12.523 3.682
## .ssno (.48.) 0.092 0.037 2.468 0.014 0.019 0.166 0.092 0.100
## .sscs (.49.) -0.054 0.035 -1.545 0.122 -0.122 0.014 -0.054 -0.059
## .sswk (.50.) 25.796 0.329 78.367 0.000 25.151 26.441 25.796 3.437
## .sspc 11.219 0.149 75.201 0.000 10.927 11.512 11.219 3.511
## math -0.447 0.070 -6.370 0.000 -0.585 -0.310 -0.447 -0.447
## elctrnc -1.743 0.092 -18.954 0.000 -1.923 -1.563 -4.114 -4.114
## speed 0.679 0.082 8.266 0.000 0.518 0.840 0.679 0.679
## .g 0.054 0.049 1.119 0.263 -0.041 0.150 0.061 0.061
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.650 2.293 0.720 0.472 -2.845 6.145 1.650 0.034
## .ssmk 11.464 1.044 10.980 0.000 9.417 13.510 11.464 0.285
## .ssmc 8.031 0.481 16.696 0.000 7.088 8.973 8.031 0.457
## .ssgs 4.579 0.305 15.009 0.000 3.981 5.177 4.579 0.209
## .ssasi 5.774 0.427 13.524 0.000 4.937 6.610 5.774 0.368
## .ssei 4.337 0.273 15.868 0.000 3.801 4.873 4.337 0.375
## .ssno 0.387 0.032 12.116 0.000 0.324 0.450 0.387 0.450
## .sscs 0.059 0.090 0.659 0.510 -0.117 0.235 0.059 0.071
## .sswk 8.451 0.711 11.889 0.000 7.058 9.844 8.451 0.150
## .sspc 2.712 0.169 16.068 0.000 2.381 3.043 2.712 0.266
## electronic 0.179 0.041 4.424 0.000 0.100 0.259 1.000 1.000
## .g 0.765 0.048 15.926 0.000 0.671 0.859 0.972 0.972
# MGCFA USING FULL DATA NOT JUST SIBLING
# WHITE RESPONDENTS
dw<- filter(dk, bhw==3)
nrow(dw)
## [1] 6161
dgroup<- dplyr::select(dw, id, starts_with("ss"), afqt, efa, educ2000, age, sex, agesex, age2, agesex2, age14:age22, sweight, weight2000, cweight, asvabweight)
fit<-lm(efa ~ sex + rcs(age, 3) + sex*rcs(age, 3), data=dgroup)
summary(fit)
##
## Call:
## lm(formula = efa ~ sex + rcs(age, 3) + sex * rcs(age, 3), data = dgroup)
##
## Residuals:
## Min 1Q Median 3Q Max
## -48.604 -7.950 1.668 9.515 28.890
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 109.0842 0.5802 188.024 < 2e-16 ***
## sex -3.8929 0.8215 -4.739 2.20e-06 ***
## rcs(age, 3)age 2.0341 0.2473 8.224 2.38e-16 ***
## rcs(age, 3)age' -0.3847 0.3183 -1.209 0.227
## sex:rcs(age, 3)age -0.5654 0.3556 -1.590 0.112
## sex:rcs(age, 3)age' 0.1191 0.4573 0.260 0.795
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.75 on 6155 degrees of freedom
## Multiple R-squared: 0.09098, Adjusted R-squared: 0.09024
## F-statistic: 123.2 on 5 and 6155 DF, p-value: < 2.2e-16
dgroup$pred1<-fitted(fit)
original_age_min <- 14
original_age_max <- 22
mean_centered_min <- min(dgroup$age)
mean_centered_max <- max(dgroup$age)
original_age_mean <- (original_age_min + original_age_max) / 2
mean_centered_age_mean <- (mean_centered_min + mean_centered_max) / 2
age_difference <- original_age_mean - mean_centered_age_mean
xyplot(dgroup$pred1 ~ dgroup$age, data=dgroup, groups=sex, pch=19, type=c("p"), col=c('red', 'blue'), grid=TRUE, ylab="Predicted IQ", xlab="age", key=list(text=list(c("White Male", "White Female")), points=list(pch=c(19,19), col=c("red", "blue")), columns=2))
xyplot(dgroup$pred1 ~ dgroup$age, data=dgroup, groups=sex, pch=19, type=c("p"), col=c('red', 'blue'), grid=TRUE, ylab="Predicted IQ", xlab="Age", key=list(text=list(c("White Male", "White Female")), points=list(pch=c(19,19), col=c("red", "blue")), columns=2), scales=list(x=list(at=seq(mean_centered_min, mean_centered_max), labels=seq(original_age_min, original_age_max))))
describeBy(dgroup$pred1, dgroup$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 3094 108.39 4.18 108.8 108.56 5.62 100.95 114.91 13.97 -0.27 -1.15 0.08
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 3067 104.8 2.93 104.99 104.94 3.46 99.32 109.47 10.16 -0.33 -1.06 0.05
describeBy(dgroup$efa, dgroup$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 3094 108.39 14.33 110.82 109.58 14.33 66.31 133.69 67.38 -0.66 -0.28 0.26
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 3067 104.8 12.07 106 105.43 12.75 62.97 130.66 67.68 -0.43 -0.35 0.22
describeBy(dgroup$afqt, dgroup$sex)
##
## Descriptive statistics by group
## INDICES: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## V1 1 3094 105.7 14.84 106.36 106 18.91 77.91 130.02 52.11 -0.13 -1.16 0.27
## --------------------------------------------------------------------------
## INDICES: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## V1 1 3067 105.87 13.85 106.24 106.13 16.81 78.04 130.02 51.98 -0.12 -1.03 0.25
describeBy(dgroup$educ2000, dgroup$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1696 13.57 2.59 12 13.42 1.48 7 20 13 0.49 -0.1 0.06
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1744 13.76 2.44 13 13.57 1.48 6 20 14 0.45 -0.22 0.06
cor(dgroup$efa, dgroup$afqt, use="pairwise.complete.obs", method="pearson")
## [,1]
## [1,] 0.9063014
# Lynn's developmental theory of sex difference is supported here
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(age, sex) %>% summarise(MEAN = survey_mean(pred1), SD = survey_sd(pred1))
## # A tibble: 18 Ă— 5
## # Groups: age [9]
## age sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -4 0 101. 6.63e-16 8.56e-15
## 2 -4 1 99.3 0 0
## 3 -3 0 103. 1.19e-16 2.32e-15
## 4 -3 1 101. 0 0
## 5 -2 0 105. 6.37e-17 1.13e-15
## 6 -2 1 102. 1.38e-14 2.13e-13
## 7 -1 0 107. 0 0
## 8 -1 1 104. 4.89e-16 8.66e-15
## 9 0 0 109. 9.89e-15 1.45e-13
## 10 0 1 105. 0 0
## 11 1 0 110. 3.75e-15 5.12e-14
## 12 1 1 106. 1.75e-16 2.92e-15
## 13 2 0 112. 1.86e-16 3.07e-15
## 14 2 1 107. 1.30e-13 1.72e-12
## 15 3 0 113. 1.62e-16 2.50e-15
## 16 3 1 108. 6.67e-16 1.08e-14
## 17 4 0 115. 0 0
## 18 4 1 109. 8.82e-16 6.58e-15
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(age, sex) %>% summarise(MEAN = survey_mean(efa), SD = survey_sd(efa))
## # A tibble: 18 Ă— 5
## # Groups: age [9]
## age sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -4 0 102. 0.919 13.6
## 2 -4 1 103. 0.833 11.2
## 3 -3 0 106. 0.766 13.7
## 4 -3 1 103. 0.698 11.7
## 5 -2 0 108. 0.764 13.5
## 6 -2 1 103. 0.675 11.4
## 7 -1 0 110. 0.759 12.9
## 8 -1 1 106. 0.663 11.5
## 9 0 0 111. 0.753 12.8
## 10 0 1 106. 0.652 10.9
## 11 1 0 111. 0.790 13.4
## 12 1 1 106. 0.728 12.3
## 13 2 0 114. 0.726 11.7
## 14 2 1 107. 0.747 11.7
## 15 3 0 114. 0.783 12.5
## 16 3 1 108. 0.691 11.5
## 17 4 0 112. 1.58 13.1
## 18 4 1 110. 1.29 8.99
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(age, sex) %>% summarise(MEAN = survey_mean(afqt), SD = survey_sd(afqt))
## # A tibble: 18 Ă— 5
## # Groups: age [9]
## age sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -4 0 106. 1.03 15.1
## 2 -4 1 110. 1.02 13.6
## 3 -3 0 107. 0.863 15.2
## 4 -3 1 108. 0.828 13.9
## 5 -2 0 108. 0.836 14.7
## 6 -2 1 107. 0.809 13.7
## 7 -1 0 108. 0.883 14.6
## 8 -1 1 107. 0.790 13.9
## 9 0 0 107. 0.861 14.3
## 10 0 1 108. 0.806 13.4
## 11 1 0 107. 0.880 14.5
## 12 1 1 107. 0.845 14.3
## 13 2 0 108. 0.861 13.8
## 14 2 1 105. 0.905 14.1
## 15 3 0 108. 0.911 14.3
## 16 3 1 107. 0.852 13.9
## 17 4 0 107. 1.85 15.3
## 18 4 1 108. 1.69 11.9
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(sex) %>% summarise(MEAN = survey_mean(pred1), SD = survey_sd(pred1))
## # A tibble: 2 Ă— 4
## sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl>
## 1 0 108. 0.0909 4.19
## 2 1 104. 0.0665 2.99
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(sex) %>% summarise(MEAN = survey_mean(efa), SD = survey_sd(efa))
## # A tibble: 2 Ă— 4
## sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl>
## 1 0 110. 0.282 13.5
## 2 1 106. 0.250 11.7
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(sex) %>% summarise(MEAN = survey_mean(afqt), SD = survey_sd(afqt))
## # A tibble: 2 Ă— 4
## sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl>
## 1 0 107. 0.310 14.6
## 2 1 107. 0.298 13.8
dgroup %>% as_survey_design(ids = id, weights = weight2000) %>% group_by(sex) %>% summarise(MEAN = survey_mean(educ2000, na.rm = TRUE), SD = survey_sd(educ2000, na.rm = TRUE))
## # A tibble: 2 Ă— 4
## sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl>
## 1 0 13.6 0.0648 2.60
## 2 1 13.8 0.0606 2.46
# CORRELATED FACTOR MODEL
cf.model<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
'
cf.lv<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
verbal~~1*verbal
math~~1*math
speed~~1*speed
'
cf.reduced<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
verbal~~1*verbal
math~~1*math
speed~~1*speed
math~0*1
'
baseline<-cfa(cf.model, data=dgroup, meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1805.040 27.000 0.000 0.961 0.103 0.040 286861.627 287117.215
Mc(baseline)
## [1] 0.8656095
configural<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1103.587 54.000 0.000 0.976 0.079 0.024 281137.771 281648.947
Mc(configural)
## [1] 0.9183343
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 47 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 76
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1103.587 743.522
## Degrees of freedom 54 54
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.484
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 339.719 228.880
## 0 763.868 514.642
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs 1.686 0.198 8.507 0.000 1.298 2.075 1.686 0.405
## sswk 5.855 0.127 46.151 0.000 5.607 6.104 5.855 0.915
## sspc 2.239 0.064 35.077 0.000 2.113 2.364 2.239 0.810
## math =~
## ssar 6.281 0.087 72.055 0.000 6.111 6.452 6.281 0.931
## ssmk 5.194 0.079 65.998 0.000 5.040 5.349 5.194 0.866
## ssmc 1.577 0.125 12.575 0.000 1.331 1.823 1.577 0.380
## electronic =~
## ssgs 1.963 0.203 9.657 0.000 1.564 2.361 1.963 0.472
## ssasi 2.309 0.071 32.473 0.000 2.170 2.448 2.309 0.669
## ssmc 1.628 0.131 12.425 0.000 1.371 1.885 1.628 0.392
## ssei 2.672 0.061 43.961 0.000 2.553 2.792 2.672 0.801
## speed =~
## ssno 0.739 0.016 45.380 0.000 0.707 0.771 0.739 0.890
## sscs 0.608 0.020 31.136 0.000 0.570 0.647 0.608 0.716
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.798 0.010 80.678 0.000 0.779 0.817 0.798 0.798
## electronic 0.841 0.013 64.234 0.000 0.815 0.866 0.841 0.841
## speed 0.636 0.021 30.429 0.000 0.595 0.677 0.636 0.636
## math ~~
## electronic 0.757 0.017 45.420 0.000 0.724 0.790 0.757 0.757
## speed 0.690 0.015 45.932 0.000 0.660 0.719 0.690 0.690
## electronic ~~
## speed 0.490 0.024 20.321 0.000 0.443 0.537 0.490 0.490
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 15.782 0.090 175.509 0.000 15.606 15.959 15.782 3.793
## .sswk 27.503 0.136 202.254 0.000 27.237 27.770 27.503 4.296
## .sspc 11.863 0.059 201.639 0.000 11.748 11.978 11.863 4.290
## .ssar 18.133 0.146 124.361 0.000 17.847 18.418 18.133 2.688
## .ssmk 14.248 0.130 109.820 0.000 13.994 14.503 14.248 2.375
## .ssmc 12.747 0.090 141.504 0.000 12.570 12.923 12.747 3.072
## .ssasi 11.812 0.074 158.855 0.000 11.666 11.957 11.812 3.421
## .ssei 10.402 0.072 144.049 0.000 10.261 10.544 10.402 3.117
## .ssno 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.571
## .sscs 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.653
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.056 0.220 22.997 0.000 4.625 5.487 5.056 0.292
## .sswk 6.704 0.510 13.139 0.000 5.704 7.704 6.704 0.164
## .sspc 2.635 0.118 22.409 0.000 2.405 2.866 2.635 0.345
## .ssar 6.039 0.504 11.978 0.000 5.050 7.027 6.039 0.133
## .ssmk 9.000 0.398 22.598 0.000 8.219 9.780 9.000 0.250
## .ssmc 8.189 0.282 29.035 0.000 7.636 8.741 8.189 0.476
## .ssasi 6.592 0.246 26.819 0.000 6.110 7.074 6.592 0.553
## .ssei 3.996 0.203 19.717 0.000 3.599 4.393 3.996 0.359
## .ssno 0.143 0.016 8.716 0.000 0.111 0.175 0.143 0.208
## .sscs 0.351 0.019 18.259 0.000 0.314 0.389 0.351 0.487
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs 2.871 0.143 20.047 0.000 2.590 3.152 2.871 0.622
## sswk 6.272 0.128 48.901 0.000 6.020 6.523 6.272 0.914
## sspc 2.727 0.059 46.467 0.000 2.612 2.842 2.727 0.845
## math =~
## ssar 6.582 0.089 74.027 0.000 6.408 6.756 6.582 0.929
## ssmk 5.721 0.078 73.378 0.000 5.568 5.874 5.721 0.883
## ssmc 0.967 0.116 8.325 0.000 0.739 1.195 0.967 0.196
## electronic =~
## ssgs 1.330 0.144 9.265 0.000 1.048 1.611 1.330 0.288
## ssasi 3.667 0.093 39.268 0.000 3.484 3.850 3.667 0.765
## ssmc 3.292 0.123 26.751 0.000 3.051 3.533 3.292 0.669
## ssei 3.494 0.060 58.108 0.000 3.376 3.612 3.494 0.910
## speed =~
## ssno 0.781 0.016 50.402 0.000 0.751 0.812 0.781 0.874
## sscs 0.697 0.017 40.971 0.000 0.664 0.730 0.697 0.786
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.843 0.009 91.927 0.000 0.825 0.861 0.843 0.843
## electronic 0.815 0.012 66.697 0.000 0.791 0.838 0.815 0.815
## speed 0.730 0.015 48.596 0.000 0.700 0.759 0.730 0.730
## math ~~
## electronic 0.699 0.015 47.386 0.000 0.670 0.728 0.699 0.699
## speed 0.798 0.012 66.516 0.000 0.775 0.822 0.798 0.798
## electronic ~~
## speed 0.539 0.022 24.977 0.000 0.496 0.581 0.539 0.539
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 17.613 0.097 181.519 0.000 17.422 17.803 17.613 3.815
## .sswk 27.329 0.142 191.949 0.000 27.050 27.608 27.329 3.984
## .sspc 11.086 0.068 163.704 0.000 10.953 11.219 11.086 3.434
## .ssar 20.009 0.151 132.770 0.000 19.714 20.305 20.009 2.823
## .ssmk 14.749 0.139 105.881 0.000 14.476 15.022 14.749 2.275
## .ssmc 16.924 0.104 162.135 0.000 16.719 17.128 16.924 3.438
## .ssasi 17.810 0.102 175.227 0.000 17.610 18.009 17.810 3.713
## .ssei 13.561 0.080 169.041 0.000 13.404 13.718 13.561 3.533
## .ssno 0.253 0.019 13.436 0.000 0.216 0.290 0.253 0.283
## .sscs 0.112 0.019 5.896 0.000 0.075 0.149 0.112 0.126
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.088 0.195 26.153 0.000 4.707 5.470 5.088 0.239
## .sswk 7.718 0.531 14.546 0.000 6.678 8.758 7.718 0.164
## .sspc 2.988 0.131 22.825 0.000 2.732 3.245 2.988 0.287
## .ssar 6.926 0.480 14.421 0.000 5.985 7.867 6.926 0.138
## .ssmk 9.289 0.419 22.146 0.000 8.467 10.111 9.289 0.221
## .ssmc 8.003 0.325 24.608 0.000 7.365 8.640 8.003 0.330
## .ssasi 9.562 0.392 24.413 0.000 8.795 10.330 9.562 0.416
## .ssei 2.524 0.184 13.684 0.000 2.162 2.885 2.524 0.171
## .ssno 0.188 0.014 13.286 0.000 0.160 0.216 0.188 0.235
## .sscs 0.300 0.018 16.692 0.000 0.265 0.335 0.300 0.382
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
modificationIndices(configural, sort=T, maximum.number=30)
## lhs op rhs block group level mi epc sepc.lv sepc.all sepc.nox
## 229 ssmc ~~ ssasi 2 2 1 236.768 3.212 3.212 0.367 0.367
## 170 verbal =~ ssei 2 2 1 233.692 2.310 2.310 0.602 0.602
## 225 ssmk ~~ ssasi 2 2 1 195.106 -2.939 -2.939 -0.312 -0.312
## 174 math =~ sswk 2 2 1 138.857 -2.468 -2.468 -0.360 -0.360
## 176 math =~ ssasi 2 2 1 134.552 -1.288 -1.288 -0.269 -0.269
## 230 ssmc ~~ ssei 2 2 1 105.535 -1.939 -1.939 -0.431 -0.431
## 169 verbal =~ ssasi 2 2 1 100.876 -1.606 -1.606 -0.335 -0.335
## 177 math =~ ssei 2 2 1 88.256 0.966 0.966 0.252 0.252
## 197 ssgs ~~ ssmk 2 2 1 87.436 1.480 1.480 0.215 0.215
## 193 speed =~ ssei 2 2 1 79.641 0.665 0.665 0.173 0.173
## 101 math =~ sswk 1 1 1 74.771 -1.883 -1.883 -0.294 -0.294
## 188 speed =~ sspc 2 2 1 73.944 0.585 0.585 0.181 0.181
## 156 ssmc ~~ ssasi 1 1 1 69.481 1.313 1.313 0.179 0.179
## 124 ssgs ~~ ssmk 1 1 1 57.416 1.196 1.196 0.177 0.177
## 195 ssgs ~~ sspc 2 2 1 56.766 -0.736 -0.736 -0.189 -0.189
## 175 math =~ sspc 2 2 1 55.358 0.703 0.703 0.218 0.218
## 168 verbal =~ ssmc 2 2 1 51.155 -1.368 -1.368 -0.278 -0.278
## 192 speed =~ ssasi 2 2 1 46.761 -0.608 -0.608 -0.127 -0.127
## 182 electronic =~ ssar 2 2 1 46.485 1.042 1.042 0.147 0.147
## 183 electronic =~ ssmk 2 2 1 46.484 -0.906 -0.906 -0.140 -0.140
## 152 ssmk ~~ ssasi 1 1 1 45.605 -1.159 -1.159 -0.150 -0.150
## 99 verbal =~ sscs 1 1 1 42.571 0.204 0.204 0.240 0.240
## 98 verbal =~ ssno 1 1 1 42.571 -0.248 -0.248 -0.299 -0.299
## 218 ssar ~~ ssmk 2 2 1 42.274 -11.739 -11.739 -1.464 -1.464
## 122 ssgs ~~ sspc 1 1 1 41.616 -0.608 -0.608 -0.166 -0.166
## 187 speed =~ sswk 2 2 1 40.798 -0.939 -0.939 -0.137 -0.137
## 219 ssar ~~ ssmc 2 2 1 39.186 1.361 1.361 0.183 0.183
## 115 speed =~ sspc 1 1 1 39.162 0.347 0.347 0.125 0.125
## 102 math =~ sspc 1 1 1 38.720 0.531 0.531 0.192 0.192
## 208 sswk ~~ ssei 2 2 1 38.707 0.914 0.914 0.207 0.207
metric<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1249.911 62.000 0.000 0.973 0.079 0.031 281268.096 281725.463
Mc(metric)
## [1] 0.9080813
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 64 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 80
## Number of equality constraints 12
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1249.911 846.555
## Degrees of freedom 62 62
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.476
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 440.312 298.220
## 0 809.599 548.335
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.401 0.104 22.982 0.000 2.196 2.606 2.401 0.584
## sswk (.p2.) 5.688 0.126 45.089 0.000 5.440 5.935 5.688 0.900
## sspc (.p3.) 2.339 0.056 42.026 0.000 2.230 2.448 2.339 0.823
## math =~
## ssar (.p4.) 6.228 0.084 74.460 0.000 6.064 6.392 6.228 0.928
## ssmk (.p5.) 5.281 0.071 74.684 0.000 5.142 5.419 5.281 0.872
## ssmc (.p6.) 1.139 0.084 13.509 0.000 0.974 1.305 1.139 0.272
## electronic =~
## ssgs (.p7.) 1.126 0.094 11.915 0.000 0.941 1.311 1.126 0.274
## ssasi (.p8.) 2.500 0.056 44.463 0.000 2.390 2.611 2.500 0.705
## ssmc (.p9.) 2.151 0.080 26.885 0.000 1.994 2.308 2.151 0.513
## ssei (.10.) 2.555 0.056 45.581 0.000 2.445 2.665 2.555 0.781
## speed =~
## ssno (.11.) 0.725 0.015 46.951 0.000 0.695 0.755 0.725 0.878
## sscs (.12.) 0.627 0.015 41.278 0.000 0.598 0.657 0.627 0.731
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.810 0.009 86.834 0.000 0.791 0.828 0.810 0.810
## electronic 0.845 0.012 69.286 0.000 0.821 0.869 0.845 0.845
## speed 0.644 0.020 32.889 0.000 0.606 0.683 0.644 0.644
## math ~~
## electronic 0.753 0.015 49.362 0.000 0.723 0.783 0.753 0.753
## speed 0.695 0.015 47.349 0.000 0.666 0.724 0.695 0.695
## electronic ~~
## speed 0.496 0.023 21.585 0.000 0.451 0.541 0.496 0.496
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 15.782 0.090 175.509 0.000 15.606 15.959 15.782 3.836
## .sswk 27.503 0.136 202.254 0.000 27.237 27.770 27.503 4.351
## .sspc 11.863 0.059 201.639 0.000 11.748 11.978 11.863 4.174
## .ssar 18.133 0.146 124.361 0.000 17.847 18.418 18.133 2.702
## .ssmk 14.248 0.130 109.820 0.000 13.994 14.503 14.248 2.352
## .ssmc 12.747 0.090 141.504 0.000 12.570 12.923 12.747 3.043
## .ssasi 11.812 0.074 158.855 0.000 11.666 11.957 11.812 3.332
## .ssei 10.402 0.072 144.049 0.000 10.261 10.544 10.402 3.181
## .ssno 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.574
## .sscs 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.647
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.328 0.201 26.538 0.000 4.935 5.722 5.328 0.315
## .sswk 7.603 0.481 15.806 0.000 6.660 8.546 7.603 0.190
## .sspc 2.608 0.118 22.176 0.000 2.378 2.839 2.608 0.323
## .ssar 6.247 0.485 12.890 0.000 5.297 7.196 6.247 0.139
## .ssmk 8.805 0.381 23.108 0.000 8.058 9.552 8.805 0.240
## .ssmc 7.933 0.279 28.444 0.000 7.386 8.480 7.933 0.452
## .ssasi 6.314 0.237 26.604 0.000 5.849 6.779 6.314 0.502
## .ssei 4.164 0.182 22.892 0.000 3.807 4.520 4.164 0.389
## .ssno 0.157 0.014 11.367 0.000 0.130 0.184 0.157 0.230
## .sscs 0.342 0.018 19.066 0.000 0.307 0.377 0.342 0.465
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.401 0.104 22.982 0.000 2.196 2.606 2.694 0.579
## sswk (.p2.) 5.688 0.126 45.089 0.000 5.440 5.935 6.382 0.921
## sspc (.p3.) 2.339 0.056 42.026 0.000 2.230 2.448 2.625 0.833
## math =~
## ssar (.p4.) 6.228 0.084 74.460 0.000 6.064 6.392 6.641 0.933
## ssmk (.p5.) 5.281 0.071 74.684 0.000 5.142 5.419 5.631 0.876
## ssmc (.p6.) 1.139 0.084 13.509 0.000 0.974 1.305 1.215 0.249
## electronic =~
## ssgs (.p7.) 1.126 0.094 11.915 0.000 0.941 1.311 1.569 0.337
## ssasi (.p8.) 2.500 0.056 44.463 0.000 2.390 2.611 3.485 0.742
## ssmc (.p9.) 2.151 0.080 26.885 0.000 1.994 2.308 2.998 0.613
## ssei (.10.) 2.555 0.056 45.581 0.000 2.445 2.665 3.561 0.920
## speed =~
## ssno (.11.) 0.725 0.015 46.951 0.000 0.695 0.755 0.791 0.881
## sscs (.12.) 0.627 0.015 41.278 0.000 0.598 0.657 0.684 0.778
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 1.003 0.042 24.102 0.000 0.922 1.085 0.839 0.839
## electronic 1.266 0.065 19.607 0.000 1.140 1.393 0.810 0.810
## speed 0.888 0.049 17.963 0.000 0.791 0.985 0.726 0.726
## math ~~
## electronic 1.039 0.045 23.151 0.000 0.951 1.127 0.699 0.699
## speed 0.924 0.038 24.272 0.000 0.849 0.998 0.795 0.795
## electronic ~~
## speed 0.814 0.052 15.774 0.000 0.713 0.915 0.536 0.536
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 17.613 0.097 181.519 0.000 17.422 17.803 17.613 3.783
## .sswk 27.329 0.142 191.949 0.000 27.050 27.608 27.329 3.944
## .sspc 11.086 0.068 163.704 0.000 10.953 11.219 11.086 3.517
## .ssar 20.009 0.151 132.770 0.000 19.714 20.305 20.009 2.810
## .ssmk 14.749 0.139 105.881 0.000 14.476 15.022 14.749 2.296
## .ssmc 16.924 0.104 162.135 0.000 16.719 17.128 16.924 3.463
## .ssasi 17.810 0.102 175.227 0.000 17.610 18.009 17.810 3.793
## .ssei 13.561 0.080 169.041 0.000 13.404 13.718 13.561 3.505
## .ssno 0.253 0.019 13.436 0.000 0.216 0.290 0.253 0.282
## .sscs 0.112 0.019 5.896 0.000 0.075 0.149 0.112 0.127
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.113 0.194 26.337 0.000 4.733 5.494 5.113 0.236
## .sswk 7.287 0.519 14.036 0.000 6.270 8.305 7.287 0.152
## .sspc 3.048 0.133 22.992 0.000 2.788 3.308 3.048 0.307
## .ssar 6.612 0.453 14.589 0.000 5.723 7.500 6.612 0.130
## .ssmk 9.568 0.399 24.006 0.000 8.787 10.350 9.568 0.232
## .ssmc 8.331 0.316 26.397 0.000 7.712 8.950 8.331 0.349
## .ssasi 9.899 0.387 25.549 0.000 9.139 10.658 9.899 0.449
## .ssei 2.287 0.178 12.873 0.000 1.939 2.636 2.287 0.153
## .ssno 0.180 0.013 13.390 0.000 0.154 0.207 0.180 0.224
## .sscs 0.306 0.017 17.645 0.000 0.272 0.340 0.306 0.395
## verbal 1.259 0.070 18.075 0.000 1.122 1.396 1.000 1.000
## math 1.137 0.038 29.563 0.000 1.062 1.213 1.000 1.000
## electronic 1.942 0.100 19.360 0.000 1.746 2.139 1.000 1.000
## speed 1.189 0.062 19.108 0.000 1.067 1.311 1.000 1.000
lavTestScore(metric, release = 1:12)
## 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 140.566 12 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p47. 1.553 1 0.213
## 2 .p2. == .p48. 17.542 1 0.000
## 3 .p3. == .p49. 30.588 1 0.000
## 4 .p4. == .p50. 5.041 1 0.025
## 5 .p5. == .p51. 6.071 1 0.014
## 6 .p6. == .p52. 0.509 1 0.475
## 7 .p7. == .p53. 14.449 1 0.000
## 8 .p8. == .p54. 23.424 1 0.000
## 9 .p9. == .p55. 7.444 1 0.006
## 10 .p10. == .p56. 20.225 1 0.000
## 11 .p11. == .p57. 5.014 1 0.025
## 12 .p12. == .p58. 5.014 1 0.025
scalar<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2461.668 68.000 0.000 0.946 0.107 0.063 282467.852 282884.864
Mc(scalar)
## [1] 0.8234181
summary(scalar, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 100 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 84
## Number of equality constraints 22
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2461.668 1667.207
## Degrees of freedom 68 68
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.477
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1095.851 742.184
## 0 1365.817 925.023
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.332 0.074 31.509 0.000 2.187 2.477 2.332 0.570
## sswk (.p2.) 5.672 0.128 44.217 0.000 5.420 5.923 5.672 0.897
## sspc (.p3.) 2.356 0.054 43.586 0.000 2.250 2.462 2.356 0.822
## math =~
## ssar (.p4.) 6.265 0.083 75.319 0.000 6.102 6.428 6.265 0.930
## ssmk (.p5.) 5.228 0.071 73.196 0.000 5.088 5.368 5.228 0.866
## ssmc (.p6.) 1.026 0.072 14.262 0.000 0.885 1.167 1.026 0.247
## electronic =~
## ssgs (.p7.) 1.163 0.046 25.257 0.000 1.072 1.253 1.163 0.284
## ssasi (.p8.) 2.796 0.056 50.056 0.000 2.686 2.905 2.796 0.741
## ssmc (.p9.) 2.209 0.064 34.264 0.000 2.082 2.335 2.209 0.532
## ssei (.10.) 2.187 0.052 41.720 0.000 2.084 2.290 2.187 0.697
## speed =~
## ssno (.11.) 0.702 0.016 43.815 0.000 0.670 0.733 0.702 0.855
## sscs (.12.) 0.649 0.015 42.799 0.000 0.619 0.678 0.649 0.744
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.810 0.009 86.404 0.000 0.792 0.829 0.810 0.810
## electronic 0.848 0.013 65.615 0.000 0.822 0.873 0.848 0.848
## speed 0.655 0.019 33.889 0.000 0.617 0.692 0.655 0.655
## math ~~
## electronic 0.763 0.015 49.460 0.000 0.733 0.794 0.763 0.763
## speed 0.701 0.015 47.576 0.000 0.672 0.730 0.701 0.701
## electronic ~~
## speed 0.512 0.023 22.199 0.000 0.467 0.557 0.512 0.512
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 15.808 0.089 178.332 0.000 15.634 15.982 15.808 3.863
## .sswk (.34.) 27.769 0.133 208.451 0.000 27.508 28.031 27.769 4.392
## .sspc (.35.) 11.632 0.059 197.163 0.000 11.516 11.747 11.632 4.058
## .ssar (.36.) 18.332 0.145 126.360 0.000 18.047 18.616 18.332 2.721
## .ssmk (.37.) 13.892 0.125 111.154 0.000 13.647 14.137 13.892 2.300
## .ssmc (.38.) 12.754 0.087 147.038 0.000 12.584 12.924 12.754 3.075
## .ssasi (.39.) 12.235 0.080 153.177 0.000 12.078 12.392 12.235 3.244
## .ssei (.40.) 9.957 0.067 149.065 0.000 9.827 10.088 9.957 3.174
## .ssno (.41.) 0.516 0.017 29.749 0.000 0.482 0.550 0.516 0.628
## .sscs (.42.) 0.469 0.019 25.065 0.000 0.433 0.506 0.469 0.538
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.359 0.202 26.502 0.000 4.963 5.755 5.359 0.320
## .sswk 7.805 0.495 15.775 0.000 6.836 8.775 7.805 0.195
## .sspc 2.664 0.121 22.094 0.000 2.428 2.900 2.664 0.324
## .ssar 6.155 0.499 12.328 0.000 5.176 7.133 6.155 0.136
## .ssmk 9.138 0.388 23.546 0.000 8.377 9.899 9.138 0.251
## .ssmc 7.814 0.276 28.294 0.000 7.272 8.355 7.814 0.454
## .ssasi 6.408 0.271 23.671 0.000 5.878 6.939 6.408 0.450
## .ssei 5.060 0.193 26.191 0.000 4.682 5.439 5.060 0.514
## .ssno 0.182 0.014 13.213 0.000 0.155 0.209 0.182 0.269
## .sscs 0.339 0.019 17.860 0.000 0.302 0.377 0.339 0.447
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.332 0.074 31.509 0.000 2.187 2.477 2.609 0.557
## sswk (.p2.) 5.672 0.128 44.217 0.000 5.420 5.923 6.346 0.918
## sspc (.p3.) 2.356 0.054 43.586 0.000 2.250 2.462 2.636 0.831
## math =~
## ssar (.p4.) 6.265 0.083 75.319 0.000 6.102 6.428 6.668 0.933
## ssmk (.p5.) 5.228 0.071 73.196 0.000 5.088 5.368 5.564 0.870
## ssmc (.p6.) 1.026 0.072 14.262 0.000 0.885 1.167 1.092 0.222
## electronic =~
## ssgs (.p7.) 1.163 0.046 25.257 0.000 1.072 1.253 1.704 0.364
## ssasi (.p8.) 2.796 0.056 50.056 0.000 2.686 2.905 4.097 0.798
## ssmc (.p9.) 2.209 0.064 34.264 0.000 2.082 2.335 3.236 0.657
## ssei (.10.) 2.187 0.052 41.720 0.000 2.084 2.290 3.205 0.870
## speed =~
## ssno (.11.) 0.702 0.016 43.815 0.000 0.670 0.733 0.768 0.864
## sscs (.12.) 0.649 0.015 42.799 0.000 0.619 0.678 0.710 0.790
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.999 0.041 24.080 0.000 0.918 1.080 0.839 0.839
## electronic 1.321 0.067 19.616 0.000 1.189 1.453 0.806 0.806
## speed 0.898 0.050 17.799 0.000 0.799 0.997 0.734 0.734
## math ~~
## electronic 1.091 0.048 22.822 0.000 0.997 1.184 0.699 0.699
## speed 0.932 0.039 24.059 0.000 0.856 1.008 0.800 0.800
## electronic ~~
## speed 0.859 0.056 15.371 0.000 0.750 0.969 0.536 0.536
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 15.808 0.089 178.332 0.000 15.634 15.982 15.808 3.376
## .sswk (.34.) 27.769 0.133 208.451 0.000 27.508 28.031 27.769 4.017
## .sspc (.35.) 11.632 0.059 197.163 0.000 11.516 11.747 11.632 3.667
## .ssar (.36.) 18.332 0.145 126.360 0.000 18.047 18.616 18.332 2.566
## .ssmk (.37.) 13.892 0.125 111.154 0.000 13.647 14.137 13.892 2.173
## .ssmc (.38.) 12.754 0.087 147.038 0.000 12.584 12.924 12.754 2.587
## .ssasi (.39.) 12.235 0.080 153.177 0.000 12.078 12.392 12.235 2.382
## .ssei (.40.) 9.957 0.067 149.065 0.000 9.827 10.088 9.957 2.703
## .ssno (.41.) 0.516 0.017 29.749 0.000 0.482 0.550 0.516 0.580
## .sscs (.42.) 0.469 0.019 25.065 0.000 0.433 0.506 0.469 0.523
## verbal -0.121 0.035 -3.413 0.001 -0.191 -0.052 -0.108 -0.108
## math 0.235 0.034 6.974 0.000 0.169 0.301 0.221 0.221
## elctrnc 1.775 0.062 28.708 0.000 1.654 1.897 1.212 1.212
## speed -0.439 0.040 -10.924 0.000 -0.518 -0.360 -0.401 -0.401
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.046 0.195 25.839 0.000 4.664 5.429 5.046 0.230
## .sswk 7.513 0.530 14.173 0.000 6.474 8.551 7.513 0.157
## .sspc 3.113 0.139 22.319 0.000 2.840 3.386 3.113 0.309
## .ssar 6.570 0.473 13.884 0.000 5.643 7.498 6.570 0.129
## .ssmk 9.908 0.417 23.739 0.000 9.090 10.726 9.908 0.242
## .ssmc 7.690 0.301 25.560 0.000 7.100 8.279 7.690 0.316
## .ssasi 9.603 0.436 22.028 0.000 8.749 10.457 9.603 0.364
## .ssei 3.304 0.182 18.173 0.000 2.948 3.660 3.304 0.243
## .ssno 0.201 0.014 14.669 0.000 0.174 0.228 0.201 0.254
## .sscs 0.302 0.018 16.578 0.000 0.266 0.338 0.302 0.375
## verbal 1.252 0.070 17.946 0.000 1.115 1.389 1.000 1.000
## math 1.133 0.038 29.429 0.000 1.057 1.208 1.000 1.000
## electronic 2.147 0.110 19.458 0.000 1.931 2.364 1.000 1.000
## speed 1.197 0.064 18.585 0.000 1.071 1.323 1.000 1.000
lavTestScore(scalar, release = 13:22) # ssasi also has large misfit, similar to ssei but it barely changes fit indices after freeing ssei, also, if ssar is not further released at the end, RMSEAD indicates huge misfit
## 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 1159.178 10 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p33. == .p79. 3.693 1 0.055
## 2 .p34. == .p80. 158.154 1 0.000
## 3 .p35. == .p81. 186.081 1 0.000
## 4 .p36. == .p82. 125.254 1 0.000
## 5 .p37. == .p83. 127.631 1 0.000
## 6 .p38. == .p84. 0.122 1 0.727
## 7 .p39. == .p85. 545.788 1 0.000
## 8 .p40. == .p86. 558.462 1 0.000
## 9 .p41. == .p87. 195.043 1 0.000
## 10 .p42. == .p88. 195.043 1 0.000
scalar2<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1")) # no and cs biased but one needs to be constrained
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1291.424 64.000 0.000 0.972 0.079 0.033 281305.608 281749.524
Mc(scalar2)
## [1] 0.9051736
strict<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1512.562 74.000 0.000 0.968 0.079 0.043 281506.746 281883.402
Mc(strict)
## [1] 0.889793
cf.cov<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(cf.cov, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1407.608 70.000 0.000 0.970 0.079 0.093 281409.792 281813.352
Mc(cf.cov)
## [1] 0.8971142
summary(cf.cov, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 97 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 84
## Number of equality constraints 24
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1407.608 953.022
## Degrees of freedom 70 70
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.477
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 487.797 330.263
## 0 919.811 622.758
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.563 0.060 42.965 0.000 2.446 2.680 2.563 0.587
## sswk (.p2.) 6.084 0.100 60.789 0.000 5.888 6.281 6.084 0.911
## sspc (.p3.) 2.504 0.048 52.565 0.000 2.411 2.597 2.504 0.839
## math =~
## ssar (.p4.) 6.475 0.068 95.594 0.000 6.342 6.607 6.475 0.932
## ssmk (.p5.) 5.496 0.060 91.454 0.000 5.378 5.613 5.496 0.880
## ssmc (.p6.) 1.468 0.069 21.409 0.000 1.334 1.603 1.468 0.337
## electronic =~
## ssgs (.p7.) 1.250 0.046 27.266 0.000 1.160 1.340 1.250 0.286
## ssasi (.p8.) 2.794 0.059 47.248 0.000 2.678 2.910 2.794 0.743
## ssmc (.p9.) 2.039 0.061 33.250 0.000 1.919 2.159 2.039 0.468
## ssei (.10.) 2.845 0.053 53.624 0.000 2.741 2.949 2.845 0.817
## speed =~
## ssno (.11.) 0.770 0.013 58.705 0.000 0.744 0.795 0.770 0.890
## sscs (.12.) 0.666 0.014 46.601 0.000 0.638 0.694 0.666 0.751
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.27.) 0.817 0.008 98.918 0.000 0.801 0.833 0.817 0.817
## elctrnc (.28.) 0.878 0.010 91.117 0.000 0.859 0.897 0.878 0.878
## speed (.29.) 0.678 0.013 51.136 0.000 0.652 0.704 0.678 0.678
## math ~~
## elctrnc (.30.) 0.765 0.011 66.831 0.000 0.743 0.788 0.765 0.765
## speed (.31.) 0.736 0.011 67.572 0.000 0.715 0.757 0.736 0.736
## electronic ~~
## speed (.32.) 0.549 0.017 32.685 0.000 0.516 0.581 0.549 0.549
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 15.785 0.089 177.305 0.000 15.611 15.960 15.785 3.618
## .sswk 27.503 0.136 202.254 0.000 27.237 27.770 27.503 4.118
## .sspc (.35.) 11.862 0.059 202.751 0.000 11.747 11.977 11.862 3.976
## .ssar 18.133 0.146 124.361 0.000 17.847 18.418 18.133 2.611
## .ssmk (.37.) 14.278 0.130 110.059 0.000 14.024 14.533 14.278 2.287
## .ssmc (.38.) 12.643 0.088 144.281 0.000 12.472 12.815 12.643 2.903
## .ssasi (.39.) 11.869 0.075 159.199 0.000 11.723 12.016 11.869 3.156
## .ssei 10.402 0.072 144.049 0.000 10.261 10.544 10.402 2.988
## .ssno (.41.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.548
## .sscs 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.625
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.285 0.200 26.399 0.000 4.892 5.677 5.285 0.278
## .sswk 7.593 0.473 16.062 0.000 6.666 8.519 7.593 0.170
## .sspc 2.631 0.118 22.385 0.000 2.400 2.861 2.631 0.296
## .ssar 6.317 0.481 13.137 0.000 5.374 7.259 6.317 0.131
## .ssmk 8.778 0.380 23.072 0.000 8.032 9.523 8.778 0.225
## .ssmc 8.073 0.276 29.209 0.000 7.532 8.615 8.073 0.426
## .ssasi 6.335 0.239 26.506 0.000 5.867 6.804 6.335 0.448
## .ssei 4.024 0.180 22.352 0.000 3.671 4.377 4.024 0.332
## .ssno 0.156 0.014 11.537 0.000 0.130 0.183 0.156 0.209
## .sscs 0.343 0.018 19.181 0.000 0.308 0.378 0.343 0.436
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.563 0.060 42.965 0.000 2.446 2.680 2.535 0.577
## sswk (.p2.) 6.084 0.100 60.789 0.000 5.888 6.281 6.017 0.911
## sspc (.p3.) 2.504 0.048 52.565 0.000 2.411 2.597 2.476 0.818
## math =~
## ssar (.p4.) 6.475 0.068 95.594 0.000 6.342 6.607 6.397 0.927
## ssmk (.p5.) 5.496 0.060 91.454 0.000 5.378 5.613 5.430 0.869
## ssmc (.p6.) 1.468 0.069 21.409 0.000 1.334 1.603 1.450 0.316
## electronic =~
## ssgs (.p7.) 1.250 0.046 27.266 0.000 1.160 1.340 1.465 0.333
## ssasi (.p8.) 2.794 0.059 47.248 0.000 2.678 2.910 3.274 0.720
## ssmc (.p9.) 2.039 0.061 33.250 0.000 1.919 2.159 2.389 0.520
## ssei (.10.) 2.845 0.053 53.624 0.000 2.741 2.949 3.334 0.918
## speed =~
## ssno (.11.) 0.770 0.013 58.705 0.000 0.744 0.795 0.750 0.870
## sscs (.12.) 0.666 0.014 46.601 0.000 0.638 0.694 0.650 0.762
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.27.) 0.817 0.008 98.918 0.000 0.801 0.833 0.836 0.836
## elctrnc (.28.) 0.878 0.010 91.117 0.000 0.859 0.897 0.757 0.757
## speed (.29.) 0.678 0.013 51.136 0.000 0.652 0.704 0.703 0.703
## math ~~
## elctrnc (.30.) 0.765 0.011 66.831 0.000 0.743 0.788 0.661 0.661
## speed (.31.) 0.736 0.011 67.572 0.000 0.715 0.757 0.764 0.764
## electronic ~~
## speed (.32.) 0.549 0.017 32.685 0.000 0.516 0.581 0.480 0.480
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 15.785 0.089 177.305 0.000 15.611 15.960 15.785 3.591
## .sswk 29.211 0.177 164.673 0.000 28.863 29.558 29.211 4.424
## .sspc (.35.) 11.862 0.059 202.751 0.000 11.747 11.977 11.862 3.920
## .ssar 19.492 0.180 108.257 0.000 19.139 19.845 19.492 2.826
## .ssmk (.37.) 14.278 0.130 110.059 0.000 14.024 14.533 14.278 2.284
## .ssmc (.38.) 12.643 0.088 144.281 0.000 12.472 12.815 12.643 2.752
## .ssasi (.39.) 11.869 0.075 159.199 0.000 11.723 12.016 11.869 2.608
## .ssei 7.603 0.171 44.474 0.000 7.267 7.938 7.603 2.092
## .ssno (.41.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.550
## .sscs 0.303 0.022 14.010 0.000 0.261 0.346 0.303 0.355
## verbal -0.309 0.036 -8.556 0.000 -0.380 -0.238 -0.313 -0.313
## math 0.080 0.035 2.309 0.021 0.012 0.148 0.081 0.081
## elctrnc 2.095 0.070 29.879 0.000 1.957 2.232 1.787 1.787
## speed -0.287 0.034 -8.384 0.000 -0.354 -0.220 -0.295 -0.295
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.135 0.195 26.357 0.000 4.753 5.517 5.135 0.266
## .sswk 7.388 0.512 14.429 0.000 6.384 8.392 7.388 0.169
## .sspc 3.026 0.130 23.198 0.000 2.770 3.282 3.026 0.330
## .ssar 6.668 0.446 14.941 0.000 5.793 7.543 6.668 0.140
## .ssmk 9.592 0.394 24.355 0.000 8.820 10.364 9.592 0.245
## .ssmc 8.713 0.308 28.323 0.000 8.110 9.316 8.713 0.413
## .ssasi 9.985 0.393 25.427 0.000 9.215 10.755 9.985 0.482
## .ssei 2.088 0.177 11.824 0.000 1.742 2.434 2.088 0.158
## .ssno 0.181 0.014 13.296 0.000 0.154 0.207 0.181 0.243
## .sscs 0.306 0.017 17.580 0.000 0.272 0.340 0.306 0.420
## verbal 0.978 0.020 48.556 0.000 0.939 1.017 1.000 1.000
## math 0.976 0.017 58.416 0.000 0.943 1.009 1.000 1.000
## electronic 1.373 0.043 32.081 0.000 1.289 1.457 1.000 1.000
## speed 0.951 0.029 32.665 0.000 0.894 1.008 1.000 1.000
cf.vcov<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances", "lv.variances"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(cf.vcov, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1602.843 74.000 0.000 0.966 0.082 0.106 281597.027 281973.683
Mc(cf.vcov)
## [1] 0.8832965
cf.cov2<-cfa(cf.lv, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(cf.cov2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1417.225 73.000 0.000 0.970 0.077 0.092 281413.409 281796.791
Mc(cf.cov2)
## [1] 0.8966326
summary(cf.cov2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 97 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 81
## Number of equality constraints 24
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1417.225 961.720
## Degrees of freedom 73 73
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.474
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 489.927 332.461
## 0 927.298 629.259
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.548 0.057 44.963 0.000 2.437 2.659 2.548 0.585
## sswk (.p2.) 6.047 0.090 67.053 0.000 5.870 6.223 6.047 0.908
## sspc (.p3.) 2.489 0.044 56.815 0.000 2.403 2.575 2.489 0.838
## math =~
## ssar (.p4.) 6.439 0.062 103.330 0.000 6.316 6.561 6.439 0.930
## ssmk (.p5.) 5.464 0.056 98.406 0.000 5.355 5.573 5.464 0.879
## ssmc (.p6.) 1.460 0.068 21.568 0.000 1.327 1.593 1.460 0.335
## electronic =~
## ssgs (.p7.) 1.251 0.046 27.274 0.000 1.161 1.341 1.251 0.287
## ssasi (.p8.) 2.796 0.059 47.128 0.000 2.680 2.912 2.796 0.743
## ssmc (.p9.) 2.041 0.062 33.174 0.000 1.920 2.161 2.041 0.469
## ssei (.10.) 2.851 0.053 53.650 0.000 2.747 2.955 2.851 0.818
## speed =~
## ssno (.11.) 0.759 0.011 67.448 0.000 0.737 0.781 0.759 0.883
## sscs (.12.) 0.657 0.013 51.258 0.000 0.632 0.682 0.657 0.746
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.27.) 0.827 0.007 124.118 0.000 0.814 0.840 0.827 0.827
## elctrnc (.28.) 0.880 0.009 93.674 0.000 0.862 0.899 0.880 0.880
## speed (.29.) 0.690 0.012 56.051 0.000 0.666 0.714 0.690 0.690
## math ~~
## elctrnc (.30.) 0.769 0.011 69.824 0.000 0.747 0.790 0.769 0.769
## speed (.31.) 0.749 0.010 78.310 0.000 0.730 0.767 0.749 0.749
## electronic ~~
## speed (.32.) 0.555 0.017 33.418 0.000 0.522 0.587 0.555 0.555
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 15.785 0.089 177.193 0.000 15.610 15.959 15.785 3.626
## .sswk 27.503 0.136 202.254 0.000 27.237 27.770 27.503 4.131
## .sspc (.35.) 11.862 0.058 202.852 0.000 11.747 11.977 11.862 3.992
## .ssar 18.133 0.146 124.361 0.000 17.847 18.418 18.133 2.620
## .ssmk (.37.) 14.278 0.130 110.038 0.000 14.024 14.533 14.278 2.297
## .ssmc (.38.) 12.643 0.088 144.450 0.000 12.472 12.815 12.643 2.904
## .ssasi (.39.) 11.870 0.075 159.094 0.000 11.723 12.016 11.870 3.154
## .ssei 10.402 0.072 144.049 0.000 10.261 10.544 10.402 2.985
## .ssno (.41.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.551
## .sscs 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.630
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssgs 5.278 0.200 26.385 0.000 4.885 5.670 5.278 0.279
## .sswk 7.762 0.459 16.923 0.000 6.863 8.661 7.762 0.175
## .sspc 2.635 0.117 22.449 0.000 2.405 2.865 2.635 0.298
## .ssar 6.454 0.468 13.790 0.000 5.536 7.371 6.454 0.135
## .ssmk 8.779 0.376 23.338 0.000 8.042 9.516 8.779 0.227
## .ssmc 8.083 0.277 29.221 0.000 7.541 8.625 8.083 0.426
## .ssasi 6.345 0.239 26.549 0.000 5.877 6.814 6.345 0.448
## .ssei 4.022 0.180 22.345 0.000 3.669 4.375 4.022 0.331
## .ssno 0.163 0.013 12.756 0.000 0.138 0.188 0.163 0.220
## .sscs 0.343 0.018 19.363 0.000 0.308 0.378 0.343 0.443
## electronic 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.548 0.057 44.963 0.000 2.437 2.659 2.548 0.579
## sswk (.p2.) 6.047 0.090 67.053 0.000 5.870 6.223 6.047 0.914
## sspc (.p3.) 2.489 0.044 56.815 0.000 2.403 2.575 2.489 0.820
## math =~
## ssar (.p4.) 6.439 0.062 103.330 0.000 6.316 6.561 6.439 0.930
## ssmk (.p5.) 5.464 0.056 98.406 0.000 5.355 5.573 5.464 0.870
## ssmc (.p6.) 1.460 0.068 21.568 0.000 1.327 1.593 1.460 0.318
## electronic =~
## ssgs (.p7.) 1.251 0.046 27.274 0.000 1.161 1.341 1.461 0.332
## ssasi (.p8.) 2.796 0.059 47.128 0.000 2.680 2.912 3.266 0.719
## ssmc (.p9.) 2.041 0.062 33.174 0.000 1.920 2.161 2.383 0.519
## ssei (.10.) 2.851 0.053 53.650 0.000 2.747 2.955 3.329 0.918
## speed =~
## ssno (.11.) 0.759 0.011 67.448 0.000 0.737 0.781 0.759 0.876
## sscs (.12.) 0.657 0.013 51.258 0.000 0.632 0.682 0.657 0.765
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.27.) 0.827 0.007 124.118 0.000 0.814 0.840 0.827 0.827
## elctrnc (.28.) 0.880 0.009 93.674 0.000 0.862 0.899 0.754 0.754
## speed (.29.) 0.690 0.012 56.051 0.000 0.666 0.714 0.690 0.690
## math ~~
## elctrnc (.30.) 0.769 0.011 69.824 0.000 0.747 0.790 0.658 0.658
## speed (.31.) 0.749 0.010 78.310 0.000 0.730 0.767 0.749 0.749
## electronic ~~
## speed (.32.) 0.555 0.017 33.418 0.000 0.522 0.587 0.475 0.475
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 15.785 0.089 177.193 0.000 15.610 15.959 15.785 3.586
## .sswk 29.211 0.177 164.666 0.000 28.863 29.558 29.211 4.415
## .sspc (.35.) 11.862 0.058 202.852 0.000 11.747 11.977 11.862 3.906
## .ssar 19.492 0.180 108.180 0.000 19.139 19.845 19.492 2.816
## .ssmk (.37.) 14.278 0.130 110.038 0.000 14.024 14.533 14.278 2.273
## .ssmc (.38.) 12.643 0.088 144.450 0.000 12.472 12.815 12.643 2.752
## .ssasi (.39.) 11.870 0.075 159.094 0.000 11.723 12.016 11.870 2.612
## .ssei 7.595 0.172 44.165 0.000 7.258 7.932 7.595 2.093
## .ssno (.41.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.547
## .sscs 0.303 0.022 14.012 0.000 0.261 0.345 0.303 0.353
## verbal -0.311 0.036 -8.663 0.000 -0.382 -0.241 -0.311 -0.311
## math 0.080 0.035 2.308 0.021 0.012 0.149 0.080 0.080
## elctrnc 2.093 0.070 29.872 0.000 1.955 2.230 1.792 1.792
## speed -0.291 0.035 -8.425 0.000 -0.359 -0.223 -0.291 -0.291
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssgs 5.140 0.195 26.383 0.000 4.758 5.522 5.140 0.265
## .sswk 7.213 0.490 14.713 0.000 6.252 8.174 7.213 0.165
## .sspc 3.027 0.130 23.197 0.000 2.771 3.282 3.027 0.328
## .ssar 6.472 0.437 14.813 0.000 5.616 7.329 6.472 0.135
## .ssmk 9.621 0.399 24.117 0.000 8.839 10.403 9.621 0.244
## .ssmc 8.714 0.308 28.301 0.000 8.110 9.317 8.714 0.413
## .ssasi 9.992 0.393 25.440 0.000 9.222 10.761 9.992 0.484
## .ssei 2.078 0.177 11.746 0.000 1.731 2.425 2.078 0.158
## .ssno 0.175 0.013 13.169 0.000 0.149 0.201 0.175 0.233
## .sscs 0.305 0.018 17.347 0.000 0.271 0.340 0.305 0.415
## electronic 1.364 0.042 32.228 0.000 1.281 1.447 1.000 1.000
reduced<-cfa(cf.reduced, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(reduced, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1424.863 74.000 0.000 0.970 0.077 0.092 281419.047 281795.703
Mc(reduced)
## [1] 0.8961496
summary(reduced, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 91 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 80
## Number of equality constraints 24
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1424.863 967.240
## Degrees of freedom 74 74
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.473
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 494.782 335.873
## 0 930.080 631.367
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.550 0.057 45.062 0.000 2.439 2.661 2.550 0.586
## sswk (.p2.) 6.049 0.090 67.094 0.000 5.872 6.225 6.049 0.908
## sspc (.p3.) 2.490 0.044 56.811 0.000 2.404 2.576 2.490 0.838
## math =~
## ssar (.p4.) 6.442 0.062 103.681 0.000 6.320 6.564 6.442 0.930
## ssmk (.p5.) 5.467 0.056 98.262 0.000 5.358 5.576 5.467 0.879
## ssmc (.p6.) 1.456 0.067 21.572 0.000 1.324 1.588 1.456 0.334
## electronic =~
## ssgs (.p7.) 1.250 0.046 27.285 0.000 1.161 1.340 1.250 0.287
## ssasi (.p8.) 2.795 0.059 47.114 0.000 2.679 2.912 2.795 0.743
## ssmc (.p9.) 2.048 0.061 33.491 0.000 1.929 2.168 2.048 0.470
## ssei (.10.) 2.851 0.053 53.692 0.000 2.747 2.955 2.851 0.818
## speed =~
## ssno (.11.) 0.759 0.011 67.430 0.000 0.737 0.781 0.759 0.883
## sscs (.12.) 0.657 0.013 51.248 0.000 0.632 0.682 0.657 0.747
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.28.) 0.827 0.007 124.185 0.000 0.814 0.840 0.827 0.827
## elctrnc (.29.) 0.880 0.009 93.758 0.000 0.862 0.899 0.880 0.880
## speed (.30.) 0.690 0.012 56.100 0.000 0.666 0.715 0.690 0.690
## math ~~
## elctrnc (.31.) 0.769 0.011 69.808 0.000 0.747 0.790 0.769 0.769
## speed (.32.) 0.749 0.010 78.367 0.000 0.730 0.768 0.749 0.749
## electronic ~~
## speed (.33.) 0.555 0.017 33.445 0.000 0.523 0.588 0.555 0.555
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.34.) 15.881 0.080 197.461 0.000 15.723 16.039 15.881 3.647
## .sswk 27.660 0.123 224.766 0.000 27.419 27.902 27.660 4.154
## .sspc (.36.) 11.927 0.053 224.215 0.000 11.823 12.031 11.927 4.013
## .ssar 18.335 0.122 150.384 0.000 18.096 18.574 18.335 2.648
## .ssmk (.38.) 14.500 0.095 152.000 0.000 14.313 14.687 14.500 2.331
## .ssmc (.39.) 12.742 0.080 160.180 0.000 12.586 12.898 12.742 2.925
## .ssasi (.40.) 11.936 0.073 163.677 0.000 11.793 12.079 11.936 3.172
## .ssei 10.471 0.068 154.251 0.000 10.338 10.604 10.471 3.004
## .ssno (.42.) 0.492 0.017 29.765 0.000 0.459 0.524 0.492 0.572
## .sscs 0.570 0.018 32.357 0.000 0.536 0.605 0.570 0.648
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssgs 5.278 0.200 26.386 0.000 4.886 5.670 5.278 0.278
## .sswk 7.763 0.459 16.923 0.000 6.864 8.662 7.763 0.175
## .sspc 2.635 0.117 22.448 0.000 2.405 2.865 2.635 0.298
## .ssar 6.449 0.468 13.777 0.000 5.532 7.367 6.449 0.135
## .ssmk 8.789 0.377 23.325 0.000 8.050 9.527 8.789 0.227
## .ssmc 8.080 0.277 29.200 0.000 7.538 8.623 8.080 0.426
## .ssasi 6.345 0.239 26.558 0.000 5.877 6.814 6.345 0.448
## .ssei 4.023 0.180 22.355 0.000 3.671 4.376 4.023 0.331
## .ssno 0.163 0.013 12.755 0.000 0.138 0.188 0.163 0.220
## .sscs 0.343 0.018 19.363 0.000 0.308 0.378 0.343 0.443
## electronic 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.550 0.057 45.062 0.000 2.439 2.661 2.550 0.579
## sswk (.p2.) 6.049 0.090 67.094 0.000 5.872 6.225 6.049 0.914
## sspc (.p3.) 2.490 0.044 56.811 0.000 2.404 2.576 2.490 0.820
## math =~
## ssar (.p4.) 6.442 0.062 103.681 0.000 6.320 6.564 6.442 0.930
## ssmk (.p5.) 5.467 0.056 98.262 0.000 5.358 5.576 5.467 0.870
## ssmc (.p6.) 1.456 0.067 21.572 0.000 1.324 1.588 1.456 0.317
## electronic =~
## ssgs (.p7.) 1.250 0.046 27.285 0.000 1.161 1.340 1.460 0.332
## ssasi (.p8.) 2.795 0.059 47.114 0.000 2.679 2.912 3.264 0.718
## ssmc (.p9.) 2.048 0.061 33.491 0.000 1.929 2.168 2.392 0.520
## ssei (.10.) 2.851 0.053 53.692 0.000 2.747 2.955 3.330 0.918
## speed =~
## ssno (.11.) 0.759 0.011 67.430 0.000 0.737 0.781 0.759 0.876
## sscs (.12.) 0.657 0.013 51.248 0.000 0.632 0.682 0.657 0.765
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.28.) 0.827 0.007 124.185 0.000 0.814 0.840 0.827 0.827
## elctrnc (.29.) 0.880 0.009 93.758 0.000 0.862 0.899 0.754 0.754
## speed (.30.) 0.690 0.012 56.100 0.000 0.666 0.715 0.690 0.690
## math ~~
## elctrnc (.31.) 0.769 0.011 69.808 0.000 0.747 0.790 0.658 0.658
## speed (.32.) 0.749 0.010 78.367 0.000 0.730 0.768 0.749 0.749
## electronic ~~
## speed (.33.) 0.555 0.017 33.445 0.000 0.523 0.588 0.475 0.475
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.34.) 15.881 0.080 197.461 0.000 15.723 16.039 15.881 3.607
## .sswk 29.369 0.163 179.704 0.000 29.048 29.689 29.369 4.438
## .sspc (.36.) 11.927 0.053 224.215 0.000 11.823 12.031 11.927 3.927
## .ssar 19.814 0.121 163.633 0.000 19.577 20.052 19.814 2.861
## .ssmk (.38.) 14.500 0.095 152.000 0.000 14.313 14.687 14.500 2.306
## .ssmc (.39.) 12.742 0.080 160.180 0.000 12.586 12.898 12.742 2.772
## .ssasi (.40.) 11.936 0.073 163.677 0.000 11.793 12.079 11.936 2.627
## .ssei 7.657 0.172 44.564 0.000 7.320 7.994 7.657 2.110
## .ssno (.42.) 0.492 0.017 29.765 0.000 0.459 0.524 0.492 0.568
## .sscs 0.319 0.021 15.104 0.000 0.277 0.360 0.319 0.371
## verbal -0.362 0.028 -12.849 0.000 -0.417 -0.307 -0.362 -0.362
## elctrnc 2.047 0.067 30.376 0.000 1.915 2.179 1.753 1.753
## speed -0.337 0.028 -11.953 0.000 -0.393 -0.282 -0.337 -0.337
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssgs 5.139 0.195 26.382 0.000 4.758 5.521 5.139 0.265
## .sswk 7.213 0.490 14.715 0.000 6.253 8.174 7.213 0.165
## .sspc 3.027 0.130 23.199 0.000 2.771 3.282 3.027 0.328
## .ssar 6.468 0.437 14.792 0.000 5.611 7.325 6.468 0.135
## .ssmk 9.631 0.399 24.112 0.000 8.848 10.413 9.631 0.244
## .ssmc 8.703 0.308 28.255 0.000 8.100 9.307 8.703 0.412
## .ssasi 9.990 0.393 25.441 0.000 9.220 10.759 9.990 0.484
## .ssei 2.082 0.177 11.777 0.000 1.735 2.428 2.082 0.158
## .ssno 0.175 0.013 13.167 0.000 0.149 0.201 0.175 0.233
## .sscs 0.305 0.018 17.348 0.000 0.271 0.340 0.305 0.414
## electronic 1.364 0.042 32.250 0.000 1.281 1.447 1.000 1.000
tests<-lavTestLRT(configural, metric, scalar2, cf.cov, cf.cov2, reduced)
Td=tests[2:6,"Chisq diff"]
Td
## [1] 102.769438 26.558642 79.920185 6.892478 5.320494
dfd=tests[2:6,"Df diff"]
dfd
## [1] 8 2 6 3 1
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-3067+ 3094 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.06202247 0.06314618 0.06325077 0.02052638 0.03745645
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.05164505 0.07298988
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.04317702 0.08553378
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.05133509 0.07594577
RMSEA.CI(T=Td[4],df=dfd[4],N=N,G=2)
## [1] NA 0.04115955
RMSEA.CI(T=Td[5],df=dfd[5],N=N,G=2)
## [1] 0.01164570 0.07120059
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 0.971 0.641 0.003 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 0.868 0.634 0.113 0.003
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 0.966 0.688 0.014 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
## 0.925 0.849 0.007 0.000 0.000 0.000
round(pvals(T=Td[5],df=dfd[5],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 0.979 0.958 0.320 0.153 0.016 0.001
tests<-lavTestLRT(configural, metric, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 102.76944 26.55864 129.94358
dfd=tests[2:4,"Df diff"]
dfd
## [1] 8 2 10
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-3067+ 3094 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.06202247 0.06314618 0.06240917
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.05164505 0.07298988
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.04317702 0.08553378
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.05309445 0.07219053
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 0.971 0.641 0.003 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 0.868 0.634 0.113 0.003
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 0.985 0.677 0.001 0.000
tests<-lavTestLRT(configural, metric, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 102.7694 820.3741
dfd=tests[2:3,"Df diff"]
dfd
## [1] 8 6
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-3067+ 3094 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.06202247 0.20994050
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.05164505 0.07298988
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.1979331 0.2221698
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 0.971 0.641 0.003 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
# ONE FACTOR, just for checking if gap direction aligns with HOF
fmodel<-'
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
'
configural<-cfa(fmodel, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 6909.756 70.000 0.000 0.846 0.178 0.065 286911.940 287315.500
Mc(configural)
## [1] 0.5739718
metric<-cfa(fmodel, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 7056.036 79.000 0.000 0.843 0.169 0.073 287040.220 287383.246
Mc(metric)
## [1] 0.5676116
scalar<-cfa(fmodel, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 15754.561 88.000 0.000 0.647 0.240 0.158 295720.746 296003.237
Mc(scalar)
## [1] 0.2803724
summary(scalar, standardized=T, ci=T) # -0.299 Std.all
## lavaan 0.6-18 ended normally after 73 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 62
## Number of equality constraints 20
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 15754.561 10551.530
## Degrees of freedom 88 88
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.493
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 6283.739 4208.499
## 0 9470.822 6343.030
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g =~
## ssgs (.p1.) 3.449 0.061 56.428 0.000 3.329 3.569 3.449 0.817
## ssar (.p2.) 5.430 0.090 60.591 0.000 5.255 5.606 5.430 0.834
## sswk (.p3.) 5.048 0.105 48.086 0.000 4.843 5.254 5.048 0.808
## sspc (.p4.) 2.077 0.050 41.192 0.000 1.978 2.176 2.077 0.734
## ssno (.p5.) 0.483 0.014 34.391 0.000 0.455 0.510 0.483 0.573
## sscs (.p6.) 0.419 0.015 28.261 0.000 0.390 0.448 0.419 0.467
## ssasi (.p7.) 2.489 0.077 32.531 0.000 2.339 2.639 2.489 0.629
## ssmk (.p8.) 4.588 0.080 57.504 0.000 4.431 4.744 4.588 0.784
## ssmc (.p9.) 3.255 0.064 50.470 0.000 3.129 3.381 3.255 0.706
## ssei (.10.) 2.659 0.052 51.150 0.000 2.558 2.761 2.659 0.712
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.22.) 16.110 0.093 172.680 0.000 15.927 16.293 16.110 3.817
## .ssar (.23.) 18.127 0.148 122.669 0.000 17.837 18.416 18.127 2.784
## .sswk (.24.) 26.493 0.153 172.750 0.000 26.192 26.794 26.493 4.238
## .sspc (.25.) 11.148 0.073 153.535 0.000 11.006 11.291 11.148 3.937
## .ssno (.26.) 0.275 0.017 16.062 0.000 0.242 0.309 0.275 0.327
## .sscs (.27.) 0.237 0.019 12.376 0.000 0.199 0.274 0.237 0.264
## .ssasi (.28.) 13.087 0.121 108.347 0.000 12.851 13.324 13.087 3.306
## .ssmk (.29.) 13.711 0.127 108.148 0.000 13.462 13.959 13.711 2.344
## .ssmc (.30.) 14.100 0.107 132.075 0.000 13.891 14.310 14.100 3.059
## .ssei (.31.) 11.536 0.085 135.420 0.000 11.369 11.703 11.536 3.089
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.913 0.237 24.997 0.000 5.450 6.377 5.913 0.332
## .ssar 12.908 0.530 24.377 0.000 11.870 13.946 12.908 0.304
## .sswk 13.590 0.593 22.924 0.000 12.428 14.752 13.590 0.348
## .sspc 3.703 0.164 22.564 0.000 3.381 4.025 3.703 0.462
## .ssno 0.476 0.015 32.421 0.000 0.448 0.505 0.476 0.672
## .sscs 0.630 0.024 26.061 0.000 0.582 0.677 0.630 0.782
## .ssasi 9.478 0.468 20.243 0.000 8.560 10.396 9.478 0.605
## .ssmk 13.178 0.455 28.962 0.000 12.286 14.070 13.178 0.385
## .ssmc 10.654 0.453 23.517 0.000 9.766 11.542 10.654 0.501
## .ssei 6.870 0.284 24.203 0.000 6.314 7.426 6.870 0.493
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g =~
## ssgs (.p1.) 3.449 0.061 56.428 0.000 3.329 3.569 4.013 0.860
## ssar (.p2.) 5.430 0.090 60.591 0.000 5.255 5.606 6.317 0.865
## sswk (.p3.) 5.048 0.105 48.086 0.000 4.843 5.254 5.873 0.854
## sspc (.p4.) 2.077 0.050 41.192 0.000 1.978 2.176 2.416 0.762
## ssno (.p5.) 0.483 0.014 34.391 0.000 0.455 0.510 0.561 0.632
## sscs (.p6.) 0.419 0.015 28.261 0.000 0.390 0.448 0.487 0.546
## ssasi (.p7.) 2.489 0.077 32.531 0.000 2.339 2.639 2.896 0.469
## ssmk (.p8.) 4.588 0.080 57.504 0.000 4.431 4.744 5.337 0.817
## ssmc (.p9.) 3.255 0.064 50.470 0.000 3.129 3.381 3.787 0.713
## ssei (.10.) 2.659 0.052 51.150 0.000 2.558 2.761 3.094 0.762
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.22.) 16.110 0.093 172.680 0.000 15.927 16.293 16.110 3.452
## .ssar (.23.) 18.127 0.148 122.669 0.000 17.837 18.416 18.127 2.482
## .sswk (.24.) 26.493 0.153 172.750 0.000 26.192 26.794 26.493 3.850
## .sspc (.25.) 11.148 0.073 153.535 0.000 11.006 11.291 11.148 3.515
## .ssno (.26.) 0.275 0.017 16.062 0.000 0.242 0.309 0.275 0.310
## .sscs (.27.) 0.237 0.019 12.376 0.000 0.199 0.274 0.237 0.266
## .ssasi (.28.) 13.087 0.121 108.347 0.000 12.851 13.324 13.087 2.119
## .ssmk (.29.) 13.711 0.127 108.148 0.000 13.462 13.959 13.711 2.099
## .ssmc (.30.) 14.100 0.107 132.075 0.000 13.891 14.310 14.100 2.657
## .ssei (.31.) 11.536 0.085 135.420 0.000 11.369 11.703 11.536 2.840
## g 0.348 0.041 8.420 0.000 0.267 0.429 0.299 0.299
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.676 0.236 24.102 0.000 5.214 6.138 5.676 0.261
## .ssar 13.421 0.561 23.922 0.000 12.322 14.521 13.421 0.252
## .sswk 12.850 0.573 22.434 0.000 11.728 13.973 12.850 0.271
## .sspc 4.222 0.194 21.727 0.000 3.841 4.603 4.222 0.420
## .ssno 0.474 0.015 30.593 0.000 0.444 0.504 0.474 0.601
## .sscs 0.558 0.024 23.446 0.000 0.511 0.604 0.558 0.701
## .ssasi 29.759 1.456 20.446 0.000 26.906 32.612 29.759 0.780
## .ssmk 14.185 0.527 26.934 0.000 13.152 15.217 14.185 0.332
## .ssmc 13.828 0.576 24.022 0.000 12.700 14.956 13.828 0.491
## .ssei 6.930 0.337 20.589 0.000 6.270 7.589 6.930 0.420
## g 1.353 0.056 24.111 0.000 1.243 1.463 1.000 1.000
# HIGH ORDER FACTOR, FREEING SSAR FITS TINY BIT BETTER THAN SSMK BUT CAUSES NONPOSITIVE MATRIX BECAUSE THERE IS NO LATENT INTERCEPT TO FIX
hof.model<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
'
hof.lv<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
'
hof.weak<-' # only used if ssmk is free instead of ssar
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
math~0*1
'
baseline<-cfa(hof.model, data=dgroup, meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2506.851 29.000 0.000 0.946 0.118 0.058 287559.438 287801.574
Mc(baseline)
## [1] 0.8178108
configural<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1639.317 58.000 0.000 0.964 0.094 0.034 281665.501 282149.773
Mc(configural)
## [1] 0.8795423
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 89 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 72
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1639.317 1098.194
## Degrees of freedom 58 58
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.493
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 547.664 366.885
## 0 1091.653 731.308
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs 0.695 0.071 9.836 0.000 0.556 0.833 1.864 0.449
## sswk 2.177 0.155 14.037 0.000 1.873 2.481 5.841 0.912
## sspc 0.838 0.059 14.083 0.000 0.721 0.954 2.248 0.813
## math =~
## ssar 2.987 0.118 25.417 0.000 2.757 3.218 6.289 0.932
## ssmk 2.463 0.097 25.379 0.000 2.273 2.654 5.186 0.865
## ssmc 0.757 0.071 10.727 0.000 0.619 0.896 1.595 0.384
## electronic =~
## ssgs 0.927 0.075 12.342 0.000 0.780 1.074 1.801 0.434
## ssasi 1.205 0.062 19.492 0.000 1.083 1.326 2.341 0.678
## ssmc 0.835 0.080 10.493 0.000 0.679 0.991 1.623 0.391
## ssei 1.382 0.065 21.421 0.000 1.255 1.508 2.685 0.804
## speed =~
## ssno 0.511 0.016 32.766 0.000 0.480 0.541 0.719 0.866
## sscs 0.445 0.015 30.628 0.000 0.416 0.473 0.626 0.736
## g =~
## verbal 2.490 0.199 12.517 0.000 2.100 2.880 0.928 0.928
## math 1.853 0.091 20.251 0.000 1.673 2.032 0.880 0.880
## electronic 1.666 0.093 17.883 0.000 1.483 1.849 0.857 0.857
## speed 0.990 0.048 20.430 0.000 0.895 1.085 0.704 0.704
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 15.782 0.090 175.509 0.000 15.606 15.959 15.782 3.799
## .sswk 27.503 0.136 202.254 0.000 27.237 27.770 27.503 4.296
## .sspc 11.863 0.059 201.639 0.000 11.748 11.978 11.863 4.290
## .ssar 18.133 0.146 124.361 0.000 17.847 18.418 18.133 2.688
## .ssmk 14.248 0.130 109.820 0.000 13.994 14.503 14.248 2.375
## .ssmc 12.747 0.090 141.504 0.000 12.570 12.923 12.747 3.071
## .ssasi 11.812 0.074 158.855 0.000 11.666 11.957 11.812 3.421
## .ssei 10.402 0.072 144.049 0.000 10.261 10.544 10.402 3.117
## .ssno 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.571
## .sscs 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.653
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.195 0.212 24.493 0.000 4.779 5.610 5.195 0.301
## .sswk 6.875 0.508 13.535 0.000 5.879 7.871 6.875 0.168
## .sspc 2.595 0.116 22.353 0.000 2.367 2.822 2.595 0.339
## .ssar 5.941 0.500 11.877 0.000 4.961 6.922 5.941 0.131
## .ssmk 9.084 0.405 22.424 0.000 8.290 9.878 9.084 0.252
## .ssmc 8.148 0.283 28.802 0.000 7.594 8.702 8.148 0.473
## .ssasi 6.445 0.246 26.208 0.000 5.963 6.927 6.445 0.541
## .ssei 3.929 0.196 20.097 0.000 3.546 4.313 3.929 0.353
## .ssno 0.173 0.017 10.340 0.000 0.140 0.206 0.173 0.251
## .sscs 0.330 0.020 16.471 0.000 0.291 0.369 0.330 0.458
## .verbal 1.000 1.000 1.000 0.139 0.139
## .math 1.000 1.000 1.000 0.226 0.226
## .electronic 1.000 1.000 1.000 0.265 0.265
## .speed 1.000 1.000 1.000 0.505 0.505
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs 0.852 0.077 11.073 0.000 0.701 1.003 2.698 0.586
## sswk 1.975 0.179 11.038 0.000 1.624 2.325 6.250 0.911
## sspc 0.868 0.077 11.214 0.000 0.717 1.020 2.748 0.851
## math =~
## ssar 2.828 0.137 20.693 0.000 2.560 3.096 6.602 0.931
## ssmk 2.442 0.113 21.561 0.000 2.220 2.664 5.700 0.879
## ssmc 0.395 0.058 6.835 0.000 0.282 0.509 0.923 0.187
## electronic =~
## ssgs 0.921 0.075 12.332 0.000 0.775 1.068 1.546 0.336
## ssasi 2.188 0.081 26.919 0.000 2.029 2.348 3.673 0.766
## ssmc 1.987 0.093 21.325 0.000 1.804 2.169 3.335 0.676
## ssei 2.076 0.060 34.467 0.000 1.958 2.194 3.484 0.908
## speed =~
## ssno 0.469 0.016 30.009 0.000 0.439 0.500 0.773 0.865
## sscs 0.428 0.015 29.151 0.000 0.399 0.457 0.705 0.795
## g =~
## verbal 3.003 0.303 9.903 0.000 2.409 3.598 0.949 0.949
## math 2.109 0.118 17.882 0.000 1.878 2.341 0.904 0.904
## electronic 1.348 0.065 20.736 0.000 1.221 1.475 0.803 0.803
## speed 1.308 0.063 20.853 0.000 1.185 1.431 0.794 0.794
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 17.613 0.097 181.519 0.000 17.422 17.803 17.613 3.827
## .sswk 27.329 0.142 191.949 0.000 27.050 27.608 27.329 3.984
## .sspc 11.086 0.068 163.704 0.000 10.953 11.219 11.086 3.434
## .ssar 20.009 0.151 132.770 0.000 19.714 20.305 20.009 2.823
## .ssmk 14.749 0.139 105.881 0.000 14.476 15.022 14.749 2.275
## .ssmc 16.924 0.104 162.135 0.000 16.719 17.128 16.924 3.433
## .ssasi 17.810 0.102 175.227 0.000 17.610 18.009 17.810 3.713
## .ssei 13.561 0.080 169.041 0.000 13.404 13.718 13.561 3.533
## .ssno 0.253 0.019 13.436 0.000 0.216 0.290 0.253 0.283
## .sscs 0.112 0.019 5.896 0.000 0.075 0.149 0.112 0.126
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.156 0.195 26.431 0.000 4.773 5.538 5.156 0.243
## .sswk 7.987 0.552 14.459 0.000 6.905 9.070 7.987 0.170
## .sspc 2.870 0.126 22.795 0.000 2.624 3.117 2.870 0.275
## .ssar 6.664 0.494 13.495 0.000 5.696 7.632 6.664 0.133
## .ssmk 9.522 0.430 22.139 0.000 8.679 10.365 9.522 0.227
## .ssmc 7.866 0.335 23.458 0.000 7.208 8.523 7.866 0.324
## .ssasi 9.522 0.392 24.286 0.000 8.753 10.290 9.522 0.414
## .ssei 2.594 0.195 13.329 0.000 2.213 2.976 2.594 0.176
## .ssno 0.201 0.014 13.980 0.000 0.173 0.229 0.201 0.252
## .sscs 0.289 0.018 15.716 0.000 0.253 0.325 0.289 0.368
## .verbal 1.000 1.000 1.000 0.100 0.100
## .math 1.000 1.000 1.000 0.184 0.184
## .electronic 1.000 1.000 1.000 0.355 0.355
## .speed 1.000 1.000 1.000 0.369 0.369
## g 1.000 1.000 1.000 1.000 1.000
#modificationIndices(configural, sort=T, maximum.number=30)
metric<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1805.808 69.000 0.000 0.961 0.090 0.044 281809.992 282220.278
Mc(metric)
## [1] 0.8685113
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 88 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 77
## Number of equality constraints 16
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1805.808 1219.645
## Degrees of freedom 69 69
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.481
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 650.734 439.507
## 0 1155.074 780.139
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.827 0.059 14.016 0.000 0.712 0.943 2.285 0.554
## sswk (.p2.) 2.034 0.140 14.487 0.000 1.759 2.309 5.620 0.897
## sspc (.p3.) 0.845 0.058 14.609 0.000 0.732 0.958 2.335 0.825
## math =~
## ssar (.p4.) 3.005 0.103 29.272 0.000 2.804 3.206 6.108 0.926
## ssmk (.p5.) 2.541 0.085 29.791 0.000 2.374 2.708 5.165 0.866
## ssmc (.p6.) 0.541 0.049 11.119 0.000 0.446 0.636 1.099 0.260
## electronic =~
## ssgs (.p7.) 0.613 0.048 12.731 0.000 0.518 0.707 1.278 0.310
## ssasi (.p8.) 1.239 0.060 20.689 0.000 1.122 1.357 2.584 0.719
## ssmc (.p9.) 1.072 0.058 18.478 0.000 0.959 1.186 2.236 0.529
## ssei (.10.) 1.270 0.061 20.783 0.000 1.151 1.390 2.649 0.792
## speed =~
## ssno (.11.) 0.502 0.014 36.679 0.000 0.475 0.529 0.724 0.862
## sscs (.12.) 0.450 0.013 35.417 0.000 0.425 0.475 0.649 0.752
## g =~
## verbal (.13.) 2.575 0.182 14.118 0.000 2.218 2.933 0.932 0.932
## math (.14.) 1.770 0.078 22.748 0.000 1.617 1.922 0.871 0.871
## elctrnc (.15.) 1.830 0.096 19.119 0.000 1.642 2.017 0.878 0.878
## speed (.16.) 1.038 0.039 26.321 0.000 0.961 1.116 0.720 0.720
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 15.782 0.090 175.509 0.000 15.606 15.959 15.782 3.824
## .sswk 27.503 0.136 202.254 0.000 27.237 27.770 27.503 4.392
## .sspc 11.863 0.059 201.639 0.000 11.748 11.978 11.863 4.194
## .ssar 18.133 0.146 124.361 0.000 17.847 18.418 18.133 2.749
## .ssmk 14.248 0.130 109.820 0.000 13.994 14.503 14.248 2.390
## .ssmc 12.747 0.090 141.504 0.000 12.570 12.923 12.747 3.016
## .ssasi 11.812 0.074 158.855 0.000 11.666 11.957 11.812 3.285
## .ssei 10.402 0.072 144.049 0.000 10.261 10.544 10.402 3.108
## .ssno 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.564
## .sscs 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.643
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.401 0.201 26.843 0.000 5.007 5.796 5.401 0.317
## .sswk 7.627 0.483 15.805 0.000 6.681 8.573 7.627 0.195
## .sspc 2.552 0.116 22.050 0.000 2.326 2.779 2.552 0.319
## .ssar 6.188 0.481 12.851 0.000 5.244 7.131 6.188 0.142
## .ssmk 8.864 0.386 22.945 0.000 8.107 9.621 8.864 0.249
## .ssmc 7.897 0.279 28.259 0.000 7.349 8.445 7.897 0.442
## .ssasi 6.248 0.239 26.088 0.000 5.778 6.717 6.248 0.483
## .ssei 4.182 0.184 22.706 0.000 3.821 4.543 4.182 0.373
## .ssno 0.182 0.014 12.950 0.000 0.154 0.209 0.182 0.258
## .sscs 0.323 0.018 17.628 0.000 0.287 0.359 0.323 0.434
## .verbal 1.000 1.000 1.000 0.131 0.131
## .math 1.000 1.000 1.000 0.242 0.242
## .electronic 1.000 1.000 1.000 0.230 0.230
## .speed 1.000 1.000 1.000 0.481 0.481
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.827 0.059 14.016 0.000 0.712 0.943 2.607 0.567
## sswk (.p2.) 2.034 0.140 14.487 0.000 1.759 2.309 6.410 0.918
## sspc (.p3.) 0.845 0.058 14.609 0.000 0.732 0.958 2.663 0.841
## math =~
## ssar (.p4.) 3.005 0.103 29.272 0.000 2.804 3.206 6.752 0.936
## ssmk (.p5.) 2.541 0.085 29.791 0.000 2.374 2.708 5.710 0.878
## ssmc (.p6.) 0.541 0.049 11.119 0.000 0.446 0.636 1.215 0.252
## electronic =~
## ssgs (.p7.) 0.613 0.048 12.731 0.000 0.518 0.707 1.667 0.363
## ssasi (.p8.) 1.239 0.060 20.689 0.000 1.122 1.357 3.371 0.731
## ssmc (.p9.) 1.072 0.058 18.478 0.000 0.959 1.186 2.918 0.605
## ssei (.10.) 1.270 0.061 20.783 0.000 1.151 1.390 3.456 0.916
## speed =~
## ssno (.11.) 0.502 0.014 36.679 0.000 0.475 0.529 0.766 0.866
## sscs (.12.) 0.450 0.013 35.417 0.000 0.425 0.475 0.687 0.785
## g =~
## verbal (.13.) 2.575 0.182 14.118 0.000 2.218 2.933 0.945 0.945
## math (.14.) 1.770 0.078 22.748 0.000 1.617 1.922 0.911 0.911
## elctrnc (.15.) 1.830 0.096 19.119 0.000 1.642 2.017 0.778 0.778
## speed (.16.) 1.038 0.039 26.321 0.000 0.961 1.116 0.787 0.787
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 17.613 0.097 181.519 0.000 17.422 17.803 17.613 3.833
## .sswk 27.329 0.142 191.949 0.000 27.050 27.608 27.329 3.912
## .sspc 11.086 0.068 163.704 0.000 10.953 11.219 11.086 3.501
## .ssar 20.009 0.151 132.770 0.000 19.714 20.305 20.009 2.773
## .ssmk 14.749 0.139 105.881 0.000 14.476 15.022 14.749 2.268
## .ssmc 16.924 0.104 162.135 0.000 16.719 17.128 16.924 3.508
## .ssasi 17.810 0.102 175.227 0.000 17.610 18.009 17.810 3.864
## .ssei 13.561 0.080 169.041 0.000 13.404 13.718 13.561 3.593
## .ssno 0.253 0.019 13.436 0.000 0.216 0.290 0.253 0.286
## .sscs 0.112 0.019 5.896 0.000 0.075 0.149 0.112 0.128
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.146 0.194 26.543 0.000 4.766 5.526 5.146 0.244
## .sswk 7.708 0.545 14.144 0.000 6.640 8.776 7.708 0.158
## .sspc 2.936 0.128 22.904 0.000 2.685 3.187 2.936 0.293
## .ssar 6.480 0.462 14.040 0.000 5.575 7.384 6.480 0.124
## .ssmk 9.706 0.404 23.995 0.000 8.913 10.498 9.706 0.229
## .ssmc 8.257 0.325 25.377 0.000 7.619 8.894 8.257 0.355
## .ssasi 9.880 0.391 25.280 0.000 9.114 10.646 9.880 0.465
## .ssei 2.301 0.189 12.192 0.000 1.931 2.671 2.301 0.162
## .ssno 0.196 0.014 14.373 0.000 0.169 0.223 0.196 0.250
## .sscs 0.293 0.018 16.640 0.000 0.259 0.328 0.293 0.383
## .verbal 1.054 0.195 5.416 0.000 0.672 1.435 0.106 0.106
## .math 0.858 0.084 10.190 0.000 0.693 1.024 0.170 0.170
## .electronic 2.920 0.314 9.293 0.000 2.304 3.536 0.395 0.395
## .speed 0.885 0.067 13.258 0.000 0.755 1.016 0.380 0.380
## g 1.338 0.061 21.771 0.000 1.218 1.459 1.000 1.000
lavTestScore(metric, release = 1:16)
## 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 168.381 16 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p47. 0.674 1 0.412
## 2 .p2. == .p48. 28.684 1 0.000
## 3 .p3. == .p49. 25.089 1 0.000
## 4 .p4. == .p50. 16.358 1 0.000
## 5 .p5. == .p51. 1.116 1 0.291
## 6 .p6. == .p52. 0.040 1 0.841
## 7 .p7. == .p53. 8.785 1 0.003
## 8 .p8. == .p54. 34.973 1 0.000
## 9 .p9. == .p55. 11.735 1 0.001
## 10 .p10. == .p56. 1.374 1 0.241
## 11 .p11. == .p57. 0.576 1 0.448
## 12 .p12. == .p58. 3.780 1 0.052
## 13 .p13. == .p59. 4.071 1 0.044
## 14 .p14. == .p60. 15.311 1 0.000
## 15 .p15. == .p61. 25.519 1 0.000
## 16 .p16. == .p62. 6.773 1 0.009
scalar<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= 1.401279e-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 aic bic
## 2989.310 74.000 0.000 0.934 0.113 0.071 282983.494 283360.150
Mc(scalar)
## [1] 0.7892815
summary(scalar, standardized=T, ci=T) # g -.309 Std.all
## lavaan 0.6-18 ended normally after 130 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 26
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2989.310 1996.428
## Degrees of freedom 74 74
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.497
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1289.951 861.502
## 0 1699.359 1134.927
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.850 0.059 14.318 0.000 0.734 0.967 2.299 0.559
## sswk (.p2.) 2.063 0.138 14.971 0.000 1.793 2.333 5.577 0.893
## sspc (.p3.) 0.866 0.057 15.311 0.000 0.755 0.977 2.342 0.823
## math =~
## ssar (.p4.) 2.993 0.105 28.512 0.000 2.788 3.199 6.139 0.928
## ssmk (.p5.) 2.492 0.085 29.207 0.000 2.325 2.659 5.110 0.860
## ssmc (.p6.) 0.482 0.040 12.124 0.000 0.404 0.560 0.989 0.235
## electronic =~
## ssgs (.p7.) 0.575 0.035 16.273 0.000 0.506 0.644 1.237 0.301
## ssasi (.p8.) 1.357 0.072 18.943 0.000 1.216 1.497 2.920 0.757
## ssmc (.p9.) 1.077 0.058 18.468 0.000 0.963 1.191 2.318 0.552
## ssei (.10.) 1.054 0.055 19.138 0.000 0.946 1.162 2.269 0.710
## speed =~
## ssno (.11.) 0.479 0.013 36.315 0.000 0.453 0.505 0.699 0.839
## sscs (.12.) 0.461 0.013 34.171 0.000 0.434 0.487 0.672 0.766
## g =~
## verbal (.13.) 2.512 0.172 14.596 0.000 2.175 2.849 0.929 0.929
## math (.14.) 1.791 0.080 22.332 0.000 1.633 1.948 0.873 0.873
## elctrnc (.15.) 1.906 0.112 17.052 0.000 1.687 2.125 0.885 0.885
## speed (.16.) 1.063 0.041 26.205 0.000 0.983 1.142 0.728 0.728
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 15.791 0.088 179.478 0.000 15.619 15.964 15.791 3.837
## .sswk (.33.) 27.783 0.133 208.796 0.000 27.522 28.044 27.783 4.449
## .sspc (.34.) 11.639 0.059 196.737 0.000 11.523 11.755 11.639 4.090
## .ssar (.35.) 18.330 0.145 126.138 0.000 18.045 18.615 18.330 2.771
## .ssmk (.36.) 13.892 0.125 111.148 0.000 13.647 14.137 13.892 2.338
## .ssmc (.37.) 12.737 0.087 146.312 0.000 12.566 12.907 12.737 3.032
## .ssasi (.38.) 12.233 0.080 153.532 0.000 12.077 12.390 12.233 3.171
## .ssei (.39.) 9.973 0.067 149.579 0.000 9.842 10.103 9.973 3.121
## .ssno (.40.) 0.521 0.017 30.375 0.000 0.487 0.554 0.521 0.624
## .sscs (.41.) 0.480 0.019 25.198 0.000 0.443 0.517 0.480 0.547
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.441 0.202 26.885 0.000 5.044 5.838 5.441 0.321
## .sswk 7.905 0.503 15.710 0.000 6.919 8.891 7.905 0.203
## .sspc 2.614 0.119 21.926 0.000 2.380 2.847 2.614 0.323
## .ssar 6.079 0.497 12.229 0.000 5.105 7.054 6.079 0.139
## .ssmk 9.205 0.393 23.411 0.000 8.434 9.975 9.205 0.261
## .ssmc 7.749 0.275 28.133 0.000 7.209 8.288 7.749 0.439
## .ssasi 6.358 0.274 23.163 0.000 5.820 6.895 6.358 0.427
## .ssei 5.061 0.194 26.139 0.000 4.682 5.441 5.061 0.496
## .ssno 0.206 0.014 14.785 0.000 0.179 0.234 0.206 0.297
## .sscs 0.318 0.019 16.302 0.000 0.279 0.356 0.318 0.413
## .verbal 1.000 1.000 1.000 0.137 0.137
## .math 1.000 1.000 1.000 0.238 0.238
## .electronic 1.000 1.000 1.000 0.216 0.216
## .speed 1.000 1.000 1.000 0.470 0.470
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.850 0.059 14.318 0.000 0.734 0.967 2.633 0.573
## sswk (.p2.) 2.063 0.138 14.971 0.000 1.793 2.333 6.387 0.915
## sspc (.p3.) 0.866 0.057 15.311 0.000 0.755 0.977 2.682 0.840
## math =~
## ssar (.p4.) 2.993 0.105 28.512 0.000 2.788 3.199 6.781 0.936
## ssmk (.p5.) 2.492 0.085 29.207 0.000 2.325 2.659 5.645 0.872
## ssmc (.p6.) 0.482 0.040 12.124 0.000 0.404 0.560 1.092 0.227
## electronic =~
## ssgs (.p7.) 0.575 0.035 16.273 0.000 0.506 0.644 1.672 0.364
## ssasi (.p8.) 1.357 0.072 18.943 0.000 1.216 1.497 3.946 0.792
## ssmc (.p9.) 1.077 0.058 18.468 0.000 0.963 1.191 3.133 0.650
## ssei (.10.) 1.054 0.055 19.138 0.000 0.946 1.162 3.066 0.854
## speed =~
## ssno (.11.) 0.479 0.013 36.315 0.000 0.453 0.505 0.741 0.845
## sscs (.12.) 0.461 0.013 34.171 0.000 0.434 0.487 0.712 0.800
## g =~
## verbal (.13.) 2.512 0.172 14.596 0.000 2.175 2.849 0.941 0.941
## math (.14.) 1.791 0.080 22.332 0.000 1.633 1.948 0.916 0.916
## elctrnc (.15.) 1.906 0.112 17.052 0.000 1.687 2.125 0.760 0.760
## speed (.16.) 1.063 0.041 26.205 0.000 0.983 1.142 0.797 0.797
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 15.791 0.088 179.478 0.000 15.619 15.964 15.791 3.437
## .sswk (.33.) 27.783 0.133 208.796 0.000 27.522 28.044 27.783 3.978
## .sspc (.34.) 11.639 0.059 196.737 0.000 11.523 11.755 11.639 3.646
## .ssar (.35.) 18.330 0.145 126.138 0.000 18.045 18.615 18.330 2.531
## .ssmk (.36.) 13.892 0.125 111.148 0.000 13.647 14.137 13.892 2.147
## .ssmc (.37.) 12.737 0.087 146.312 0.000 12.566 12.907 12.737 2.643
## .ssasi (.38.) 12.233 0.080 153.532 0.000 12.077 12.390 12.233 2.456
## .ssei (.39.) 9.973 0.067 149.579 0.000 9.842 10.103 9.973 2.777
## .ssno (.40.) 0.521 0.017 30.375 0.000 0.487 0.554 0.521 0.594
## .sscs (.41.) 0.480 0.019 25.198 0.000 0.443 0.517 0.480 0.539
## .verbal -1.251 0.081 -15.409 0.000 -1.410 -1.092 -0.404 -0.404
## .math -0.147 0.059 -2.493 0.013 -0.263 -0.032 -0.065 -0.065
## .elctrnc 2.993 0.131 22.774 0.000 2.735 3.250 1.029 1.029
## .speed -1.039 0.053 -19.444 0.000 -1.144 -0.934 -0.672 -0.672
## g 0.358 0.043 8.356 0.000 0.274 0.442 0.309 0.309
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.086 0.195 26.108 0.000 4.704 5.468 5.086 0.241
## .sswk 7.976 0.569 14.015 0.000 6.861 9.091 7.976 0.164
## .sspc 3.000 0.135 22.292 0.000 2.736 3.264 3.000 0.294
## .ssar 6.464 0.481 13.444 0.000 5.522 7.406 6.464 0.123
## .ssmk 10.009 0.422 23.742 0.000 9.183 10.836 10.009 0.239
## .ssmc 7.453 0.301 24.777 0.000 6.863 8.042 7.453 0.321
## .ssasi 9.246 0.438 21.119 0.000 8.388 10.104 9.246 0.373
## .ssei 3.495 0.195 17.925 0.000 3.113 3.877 3.495 0.271
## .ssno 0.220 0.014 15.854 0.000 0.193 0.247 0.220 0.286
## .sscs 0.285 0.018 15.504 0.000 0.249 0.322 0.285 0.360
## .verbal 1.104 0.198 5.581 0.000 0.717 1.492 0.115 0.115
## .math 0.821 0.086 9.579 0.000 0.653 0.989 0.160 0.160
## .electronic 3.578 0.409 8.738 0.000 2.775 4.380 0.423 0.423
## .speed 0.872 0.068 12.738 0.000 0.738 1.006 0.365 0.365
## g 1.345 0.062 21.666 0.000 1.223 1.466 1.000 1.000
lavTestScore(scalar, release = 17:26)
## 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 1133.9 10 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p32. == .p78. 0.337 1 0.561
## 2 .p33. == .p79. 164.705 1 0.000
## 3 .p34. == .p80. 180.852 1 0.000
## 4 .p35. == .p81. 126.476 1 0.000
## 5 .p36. == .p82. 125.939 1 0.000
## 6 .p37. == .p83. 0.252 1 0.615
## 7 .p38. == .p84. 556.591 1 0.000
## 8 .p39. == .p85. 534.948 1 0.000
## 9 .p40. == .p86. 178.853 1 0.000
## 10 .p41. == .p87. 178.853 1 0.000
scalar2<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~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 (= 5.299926e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1874.522 70.000 0.000 0.959 0.091 0.046 281876.706 282280.266
Mc(scalar2)
## [1] 0.8637508
summary(scalar2, standardized=T, ci=T) # -.342 if ssmk is free and -.297 if ssar is free
## lavaan 0.6-18 ended normally after 155 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 22
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1874.522 1249.041
## Degrees of freedom 70 70
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.501
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 655.180 436.563
## 0 1219.342 812.478
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.828 0.060 13.867 0.000 0.711 0.945 2.350 0.570
## sswk (.p2.) 1.975 0.141 13.997 0.000 1.699 2.252 5.608 0.897
## sspc (.p3.) 0.820 0.058 14.129 0.000 0.707 0.934 2.330 0.824
## math =~
## ssar (.p4.) 3.031 0.100 30.312 0.000 2.835 3.227 6.112 0.926
## ssmk (.p5.) 2.562 0.083 30.750 0.000 2.399 2.725 5.167 0.866
## ssmc (.p6.) 0.707 0.042 16.640 0.000 0.623 0.790 1.425 0.341
## electronic =~
## ssgs (.p7.) 0.595 0.033 18.020 0.000 0.530 0.659 1.211 0.293
## ssasi (.p8.) 1.308 0.061 21.513 0.000 1.189 1.427 2.664 0.731
## ssmc (.p9.) 0.910 0.048 19.002 0.000 0.816 1.004 1.853 0.443
## ssei (.10.) 1.312 0.061 21.635 0.000 1.193 1.431 2.672 0.798
## speed =~
## ssno (.11.) 0.503 0.014 36.679 0.000 0.476 0.529 0.723 0.861
## sscs (.12.) 0.451 0.013 35.445 0.000 0.426 0.476 0.649 0.752
## g =~
## verbal (.13.) 2.658 0.195 13.603 0.000 2.275 3.040 0.936 0.936
## math (.14.) 1.751 0.075 23.505 0.000 1.605 1.897 0.868 0.868
## elctrnc (.15.) 1.774 0.090 19.754 0.000 1.598 1.950 0.871 0.871
## speed (.16.) 1.035 0.039 26.312 0.000 0.958 1.113 0.719 0.719
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 15.775 0.089 178.033 0.000 15.601 15.949 15.775 3.823
## .sswk 27.503 0.136 202.254 0.000 27.237 27.770 27.503 4.397
## .sspc (.34.) 11.867 0.058 203.085 0.000 11.752 11.981 11.867 4.199
## .ssar (.35.) 18.158 0.146 124.591 0.000 17.872 18.443 18.158 2.750
## .ssmk 14.248 0.130 109.820 0.000 13.994 14.503 14.248 2.389
## .ssmc (.37.) 12.609 0.087 144.592 0.000 12.438 12.780 12.609 3.014
## .ssasi (.38.) 11.890 0.075 158.747 0.000 11.743 12.036 11.890 3.262
## .ssei 10.402 0.072 144.049 0.000 10.261 10.544 10.402 3.106
## .ssno (.40.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.564
## .sscs 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.643
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.400 0.201 26.897 0.000 5.007 5.794 5.400 0.317
## .sswk 7.679 0.479 16.025 0.000 6.740 8.619 7.679 0.196
## .sspc 2.559 0.116 22.141 0.000 2.333 2.786 2.559 0.320
## .ssar 6.227 0.471 13.214 0.000 5.304 7.151 6.227 0.143
## .ssmk 8.872 0.384 23.104 0.000 8.120 9.625 8.872 0.249
## .ssmc 8.042 0.275 29.251 0.000 7.503 8.580 8.042 0.459
## .ssasi 6.187 0.243 25.510 0.000 5.711 6.662 6.187 0.466
## .ssei 4.076 0.185 22.074 0.000 3.714 4.437 4.076 0.363
## .ssno 0.182 0.014 12.969 0.000 0.155 0.210 0.182 0.258
## .sscs 0.323 0.018 17.611 0.000 0.287 0.359 0.323 0.434
## .verbal 1.000 1.000 1.000 0.124 0.124
## .math 1.000 1.000 1.000 0.246 0.246
## .electronic 1.000 1.000 1.000 0.241 0.241
## .speed 1.000 1.000 1.000 0.483 0.483
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.828 0.060 13.867 0.000 0.711 0.945 2.687 0.585
## sswk (.p2.) 1.975 0.141 13.997 0.000 1.699 2.252 6.412 0.917
## sspc (.p3.) 0.820 0.058 14.129 0.000 0.707 0.934 2.664 0.841
## math =~
## ssar (.p4.) 3.031 0.100 30.312 0.000 2.835 3.227 6.746 0.935
## ssmk (.p5.) 2.562 0.083 30.750 0.000 2.399 2.725 5.703 0.877
## ssmc (.p6.) 0.707 0.042 16.640 0.000 0.623 0.790 1.573 0.332
## electronic =~
## ssgs (.p7.) 0.595 0.033 18.020 0.000 0.530 0.659 1.581 0.344
## ssasi (.p8.) 1.308 0.061 21.513 0.000 1.189 1.427 3.477 0.740
## ssmc (.p9.) 0.910 0.048 19.002 0.000 0.816 1.004 2.419 0.511
## ssei (.10.) 1.312 0.061 21.635 0.000 1.193 1.431 3.488 0.926
## speed =~
## ssno (.11.) 0.503 0.014 36.679 0.000 0.476 0.529 0.767 0.866
## sscs (.12.) 0.451 0.013 35.445 0.000 0.426 0.476 0.688 0.786
## g =~
## verbal (.13.) 2.658 0.195 13.603 0.000 2.275 3.040 0.948 0.948
## math (.14.) 1.751 0.075 23.505 0.000 1.605 1.897 0.911 0.911
## elctrnc (.15.) 1.774 0.090 19.754 0.000 1.598 1.950 0.773 0.773
## speed (.16.) 1.035 0.039 26.312 0.000 0.958 1.113 0.786 0.786
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 15.775 0.089 178.033 0.000 15.601 15.949 15.775 3.434
## .sswk 29.218 0.175 167.166 0.000 28.876 29.561 29.218 4.179
## .sspc (.34.) 11.867 0.058 203.085 0.000 11.752 11.981 11.867 3.746
## .ssar (.35.) 18.158 0.146 124.591 0.000 17.872 18.443 18.158 2.516
## .ssmk 13.205 0.148 89.461 0.000 12.916 13.495 13.205 2.031
## .ssmc (.37.) 12.609 0.087 144.592 0.000 12.438 12.780 12.609 2.661
## .ssasi (.38.) 11.890 0.075 158.747 0.000 11.743 12.036 11.890 2.531
## .ssei 7.744 0.171 45.275 0.000 7.409 8.079 7.744 2.055
## .ssno (.40.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.535
## .sscs 0.310 0.022 13.985 0.000 0.267 0.354 0.310 0.354
## .verbal -2.008 0.110 -18.298 0.000 -2.223 -1.793 -0.619 -0.619
## .math -0.091 0.070 -1.292 0.196 -0.228 0.047 -0.041 -0.041
## .elctrnc 3.731 0.165 22.623 0.000 3.407 4.054 1.404 1.404
## .speed -0.850 0.056 -15.120 0.000 -0.960 -0.739 -0.557 -0.557
## g 0.396 0.049 8.101 0.000 0.300 0.492 0.342 0.342
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.162 0.194 26.556 0.000 4.781 5.543 5.162 0.245
## .sswk 7.759 0.540 14.381 0.000 6.702 8.817 7.759 0.159
## .sspc 2.941 0.127 23.158 0.000 2.693 3.190 2.941 0.293
## .ssar 6.558 0.455 14.427 0.000 5.667 7.449 6.558 0.126
## .ssmk 9.753 0.401 24.337 0.000 8.967 10.538 9.753 0.231
## .ssmc 8.760 0.313 27.952 0.000 8.146 9.374 8.760 0.390
## .ssasi 9.978 0.399 24.982 0.000 9.195 10.761 9.978 0.452
## .ssei 2.028 0.185 10.980 0.000 1.666 2.390 2.028 0.143
## .ssno 0.196 0.014 14.384 0.000 0.169 0.223 0.196 0.250
## .sscs 0.293 0.018 16.624 0.000 0.259 0.328 0.293 0.383
## .verbal 1.069 0.204 5.230 0.000 0.669 1.470 0.101 0.101
## .math 0.841 0.082 10.250 0.000 0.680 1.002 0.170 0.170
## .electronic 2.847 0.296 9.626 0.000 2.268 3.427 0.403 0.403
## .speed 0.888 0.067 13.291 0.000 0.757 1.019 0.382 0.382
## g 1.341 0.062 21.775 0.000 1.220 1.462 1.000 1.000
strict<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~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 (= 7.112534e-14) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2087.094 80.000 0.000 0.955 0.090 0.054 282069.279 282405.578
Mc(strict)
## [1] 0.8496647
summary(strict, standardized=T, ci=T) # -.302 if ssmk is free and -.245 if ssar is free
## lavaan 0.6-18 ended normally after 114 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 32
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2087.094 1367.411
## Degrees of freedom 80 80
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.526
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 772.558 506.160
## 0 1314.536 861.251
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.806 0.059 13.596 0.000 0.690 0.922 2.323 0.565
## sswk (.p2.) 1.943 0.142 13.715 0.000 1.665 2.220 5.599 0.895
## sspc (.p3.) 0.810 0.058 13.935 0.000 0.696 0.924 2.335 0.816
## math =~
## ssar (.p4.) 3.006 0.100 30.192 0.000 2.811 3.202 6.119 0.924
## ssmk (.p5.) 2.542 0.083 30.570 0.000 2.379 2.705 5.174 0.861
## ssmc (.p6.) 0.667 0.041 16.123 0.000 0.586 0.748 1.357 0.322
## electronic =~
## ssgs (.p7.) 0.623 0.033 19.004 0.000 0.559 0.688 1.250 0.304
## ssasi (.p8.) 1.377 0.060 23.055 0.000 1.260 1.494 2.762 0.706
## ssmc (.p9.) 0.972 0.046 21.016 0.000 0.881 1.063 1.949 0.462
## ssei (.10.) 1.313 0.062 21.268 0.000 1.192 1.434 2.634 0.819
## speed =~
## ssno (.11.) 0.502 0.013 39.603 0.000 0.477 0.527 0.725 0.857
## sscs (.12.) 0.450 0.012 36.418 0.000 0.426 0.475 0.650 0.761
## g =~
## verbal (.13.) 2.703 0.203 13.327 0.000 2.306 3.101 0.938 0.938
## math (.14.) 1.773 0.077 23.167 0.000 1.623 1.923 0.871 0.871
## elctrnc (.15.) 1.739 0.086 20.168 0.000 1.570 1.908 0.867 0.867
## speed (.16.) 1.040 0.038 27.115 0.000 0.965 1.116 0.721 0.721
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 15.777 0.088 178.419 0.000 15.604 15.951 15.777 3.835
## .sswk 27.503 0.136 202.254 0.000 27.237 27.770 27.503 4.398
## .sspc (.34.) 11.866 0.059 202.571 0.000 11.751 11.981 11.866 4.145
## .ssar (.35.) 18.160 0.146 124.515 0.000 17.874 18.446 18.160 2.744
## .ssmk 14.248 0.130 109.820 0.000 13.994 14.503 14.248 2.372
## .ssmc (.37.) 12.589 0.087 145.397 0.000 12.419 12.758 12.589 2.984
## .ssasi (.38.) 11.920 0.075 158.619 0.000 11.773 12.067 11.920 3.046
## .ssei 10.402 0.072 144.049 0.000 10.261 10.544 10.402 3.235
## .ssno (.40.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.561
## .sscs 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.649
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.17.) 5.239 0.142 37.009 0.000 4.962 5.517 5.239 0.310
## .sswk (.18.) 7.750 0.379 20.471 0.000 7.008 8.492 7.750 0.198
## .sspc (.19.) 2.744 0.085 32.258 0.000 2.577 2.911 2.744 0.335
## .ssar (.20.) 6.366 0.347 18.369 0.000 5.687 7.045 6.366 0.145
## .ssmk (.21.) 9.318 0.294 31.718 0.000 8.742 9.894 9.318 0.258
## .ssmc (.22.) 8.160 0.210 38.798 0.000 7.747 8.572 8.160 0.459
## .ssasi (.23.) 7.684 0.240 31.970 0.000 7.213 8.155 7.684 0.502
## .ssei (.24.) 3.401 0.147 23.163 0.000 3.114 3.689 3.401 0.329
## .ssno (.25.) 0.189 0.011 17.492 0.000 0.168 0.211 0.189 0.265
## .sscs (.26.) 0.308 0.014 22.681 0.000 0.281 0.334 0.308 0.421
## .verbal 1.000 1.000 1.000 0.120 0.120
## .math 1.000 1.000 1.000 0.241 0.241
## .elctrnc 1.000 1.000 1.000 0.249 0.249
## .speed 1.000 1.000 1.000 0.480 0.480
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.806 0.059 13.596 0.000 0.690 0.922 2.662 0.577
## sswk (.p2.) 1.943 0.142 13.715 0.000 1.665 2.220 6.416 0.917
## sspc (.p3.) 0.810 0.058 13.935 0.000 0.696 0.924 2.675 0.850
## math =~
## ssar (.p4.) 3.006 0.100 30.192 0.000 2.811 3.202 6.744 0.937
## ssmk (.p5.) 2.542 0.083 30.570 0.000 2.379 2.705 5.702 0.882
## ssmc (.p6.) 0.667 0.041 16.123 0.000 0.586 0.748 1.496 0.318
## electronic =~
## ssgs (.p7.) 0.623 0.033 19.004 0.000 0.559 0.688 1.630 0.353
## ssasi (.p8.) 1.377 0.060 23.055 0.000 1.260 1.494 3.601 0.792
## ssmc (.p9.) 0.972 0.046 21.016 0.000 0.881 1.063 2.542 0.540
## ssei (.10.) 1.313 0.062 21.268 0.000 1.192 1.434 3.435 0.881
## speed =~
## ssno (.11.) 0.502 0.013 39.603 0.000 0.477 0.527 0.766 0.869
## sscs (.12.) 0.450 0.012 36.418 0.000 0.426 0.475 0.687 0.778
## g =~
## verbal (.13.) 2.703 0.203 13.327 0.000 2.306 3.101 0.944 0.944
## math (.14.) 1.773 0.077 23.167 0.000 1.623 1.923 0.911 0.911
## elctrnc (.15.) 1.739 0.086 20.168 0.000 1.570 1.908 0.767 0.767
## speed (.16.) 1.040 0.038 27.115 0.000 0.965 1.116 0.787 0.787
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 15.777 0.088 178.419 0.000 15.604 15.951 15.777 3.421
## .sswk 29.205 0.173 168.746 0.000 28.866 29.544 29.205 4.176
## .sspc (.34.) 11.866 0.059 202.571 0.000 11.751 11.981 11.866 3.771
## .ssar (.35.) 18.160 0.146 124.515 0.000 17.874 18.446 18.160 2.522
## .ssmk 13.208 0.148 89.500 0.000 12.919 13.497 13.208 2.042
## .ssmc (.37.) 12.589 0.087 145.397 0.000 12.419 12.758 12.589 2.674
## .ssasi (.38.) 11.920 0.075 158.619 0.000 11.773 12.067 11.920 2.623
## .ssei 8.043 0.156 51.572 0.000 7.737 8.349 8.043 2.063
## .ssno (.40.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.538
## .sscs 0.310 0.022 14.009 0.000 0.267 0.353 0.310 0.351
## .verbal -1.908 0.103 -18.441 0.000 -2.111 -1.705 -0.578 -0.578
## .math -0.012 0.067 -0.176 0.860 -0.142 0.119 -0.005 -0.005
## .elctrnc 3.595 0.150 23.992 0.000 3.301 3.889 1.375 1.375
## .speed -0.803 0.054 -14.794 0.000 -0.909 -0.696 -0.527 -0.527
## g 0.349 0.048 7.303 0.000 0.255 0.442 0.302 0.302
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.17.) 5.239 0.142 37.009 0.000 4.962 5.517 5.239 0.246
## .sswk (.18.) 7.750 0.379 20.471 0.000 7.008 8.492 7.750 0.158
## .sspc (.19.) 2.744 0.085 32.258 0.000 2.577 2.911 2.744 0.277
## .ssar (.20.) 6.366 0.347 18.369 0.000 5.687 7.045 6.366 0.123
## .ssmk (.21.) 9.318 0.294 31.718 0.000 8.742 9.894 9.318 0.223
## .ssmc (.22.) 8.160 0.210 38.798 0.000 7.747 8.572 8.160 0.368
## .ssasi (.23.) 7.684 0.240 31.970 0.000 7.213 8.155 7.684 0.372
## .ssei (.24.) 3.401 0.147 23.163 0.000 3.114 3.689 3.401 0.224
## .ssno (.25.) 0.189 0.011 17.492 0.000 0.168 0.211 0.189 0.244
## .sscs (.26.) 0.308 0.014 22.681 0.000 0.281 0.334 0.308 0.395
## .verbal 1.186 0.211 5.612 0.000 0.772 1.600 0.109 0.109
## .math 0.852 0.078 10.909 0.000 0.699 1.005 0.169 0.169
## .elctrnc 2.818 0.306 9.196 0.000 2.217 3.419 0.412 0.412
## .speed 0.884 0.060 14.790 0.000 0.767 1.001 0.380 0.380
## g 1.330 0.061 21.820 0.000 1.211 1.450 1.000 1.000
latent<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~1"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= 4.109730e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(latent, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2128.520 75.000 0.000 0.954 0.094 0.109 282120.704 282490.634
Mc(latent)
## [1] 0.8464689
summary(latent, standardized=T, ci=T) # -.180 if ssmk is free and -.118 if ssar is free
## lavaan 0.6-18 ended normally after 119 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 77
## Number of equality constraints 22
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2128.520 1424.065
## Degrees of freedom 75 75
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.495
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 798.277 534.079
## 0 1330.243 889.986
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.824 0.051 16.032 0.000 0.723 0.925 2.533 0.576
## sswk (.p2.) 1.964 0.121 16.197 0.000 1.726 2.202 6.037 0.908
## sspc (.p3.) 0.813 0.049 16.467 0.000 0.717 0.910 2.500 0.844
## math =~
## ssar (.p4.) 2.942 0.088 33.539 0.000 2.770 3.114 6.452 0.932
## ssmk (.p5.) 2.484 0.072 34.278 0.000 2.342 2.626 5.447 0.878
## ssmc (.p6.) 0.704 0.039 18.290 0.000 0.629 0.780 1.544 0.348
## electronic =~
## ssgs (.p7.) 0.829 0.032 25.762 0.000 0.766 0.892 1.423 0.324
## ssasi (.p8.) 1.801 0.051 35.109 0.000 1.700 1.901 3.092 0.783
## ssmc (.p9.) 1.245 0.049 25.214 0.000 1.148 1.342 2.138 0.481
## ssei (.10.) 1.853 0.043 43.113 0.000 1.768 1.937 3.181 0.855
## speed =~
## ssno (.11.) 0.490 0.011 45.238 0.000 0.469 0.512 0.746 0.868
## sscs (.12.) 0.439 0.010 43.184 0.000 0.419 0.459 0.668 0.761
## g =~
## verbal (.13.) 2.907 0.199 14.628 0.000 2.517 3.296 0.946 0.946
## math (.14.) 1.952 0.070 27.886 0.000 1.815 2.089 0.890 0.890
## elctrnc (.15.) 1.396 0.048 29.329 0.000 1.303 1.489 0.813 0.813
## speed (.16.) 1.146 0.039 29.680 0.000 1.070 1.221 0.753 0.753
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 15.765 0.089 177.697 0.000 15.592 15.939 15.765 3.584
## .sswk 27.503 0.136 202.254 0.000 27.237 27.770 27.503 4.139
## .sspc (.34.) 11.871 0.058 203.274 0.000 11.757 11.986 11.871 4.005
## .ssar (.35.) 18.157 0.146 124.576 0.000 17.871 18.442 18.157 2.624
## .ssmk 14.248 0.130 109.820 0.000 13.994 14.503 14.248 2.296
## .ssmc (.37.) 12.617 0.087 144.847 0.000 12.447 12.788 12.617 2.841
## .ssasi (.38.) 11.888 0.075 158.559 0.000 11.741 12.035 11.888 3.009
## .ssei 10.402 0.072 144.049 0.000 10.261 10.544 10.402 2.795
## .ssno (.40.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.552
## .sscs 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.632
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.362 0.200 26.773 0.000 4.969 5.754 5.362 0.277
## .sswk 7.715 0.466 16.557 0.000 6.801 8.628 7.715 0.175
## .sspc 2.533 0.114 22.144 0.000 2.308 2.757 2.533 0.288
## .ssar 6.253 0.462 13.550 0.000 5.349 7.158 6.253 0.131
## .ssmk 8.839 0.383 23.076 0.000 8.088 9.589 8.839 0.229
## .ssmc 7.989 0.277 28.805 0.000 7.446 8.533 7.989 0.405
## .ssasi 6.049 0.247 24.491 0.000 5.565 6.533 6.049 0.388
## .ssei 3.727 0.192 19.383 0.000 3.351 4.104 3.727 0.269
## .ssno 0.182 0.013 13.677 0.000 0.156 0.208 0.182 0.247
## .sscs 0.325 0.018 17.858 0.000 0.289 0.360 0.325 0.421
## .verbal 1.000 1.000 1.000 0.106 0.106
## .math 1.000 1.000 1.000 0.208 0.208
## .electronic 1.000 1.000 1.000 0.339 0.339
## .speed 1.000 1.000 1.000 0.432 0.432
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.824 0.051 16.032 0.000 0.723 0.925 2.533 0.579
## sswk (.p2.) 1.964 0.121 16.197 0.000 1.726 2.202 6.037 0.910
## sspc (.p3.) 0.813 0.049 16.467 0.000 0.717 0.910 2.500 0.823
## math =~
## ssar (.p4.) 2.942 0.088 33.539 0.000 2.770 3.114 6.452 0.931
## ssmk (.p5.) 2.484 0.072 34.278 0.000 2.342 2.626 5.447 0.866
## ssmc (.p6.) 0.704 0.039 18.290 0.000 0.629 0.780 1.544 0.340
## electronic =~
## ssgs (.p7.) 0.829 0.032 25.762 0.000 0.766 0.892 1.423 0.325
## ssasi (.p8.) 1.801 0.051 35.109 0.000 1.700 1.901 3.092 0.695
## ssmc (.p9.) 1.245 0.049 25.214 0.000 1.148 1.342 2.138 0.470
## ssei (.10.) 1.853 0.043 43.113 0.000 1.768 1.937 3.181 0.905
## speed =~
## ssno (.11.) 0.490 0.011 45.238 0.000 0.469 0.512 0.746 0.860
## sscs (.12.) 0.439 0.010 43.184 0.000 0.419 0.459 0.668 0.777
## g =~
## verbal (.13.) 2.907 0.199 14.628 0.000 2.517 3.296 0.946 0.946
## math (.14.) 1.952 0.070 27.886 0.000 1.815 2.089 0.890 0.890
## elctrnc (.15.) 1.396 0.048 29.329 0.000 1.303 1.489 0.813 0.813
## speed (.16.) 1.146 0.039 29.680 0.000 1.070 1.221 0.753 0.753
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 15.765 0.089 177.697 0.000 15.592 15.939 15.765 3.605
## .sswk 29.247 0.176 166.056 0.000 28.902 29.593 29.247 4.410
## .sspc (.34.) 11.871 0.058 203.274 0.000 11.757 11.986 11.871 3.905
## .ssar (.35.) 18.157 0.146 124.576 0.000 17.871 18.442 18.157 2.619
## .ssmk 13.206 0.147 89.553 0.000 12.917 13.495 13.206 2.100
## .ssmc (.37.) 12.617 0.087 144.847 0.000 12.447 12.788 12.617 2.776
## .ssasi (.38.) 11.888 0.075 158.559 0.000 11.741 12.035 11.888 2.673
## .ssei 7.597 0.171 44.326 0.000 7.261 7.933 7.597 2.160
## .ssno (.40.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.547
## .sscs 0.310 0.022 13.980 0.000 0.266 0.353 0.310 0.360
## .verbal -1.501 0.068 -22.086 0.000 -1.634 -1.368 -0.488 -0.488
## .math 0.269 0.049 5.488 0.000 0.173 0.366 0.123 0.123
## .elctrnc 2.967 0.106 27.956 0.000 2.759 3.175 1.728 1.728
## .speed -0.657 0.047 -13.987 0.000 -0.750 -0.565 -0.432 -0.432
## g 0.180 0.036 5.004 0.000 0.110 0.251 0.180 0.180
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.143 0.194 26.564 0.000 4.764 5.523 5.143 0.269
## .sswk 7.530 0.499 15.105 0.000 6.553 8.508 7.530 0.171
## .sspc 2.988 0.129 23.150 0.000 2.735 3.241 2.988 0.323
## .ssar 6.439 0.442 14.562 0.000 5.572 7.305 6.439 0.134
## .ssmk 9.879 0.403 24.502 0.000 9.088 10.669 9.879 0.250
## .ssmc 8.926 0.305 29.226 0.000 8.328 9.525 8.926 0.432
## .ssasi 10.221 0.389 26.283 0.000 9.459 10.983 10.221 0.517
## .ssei 2.246 0.171 13.151 0.000 1.911 2.581 2.246 0.182
## .ssno 0.195 0.013 14.579 0.000 0.169 0.221 0.195 0.260
## .sscs 0.292 0.018 16.461 0.000 0.258 0.327 0.292 0.396
## .verbal 1.000 1.000 1.000 0.106 0.106
## .math 1.000 1.000 1.000 0.208 0.208
## .electronic 1.000 1.000 1.000 0.339 0.339
## .speed 1.000 1.000 1.000 0.432 0.432
## g 1.000 1.000 1.000 1.000 1.000
latent2<-cfa(hof.lv, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~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 (= 2.319702e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(latent2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1881.387 73.000 0.000 0.959 0.090 0.047 281877.572 282260.953
Mc(latent2)
## [1] 0.8634799
summary(latent2, standardized=T, ci=T) # -.334 if ssmk is free and -.292 if ssar is free
## lavaan 0.6-18 ended normally after 136 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 79
## Number of equality constraints 22
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1881.387 1257.115
## Degrees of freedom 73 73
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.497
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 657.970 439.646
## 0 1223.417 817.469
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.831 0.050 16.708 0.000 0.734 0.929 2.356 0.570
## sswk (.p2.) 1.984 0.118 16.850 0.000 1.753 2.215 5.623 0.897
## sspc (.p3.) 0.824 0.048 17.151 0.000 0.730 0.918 2.335 0.825
## math =~
## ssar (.p4.) 2.928 0.086 33.909 0.000 2.759 3.097 6.061 0.923
## ssmk (.p5.) 2.476 0.071 34.711 0.000 2.336 2.615 5.125 0.865
## ssmc (.p6.) 0.682 0.039 17.408 0.000 0.605 0.758 1.411 0.337
## electronic =~
## ssgs (.p7.) 0.598 0.033 18.134 0.000 0.533 0.662 1.213 0.293
## ssasi (.p8.) 1.315 0.061 21.727 0.000 1.197 1.434 2.670 0.732
## ssmc (.p9.) 0.916 0.048 19.181 0.000 0.822 1.009 1.859 0.445
## ssei (.10.) 1.320 0.060 21.864 0.000 1.202 1.439 2.680 0.799
## speed =~
## ssno (.11.) 0.489 0.011 45.188 0.000 0.468 0.510 0.713 0.856
## sscs (.12.) 0.439 0.010 43.382 0.000 0.419 0.458 0.640 0.747
## g =~
## verbal (.13.) 2.652 0.171 15.508 0.000 2.317 2.987 0.936 0.936
## math (.14.) 1.813 0.072 25.121 0.000 1.671 1.954 0.876 0.876
## elctrnc (.15.) 1.766 0.088 19.967 0.000 1.593 1.939 0.870 0.870
## speed (.16.) 1.062 0.038 27.673 0.000 0.986 1.137 0.728 0.728
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 15.776 0.089 177.974 0.000 15.602 15.949 15.776 3.818
## .sswk 27.503 0.136 202.254 0.000 27.237 27.770 27.503 4.386
## .sspc (.34.) 11.866 0.058 203.103 0.000 11.752 11.981 11.866 4.193
## .ssar (.35.) 18.158 0.146 124.579 0.000 17.873 18.444 18.158 2.766
## .ssmk 14.248 0.130 109.820 0.000 13.994 14.503 14.248 2.404
## .ssmc (.37.) 12.607 0.087 144.690 0.000 12.437 12.778 12.607 3.015
## .ssasi (.38.) 11.890 0.075 158.665 0.000 11.743 12.037 11.890 3.258
## .ssei 10.402 0.072 144.049 0.000 10.261 10.544 10.402 3.101
## .ssno (.40.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.568
## .sscs 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.648
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.124 0.124
## .math 1.000 1.000 1.000 0.233 0.233
## .speed 1.000 1.000 1.000 0.470 0.470
## .ssgs 5.402 0.201 26.911 0.000 5.009 5.796 5.402 0.316
## .sswk 7.708 0.464 16.623 0.000 6.799 8.616 7.708 0.196
## .sspc 2.558 0.115 22.174 0.000 2.332 2.784 2.558 0.319
## .ssar 6.363 0.459 13.852 0.000 5.463 7.263 6.363 0.148
## .ssmk 8.869 0.380 23.343 0.000 8.124 9.613 8.869 0.252
## .ssmc 8.040 0.275 29.238 0.000 7.501 8.579 8.040 0.460
## .ssasi 6.190 0.243 25.525 0.000 5.715 6.666 6.190 0.465
## .ssei 4.076 0.185 22.074 0.000 3.714 4.438 4.076 0.362
## .ssno 0.186 0.013 13.982 0.000 0.160 0.212 0.186 0.268
## .sscs 0.324 0.018 17.812 0.000 0.288 0.359 0.324 0.442
## .electronic 1.000 1.000 1.000 0.243 0.243
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.831 0.050 16.708 0.000 0.734 0.929 2.682 0.584
## sswk (.p2.) 1.984 0.118 16.850 0.000 1.753 2.215 6.401 0.918
## sspc (.p3.) 0.824 0.048 17.151 0.000 0.730 0.918 2.658 0.840
## math =~
## ssar (.p4.) 2.928 0.086 33.909 0.000 2.759 3.097 6.801 0.937
## ssmk (.p5.) 2.476 0.071 34.711 0.000 2.336 2.615 5.750 0.879
## ssmc (.p6.) 0.682 0.039 17.408 0.000 0.605 0.758 1.583 0.334
## electronic =~
## ssgs (.p7.) 0.598 0.033 18.134 0.000 0.533 0.662 1.576 0.343
## ssasi (.p8.) 1.315 0.061 21.727 0.000 1.197 1.434 3.469 0.739
## ssmc (.p9.) 0.916 0.048 19.181 0.000 0.822 1.009 2.415 0.510
## ssei (.10.) 1.320 0.060 21.864 0.000 1.202 1.439 3.482 0.926
## speed =~
## ssno (.11.) 0.489 0.011 45.188 0.000 0.468 0.510 0.775 0.870
## sscs (.12.) 0.439 0.010 43.382 0.000 0.419 0.458 0.695 0.789
## g =~
## verbal (.13.) 2.652 0.171 15.508 0.000 2.317 2.987 0.951 0.951
## math (.14.) 1.813 0.072 25.121 0.000 1.671 1.954 0.903 0.903
## elctrnc (.15.) 1.766 0.088 19.967 0.000 1.593 1.939 0.775 0.775
## speed (.16.) 1.062 0.038 27.673 0.000 0.986 1.137 0.775 0.775
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 15.776 0.089 177.974 0.000 15.602 15.949 15.776 3.437
## .sswk 29.217 0.175 166.841 0.000 28.874 29.560 29.217 4.189
## .sspc (.34.) 11.866 0.058 203.103 0.000 11.752 11.981 11.866 3.750
## .ssar (.35.) 18.158 0.146 124.579 0.000 17.873 18.444 18.158 2.503
## .ssmk 13.205 0.148 89.463 0.000 12.916 13.495 13.205 2.018
## .ssmc (.37.) 12.607 0.087 144.690 0.000 12.437 12.778 12.607 2.661
## .ssasi (.38.) 11.890 0.075 158.665 0.000 11.743 12.037 11.890 2.534
## .ssei 7.741 0.171 45.207 0.000 7.405 8.077 7.741 2.058
## .ssno (.40.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.532
## .sscs 0.310 0.022 13.985 0.000 0.267 0.353 0.310 0.352
## .verbal -1.976 0.102 -19.460 0.000 -2.175 -1.777 -0.612 -0.612
## .math -0.076 0.066 -1.165 0.244 -0.205 0.052 -0.033 -0.033
## .elctrnc 3.726 0.164 22.746 0.000 3.405 4.047 1.413 1.413
## .speed -0.862 0.055 -15.802 0.000 -0.969 -0.755 -0.544 -0.544
## g 0.386 0.043 8.926 0.000 0.301 0.471 0.334 0.334
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.096 0.096
## .math 1.000 1.000 1.000 0.185 0.185
## .speed 1.000 1.000 1.000 0.399 0.399
## .ssgs 5.166 0.194 26.588 0.000 4.785 5.546 5.166 0.245
## .sswk 7.686 0.514 14.948 0.000 6.678 8.694 7.686 0.158
## .sspc 2.948 0.127 23.146 0.000 2.698 3.198 2.948 0.294
## .ssar 6.389 0.447 14.302 0.000 5.514 7.265 6.389 0.121
## .ssmk 9.764 0.406 24.023 0.000 8.967 10.561 9.764 0.228
## .ssmc 8.765 0.313 28.010 0.000 8.152 9.379 8.765 0.390
## .ssasi 9.980 0.399 25.005 0.000 9.198 10.763 9.980 0.453
## .ssei 2.026 0.184 11.015 0.000 1.665 2.386 2.026 0.143
## .ssno 0.192 0.013 14.370 0.000 0.166 0.218 0.192 0.243
## .sscs 0.293 0.018 16.429 0.000 0.258 0.327 0.293 0.377
## .electronic 2.782 0.286 9.723 0.000 2.221 3.343 0.400 0.400
## g 1.338 0.062 21.522 0.000 1.216 1.460 1.000 1.000
weak<-cfa(hof.weak, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~1"))
fitMeasures(weak, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1881.387 74.000 0.000 0.959 0.089 0.047 281875.572 282252.227
Mc(weak)
## [1] 0.86355
summary(weak, standardized=T, ci=T) # -.298
## lavaan 0.6-18 ended normally after 138 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 78
## Number of equality constraints 22
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1881.387 1274.335
## Degrees of freedom 74 74
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.476
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 657.970 445.668
## 0 1223.417 828.667
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.831 0.050 16.708 0.000 0.734 0.929 2.356 0.570
## sswk (.p2.) 1.984 0.118 16.851 0.000 1.753 2.215 5.623 0.897
## sspc (.p3.) 0.824 0.048 17.151 0.000 0.730 0.918 2.335 0.825
## math =~
## ssar (.p4.) 2.928 0.086 33.909 0.000 2.759 3.097 6.061 0.923
## ssmk (.p5.) 2.476 0.071 34.712 0.000 2.336 2.615 5.125 0.865
## ssmc (.p6.) 0.682 0.039 17.408 0.000 0.605 0.758 1.411 0.337
## electronic =~
## ssgs (.p7.) 0.598 0.033 18.134 0.000 0.533 0.662 1.213 0.293
## ssasi (.p8.) 1.315 0.061 21.727 0.000 1.197 1.434 2.670 0.732
## ssmc (.p9.) 0.916 0.048 19.181 0.000 0.822 1.009 1.859 0.445
## ssei (.10.) 1.320 0.060 21.864 0.000 1.202 1.439 2.680 0.799
## speed =~
## ssno (.11.) 0.489 0.011 45.188 0.000 0.468 0.510 0.713 0.856
## sscs (.12.) 0.439 0.010 43.382 0.000 0.419 0.458 0.640 0.747
## g =~
## verbal (.13.) 2.652 0.171 15.508 0.000 2.317 2.987 0.936 0.936
## math (.14.) 1.813 0.072 25.121 0.000 1.671 1.954 0.876 0.876
## elctrnc (.15.) 1.766 0.088 19.967 0.000 1.593 1.939 0.870 0.870
## speed (.16.) 1.062 0.038 27.673 0.000 0.986 1.137 0.728 0.728
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.33.) 15.776 0.089 177.974 0.000 15.602 15.949 15.776 3.818
## .sswk 27.503 0.136 202.254 0.000 27.237 27.770 27.503 4.386
## .sspc (.35.) 11.866 0.058 203.103 0.000 11.752 11.981 11.866 4.193
## .ssar (.36.) 18.158 0.146 124.579 0.000 17.873 18.444 18.158 2.766
## .ssmk 14.248 0.130 109.820 0.000 13.994 14.503 14.248 2.404
## .ssmc (.38.) 12.607 0.087 144.690 0.000 12.437 12.778 12.607 3.015
## .ssasi (.39.) 11.890 0.075 158.665 0.000 11.743 12.037 11.890 3.258
## .ssei 10.402 0.072 144.049 0.000 10.261 10.544 10.402 3.101
## .ssno (.41.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.568
## .sscs 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.648
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.124 0.124
## .math 1.000 1.000 1.000 0.233 0.233
## .speed 1.000 1.000 1.000 0.470 0.470
## .ssgs 5.402 0.201 26.911 0.000 5.009 5.796 5.402 0.316
## .sswk 7.708 0.464 16.623 0.000 6.799 8.616 7.708 0.196
## .sspc 2.558 0.115 22.174 0.000 2.332 2.784 2.558 0.319
## .ssar 6.363 0.459 13.852 0.000 5.463 7.263 6.363 0.148
## .ssmk 8.869 0.380 23.343 0.000 8.124 9.613 8.869 0.252
## .ssmc 8.040 0.275 29.238 0.000 7.501 8.579 8.040 0.460
## .ssasi 6.190 0.243 25.525 0.000 5.715 6.666 6.190 0.465
## .ssei 4.076 0.185 22.074 0.000 3.714 4.438 4.076 0.362
## .ssno 0.186 0.013 13.982 0.000 0.160 0.212 0.186 0.268
## .sscs 0.324 0.018 17.812 0.000 0.288 0.359 0.324 0.442
## .electronic 1.000 1.000 1.000 0.243 0.243
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.831 0.050 16.708 0.000 0.734 0.929 2.682 0.584
## sswk (.p2.) 1.984 0.118 16.851 0.000 1.753 2.215 6.401 0.918
## sspc (.p3.) 0.824 0.048 17.151 0.000 0.730 0.918 2.658 0.840
## math =~
## ssar (.p4.) 2.928 0.086 33.909 0.000 2.759 3.097 6.801 0.937
## ssmk (.p5.) 2.476 0.071 34.712 0.000 2.336 2.615 5.750 0.879
## ssmc (.p6.) 0.682 0.039 17.408 0.000 0.605 0.758 1.583 0.334
## electronic =~
## ssgs (.p7.) 0.598 0.033 18.134 0.000 0.533 0.662 1.576 0.343
## ssasi (.p8.) 1.315 0.061 21.727 0.000 1.197 1.434 3.469 0.739
## ssmc (.p9.) 0.916 0.048 19.181 0.000 0.822 1.009 2.415 0.510
## ssei (.10.) 1.320 0.060 21.864 0.000 1.202 1.439 3.482 0.926
## speed =~
## ssno (.11.) 0.489 0.011 45.188 0.000 0.468 0.510 0.775 0.870
## sscs (.12.) 0.439 0.010 43.382 0.000 0.419 0.458 0.695 0.789
## g =~
## verbal (.13.) 2.652 0.171 15.508 0.000 2.317 2.987 0.951 0.951
## math (.14.) 1.813 0.072 25.121 0.000 1.671 1.954 0.903 0.903
## elctrnc (.15.) 1.766 0.088 19.967 0.000 1.593 1.939 0.775 0.775
## speed (.16.) 1.062 0.038 27.673 0.000 0.986 1.137 0.775 0.775
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.33.) 15.776 0.089 177.974 0.000 15.602 15.949 15.776 3.437
## .sswk 29.217 0.175 166.841 0.000 28.874 29.560 29.217 4.189
## .sspc (.35.) 11.866 0.058 203.103 0.000 11.752 11.981 11.866 3.750
## .ssar (.36.) 18.158 0.146 124.579 0.000 17.873 18.444 18.158 2.503
## .ssmk 13.205 0.148 89.463 0.000 12.916 13.495 13.205 2.018
## .ssmc (.38.) 12.607 0.087 144.690 0.000 12.437 12.778 12.607 2.661
## .ssasi (.39.) 11.890 0.075 158.665 0.000 11.743 12.037 11.890 2.534
## .ssei 7.741 0.171 45.207 0.000 7.405 8.077 7.741 2.058
## .ssno (.41.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.532
## .sscs 0.310 0.022 13.985 0.000 0.267 0.353 0.310 0.352
## .verbal -1.864 0.147 -12.678 0.000 -2.152 -1.576 -0.578 -0.578
## .elctrnc 3.800 0.200 19.012 0.000 3.408 4.192 1.441 1.441
## .speed -0.817 0.047 -17.220 0.000 -0.910 -0.724 -0.516 -0.516
## g 0.344 0.039 8.719 0.000 0.267 0.421 0.298 0.298
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.096 0.096
## .math 1.000 1.000 1.000 0.185 0.185
## .speed 1.000 1.000 1.000 0.399 0.399
## .ssgs 5.166 0.194 26.588 0.000 4.785 5.546 5.166 0.245
## .sswk 7.686 0.514 14.948 0.000 6.678 8.694 7.686 0.158
## .sspc 2.948 0.127 23.146 0.000 2.698 3.198 2.948 0.294
## .ssar 6.389 0.447 14.302 0.000 5.514 7.265 6.389 0.121
## .ssmk 9.764 0.406 24.023 0.000 8.967 10.561 9.764 0.228
## .ssmc 8.765 0.313 28.010 0.000 8.152 9.379 8.765 0.390
## .ssasi 9.980 0.399 25.005 0.000 9.198 10.763 9.980 0.453
## .ssei 2.026 0.184 11.015 0.000 1.665 2.386 2.026 0.143
## .ssno 0.192 0.013 14.370 0.000 0.166 0.218 0.192 0.243
## .sscs 0.293 0.018 16.429 0.000 0.258 0.327 0.293 0.377
## .electronic 2.782 0.286 9.723 0.000 2.221 3.343 0.400 0.400
## g 1.338 0.062 21.522 0.000 1.216 1.460 1.000 1.000
standardizedSolution(weak) # get the correct SEs for standardized solution
## lhs op rhs group label est.std se z pvalue ci.lower ci.upper
## 1 verbal =~ ssgs 1 .p1. 0.570 0.011 50.979 0 0.548 0.592
## 2 verbal =~ sswk 1 .p2. 0.897 0.007 132.083 0 0.883 0.910
## 3 verbal =~ sspc 1 .p3. 0.825 0.007 110.601 0 0.810 0.840
## 4 math =~ ssar 1 .p4. 0.923 0.006 159.775 0 0.912 0.935
## 5 math =~ ssmk 1 .p5. 0.865 0.006 135.627 0 0.852 0.877
## 6 math =~ ssmc 1 .p6. 0.337 0.016 21.472 0 0.307 0.368
## 7 electronic =~ ssgs 1 .p7. 0.293 0.010 29.416 0 0.274 0.313
## 8 electronic =~ ssasi 1 .p8. 0.732 0.010 70.115 0 0.711 0.752
## 9 electronic =~ ssmc 1 .p9. 0.445 0.014 30.682 0 0.416 0.473
## 10 electronic =~ ssei 1 .p10. 0.799 0.010 79.128 0 0.779 0.818
## 11 speed =~ ssno 1 .p11. 0.856 0.010 81.704 0 0.835 0.876
## 12 speed =~ sscs 1 .p12. 0.747 0.013 59.673 0 0.723 0.772
## 13 g =~ verbal 1 .p13. 0.936 0.008 124.584 0 0.921 0.950
## 14 g =~ math 1 .p14. 0.876 0.008 107.649 0 0.860 0.892
## 15 g =~ electronic 1 .p15. 0.870 0.011 82.243 0 0.849 0.891
## 16 g =~ speed 1 .p16. 0.728 0.012 58.858 0 0.704 0.752
## 17 verbal ~~ verbal 1 0.124 0.014 8.857 0 0.097 0.152
## 18 math ~~ math 1 0.233 0.014 16.384 0 0.205 0.261
## 19 speed ~~ speed 1 0.470 0.018 26.114 0 0.435 0.505
## 20 math ~1 1 0.000 0.000 NA NA 0.000 0.000
## 21 ssgs ~~ ssgs 1 0.316 0.012 26.942 0 0.293 0.339
## 22 sswk ~~ sswk 1 0.196 0.012 16.100 0 0.172 0.220
## 23 sspc ~~ sspc 1 0.319 0.012 25.957 0 0.295 0.344
## 24 ssar ~~ ssar 1 0.148 0.011 13.835 0 0.127 0.169
## 25 ssmk ~~ ssmk 1 0.252 0.011 22.900 0 0.231 0.274
## 26 ssmc ~~ ssmc 1 0.460 0.013 35.702 0 0.435 0.485
## 27 ssasi ~~ ssasi 1 0.465 0.015 30.448 0 0.435 0.495
## 28 ssei ~~ ssei 1 0.362 0.016 22.459 0 0.331 0.394
## 29 ssno ~~ ssno 1 0.268 0.018 14.952 0 0.233 0.303
## 30 sscs ~~ sscs 1 0.442 0.019 23.602 0 0.405 0.478
## 31 electronic ~~ electronic 1 0.243 0.018 13.184 0 0.207 0.279
## 32 g ~~ g 1 1.000 0.000 NA NA 1.000 1.000
## 33 ssgs ~1 1 .p33. 3.818 0.056 67.642 0 3.707 3.928
## 34 sswk ~1 1 4.386 0.081 54.482 0 4.228 4.544
## 35 sspc ~1 1 .p35. 4.193 0.085 49.622 0 4.027 4.359
## 36 ssar ~1 1 .p36. 2.766 0.040 69.194 0 2.687 2.844
## 37 ssmk ~1 1 2.404 0.033 72.365 0 2.339 2.469
## 38 ssmc ~1 1 .p38. 3.015 0.042 72.171 0 2.933 3.097
## 39 ssasi ~1 1 .p39. 3.258 0.047 68.614 0 3.165 3.351
## 40 ssei ~1 1 3.101 0.045 68.621 0 3.012 3.189
## 41 ssno ~1 1 .p41. 0.568 0.025 23.032 0 0.520 0.617
## 42 sscs ~1 1 0.648 0.026 25.076 0 0.597 0.698
## 43 verbal ~1 1 0.000 0.000 NA NA 0.000 0.000
## 44 electronic ~1 1 0.000 0.000 NA NA 0.000 0.000
## 45 speed ~1 1 0.000 0.000 NA NA 0.000 0.000
## 46 g ~1 1 0.000 0.000 NA NA 0.000 0.000
## 47 verbal =~ ssgs 2 .p1. 0.584 0.010 56.315 0 0.564 0.605
## 48 verbal =~ sswk 2 .p2. 0.918 0.006 160.107 0 0.906 0.929
## 49 verbal =~ sspc 2 .p3. 0.840 0.008 111.188 0 0.825 0.855
## 50 math =~ ssar 2 .p4. 0.937 0.005 203.818 0 0.928 0.946
## 51 math =~ ssmk 2 .p5. 0.879 0.006 158.005 0 0.868 0.890
## 52 math =~ ssmc 2 .p6. 0.334 0.016 21.530 0 0.304 0.365
## 53 electronic =~ ssgs 2 .p7. 0.343 0.011 30.650 0 0.321 0.365
## 54 electronic =~ ssasi 2 .p8. 0.739 0.011 64.980 0 0.717 0.762
## 55 electronic =~ ssmc 2 .p9. 0.510 0.017 29.481 0 0.476 0.544
## 56 electronic =~ ssei 2 .p10. 0.926 0.007 135.672 0 0.912 0.939
## 57 speed =~ ssno 2 .p11. 0.870 0.009 92.506 0 0.852 0.889
## 58 speed =~ sscs 2 .p12. 0.789 0.013 63.090 0 0.764 0.814
## 59 g =~ verbal 2 .p13. 0.951 0.006 153.916 0 0.939 0.963
## 60 g =~ math 2 .p14. 0.903 0.006 153.488 0 0.891 0.914
## 61 g =~ electronic 2 .p15. 0.775 0.013 60.897 0 0.750 0.800
## 62 g =~ speed 2 .p16. 0.775 0.011 71.701 0 0.754 0.797
## 63 verbal ~~ verbal 2 0.096 0.012 8.178 0 0.073 0.119
## 64 math ~~ math 2 0.185 0.011 17.460 0 0.165 0.206
## 65 speed ~~ speed 2 0.399 0.017 23.777 0 0.366 0.432
## 66 math ~1 2 0.000 0.000 NA NA 0.000 0.000
## 67 ssgs ~~ ssgs 2 0.245 0.010 25.060 0 0.226 0.264
## 68 sswk ~~ sswk 2 0.158 0.011 15.018 0 0.137 0.179
## 69 sspc ~~ sspc 2 0.294 0.013 23.203 0 0.270 0.319
## 70 ssar ~~ ssar 2 0.121 0.009 14.076 0 0.104 0.138
## 71 ssmk ~~ ssmk 2 0.228 0.010 23.329 0 0.209 0.247
## 72 ssmc ~~ ssmc 2 0.390 0.014 28.205 0 0.363 0.417
## 73 ssasi ~~ ssasi 2 0.453 0.017 26.944 0 0.420 0.486
## 74 ssei ~~ ssei 2 0.143 0.013 11.335 0 0.118 0.168
## 75 ssno ~~ ssno 2 0.243 0.016 14.808 0 0.210 0.275
## 76 sscs ~~ sscs 2 0.377 0.020 19.126 0 0.339 0.416
## 77 electronic ~~ electronic 2 0.400 0.020 20.300 0 0.361 0.439
## 78 g ~~ g 2 1.000 0.000 NA NA 1.000 1.000
## 79 ssgs ~1 2 .p33. 3.437 0.049 70.706 0 3.342 3.532
## 80 sswk ~1 2 4.189 0.071 58.720 0 4.049 4.328
## 81 sspc ~1 2 .p35. 3.750 0.062 60.056 0 3.628 3.873
## 82 ssar ~1 2 .p36. 2.503 0.032 78.792 0 2.440 2.565
## 83 ssmk ~1 2 2.018 0.028 72.320 0 1.963 2.072
## 84 ssmc ~1 2 .p38. 2.661 0.035 76.649 0 2.593 2.729
## 85 ssasi ~1 2 .p39. 2.534 0.034 74.053 0 2.467 2.601
## 86 ssei ~1 2 2.058 0.053 38.766 0 1.954 2.162
## 87 ssno ~1 2 .p41. 0.532 0.021 24.769 0 0.490 0.575
## 88 sscs ~1 2 0.352 0.026 13.446 0 0.301 0.403
## 89 verbal ~1 2 -0.578 0.027 -21.740 0 -0.630 -0.526
## 90 electronic ~1 2 1.441 0.054 26.679 0 1.335 1.547
## [ reached 'max' / getOption("max.print") -- omitted 2 rows ]
tests<-lavTestLRT(configural, metric, scalar2, latent2, weak)
Td=tests[2:5,"Chisq diff"]
Td
## [1] 1.175285e+02 2.375682e+01 4.907002e+00 -1.617550e-05
dfd=tests[2:5,"Df diff"]
dfd
## [1] 11 1 3 1
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-3067+ 3094 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
## Warning in sqrt((ld) * G/(N - G)): NaNs produced
RMSEAD
## [1] 0.05607851 0.08596382 0.01436729 NaN
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04716406 0.06545511
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.05818692 0.11746334
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] NA 0.0363566
RMSEA.CI(T=Td[4],df=dfd[4],N=N,G=2)
## [1] NA NA
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.872 0.255 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 0.982 0.939 0.668 0.250
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
## 0.821 0.708 0.002 0.000 0.000 0.000
round(pvals(T=Td[4],df=dfd[4],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 0 0 0 0 0 0
tests<-lavTestLRT(configural, metric, scalar2, latent)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 117.52851 23.75682 180.21631
dfd=tests[2:4,"Df diff"]
dfd
## [1] 11 1 5
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-3067+ 3094 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.05607851 0.08596382 0.10667488
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.05818692 0.11746334
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.09363226 0.12029312
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 0.982 0.939 0.668 0.250
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 1.000 1.000 0.805
tests<-lavTestLRT(configural, metric, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 117.52851 23.75682 124.66844
dfd=tests[2:4,"Df diff"]
dfd
## [1] 11 1 10
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-3067+ 3094 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.05607851 0.08596382 0.06102136
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04716406 0.06545511
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.05818692 0.11746334
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.05170305 0.07081529
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 0.872 0.255 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 0.982 0.939 0.668 0.250
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 0.974 0.587 0.001 0.000
tests<-lavTestLRT(configural, metric, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 117.5285 684.8267
dfd=tests[2:3,"Df diff"]
dfd
## [1] 11 5
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-3067+ 3094 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.05607851 0.21012319
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04716406 0.06545511
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.1969855 0.2235338
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 0.872 0.255 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
hof.age<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
math~0*1
g ~age
'
hof.ageq<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
math~0*1
g ~c(a,a)*age
'
hof.age2<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
math~0*1
g ~age + age2
'
hof.age2q<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
math~0*1
g ~c(a,a)*age + c(b,b)*age2
'
sem.age<-sem(hof.age, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~1"))
fitMeasures(sem.age, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 2599.370 92.000 0.000 0.945 0.094 0.052 0.441 281593.141 281983.249
Mc(sem.age)
## [1] 0.8158537
summary(sem.age, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 140 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 80
## Number of equality constraints 22
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2599.370 1746.704
## Degrees of freedom 92 92
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.488
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1050.250 705.739
## 0 1549.119 1040.965
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.808 0.049 16.530 0.000 0.712 0.904 2.351 0.569
## sswk (.p2.) 1.934 0.117 16.594 0.000 1.705 2.162 5.627 0.898
## sspc (.p3.) 0.800 0.047 16.870 0.000 0.707 0.893 2.329 0.823
## math =~
## ssar (.p4.) 3.028 0.083 36.702 0.000 2.867 3.190 6.078 0.925
## ssmk (.p5.) 2.549 0.068 37.590 0.000 2.417 2.682 5.117 0.863
## ssmc (.p6.) 0.705 0.039 17.922 0.000 0.628 0.782 1.414 0.338
## electronic =~
## ssgs (.p7.) 0.582 0.033 17.810 0.000 0.518 0.646 1.208 0.292
## ssasi (.p8.) 1.286 0.061 21.170 0.000 1.167 1.405 2.669 0.731
## ssmc (.p9.) 0.894 0.048 18.809 0.000 0.801 0.987 1.856 0.444
## ssei (.10.) 1.293 0.061 21.285 0.000 1.174 1.412 2.684 0.800
## speed =~
## ssno (.11.) 0.490 0.011 45.466 0.000 0.469 0.511 0.712 0.853
## sscs (.12.) 0.442 0.010 43.623 0.000 0.422 0.462 0.641 0.749
## g =~
## verbal (.13.) 2.683 0.172 15.576 0.000 2.345 3.021 0.939 0.939
## math (.14.) 1.708 0.067 25.660 0.000 1.578 1.839 0.867 0.867
## elctrnc (.15.) 1.786 0.091 19.725 0.000 1.608 1.963 0.876 0.876
## speed (.16.) 1.033 0.038 26.980 0.000 0.958 1.108 0.725 0.725
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.084 0.010 8.007 0.000 0.063 0.104 0.082 0.191
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.35.) 15.837 0.088 179.279 0.000 15.664 16.010 15.837 3.832
## .sswk 27.598 0.133 206.939 0.000 27.337 27.860 27.598 4.405
## .sspc (.37.) 11.905 0.058 204.882 0.000 11.791 12.019 11.905 4.209
## .ssar (.38.) 18.252 0.147 124.305 0.000 17.965 18.540 18.252 2.779
## .ssmk 14.328 0.132 108.316 0.000 14.069 14.588 14.328 2.416
## .ssmc (.40.) 12.659 0.087 145.188 0.000 12.488 12.830 12.659 3.026
## .ssasi (.41.) 11.930 0.074 160.988 0.000 11.785 12.076 11.930 3.268
## .ssei 10.445 0.071 147.381 0.000 10.306 10.584 10.445 3.113
## .ssno (.43.) 0.483 0.018 27.053 0.000 0.448 0.518 0.483 0.579
## .sscs 0.563 0.018 30.993 0.000 0.527 0.599 0.563 0.658
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.118 0.118
## .math 1.000 1.000 1.000 0.248 0.248
## .speed 1.000 1.000 1.000 0.475 0.475
## .ssgs 5.414 0.201 26.986 0.000 5.021 5.807 5.414 0.317
## .sswk 7.579 0.461 16.455 0.000 6.677 8.482 7.579 0.193
## .sspc 2.576 0.116 22.229 0.000 2.349 2.803 2.576 0.322
## .ssar 6.199 0.460 13.465 0.000 5.297 7.101 6.199 0.144
## .ssmk 8.979 0.385 23.335 0.000 8.225 9.734 8.979 0.255
## .ssmc 8.063 0.275 29.305 0.000 7.524 8.603 8.063 0.461
## .ssasi 6.198 0.242 25.631 0.000 5.725 6.672 6.198 0.465
## .ssei 4.054 0.183 22.157 0.000 3.696 4.413 4.054 0.360
## .ssno 0.189 0.013 14.135 0.000 0.163 0.215 0.189 0.272
## .sscs 0.321 0.018 17.629 0.000 0.285 0.357 0.321 0.439
## .electronic 1.000 1.000 1.000 0.232 0.232
## .g 1.000 1.000 1.000 0.964 0.964
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.808 0.049 16.530 0.000 0.712 0.904 2.682 0.584
## sswk (.p2.) 1.934 0.117 16.594 0.000 1.705 2.162 6.418 0.919
## sspc (.p3.) 0.800 0.047 16.870 0.000 0.707 0.893 2.656 0.839
## math =~
## ssar (.p4.) 3.028 0.083 36.702 0.000 2.867 3.190 6.812 0.939
## ssmk (.p5.) 2.549 0.068 37.590 0.000 2.417 2.682 5.735 0.877
## ssmc (.p6.) 0.705 0.039 17.922 0.000 0.628 0.782 1.585 0.335
## electronic =~
## ssgs (.p7.) 0.582 0.033 17.810 0.000 0.518 0.646 1.568 0.341
## ssasi (.p8.) 1.286 0.061 21.170 0.000 1.167 1.405 3.462 0.739
## ssmc (.p9.) 0.894 0.048 18.809 0.000 0.801 0.987 2.408 0.508
## ssei (.10.) 1.293 0.061 21.285 0.000 1.174 1.412 3.482 0.926
## speed =~
## ssno (.11.) 0.490 0.011 45.466 0.000 0.469 0.511 0.773 0.868
## sscs (.12.) 0.442 0.010 43.623 0.000 0.422 0.462 0.696 0.791
## g =~
## verbal (.13.) 2.683 0.172 15.576 0.000 2.345 3.021 0.954 0.954
## math (.14.) 1.708 0.067 25.660 0.000 1.578 1.839 0.896 0.896
## elctrnc (.15.) 1.786 0.091 19.725 0.000 1.608 1.963 0.782 0.782
## speed (.16.) 1.033 0.038 26.980 0.000 0.958 1.108 0.773 0.773
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.127 0.011 11.128 0.000 0.105 0.150 0.108 0.255
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.35.) 15.837 0.088 179.279 0.000 15.664 16.010 15.837 3.447
## .sswk 29.313 0.175 167.252 0.000 28.969 29.656 29.313 4.199
## .sspc (.37.) 11.905 0.058 204.882 0.000 11.791 12.019 11.905 3.760
## .ssar (.38.) 18.252 0.147 124.305 0.000 17.965 18.540 18.252 2.517
## .ssmk 13.290 0.148 89.888 0.000 13.001 13.580 13.290 2.032
## .ssmc (.40.) 12.659 0.087 145.188 0.000 12.488 12.830 12.659 2.672
## .ssasi (.41.) 11.930 0.074 160.988 0.000 11.785 12.076 11.930 2.545
## .ssei 7.768 0.170 45.661 0.000 7.434 8.101 7.768 2.065
## .ssno (.43.) 0.483 0.018 27.053 0.000 0.448 0.518 0.483 0.543
## .sscs 0.319 0.022 14.291 0.000 0.276 0.363 0.319 0.363
## .verbal -1.925 0.152 -12.676 0.000 -2.222 -1.627 -0.580 -0.580
## .elctrnc 3.882 0.209 18.616 0.000 3.473 4.291 1.442 1.442
## .speed -0.816 0.047 -17.242 0.000 -0.909 -0.723 -0.518 -0.518
## .g 0.362 0.040 9.004 0.000 0.283 0.441 0.307 0.307
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.091 0.091
## .math 1.000 1.000 1.000 0.198 0.198
## .speed 1.000 1.000 1.000 0.402 0.402
## .ssgs 5.194 0.195 26.601 0.000 4.811 5.576 5.194 0.246
## .sswk 7.533 0.510 14.769 0.000 6.534 8.533 7.533 0.155
## .sspc 2.969 0.128 23.179 0.000 2.717 3.220 2.969 0.296
## .ssar 6.200 0.448 13.833 0.000 5.321 7.078 6.200 0.118
## .ssmk 9.910 0.410 24.179 0.000 9.106 10.713 9.910 0.232
## .ssmc 8.780 0.312 28.163 0.000 8.169 9.391 8.780 0.391
## .ssasi 9.982 0.398 25.100 0.000 9.203 10.762 9.982 0.454
## .ssei 2.020 0.181 11.149 0.000 1.665 2.375 2.020 0.143
## .ssno 0.195 0.013 14.556 0.000 0.169 0.221 0.195 0.246
## .sscs 0.291 0.018 16.282 0.000 0.256 0.326 0.291 0.375
## .electronic 2.813 0.297 9.474 0.000 2.231 3.395 0.388 0.388
## .g 1.301 0.065 20.169 0.000 1.175 1.428 0.935 0.935
sem.ageq<-sem(hof.ageq, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~1"))
fitMeasures(sem.ageq, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 2611.674 93.000 0.000 0.944 0.094 0.057 0.442 281603.445 281986.827
Mc(sem.ageq)
## [1] 0.8151054
summary(sem.ageq, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 135 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 80
## Number of equality constraints 23
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2611.674 1755.501
## Degrees of freedom 93 93
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.488
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1055.282 709.334
## 0 1556.392 1046.167
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.804 0.049 16.369 0.000 0.707 0.900 2.374 0.571
## sswk (.p2.) 1.923 0.117 16.425 0.000 1.694 2.153 5.680 0.900
## sspc (.p3.) 0.796 0.048 16.696 0.000 0.702 0.889 2.350 0.826
## math =~
## ssar (.p4.) 3.034 0.082 36.884 0.000 2.873 3.196 6.127 0.927
## ssmk (.p5.) 2.554 0.068 37.752 0.000 2.422 2.687 5.158 0.864
## ssmc (.p6.) 0.706 0.039 17.942 0.000 0.629 0.783 1.426 0.339
## electronic =~
## ssgs (.p7.) 0.580 0.033 17.792 0.000 0.516 0.644 1.217 0.292
## ssasi (.p8.) 1.282 0.061 21.127 0.000 1.163 1.401 2.688 0.734
## ssmc (.p9.) 0.891 0.047 18.775 0.000 0.798 0.984 1.869 0.445
## ssei (.10.) 1.289 0.061 21.233 0.000 1.170 1.408 2.704 0.802
## speed =~
## ssno (.11.) 0.490 0.011 45.484 0.000 0.469 0.512 0.716 0.854
## sscs (.12.) 0.442 0.010 43.639 0.000 0.422 0.462 0.645 0.751
## g =~
## verbal (.13.) 2.702 0.175 15.422 0.000 2.359 3.046 0.941 0.941
## math (.14.) 1.706 0.066 25.721 0.000 1.576 1.836 0.869 0.869
## elctrnc (.15.) 1.792 0.091 19.669 0.000 1.614 1.971 0.879 0.879
## speed (.16.) 1.033 0.038 26.930 0.000 0.958 1.109 0.728 0.728
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.104 0.008 13.012 0.000 0.088 0.119 0.101 0.234
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.35.) 15.851 0.088 179.610 0.000 15.678 16.024 15.851 3.810
## .sswk 27.621 0.133 208.244 0.000 27.361 27.881 27.621 4.377
## .sspc (.37.) 11.914 0.058 205.298 0.000 11.800 12.028 11.914 4.185
## .ssar (.38.) 18.275 0.147 124.465 0.000 17.987 18.563 18.275 2.763
## .ssmk 14.347 0.133 107.802 0.000 14.086 14.608 14.347 2.405
## .ssmc (.40.) 12.671 0.087 145.385 0.000 12.501 12.842 12.671 3.015
## .ssasi (.41.) 11.940 0.074 161.699 0.000 11.795 12.085 11.940 3.259
## .ssei 10.455 0.070 148.333 0.000 10.317 10.593 10.455 3.102
## .ssno (.43.) 0.485 0.018 27.199 0.000 0.450 0.520 0.485 0.579
## .sscs 0.565 0.018 31.215 0.000 0.530 0.600 0.565 0.658
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.115 0.115
## .math 1.000 1.000 1.000 0.245 0.245
## .speed 1.000 1.000 1.000 0.470 0.470
## .ssgs 5.416 0.201 26.991 0.000 5.023 5.809 5.416 0.313
## .sswk 7.560 0.459 16.455 0.000 6.659 8.460 7.560 0.190
## .sspc 2.580 0.116 22.247 0.000 2.352 2.807 2.580 0.318
## .ssar 6.185 0.460 13.437 0.000 5.283 7.088 6.185 0.141
## .ssmk 8.997 0.385 23.347 0.000 8.242 9.753 8.997 0.253
## .ssmc 8.068 0.275 29.310 0.000 7.528 8.607 8.068 0.457
## .ssasi 6.200 0.242 25.650 0.000 5.726 6.673 6.200 0.462
## .ssei 4.051 0.183 22.173 0.000 3.693 4.409 4.051 0.357
## .ssno 0.190 0.013 14.154 0.000 0.163 0.216 0.190 0.270
## .sscs 0.321 0.018 17.609 0.000 0.285 0.357 0.321 0.435
## .electronic 1.000 1.000 1.000 0.227 0.227
## .g 1.000 1.000 1.000 0.945 0.945
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.804 0.049 16.369 0.000 0.707 0.900 2.658 0.582
## sswk (.p2.) 1.923 0.117 16.425 0.000 1.694 2.153 6.362 0.918
## sspc (.p3.) 0.796 0.048 16.696 0.000 0.702 0.889 2.632 0.837
## math =~
## ssar (.p4.) 3.034 0.082 36.884 0.000 2.873 3.196 6.759 0.938
## ssmk (.p5.) 2.554 0.068 37.752 0.000 2.422 2.687 5.689 0.875
## ssmc (.p6.) 0.706 0.039 17.942 0.000 0.629 0.783 1.573 0.334
## electronic =~
## ssgs (.p7.) 0.580 0.033 17.792 0.000 0.516 0.644 1.558 0.341
## ssasi (.p8.) 1.282 0.061 21.127 0.000 1.163 1.401 3.443 0.737
## ssmc (.p9.) 0.891 0.047 18.775 0.000 0.798 0.984 2.394 0.508
## ssei (.10.) 1.289 0.061 21.233 0.000 1.170 1.408 3.463 0.925
## speed =~
## ssno (.11.) 0.490 0.011 45.484 0.000 0.469 0.512 0.768 0.867
## sscs (.12.) 0.442 0.010 43.639 0.000 0.422 0.462 0.692 0.789
## g =~
## verbal (.13.) 2.702 0.175 15.422 0.000 2.359 3.046 0.953 0.953
## math (.14.) 1.706 0.066 25.721 0.000 1.576 1.836 0.894 0.894
## elctrnc (.15.) 1.792 0.091 19.669 0.000 1.614 1.971 0.779 0.779
## speed (.16.) 1.033 0.038 26.930 0.000 0.958 1.109 0.770 0.770
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.104 0.008 13.012 0.000 0.088 0.119 0.089 0.210
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.35.) 15.851 0.088 179.610 0.000 15.678 16.024 15.851 3.473
## .sswk 29.335 0.175 167.354 0.000 28.992 29.679 29.335 4.233
## .sspc (.37.) 11.914 0.058 205.298 0.000 11.800 12.028 11.914 3.787
## .ssar (.38.) 18.275 0.147 124.465 0.000 17.987 18.563 18.275 2.537
## .ssmk 13.309 0.148 90.015 0.000 13.020 13.599 13.309 2.047
## .ssmc (.40.) 12.671 0.087 145.385 0.000 12.501 12.842 12.671 2.688
## .ssasi (.41.) 11.940 0.074 161.699 0.000 11.795 12.085 11.940 2.555
## .ssei 7.776 0.170 45.695 0.000 7.443 8.110 7.776 2.078
## .ssno (.43.) 0.485 0.018 27.199 0.000 0.450 0.520 0.485 0.548
## .sscs 0.321 0.022 14.377 0.000 0.278 0.365 0.321 0.366
## .verbal -1.936 0.154 -12.576 0.000 -2.238 -1.634 -0.585 -0.585
## .elctrnc 3.895 0.210 18.585 0.000 3.484 4.305 1.450 1.450
## .speed -0.816 0.047 -17.241 0.000 -0.908 -0.723 -0.521 -0.521
## .g 0.353 0.040 8.795 0.000 0.274 0.431 0.302 0.302
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.091 0.091
## .math 1.000 1.000 1.000 0.202 0.202
## .speed 1.000 1.000 1.000 0.408 0.408
## .ssgs 5.190 0.195 26.606 0.000 4.808 5.573 5.190 0.249
## .sswk 7.552 0.510 14.808 0.000 6.553 8.552 7.552 0.157
## .sspc 2.967 0.128 23.173 0.000 2.716 3.218 2.967 0.300
## .ssar 6.206 0.449 13.826 0.000 5.326 7.086 6.206 0.120
## .ssmk 9.894 0.410 24.124 0.000 9.090 10.698 9.894 0.234
## .ssmc 8.781 0.312 28.159 0.000 8.170 9.393 8.781 0.395
## .ssasi 9.986 0.398 25.099 0.000 9.206 10.765 9.986 0.457
## .ssei 2.017 0.181 11.119 0.000 1.662 2.373 2.017 0.144
## .ssno 0.195 0.013 14.543 0.000 0.168 0.221 0.195 0.248
## .sscs 0.291 0.018 16.287 0.000 0.256 0.326 0.291 0.377
## .electronic 2.841 0.300 9.466 0.000 2.253 3.430 0.394 0.394
## .g 1.301 0.065 20.132 0.000 1.175 1.428 0.956 0.956
sem.age2<-sem(hof.age2, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~1"))
fitMeasures(sem.age2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 2656.806 110.000 0.000 0.944 0.087 0.050 0.451 281585.133 281988.693
Mc(sem.age2)
## [1] 0.8132463
summary(sem.age2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 148 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 22
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2656.806 1790.121
## Degrees of freedom 110 110
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.484
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1068.667 720.054
## 0 1588.139 1070.067
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.808 0.049 16.560 0.000 0.712 0.904 2.351 0.569
## sswk (.p2.) 1.934 0.116 16.627 0.000 1.706 2.162 5.627 0.898
## sspc (.p3.) 0.800 0.047 16.905 0.000 0.708 0.893 2.329 0.823
## math =~
## ssar (.p4.) 3.030 0.082 36.746 0.000 2.868 3.191 6.078 0.925
## ssmk (.p5.) 2.551 0.068 37.650 0.000 2.418 2.684 5.117 0.863
## ssmc (.p6.) 0.705 0.039 17.920 0.000 0.628 0.782 1.414 0.338
## electronic =~
## ssgs (.p7.) 0.582 0.033 17.807 0.000 0.518 0.646 1.209 0.292
## ssasi (.p8.) 1.286 0.061 21.164 0.000 1.167 1.405 2.670 0.731
## ssmc (.p9.) 0.894 0.048 18.805 0.000 0.801 0.987 1.857 0.444
## ssei (.10.) 1.293 0.061 21.279 0.000 1.174 1.412 2.685 0.800
## speed =~
## ssno (.11.) 0.490 0.011 45.472 0.000 0.469 0.511 0.712 0.853
## sscs (.12.) 0.442 0.010 43.634 0.000 0.422 0.462 0.641 0.749
## g =~
## verbal (.13.) 2.682 0.172 15.605 0.000 2.345 3.019 0.939 0.939
## math (.14.) 1.707 0.066 25.681 0.000 1.577 1.837 0.867 0.867
## elctrnc (.15.) 1.787 0.091 19.723 0.000 1.609 1.964 0.876 0.876
## speed (.16.) 1.033 0.038 26.990 0.000 0.958 1.108 0.725 0.725
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.084 0.011 7.900 0.000 0.063 0.104 0.082 0.190
## age2 -0.001 0.004 -0.150 0.881 -0.009 0.008 -0.001 -0.003
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.38.) 15.849 0.116 137.062 0.000 15.622 16.075 15.849 3.835
## .sswk 27.617 0.183 151.308 0.000 27.259 27.975 27.617 4.408
## .sspc (.40.) 11.912 0.077 154.621 0.000 11.761 12.063 11.912 4.212
## .ssar (.41.) 18.271 0.191 95.459 0.000 17.896 18.646 18.271 2.782
## .ssmk 14.344 0.167 85.706 0.000 14.016 14.672 14.344 2.419
## .ssmc (.43.) 12.669 0.111 114.359 0.000 12.452 12.886 12.669 3.029
## .ssasi (.44.) 11.939 0.093 128.630 0.000 11.757 12.120 11.939 3.270
## .ssei 10.453 0.091 115.434 0.000 10.276 10.631 10.453 3.115
## .ssno (.46.) 0.485 0.022 22.501 0.000 0.443 0.527 0.485 0.582
## .sscs 0.565 0.021 26.412 0.000 0.523 0.607 0.565 0.660
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.118 0.118
## .math 1.000 1.000 1.000 0.249 0.249
## .speed 1.000 1.000 1.000 0.474 0.474
## .ssgs 5.414 0.201 26.991 0.000 5.021 5.807 5.414 0.317
## .sswk 7.577 0.461 16.451 0.000 6.674 8.480 7.577 0.193
## .sspc 2.576 0.116 22.229 0.000 2.349 2.803 2.576 0.322
## .ssar 6.198 0.460 13.462 0.000 5.295 7.100 6.198 0.144
## .ssmk 8.979 0.385 23.331 0.000 8.225 9.734 8.979 0.255
## .ssmc 8.063 0.275 29.307 0.000 7.524 8.603 8.063 0.461
## .ssasi 6.198 0.242 25.628 0.000 5.724 6.673 6.198 0.465
## .ssei 4.054 0.183 22.160 0.000 3.696 4.413 4.054 0.360
## .ssno 0.189 0.013 14.136 0.000 0.163 0.216 0.189 0.272
## .sscs 0.321 0.018 17.624 0.000 0.285 0.357 0.321 0.439
## .electronic 1.000 1.000 1.000 0.232 0.232
## .g 1.000 1.000 1.000 0.964 0.964
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.808 0.049 16.560 0.000 0.712 0.904 2.682 0.584
## sswk (.p2.) 1.934 0.116 16.627 0.000 1.706 2.162 6.418 0.920
## sspc (.p3.) 0.800 0.047 16.905 0.000 0.708 0.893 2.656 0.839
## math =~
## ssar (.p4.) 3.030 0.082 36.746 0.000 2.868 3.191 6.812 0.939
## ssmk (.p5.) 2.551 0.068 37.650 0.000 2.418 2.684 5.735 0.877
## ssmc (.p6.) 0.705 0.039 17.920 0.000 0.628 0.782 1.585 0.335
## electronic =~
## ssgs (.p7.) 0.582 0.033 17.807 0.000 0.518 0.646 1.567 0.341
## ssasi (.p8.) 1.286 0.061 21.164 0.000 1.167 1.405 3.462 0.739
## ssmc (.p9.) 0.894 0.048 18.805 0.000 0.801 0.987 2.408 0.508
## ssei (.10.) 1.293 0.061 21.279 0.000 1.174 1.412 3.481 0.926
## speed =~
## ssno (.11.) 0.490 0.011 45.472 0.000 0.469 0.511 0.773 0.868
## sscs (.12.) 0.442 0.010 43.634 0.000 0.422 0.462 0.696 0.791
## g =~
## verbal (.13.) 2.682 0.172 15.605 0.000 2.345 3.019 0.954 0.954
## math (.14.) 1.707 0.066 25.681 0.000 1.577 1.837 0.896 0.896
## elctrnc (.15.) 1.787 0.091 19.723 0.000 1.609 1.964 0.783 0.783
## speed (.16.) 1.033 0.038 26.990 0.000 0.958 1.108 0.773 0.773
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.121 0.012 10.400 0.000 0.098 0.143 0.102 0.242
## age2 -0.015 0.005 -2.826 0.005 -0.025 -0.004 -0.012 -0.064
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.38.) 15.849 0.116 137.062 0.000 15.622 16.075 15.849 3.449
## .sswk 29.331 0.214 137.356 0.000 28.913 29.750 29.331 4.202
## .sspc (.40.) 11.912 0.077 154.621 0.000 11.761 12.063 11.912 3.763
## .ssar (.41.) 18.271 0.191 95.459 0.000 17.896 18.646 18.271 2.519
## .ssmk 13.306 0.180 73.748 0.000 12.952 13.660 13.306 2.034
## .ssmc (.43.) 12.669 0.111 114.359 0.000 12.452 12.886 12.669 2.674
## .ssasi (.44.) 11.939 0.093 128.630 0.000 11.757 12.120 11.939 2.547
## .ssei 7.776 0.178 43.638 0.000 7.427 8.125 7.776 2.068
## .ssno (.46.) 0.485 0.022 22.501 0.000 0.443 0.527 0.485 0.545
## .sscs 0.321 0.025 12.860 0.000 0.272 0.370 0.321 0.364
## .verbal -1.924 0.152 -12.695 0.000 -2.221 -1.627 -0.580 -0.580
## .elctrnc 3.882 0.209 18.612 0.000 3.474 4.291 1.442 1.442
## .speed -0.816 0.047 -17.243 0.000 -0.909 -0.723 -0.518 -0.518
## .g 0.440 0.054 8.073 0.000 0.333 0.547 0.373 0.373
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.091 0.091
## .math 1.000 1.000 1.000 0.198 0.198
## .speed 1.000 1.000 1.000 0.402 0.402
## .ssgs 5.195 0.195 26.594 0.000 4.812 5.577 5.195 0.246
## .sswk 7.528 0.509 14.794 0.000 6.530 8.525 7.528 0.154
## .sspc 2.969 0.128 23.173 0.000 2.718 3.220 2.969 0.296
## .ssar 6.205 0.448 13.840 0.000 5.327 7.084 6.205 0.118
## .ssmk 9.906 0.410 24.179 0.000 9.103 10.710 9.906 0.231
## .ssmc 8.780 0.312 28.167 0.000 8.169 9.391 8.780 0.391
## .ssasi 9.980 0.398 25.102 0.000 9.201 10.760 9.980 0.454
## .ssei 2.021 0.181 11.161 0.000 1.666 2.376 2.021 0.143
## .ssno 0.195 0.013 14.561 0.000 0.169 0.221 0.195 0.246
## .sscs 0.291 0.018 16.282 0.000 0.256 0.326 0.291 0.375
## .electronic 2.810 0.297 9.469 0.000 2.229 3.392 0.387 0.387
## .g 1.296 0.064 20.222 0.000 1.170 1.422 0.931 0.931
sem.age2q<-sem(hof.age2q, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~1"))
fitMeasures(sem.age2q, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 2675.112 112.000 0.000 0.944 0.086 0.055 0.453 281599.439 281989.547
Mc(sem.age2q)
## [1] 0.8121706
summary(sem.age2q, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 140 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 24
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2675.112 1804.027
## Degrees of freedom 112 112
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.483
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1076.378 725.882
## 0 1598.734 1078.145
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.803 0.049 16.385 0.000 0.707 0.900 2.376 0.571
## sswk (.p2.) 1.923 0.117 16.441 0.000 1.694 2.152 5.686 0.900
## sspc (.p3.) 0.796 0.048 16.714 0.000 0.702 0.889 2.353 0.826
## math =~
## ssar (.p4.) 3.036 0.082 36.934 0.000 2.875 3.197 6.133 0.927
## ssmk (.p5.) 2.556 0.068 37.812 0.000 2.423 2.688 5.162 0.865
## ssmc (.p6.) 0.707 0.039 17.950 0.000 0.629 0.784 1.427 0.339
## electronic =~
## ssgs (.p7.) 0.580 0.033 17.782 0.000 0.516 0.644 1.218 0.293
## ssasi (.p8.) 1.281 0.061 21.111 0.000 1.162 1.400 2.690 0.734
## ssmc (.p9.) 0.891 0.047 18.767 0.000 0.798 0.984 1.871 0.445
## ssei (.10.) 1.289 0.061 21.216 0.000 1.170 1.408 2.706 0.802
## speed =~
## ssno (.11.) 0.490 0.011 45.482 0.000 0.469 0.511 0.716 0.854
## sscs (.12.) 0.442 0.010 43.643 0.000 0.422 0.462 0.645 0.752
## g =~
## verbal (.13.) 2.704 0.175 15.435 0.000 2.361 3.047 0.941 0.941
## math (.14.) 1.705 0.066 25.747 0.000 1.576 1.835 0.869 0.869
## elctrnc (.15.) 1.794 0.091 19.652 0.000 1.615 1.973 0.879 0.879
## speed (.16.) 1.034 0.038 26.927 0.000 0.959 1.109 0.729 0.729
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.100 0.008 12.455 0.000 0.085 0.116 0.098 0.226
## age2 (b) -0.007 0.003 -2.069 0.039 -0.014 -0.000 -0.007 -0.035
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.38.) 15.972 0.104 152.900 0.000 15.767 16.177 15.972 3.837
## .sswk 27.816 0.161 172.578 0.000 27.501 28.132 27.816 4.404
## .sspc (.40.) 11.995 0.069 174.763 0.000 11.860 12.129 11.995 4.211
## .ssar (.41.) 18.469 0.173 106.704 0.000 18.130 18.809 18.469 2.791
## .ssmk 14.511 0.153 94.605 0.000 14.210 14.812 14.511 2.430
## .ssmc (.43.) 12.777 0.101 126.429 0.000 12.579 12.975 12.777 3.038
## .ssasi (.44.) 12.027 0.085 141.252 0.000 11.860 12.193 12.027 3.281
## .ssei 10.542 0.082 127.973 0.000 10.380 10.703 10.542 3.126
## .ssno (.46.) 0.504 0.020 25.377 0.000 0.466 0.543 0.504 0.602
## .sscs 0.582 0.020 29.233 0.000 0.543 0.621 0.582 0.678
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.114 0.114
## .math 1.000 1.000 1.000 0.245 0.245
## .speed 1.000 1.000 1.000 0.469 0.469
## .ssgs 5.417 0.201 26.989 0.000 5.024 5.810 5.417 0.313
## .sswk 7.557 0.460 16.446 0.000 6.656 8.458 7.557 0.189
## .sspc 2.580 0.116 22.253 0.000 2.353 2.807 2.580 0.318
## .ssar 6.183 0.460 13.438 0.000 5.281 7.085 6.183 0.141
## .ssmk 8.999 0.386 23.341 0.000 8.244 9.755 8.999 0.252
## .ssmc 8.067 0.275 29.311 0.000 7.528 8.606 8.067 0.456
## .ssasi 6.199 0.242 25.652 0.000 5.725 6.672 6.199 0.461
## .ssei 4.052 0.183 22.184 0.000 3.694 4.410 4.052 0.356
## .ssno 0.190 0.013 14.163 0.000 0.163 0.216 0.190 0.270
## .sscs 0.321 0.018 17.603 0.000 0.285 0.357 0.321 0.435
## .electronic 1.000 1.000 1.000 0.227 0.227
## .g 1.000 1.000 1.000 0.944 0.944
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.803 0.049 16.385 0.000 0.707 0.900 2.656 0.582
## sswk (.p2.) 1.923 0.117 16.441 0.000 1.694 2.152 6.356 0.918
## sspc (.p3.) 0.796 0.048 16.714 0.000 0.702 0.889 2.630 0.837
## math =~
## ssar (.p4.) 3.036 0.082 36.934 0.000 2.875 3.197 6.753 0.938
## ssmk (.p5.) 2.556 0.068 37.812 0.000 2.423 2.688 5.685 0.875
## ssmc (.p6.) 0.707 0.039 17.950 0.000 0.629 0.784 1.572 0.334
## electronic =~
## ssgs (.p7.) 0.580 0.033 17.782 0.000 0.516 0.644 1.557 0.341
## ssasi (.p8.) 1.281 0.061 21.111 0.000 1.162 1.400 3.440 0.737
## ssmc (.p9.) 0.891 0.047 18.767 0.000 0.798 0.984 2.393 0.508
## ssei (.10.) 1.289 0.061 21.216 0.000 1.170 1.408 3.460 0.925
## speed =~
## ssno (.11.) 0.490 0.011 45.482 0.000 0.469 0.511 0.768 0.867
## sscs (.12.) 0.442 0.010 43.643 0.000 0.422 0.462 0.692 0.789
## g =~
## verbal (.13.) 2.704 0.175 15.435 0.000 2.361 3.047 0.953 0.953
## math (.14.) 1.705 0.066 25.747 0.000 1.576 1.835 0.893 0.893
## elctrnc (.15.) 1.794 0.091 19.652 0.000 1.615 1.973 0.778 0.778
## speed (.16.) 1.034 0.038 26.927 0.000 0.959 1.109 0.769 0.769
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.100 0.008 12.455 0.000 0.085 0.116 0.086 0.203
## age2 (b) -0.007 0.003 -2.069 0.039 -0.014 -0.000 -0.006 -0.031
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.38.) 15.972 0.104 152.900 0.000 15.767 16.177 15.972 3.502
## .sswk 29.531 0.197 149.843 0.000 29.144 29.917 29.531 4.265
## .sspc (.40.) 11.995 0.069 174.763 0.000 11.860 12.129 11.995 3.815
## .ssar (.41.) 18.469 0.173 106.704 0.000 18.130 18.809 18.469 2.566
## .ssmk 13.473 0.167 80.860 0.000 13.147 13.800 13.473 2.074
## .ssmc (.43.) 12.777 0.101 126.429 0.000 12.579 12.975 12.777 2.711
## .ssasi (.44.) 12.027 0.085 141.252 0.000 11.860 12.193 12.027 2.575
## .ssei 7.863 0.175 44.842 0.000 7.520 8.207 7.863 2.102
## .ssno (.46.) 0.504 0.020 25.377 0.000 0.466 0.543 0.504 0.570
## .sscs 0.339 0.024 14.244 0.000 0.292 0.385 0.339 0.386
## .verbal -1.936 0.154 -12.587 0.000 -2.238 -1.635 -0.586 -0.586
## .elctrnc 3.896 0.210 18.573 0.000 3.485 4.307 1.451 1.451
## .speed -0.816 0.047 -17.243 0.000 -0.909 -0.723 -0.521 -0.521
## .g 0.354 0.040 8.829 0.000 0.275 0.433 0.304 0.304
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.092 0.092
## .math 1.000 1.000 1.000 0.202 0.202
## .speed 1.000 1.000 1.000 0.408 0.408
## .ssgs 5.191 0.195 26.603 0.000 4.808 5.573 5.191 0.250
## .sswk 7.549 0.509 14.818 0.000 6.550 8.547 7.549 0.157
## .sspc 2.967 0.128 23.169 0.000 2.716 3.218 2.967 0.300
## .ssar 6.207 0.449 13.825 0.000 5.327 7.087 6.207 0.120
## .ssmk 9.893 0.410 24.123 0.000 9.089 10.697 9.893 0.234
## .ssmc 8.781 0.312 28.161 0.000 8.170 9.392 8.781 0.395
## .ssasi 9.984 0.398 25.099 0.000 9.205 10.764 9.984 0.458
## .ssei 2.018 0.181 11.126 0.000 1.662 2.373 2.018 0.144
## .ssno 0.195 0.013 14.550 0.000 0.169 0.221 0.195 0.248
## .sscs 0.291 0.018 16.286 0.000 0.256 0.326 0.291 0.378
## .electronic 2.842 0.300 9.458 0.000 2.253 3.431 0.394 0.394
## .g 1.296 0.064 20.168 0.000 1.170 1.422 0.955 0.955
# BIFACTOR (a model with verbal =~ gs + pc and without gs cross loading was fitted, but loadings on verbal were zero or negative)
bf.notworking<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
'
baseline<-cfa(bf.notworking, data=dgroup, meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1579.247 23.000 0.000 0.966 0.105 0.046 286643.835 286926.326
Mc(baseline)
## [1] 0.8813338
summary(baseline, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 41 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 42
##
## Number of observations 6161
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1579.247 1034.260
## Degrees of freedom 23 23
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.527
## Yuan-Bentler correction (Mplus variant)
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs 0.524 0.113 4.649 0.000 0.303 0.745 0.524 0.117
## sswk 4.752 0.752 6.319 0.000 3.278 6.226 4.752 0.716
## sspc 0.560 0.113 4.965 0.000 0.339 0.781 0.560 0.184
## math =~
## ssar 2.646 0.146 18.121 0.000 2.360 2.932 2.646 0.379
## ssmk 1.983 0.118 16.748 0.000 1.751 2.215 1.983 0.317
## ssmc 1.238 0.082 15.045 0.000 1.076 1.399 1.238 0.248
## electronic =~
## ssgs 1.229 0.048 25.644 0.000 1.135 1.323 1.229 0.275
## ssasi 3.850 0.062 62.192 0.000 3.728 3.971 3.850 0.747
## ssmc 2.823 0.059 48.095 0.000 2.708 2.938 2.823 0.567
## ssei 2.156 0.047 45.868 0.000 2.064 2.249 2.156 0.548
## speed =~
## ssno 0.462 0.014 32.260 0.000 0.433 0.490 0.462 0.530
## sscs 0.535 0.003 166.250 0.000 0.528 0.541 0.535 0.597
## g =~
## ssgs 3.552 0.061 57.997 0.000 3.432 3.672 3.552 0.795
## ssar 5.914 0.073 80.945 0.000 5.771 6.058 5.914 0.847
## sswk 5.438 0.104 52.187 0.000 5.233 5.642 5.438 0.819
## sspc 2.313 0.049 47.679 0.000 2.218 2.408 2.313 0.762
## ssno 0.567 0.013 43.447 0.000 0.541 0.592 0.567 0.651
## sscs 0.486 0.014 34.062 0.000 0.458 0.514 0.486 0.543
## ssasi 2.259 0.081 27.919 0.000 2.100 2.417 2.259 0.438
## ssmk 5.090 0.064 79.688 0.000 4.965 5.216 5.090 0.814
## ssmc 2.975 0.068 43.711 0.000 2.842 3.109 2.975 0.597
## ssei 2.619 0.054 48.707 0.000 2.514 2.724 2.619 0.666
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.000 0.000 0.000 0.000 0.000
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 16.715 0.068 246.365 0.000 16.582 16.848 16.715 3.743
## .sswk 27.415 0.099 278.206 0.000 27.221 27.608 27.415 4.129
## .sspc 11.467 0.045 252.947 0.000 11.378 11.556 11.467 3.778
## .ssar 19.089 0.106 180.011 0.000 18.881 19.297 19.089 2.733
## .ssmk 14.504 0.095 151.975 0.000 14.317 14.691 14.504 2.319
## .ssmc 14.875 0.076 194.568 0.000 14.725 15.025 14.875 2.985
## .ssasi 14.868 0.079 189.000 0.000 14.713 15.022 14.868 2.885
## .ssei 12.012 0.060 201.824 0.000 11.895 12.128 12.012 3.055
## .ssno 0.361 0.013 27.622 0.000 0.336 0.387 0.361 0.415
## .sscs 0.329 0.014 24.174 0.000 0.302 0.356 0.329 0.367
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.543 0.159 34.946 0.000 5.232 5.854 5.543 0.278
## .sswk -8.060 7.293 -1.105 0.269 -22.354 6.234 -8.060 -0.183
## .sspc 3.548 0.118 29.961 0.000 3.316 3.780 3.548 0.385
## .ssar 6.818 0.535 12.752 0.000 5.770 7.866 6.818 0.140
## .ssmk 9.276 0.363 25.529 0.000 8.564 9.988 9.276 0.237
## .ssmc 6.471 0.263 24.595 0.000 5.956 6.987 6.471 0.261
## .ssasi 6.642 0.306 21.705 0.000 6.042 7.242 6.642 0.250
## .ssei 3.953 0.127 31.059 0.000 3.704 4.202 3.953 0.256
## .ssno 0.223 0.011 21.062 0.000 0.202 0.243 0.223 0.294
## .sscs 0.281 0.013 21.553 0.000 0.255 0.306 0.281 0.350
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
bf.model<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
'
bf.lv<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
'
baseline<-cfa(bf.model, data=dgroup, meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= -9.198506e-06) is smaller than zero. This may
## be a symptom that the model is not identified.
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1976.198 26.000 0.000 0.957 0.110 0.048 287034.785 287297.099
Mc(baseline)
## [1] 0.8535977
summary(baseline, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 30 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 39
##
## Number of observations 6161
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1976.198 1267.501
## Degrees of freedom 26 26
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.559
## Yuan-Bentler correction (Mplus variant)
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar 3.461 0.119 29.094 0.000 3.228 3.695 3.461 0.496
## ssmk 2.645 0.099 26.835 0.000 2.452 2.838 2.645 0.423
## ssmc 1.189 0.061 19.598 0.000 1.070 1.307 1.189 0.240
## electronic =~
## ssgs 1.284 0.047 27.205 0.000 1.191 1.376 1.284 0.286
## ssasi 3.888 0.060 65.020 0.000 3.770 4.005 3.888 0.754
## ssmc 2.797 0.056 49.546 0.000 2.687 2.908 2.797 0.566
## ssei 2.167 0.044 49.290 0.000 2.081 2.254 2.167 0.551
## speed =~
## ssno 0.431 0.011 39.690 0.000 0.410 0.453 0.431 0.496
## sscs 0.608 0.005 112.262 0.000 0.597 0.618 0.608 0.678
## g =~
## ssgs 3.657 0.055 67.014 0.000 3.550 3.764 3.657 0.814
## ssar 5.510 0.071 77.859 0.000 5.371 5.649 5.510 0.789
## sswk 5.948 0.092 64.681 0.000 5.768 6.128 5.948 0.896
## sspc 2.476 0.045 55.615 0.000 2.389 2.564 2.476 0.816
## ssno 0.542 0.013 41.175 0.000 0.516 0.568 0.542 0.623
## sscs 0.480 0.014 34.071 0.000 0.453 0.508 0.480 0.536
## ssasi 2.230 0.077 28.780 0.000 2.078 2.382 2.230 0.433
## ssmk 4.754 0.062 76.691 0.000 4.633 4.876 4.754 0.760
## ssmc 2.893 0.065 44.292 0.000 2.765 3.021 2.893 0.585
## ssei 2.603 0.050 52.085 0.000 2.505 2.701 2.603 0.662
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 19.089 0.106 180.011 0.000 18.881 19.297 19.089 2.733
## .ssmk 14.504 0.095 151.975 0.000 14.317 14.691 14.504 2.319
## .ssmc 14.875 0.076 194.568 0.000 14.725 15.025 14.875 3.010
## .ssgs 16.715 0.068 246.365 0.000 16.582 16.848 16.715 3.720
## .ssasi 14.868 0.079 189.000 0.000 14.713 15.022 14.868 2.885
## .ssei 12.012 0.060 201.824 0.000 11.895 12.128 12.012 3.055
## .ssno 0.361 0.013 27.622 0.000 0.336 0.387 0.361 0.415
## .sscs 0.329 0.014 24.174 0.000 0.302 0.356 0.329 0.367
## .sswk 27.415 0.099 278.206 0.000 27.221 27.608 27.415 4.129
## .sspc 11.467 0.045 252.947 0.000 11.378 11.556 11.467 3.778
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.455 0.673 9.592 0.000 5.136 7.774 6.455 0.132
## .ssmk 9.520 0.448 21.228 0.000 8.641 10.399 9.520 0.243
## .ssmc 6.823 0.228 29.959 0.000 6.377 7.270 6.823 0.279
## .ssgs 5.168 0.144 35.982 0.000 4.887 5.450 5.168 0.256
## .ssasi 6.479 0.303 21.355 0.000 5.884 7.074 6.479 0.244
## .ssei 3.987 0.125 31.801 0.000 3.741 4.233 3.987 0.258
## .ssno 0.277 0.010 28.651 0.000 0.258 0.296 0.277 0.366
## .sscs 0.203 0.012 17.124 0.000 0.180 0.226 0.203 0.253
## .sswk 8.709 0.368 23.690 0.000 7.988 9.429 8.709 0.198
## .sspc 3.080 0.095 32.593 0.000 2.895 3.265 3.080 0.334
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
configural<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1460.414 52.000 0.000 0.968 0.094 0.033 281498.599 282023.226
Mc(configural)
## [1] 0.8919731
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 39 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 78
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1460.414 935.653
## Degrees of freedom 52 52
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.561
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 567.753 363.745
## 0 892.662 571.907
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar 3.393 0.157 21.626 0.000 3.085 3.700 3.393 0.503
## ssmk 2.781 0.139 20.071 0.000 2.510 3.053 2.781 0.464
## ssmc 1.225 0.083 14.703 0.000 1.062 1.388 1.225 0.296
## electronic =~
## ssgs 0.800 0.097 8.250 0.000 0.610 0.991 0.800 0.192
## ssasi 1.556 0.107 14.539 0.000 1.346 1.765 1.556 0.450
## ssmc 1.396 0.113 12.393 0.000 1.175 1.617 1.396 0.337
## ssei 1.059 0.095 11.177 0.000 0.873 1.244 1.059 0.317
## speed =~
## ssno 0.516 0.017 30.609 0.000 0.483 0.549 0.516 0.622
## sscs 0.470 0.008 62.351 0.000 0.455 0.485 0.470 0.554
## g =~
## ssgs 3.382 0.073 46.509 0.000 3.239 3.524 3.382 0.813
## ssar 5.277 0.097 54.462 0.000 5.087 5.467 5.277 0.782
## sswk 5.724 0.127 45.101 0.000 5.475 5.972 5.724 0.894
## sspc 2.229 0.064 34.980 0.000 2.104 2.354 2.229 0.806
## ssno 0.484 0.019 25.515 0.000 0.446 0.521 0.484 0.583
## sscs 0.428 0.020 21.336 0.000 0.389 0.467 0.428 0.504
## ssasi 1.947 0.070 27.839 0.000 1.810 2.084 1.947 0.564
## ssmk 4.381 0.085 51.610 0.000 4.215 4.548 4.381 0.730
## ssmc 2.559 0.074 34.611 0.000 2.414 2.704 2.559 0.618
## ssei 2.338 0.058 40.319 0.000 2.224 2.451 2.338 0.700
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 18.133 0.146 124.361 0.000 17.847 18.418 18.133 2.688
## .ssmk 14.248 0.130 109.820 0.000 13.994 14.503 14.248 2.375
## .ssmc 12.747 0.090 141.504 0.000 12.570 12.923 12.747 3.078
## .ssgs 15.782 0.090 175.509 0.000 15.606 15.959 15.782 3.793
## .ssasi 11.812 0.074 158.855 0.000 11.666 11.957 11.812 3.421
## .ssei 10.402 0.072 144.049 0.000 10.261 10.544 10.402 3.117
## .ssno 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.571
## .sscs 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.653
## .sswk 27.503 0.136 202.254 0.000 27.237 27.770 27.503 4.296
## .sspc 11.863 0.059 201.639 0.000 11.748 11.978 11.863 4.290
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.137 0.853 7.193 0.000 4.465 7.809 6.137 0.135
## .ssmk 9.047 0.653 13.846 0.000 7.767 10.328 9.047 0.251
## .ssmc 7.150 0.346 20.660 0.000 6.472 7.829 7.150 0.417
## .ssgs 5.240 0.214 24.492 0.000 4.821 5.660 5.240 0.303
## .ssasi 5.713 0.309 18.485 0.000 5.108 6.319 5.713 0.479
## .ssei 4.553 0.199 22.889 0.000 4.163 4.942 4.553 0.409
## .ssno 0.189 0.015 12.536 0.000 0.159 0.219 0.189 0.274
## .sscs 0.317 0.017 18.233 0.000 0.283 0.352 0.317 0.440
## .sswk 8.229 0.475 17.326 0.000 7.298 9.160 8.229 0.201
## .sspc 2.677 0.114 23.416 0.000 2.453 2.902 2.677 0.350
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar 3.378 0.184 18.360 0.000 3.018 3.739 3.378 0.477
## ssmk 2.627 0.150 17.474 0.000 2.333 2.922 2.627 0.405
## ssmc 0.956 0.088 10.919 0.000 0.784 1.127 0.956 0.194
## electronic =~
## ssgs 0.793 0.076 10.425 0.000 0.644 0.943 0.793 0.172
## ssasi 2.976 0.094 31.621 0.000 2.791 3.160 2.976 0.620
## ssmc 2.432 0.090 27.048 0.000 2.255 2.608 2.432 0.493
## ssei 1.627 0.070 23.153 0.000 1.489 1.765 1.627 0.424
## speed =~
## ssno 0.434 0.017 24.934 0.000 0.400 0.468 0.434 0.485
## sscs 0.525 0.007 80.461 0.000 0.512 0.538 0.525 0.592
## g =~
## ssgs 3.944 0.077 51.543 0.000 3.794 4.094 3.944 0.854
## ssar 5.718 0.098 58.381 0.000 5.526 5.910 5.718 0.807
## sswk 6.186 0.129 47.969 0.000 5.933 6.439 6.186 0.902
## sspc 2.726 0.059 46.547 0.000 2.611 2.840 2.726 0.844
## ssno 0.590 0.018 33.379 0.000 0.555 0.624 0.590 0.660
## sscs 0.537 0.018 29.708 0.000 0.502 0.573 0.537 0.606
## ssasi 2.674 0.111 24.058 0.000 2.456 2.892 2.674 0.557
## ssmk 5.020 0.087 57.381 0.000 4.849 5.192 5.020 0.774
## ssmc 3.326 0.091 36.577 0.000 3.147 3.504 3.326 0.674
## ssei 2.934 0.070 41.816 0.000 2.797 3.072 2.934 0.764
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 20.009 0.151 132.770 0.000 19.714 20.305 20.009 2.823
## .ssmk 14.749 0.139 105.881 0.000 14.476 15.022 14.749 2.275
## .ssmc 16.924 0.104 162.135 0.000 16.719 17.128 16.924 3.428
## .ssgs 17.613 0.097 181.519 0.000 17.422 17.803 17.613 3.815
## .ssasi 17.810 0.102 175.227 0.000 17.610 18.009 17.810 3.713
## .ssei 13.561 0.080 169.041 0.000 13.404 13.718 13.561 3.533
## .ssno 0.253 0.019 13.436 0.000 0.216 0.290 0.253 0.283
## .sscs 0.112 0.019 5.896 0.000 0.075 0.149 0.112 0.126
## .sswk 27.329 0.142 191.949 0.000 27.050 27.608 27.329 3.984
## .sspc 11.086 0.068 163.704 0.000 10.953 11.219 11.086 3.434
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.142 1.076 5.707 0.000 4.033 8.251 6.142 0.122
## .ssmk 9.912 0.711 13.938 0.000 8.518 11.306 9.912 0.236
## .ssmc 6.484 0.347 18.700 0.000 5.804 7.163 6.484 0.266
## .ssgs 5.131 0.197 26.098 0.000 4.746 5.516 5.131 0.241
## .ssasi 7.005 0.435 16.122 0.000 6.153 7.857 7.005 0.304
## .ssei 3.475 0.159 21.897 0.000 3.164 3.786 3.475 0.236
## .ssno 0.262 0.013 20.157 0.000 0.237 0.288 0.262 0.329
## .sscs 0.221 0.016 13.468 0.000 0.189 0.253 0.221 0.282
## .sswk 8.788 0.494 17.779 0.000 7.819 9.757 8.788 0.187
## .sspc 2.996 0.127 23.627 0.000 2.747 3.244 2.996 0.287
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
#modificationIndices(configural, sort=T, maximum.number=30)
metric<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1560.097 67.000 0.000 0.966 0.085 0.041 281568.282 281992.019
Mc(metric)
## [1] 0.885863
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 64 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 19
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1560.097 1031.141
## Degrees of freedom 67 67
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.513
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 625.800 413.620
## 0 934.297 617.521
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.424 0.129 26.608 0.000 3.171 3.676 3.424 0.517
## ssmk (.p2.) 2.769 0.113 24.486 0.000 2.548 2.991 2.769 0.462
## ssmc (.p3.) 1.113 0.066 16.844 0.000 0.984 1.243 1.113 0.265
## electronic =~
## ssgs (.p4.) 0.499 0.043 11.546 0.000 0.414 0.584 0.499 0.120
## ssasi (.p5.) 1.664 0.072 23.213 0.000 1.524 1.805 1.664 0.471
## ssmc (.p6.) 1.385 0.065 21.199 0.000 1.257 1.513 1.385 0.329
## ssei (.p7.) 0.931 0.047 19.786 0.000 0.839 1.023 0.931 0.275
## speed =~
## ssno (.p8.) 0.421 0.013 32.435 0.000 0.396 0.447 0.421 0.501
## sscs (.p9.) 0.576 0.021 27.361 0.000 0.535 0.617 0.576 0.668
## g =~
## ssgs (.10.) 3.403 0.064 52.873 0.000 3.277 3.529 3.403 0.820
## ssar (.11.) 5.114 0.094 54.414 0.000 4.930 5.298 5.114 0.772
## sswk (.12.) 5.522 0.112 49.418 0.000 5.303 5.741 5.522 0.882
## sspc (.13.) 2.307 0.051 45.139 0.000 2.207 2.407 2.307 0.816
## ssno (.14.) 0.502 0.014 36.557 0.000 0.475 0.529 0.502 0.596
## sscs (.15.) 0.452 0.014 32.795 0.000 0.425 0.479 0.452 0.525
## ssasi (.16.) 2.100 0.059 35.796 0.000 1.985 2.215 2.100 0.594
## ssmk (.17.) 4.384 0.083 52.819 0.000 4.221 4.547 4.384 0.731
## ssmc (.18.) 2.711 0.058 46.453 0.000 2.596 2.825 2.711 0.644
## ssei (.19.) 2.440 0.048 51.307 0.000 2.347 2.533 2.440 0.720
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 18.133 0.146 124.361 0.000 17.847 18.418 18.133 2.736
## .ssmk 14.248 0.130 109.820 0.000 13.994 14.503 14.248 2.376
## .ssmc 12.747 0.090 141.504 0.000 12.570 12.923 12.747 3.028
## .ssgs 15.782 0.090 175.509 0.000 15.606 15.959 15.782 3.804
## .ssasi 11.812 0.074 158.855 0.000 11.666 11.957 11.812 3.343
## .ssei 10.402 0.072 144.049 0.000 10.261 10.544 10.402 3.068
## .ssno 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.563
## .sscs 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.644
## .sswk 27.503 0.136 202.254 0.000 27.237 27.770 27.503 4.392
## .sspc 11.863 0.059 201.639 0.000 11.748 11.978 11.863 4.194
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.052 0.734 8.248 0.000 4.613 7.490 6.052 0.138
## .ssmk 9.060 0.561 16.156 0.000 7.961 10.159 9.060 0.252
## .ssmc 7.211 0.285 25.293 0.000 6.652 7.769 7.211 0.407
## .ssgs 5.381 0.204 26.439 0.000 4.982 5.780 5.381 0.313
## .ssasi 5.304 0.253 20.976 0.000 4.809 5.800 5.304 0.425
## .ssei 4.674 0.169 27.638 0.000 4.343 5.006 4.674 0.407
## .ssno 0.278 0.013 20.962 0.000 0.252 0.304 0.278 0.393
## .sscs 0.206 0.025 8.209 0.000 0.157 0.256 0.206 0.278
## .sswk 8.726 0.452 19.293 0.000 7.839 9.612 8.726 0.223
## .sspc 2.676 0.115 23.272 0.000 2.451 2.902 2.676 0.335
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.424 0.129 26.608 0.000 3.171 3.676 3.279 0.456
## ssmk (.p2.) 2.769 0.113 24.486 0.000 2.548 2.991 2.652 0.409
## ssmc (.p3.) 1.113 0.066 16.844 0.000 0.984 1.243 1.066 0.221
## electronic =~
## ssgs (.p4.) 0.499 0.043 11.546 0.000 0.414 0.584 0.894 0.195
## ssasi (.p5.) 1.664 0.072 23.213 0.000 1.524 1.805 2.982 0.638
## ssmc (.p6.) 1.385 0.065 21.199 0.000 1.257 1.513 2.481 0.514
## ssei (.p7.) 0.931 0.047 19.786 0.000 0.839 1.023 1.668 0.445
## speed =~
## ssno (.p8.) 0.421 0.013 32.190 0.000 0.396 0.447 0.409 0.462
## sscs (.p9.) 0.576 0.021 27.430 0.000 0.535 0.617 0.559 0.638
## g =~
## ssgs (.10.) 3.403 0.064 52.873 0.000 3.277 3.529 3.902 0.849
## ssar (.11.) 5.114 0.094 54.414 0.000 4.930 5.298 5.864 0.815
## sswk (.12.) 5.522 0.112 49.418 0.000 5.303 5.741 6.331 0.907
## sspc (.13.) 2.307 0.051 45.139 0.000 2.207 2.407 2.645 0.835
## ssno (.14.) 0.502 0.014 36.557 0.000 0.475 0.529 0.575 0.651
## sscs (.15.) 0.452 0.014 32.795 0.000 0.425 0.479 0.518 0.592
## ssasi (.16.) 2.100 0.059 35.796 0.000 1.985 2.215 2.408 0.516
## ssmk (.17.) 4.384 0.083 52.819 0.000 4.221 4.547 5.027 0.776
## ssmc (.18.) 2.711 0.058 46.453 0.000 2.596 2.825 3.108 0.644
## ssei (.19.) 2.440 0.048 51.307 0.000 2.347 2.533 2.798 0.746
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 20.009 0.151 132.770 0.000 19.714 20.305 20.009 2.781
## .ssmk 14.749 0.139 105.881 0.000 14.476 15.022 14.749 2.277
## .ssmc 16.924 0.104 162.135 0.000 16.719 17.128 16.924 3.505
## .ssgs 17.613 0.097 181.519 0.000 17.422 17.803 17.613 3.832
## .ssasi 17.810 0.102 175.227 0.000 17.610 18.009 17.810 3.814
## .ssei 13.561 0.080 169.041 0.000 13.404 13.718 13.561 3.616
## .ssno 0.253 0.019 13.436 0.000 0.216 0.290 0.253 0.286
## .sscs 0.112 0.019 5.896 0.000 0.075 0.149 0.112 0.128
## .sswk 27.329 0.142 191.949 0.000 27.050 27.608 27.329 3.914
## .sspc 11.086 0.068 163.704 0.000 10.953 11.219 11.086 3.499
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.646 0.733 9.062 0.000 5.209 8.083 6.646 0.128
## .ssmk 9.675 0.536 18.045 0.000 8.625 10.726 9.675 0.230
## .ssmc 6.358 0.334 19.037 0.000 5.704 7.013 6.358 0.273
## .ssgs 5.102 0.194 26.274 0.000 4.721 5.483 5.102 0.241
## .ssasi 7.120 0.419 17.009 0.000 6.299 7.940 7.120 0.326
## .ssei 3.454 0.157 21.936 0.000 3.145 3.763 3.454 0.246
## .ssno 0.283 0.014 20.856 0.000 0.257 0.310 0.283 0.363
## .sscs 0.186 0.018 10.466 0.000 0.151 0.221 0.186 0.243
## .sswk 8.664 0.484 17.892 0.000 7.715 9.613 8.664 0.178
## .sspc 3.039 0.129 23.636 0.000 2.787 3.291 3.039 0.303
## math 0.917 0.065 14.205 0.000 0.791 1.044 1.000 1.000
## electronic 3.211 0.289 11.122 0.000 2.645 3.776 1.000 1.000
## speed 0.941 0.065 14.402 0.000 0.813 1.069 1.000 1.000
## g 1.315 0.063 20.928 0.000 1.192 1.438 1.000 1.000
lavTestScore(metric, release = 1:19)
## 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 102.567 19 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p54. 1.446 1 0.229
## 2 .p2. == .p55. 0.178 1 0.673
## 3 .p3. == .p56. 2.885 1 0.089
## 4 .p4. == .p57. 11.964 1 0.001
## 5 .p5. == .p58. 2.145 1 0.143
## 6 .p6. == .p59. 0.862 1 0.353
## 7 .p7. == .p60. 0.026 1 0.872
## 8 .p8. == .p61. 0.000 1 1.000
## 9 .p9. == .p62. 0.000 1 1.000
## 10 .p10. == .p63. 0.658 1 0.417
## 11 .p11. == .p64. 14.995 1 0.000
## 12 .p12. == .p65. 27.751 1 0.000
## 13 .p13. == .p66. 16.802 1 0.000
## 14 .p14. == .p67. 1.079 1 0.299
## 15 .p15. == .p68. 2.419 1 0.120
## 16 .p16. == .p69. 5.947 1 0.015
## 17 .p17. == .p70. 2.265 1 0.132
## 18 .p18. == .p71. 5.348 1 0.021
## 19 .p19. == .p72. 2.021 1 0.155
scalar<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1845.784 73.000 0.000 0.960 0.089 0.043 281841.968 282225.350
Mc(scalar)
## [1] 0.8659788
summary(scalar, standardized=T, ci=T) # +.119
## lavaan 0.6-18 ended normally after 113 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 29
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1845.784 1242.730
## Degrees of freedom 73 73
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.485
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 761.901 512.973
## 0 1083.883 729.757
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.039 0.145 27.838 0.000 3.755 4.324 4.039 0.610
## ssmk (.p2.) 2.217 0.101 22.011 0.000 2.019 2.414 2.217 0.371
## ssmc (.p3.) 0.841 0.067 12.473 0.000 0.709 0.973 0.841 0.200
## electronic =~
## ssgs (.p4.) 0.602 0.031 19.733 0.000 0.542 0.662 0.602 0.145
## ssasi (.p5.) 1.733 0.071 24.560 0.000 1.595 1.872 1.733 0.491
## ssmc (.p6.) 1.173 0.051 23.193 0.000 1.074 1.272 1.173 0.279
## ssei (.p7.) 0.965 0.041 23.386 0.000 0.884 1.046 0.965 0.285
## speed =~
## ssno (.p8.) 0.310 0.020 15.466 0.000 0.271 0.350 0.310 0.369
## sscs (.p9.) 0.776 0.052 14.940 0.000 0.675 0.878 0.776 0.901
## g =~
## ssgs (.10.) 3.383 0.065 52.043 0.000 3.255 3.510 3.383 0.816
## ssar (.11.) 5.129 0.094 54.651 0.000 4.945 5.313 5.129 0.775
## sswk (.12.) 5.483 0.114 48.196 0.000 5.260 5.706 5.483 0.876
## sspc (.13.) 2.322 0.050 46.792 0.000 2.225 2.419 2.322 0.815
## ssno (.14.) 0.504 0.014 36.976 0.000 0.477 0.531 0.504 0.599
## sscs (.15.) 0.454 0.014 33.043 0.000 0.427 0.481 0.454 0.527
## ssasi (.16.) 2.077 0.059 35.331 0.000 1.962 2.192 2.077 0.588
## ssmk (.17.) 4.419 0.082 53.669 0.000 4.258 4.581 4.419 0.739
## ssmc (.18.) 2.757 0.058 47.259 0.000 2.643 2.871 2.757 0.657
## ssei (.19.) 2.428 0.048 50.779 0.000 2.334 2.521 2.428 0.716
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.145 0.147 123.402 0.000 17.856 18.433 18.145 2.740
## .ssmk (.41.) 14.102 0.125 112.761 0.000 13.857 14.347 14.102 2.359
## .ssmc (.42.) 12.643 0.088 143.220 0.000 12.469 12.816 12.643 3.013
## .ssgs (.43.) 15.847 0.088 179.651 0.000 15.674 16.020 15.847 3.825
## .ssasi (.44.) 11.830 0.074 159.687 0.000 11.685 11.975 11.830 3.350
## .ssei (.45.) 10.412 0.071 146.053 0.000 10.272 10.552 10.412 3.073
## .ssno (.46.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.563
## .sscs (.47.) 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.643
## .sswk (.48.) 27.797 0.131 212.415 0.000 27.540 28.053 27.797 4.444
## .sspc (.49.) 11.642 0.059 197.588 0.000 11.527 11.758 11.642 4.085
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 1.218 1.082 1.126 0.260 -0.902 3.338 1.218 0.028
## .ssmk 11.284 0.468 24.115 0.000 10.367 12.201 11.284 0.316
## .ssmc 7.921 0.277 28.632 0.000 7.378 8.463 7.921 0.450
## .ssgs 5.361 0.204 26.307 0.000 4.962 5.761 5.361 0.312
## .ssasi 5.153 0.250 20.604 0.000 4.663 5.643 5.153 0.413
## .ssei 4.656 0.167 27.805 0.000 4.328 4.985 4.656 0.406
## .ssno 0.357 0.017 20.631 0.000 0.323 0.391 0.357 0.505
## .sscs -0.066 0.082 -0.808 0.419 -0.226 0.094 -0.066 -0.089
## .sswk 9.070 0.473 19.167 0.000 8.143 9.998 9.070 0.232
## .sspc 2.732 0.118 23.212 0.000 2.502 2.963 2.732 0.336
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.039 0.145 27.838 0.000 3.755 4.324 3.905 0.542
## ssmk (.p2.) 2.217 0.101 22.011 0.000 2.019 2.414 2.143 0.331
## ssmc (.p3.) 0.841 0.067 12.473 0.000 0.709 0.973 0.813 0.171
## electronic =~
## ssgs (.p4.) 0.602 0.031 19.733 0.000 0.542 0.662 1.078 0.233
## ssasi (.p5.) 1.733 0.071 24.560 0.000 1.595 1.872 3.102 0.659
## ssmc (.p6.) 1.173 0.051 23.193 0.000 1.074 1.272 2.099 0.443
## ssei (.p7.) 0.965 0.041 23.386 0.000 0.884 1.046 1.727 0.459
## speed =~
## ssno (.p8.) 0.310 0.020 15.466 0.000 0.271 0.350 0.300 0.339
## sscs (.p9.) 0.776 0.052 14.940 0.000 0.675 0.878 0.751 0.857
## g =~
## ssgs (.10.) 3.383 0.065 52.043 0.000 3.255 3.510 3.881 0.840
## ssar (.11.) 5.129 0.094 54.651 0.000 4.945 5.313 5.884 0.817
## sswk (.12.) 5.483 0.114 48.196 0.000 5.260 5.706 6.290 0.903
## sspc (.13.) 2.322 0.050 46.792 0.000 2.225 2.419 2.664 0.835
## ssno (.14.) 0.504 0.014 36.976 0.000 0.477 0.531 0.578 0.654
## sscs (.15.) 0.454 0.014 33.043 0.000 0.427 0.481 0.521 0.595
## ssasi (.16.) 2.077 0.059 35.331 0.000 1.962 2.192 2.383 0.506
## ssmk (.17.) 4.419 0.082 53.669 0.000 4.258 4.581 5.070 0.782
## ssmc (.18.) 2.757 0.058 47.259 0.000 2.643 2.871 3.163 0.667
## ssei (.19.) 2.428 0.048 50.779 0.000 2.334 2.521 2.785 0.741
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.145 0.147 123.402 0.000 17.856 18.433 18.145 2.518
## .ssmk (.41.) 14.102 0.125 112.761 0.000 13.857 14.347 14.102 2.176
## .ssmc (.42.) 12.643 0.088 143.220 0.000 12.469 12.816 12.643 2.666
## .ssgs (.43.) 15.847 0.088 179.651 0.000 15.674 16.020 15.847 3.429
## .ssasi (.44.) 11.830 0.074 159.687 0.000 11.685 11.975 11.830 2.514
## .ssei (.45.) 10.412 0.071 146.053 0.000 10.272 10.552 10.412 2.769
## .ssno (.46.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.536
## .sscs (.47.) 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.633
## .sswk (.48.) 27.797 0.131 212.415 0.000 27.540 28.053 27.797 3.989
## .sspc (.49.) 11.642 0.059 197.588 0.000 11.527 11.758 11.642 3.651
## math 0.630 0.039 16.287 0.000 0.554 0.706 0.652 0.652
## elctrnc 3.600 0.158 22.822 0.000 3.291 3.909 2.012 2.012
## speed -0.491 0.046 -10.559 0.000 -0.582 -0.399 -0.507 -0.507
## g -0.136 0.036 -3.789 0.000 -0.207 -0.066 -0.119 -0.119
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 2.036 1.084 1.879 0.060 -0.088 4.161 2.036 0.039
## .ssmk 11.711 0.497 23.580 0.000 10.737 12.684 11.711 0.279
## .ssmc 7.418 0.288 25.713 0.000 6.853 7.984 7.418 0.330
## .ssgs 5.131 0.196 26.134 0.000 4.746 5.516 5.131 0.240
## .ssasi 6.837 0.384 17.804 0.000 6.084 7.589 6.837 0.309
## .ssei 3.397 0.154 22.063 0.000 3.095 3.698 3.397 0.240
## .ssno 0.357 0.015 23.468 0.000 0.327 0.387 0.357 0.457
## .sscs -0.068 0.070 -0.971 0.332 -0.206 0.069 -0.068 -0.089
## .sswk 9.002 0.513 17.557 0.000 7.997 10.007 9.002 0.185
## .sspc 3.074 0.134 22.923 0.000 2.811 3.337 3.074 0.302
## math 0.935 0.066 14.158 0.000 0.805 1.064 1.000 1.000
## electronic 3.203 0.295 10.842 0.000 2.624 3.781 1.000 1.000
## speed 0.934 0.065 14.291 0.000 0.806 1.063 1.000 1.000
## g 1.316 0.063 20.997 0.000 1.193 1.439 1.000 1.000
lavTestScore(scalar, release = 20:29)
## 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 273.985 10 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p40. == .p93. 57.422 1 0.000
## 2 .p41. == .p94. 29.128 1 0.000
## 3 .p42. == .p95. 46.240 1 0.000
## 4 .p43. == .p96. 19.589 1 0.000
## 5 .p44. == .p97. 6.167 1 0.013
## 6 .p45. == .p98. 0.552 1 0.457
## 7 .p46. == .p99. 0.000 1 1.000
## 8 .p47. == .p100. 0.000 1 1.000
## 9 .p48. == .p101. 139.584 1 0.000
## 10 .p49. == .p102. 169.131 1 0.000
scalar2<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1675.496 72.000 0.000 0.964 0.085 0.042 281673.680 282063.788
Mc(scalar2)
## [1] 0.8779603
summary(scalar2, standardized=T, ci=T) # +.034
## lavaan 0.6-18 ended normally after 113 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 28
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1675.496 1127.904
## Degrees of freedom 72 72
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.485
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 681.280 458.622
## 0 994.216 669.283
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.062 0.165 24.545 0.000 3.737 4.386 4.062 0.613
## ssmk (.p2.) 2.217 0.116 19.154 0.000 1.991 2.444 2.217 0.371
## ssmc (.p3.) 0.852 0.075 11.387 0.000 0.705 0.999 0.852 0.203
## electronic =~
## ssgs (.p4.) 0.552 0.030 18.689 0.000 0.494 0.610 0.552 0.133
## ssasi (.p5.) 1.757 0.071 24.643 0.000 1.617 1.897 1.757 0.497
## ssmc (.p6.) 1.181 0.051 23.275 0.000 1.081 1.280 1.181 0.281
## ssei (.p7.) 0.946 0.041 23.344 0.000 0.867 1.026 0.946 0.279
## speed =~
## ssno (.p8.) 0.338 0.017 19.689 0.000 0.305 0.372 0.338 0.402
## sscs (.p9.) 0.714 0.038 18.671 0.000 0.639 0.789 0.714 0.829
## g =~
## ssgs (.10.) 3.394 0.065 52.498 0.000 3.267 3.520 3.394 0.818
## ssar (.11.) 5.121 0.094 54.665 0.000 4.937 5.304 5.121 0.773
## sswk (.12.) 5.511 0.112 49.349 0.000 5.293 5.730 5.511 0.880
## sspc (.13.) 2.309 0.051 45.407 0.000 2.210 2.409 2.309 0.816
## ssno (.14.) 0.503 0.014 36.871 0.000 0.476 0.529 0.503 0.597
## sscs (.15.) 0.453 0.014 32.970 0.000 0.426 0.480 0.453 0.526
## ssasi (.16.) 2.082 0.059 35.487 0.000 1.967 2.197 2.082 0.589
## ssmk (.17.) 4.406 0.082 53.986 0.000 4.246 4.566 4.406 0.738
## ssmc (.18.) 2.753 0.058 47.126 0.000 2.639 2.868 2.753 0.656
## ssei (.19.) 2.433 0.048 51.008 0.000 2.340 2.527 2.433 0.718
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.147 0.149 122.013 0.000 17.856 18.439 18.147 2.741
## .ssmk (.41.) 14.029 0.123 113.672 0.000 13.787 14.271 14.029 2.349
## .ssmc (.42.) 12.648 0.088 143.823 0.000 12.475 12.820 12.648 3.014
## .ssgs (.43.) 15.820 0.088 179.222 0.000 15.647 15.993 15.820 3.815
## .ssasi (.44.) 11.839 0.074 159.554 0.000 11.694 11.984 11.839 3.350
## .ssei (.45.) 10.409 0.071 146.319 0.000 10.270 10.549 10.409 3.070
## .ssno (.46.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.563
## .sscs (.47.) 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.644
## .sswk (.48.) 27.525 0.135 204.005 0.000 27.260 27.789 27.525 4.395
## .sspc 11.863 0.059 201.639 0.000 11.748 11.978 11.863 4.193
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 1.131 1.288 0.878 0.380 -1.393 3.656 1.131 0.026
## .ssmk 11.352 0.513 22.137 0.000 10.347 12.357 11.352 0.318
## .ssmc 7.914 0.280 28.278 0.000 7.365 8.462 7.914 0.449
## .ssgs 5.376 0.203 26.446 0.000 4.977 5.774 5.376 0.313
## .ssasi 5.065 0.253 20.038 0.000 4.570 5.561 5.065 0.406
## .ssei 4.680 0.167 27.956 0.000 4.352 5.008 4.680 0.407
## .ssno 0.340 0.016 20.797 0.000 0.308 0.372 0.340 0.481
## .sscs 0.027 0.056 0.479 0.632 -0.083 0.137 0.027 0.036
## .sswk 8.840 0.457 19.337 0.000 7.944 9.736 8.840 0.225
## .sspc 2.672 0.115 23.276 0.000 2.447 2.897 2.672 0.334
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.062 0.165 24.545 0.000 3.737 4.386 3.931 0.546
## ssmk (.p2.) 2.217 0.116 19.154 0.000 1.991 2.444 2.146 0.331
## ssmc (.p3.) 0.852 0.075 11.387 0.000 0.705 0.999 0.825 0.174
## electronic =~
## ssgs (.p4.) 0.552 0.030 18.689 0.000 0.494 0.610 0.988 0.214
## ssasi (.p5.) 1.757 0.071 24.643 0.000 1.617 1.897 3.146 0.667
## ssmc (.p6.) 1.181 0.051 23.275 0.000 1.081 1.280 2.115 0.446
## ssei (.p7.) 0.946 0.041 23.344 0.000 0.867 1.026 1.695 0.451
## speed =~
## ssno (.p8.) 0.338 0.017 19.689 0.000 0.305 0.372 0.328 0.371
## sscs (.p9.) 0.714 0.038 18.671 0.000 0.639 0.789 0.692 0.791
## g =~
## ssgs (.10.) 3.394 0.065 52.498 0.000 3.267 3.520 3.893 0.844
## ssar (.11.) 5.121 0.094 54.665 0.000 4.937 5.304 5.874 0.815
## sswk (.12.) 5.511 0.112 49.349 0.000 5.293 5.730 6.322 0.906
## sspc (.13.) 2.309 0.051 45.407 0.000 2.210 2.409 2.649 0.836
## ssno (.14.) 0.503 0.014 36.871 0.000 0.476 0.529 0.576 0.652
## sscs (.15.) 0.453 0.014 32.970 0.000 0.426 0.480 0.520 0.593
## ssasi (.16.) 2.082 0.059 35.487 0.000 1.967 2.197 2.388 0.507
## ssmk (.17.) 4.406 0.082 53.986 0.000 4.246 4.566 5.054 0.781
## ssmc (.18.) 2.753 0.058 47.126 0.000 2.639 2.868 3.158 0.666
## ssei (.19.) 2.433 0.048 51.008 0.000 2.340 2.527 2.791 0.743
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.147 0.149 122.013 0.000 17.856 18.439 18.147 2.518
## .ssmk (.41.) 14.029 0.123 113.672 0.000 13.787 14.271 14.029 2.166
## .ssmc (.42.) 12.648 0.088 143.823 0.000 12.475 12.820 12.648 2.666
## .ssgs (.43.) 15.820 0.088 179.222 0.000 15.647 15.993 15.820 3.432
## .ssasi (.44.) 11.839 0.074 159.554 0.000 11.694 11.984 11.839 2.511
## .ssei (.45.) 10.409 0.071 146.319 0.000 10.270 10.549 10.409 2.772
## .ssno (.46.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.536
## .sscs (.47.) 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.633
## .sswk (.48.) 27.525 0.135 204.005 0.000 27.260 27.789 27.525 3.943
## .sspc 11.177 0.071 157.324 0.000 11.037 11.316 11.177 3.528
## math 0.502 0.038 13.184 0.000 0.427 0.576 0.518 0.518
## elctrnc 3.425 0.151 22.726 0.000 3.130 3.721 1.913 1.913
## speed -0.595 0.047 -12.747 0.000 -0.686 -0.503 -0.614 -0.614
## g -0.039 0.036 -1.098 0.272 -0.109 0.031 -0.034 -0.034
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 1.969 1.282 1.535 0.125 -0.544 4.483 1.969 0.038
## .ssmk 11.781 0.534 22.042 0.000 10.733 12.828 11.781 0.281
## .ssmc 7.384 0.291 25.400 0.000 6.814 7.953 7.384 0.328
## .ssgs 5.119 0.195 26.290 0.000 4.738 5.501 5.119 0.241
## .ssasi 6.619 0.386 17.150 0.000 5.863 7.376 6.619 0.298
## .ssei 3.442 0.154 22.329 0.000 3.140 3.744 3.442 0.244
## .ssno 0.341 0.015 23.486 0.000 0.313 0.370 0.341 0.437
## .sscs 0.018 0.047 0.376 0.707 -0.074 0.109 0.018 0.023
## .sswk 8.767 0.494 17.733 0.000 7.798 9.736 8.767 0.180
## .sspc 3.017 0.128 23.555 0.000 2.766 3.268 3.017 0.301
## math 0.937 0.065 14.318 0.000 0.809 1.065 1.000 1.000
## electronic 3.208 0.294 10.921 0.000 2.632 3.783 1.000 1.000
## speed 0.939 0.065 14.353 0.000 0.811 1.067 1.000 1.000
## g 1.316 0.063 21.041 0.000 1.193 1.438 1.000 1.000
lavTestScore(scalar2, release = 20:28)
## 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 110.241 9 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p40. == .p93. 80.130 1 0.000
## 2 .p41. == .p94. 51.423 1 0.000
## 3 .p42. == .p95. 38.192 1 0.000
## 4 .p43. == .p96. 6.279 1 0.012
## 5 .p44. == .p97. 13.394 1 0.000
## 6 .p45. == .p98. 0.272 1 0.602
## 7 .p46. == .p99. 0.000 1 1.000
## 8 .p47. == .p100. 0.000 1 1.000
## 9 .p48. == .p101. 2.504 1 0.114
strict<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("sspc~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1750.323 82.000 0.000 0.962 0.081 0.042 281728.507 282051.355
Mc(strict)
## [1] 0.8733527
summary(strict, standardized=T, ci=T) # +.030
## lavaan 0.6-18 ended normally after 99 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 38
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1750.323 1163.192
## Degrees of freedom 82 82
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.505
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 714.983 475.148
## 0 1035.340 688.044
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.985 0.154 25.932 0.000 3.684 4.286 3.985 0.602
## ssmk (.p2.) 2.204 0.117 18.819 0.000 1.975 2.434 2.204 0.368
## ssmc (.p3.) 0.851 0.075 11.291 0.000 0.703 0.998 0.851 0.204
## electronic =~
## ssgs (.p4.) 0.535 0.028 18.805 0.000 0.479 0.591 0.535 0.129
## ssasi (.p5.) 1.734 0.069 25.161 0.000 1.598 1.869 1.734 0.482
## ssmc (.p6.) 1.147 0.049 23.287 0.000 1.051 1.244 1.147 0.276
## ssei (.p7.) 0.915 0.039 23.293 0.000 0.838 0.992 0.915 0.278
## speed =~
## ssno (.p8.) 0.341 0.018 19.353 0.000 0.306 0.376 0.341 0.405
## sscs (.p9.) 0.718 0.033 21.492 0.000 0.652 0.783 0.718 0.832
## g =~
## ssgs (.10.) 3.397 0.065 52.511 0.000 3.270 3.524 3.397 0.822
## ssar (.11.) 5.119 0.094 54.626 0.000 4.936 5.303 5.119 0.773
## sswk (.12.) 5.508 0.112 49.269 0.000 5.289 5.728 5.508 0.880
## sspc (.13.) 2.314 0.050 46.139 0.000 2.215 2.412 2.314 0.808
## ssno (.14.) 0.502 0.014 36.911 0.000 0.476 0.529 0.502 0.597
## sscs (.15.) 0.453 0.014 32.967 0.000 0.426 0.480 0.453 0.525
## ssasi (.16.) 2.087 0.059 35.584 0.000 1.972 2.202 2.087 0.581
## ssmk (.17.) 4.410 0.082 53.868 0.000 4.250 4.571 4.410 0.737
## ssmc (.18.) 2.754 0.058 47.238 0.000 2.640 2.869 2.754 0.662
## ssei (.19.) 2.432 0.047 51.323 0.000 2.339 2.525 2.432 0.737
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.157 0.149 121.716 0.000 17.864 18.449 18.157 2.741
## .ssmk (.41.) 14.016 0.124 113.470 0.000 13.774 14.258 14.016 2.343
## .ssmc (.42.) 12.665 0.088 144.403 0.000 12.493 12.837 12.665 3.044
## .ssgs (.43.) 15.824 0.088 179.323 0.000 15.651 15.997 15.824 3.830
## .ssasi (.44.) 11.820 0.074 159.076 0.000 11.675 11.966 11.820 3.289
## .ssei (.45.) 10.426 0.071 147.337 0.000 10.288 10.565 10.426 3.161
## .ssno (.46.) 0.474 0.018 26.736 0.000 0.439 0.508 0.474 0.562
## .sscs (.47.) 0.555 0.018 30.306 0.000 0.519 0.590 0.555 0.643
## .sswk (.48.) 27.513 0.135 203.386 0.000 27.247 27.778 27.513 4.394
## .sspc 11.863 0.059 201.639 0.000 11.748 11.978 11.863 4.143
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.20.) 1.796 1.213 1.480 0.139 -0.583 4.174 1.796 0.041
## .ssmk (.21.) 11.491 0.455 25.232 0.000 10.598 12.383 11.491 0.321
## .ssmc (.22.) 7.684 0.207 37.128 0.000 7.278 8.089 7.684 0.444
## .ssgs (.23.) 5.249 0.143 36.619 0.000 4.968 5.530 5.249 0.307
## .ssasi (.24.) 5.559 0.225 24.699 0.000 5.118 6.000 5.559 0.430
## .ssei (.25.) 4.123 0.116 35.422 0.000 3.895 4.351 4.123 0.379
## .ssno (.26.) 0.341 0.013 26.441 0.000 0.316 0.366 0.341 0.480
## .sscs (.27.) 0.023 0.046 0.500 0.617 -0.068 0.114 0.023 0.031
## .sswk (.28.) 8.854 0.349 25.379 0.000 8.171 9.538 8.854 0.226
## .sspc (.29.) 2.848 0.085 33.339 0.000 2.680 3.015 2.848 0.347
## math 1.000 1.000 1.000 1.000 1.000
## elctrnc 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.985 0.154 25.932 0.000 3.684 4.286 3.948 0.548
## ssmk (.p2.) 2.204 0.117 18.819 0.000 1.975 2.434 2.184 0.338
## ssmc (.p3.) 0.851 0.075 11.291 0.000 0.703 0.998 0.843 0.176
## electronic =~
## ssgs (.p4.) 0.535 0.028 18.805 0.000 0.479 0.591 0.991 0.214
## ssasi (.p5.) 1.734 0.069 25.161 0.000 1.598 1.869 3.210 0.691
## ssmc (.p6.) 1.147 0.049 23.287 0.000 1.051 1.244 2.124 0.444
## ssei (.p7.) 0.915 0.039 23.293 0.000 0.838 0.992 1.695 0.441
## speed =~
## ssno (.p8.) 0.341 0.018 19.353 0.000 0.306 0.376 0.327 0.370
## sscs (.p9.) 0.718 0.033 21.492 0.000 0.652 0.783 0.688 0.786
## g =~
## ssgs (.10.) 3.397 0.065 52.511 0.000 3.270 3.524 3.896 0.842
## ssar (.11.) 5.119 0.094 54.626 0.000 4.936 5.303 5.872 0.815
## sswk (.12.) 5.508 0.112 49.269 0.000 5.289 5.728 6.318 0.905
## sspc (.13.) 2.314 0.050 46.139 0.000 2.215 2.412 2.654 0.844
## ssno (.14.) 0.502 0.014 36.911 0.000 0.476 0.529 0.576 0.653
## sscs (.15.) 0.453 0.014 32.967 0.000 0.426 0.480 0.520 0.594
## ssasi (.16.) 2.087 0.059 35.584 0.000 1.972 2.202 2.394 0.515
## ssmk (.17.) 4.410 0.082 53.868 0.000 4.250 4.571 5.059 0.782
## ssmc (.18.) 2.754 0.058 47.238 0.000 2.640 2.869 3.160 0.660
## ssei (.19.) 2.432 0.047 51.323 0.000 2.339 2.525 2.790 0.726
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.157 0.149 121.716 0.000 17.864 18.449 18.157 2.521
## .ssmk (.41.) 14.016 0.124 113.470 0.000 13.774 14.258 14.016 2.167
## .ssmc (.42.) 12.665 0.088 144.403 0.000 12.493 12.837 12.665 2.647
## .ssgs (.43.) 15.824 0.088 179.323 0.000 15.651 15.997 15.824 3.420
## .ssasi (.44.) 11.820 0.074 159.076 0.000 11.675 11.966 11.820 2.544
## .ssei (.45.) 10.426 0.071 147.337 0.000 10.288 10.565 10.426 2.712
## .ssno (.46.) 0.474 0.018 26.736 0.000 0.439 0.508 0.474 0.536
## .sscs (.47.) 0.555 0.018 30.306 0.000 0.519 0.590 0.555 0.634
## .sswk (.48.) 27.513 0.135 203.386 0.000 27.247 27.778 27.513 3.939
## .sspc 11.167 0.071 156.257 0.000 11.027 11.307 11.167 3.551
## math 0.504 0.039 13.000 0.000 0.428 0.580 0.509 0.509
## elctrnc 3.492 0.151 23.131 0.000 3.196 3.788 1.886 1.886
## speed -0.595 0.047 -12.777 0.000 -0.686 -0.504 -0.621 -0.621
## g -0.035 0.036 -0.978 0.328 -0.105 0.035 -0.030 -0.030
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.20.) 1.796 1.213 1.480 0.139 -0.583 4.174 1.796 0.035
## .ssmk (.21.) 11.491 0.455 25.232 0.000 10.598 12.383 11.491 0.275
## .ssmc (.22.) 7.684 0.207 37.128 0.000 7.278 8.089 7.684 0.336
## .ssgs (.23.) 5.249 0.143 36.619 0.000 4.968 5.530 5.249 0.245
## .ssasi (.24.) 5.559 0.225 24.699 0.000 5.118 6.000 5.559 0.257
## .ssei (.25.) 4.123 0.116 35.422 0.000 3.895 4.351 4.123 0.279
## .ssno (.26.) 0.341 0.013 26.441 0.000 0.316 0.366 0.341 0.437
## .sscs (.27.) 0.023 0.046 0.500 0.617 -0.068 0.114 0.023 0.030
## .sswk (.28.) 8.854 0.349 25.379 0.000 8.171 9.538 8.854 0.182
## .sspc (.29.) 2.848 0.085 33.339 0.000 2.680 3.015 2.848 0.288
## math 0.982 0.054 18.195 0.000 0.876 1.087 1.000 1.000
## elctrnc 3.430 0.298 11.495 0.000 2.845 4.014 1.000 1.000
## speed 0.918 0.051 18.098 0.000 0.818 1.017 1.000 1.000
## g 1.316 0.063 20.987 0.000 1.193 1.439 1.000 1.000
latent<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("sspc~1"))
fitMeasures(latent, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2029.670 76.000 0.000 0.956 0.091 0.109 282019.855 282383.058
Mc(latent)
## [1] 0.8533571
summary(latent, standardized=T, ci=T) # +.041
## lavaan 0.6-18 ended normally after 83 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 28
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2029.670 1373.108
## Degrees of freedom 76 76
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.478
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 887.675 600.528
## 0 1141.996 772.580
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.069 0.158 25.713 0.000 3.759 4.379 4.069 0.588
## ssmk (.p2.) 2.178 0.108 20.234 0.000 1.967 2.389 2.178 0.351
## ssmc (.p3.) 0.814 0.071 11.503 0.000 0.675 0.952 0.814 0.180
## electronic =~
## ssgs (.p4.) 0.799 0.032 25.345 0.000 0.737 0.861 0.799 0.181
## ssasi (.p5.) 2.488 0.056 44.125 0.000 2.378 2.599 2.488 0.626
## ssmc (.p6.) 1.676 0.048 34.622 0.000 1.581 1.771 1.676 0.371
## ssei (.p7.) 1.360 0.036 37.573 0.000 1.289 1.431 1.360 0.368
## speed =~
## ssno (.p8.) 0.333 0.017 20.011 0.000 0.300 0.365 0.333 0.387
## sscs (.p9.) 0.708 0.036 19.864 0.000 0.638 0.777 0.708 0.807
## g =~
## ssgs (.10.) 3.677 0.053 69.976 0.000 3.574 3.780 3.677 0.832
## ssar (.11.) 5.509 0.069 80.131 0.000 5.375 5.644 5.509 0.797
## sswk (.12.) 5.953 0.091 65.594 0.000 5.775 6.131 5.953 0.896
## sspc (.13.) 2.486 0.044 56.823 0.000 2.400 2.572 2.486 0.838
## ssno (.14.) 0.540 0.013 41.785 0.000 0.514 0.565 0.540 0.628
## sscs (.15.) 0.487 0.013 36.244 0.000 0.460 0.513 0.487 0.555
## ssasi (.16.) 2.306 0.065 35.222 0.000 2.178 2.435 2.306 0.580
## ssmk (.17.) 4.731 0.061 77.123 0.000 4.611 4.851 4.731 0.762
## ssmc (.18.) 3.020 0.060 50.292 0.000 2.902 3.138 3.020 0.668
## ssei (.19.) 2.666 0.046 57.639 0.000 2.575 2.756 2.666 0.722
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.143 0.148 122.578 0.000 17.853 18.433 18.143 2.624
## .ssmk (.41.) 14.042 0.124 113.448 0.000 13.800 14.285 14.042 2.262
## .ssmc (.42.) 12.662 0.088 143.355 0.000 12.489 12.835 12.662 2.800
## .ssgs (.43.) 15.809 0.088 178.852 0.000 15.636 15.982 15.809 3.575
## .ssasi (.44.) 11.842 0.074 159.064 0.000 11.696 11.987 11.842 2.980
## .ssei (.45.) 10.391 0.072 145.328 0.000 10.251 10.532 10.391 2.814
## .ssno (.46.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.551
## .sscs (.47.) 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.632
## .sswk (.48.) 27.539 0.135 204.425 0.000 27.275 27.803 27.539 4.147
## .sspc 11.863 0.059 201.639 0.000 11.748 11.978 11.863 3.998
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 0.903 1.291 0.699 0.484 -1.627 3.434 0.903 0.019
## .ssmk 11.399 0.508 22.442 0.000 10.404 12.395 11.399 0.296
## .ssmc 7.852 0.287 27.394 0.000 7.290 8.414 7.852 0.384
## .ssgs 5.397 0.204 26.492 0.000 4.998 5.796 5.397 0.276
## .ssasi 4.281 0.254 16.842 0.000 3.783 4.779 4.281 0.271
## .ssei 4.682 0.173 27.094 0.000 4.343 5.021 4.682 0.343
## .ssno 0.338 0.016 21.051 0.000 0.306 0.369 0.338 0.456
## .sscs 0.032 0.054 0.587 0.557 -0.074 0.138 0.032 0.041
## .sswk 8.661 0.462 18.735 0.000 7.755 9.567 8.661 0.196
## .sspc 2.623 0.113 23.123 0.000 2.401 2.845 2.623 0.298
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.069 0.158 25.713 0.000 3.759 4.379 4.069 0.587
## ssmk (.p2.) 2.178 0.108 20.234 0.000 1.967 2.389 2.178 0.348
## ssmc (.p3.) 0.814 0.071 11.503 0.000 0.675 0.952 0.814 0.180
## electronic =~
## ssgs (.p4.) 0.799 0.032 25.345 0.000 0.737 0.861 0.799 0.182
## ssasi (.p5.) 2.488 0.056 44.125 0.000 2.378 2.599 2.488 0.570
## ssmc (.p6.) 1.676 0.048 34.622 0.000 1.581 1.771 1.676 0.372
## ssei (.p7.) 1.360 0.036 37.573 0.000 1.289 1.431 1.360 0.385
## speed =~
## ssno (.p8.) 0.333 0.017 20.011 0.000 0.300 0.365 0.333 0.384
## sscs (.p9.) 0.708 0.036 19.864 0.000 0.638 0.777 0.708 0.822
## g =~
## ssgs (.10.) 3.677 0.053 69.976 0.000 3.574 3.780 3.677 0.838
## ssar (.11.) 5.509 0.069 80.131 0.000 5.375 5.644 5.509 0.794
## sswk (.12.) 5.953 0.091 65.594 0.000 5.775 6.131 5.953 0.897
## sspc (.13.) 2.486 0.044 56.823 0.000 2.400 2.572 2.486 0.818
## ssno (.14.) 0.540 0.013 41.785 0.000 0.514 0.565 0.540 0.623
## sscs (.15.) 0.487 0.013 36.244 0.000 0.460 0.513 0.487 0.566
## ssasi (.16.) 2.306 0.065 35.222 0.000 2.178 2.435 2.306 0.529
## ssmk (.17.) 4.731 0.061 77.123 0.000 4.611 4.851 4.731 0.755
## ssmc (.18.) 3.020 0.060 50.292 0.000 2.902 3.138 3.020 0.669
## ssei (.19.) 2.666 0.046 57.639 0.000 2.575 2.756 2.666 0.755
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.143 0.148 122.578 0.000 17.853 18.433 18.143 2.616
## .ssmk (.41.) 14.042 0.124 113.448 0.000 13.800 14.285 14.042 2.242
## .ssmc (.42.) 12.662 0.088 143.355 0.000 12.489 12.835 12.662 2.807
## .ssgs (.43.) 15.809 0.088 178.852 0.000 15.636 15.982 15.809 3.603
## .ssasi (.44.) 11.842 0.074 159.064 0.000 11.696 11.987 11.842 2.715
## .ssei (.45.) 10.391 0.072 145.328 0.000 10.251 10.532 10.391 2.945
## .ssno (.46.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.547
## .sscs (.47.) 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.645
## .sswk (.48.) 27.539 0.135 204.425 0.000 27.275 27.803 27.539 4.150
## .sspc 11.188 0.071 158.360 0.000 11.050 11.327 11.188 3.680
## math 0.511 0.039 13.154 0.000 0.435 0.587 0.511 0.511
## elctrnc 2.417 0.071 34.010 0.000 2.277 2.556 2.417 2.417
## speed -0.597 0.046 -12.856 0.000 -0.689 -0.506 -0.597 -0.597
## g -0.041 0.033 -1.257 0.209 -0.105 0.023 -0.041 -0.041
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 1.186 1.318 0.900 0.368 -1.396 3.769 1.186 0.025
## .ssmk 12.117 0.537 22.554 0.000 11.064 13.170 12.117 0.309
## .ssmc 7.758 0.293 26.488 0.000 7.184 8.332 7.758 0.381
## .ssgs 5.089 0.194 26.204 0.000 4.709 5.470 5.089 0.264
## .ssasi 7.515 0.387 19.399 0.000 6.756 8.274 7.515 0.395
## .ssei 3.498 0.154 22.668 0.000 3.195 3.800 3.498 0.281
## .ssno 0.347 0.015 23.245 0.000 0.318 0.377 0.347 0.464
## .sscs 0.003 0.048 0.057 0.955 -0.092 0.098 0.003 0.004
## .sswk 8.597 0.465 18.505 0.000 7.687 9.508 8.597 0.195
## .sspc 3.062 0.130 23.521 0.000 2.807 3.317 3.062 0.331
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
latent2<-cfa(bf.lv, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
fitMeasures(latent2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1677.559 74.000 0.000 0.964 0.084 0.042 281671.743 282048.399
Mc(latent2)
## [1] 0.8779558
summary(latent2, standardized=T, ci=T) # +.034
## lavaan 0.6-18 ended normally after 104 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 84
## Number of equality constraints 28
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1677.559 1133.573
## Degrees of freedom 74 74
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.480
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 682.504 461.187
## 0 995.055 672.386
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.006 0.155 25.883 0.000 3.703 4.310 4.006 0.607
## ssmk (.p2.) 2.181 0.109 20.034 0.000 1.968 2.395 2.181 0.366
## ssmc (.p3.) 0.835 0.071 11.734 0.000 0.696 0.974 0.835 0.199
## electronic =~
## ssgs (.p4.) 0.552 0.030 18.692 0.000 0.494 0.610 0.552 0.133
## ssasi (.p5.) 1.758 0.071 24.671 0.000 1.618 1.897 1.758 0.497
## ssmc (.p6.) 1.182 0.051 23.309 0.000 1.082 1.281 1.182 0.282
## ssei (.p7.) 0.947 0.041 23.365 0.000 0.867 1.026 0.947 0.279
## speed =~
## ssno (.p8.) 0.333 0.016 20.238 0.000 0.301 0.365 0.333 0.398
## sscs (.p9.) 0.703 0.035 20.066 0.000 0.635 0.772 0.703 0.820
## g =~
## ssgs (.10.) 3.394 0.065 52.534 0.000 3.268 3.521 3.394 0.818
## ssar (.11.) 5.121 0.093 54.897 0.000 4.938 5.304 5.121 0.776
## sswk (.12.) 5.513 0.112 49.427 0.000 5.294 5.731 5.513 0.880
## sspc (.13.) 2.309 0.051 45.429 0.000 2.210 2.409 2.309 0.816
## ssno (.14.) 0.502 0.014 36.869 0.000 0.475 0.529 0.502 0.600
## sscs (.15.) 0.452 0.014 32.969 0.000 0.426 0.479 0.452 0.527
## ssasi (.16.) 2.083 0.059 35.522 0.000 1.968 2.198 2.083 0.589
## ssmk (.17.) 4.407 0.081 54.212 0.000 4.248 4.566 4.407 0.740
## ssmc (.18.) 2.755 0.058 47.235 0.000 2.640 2.869 2.755 0.657
## ssei (.19.) 2.434 0.048 51.060 0.000 2.340 2.527 2.434 0.718
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.149 0.149 122.080 0.000 17.858 18.441 18.149 2.750
## .ssmk (.41.) 14.031 0.124 113.564 0.000 13.789 14.273 14.031 2.356
## .ssmc (.42.) 12.648 0.088 143.788 0.000 12.476 12.821 12.648 3.016
## .ssgs (.43.) 15.821 0.088 179.203 0.000 15.648 15.994 15.821 3.814
## .ssasi (.44.) 11.839 0.074 159.561 0.000 11.693 11.984 11.839 3.350
## .ssei (.45.) 10.409 0.071 146.344 0.000 10.270 10.549 10.409 3.069
## .ssno (.46.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.566
## .sscs (.47.) 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.647
## .sswk (.48.) 27.525 0.135 203.997 0.000 27.260 27.789 27.525 4.392
## .sspc 11.863 0.059 201.639 0.000 11.748 11.978 11.863 4.192
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.289 1.248 1.033 0.302 -1.158 3.735 1.289 0.030
## .ssmk 11.301 0.503 22.480 0.000 10.316 12.286 11.301 0.319
## .ssmc 7.905 0.279 28.303 0.000 7.358 8.453 7.905 0.450
## .ssgs 5.380 0.203 26.454 0.000 4.982 5.779 5.380 0.313
## .ssasi 5.064 0.253 20.043 0.000 4.569 5.559 5.064 0.405
## .ssei 4.683 0.167 27.959 0.000 4.354 5.011 4.683 0.407
## .ssno 0.338 0.016 21.185 0.000 0.307 0.369 0.338 0.482
## .sscs 0.036 0.053 0.684 0.494 -0.068 0.140 0.036 0.049
## .sswk 8.883 0.457 19.442 0.000 7.987 9.778 8.883 0.226
## .sspc 2.675 0.115 23.332 0.000 2.450 2.899 2.675 0.334
## electronic 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.006 0.155 25.883 0.000 3.703 4.310 4.006 0.554
## ssmk (.p2.) 2.181 0.109 20.034 0.000 1.968 2.395 2.181 0.336
## ssmc (.p3.) 0.835 0.071 11.734 0.000 0.696 0.974 0.835 0.176
## electronic =~
## ssgs (.p4.) 0.552 0.030 18.692 0.000 0.494 0.610 0.987 0.214
## ssasi (.p5.) 1.758 0.071 24.671 0.000 1.618 1.897 3.143 0.667
## ssmc (.p6.) 1.182 0.051 23.309 0.000 1.082 1.281 2.113 0.445
## ssei (.p7.) 0.947 0.041 23.365 0.000 0.867 1.026 1.693 0.451
## speed =~
## ssno (.p8.) 0.333 0.016 20.238 0.000 0.301 0.365 0.333 0.376
## sscs (.p9.) 0.703 0.035 20.066 0.000 0.635 0.772 0.703 0.800
## g =~
## ssgs (.10.) 3.394 0.065 52.534 0.000 3.268 3.521 3.893 0.845
## ssar (.11.) 5.121 0.093 54.897 0.000 4.938 5.304 5.873 0.813
## sswk (.12.) 5.513 0.112 49.427 0.000 5.294 5.731 6.323 0.906
## sspc (.13.) 2.309 0.051 45.429 0.000 2.210 2.409 2.649 0.836
## ssno (.14.) 0.502 0.014 36.869 0.000 0.475 0.529 0.576 0.649
## sscs (.15.) 0.452 0.014 32.969 0.000 0.426 0.479 0.519 0.590
## ssasi (.16.) 2.083 0.059 35.522 0.000 1.968 2.198 2.389 0.507
## ssmk (.17.) 4.407 0.081 54.212 0.000 4.248 4.566 5.054 0.778
## ssmc (.18.) 2.755 0.058 47.235 0.000 2.640 2.869 3.159 0.665
## ssei (.19.) 2.434 0.048 51.060 0.000 2.340 2.527 2.791 0.743
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 18.149 0.149 122.080 0.000 17.858 18.441 18.149 2.511
## .ssmk (.41.) 14.031 0.124 113.564 0.000 13.789 14.273 14.031 2.161
## .ssmc (.42.) 12.648 0.088 143.788 0.000 12.476 12.821 12.648 2.664
## .ssgs (.43.) 15.821 0.088 179.203 0.000 15.648 15.994 15.821 3.433
## .ssasi (.44.) 11.839 0.074 159.561 0.000 11.693 11.984 11.839 2.512
## .ssei (.45.) 10.409 0.071 146.344 0.000 10.270 10.549 10.409 2.772
## .ssno (.46.) 0.474 0.018 26.603 0.000 0.439 0.509 0.474 0.534
## .sscs (.47.) 0.555 0.018 30.291 0.000 0.519 0.591 0.555 0.631
## .sswk (.48.) 27.525 0.135 203.997 0.000 27.260 27.789 27.525 3.946
## .sspc 11.176 0.071 157.355 0.000 11.037 11.316 11.176 3.529
## math 0.509 0.039 12.948 0.000 0.432 0.586 0.509 0.509
## elctrnc 3.424 0.150 22.756 0.000 3.129 3.719 1.915 1.915
## speed -0.604 0.047 -12.962 0.000 -0.696 -0.513 -0.604 -0.604
## g -0.039 0.036 -1.097 0.273 -0.109 0.031 -0.034 -0.034
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.686 1.283 1.314 0.189 -0.828 4.201 1.686 0.032
## .ssmk 11.867 0.543 21.862 0.000 10.803 12.931 11.867 0.281
## .ssmc 7.396 0.291 25.434 0.000 6.826 7.966 7.396 0.328
## .ssgs 5.114 0.194 26.309 0.000 4.733 5.495 5.114 0.241
## .ssasi 6.629 0.386 17.177 0.000 5.873 7.386 6.629 0.298
## .ssei 3.440 0.154 22.339 0.000 3.138 3.742 3.440 0.244
## .ssno 0.344 0.015 23.124 0.000 0.315 0.373 0.344 0.437
## .sscs 0.008 0.047 0.174 0.862 -0.085 0.101 0.008 0.011
## .sswk 8.689 0.482 18.027 0.000 7.744 9.634 8.689 0.179
## .sspc 3.016 0.128 23.549 0.000 2.765 3.267 3.016 0.301
## electronic 3.197 0.293 10.923 0.000 2.624 3.771 1.000 1.000
## g 1.315 0.062 21.057 0.000 1.193 1.438 1.000 1.000
standardizedSolution(latent2) # get the correct SEs for standardized solution
## lhs op rhs group label est.std se z pvalue ci.lower ci.upper
## 1 math =~ ssar 1 .p1. 0.607 0.024 25.078 0.000 0.560 0.654
## 2 math =~ ssmk 1 .p2. 0.366 0.018 20.112 0.000 0.330 0.402
## 3 math =~ ssmc 1 .p3. 0.199 0.017 11.776 0.000 0.166 0.232
## 4 electronic =~ ssgs 1 .p4. 0.133 0.007 17.973 0.000 0.119 0.148
## 5 electronic =~ ssasi 1 .p5. 0.497 0.019 26.569 0.000 0.461 0.534
## 6 electronic =~ ssmc 1 .p6. 0.282 0.012 23.485 0.000 0.258 0.305
## 7 electronic =~ ssei 1 .p7. 0.279 0.012 23.469 0.000 0.256 0.302
## 8 speed =~ ssno 1 .p8. 0.398 0.020 19.589 0.000 0.358 0.438
## 9 speed =~ sscs 1 .p9. 0.820 0.043 19.048 0.000 0.736 0.904
## 10 g =~ ssgs 1 .p10. 0.818 0.008 107.254 0.000 0.803 0.833
## 11 g =~ ssar 1 .p11. 0.776 0.008 92.993 0.000 0.760 0.792
## 12 g =~ sswk 1 .p12. 0.880 0.007 126.779 0.000 0.866 0.893
## 13 g =~ sspc 1 .p13. 0.816 0.008 107.084 0.000 0.801 0.831
## 14 g =~ ssno 1 .p14. 0.600 0.013 47.931 0.000 0.575 0.624
## 15 g =~ sscs 1 .p15. 0.527 0.014 38.559 0.000 0.501 0.554
## 16 g =~ ssasi 1 .p16. 0.589 0.013 45.981 0.000 0.564 0.614
## 17 g =~ ssmk 1 .p17. 0.740 0.009 84.249 0.000 0.723 0.757
## 18 g =~ ssmc 1 .p18. 0.657 0.010 65.878 0.000 0.637 0.676
## 19 g =~ ssei 1 .p19. 0.718 0.009 79.052 0.000 0.700 0.735
## 20 math ~~ math 1 1.000 0.000 NA NA 1.000 1.000
## 21 speed ~~ speed 1 1.000 0.000 NA NA 1.000 1.000
## 22 ssar ~~ ssar 1 0.030 0.029 1.035 0.301 -0.026 0.086
## 23 ssmk ~~ ssmk 1 0.319 0.014 22.002 0.000 0.290 0.347
## 24 ssmc ~~ ssmc 1 0.450 0.013 34.420 0.000 0.424 0.475
## 25 ssgs ~~ ssgs 1 0.313 0.012 25.894 0.000 0.289 0.336
## 26 ssasi ~~ ssasi 1 0.405 0.019 21.707 0.000 0.369 0.442
## 27 ssei ~~ ssei 1 0.407 0.012 32.608 0.000 0.383 0.432
## 28 ssno ~~ ssno 1 0.482 0.020 24.126 0.000 0.443 0.521
## 29 sscs ~~ sscs 1 0.049 0.072 0.688 0.491 -0.091 0.189
## 30 sswk ~~ sswk 1 0.226 0.012 18.528 0.000 0.202 0.250
## 31 sspc ~~ sspc 1 0.334 0.012 26.851 0.000 0.310 0.358
## 32 electronic ~~ electronic 1 1.000 0.000 NA NA 1.000 1.000
## 33 g ~~ g 1 1.000 0.000 NA NA 1.000 1.000
## 34 math ~~ electronic 1 0.000 0.000 NA NA 0.000 0.000
## 35 math ~~ speed 1 0.000 0.000 NA NA 0.000 0.000
## 36 math ~~ g 1 0.000 0.000 NA NA 0.000 0.000
## 37 electronic ~~ speed 1 0.000 0.000 NA NA 0.000 0.000
## 38 electronic ~~ g 1 0.000 0.000 NA NA 0.000 0.000
## 39 speed ~~ g 1 0.000 0.000 NA NA 0.000 0.000
## 40 ssar ~1 1 .p40. 2.750 0.039 69.628 0.000 2.672 2.827
## 41 ssmk ~1 1 .p41. 2.356 0.033 71.410 0.000 2.291 2.420
## 42 ssmc ~1 1 .p42. 3.016 0.041 72.778 0.000 2.935 3.097
## 43 ssgs ~1 1 .p43. 3.814 0.059 64.743 0.000 3.699 3.929
## 44 ssasi ~1 1 .p44. 3.350 0.050 66.393 0.000 3.251 3.449
## 45 ssei ~1 1 .p45. 3.069 0.044 69.380 0.000 2.982 3.156
## 46 ssno ~1 1 .p46. 0.566 0.025 22.990 0.000 0.518 0.614
## 47 sscs ~1 1 .p47. 0.647 0.026 25.047 0.000 0.596 0.697
## 48 sswk ~1 1 .p48. 4.392 0.084 52.104 0.000 4.227 4.557
## 49 sspc ~1 1 4.192 0.088 47.615 0.000 4.020 4.365
## 50 math ~1 1 0.000 0.000 NA NA 0.000 0.000
## 51 electronic ~1 1 0.000 0.000 NA NA 0.000 0.000
## 52 speed ~1 1 0.000 0.000 NA NA 0.000 0.000
## 53 g ~1 1 0.000 0.000 NA NA 0.000 0.000
## 54 math =~ ssar 2 .p1. 0.554 0.022 24.731 0.000 0.510 0.598
## 55 math =~ ssmk 2 .p2. 0.336 0.017 19.964 0.000 0.303 0.369
## 56 math =~ ssmc 2 .p3. 0.176 0.015 11.689 0.000 0.146 0.205
## 57 electronic =~ ssgs 2 .p4. 0.214 0.009 24.100 0.000 0.197 0.232
## 58 electronic =~ ssasi 2 .p5. 0.667 0.014 46.090 0.000 0.638 0.695
## 59 electronic =~ ssmc 2 .p6. 0.445 0.014 32.837 0.000 0.419 0.472
## 60 electronic =~ ssei 2 .p7. 0.451 0.013 35.321 0.000 0.426 0.476
## 61 speed =~ ssno 2 .p8. 0.376 0.019 19.895 0.000 0.339 0.413
## 62 speed =~ sscs 2 .p9. 0.800 0.039 20.357 0.000 0.723 0.877
## 63 g =~ ssgs 2 .p10. 0.845 0.006 135.035 0.000 0.832 0.857
## 64 g =~ ssar 2 .p11. 0.813 0.007 114.819 0.000 0.799 0.827
## 65 g =~ sswk 2 .p12. 0.906 0.006 162.227 0.000 0.895 0.917
## 66 g =~ sspc 2 .p13. 0.836 0.008 109.154 0.000 0.821 0.851
## 67 g =~ ssno 2 .p14. 0.649 0.012 53.269 0.000 0.625 0.673
## 68 g =~ sscs 2 .p15. 0.590 0.014 41.380 0.000 0.563 0.618
## 69 g =~ ssasi 2 .p16. 0.507 0.014 35.630 0.000 0.479 0.535
## 70 g =~ ssmk 2 .p17. 0.778 0.008 103.067 0.000 0.764 0.793
## 71 g =~ ssmc 2 .p18. 0.665 0.011 59.161 0.000 0.643 0.687
## 72 g =~ ssei 2 .p19. 0.743 0.010 75.744 0.000 0.724 0.763
## 73 math ~~ math 2 1.000 0.000 NA NA 1.000 1.000
## 74 speed ~~ speed 2 1.000 0.000 NA NA 1.000 1.000
## 75 ssar ~~ ssar 2 0.032 0.024 1.319 0.187 -0.016 0.080
## 76 ssmk ~~ ssmk 2 0.281 0.013 21.162 0.000 0.255 0.307
## 77 ssmc ~~ ssmc 2 0.328 0.013 25.967 0.000 0.303 0.353
## 78 ssgs ~~ ssgs 2 0.241 0.010 24.666 0.000 0.222 0.260
## 79 ssasi ~~ ssasi 2 0.298 0.016 18.956 0.000 0.268 0.329
## 80 ssei ~~ ssei 2 0.244 0.011 22.784 0.000 0.223 0.265
## 81 ssno ~~ ssno 2 0.437 0.018 23.983 0.000 0.402 0.473
## 82 sscs ~~ sscs 2 0.011 0.061 0.174 0.862 -0.109 0.131
## 83 sswk ~~ sswk 2 0.179 0.010 17.631 0.000 0.159 0.198
## 84 sspc ~~ sspc 2 0.301 0.013 23.467 0.000 0.276 0.326
## 85 electronic ~~ electronic 2 1.000 0.000 NA NA 1.000 1.000
## 86 g ~~ g 2 1.000 0.000 NA NA 1.000 1.000
## 87 math ~~ electronic 2 0.000 0.000 NA NA 0.000 0.000
## 88 math ~~ speed 2 0.000 0.000 NA NA 0.000 0.000
## 89 math ~~ g 2 0.000 0.000 NA NA 0.000 0.000
## 90 electronic ~~ speed 2 0.000 0.000 NA NA 0.000 0.000
## [ reached 'max' / getOption("max.print") -- omitted 16 rows ]
tests<-lavTestLRT(configural, metric, scalar2, latent2)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 74.001954 103.294892 1.614444
dfd=tests[2:4,"Df diff"]
dfd
## [1] 15 5 2
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-3067+ 3094 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
## Warning in sqrt((ld) * G/(N - G)): NaNs produced
RMSEAD
## [1] 0.03573942 0.07989882 NaN
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.02785454 0.04406043
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.06688974 0.09366983
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] NA 0.03350834
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 0.994 0.515 0.008
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
## 0.554 0.453 0.002 0.000 0.000 0.000
tests<-lavTestLRT(configural, metric, scalar2, latent)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 74.00195 103.29489 263.11388
dfd=tests[2:4,"Df diff"]
dfd
## [1] 15 5 4
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-3067+ 3094 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.03573942 0.07989882 0.14503581
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.06688974 0.09366983
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.1304381 0.1601622
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 0.994 0.515 0.008
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 1 1 1 1
tests<-lavTestLRT(configural, metric, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 74.00195 103.29489 45.53035
dfd=tests[2:4,"Df diff"]
dfd
## [1] 15 5 10
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-3067+ 3094 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.03573942 0.07989882 0.03396719
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.02785454 0.04406043
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.06688974 0.09366983
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.02433174 0.04427008
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 0.994 0.515 0.008
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 0.005 0.000 0.000 0.000
tests<-lavTestLRT(configural, metric, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 74.00195 242.97927
dfd=tests[2:3,"Df diff"]
dfd
## [1] 15 6
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-3067+ 3094 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.03573942 0.11325032
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.02785454 0.04406043
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.1013107 0.1256380
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 1.000 0.966
bf.age<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
g ~ age
'
bf.ageq<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
g ~ c(b,b)*age
'
bf.age2<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
g ~ age + age2
'
bf.age2q<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
g ~ c(b,b)*age+c(c,c)*age2
'
sem.age<-sem(bf.age, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
fitMeasures(sem.age, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 2398.566 92.000 0.000 0.949 0.090 0.049 0.408 281392.337 281782.445
Mc(sem.age)
## [1] 0.8292602
summary(sem.age, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 115 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 28
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2398.566 1609.937
## Degrees of freedom 92 92
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.490
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1065.100 714.903
## 0 1333.466 895.033
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.027 0.155 26.033 0.000 3.724 4.331 4.027 0.610
## ssmk (.p2.) 2.217 0.110 20.108 0.000 2.001 2.433 2.217 0.372
## ssmc (.p3.) 0.841 0.072 11.759 0.000 0.701 0.981 0.841 0.201
## electronic =~
## ssgs (.p4.) 0.544 0.029 18.490 0.000 0.487 0.602 0.544 0.131
## ssasi (.p5.) 1.742 0.072 24.345 0.000 1.602 1.883 1.742 0.492
## ssmc (.p6.) 1.173 0.051 23.008 0.000 1.074 1.273 1.173 0.280
## ssei (.p7.) 0.938 0.041 23.102 0.000 0.858 1.017 0.938 0.276
## speed =~
## ssno (.p8.) 0.334 0.016 20.298 0.000 0.302 0.366 0.334 0.399
## sscs (.p9.) 0.703 0.035 20.137 0.000 0.635 0.772 0.703 0.820
## g =~
## ssgs (.10.) 3.328 0.066 50.097 0.000 3.198 3.458 3.394 0.818
## ssar (.11.) 5.011 0.097 51.457 0.000 4.820 5.202 5.110 0.774
## sswk (.12.) 5.418 0.114 47.674 0.000 5.195 5.641 5.525 0.882
## sspc (.13.) 2.262 0.052 43.330 0.000 2.160 2.364 2.307 0.815
## ssno (.14.) 0.491 0.014 35.410 0.000 0.464 0.518 0.501 0.598
## sscs (.15.) 0.444 0.014 32.325 0.000 0.417 0.471 0.453 0.528
## ssasi (.16.) 2.057 0.058 35.592 0.000 1.944 2.170 2.098 0.593
## ssmk (.17.) 4.298 0.085 50.298 0.000 4.131 4.466 4.383 0.736
## ssmc (.18.) 2.703 0.059 45.941 0.000 2.587 2.818 2.756 0.657
## ssei (.19.) 2.395 0.048 50.408 0.000 2.302 2.488 2.443 0.720
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.086 0.010 8.420 0.000 0.066 0.106 0.085 0.196
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.39.) 18.244 0.150 121.916 0.000 17.951 18.538 18.244 2.763
## .ssmk (.40.) 14.105 0.125 112.603 0.000 13.860 14.351 14.105 2.367
## .ssmc (.41.) 12.695 0.088 144.027 0.000 12.523 12.868 12.695 3.026
## .ssgs (.42.) 15.887 0.088 181.018 0.000 15.715 16.059 15.887 3.830
## .ssasi (.43.) 11.878 0.073 161.897 0.000 11.734 12.022 11.878 3.357
## .ssei (.44.) 10.456 0.070 149.679 0.000 10.319 10.593 10.456 3.082
## .ssno (.45.) 0.483 0.018 27.065 0.000 0.448 0.518 0.483 0.577
## .sscs (.46.) 0.563 0.018 31.011 0.000 0.527 0.599 0.563 0.656
## .sswk (.47.) 27.623 0.133 208.316 0.000 27.363 27.883 27.623 4.410
## .sspc 11.906 0.059 203.287 0.000 11.791 12.021 11.906 4.207
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.264 1.256 1.006 0.314 -1.198 3.727 1.264 0.029
## .ssmk 11.370 0.513 22.179 0.000 10.365 12.375 11.370 0.320
## .ssmc 7.916 0.280 28.285 0.000 7.367 8.464 7.916 0.450
## .ssgs 5.393 0.203 26.546 0.000 4.995 5.791 5.393 0.313
## .ssasi 5.080 0.253 20.110 0.000 4.585 5.575 5.080 0.406
## .ssei 4.663 0.167 27.955 0.000 4.336 4.990 4.663 0.405
## .ssno 0.339 0.016 21.201 0.000 0.308 0.371 0.339 0.484
## .sscs 0.036 0.053 0.680 0.497 -0.068 0.139 0.036 0.049
## .sswk 8.711 0.454 19.198 0.000 7.822 9.601 8.711 0.222
## .sspc 2.686 0.115 23.328 0.000 2.461 2.912 2.686 0.335
## electronic 1.000 1.000 1.000 1.000 1.000
## .g 1.000 1.000 1.000 0.962 0.962
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.027 0.155 26.033 0.000 3.724 4.331 4.027 0.557
## ssmk (.p2.) 2.217 0.110 20.108 0.000 2.001 2.433 2.217 0.342
## ssmc (.p3.) 0.841 0.072 11.759 0.000 0.701 0.981 0.841 0.177
## electronic =~
## ssgs (.p4.) 0.544 0.029 18.490 0.000 0.487 0.602 0.973 0.211
## ssasi (.p5.) 1.742 0.072 24.345 0.000 1.602 1.883 3.115 0.662
## ssmc (.p6.) 1.173 0.051 23.008 0.000 1.074 1.273 2.098 0.442
## ssei (.p7.) 0.938 0.041 23.102 0.000 0.858 1.017 1.676 0.447
## speed =~
## ssno (.p8.) 0.334 0.016 20.298 0.000 0.302 0.366 0.334 0.377
## sscs (.p9.) 0.703 0.035 20.137 0.000 0.635 0.772 0.703 0.800
## g =~
## ssgs (.10.) 3.328 0.066 50.097 0.000 3.198 3.458 3.893 0.845
## ssar (.11.) 5.011 0.097 51.457 0.000 4.820 5.202 5.861 0.811
## sswk (.12.) 5.418 0.114 47.674 0.000 5.195 5.641 6.337 0.908
## sspc (.13.) 2.262 0.052 43.330 0.000 2.160 2.364 2.646 0.835
## ssno (.14.) 0.491 0.014 35.410 0.000 0.464 0.518 0.574 0.648
## sscs (.15.) 0.444 0.014 32.325 0.000 0.417 0.471 0.519 0.591
## ssasi (.16.) 2.057 0.058 35.592 0.000 1.944 2.170 2.406 0.511
## ssmk (.17.) 4.298 0.085 50.298 0.000 4.131 4.466 5.027 0.774
## ssmc (.18.) 2.703 0.059 45.941 0.000 2.587 2.818 3.161 0.666
## ssei (.19.) 2.395 0.048 50.408 0.000 2.302 2.488 2.801 0.746
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.120 0.011 10.696 0.000 0.098 0.142 0.103 0.242
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.39.) 18.244 0.150 121.916 0.000 17.951 18.538 18.244 2.525
## .ssmk (.40.) 14.105 0.125 112.603 0.000 13.860 14.351 14.105 2.173
## .ssmc (.41.) 12.695 0.088 144.027 0.000 12.523 12.868 12.695 2.676
## .ssgs (.42.) 15.887 0.088 181.018 0.000 15.715 16.059 15.887 3.447
## .ssasi (.43.) 11.878 0.073 161.897 0.000 11.734 12.022 11.878 2.523
## .ssei (.44.) 10.456 0.070 149.679 0.000 10.319 10.593 10.456 2.786
## .ssno (.45.) 0.483 0.018 27.065 0.000 0.448 0.518 0.483 0.545
## .sscs (.46.) 0.563 0.018 31.011 0.000 0.527 0.599 0.563 0.641
## .sswk (.47.) 27.623 0.133 208.316 0.000 27.363 27.883 27.623 3.958
## .sspc 11.216 0.070 159.752 0.000 11.078 11.354 11.216 3.541
## math 0.504 0.039 12.904 0.000 0.428 0.581 0.504 0.504
## elctrnc 3.452 0.153 22.498 0.000 3.152 3.753 1.931 1.931
## speed -0.605 0.047 -12.994 0.000 -0.697 -0.514 -0.605 -0.605
## .g -0.032 0.036 -0.888 0.374 -0.102 0.038 -0.027 -0.027
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.637 1.292 1.267 0.205 -0.895 4.170 1.637 0.031
## .ssmk 11.950 0.552 21.665 0.000 10.869 13.031 11.950 0.284
## .ssmc 7.401 0.291 25.411 0.000 6.830 7.972 7.401 0.329
## .ssgs 5.146 0.195 26.326 0.000 4.763 5.529 5.146 0.242
## .ssasi 6.672 0.386 17.296 0.000 5.916 7.428 6.672 0.301
## .ssei 3.431 0.153 22.364 0.000 3.130 3.732 3.431 0.244
## .ssno 0.345 0.015 23.165 0.000 0.316 0.374 0.345 0.438
## .sscs 0.008 0.047 0.174 0.862 -0.084 0.101 0.008 0.011
## .sswk 8.544 0.478 17.886 0.000 7.608 9.480 8.544 0.175
## .sspc 3.032 0.129 23.578 0.000 2.780 3.284 3.032 0.302
## electronic 3.197 0.296 10.782 0.000 2.616 3.778 1.000 1.000
## .g 1.288 0.065 19.865 0.000 1.161 1.415 0.941 0.941
sem.ageq<-sem(bf.ageq, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
fitMeasures(sem.ageq, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 2406.297 93.000 0.000 0.949 0.090 0.053 0.409 281398.069 281781.450
Mc(sem.ageq)
## [1] 0.8288073
summary(sem.ageq, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 100 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 29
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2406.297 1615.517
## Degrees of freedom 93 93
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.489
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1068.172 717.139
## 0 1338.126 898.378
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.027 0.154 26.074 0.000 3.725 4.330 4.027 0.607
## ssmk (.p2.) 2.219 0.110 20.136 0.000 2.003 2.435 2.219 0.371
## ssmc (.p3.) 0.842 0.072 11.779 0.000 0.702 0.983 0.842 0.200
## electronic =~
## ssgs (.p4.) 0.544 0.029 18.488 0.000 0.486 0.602 0.544 0.130
## ssasi (.p5.) 1.741 0.072 24.315 0.000 1.600 1.881 1.741 0.491
## ssmc (.p6.) 1.172 0.051 22.978 0.000 1.072 1.272 1.172 0.278
## ssei (.p7.) 0.937 0.041 23.080 0.000 0.857 1.016 0.937 0.275
## speed =~
## ssno (.p8.) 0.334 0.016 20.299 0.000 0.302 0.366 0.334 0.397
## sscs (.p9.) 0.703 0.035 20.136 0.000 0.635 0.772 0.703 0.818
## g =~
## ssgs (.10.) 3.330 0.067 49.931 0.000 3.200 3.461 3.422 0.820
## ssar (.11.) 5.013 0.098 51.206 0.000 4.822 5.205 5.151 0.776
## sswk (.12.) 5.423 0.114 47.524 0.000 5.199 5.647 5.572 0.884
## sspc (.13.) 2.263 0.052 43.189 0.000 2.161 2.366 2.326 0.817
## ssno (.14.) 0.491 0.014 35.318 0.000 0.464 0.519 0.505 0.601
## sscs (.15.) 0.444 0.014 32.256 0.000 0.417 0.471 0.456 0.531
## ssasi (.16.) 2.057 0.058 35.519 0.000 1.944 2.171 2.113 0.596
## ssmk (.17.) 4.300 0.086 50.096 0.000 4.132 4.469 4.418 0.738
## ssmc (.18.) 2.703 0.059 45.807 0.000 2.587 2.819 2.777 0.660
## ssei (.19.) 2.396 0.048 50.264 0.000 2.303 2.490 2.462 0.723
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (b) 0.102 0.008 13.071 0.000 0.086 0.117 0.099 0.230
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.39.) 18.262 0.150 122.138 0.000 17.968 18.555 18.262 2.752
## .ssmk (.40.) 14.119 0.126 112.289 0.000 13.873 14.365 14.119 2.359
## .ssmc (.41.) 12.705 0.088 144.116 0.000 12.532 12.877 12.705 3.019
## .ssgs (.42.) 15.898 0.088 181.334 0.000 15.726 16.069 15.898 3.811
## .ssasi (.43.) 11.885 0.073 162.498 0.000 11.741 12.028 11.885 3.351
## .ssei (.44.) 10.464 0.070 150.485 0.000 10.328 10.600 10.464 3.072
## .ssno (.45.) 0.485 0.018 27.183 0.000 0.450 0.520 0.485 0.577
## .sscs (.46.) 0.565 0.018 31.186 0.000 0.529 0.600 0.565 0.657
## .sswk (.47.) 27.642 0.132 209.225 0.000 27.383 27.901 27.642 4.386
## .sspc 11.914 0.059 203.575 0.000 11.799 12.028 11.914 4.187
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.269 1.255 1.012 0.312 -1.189 3.728 1.269 0.029
## .ssmk 11.378 0.513 22.167 0.000 10.372 12.385 11.378 0.318
## .ssmc 7.917 0.280 28.282 0.000 7.369 8.466 7.917 0.447
## .ssgs 5.394 0.203 26.552 0.000 4.996 5.792 5.394 0.310
## .ssasi 5.082 0.253 20.122 0.000 4.587 5.577 5.082 0.404
## .ssei 4.660 0.167 27.963 0.000 4.333 4.986 4.660 0.402
## .ssno 0.339 0.016 21.201 0.000 0.308 0.371 0.339 0.481
## .sscs 0.036 0.053 0.676 0.499 -0.068 0.139 0.036 0.048
## .sswk 8.683 0.452 19.207 0.000 7.797 9.569 8.683 0.219
## .sspc 2.689 0.115 23.330 0.000 2.463 2.915 2.689 0.332
## electronic 1.000 1.000 1.000 1.000 1.000
## .g 1.000 1.000 1.000 0.947 0.947
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.027 0.154 26.074 0.000 3.725 4.330 4.027 0.560
## ssmk (.p2.) 2.219 0.110 20.136 0.000 2.003 2.435 2.219 0.344
## ssmc (.p3.) 0.842 0.072 11.779 0.000 0.702 0.983 0.842 0.178
## electronic =~
## ssgs (.p4.) 0.544 0.029 18.488 0.000 0.486 0.602 0.975 0.213
## ssasi (.p5.) 1.741 0.072 24.315 0.000 1.600 1.881 3.119 0.664
## ssmc (.p6.) 1.172 0.051 22.978 0.000 1.072 1.272 2.101 0.444
## ssei (.p7.) 0.937 0.041 23.080 0.000 0.857 1.016 1.678 0.449
## speed =~
## ssno (.p8.) 0.334 0.016 20.299 0.000 0.302 0.366 0.334 0.378
## sscs (.p9.) 0.703 0.035 20.136 0.000 0.635 0.772 0.703 0.802
## g =~
## ssgs (.10.) 3.330 0.067 49.931 0.000 3.200 3.461 3.863 0.843
## ssar (.11.) 5.013 0.098 51.206 0.000 4.822 5.205 5.815 0.809
## sswk (.12.) 5.423 0.114 47.524 0.000 5.199 5.647 6.290 0.907
## sspc (.13.) 2.263 0.052 43.189 0.000 2.161 2.366 2.625 0.833
## ssno (.14.) 0.491 0.014 35.318 0.000 0.464 0.519 0.570 0.645
## sscs (.15.) 0.444 0.014 32.256 0.000 0.417 0.471 0.515 0.588
## ssasi (.16.) 2.057 0.058 35.519 0.000 1.944 2.171 2.386 0.508
## ssmk (.17.) 4.300 0.086 50.096 0.000 4.132 4.469 4.988 0.772
## ssmc (.18.) 2.703 0.059 45.807 0.000 2.587 2.819 3.135 0.663
## ssei (.19.) 2.396 0.048 50.264 0.000 2.303 2.490 2.780 0.744
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (b) 0.102 0.008 13.071 0.000 0.086 0.117 0.088 0.207
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.39.) 18.262 0.150 122.138 0.000 17.968 18.555 18.262 2.540
## .ssmk (.40.) 14.119 0.126 112.289 0.000 13.873 14.365 14.119 2.185
## .ssmc (.41.) 12.705 0.088 144.116 0.000 12.532 12.877 12.705 2.687
## .ssgs (.42.) 15.898 0.088 181.334 0.000 15.726 16.069 15.898 3.468
## .ssasi (.43.) 11.885 0.073 162.498 0.000 11.741 12.028 11.885 2.529
## .ssei (.44.) 10.464 0.070 150.485 0.000 10.328 10.600 10.464 2.799
## .ssno (.45.) 0.485 0.018 27.183 0.000 0.450 0.520 0.485 0.549
## .sscs (.46.) 0.565 0.018 31.186 0.000 0.529 0.600 0.565 0.644
## .sswk (.47.) 27.642 0.132 209.225 0.000 27.383 27.901 27.642 3.985
## .sspc 11.224 0.070 160.363 0.000 11.087 11.361 11.224 3.563
## math 0.504 0.039 12.903 0.000 0.428 0.581 0.504 0.504
## elctrnc 3.456 0.154 22.473 0.000 3.154 3.757 1.928 1.928
## speed -0.605 0.047 -12.992 0.000 -0.696 -0.514 -0.605 -0.605
## .g -0.039 0.036 -1.097 0.273 -0.109 0.031 -0.034 -0.034
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.657 1.290 1.285 0.199 -0.871 4.185 1.657 0.032
## .ssmk 11.937 0.552 21.642 0.000 10.856 13.018 11.937 0.286
## .ssmc 7.399 0.291 25.408 0.000 6.829 7.970 7.399 0.331
## .ssgs 5.141 0.195 26.337 0.000 4.759 5.524 5.141 0.245
## .ssasi 6.665 0.386 17.277 0.000 5.909 7.421 6.665 0.302
## .ssei 3.432 0.154 22.360 0.000 3.132 3.733 3.432 0.246
## .ssno 0.345 0.015 23.161 0.000 0.316 0.374 0.345 0.441
## .sscs 0.008 0.047 0.174 0.862 -0.084 0.101 0.008 0.011
## .sswk 8.550 0.478 17.885 0.000 7.613 9.487 8.550 0.178
## .sspc 3.031 0.129 23.570 0.000 2.779 3.283 3.031 0.305
## electronic 3.212 0.298 10.785 0.000 2.628 3.796 1.000 1.000
## .g 1.288 0.065 19.844 0.000 1.160 1.415 0.957 0.957
sem.age2<-sem(bf.age2, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
fitMeasures(sem.age2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 2457.193 110.000 0.000 0.948 0.083 0.047 0.418 281385.520 281789.080
Mc(sem.age2)
## [1] 0.8265301
summary(sem.age2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 133 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 88
## Number of equality constraints 28
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2457.193 1654.234
## Degrees of freedom 110 110
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.485
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1083.511 729.443
## 0 1373.682 924.791
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.028 0.155 26.035 0.000 3.725 4.331 4.028 0.610
## ssmk (.p2.) 2.217 0.110 20.107 0.000 2.001 2.433 2.217 0.372
## ssmc (.p3.) 0.841 0.072 11.761 0.000 0.701 0.982 0.841 0.201
## electronic =~
## ssgs (.p4.) 0.544 0.029 18.483 0.000 0.486 0.602 0.544 0.131
## ssasi (.p5.) 1.742 0.072 24.340 0.000 1.602 1.882 1.742 0.492
## ssmc (.p6.) 1.174 0.051 23.004 0.000 1.074 1.274 1.174 0.280
## ssei (.p7.) 0.937 0.041 23.098 0.000 0.858 1.017 0.937 0.276
## speed =~
## ssno (.p8.) 0.334 0.016 20.299 0.000 0.302 0.366 0.334 0.399
## sscs (.p9.) 0.703 0.035 20.139 0.000 0.635 0.772 0.703 0.820
## g =~
## ssgs (.10.) 3.328 0.066 50.093 0.000 3.198 3.458 3.394 0.818
## ssar (.11.) 5.010 0.097 51.449 0.000 4.819 5.201 5.110 0.774
## sswk (.12.) 5.418 0.114 47.673 0.000 5.195 5.641 5.525 0.882
## sspc (.13.) 2.262 0.052 43.324 0.000 2.159 2.364 2.307 0.815
## ssno (.14.) 0.491 0.014 35.410 0.000 0.464 0.518 0.501 0.598
## sscs (.15.) 0.444 0.014 32.328 0.000 0.417 0.471 0.453 0.528
## ssasi (.16.) 2.058 0.058 35.598 0.000 1.945 2.171 2.099 0.593
## ssmk (.17.) 4.298 0.085 50.286 0.000 4.130 4.465 4.383 0.736
## ssmc (.18.) 2.703 0.059 45.940 0.000 2.587 2.818 2.756 0.657
## ssei (.19.) 2.395 0.048 50.412 0.000 2.302 2.489 2.443 0.720
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.086 0.010 8.334 0.000 0.066 0.106 0.084 0.196
## age2 -0.000 0.004 -0.090 0.928 -0.009 0.008 -0.000 -0.002
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.42.) 18.255 0.190 95.964 0.000 17.882 18.628 18.255 2.765
## .ssmk (.43.) 14.114 0.160 88.416 0.000 13.801 14.427 14.114 2.369
## .ssmc (.44.) 12.701 0.110 115.797 0.000 12.486 12.916 12.701 3.028
## .ssgs (.45.) 15.894 0.116 136.636 0.000 15.666 16.122 15.894 3.831
## .ssasi (.46.) 11.882 0.089 133.858 0.000 11.708 12.056 11.882 3.358
## .ssei (.47.) 10.461 0.090 115.820 0.000 10.284 10.638 10.461 3.084
## .ssno (.48.) 0.484 0.021 22.761 0.000 0.443 0.526 0.484 0.578
## .sscs (.49.) 0.564 0.021 26.657 0.000 0.522 0.605 0.564 0.658
## .sswk (.50.) 27.635 0.184 150.119 0.000 27.274 27.996 27.635 4.412
## .sspc 11.911 0.079 151.224 0.000 11.756 12.065 11.911 4.209
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.264 1.257 1.006 0.315 -1.199 3.727 1.264 0.029
## .ssmk 11.370 0.513 22.175 0.000 10.365 12.375 11.370 0.320
## .ssmc 7.916 0.280 28.284 0.000 7.367 8.464 7.916 0.450
## .ssgs 5.393 0.203 26.551 0.000 4.995 5.791 5.393 0.313
## .ssasi 5.081 0.253 20.112 0.000 4.585 5.576 5.081 0.406
## .ssei 4.663 0.167 27.955 0.000 4.336 4.990 4.663 0.405
## .ssno 0.339 0.016 21.202 0.000 0.308 0.371 0.339 0.484
## .sscs 0.036 0.053 0.681 0.496 -0.068 0.139 0.036 0.049
## .sswk 8.711 0.454 19.197 0.000 7.821 9.600 8.711 0.222
## .sspc 2.686 0.115 23.329 0.000 2.461 2.912 2.686 0.336
## electronic 1.000 1.000 1.000 1.000 1.000
## .g 1.000 1.000 1.000 0.962 0.962
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.028 0.155 26.035 0.000 3.725 4.331 4.028 0.557
## ssmk (.p2.) 2.217 0.110 20.107 0.000 2.001 2.433 2.217 0.342
## ssmc (.p3.) 0.841 0.072 11.761 0.000 0.701 0.982 0.841 0.177
## electronic =~
## ssgs (.p4.) 0.544 0.029 18.483 0.000 0.486 0.602 0.972 0.211
## ssasi (.p5.) 1.742 0.072 24.340 0.000 1.602 1.882 3.113 0.661
## ssmc (.p6.) 1.174 0.051 23.004 0.000 1.074 1.274 2.097 0.442
## ssei (.p7.) 0.937 0.041 23.098 0.000 0.858 1.017 1.675 0.446
## speed =~
## ssno (.p8.) 0.334 0.016 20.299 0.000 0.302 0.366 0.334 0.377
## sscs (.p9.) 0.703 0.035 20.139 0.000 0.635 0.772 0.703 0.800
## g =~
## ssgs (.10.) 3.328 0.066 50.093 0.000 3.198 3.458 3.893 0.845
## ssar (.11.) 5.010 0.097 51.449 0.000 4.819 5.201 5.860 0.811
## sswk (.12.) 5.418 0.114 47.673 0.000 5.195 5.641 6.337 0.908
## sspc (.13.) 2.262 0.052 43.324 0.000 2.159 2.364 2.646 0.835
## ssno (.14.) 0.491 0.014 35.410 0.000 0.464 0.518 0.575 0.648
## sscs (.15.) 0.444 0.014 32.328 0.000 0.417 0.471 0.519 0.591
## ssasi (.16.) 2.058 0.058 35.598 0.000 1.945 2.171 2.407 0.511
## ssmk (.17.) 4.298 0.085 50.286 0.000 4.130 4.465 5.027 0.774
## ssmc (.18.) 2.703 0.059 45.940 0.000 2.587 2.818 3.161 0.666
## ssei (.19.) 2.395 0.048 50.412 0.000 2.302 2.489 2.802 0.746
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.114 0.011 10.000 0.000 0.092 0.136 0.097 0.230
## age2 -0.014 0.005 -2.671 0.008 -0.024 -0.004 -0.012 -0.060
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.42.) 18.255 0.190 95.964 0.000 17.882 18.628 18.255 2.527
## .ssmk (.43.) 14.114 0.160 88.416 0.000 13.801 14.427 14.114 2.174
## .ssmc (.44.) 12.701 0.110 115.797 0.000 12.486 12.916 12.701 2.678
## .ssgs (.45.) 15.894 0.116 136.636 0.000 15.666 16.122 15.894 3.448
## .ssasi (.46.) 11.882 0.089 133.858 0.000 11.708 12.056 11.882 2.524
## .ssei (.47.) 10.461 0.090 115.820 0.000 10.284 10.638 10.461 2.787
## .ssno (.48.) 0.484 0.021 22.761 0.000 0.443 0.526 0.484 0.546
## .sscs (.49.) 0.564 0.021 26.657 0.000 0.522 0.605 0.564 0.642
## .sswk (.50.) 27.635 0.184 150.119 0.000 27.274 27.996 27.635 3.960
## .sspc 11.221 0.088 127.489 0.000 11.048 11.393 11.221 3.543
## math 0.504 0.039 12.902 0.000 0.428 0.581 0.504 0.504
## elctrnc 3.452 0.153 22.495 0.000 3.152 3.753 1.932 1.932
## speed -0.605 0.047 -12.995 0.000 -0.697 -0.514 -0.605 -0.605
## .g 0.042 0.050 0.842 0.400 -0.055 0.139 0.036 0.036
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.639 1.292 1.268 0.205 -0.894 4.172 1.639 0.031
## .ssmk 11.949 0.552 21.663 0.000 10.868 13.030 11.949 0.284
## .ssmc 7.401 0.291 25.408 0.000 6.830 7.972 7.401 0.329
## .ssgs 5.148 0.196 26.319 0.000 4.764 5.531 5.148 0.242
## .ssasi 6.676 0.386 17.305 0.000 5.920 7.432 6.676 0.301
## .ssei 3.431 0.153 22.364 0.000 3.130 3.732 3.431 0.244
## .ssno 0.345 0.015 23.169 0.000 0.316 0.374 0.345 0.438
## .sscs 0.008 0.047 0.175 0.861 -0.084 0.101 0.008 0.011
## .sswk 8.541 0.476 17.931 0.000 7.608 9.475 8.541 0.175
## .sspc 3.033 0.129 23.572 0.000 2.781 3.285 3.033 0.302
## electronic 3.194 0.296 10.778 0.000 2.613 3.774 1.000 1.000
## .g 1.283 0.064 19.924 0.000 1.157 1.409 0.938 0.938
sem.age2q<-sem(bf.age2q, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
fitMeasures(sem.age2q, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 2470.480 112.000 0.000 0.948 0.083 0.052 0.420 281394.807 281784.915
Mc(sem.age2q)
## [1] 0.8257733
summary(sem.age2q, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 108 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 88
## Number of equality constraints 30
##
## Number of observations per group:
## 1 3067
## 0 3094
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2470.480 1664.450
## Degrees of freedom 112 112
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.484
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1089.084 733.755
## 0 1381.396 930.695
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.028 0.154 26.075 0.000 3.725 4.331 4.028 0.607
## ssmk (.p2.) 2.220 0.110 20.137 0.000 2.004 2.436 2.220 0.371
## ssmc (.p3.) 0.842 0.072 11.779 0.000 0.702 0.983 0.842 0.200
## electronic =~
## ssgs (.p4.) 0.544 0.029 18.479 0.000 0.486 0.601 0.544 0.130
## ssasi (.p5.) 1.740 0.072 24.304 0.000 1.600 1.880 1.740 0.490
## ssmc (.p6.) 1.172 0.051 22.971 0.000 1.072 1.272 1.172 0.278
## ssei (.p7.) 0.936 0.041 23.069 0.000 0.857 1.016 0.936 0.275
## speed =~
## ssno (.p8.) 0.334 0.016 20.298 0.000 0.302 0.366 0.334 0.397
## sscs (.p9.) 0.703 0.035 20.138 0.000 0.635 0.772 0.703 0.818
## g =~
## ssgs (.10.) 3.332 0.067 49.912 0.000 3.201 3.463 3.425 0.821
## ssar (.11.) 5.015 0.098 51.210 0.000 4.823 5.207 5.156 0.777
## sswk (.12.) 5.426 0.114 47.491 0.000 5.202 5.649 5.577 0.884
## sspc (.13.) 2.264 0.052 43.143 0.000 2.162 2.367 2.328 0.818
## ssno (.14.) 0.492 0.014 35.304 0.000 0.464 0.519 0.505 0.601
## sscs (.15.) 0.445 0.014 32.251 0.000 0.418 0.472 0.457 0.531
## ssasi (.16.) 2.058 0.058 35.491 0.000 1.945 2.172 2.116 0.596
## ssmk (.17.) 4.302 0.086 50.086 0.000 4.134 4.470 4.422 0.738
## ssmc (.18.) 2.704 0.059 45.760 0.000 2.589 2.820 2.780 0.660
## ssei (.19.) 2.398 0.048 50.230 0.000 2.304 2.491 2.465 0.723
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (b) 0.099 0.008 12.531 0.000 0.083 0.114 0.096 0.223
## age2 (c) -0.007 0.003 -1.932 0.053 -0.013 0.000 -0.006 -0.032
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.42.) 18.435 0.173 106.395 0.000 18.095 18.775 18.435 2.777
## .ssmk (.43.) 14.268 0.146 97.739 0.000 13.982 14.554 14.268 2.382
## .ssmc (.44.) 12.798 0.101 126.893 0.000 12.600 12.996 12.798 3.039
## .ssgs (.45.) 16.013 0.105 153.062 0.000 15.808 16.218 16.013 3.836
## .ssasi (.46.) 11.956 0.082 145.277 0.000 11.795 12.117 11.956 3.370
## .ssei (.47.) 10.547 0.082 128.659 0.000 10.386 10.708 10.547 3.095
## .ssno (.48.) 0.502 0.020 25.457 0.000 0.463 0.541 0.502 0.597
## .sscs (.49.) 0.580 0.020 29.313 0.000 0.541 0.619 0.580 0.674
## .sswk (.50.) 27.830 0.162 172.062 0.000 27.513 28.147 27.830 4.412
## .sspc 11.992 0.070 171.677 0.000 11.855 12.129 11.992 4.212
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.268 1.255 1.010 0.312 -1.192 3.727 1.268 0.029
## .ssmk 11.380 0.514 22.158 0.000 10.374 12.387 11.380 0.317
## .ssmc 7.917 0.280 28.282 0.000 7.369 8.466 7.917 0.447
## .ssgs 5.395 0.203 26.550 0.000 4.997 5.793 5.395 0.310
## .ssasi 5.082 0.253 20.124 0.000 4.587 5.577 5.082 0.404
## .ssei 4.660 0.167 27.970 0.000 4.334 4.987 4.660 0.401
## .ssno 0.339 0.016 21.204 0.000 0.308 0.371 0.339 0.481
## .sscs 0.036 0.053 0.676 0.499 -0.068 0.139 0.036 0.048
## .sswk 8.681 0.452 19.194 0.000 7.794 9.567 8.681 0.218
## .sspc 2.689 0.115 23.336 0.000 2.463 2.915 2.689 0.332
## electronic 1.000 1.000 1.000 1.000 1.000
## .g 1.000 1.000 1.000 0.946 0.946
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.028 0.154 26.075 0.000 3.725 4.331 4.028 0.561
## ssmk (.p2.) 2.220 0.110 20.137 0.000 2.004 2.436 2.220 0.344
## ssmc (.p3.) 0.842 0.072 11.779 0.000 0.702 0.983 0.842 0.178
## electronic =~
## ssgs (.p4.) 0.544 0.029 18.479 0.000 0.486 0.601 0.974 0.213
## ssasi (.p5.) 1.740 0.072 24.304 0.000 1.600 1.880 3.118 0.664
## ssmc (.p6.) 1.172 0.051 22.971 0.000 1.072 1.272 2.100 0.444
## ssei (.p7.) 0.936 0.041 23.069 0.000 0.857 1.016 1.678 0.449
## speed =~
## ssno (.p8.) 0.334 0.016 20.298 0.000 0.302 0.366 0.334 0.378
## sscs (.p9.) 0.703 0.035 20.138 0.000 0.635 0.772 0.703 0.803
## g =~
## ssgs (.10.) 3.332 0.067 49.912 0.000 3.201 3.463 3.859 0.842
## ssar (.11.) 5.015 0.098 51.210 0.000 4.823 5.207 5.809 0.809
## sswk (.12.) 5.426 0.114 47.491 0.000 5.202 5.649 6.284 0.907
## sspc (.13.) 2.264 0.052 43.143 0.000 2.162 2.367 2.623 0.833
## ssno (.14.) 0.492 0.014 35.304 0.000 0.464 0.519 0.569 0.645
## sscs (.15.) 0.445 0.014 32.251 0.000 0.418 0.472 0.515 0.588
## ssasi (.16.) 2.058 0.058 35.491 0.000 1.945 2.172 2.384 0.507
## ssmk (.17.) 4.302 0.086 50.086 0.000 4.134 4.470 4.983 0.772
## ssmc (.18.) 2.704 0.059 45.760 0.000 2.589 2.820 3.133 0.663
## ssei (.19.) 2.398 0.048 50.230 0.000 2.304 2.491 2.777 0.743
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (b) 0.099 0.008 12.531 0.000 0.083 0.114 0.085 0.201
## age2 (c) -0.007 0.003 -1.932 0.053 -0.013 0.000 -0.006 -0.029
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.42.) 18.435 0.173 106.395 0.000 18.095 18.775 18.435 2.566
## .ssmk (.43.) 14.268 0.146 97.739 0.000 13.982 14.554 14.268 2.210
## .ssmc (.44.) 12.798 0.101 126.893 0.000 12.600 12.996 12.798 2.708
## .ssgs (.45.) 16.013 0.105 153.062 0.000 15.808 16.218 16.013 3.496
## .ssasi (.46.) 11.956 0.082 145.277 0.000 11.795 12.117 11.956 2.545
## .ssei (.47.) 10.547 0.082 128.659 0.000 10.386 10.708 10.547 2.823
## .ssno (.48.) 0.502 0.020 25.457 0.000 0.463 0.541 0.502 0.568
## .sscs (.49.) 0.580 0.020 29.313 0.000 0.541 0.619 0.580 0.662
## .sswk (.50.) 27.830 0.162 172.062 0.000 27.513 28.147 27.830 4.015
## .sspc 11.302 0.079 142.221 0.000 11.146 11.458 11.302 3.590
## math 0.504 0.039 12.903 0.000 0.428 0.581 0.504 0.504
## elctrnc 3.457 0.154 22.463 0.000 3.155 3.759 1.929 1.929
## speed -0.605 0.047 -12.993 0.000 -0.697 -0.514 -0.605 -0.605
## .g -0.038 0.036 -1.059 0.290 -0.107 0.032 -0.032 -0.032
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.657 1.290 1.284 0.199 -0.872 4.185 1.657 0.032
## .ssmk 11.937 0.552 21.639 0.000 10.856 13.018 11.937 0.286
## .ssmc 7.399 0.291 25.407 0.000 6.829 7.970 7.399 0.331
## .ssgs 5.142 0.195 26.333 0.000 4.759 5.525 5.142 0.245
## .ssasi 6.667 0.386 17.281 0.000 5.911 7.423 6.667 0.302
## .ssei 3.432 0.154 22.360 0.000 3.131 3.733 3.432 0.246
## .ssno 0.345 0.015 23.164 0.000 0.316 0.374 0.345 0.442
## .sscs 0.008 0.047 0.175 0.861 -0.084 0.101 0.008 0.011
## .sswk 8.548 0.477 17.905 0.000 7.612 9.484 8.548 0.178
## .sspc 3.031 0.129 23.566 0.000 2.779 3.283 3.031 0.306
## electronic 3.212 0.298 10.780 0.000 2.628 3.796 1.000 1.000
## .g 1.283 0.065 19.886 0.000 1.156 1.409 0.956 0.956
# CROSS VALIDATION
set.seed(123) # For reproducibility, set seed if needed
split_indices <- sample(1:nrow(dgroup), size = nrow(dgroup) / 2)
dhalf1 <- dgroup[split_indices, ]
dhalf2 <- dgroup[-split_indices, ]
# WHITE GROUP
# CORRELATED FACTOR MODEL
cf.model<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
'
cf.lv<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
verbal~~1*verbal
math~~1*math
speed~~1*speed
'
cf.reduced<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
verbal~~1*verbal
math~~1*math
speed~~1*speed
math~0*1
'
baseline<-cfa(cf.model, data=dhalf1, meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 964.047 27.000 0.000 0.959 0.859 0.106 0.041 143249.669 143478.911
configural<-cfa(cf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 635.801 54.000 0.000 0.974 0.910 0.084 0.025 140361.694 140820.178
metric<-cfa(cf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 730.910 62.000 0.000 0.970 0.897 0.084 0.035 140440.803 140851.026
scalar<-cfa(cf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1413.127 68.000 0.000 0.939 0.804 0.113 0.070 141111.021 141485.047
scalar2<-cfa(cf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1")) # no and cs biased but one needs to be constrained
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 766.730 64.000 0.000 0.968 0.892 0.084 0.037 140472.623 140870.780
strict<-cfa(cf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 890.976 74.000 0.000 0.963 0.876 0.085 0.048 140576.869 140914.700
cf.cov<-cfa(cf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(cf.cov, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 825.330 70.000 0.000 0.966 0.885 0.084 0.087 140519.223 140881.184
cf.vcov<-cfa(cf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances", "lv.variances"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(cf.vcov, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 904.895 74.000 0.000 0.963 0.874 0.085 0.099 140590.788 140928.618
cf.cov2<-cfa(cf.lv, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(cf.cov2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 834.511 73.000 0.000 0.966 0.884 0.082 0.086 140522.404 140866.267
reduced<-cfa(cf.reduced, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(reduced, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 840.646 74.000 0.000 0.965 0.883 0.082 0.087 140526.539 140864.369
baseline<-cfa(cf.model, data=dhalf2, meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 892.601 27.000 0.000 0.962 0.869 0.102 0.040 143621.485 143850.740
configural<-cfa(cf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 568.580 54.000 0.000 0.977 0.920 0.079 0.026 140801.011 141259.519
metric<-cfa(cf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 638.658 62.000 0.000 0.974 0.911 0.078 0.032 140855.088 141265.333
scalar<-cfa(cf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1193.114 68.000 0.000 0.950 0.833 0.104 0.059 141397.544 141771.591
scalar2<-cfa(cf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1")) # no and cs biased but one needs to be constrained
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 655.979 64.000 0.000 0.973 0.908 0.077 0.033 140868.409 141266.588
strict<-cfa(cf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 762.840 74.000 0.000 0.969 0.894 0.078 0.041 140955.270 141293.118
cf.cov<-cfa(cf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(cf.cov, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 723.787 70.000 0.000 0.971 0.899 0.078 0.101 140924.218 141286.198
cf.vcov<-cfa(cf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances", "lv.variances"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(cf.vcov, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 845.460 74.000 0.000 0.965 0.882 0.082 0.115 141037.891 141375.739
cf.cov2<-cfa(cf.lv, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(cf.cov2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 726.816 73.000 0.000 0.971 0.899 0.076 0.100 140921.246 141265.128
reduced<-cfa(cf.reduced, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("sswk~1", "ssar~1", "ssei~1", "sscs~1"))
fitMeasures(reduced, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 728.817 74.000 0.000 0.971 0.899 0.076 0.100 140921.247 141259.096
# HIGH ORDER FACTOR
hof.model<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
'
hof.lv<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
'
hof.weak<-' # only used if ssmk is free instead of ssar
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
math~0*1
'
baseline<-cfa(hof.model, data=dhalf1, meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1264.006 29.000 0.000 0.946 0.818 0.118 0.057 143545.628 143762.804
configural<-cfa(hof.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 846.130 58.000 0.000 0.964 0.880 0.094 0.032 140564.024 140998.377
metric<-cfa(hof.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 958.784 69.000 0.000 0.960 0.866 0.092 0.048 140654.677 141022.671
scalar<-cfa(hof.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", 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 (= 4.373134e-14) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1635.661 74.000 0.000 0.930 0.776 0.117 0.078 141321.554 141659.385
scalar2<-cfa(hof.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~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 (= 2.476674e-14) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1012.280 70.000 0.000 0.958 0.858 0.093 0.050 140706.173 141068.134
strict<-cfa(hof.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~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 (= 1.322183e-13) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1131.116 80.000 0.000 0.953 0.843 0.092 0.060 140805.009 141106.643
latent<-cfa(hof.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~1"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= 4.436381e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(latent, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1112.555 75.000 0.000 0.953 0.845 0.095 0.101 140796.448 141128.245
latent2<-cfa(hof.lv, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~1"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= 4.938745e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(latent2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1019.537 73.000 0.000 0.957 0.858 0.092 0.051 140707.431 141051.294
weak<-cfa(hof.weak, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~1"))
fitMeasures(weak, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1019.537 74.000 0.000 0.957 0.858 0.091 0.051 140705.431 141043.261
baseline<-cfa(hof.model, data=dhalf2, meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1296.360 29.000 0.000 0.945 0.814 0.119 0.060 144021.244 144238.433
configural<-cfa(hof.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 905.737 58.000 0.000 0.962 0.871 0.097 0.038 141130.167 141564.544
metric<-cfa(hof.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 981.720 69.000 0.000 0.959 0.862 0.093 0.045 141184.151 141552.164
scalar<-cfa(hof.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", 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 (= 2.846783e-14) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1514.387 74.000 0.000 0.935 0.792 0.112 0.067 141706.817 142044.666
scalar2<-cfa(hof.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~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 (= 1.592286e-14) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1007.462 70.000 0.000 0.958 0.859 0.093 0.047 141207.892 141569.873
strict<-cfa(hof.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~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 (= 1.730658e-13) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1110.119 80.000 0.000 0.954 0.846 0.091 0.053 141290.549 141592.200
latent<-cfa(hof.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~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 (= 7.656910e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(latent, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1169.274 75.000 0.000 0.951 0.837 0.097 0.119 141359.704 141691.519
latent2<-cfa(hof.lv, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~1"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= 4.550519e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(latent2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1011.214 73.000 0.000 0.958 0.859 0.091 0.047 141205.644 141549.526
weak<-cfa(hof.weak, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("sswk~1", "ssmk~1", "ssei~1", "sscs~1"))
fitMeasures(weak, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1011.214 74.000 0.000 0.958 0.859 0.091 0.047 141203.644 141541.493
# BIFACTOR
bf.model<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
'
bf.lv<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
'
baseline<-cfa(bf.model, data=dhalf1, meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 986.871 26.000 0.000 0.958 0.856 0.110 0.046 143274.492 143509.767
configural<-cfa(bf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= -1.693102e-06) is smaller than zero. This may
## be a symptom that the model is not identified.
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 768.612 52.000 0.000 0.968 0.890 0.095 0.030 140498.505 140969.054
metric<-cfa(bf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 851.931 67.000 0.000 0.965 0.880 0.087 0.045 140551.824 140931.883
scalar<-cfa(bf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 961.121 73.000 0.000 0.960 0.866 0.089 0.046 140649.014 140992.877
scalar2<-cfa(bf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 898.929 72.000 0.000 0.963 0.874 0.086 0.045 140588.822 140938.718
strict<-cfa(bf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("sspc~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 944.931 82.000 0.000 0.961 0.869 0.083 0.046 140614.825 140904.393
latent<-cfa(bf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("sspc~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(latent, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1037.052 76.000 0.000 0.957 0.856 0.091 0.100 140718.946 141044.711
latent2<-cfa(bf.lv, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(latent2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 901.705 74.000 0.000 0.963 0.874 0.085 0.046 140587.599 140925.429
baseline<-cfa(bf.model, data=dhalf2, meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= -1.904191e-06) is smaller than zero. This may
## be a symptom that the model is not identified.
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1036.229 26.000 0.000 0.956 0.849 0.112 0.050 143767.113 144002.400
configural<-cfa(bf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 795.842 52.000 0.000 0.967 0.886 0.096 0.037 141032.273 141502.847
metric<-cfa(bf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 838.039 67.000 0.000 0.965 0.882 0.086 0.043 141044.470 141424.549
scalar<-cfa(bf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1023.337 73.000 0.000 0.957 0.857 0.092 0.045 141217.768 141561.649
scalar2<-cfa(bf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 911.659 72.000 0.000 0.962 0.873 0.087 0.043 141108.089 141458.004
strict<-cfa(bf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("sspc~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 951.183 82.000 0.000 0.961 0.868 0.083 0.044 141127.613 141417.197
latent<-cfa(bf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("sspc~1"))
fitMeasures(latent, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1133.348 76.000 0.000 0.953 0.842 0.095 0.120 141321.778 141647.560
latent2<-cfa(bf.lv, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
fitMeasures(latent2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 912.116 74.000 0.000 0.962 0.873 0.086 0.043 141104.546 141442.395
# ALL RACE RESPONDENTS
dgroup<- dplyr::select(dk, id, starts_with("ss"), afqt, efa, educ2000, age, age2, sex, agesex, agesex2, age14:age22, sweight, weight2000, cweight, asvabweight)
nrow(dgroup)
## [1] 10918
fit<-lm(efa ~ sex + rcs(age, 3) + sex*rcs(age, 3), data=dgroup)
summary(fit)
##
## Call:
## lm(formula = efa ~ sex + rcs(age, 3) + sex * rcs(age, 3), data = dgroup)
##
## Residuals:
## Min 1Q Median 3Q Max
## -49.657 -11.349 0.808 11.795 35.347
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 101.17412 0.50603 199.939 < 2e-16 ***
## sex -3.21041 0.71719 -4.476 7.67e-06 ***
## rcs(age, 3)age 1.54991 0.21622 7.168 8.10e-13 ***
## rcs(age, 3)age' 0.19418 0.28131 0.690 0.4901
## sex:rcs(age, 3)age -0.51893 0.30999 -1.674 0.0942 .
## sex:rcs(age, 3)age' 0.07937 0.40328 0.197 0.8440
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.95 on 10912 degrees of freedom
## Multiple R-squared: 0.05827, Adjusted R-squared: 0.05784
## F-statistic: 135 on 5 and 10912 DF, p-value: < 2.2e-16
dgroup$pred1<-fitted(fit)
original_age_min <- 14
original_age_max <- 22
mean_centered_min <- min(dgroup$age)
mean_centered_max <- max(dgroup$age)
original_age_mean <- (original_age_min + original_age_max) / 2
mean_centered_age_mean <- (mean_centered_min + mean_centered_max) / 2
age_difference <- original_age_mean - mean_centered_age_mean
xyplot(dgroup$pred1 ~ dgroup$age, data=dgroup, groups=sex, pch=19, type=c("p"), col=c('red', 'blue'), grid=TRUE, ylab="Predicted IQ", xlab="age", key=list(text=list(c("Male", "Female")), points=list(pch=c(19,19), col=c("red", "blue")), columns=2))
xyplot(dgroup$pred1 ~ dgroup$age, data=dgroup, groups=sex, pch=19, type=c("p"), col=c('red', 'blue'), grid=TRUE, ylab="Predicted IQ", xlab="Age", key=list(text=list(c("Male", "Female")), points=list(pch=c(19,19), col=c("red", "blue")), columns=2), scales=list(x=list(at=seq(mean_centered_min, mean_centered_max), labels=seq(original_age_min, original_age_max))))
describeBy(dgroup$pred1, dgroup$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 5469 101.19 3.94 101.32 101.15 5.25 94.97 108.54 13.56 0.1 -1.15 0.05
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 5449 98.26 2.79 98.17 98.23 3.35 93.84 103.73 9.89 0.13 -1.12 0.04
describeBy(dgroup$efa, dgroup$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 5469 101.19 16.46 102.26 101.51 20.13 54.86 133.69 78.84 -0.16 -0.99 0.22
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 5449 98.26 14.1 98.5 98.37 16.45 54.86 130.66 75.8 -0.09 -0.75 0.19
describeBy(dgroup$afqt, dgroup$sex)
##
## Descriptive statistics by group
## INDICES: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## V1 1 5469 99.84 15.36 97.51 99.07 19.15 77.91 130.02 52.11 0.33 -1.13 0.21
## --------------------------------------------------------------------------
## INDICES: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## V1 1 5449 99.77 14.69 97.9 99.07 18.14 77.91 130.02 52.11 0.32 -1.07 0.2
describeBy(dgroup$educ2000, dgroup$sex)
##
## Descriptive statistics by group
## group: 0
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 3482 13.06 2.49 12 12.95 1.48 1 20 19 0.47 0.96 0.04
## --------------------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 3678 13.31 2.46 12 13.22 1.48 0 20 20 0.16 1.09 0.04
cor(dgroup$efa, dgroup$afqt, use="pairwise.complete.obs", method="pearson")
## [,1]
## [1,] 0.9255344
# Lynn's developmental theory is supported here too
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(age, sex) %>% summarise(MEAN = survey_mean(pred1), SD = survey_sd(pred1))
## # A tibble: 18 Ă— 5
## # Groups: age [9]
## age sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -4 0 95.0 1.26e-16 1.96e-15
## 2 -4 1 93.8 0 0
## 3 -3 0 96.5 4.50e-16 9.70e-15
## 4 -3 1 94.9 6.00e-18 2.92e-16
## 5 -2 0 98.1 4.45e-16 9.70e-15
## 6 -2 1 95.9 2.14e-14 3.73e-13
## 7 -1 0 99.7 4.54e-16 9.34e-15
## 8 -1 1 97.0 7.87e-17 1.58e-15
## 9 0 0 101. 2.71e-15 4.52e-14
## 10 0 1 98.2 4.11e-16 8.70e-15
## 11 1 0 103. 1.04e-15 1.59e-14
## 12 1 1 99.5 0 0
## 13 2 0 105. 0 0
## 14 2 1 101. 6.94e-15 1.04e-13
## 15 3 0 107. 9.66e-17 2.26e-15
## 16 3 1 102. 0 0
## 17 4 0 109. 1.26e-16 1.95e-15
## 18 4 1 104. 0 0
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(age, sex) %>% summarise(MEAN = survey_mean(efa), SD = survey_sd(efa))
## # A tibble: 18 Ă— 5
## # Groups: age [9]
## age sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -4 0 98.7 0.797 14.6
## 2 -4 1 99.3 0.755 12.9
## 3 -3 0 102. 0.672 15.2
## 4 -3 1 99.1 0.606 13.0
## 5 -2 0 104. 0.681 15.5
## 6 -2 1 100. 0.585 12.6
## 7 -1 0 106. 0.677 14.9
## 8 -1 1 102. 0.583 12.9
## 9 0 0 106. 0.695 15.7
## 10 0 1 102. 0.601 13.6
## 11 1 0 107. 0.721 15.4
## 12 1 1 103. 0.650 14.1
## 13 2 0 111. 0.695 14.8
## 14 2 1 104. 0.655 13.4
## 15 3 0 110. 0.737 15.4
## 16 3 1 105. 0.639 13.8
## 17 4 0 109. 1.48 15.5
## 18 4 1 106. 1.21 11.9
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(age, sex) %>% summarise(MEAN = survey_mean(afqt), SD = survey_sd(afqt))
## # A tibble: 18 Ă— 5
## # Groups: age [9]
## age sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -4 0 103. 0.873 15.5
## 2 -4 1 106. 0.885 14.8
## 3 -3 0 104. 0.727 15.8
## 4 -3 1 104. 0.706 14.9
## 5 -2 0 104. 0.712 15.6
## 6 -2 1 104. 0.687 14.5
## 7 -1 0 104. 0.748 15.6
## 8 -1 1 104. 0.679 14.8
## 9 0 0 103. 0.731 15.4
## 10 0 1 104. 0.691 14.7
## 11 1 0 105. 0.761 15.3
## 12 1 1 103. 0.728 15.2
## 13 2 0 106. 0.762 15.0
## 14 2 1 102. 0.761 14.8
## 15 3 0 105. 0.795 15.6
## 16 3 1 103. 0.738 15.0
## 17 4 0 104. 1.63 16.0
## 18 4 1 104. 1.47 13.5
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(sex) %>% summarise(MEAN = survey_mean(pred1), SD = survey_sd(pred1))
## # A tibble: 2 Ă— 4
## sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl>
## 1 0 101. 0.0712 3.97
## 2 1 98.1 0.0514 2.83
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(sex) %>% summarise(MEAN = survey_mean(efa), SD = survey_sd(efa))
## # A tibble: 2 Ă— 4
## sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl>
## 1 0 106. 0.256 15.6
## 2 1 102. 0.222 13.4
dgroup %>% as_survey_design(ids = id, weights = sweight) %>% group_by(sex) %>% summarise(MEAN = survey_mean(afqt), SD = survey_sd(afqt))
## # A tibble: 2 Ă— 4
## sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl>
## 1 0 104. 0.267 15.5
## 2 1 104. 0.255 14.8
dgroup %>% as_survey_design(ids = id, weights = weight2000) %>% group_by(sex) %>% summarise(MEAN = survey_mean(educ2000, na.rm = TRUE), SD = survey_sd(educ2000, na.rm = TRUE))
## # A tibble: 2 Ă— 4
## sex MEAN MEAN_se SD
## <dbl> <dbl> <dbl> <dbl>
## 1 0 13.4 0.0523 2.55
## 2 1 13.6 0.0489 2.46
# CORRELATED FACTOR MODEL
cf.model<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
'
cf.lv<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
verbal~~1*verbal
math~~1*math
speed~~1*speed
'
baseline<-cfa(cf.model, data=dgroup, meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2635.698 27.000 0.000 0.973 0.094 0.029 512193.874 512471.204
Mc(baseline)
## [1] 0.8873829
configural<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1759.374 54.000 0.000 0.982 0.076 0.019 503353.883 503908.543
Mc(configural)
## [1] 0.924866
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 50 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 76
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1759.374 1032.860
## Degrees of freedom 54 54
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.703
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 563.494 330.806
## 0 1195.880 702.054
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs 1.972 0.176 11.184 0.000 1.626 2.317 1.972 0.424
## sswk 7.148 0.085 84.205 0.000 6.982 7.314 7.148 0.936
## sspc 2.808 0.041 67.870 0.000 2.727 2.889 2.808 0.856
## math =~
## ssar 6.530 0.073 89.278 0.000 6.386 6.673 6.530 0.933
## ssmk 5.379 0.067 80.061 0.000 5.248 5.511 5.379 0.877
## ssmc 1.581 0.119 13.302 0.000 1.348 1.814 1.581 0.367
## electronic =~
## ssgs 2.218 0.182 12.201 0.000 1.862 2.575 2.218 0.477
## ssasi 2.781 0.056 49.967 0.000 2.672 2.890 2.781 0.740
## ssmc 1.861 0.119 15.601 0.000 1.627 2.095 1.861 0.432
## ssei 2.963 0.047 63.284 0.000 2.871 3.054 2.963 0.828
## speed =~
## ssno 0.823 0.012 66.863 0.000 0.799 0.847 0.823 0.887
## sscs 0.729 0.015 49.876 0.000 0.701 0.758 0.729 0.776
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.825 0.007 125.488 0.000 0.812 0.838 0.825 0.825
## electronic 0.882 0.008 107.789 0.000 0.866 0.898 0.882 0.882
## speed 0.743 0.011 64.940 0.000 0.721 0.766 0.743 0.743
## math ~~
## electronic 0.813 0.011 75.543 0.000 0.792 0.834 0.813 0.813
## speed 0.739 0.010 73.894 0.000 0.719 0.758 0.739 0.739
## electronic ~~
## speed 0.619 0.015 42.304 0.000 0.590 0.648 0.619 0.619
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 14.716 0.078 188.083 0.000 14.563 14.869 14.716 3.165
## .sswk 25.615 0.123 208.263 0.000 25.374 25.856 25.615 3.352
## .sspc 11.115 0.053 210.841 0.000 11.011 11.218 11.115 3.390
## .ssar 16.646 0.123 135.820 0.000 16.405 16.886 16.646 2.379
## .ssmk 13.157 0.108 122.070 0.000 12.946 13.369 13.157 2.146
## .ssmc 11.841 0.076 156.606 0.000 11.693 11.989 11.841 2.749
## .ssasi 10.952 0.064 171.593 0.000 10.827 11.077 10.952 2.913
## .ssei 9.613 0.062 156.264 0.000 9.492 9.733 9.613 2.685
## .ssno 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.326
## .sscs 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.404
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.102 0.177 28.846 0.000 4.755 5.449 5.102 0.236
## .sswk 7.286 0.420 17.344 0.000 6.462 8.109 7.286 0.125
## .sspc 2.869 0.097 29.480 0.000 2.678 3.059 2.869 0.267
## .ssar 6.306 0.391 16.109 0.000 5.539 7.073 6.306 0.129
## .ssmk 8.653 0.312 27.746 0.000 8.042 9.265 8.653 0.230
## .ssmc 7.801 0.224 34.823 0.000 7.361 8.240 7.801 0.421
## .ssasi 6.396 0.201 31.843 0.000 6.003 6.790 6.396 0.453
## .ssei 4.037 0.155 26.036 0.000 3.733 4.341 4.037 0.315
## .ssno 0.184 0.013 14.628 0.000 0.159 0.209 0.184 0.214
## .sscs 0.351 0.016 22.310 0.000 0.320 0.382 0.351 0.398
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs 3.207 0.140 22.967 0.000 2.933 3.480 3.207 0.606
## sswk 7.597 0.088 86.426 0.000 7.424 7.769 7.597 0.937
## sspc 3.130 0.039 79.897 0.000 3.054 3.207 3.130 0.870
## math =~
## ssar 7.104 0.067 105.342 0.000 6.972 7.236 7.104 0.943
## ssmk 5.822 0.067 86.966 0.000 5.691 5.953 5.822 0.884
## ssmc 1.049 0.108 9.740 0.000 0.838 1.260 1.049 0.191
## electronic =~
## ssgs 1.703 0.140 12.125 0.000 1.428 1.979 1.703 0.322
## ssasi 4.658 0.065 71.175 0.000 4.530 4.787 4.658 0.834
## ssmc 3.852 0.107 35.945 0.000 3.642 4.062 3.852 0.702
## ssei 4.035 0.043 93.663 0.000 3.951 4.120 4.035 0.923
## speed =~
## ssno 0.857 0.012 71.334 0.000 0.833 0.880 0.857 0.886
## sscs 0.765 0.013 57.562 0.000 0.739 0.791 0.765 0.816
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.859 0.006 134.463 0.000 0.847 0.872 0.859 0.859
## electronic 0.868 0.007 124.500 0.000 0.854 0.882 0.868 0.868
## speed 0.787 0.009 83.883 0.000 0.769 0.805 0.787 0.787
## math ~~
## electronic 0.770 0.010 79.992 0.000 0.751 0.788 0.770 0.770
## speed 0.821 0.008 97.306 0.000 0.804 0.837 0.821 0.821
## electronic ~~
## speed 0.649 0.013 48.482 0.000 0.622 0.675 0.649 0.649
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 16.358 0.087 188.331 0.000 16.188 16.528 16.358 3.093
## .sswk 25.460 0.130 195.905 0.000 25.205 25.715 25.460 3.139
## .sspc 10.389 0.059 175.230 0.000 10.273 10.505 10.389 2.887
## .ssar 18.393 0.130 141.785 0.000 18.139 18.647 18.393 2.440
## .ssmk 13.626 0.116 116.977 0.000 13.397 13.854 13.626 2.068
## .ssmc 15.617 0.092 169.826 0.000 15.437 15.797 15.617 2.846
## .ssasi 16.348 0.092 177.720 0.000 16.168 16.528 16.348 2.926
## .ssei 12.524 0.072 174.554 0.000 12.384 12.665 12.524 2.865
## .ssno 0.084 0.016 5.181 0.000 0.052 0.116 0.084 0.087
## .sscs -0.042 0.016 -2.602 0.009 -0.073 -0.010 -0.042 -0.045
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.310 0.161 33.030 0.000 4.995 5.625 5.310 0.190
## .sswk 8.075 0.454 17.803 0.000 7.186 8.964 8.075 0.123
## .sspc 3.154 0.110 28.726 0.000 2.939 3.369 3.154 0.243
## .ssar 6.341 0.384 16.494 0.000 5.587 7.094 6.341 0.112
## .ssmk 9.519 0.327 29.068 0.000 8.877 10.161 9.519 0.219
## .ssmc 7.950 0.252 31.534 0.000 7.456 8.444 7.950 0.264
## .ssasi 9.526 0.329 28.970 0.000 8.881 10.170 9.526 0.305
## .ssei 2.830 0.141 20.039 0.000 2.553 3.107 2.830 0.148
## .ssno 0.201 0.011 17.688 0.000 0.179 0.224 0.201 0.215
## .sscs 0.294 0.014 20.362 0.000 0.265 0.322 0.294 0.334
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
modificationIndices(configural, sort=T, maximum.number=30)
## lhs op rhs block group level mi epc sepc.lv sepc.all sepc.nox
## 229 ssmc ~~ ssasi 2 2 1 361.744 3.027 3.027 0.348 0.348
## 225 ssmk ~~ ssasi 2 2 1 318.368 -2.844 -2.844 -0.299 -0.299
## 170 verbal =~ ssei 2 2 1 304.828 2.239 2.239 0.512 0.512
## 174 math =~ sswk 2 2 1 248.124 -2.693 -2.693 -0.332 -0.332
## 176 math =~ ssasi 2 2 1 162.891 -1.255 -1.255 -0.225 -0.225
## 197 ssgs ~~ ssmk 2 2 1 133.553 1.385 1.385 0.195 0.195
## 230 ssmc ~~ ssei 2 2 1 122.624 -1.452 -1.452 -0.306 -0.306
## 188 speed =~ sspc 2 2 1 106.277 0.602 0.602 0.167 0.167
## 168 verbal =~ ssmc 2 2 1 101.243 -1.567 -1.567 -0.286 -0.286
## 175 math =~ sspc 2 2 1 99.863 0.743 0.743 0.206 0.206
## 169 verbal =~ ssasi 2 2 1 93.221 -1.446 -1.446 -0.259 -0.259
## 152 ssmk ~~ ssasi 1 1 1 90.732 -1.205 -1.205 -0.162 -0.162
## 156 ssmc ~~ ssasi 1 1 1 89.041 1.089 1.089 0.154 0.154
## 101 math =~ sswk 1 1 1 88.102 -1.628 -1.628 -0.213 -0.213
## 177 math =~ ssei 2 2 1 87.685 0.775 0.775 0.177 0.177
## 182 electronic =~ ssar 2 2 1 86.268 1.351 1.351 0.179 0.179
## 183 electronic =~ ssmk 2 2 1 86.266 -1.107 -1.107 -0.168 -0.168
## 98 verbal =~ ssno 1 1 1 85.948 -0.369 -0.369 -0.397 -0.397
## 99 verbal =~ sscs 1 1 1 85.948 0.327 0.327 0.348 0.348
## 124 ssgs ~~ ssmk 1 1 1 83.594 1.070 1.070 0.161 0.161
## 115 speed =~ sspc 1 1 1 83.440 0.480 0.480 0.146 0.146
## 195 ssgs ~~ sspc 2 2 1 76.727 -0.667 -0.667 -0.163 -0.163
## 193 speed =~ ssei 2 2 1 74.282 0.525 0.525 0.120 0.120
## 122 ssgs ~~ sspc 1 1 1 64.890 -0.598 -0.598 -0.156 -0.156
## 121 ssgs ~~ sswk 1 1 1 63.015 1.387 1.387 0.228 0.228
## 95 verbal =~ ssmc 1 1 1 61.869 -1.116 -1.116 -0.259 -0.259
## 180 electronic =~ sswk 2 2 1 61.415 1.641 1.641 0.202 0.202
## 181 electronic =~ sspc 2 2 1 61.411 -0.676 -0.676 -0.188 -0.188
## 218 ssar ~~ ssmk 2 2 1 60.969 -10.929 -10.929 -1.407 -1.407
## 173 math =~ ssgs 2 2 1 60.935 0.700 0.700 0.132 0.132
metric<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 1983.273 62.000 0.000 0.980 0.075 0.026 503561.781 504058.056
Mc(metric)
## [1] 0.9157659
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 67 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 80
## Number of equality constraints 12
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1983.273 1181.060
## Degrees of freedom 62 62
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.679
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 728.861 434.044
## 0 1254.412 747.015
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.755 0.091 30.434 0.000 2.578 2.933 2.755 0.598
## sswk (.p2.) 7.075 0.084 84.277 0.000 6.911 7.240 7.075 0.930
## sspc (.p3.) 2.854 0.037 77.639 0.000 2.782 2.926 2.854 0.860
## math =~
## ssar (.p4.) 6.541 0.070 92.830 0.000 6.403 6.679 6.541 0.935
## ssmk (.p5.) 5.367 0.061 87.329 0.000 5.247 5.488 5.367 0.876
## ssmc (.p6.) 1.134 0.076 14.990 0.000 0.985 1.282 1.134 0.259
## electronic =~
## ssgs (.p7.) 1.339 0.079 16.893 0.000 1.184 1.495 1.339 0.291
## ssasi (.p8.) 3.003 0.045 66.205 0.000 2.914 3.091 3.003 0.772
## ssmc (.p9.) 2.425 0.068 35.739 0.000 2.292 2.558 2.425 0.554
## ssei (.10.) 2.784 0.044 63.605 0.000 2.698 2.870 2.784 0.804
## speed =~
## ssno (.11.) 0.822 0.012 70.547 0.000 0.799 0.845 0.822 0.886
## sscs (.12.) 0.731 0.012 60.642 0.000 0.708 0.755 0.731 0.777
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.830 0.006 128.642 0.000 0.817 0.843 0.830 0.830
## electronic 0.881 0.007 119.122 0.000 0.866 0.895 0.881 0.881
## speed 0.743 0.011 66.929 0.000 0.721 0.765 0.743 0.743
## math ~~
## electronic 0.810 0.010 78.960 0.000 0.790 0.830 0.810 0.810
## speed 0.738 0.010 73.742 0.000 0.719 0.758 0.738 0.738
## electronic ~~
## speed 0.620 0.014 43.289 0.000 0.591 0.648 0.620 0.620
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 14.716 0.078 188.083 0.000 14.563 14.869 14.716 3.193
## .sswk 25.615 0.123 208.263 0.000 25.374 25.856 25.615 3.366
## .sspc 11.115 0.053 210.841 0.000 11.011 11.218 11.115 3.350
## .ssar 16.646 0.123 135.820 0.000 16.405 16.886 16.646 2.379
## .ssmk 13.157 0.108 122.070 0.000 12.946 13.369 13.157 2.149
## .ssmc 11.841 0.076 156.606 0.000 11.693 11.989 11.841 2.704
## .ssasi 10.952 0.064 171.593 0.000 10.827 11.077 10.952 2.816
## .ssei 9.613 0.062 156.264 0.000 9.492 9.733 9.613 2.776
## .ssno 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.326
## .sscs 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.404
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.351 0.162 33.112 0.000 5.034 5.667 5.351 0.252
## .sswk 7.835 0.399 19.626 0.000 7.052 8.617 7.835 0.135
## .sspc 2.866 0.096 29.742 0.000 2.677 3.055 2.866 0.260
## .ssar 6.170 0.380 16.251 0.000 5.426 6.914 6.170 0.126
## .ssmk 8.691 0.302 28.787 0.000 8.099 9.282 8.691 0.232
## .ssmc 7.562 0.221 34.143 0.000 7.128 7.996 7.562 0.394
## .ssasi 6.108 0.195 31.390 0.000 5.726 6.489 6.108 0.404
## .ssei 4.244 0.143 29.603 0.000 3.963 4.525 4.244 0.354
## .ssno 0.185 0.011 16.272 0.000 0.163 0.207 0.185 0.215
## .sscs 0.351 0.015 23.876 0.000 0.322 0.379 0.351 0.396
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.755 0.091 30.434 0.000 2.578 2.933 2.977 0.559
## sswk (.p2.) 7.075 0.084 84.277 0.000 6.911 7.240 7.646 0.939
## sspc (.p3.) 2.854 0.037 77.639 0.000 2.782 2.926 3.084 0.866
## math =~
## ssar (.p4.) 6.541 0.070 92.830 0.000 6.403 6.679 7.103 0.942
## ssmk (.p5.) 5.367 0.061 87.329 0.000 5.247 5.488 5.829 0.884
## ssmc (.p6.) 1.134 0.076 14.990 0.000 0.985 1.282 1.231 0.227
## electronic =~
## ssgs (.p7.) 1.339 0.079 16.893 0.000 1.184 1.495 1.982 0.372
## ssasi (.p8.) 3.003 0.045 66.205 0.000 2.914 3.091 4.444 0.816
## ssmc (.p9.) 2.425 0.068 35.739 0.000 2.292 2.558 3.589 0.661
## ssei (.10.) 2.784 0.044 63.605 0.000 2.698 2.870 4.120 0.931
## speed =~
## ssno (.11.) 0.822 0.012 70.547 0.000 0.799 0.845 0.858 0.886
## sscs (.12.) 0.731 0.012 60.642 0.000 0.708 0.755 0.763 0.815
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 1.006 0.027 37.610 0.000 0.954 1.059 0.857 0.857
## electronic 1.385 0.042 32.891 0.000 1.302 1.468 0.866 0.866
## speed 0.887 0.030 29.867 0.000 0.829 0.946 0.787 0.787
## math ~~
## electronic 1.239 0.037 33.359 0.000 1.166 1.312 0.771 0.771
## speed 0.930 0.027 34.031 0.000 0.877 0.984 0.821 0.821
## electronic ~~
## speed 1.002 0.038 26.697 0.000 0.928 1.075 0.648 0.648
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 16.358 0.087 188.331 0.000 16.188 16.528 16.358 3.072
## .sswk 25.460 0.130 195.905 0.000 25.205 25.715 25.460 3.128
## .sspc 10.389 0.059 175.230 0.000 10.273 10.505 10.389 2.918
## .ssar 18.393 0.130 141.785 0.000 18.139 18.647 18.393 2.441
## .ssmk 13.626 0.116 116.977 0.000 13.397 13.854 13.626 2.066
## .ssmc 15.617 0.092 169.826 0.000 15.437 15.797 15.617 2.878
## .ssasi 16.348 0.092 177.720 0.000 16.168 16.528 16.348 3.002
## .ssei 12.524 0.072 174.554 0.000 12.384 12.665 12.524 2.829
## .ssno 0.084 0.016 5.181 0.000 0.052 0.116 0.084 0.087
## .sscs -0.042 0.016 -2.602 0.009 -0.073 -0.010 -0.042 -0.045
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.329 0.161 33.130 0.000 5.014 5.644 5.329 0.188
## .sswk 7.795 0.435 17.927 0.000 6.943 8.648 7.795 0.118
## .sspc 3.166 0.109 28.988 0.000 2.952 3.380 3.166 0.250
## .ssar 6.346 0.369 17.216 0.000 5.624 7.069 6.346 0.112
## .ssmk 9.539 0.315 30.298 0.000 8.922 10.156 9.539 0.219
## .ssmc 8.234 0.249 33.024 0.000 7.746 8.723 8.234 0.280
## .ssasi 9.914 0.327 30.332 0.000 9.274 10.555 9.914 0.334
## .ssei 2.630 0.136 19.341 0.000 2.364 2.897 2.630 0.134
## .ssno 0.201 0.011 18.603 0.000 0.179 0.222 0.201 0.214
## .sscs 0.294 0.014 21.265 0.000 0.267 0.321 0.294 0.336
## verbal 1.168 0.036 32.450 0.000 1.097 1.238 1.000 1.000
## math 1.179 0.032 36.431 0.000 1.116 1.243 1.000 1.000
## electronic 2.191 0.078 28.203 0.000 2.038 2.343 1.000 1.000
## speed 1.090 0.040 27.227 0.000 1.011 1.168 1.000 1.000
scalar<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 3571.682 68.000 0.000 0.963 0.097 0.046 505138.190 505590.677
Mc(scalar)
## [1] 0.8517441
summary(scalar, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 122 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 84
## Number of equality constraints 22
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3571.682 2136.281
## Degrees of freedom 68 68
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.672
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1632.797 976.602
## 0 1938.885 1159.679
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.731 0.062 44.023 0.000 2.609 2.853 2.731 0.595
## sswk (.p2.) 7.064 0.084 83.657 0.000 6.899 7.230 7.064 0.928
## sspc (.p3.) 2.865 0.036 80.085 0.000 2.795 2.935 2.865 0.859
## math =~
## ssar (.p4.) 6.569 0.070 94.435 0.000 6.432 6.705 6.569 0.936
## ssmk (.p5.) 5.326 0.063 84.949 0.000 5.203 5.449 5.326 0.872
## ssmc (.p6.) 1.013 0.067 15.114 0.000 0.882 1.145 1.013 0.233
## electronic =~
## ssgs (.p7.) 1.336 0.044 30.243 0.000 1.250 1.423 1.336 0.291
## ssasi (.p8.) 3.185 0.046 69.891 0.000 3.095 3.274 3.185 0.786
## ssmc (.p9.) 2.494 0.058 42.700 0.000 2.380 2.609 2.494 0.574
## ssei (.10.) 2.552 0.043 59.799 0.000 2.469 2.636 2.552 0.758
## speed =~
## ssno (.11.) 0.806 0.012 67.536 0.000 0.782 0.829 0.806 0.873
## sscs (.12.) 0.748 0.012 62.016 0.000 0.724 0.771 0.748 0.784
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.831 0.007 127.511 0.000 0.818 0.844 0.831 0.831
## electronic 0.886 0.008 116.397 0.000 0.871 0.900 0.886 0.886
## speed 0.749 0.011 68.437 0.000 0.728 0.771 0.749 0.749
## math ~~
## electronic 0.817 0.010 79.815 0.000 0.797 0.837 0.817 0.817
## speed 0.742 0.010 73.700 0.000 0.722 0.762 0.742 0.742
## electronic ~~
## speed 0.631 0.014 44.273 0.000 0.603 0.659 0.631 0.631
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 14.728 0.077 191.749 0.000 14.577 14.878 14.728 3.208
## .sswk (.34.) 25.859 0.121 214.291 0.000 25.623 26.096 25.859 3.398
## .sspc (.35.) 10.889 0.053 207.319 0.000 10.786 10.992 10.889 3.263
## .ssar (.36.) 16.819 0.122 138.333 0.000 16.581 17.058 16.819 2.397
## .ssmk (.37.) 12.834 0.104 123.850 0.000 12.631 13.037 12.834 2.101
## .ssmc (.38.) 11.881 0.072 164.808 0.000 11.739 12.022 11.881 2.733
## .ssasi (.39.) 11.331 0.066 172.095 0.000 11.202 11.460 11.331 2.798
## .ssei (.40.) 9.218 0.056 163.326 0.000 9.107 9.328 9.218 2.737
## .ssno (.41.) 0.344 0.015 23.001 0.000 0.315 0.373 0.344 0.373
## .sscs (.42.) 0.302 0.016 19.046 0.000 0.271 0.334 0.302 0.317
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.366 0.162 33.075 0.000 5.048 5.684 5.366 0.255
## .sswk 8.025 0.406 19.775 0.000 7.229 8.820 8.025 0.139
## .sspc 2.928 0.099 29.606 0.000 2.734 3.122 2.928 0.263
## .ssar 6.105 0.390 15.652 0.000 5.340 6.869 6.105 0.124
## .ssmk 8.954 0.307 29.212 0.000 8.354 9.555 8.954 0.240
## .ssmc 7.511 0.221 33.953 0.000 7.078 7.945 7.511 0.398
## .ssasi 6.260 0.213 29.356 0.000 5.842 6.678 6.260 0.382
## .ssei 4.831 0.155 31.098 0.000 4.526 5.135 4.831 0.426
## .ssno 0.203 0.011 17.842 0.000 0.180 0.225 0.203 0.238
## .sscs 0.350 0.015 22.843 0.000 0.320 0.380 0.350 0.385
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.731 0.062 44.023 0.000 2.609 2.853 2.945 0.551
## sswk (.p2.) 7.064 0.084 83.657 0.000 6.899 7.230 7.618 0.937
## sspc (.p3.) 2.865 0.036 80.085 0.000 2.795 2.935 3.089 0.864
## math =~
## ssar (.p4.) 6.569 0.070 94.435 0.000 6.432 6.705 7.123 0.943
## ssmk (.p5.) 5.326 0.063 84.949 0.000 5.203 5.449 5.776 0.879
## ssmc (.p6.) 1.013 0.067 15.114 0.000 0.882 1.145 1.099 0.200
## electronic =~
## ssgs (.p7.) 1.336 0.044 30.243 0.000 1.250 1.423 2.041 0.382
## ssasi (.p8.) 3.185 0.046 69.891 0.000 3.095 3.274 4.864 0.841
## ssmc (.p9.) 2.494 0.058 42.700 0.000 2.380 2.609 3.810 0.695
## ssei (.10.) 2.552 0.043 59.799 0.000 2.469 2.636 3.899 0.909
## speed =~
## ssno (.11.) 0.806 0.012 67.536 0.000 0.782 0.829 0.841 0.875
## sscs (.12.) 0.748 0.012 62.016 0.000 0.724 0.771 0.781 0.822
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 1.003 0.026 37.915 0.000 0.951 1.055 0.858 0.858
## electronic 1.427 0.043 33.407 0.000 1.344 1.511 0.867 0.867
## speed 0.890 0.030 29.756 0.000 0.832 0.949 0.791 0.791
## math ~~
## electronic 1.280 0.038 33.457 0.000 1.205 1.355 0.773 0.773
## speed 0.932 0.028 33.806 0.000 0.878 0.986 0.823 0.823
## electronic ~~
## speed 1.041 0.039 26.673 0.000 0.964 1.117 0.653 0.653
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 14.728 0.077 191.749 0.000 14.577 14.878 14.728 2.757
## .sswk (.34.) 25.859 0.121 214.291 0.000 25.623 26.096 25.859 3.182
## .sspc (.35.) 10.889 0.053 207.319 0.000 10.786 10.992 10.889 3.046
## .ssar (.36.) 16.819 0.122 138.333 0.000 16.581 17.058 16.819 2.227
## .ssmk (.37.) 12.834 0.104 123.850 0.000 12.631 13.037 12.834 1.954
## .ssmc (.38.) 11.881 0.072 164.808 0.000 11.739 12.022 11.881 2.167
## .ssasi (.39.) 11.331 0.066 172.095 0.000 11.202 11.460 11.331 1.960
## .ssei (.40.) 9.218 0.056 163.326 0.000 9.107 9.328 9.218 2.148
## .ssno (.41.) 0.344 0.015 23.001 0.000 0.315 0.373 0.344 0.358
## .sscs (.42.) 0.302 0.016 19.046 0.000 0.271 0.334 0.302 0.318
## verbal -0.090 0.025 -3.544 0.000 -0.140 -0.040 -0.083 -0.083
## math 0.213 0.028 7.670 0.000 0.159 0.268 0.197 0.197
## elctrnc 1.395 0.044 31.938 0.000 1.310 1.481 0.913 0.913
## speed -0.376 0.029 -13.187 0.000 -0.432 -0.320 -0.360 -0.360
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.280 0.161 32.730 0.000 4.963 5.596 5.280 0.185
## .sswk 8.002 0.441 18.151 0.000 7.138 8.866 8.002 0.121
## .sspc 3.235 0.115 28.203 0.000 3.011 3.460 3.235 0.253
## .ssar 6.300 0.382 16.496 0.000 5.552 7.049 6.300 0.110
## .ssmk 9.797 0.328 29.851 0.000 9.154 10.440 9.797 0.227
## .ssmc 7.856 0.243 32.354 0.000 7.380 8.332 7.856 0.261
## .ssasi 9.771 0.353 27.672 0.000 9.079 10.463 9.771 0.292
## .ssei 3.210 0.139 23.163 0.000 2.938 3.481 3.210 0.174
## .ssno 0.216 0.011 19.499 0.000 0.194 0.237 0.216 0.234
## .sscs 0.293 0.014 20.273 0.000 0.265 0.321 0.293 0.325
## verbal 1.163 0.036 32.518 0.000 1.093 1.233 1.000 1.000
## math 1.176 0.032 36.408 0.000 1.113 1.239 1.000 1.000
## electronic 2.333 0.082 28.436 0.000 2.172 2.494 1.000 1.000
## speed 1.090 0.041 26.702 0.000 1.010 1.170 1.000 1.000
lavTestScore(scalar, release = 13:22)
## 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 1540.604 10 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p33. == .p79. 1.179 1 0.278
## 2 .p34. == .p80. 241.868 1 0.000
## 3 .p35. == .p81. 273.270 1 0.000
## 4 .p36. == .p82. 175.673 1 0.000
## 5 .p37. == .p83. 187.883 1 0.000
## 6 .p38. == .p84. 5.275 1 0.022
## 7 .p39. == .p85. 657.006 1 0.000
## 8 .p40. == .p86. 708.709 1 0.000
## 9 .p41. == .p87. 275.574 1 0.000
## 10 .p42. == .p88. 275.574 1 0.000
scalar2<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("ssei~1", "sswk~1", "sscs~1"))
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2234.798 65.000 0.000 0.977 0.078 0.029 503807.306 504281.687
Mc(scalar2)
## [1] 0.9054013
strict<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("ssei~1", "sswk~1", "sscs~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2596.755 75.000 0.000 0.973 0.078 0.037 504149.263 504550.662
Mc(strict)
## [1] 0.8909235
cf.cov<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("ssei~1", "sswk~1", "sscs~1"))
fitMeasures(cf.cov, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2624.889 71.000 0.000 0.973 0.081 0.108 504185.397 504615.989
Mc(cf.cov)
## [1] 0.8896133
summary(cf.cov, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 107 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 84
## Number of equality constraints 25
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2624.889 1580.929
## Degrees of freedom 71 71
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.660
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 975.842 587.734
## 0 1649.047 993.195
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.891 0.054 53.943 0.000 2.786 2.996 2.891 0.588
## sswk (.p2.) 7.452 0.066 113.648 0.000 7.324 7.581 7.452 0.936
## sspc (.p3.) 3.012 0.030 99.988 0.000 2.953 3.071 3.012 0.871
## math =~
## ssar (.p4.) 6.863 0.054 126.780 0.000 6.757 6.969 6.863 0.940
## ssmk (.p5.) 5.577 0.052 107.306 0.000 5.475 5.679 5.577 0.882
## ssmc (.p6.) 1.458 0.067 21.742 0.000 1.327 1.590 1.458 0.313
## electronic =~
## ssgs (.p7.) 1.542 0.046 33.763 0.000 1.452 1.631 1.542 0.314
## ssasi (.p8.) 3.439 0.047 73.285 0.000 3.347 3.531 3.439 0.810
## ssmc (.p9.) 2.454 0.059 41.918 0.000 2.339 2.569 2.454 0.526
## ssei (.10.) 3.210 0.042 76.844 0.000 3.128 3.292 3.210 0.846
## speed =~
## ssno (.11.) 0.854 0.010 87.144 0.000 0.835 0.873 0.854 0.895
## sscs (.12.) 0.759 0.011 70.821 0.000 0.738 0.780 0.759 0.788
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.27.) 0.832 0.006 141.549 0.000 0.821 0.844 0.832 0.832
## elctrnc (.28.) 0.909 0.006 161.303 0.000 0.898 0.920 0.909 0.909
## speed (.29.) 0.743 0.009 84.940 0.000 0.726 0.760 0.743 0.743
## math ~~
## elctrnc (.30.) 0.827 0.008 110.046 0.000 0.812 0.841 0.827 0.827
## speed (.31.) 0.770 0.008 100.853 0.000 0.755 0.785 0.770 0.770
## electronic ~~
## speed (.32.) 0.656 0.010 62.811 0.000 0.636 0.677 0.656 0.656
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 14.715 0.077 190.839 0.000 14.564 14.866 14.715 2.995
## .sswk 25.615 0.123 208.263 0.000 25.374 25.856 25.615 3.218
## .sspc (.35.) 11.115 0.053 211.417 0.000 11.012 11.218 11.115 3.213
## .ssar (.36.) 16.840 0.122 138.553 0.000 16.602 17.078 16.840 2.306
## .ssmk (.37.) 12.850 0.104 123.882 0.000 12.646 13.053 12.850 2.031
## .ssmc (.38.) 11.726 0.072 161.763 0.000 11.584 11.868 11.726 2.514
## .ssasi (.39.) 11.019 0.064 173.429 0.000 10.894 11.143 11.019 2.596
## .ssei 9.613 0.062 156.264 0.000 9.492 9.733 9.613 2.533
## .ssno (.41.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.317
## .sscs 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.394
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.300 0.161 32.890 0.000 4.984 5.616 5.300 0.220
## .sswk 7.816 0.395 19.777 0.000 7.041 8.590 7.816 0.123
## .sspc 2.892 0.097 29.733 0.000 2.702 3.083 2.892 0.242
## .ssar 6.224 0.388 16.027 0.000 5.463 6.985 6.224 0.117
## .ssmk 8.907 0.305 29.163 0.000 8.308 9.505 8.907 0.223
## .ssmc 7.685 0.221 34.732 0.000 7.251 8.118 7.685 0.353
## .ssasi 6.187 0.198 31.303 0.000 5.800 6.575 6.187 0.343
## .ssei 4.092 0.141 28.965 0.000 3.815 4.369 4.092 0.284
## .ssno 0.182 0.011 16.202 0.000 0.160 0.204 0.182 0.200
## .sscs 0.353 0.015 24.102 0.000 0.324 0.382 0.353 0.380
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.891 0.054 53.943 0.000 2.786 2.996 2.815 0.568
## sswk (.p2.) 7.452 0.066 113.648 0.000 7.324 7.581 7.256 0.931
## sspc (.p3.) 3.012 0.030 99.988 0.000 2.953 3.071 2.933 0.857
## math =~
## ssar (.p4.) 6.863 0.054 126.780 0.000 6.757 6.969 6.834 0.937
## ssmk (.p5.) 5.577 0.052 107.306 0.000 5.475 5.679 5.553 0.872
## ssmc (.p6.) 1.458 0.067 21.742 0.000 1.327 1.590 1.452 0.293
## electronic =~
## ssgs (.p7.) 1.542 0.046 33.763 0.000 1.452 1.631 1.781 0.359
## ssasi (.p8.) 3.439 0.047 73.285 0.000 3.347 3.531 3.974 0.782
## ssmc (.p9.) 2.454 0.059 41.918 0.000 2.339 2.569 2.835 0.571
## ssei (.10.) 3.210 0.042 76.844 0.000 3.128 3.292 3.709 0.921
## speed =~
## ssno (.11.) 0.854 0.010 87.144 0.000 0.835 0.873 0.829 0.879
## sscs (.12.) 0.759 0.011 70.821 0.000 0.738 0.780 0.737 0.806
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.27.) 0.832 0.006 141.549 0.000 0.821 0.844 0.858 0.858
## elctrnc (.28.) 0.909 0.006 161.303 0.000 0.898 0.920 0.808 0.808
## speed (.29.) 0.743 0.009 84.940 0.000 0.726 0.760 0.786 0.786
## math ~~
## elctrnc (.30.) 0.827 0.008 110.046 0.000 0.812 0.841 0.718 0.718
## speed (.31.) 0.770 0.008 100.853 0.000 0.755 0.785 0.797 0.797
## electronic ~~
## speed (.32.) 0.656 0.010 62.811 0.000 0.636 0.677 0.585 0.585
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 14.715 0.077 190.839 0.000 14.564 14.866 14.715 2.969
## .sswk 27.258 0.157 173.823 0.000 26.951 27.565 27.258 3.498
## .sspc (.35.) 11.115 0.053 211.417 0.000 11.012 11.218 11.115 3.248
## .ssar (.36.) 16.840 0.122 138.553 0.000 16.602 17.078 16.840 2.310
## .ssmk (.37.) 12.850 0.104 123.882 0.000 12.646 13.053 12.850 2.017
## .ssmc (.38.) 11.726 0.072 161.763 0.000 11.584 11.868 11.726 2.362
## .ssasi (.39.) 11.019 0.064 173.429 0.000 10.894 11.143 11.019 2.169
## .ssei 7.648 0.102 74.990 0.000 7.448 7.848 7.648 1.899
## .ssno (.41.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.321
## .sscs 0.152 0.019 8.207 0.000 0.116 0.189 0.152 0.166
## verbal -0.241 0.026 -9.169 0.000 -0.293 -0.190 -0.248 -0.248
## math 0.198 0.026 7.579 0.000 0.147 0.249 0.199 0.199
## elctrnc 1.519 0.041 36.969 0.000 1.439 1.600 1.315 1.315
## speed -0.256 0.026 -9.643 0.000 -0.307 -0.204 -0.263 -0.263
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.352 0.161 33.146 0.000 5.036 5.669 5.352 0.218
## .sswk 8.063 0.434 18.596 0.000 7.213 8.913 8.063 0.133
## .sspc 3.111 0.106 29.220 0.000 2.903 3.320 3.111 0.266
## .ssar 6.438 0.376 17.105 0.000 5.701 7.176 6.438 0.121
## .ssmk 9.750 0.324 30.111 0.000 9.115 10.384 9.750 0.240
## .ssmc 8.577 0.248 34.628 0.000 8.092 9.063 8.577 0.348
## .ssasi 10.022 0.332 30.145 0.000 9.370 10.674 10.022 0.388
## .ssei 2.457 0.140 17.578 0.000 2.183 2.730 2.457 0.152
## .ssno 0.201 0.011 18.638 0.000 0.180 0.222 0.201 0.227
## .sscs 0.294 0.014 21.207 0.000 0.267 0.321 0.294 0.351
## verbal 0.948 0.012 80.591 0.000 0.925 0.971 1.000 1.000
## math 0.992 0.013 77.137 0.000 0.966 1.017 1.000 1.000
## electronic 1.335 0.028 48.269 0.000 1.281 1.389 1.000 1.000
## speed 0.942 0.019 48.442 0.000 0.904 0.981 1.000 1.000
cf.vcov<-cfa(cf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances", "lv.variances"), group.partial=c("ssei~1", "sswk~1", "sscs~1"))
fitMeasures(cf.vcov, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 3084.987 75.000 0.000 0.968 0.086 0.126 504637.495 505038.894
Mc(cf.vcov)
## [1] 0.8712226
cf.cov2<-cfa(cf.lv, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("ssei~1", "sswk~1", "sscs~1"))
fitMeasures(cf.cov2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2674.279 74.000 0.000 0.972 0.080 0.107 504228.787 504637.485
Mc(cf.cov2)
## [1] 0.8877251
summary(cf.cov2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 107 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 81
## Number of equality constraints 25
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2674.279 1614.431
## Degrees of freedom 74 74
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.656
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 986.682 595.649
## 0 1687.597 1018.783
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.858 0.052 54.617 0.000 2.756 2.961 2.858 0.584
## sswk (.p2.) 7.356 0.061 119.814 0.000 7.236 7.477 7.356 0.931
## sspc (.p3.) 2.977 0.029 104.407 0.000 2.921 3.032 2.977 0.868
## math =~
## ssar (.p4.) 6.851 0.049 140.454 0.000 6.756 6.947 6.851 0.939
## ssmk (.p5.) 5.564 0.049 114.396 0.000 5.468 5.659 5.564 0.881
## ssmc (.p6.) 1.461 0.067 21.908 0.000 1.330 1.592 1.461 0.313
## electronic =~
## ssgs (.p7.) 1.547 0.046 33.824 0.000 1.457 1.636 1.547 0.316
## ssasi (.p8.) 3.446 0.047 72.608 0.000 3.353 3.539 3.446 0.810
## ssmc (.p9.) 2.457 0.059 41.636 0.000 2.341 2.572 2.457 0.526
## ssei (.10.) 3.225 0.042 76.129 0.000 3.142 3.308 3.225 0.847
## speed =~
## ssno (.11.) 0.840 0.009 97.494 0.000 0.823 0.857 0.840 0.886
## sscs (.12.) 0.747 0.010 76.310 0.000 0.728 0.767 0.747 0.783
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.27.) 0.847 0.005 185.222 0.000 0.838 0.856 0.847 0.847
## elctrnc (.28.) 0.915 0.006 166.338 0.000 0.904 0.926 0.915 0.915
## speed (.29.) 0.767 0.007 105.637 0.000 0.753 0.782 0.767 0.767
## math ~~
## elctrnc (.30.) 0.827 0.007 114.940 0.000 0.813 0.841 0.827 0.827
## speed (.31.) 0.783 0.007 119.303 0.000 0.770 0.796 0.783 0.783
## electronic ~~
## speed (.32.) 0.666 0.010 66.127 0.000 0.646 0.686 0.666 0.666
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 14.714 0.077 190.746 0.000 14.563 14.865 14.714 3.007
## .sswk 25.615 0.123 208.263 0.000 25.374 25.856 25.615 3.243
## .sspc (.35.) 11.116 0.053 211.504 0.000 11.013 11.219 11.116 3.242
## .ssar (.36.) 16.843 0.122 138.440 0.000 16.605 17.082 16.843 2.308
## .ssmk (.37.) 12.850 0.104 123.949 0.000 12.647 13.053 12.850 2.036
## .ssmc (.38.) 11.727 0.072 161.854 0.000 11.585 11.869 11.727 2.511
## .ssasi (.39.) 11.019 0.064 173.348 0.000 10.894 11.143 11.019 2.591
## .ssei 9.613 0.062 156.264 0.000 9.492 9.733 9.613 2.526
## .ssno (.41.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.319
## .sscs 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.398
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssgs 5.288 0.161 32.770 0.000 4.972 5.604 5.288 0.221
## .sswk 8.280 0.389 21.291 0.000 7.518 9.042 8.280 0.133
## .sspc 2.898 0.097 29.983 0.000 2.709 3.088 2.898 0.246
## .ssar 6.335 0.374 16.931 0.000 5.601 7.068 6.335 0.119
## .ssmk 8.893 0.303 29.352 0.000 8.299 9.487 8.893 0.223
## .ssmc 7.711 0.222 34.774 0.000 7.276 8.145 7.711 0.353
## .ssasi 6.205 0.198 31.392 0.000 5.817 6.592 6.205 0.343
## .ssei 4.084 0.141 28.931 0.000 3.807 4.361 4.084 0.282
## .ssno 0.192 0.011 18.191 0.000 0.172 0.213 0.192 0.214
## .sscs 0.353 0.014 24.451 0.000 0.325 0.381 0.353 0.387
## electronic 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 2.858 0.052 54.617 0.000 2.756 2.961 2.858 0.574
## sswk (.p2.) 7.356 0.061 119.814 0.000 7.236 7.477 7.356 0.936
## sspc (.p3.) 2.977 0.029 104.407 0.000 2.921 3.032 2.977 0.860
## math =~
## ssar (.p4.) 6.851 0.049 140.454 0.000 6.756 6.947 6.851 0.939
## ssmk (.p5.) 5.564 0.049 114.396 0.000 5.468 5.659 5.564 0.871
## ssmc (.p6.) 1.461 0.067 21.908 0.000 1.330 1.592 1.461 0.295
## electronic =~
## ssgs (.p7.) 1.547 0.046 33.824 0.000 1.457 1.636 1.774 0.357
## ssasi (.p8.) 3.446 0.047 72.608 0.000 3.353 3.539 3.953 0.780
## ssmc (.p9.) 2.457 0.059 41.636 0.000 2.341 2.572 2.818 0.568
## ssei (.10.) 3.225 0.042 76.129 0.000 3.142 3.308 3.699 0.921
## speed =~
## ssno (.11.) 0.840 0.009 97.494 0.000 0.823 0.857 0.840 0.885
## sscs (.12.) 0.747 0.010 76.310 0.000 0.728 0.767 0.747 0.810
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math (.27.) 0.847 0.005 185.222 0.000 0.838 0.856 0.847 0.847
## elctrnc (.28.) 0.915 0.006 166.338 0.000 0.904 0.926 0.798 0.798
## speed (.29.) 0.767 0.007 105.637 0.000 0.753 0.782 0.767 0.767
## math ~~
## elctrnc (.30.) 0.827 0.007 114.940 0.000 0.813 0.841 0.721 0.721
## speed (.31.) 0.783 0.007 119.303 0.000 0.770 0.796 0.783 0.783
## electronic ~~
## speed (.32.) 0.666 0.010 66.127 0.000 0.646 0.686 0.581 0.581
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.33.) 14.714 0.077 190.746 0.000 14.563 14.865 14.714 2.957
## .sswk 27.259 0.157 174.061 0.000 26.952 27.566 27.259 3.469
## .sspc (.35.) 11.116 0.053 211.504 0.000 11.013 11.219 11.116 3.213
## .ssar (.36.) 16.843 0.122 138.440 0.000 16.605 17.082 16.843 2.310
## .ssmk (.37.) 12.850 0.104 123.949 0.000 12.647 13.053 12.850 2.013
## .ssmc (.38.) 11.727 0.072 161.854 0.000 11.585 11.869 11.727 2.365
## .ssasi (.39.) 11.019 0.064 173.348 0.000 10.894 11.143 11.019 2.175
## .ssei 7.636 0.103 74.146 0.000 7.434 7.838 7.636 1.902
## .ssno (.41.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.319
## .sscs 0.152 0.019 8.214 0.000 0.116 0.189 0.152 0.165
## verbal -0.245 0.027 -9.210 0.000 -0.297 -0.192 -0.245 -0.245
## math 0.199 0.026 7.599 0.000 0.147 0.250 0.199 0.199
## elctrnc 1.516 0.041 36.956 0.000 1.436 1.596 1.322 1.322
## speed -0.260 0.027 -9.660 0.000 -0.312 -0.207 -0.260 -0.260
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssgs 5.354 0.161 33.245 0.000 5.039 5.670 5.354 0.216
## .sswk 7.625 0.417 18.266 0.000 6.807 8.444 7.625 0.124
## .sspc 3.111 0.107 29.160 0.000 2.902 3.320 3.111 0.260
## .ssar 6.250 0.362 17.279 0.000 5.541 6.959 6.250 0.118
## .ssmk 9.811 0.327 29.975 0.000 9.169 10.452 9.811 0.241
## .ssmc 8.572 0.249 34.458 0.000 8.084 9.060 8.572 0.349
## .ssasi 10.043 0.333 30.124 0.000 9.389 10.696 10.043 0.391
## .ssei 2.442 0.141 17.294 0.000 2.165 2.718 2.442 0.151
## .ssno 0.194 0.011 18.333 0.000 0.174 0.215 0.194 0.216
## .sscs 0.292 0.014 20.827 0.000 0.265 0.320 0.292 0.344
## electronic 1.316 0.027 47.967 0.000 1.262 1.369 1.000 1.000
tests<-lavTestLRT(configural, metric, scalar2, cf.cov, cf.cov2)
Td=tests[2:5,"Chisq diff"]
Td
## [1] 147.68130 153.15758 264.60588 31.55765
dfd=tests[2:5,"Df diff"]
dfd
## [1] 8 3 6 3
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-5449+ 5469 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.05655974 0.09576267 0.08886419 0.04176225
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04877831 0.06471820
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.08317531 0.10896878
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.07989524 0.09816115
RMSEA.CI(T=Td[4],df=dfd[4],N=N,G=2)
## [1] 0.02934314 0.05551311
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 0.918 0.252 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 0.980 0.309
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 1.000 0.948 0.024
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 0.172 0.013 0.000 0.000
tests<-lavTestLRT(configural, metric, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 147.6813 153.1576 187.9920
dfd=tests[2:4,"Df diff"]
dfd
## [1] 8 3 10
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-5449+ 5469 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.05655974 0.09576267 0.05710623
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04877831 0.06471820
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.08317531 0.10896878
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.05012584 0.06438424
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 0.918 0.252 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 0.980 0.309
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 0.953 0.264 0.000 0.000
tests<-lavTestLRT(configural, metric, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 147.6813 995.0450
dfd=tests[2:3,"Df diff"]
dfd
## [1] 8 6
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-5449+ 5469 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.05655974 0.17378634
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04877831 0.06471820
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.1647653 0.1829662
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 0.918 0.252 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
# HIGH ORDER FACTOR
hof.model<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
'
hof.lv<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
'
hof.weak<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
math~0*1
'
baseline<-cfa(hof.model, data=dgroup, meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 3823.462 29.000 0.000 0.960 0.109 0.044 513377.638 513640.372
Mc(baseline)
## [1] 0.840476
configural<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2545.486 58.000 0.000 0.974 0.089 0.026 504131.994 504657.462
Mc(configural)
## [1] 0.8923229
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 95 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 72
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2545.486 1483.765
## Degrees of freedom 58 58
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.716
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 860.240 501.434
## 0 1685.247 982.331
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs 0.688 0.055 12.465 0.000 0.580 0.796 2.240 0.482
## sswk 2.192 0.130 16.898 0.000 1.937 2.446 7.138 0.934
## sspc 0.863 0.050 17.153 0.000 0.764 0.962 2.811 0.857
## math =~
## ssar 3.039 0.082 37.013 0.000 2.878 3.199 6.533 0.934
## ssmk 2.501 0.068 36.922 0.000 2.368 2.634 5.378 0.877
## ssmc 0.754 0.060 12.622 0.000 0.637 0.871 1.621 0.376
## electronic =~
## ssgs 0.846 0.061 13.927 0.000 0.727 0.965 1.953 0.420
## ssasi 1.219 0.051 23.699 0.000 1.118 1.320 2.815 0.749
## ssmc 0.795 0.061 12.985 0.000 0.675 0.916 1.837 0.427
## ssei 1.289 0.052 24.944 0.000 1.187 1.390 2.975 0.831
## speed =~
## ssno 0.510 0.012 43.688 0.000 0.487 0.533 0.809 0.872
## sscs 0.467 0.011 41.531 0.000 0.445 0.489 0.742 0.789
## g =~
## verbal 3.100 0.198 15.655 0.000 2.712 3.488 0.952 0.952
## math 1.903 0.063 30.176 0.000 1.780 2.027 0.885 0.885
## electronic 2.081 0.093 22.377 0.000 1.899 2.264 0.901 0.901
## speed 1.233 0.041 30.377 0.000 1.154 1.313 0.777 0.777
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 14.716 0.078 188.083 0.000 14.563 14.869 14.716 3.167
## .sswk 25.615 0.123 208.263 0.000 25.374 25.856 25.615 3.352
## .sspc 11.115 0.053 210.841 0.000 11.011 11.218 11.115 3.390
## .ssar 16.646 0.123 135.820 0.000 16.405 16.886 16.646 2.379
## .ssmk 13.157 0.108 122.070 0.000 12.946 13.369 13.157 2.146
## .ssmc 11.841 0.076 156.606 0.000 11.693 11.989 11.841 2.750
## .ssasi 10.952 0.064 171.593 0.000 10.827 11.077 10.952 2.913
## .ssei 9.613 0.062 156.264 0.000 9.492 9.733 9.613 2.685
## .ssno 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.326
## .sscs 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.404
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.252 0.170 30.968 0.000 4.920 5.585 5.252 0.243
## .sswk 7.426 0.421 17.642 0.000 6.601 8.251 7.426 0.127
## .sspc 2.852 0.096 29.716 0.000 2.664 3.041 2.852 0.265
## .ssar 6.260 0.389 16.112 0.000 5.499 7.022 6.260 0.128
## .ssmk 8.672 0.316 27.444 0.000 8.053 9.291 8.672 0.231
## .ssmc 7.784 0.224 34.764 0.000 7.345 8.223 7.784 0.420
## .ssasi 6.209 0.200 31.118 0.000 5.818 6.600 6.209 0.439
## .ssei 3.962 0.149 26.521 0.000 3.669 4.255 3.962 0.309
## .ssno 0.206 0.013 16.101 0.000 0.181 0.231 0.206 0.239
## .sscs 0.333 0.016 20.679 0.000 0.302 0.365 0.333 0.377
## .verbal 1.000 1.000 1.000 0.094 0.094
## .math 1.000 1.000 1.000 0.216 0.216
## .electronic 1.000 1.000 1.000 0.188 0.188
## .speed 1.000 1.000 1.000 0.397 0.397
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs 0.788 0.060 13.038 0.000 0.669 0.906 3.074 0.582
## sswk 1.942 0.152 12.762 0.000 1.643 2.240 7.578 0.934
## sspc 0.806 0.062 12.962 0.000 0.684 0.928 3.145 0.874
## math =~
## ssar 3.074 0.091 33.594 0.000 2.894 3.253 7.119 0.945
## ssmk 2.508 0.073 34.457 0.000 2.365 2.650 5.808 0.882
## ssmc 0.430 0.051 8.358 0.000 0.329 0.530 0.995 0.181
## electronic =~
## ssgs 0.919 0.061 15.168 0.000 0.801 1.038 1.861 0.352
## ssasi 2.305 0.064 35.811 0.000 2.179 2.432 4.666 0.835
## ssmc 1.929 0.070 27.369 0.000 1.791 2.067 3.905 0.711
## ssei 1.990 0.049 40.714 0.000 1.894 2.085 4.027 0.921
## speed =~
## ssno 0.476 0.012 39.432 0.000 0.453 0.500 0.849 0.877
## sscs 0.433 0.011 38.015 0.000 0.411 0.456 0.772 0.824
## g =~
## verbal 3.773 0.313 12.069 0.000 3.160 4.386 0.967 0.967
## math 2.089 0.073 28.713 0.000 1.947 2.232 0.902 0.902
## electronic 1.760 0.060 29.327 0.000 1.642 1.877 0.869 0.869
## speed 1.475 0.050 29.365 0.000 1.376 1.573 0.828 0.828
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 16.358 0.087 188.331 0.000 16.188 16.528 16.358 3.098
## .sswk 25.460 0.130 195.905 0.000 25.205 25.715 25.460 3.139
## .sspc 10.389 0.059 175.230 0.000 10.273 10.505 10.389 2.887
## .ssar 18.393 0.130 141.785 0.000 18.139 18.647 18.393 2.440
## .ssmk 13.626 0.116 116.977 0.000 13.397 13.854 13.626 2.068
## .ssmc 15.617 0.092 169.826 0.000 15.437 15.797 15.617 2.844
## .ssasi 16.348 0.092 177.720 0.000 16.168 16.528 16.348 2.926
## .ssei 12.524 0.072 174.554 0.000 12.384 12.665 12.524 2.865
## .ssno 0.084 0.016 5.181 0.000 0.052 0.116 0.084 0.087
## .sscs -0.042 0.016 -2.602 0.009 -0.073 -0.010 -0.042 -0.045
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.355 0.161 33.292 0.000 5.040 5.670 5.355 0.192
## .sswk 8.353 0.463 18.057 0.000 7.446 9.260 8.353 0.127
## .sspc 3.061 0.106 28.755 0.000 2.852 3.269 3.061 0.236
## .ssar 6.125 0.395 15.499 0.000 5.351 6.900 6.125 0.108
## .ssmk 9.679 0.334 28.948 0.000 9.024 10.334 9.679 0.223
## .ssmc 7.831 0.256 30.562 0.000 7.328 8.333 7.831 0.260
## .ssasi 9.454 0.328 28.814 0.000 8.811 10.097 9.454 0.303
## .ssei 2.898 0.146 19.889 0.000 2.612 3.184 2.898 0.152
## .ssno 0.215 0.012 18.638 0.000 0.193 0.238 0.215 0.230
## .sscs 0.282 0.015 19.272 0.000 0.254 0.311 0.282 0.321
## .verbal 1.000 1.000 1.000 0.066 0.066
## .math 1.000 1.000 1.000 0.186 0.186
## .electronic 1.000 1.000 1.000 0.244 0.244
## .speed 1.000 1.000 1.000 0.315 0.315
## g 1.000 1.000 1.000 1.000 1.000
#modificationIndices(configural, sort=T, maximum.number=30)
metric<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2992.380 69.000 0.000 0.969 0.088 0.052 504556.888 505002.076
Mc(metric)
## [1] 0.8746853
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 88 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 77
## Number of equality constraints 16
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2992.380 1787.849
## Degrees of freedom 69 69
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.674
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1094.578 653.975
## 0 1897.801 1133.874
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.883 0.043 20.334 0.000 0.798 0.969 2.633 0.568
## sswk (.p2.) 2.312 0.106 21.743 0.000 2.103 2.520 6.891 0.926
## sspc (.p3.) 0.939 0.043 21.998 0.000 0.855 1.022 2.798 0.856
## math =~
## ssar (.p4.) 3.035 0.078 38.895 0.000 2.882 3.188 6.428 0.933
## ssmk (.p5.) 2.487 0.063 39.413 0.000 2.364 2.611 5.268 0.872
## ssmc (.p6.) 0.522 0.040 12.966 0.000 0.443 0.600 1.105 0.246
## electronic =~
## ssgs (.p7.) 0.570 0.037 15.287 0.000 0.497 0.643 1.500 0.324
## ssasi (.p8.) 1.212 0.054 22.317 0.000 1.105 1.318 3.190 0.791
## ssmc (.p9.) 0.986 0.048 20.645 0.000 0.893 1.080 2.596 0.577
## ssei (.10.) 1.139 0.051 22.239 0.000 1.038 1.239 2.997 0.825
## speed =~
## ssno (.11.) 0.515 0.011 47.150 0.000 0.494 0.536 0.804 0.871
## sscs (.12.) 0.469 0.010 45.934 0.000 0.449 0.489 0.732 0.785
## g =~
## verbal (.13.) 2.808 0.138 20.419 0.000 2.538 3.077 0.942 0.942
## math (.14.) 1.867 0.057 32.713 0.000 1.755 1.979 0.882 0.882
## elctrnc (.15.) 2.435 0.111 22.031 0.000 2.218 2.651 0.925 0.925
## speed (.16.) 1.198 0.033 35.925 0.000 1.133 1.263 0.768 0.768
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 14.716 0.078 188.083 0.000 14.563 14.869 14.716 3.177
## .sswk 25.615 0.123 208.263 0.000 25.374 25.856 25.615 3.444
## .sspc 11.115 0.053 210.841 0.000 11.011 11.218 11.115 3.402
## .ssar 16.646 0.123 135.820 0.000 16.405 16.886 16.646 2.417
## .ssmk 13.157 0.108 122.070 0.000 12.946 13.369 13.157 2.178
## .ssmc 11.841 0.076 156.606 0.000 11.693 11.989 11.841 2.634
## .ssasi 10.952 0.064 171.593 0.000 10.827 11.077 10.952 2.717
## .ssei 9.613 0.062 156.264 0.000 9.492 9.733 9.613 2.648
## .ssno 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.328
## .sscs 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.407
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.385 0.162 33.338 0.000 5.069 5.702 5.385 0.251
## .sswk 7.842 0.402 19.529 0.000 7.055 8.629 7.842 0.142
## .sspc 2.848 0.096 29.618 0.000 2.660 3.037 2.848 0.267
## .ssar 6.110 0.380 16.092 0.000 5.366 6.854 6.110 0.129
## .ssmk 8.741 0.306 28.584 0.000 8.141 9.340 8.741 0.240
## .ssmc 7.579 0.223 33.963 0.000 7.141 8.016 7.579 0.375
## .ssasi 6.073 0.197 30.866 0.000 5.688 6.459 6.073 0.374
## .ssei 4.199 0.144 29.247 0.000 3.917 4.480 4.199 0.319
## .ssno 0.205 0.012 17.655 0.000 0.182 0.228 0.205 0.241
## .sscs 0.334 0.015 22.387 0.000 0.305 0.364 0.334 0.384
## .verbal 1.000 1.000 1.000 0.113 0.113
## .math 1.000 1.000 1.000 0.223 0.223
## .electronic 1.000 1.000 1.000 0.144 0.144
## .speed 1.000 1.000 1.000 0.411 0.411
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.883 0.043 20.334 0.000 0.798 0.969 2.965 0.569
## sswk (.p2.) 2.312 0.106 21.743 0.000 2.103 2.520 7.758 0.937
## sspc (.p3.) 0.939 0.043 21.998 0.000 0.855 1.022 3.150 0.875
## math =~
## ssar (.p4.) 3.035 0.078 38.895 0.000 2.882 3.188 7.211 0.945
## ssmk (.p5.) 2.487 0.063 39.413 0.000 2.364 2.611 5.910 0.886
## ssmc (.p6.) 0.522 0.040 12.966 0.000 0.443 0.600 1.239 0.238
## electronic =~
## ssgs (.p7.) 0.570 0.037 15.287 0.000 0.497 0.643 1.936 0.372
## ssasi (.p8.) 1.212 0.054 22.317 0.000 1.105 1.318 4.117 0.794
## ssmc (.p9.) 0.986 0.048 20.645 0.000 0.893 1.080 3.350 0.642
## ssei (.10.) 1.139 0.051 22.239 0.000 1.038 1.239 3.868 0.923
## speed =~
## ssno (.11.) 0.515 0.011 47.150 0.000 0.494 0.536 0.854 0.879
## sscs (.12.) 0.469 0.010 45.934 0.000 0.449 0.489 0.778 0.826
## g =~
## verbal (.13.) 2.808 0.138 20.419 0.000 2.538 3.077 0.968 0.968
## math (.14.) 1.867 0.057 32.713 0.000 1.755 1.979 0.909 0.909
## elctrnc (.15.) 2.435 0.111 22.031 0.000 2.218 2.651 0.829 0.829
## speed (.16.) 1.198 0.033 35.925 0.000 1.133 1.263 0.835 0.835
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 16.358 0.087 188.331 0.000 16.188 16.528 16.358 3.142
## .sswk 25.460 0.130 195.905 0.000 25.205 25.715 25.460 3.075
## .sspc 10.389 0.059 175.230 0.000 10.273 10.505 10.389 2.885
## .ssar 18.393 0.130 141.785 0.000 18.139 18.647 18.393 2.409
## .ssmk 13.626 0.116 116.977 0.000 13.397 13.854 13.626 2.042
## .ssmc 15.617 0.092 169.826 0.000 15.437 15.797 15.617 2.994
## .ssasi 16.348 0.092 177.720 0.000 16.168 16.528 16.348 3.153
## .ssei 12.524 0.072 174.554 0.000 12.384 12.665 12.524 2.988
## .ssno 0.084 0.016 5.181 0.000 0.052 0.116 0.084 0.086
## .sscs -0.042 0.016 -2.602 0.009 -0.073 -0.010 -0.042 -0.044
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.360 0.160 33.398 0.000 5.045 5.674 5.360 0.198
## .sswk 8.367 0.459 18.211 0.000 7.466 9.267 8.367 0.122
## .sspc 3.045 0.105 28.986 0.000 2.839 3.251 3.045 0.235
## .ssar 6.284 0.376 16.708 0.000 5.547 7.021 6.284 0.108
## .ssmk 9.586 0.318 30.106 0.000 8.962 10.210 9.586 0.215
## .ssmc 8.196 0.257 31.916 0.000 7.693 8.700 8.196 0.301
## .ssasi 9.928 0.331 30.030 0.000 9.280 10.576 9.928 0.369
## .ssei 2.610 0.146 17.913 0.000 2.325 2.896 2.610 0.149
## .ssno 0.215 0.011 19.779 0.000 0.194 0.236 0.215 0.228
## .sscs 0.283 0.014 20.243 0.000 0.255 0.310 0.283 0.318
## .verbal 0.711 0.117 6.089 0.000 0.482 0.939 0.063 0.063
## .math 0.980 0.072 13.689 0.000 0.840 1.121 0.174 0.174
## .electronic 3.608 0.359 10.053 0.000 2.904 4.311 0.313 0.313
## .speed 0.831 0.051 16.166 0.000 0.730 0.932 0.302 0.302
## g 1.338 0.039 34.084 0.000 1.261 1.415 1.000 1.000
lavTestScore(metric, release = 1:16)
## 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 455.652 16 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p47. 0.257 1 0.612
## 2 .p2. == .p48. 52.751 1 0.000
## 3 .p3. == .p49. 2.036 1 0.154
## 4 .p4. == .p50. 8.020 1 0.005
## 5 .p5. == .p51. 3.577 1 0.059
## 6 .p6. == .p52. 19.955 1 0.000
## 7 .p7. == .p53. 5.854 1 0.016
## 8 .p8. == .p54. 162.602 1 0.000
## 9 .p9. == .p55. 63.480 1 0.000
## 10 .p10. == .p56. 0.723 1 0.395
## 11 .p11. == .p57. 0.379 1 0.538
## 12 .p12. == .p58. 1.054 1 0.305
## 13 .p13. == .p59. 61.141 1 0.000
## 14 .p14. == .p60. 17.788 1 0.000
## 15 .p15. == .p61. 246.435 1 0.000
## 16 .p16. == .p62. 2.620 1 0.106
metric2<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"), group.partial=c("g=~electronic"))
fitMeasures(metric2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2744.061 68.000 0.000 0.972 0.085 0.032 504310.569 504763.055
Mc(metric2)
## [1] 0.8846493
scalar<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= 5.835506e-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 aic bic
## 4294.531 73.000 0.000 0.955 0.103 0.051 505851.039 506267.035
Mc(scalar)
## [1] 0.8241962
summary(scalar, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 136 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 25
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 4294.531 2537.521
## Degrees of freedom 73 73
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.692
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1883.781 1113.075
## 0 2410.750 1424.446
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.845 0.046 18.271 0.000 0.755 0.936 2.736 0.596
## sswk (.p2.) 2.175 0.116 18.823 0.000 1.949 2.402 7.040 0.927
## sspc (.p3.) 0.887 0.047 19.025 0.000 0.795 0.978 2.869 0.860
## math =~
## ssar (.p4.) 3.018 0.081 37.382 0.000 2.860 3.176 6.585 0.937
## ssmk (.p5.) 2.441 0.065 37.700 0.000 2.314 2.568 5.325 0.872
## ssmc (.p6.) 0.467 0.035 13.371 0.000 0.399 0.536 1.020 0.235
## electronic =~
## ssgs (.p7.) 0.559 0.029 19.208 0.000 0.502 0.616 1.339 0.292
## ssasi (.p8.) 1.333 0.058 23.104 0.000 1.220 1.446 3.193 0.792
## ssmc (.p9.) 1.040 0.047 22.152 0.000 0.948 1.132 2.492 0.574
## ssei (.10.) 1.061 0.046 23.022 0.000 0.971 1.152 2.542 0.754
## speed =~
## ssno (.11.) 0.494 0.011 46.184 0.000 0.473 0.515 0.796 0.860
## sscs (.12.) 0.471 0.011 44.114 0.000 0.450 0.492 0.759 0.797
## g =~
## verbal (.13.) 3.078 0.173 17.839 0.000 2.740 3.416 0.951 0.951
## math (.14.) 1.939 0.060 32.522 0.000 1.822 2.056 0.889 0.889
## elctrnc 2.177 0.104 20.879 0.000 1.973 2.381 0.909 0.909
## speed (.16.) 1.264 0.035 35.897 0.000 1.195 1.333 0.784 0.784
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 14.726 0.076 192.945 0.000 14.576 14.875 14.726 3.210
## .sswk (.33.) 25.863 0.121 214.249 0.000 25.626 26.099 25.863 3.407
## .sspc (.34.) 10.891 0.053 206.983 0.000 10.788 10.994 10.891 3.264
## .ssar (.35.) 16.817 0.122 138.261 0.000 16.579 17.056 16.817 2.393
## .ssmk (.36.) 12.834 0.104 123.935 0.000 12.631 13.037 12.834 2.100
## .ssmc (.37.) 11.874 0.072 164.263 0.000 11.733 12.016 11.874 2.735
## .ssasi (.38.) 11.315 0.066 171.926 0.000 11.186 11.444 11.315 2.807
## .ssei (.39.) 9.218 0.056 163.689 0.000 9.107 9.328 9.218 2.734
## .ssno (.40.) 0.347 0.015 23.393 0.000 0.318 0.376 0.347 0.375
## .sscs (.41.) 0.310 0.016 19.316 0.000 0.278 0.341 0.310 0.325
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.438 0.163 33.452 0.000 5.119 5.757 5.438 0.258
## .sswk 8.065 0.409 19.724 0.000 7.264 8.867 8.065 0.140
## .sspc 2.902 0.098 29.688 0.000 2.711 3.094 2.902 0.261
## .ssar 6.041 0.389 15.541 0.000 5.279 6.803 6.041 0.122
## .ssmk 8.978 0.309 29.051 0.000 8.372 9.583 8.978 0.240
## .ssmc 7.492 0.221 33.887 0.000 7.059 7.925 7.492 0.398
## .ssasi 6.057 0.212 28.535 0.000 5.641 6.473 6.057 0.373
## .ssei 4.902 0.158 30.999 0.000 4.592 5.212 4.902 0.431
## .ssno 0.223 0.012 19.357 0.000 0.200 0.245 0.223 0.260
## .sscs 0.332 0.016 21.350 0.000 0.301 0.362 0.332 0.365
## .verbal 1.000 1.000 1.000 0.095 0.095
## .math 1.000 1.000 1.000 0.210 0.210
## .electronic 1.000 1.000 1.000 0.174 0.174
## .speed 1.000 1.000 1.000 0.385 0.385
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.845 0.046 18.271 0.000 0.755 0.936 2.958 0.555
## sswk (.p2.) 2.175 0.116 18.823 0.000 1.949 2.402 7.612 0.935
## sspc (.p3.) 0.887 0.047 19.025 0.000 0.795 0.978 3.102 0.868
## math =~
## ssar (.p4.) 3.018 0.081 37.382 0.000 2.860 3.176 7.125 0.945
## ssmk (.p5.) 2.441 0.065 37.700 0.000 2.314 2.568 5.762 0.877
## ssmc (.p6.) 0.467 0.035 13.371 0.000 0.399 0.536 1.103 0.201
## electronic =~
## ssgs (.p7.) 0.559 0.029 19.208 0.000 0.502 0.616 2.049 0.384
## ssasi (.p8.) 1.333 0.058 23.104 0.000 1.220 1.446 4.886 0.844
## ssmc (.p9.) 1.040 0.047 22.152 0.000 0.948 1.132 3.814 0.695
## ssei (.10.) 1.061 0.046 23.022 0.000 0.971 1.152 3.890 0.907
## speed =~
## ssno (.11.) 0.494 0.011 46.184 0.000 0.473 0.515 0.827 0.864
## sscs (.12.) 0.471 0.011 44.114 0.000 0.450 0.492 0.788 0.831
## g =~
## verbal (.13.) 3.078 0.173 17.839 0.000 2.740 3.416 0.966 0.966
## math (.14.) 1.939 0.060 32.522 0.000 1.822 2.056 0.902 0.902
## elctrnc 2.899 0.133 21.877 0.000 2.639 3.159 0.868 0.868
## speed (.16.) 1.264 0.035 35.897 0.000 1.195 1.333 0.830 0.830
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 14.726 0.076 192.945 0.000 14.576 14.875 14.726 2.762
## .sswk (.33.) 25.863 0.121 214.249 0.000 25.626 26.099 25.863 3.176
## .sspc (.34.) 10.891 0.053 206.983 0.000 10.788 10.994 10.891 3.047
## .ssar (.35.) 16.817 0.122 138.261 0.000 16.579 17.056 16.817 2.230
## .ssmk (.36.) 12.834 0.104 123.935 0.000 12.631 13.037 12.834 1.954
## .ssmc (.37.) 11.874 0.072 164.263 0.000 11.733 12.016 11.874 2.164
## .ssasi (.38.) 11.315 0.066 171.926 0.000 11.186 11.444 11.315 1.955
## .ssei (.39.) 9.218 0.056 163.689 0.000 9.107 9.328 9.218 2.149
## .ssno (.40.) 0.347 0.015 23.393 0.000 0.318 0.376 0.347 0.363
## .sscs (.41.) 0.310 0.016 19.316 0.000 0.278 0.341 0.310 0.327
## .verbal -1.246 0.063 -19.915 0.000 -1.369 -1.124 -0.356 -0.356
## .math -0.130 0.044 -2.930 0.003 -0.217 -0.043 -0.055 -0.055
## .elctrnc 2.465 0.082 30.086 0.000 2.304 2.626 0.672 0.672
## .speed -1.014 0.042 -24.391 0.000 -1.095 -0.932 -0.606 -0.606
## g 0.308 0.030 10.273 0.000 0.249 0.366 0.280 0.280
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.312 0.161 33.036 0.000 4.997 5.628 5.312 0.187
## .sswk 8.374 0.463 18.091 0.000 7.466 9.281 8.374 0.126
## .sspc 3.156 0.112 28.258 0.000 2.937 3.375 3.156 0.247
## .ssar 6.120 0.391 15.646 0.000 5.353 6.887 6.120 0.108
## .ssmk 9.933 0.334 29.742 0.000 9.279 10.588 9.933 0.230
## .ssmc 7.742 0.244 31.785 0.000 7.265 8.220 7.742 0.257
## .ssasi 9.615 0.352 27.329 0.000 8.926 10.305 9.615 0.287
## .ssei 3.263 0.143 22.866 0.000 2.983 3.543 3.263 0.177
## .ssno 0.233 0.011 20.776 0.000 0.211 0.255 0.233 0.254
## .sscs 0.278 0.015 19.097 0.000 0.249 0.307 0.278 0.309
## .verbal 0.818 0.133 6.167 0.000 0.558 1.077 0.067 0.067
## .math 1.038 0.075 13.838 0.000 0.891 1.185 0.186 0.186
## .electronic 3.303 0.331 9.965 0.000 2.654 3.953 0.246 0.246
## .speed 0.872 0.055 15.826 0.000 0.764 0.980 0.312 0.312
## g 1.206 0.035 34.470 0.000 1.138 1.275 1.000 1.000
lavTestScore(scalar, release = 16:25)
## 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 1502.515 10 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p32. == .p78. 0.700 1 0.403
## 2 .p33. == .p79. 242.075 1 0.000
## 3 .p34. == .p80. 271.793 1 0.000
## 4 .p35. == .p81. 175.625 1 0.000
## 5 .p36. == .p82. 186.312 1 0.000
## 6 .p37. == .p83. 3.779 1 0.052
## 7 .p38. == .p84. 644.396 1 0.000
## 8 .p39. == .p85. 688.394 1 0.000
## 9 .p40. == .p86. 258.153 1 0.000
## 10 .p41. == .p87. 258.153 1 0.000
scalar2<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~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 (= 5.967310e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2991.943 70.000 0.000 0.969 0.087 0.034 504554.451 504992.341
Mc(scalar2)
## [1] 0.8747428
summary(scalar2, standardized=T, ci=T) # g -.285 Std.all
## lavaan 0.6-18 ended normally after 148 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 22
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2991.943 1761.746
## Degrees of freedom 70 70
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.698
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1094.943 644.736
## 0 1896.999 1117.011
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.828 0.046 18.029 0.000 0.738 0.918 2.741 0.596
## sswk (.p2.) 2.129 0.117 18.249 0.000 1.901 2.358 7.049 0.929
## sspc (.p3.) 0.863 0.047 18.387 0.000 0.771 0.955 2.858 0.861
## math =~
## ssar (.p4.) 3.042 0.079 38.620 0.000 2.887 3.196 6.578 0.936
## ssmk (.p5.) 2.464 0.064 38.753 0.000 2.339 2.589 5.329 0.872
## ssmc (.p6.) 0.642 0.035 18.357 0.000 0.573 0.710 1.387 0.318
## electronic =~
## ssgs (.p7.) 0.592 0.028 21.227 0.000 0.537 0.647 1.357 0.295
## ssasi (.p8.) 1.332 0.052 25.423 0.000 1.230 1.435 3.055 0.782
## ssmc (.p9.) 0.946 0.041 23.151 0.000 0.866 1.026 2.169 0.497
## ssei (.10.) 1.212 0.048 25.384 0.000 1.119 1.306 2.779 0.803
## speed =~
## ssno (.11.) 0.509 0.011 46.606 0.000 0.488 0.531 0.813 0.874
## sscs (.12.) 0.465 0.010 45.310 0.000 0.445 0.485 0.742 0.789
## g =~
## verbal (.13.) 3.156 0.182 17.297 0.000 2.798 3.514 0.953 0.953
## math (.14.) 1.918 0.057 33.487 0.000 1.805 2.030 0.887 0.887
## elctrnc 2.063 0.090 22.996 0.000 1.887 2.239 0.900 0.900
## speed (.16.) 1.245 0.034 36.113 0.000 1.177 1.312 0.780 0.780
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 14.719 0.077 191.746 0.000 14.569 14.870 14.719 3.200
## .sswk 25.615 0.123 208.263 0.000 25.374 25.856 25.615 3.376
## .sspc (.34.) 11.113 0.053 211.279 0.000 11.010 11.216 11.113 3.350
## .ssar (.35.) 16.836 0.122 138.397 0.000 16.598 17.075 16.836 2.395
## .ssmk (.36.) 12.849 0.104 123.936 0.000 12.646 13.052 12.849 2.103
## .ssmc (.37.) 11.729 0.073 161.511 0.000 11.587 11.871 11.729 2.687
## .ssasi (.38.) 11.012 0.064 173.283 0.000 10.888 11.137 11.012 2.821
## .ssei 9.613 0.062 156.264 0.000 9.492 9.733 9.613 2.777
## .ssno (.40.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.325
## .sscs 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.404
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.413 0.162 33.448 0.000 5.096 5.731 5.413 0.256
## .sswk 7.886 0.397 19.847 0.000 7.107 8.664 7.886 0.137
## .sspc 2.838 0.095 29.924 0.000 2.652 3.024 2.838 0.258
## .ssar 6.141 0.382 16.093 0.000 5.393 6.889 6.141 0.124
## .ssmk 8.933 0.307 29.052 0.000 8.330 9.535 8.933 0.239
## .ssmc 7.626 0.220 34.707 0.000 7.195 8.056 7.626 0.400
## .ssasi 5.908 0.196 30.122 0.000 5.524 6.293 5.908 0.388
## .ssei 4.260 0.146 29.185 0.000 3.974 4.546 4.260 0.355
## .ssno 0.205 0.012 17.797 0.000 0.182 0.228 0.205 0.237
## .sscs 0.334 0.015 22.454 0.000 0.305 0.363 0.334 0.377
## .verbal 1.000 1.000 1.000 0.091 0.091
## .math 1.000 1.000 1.000 0.214 0.214
## .electronic 1.000 1.000 1.000 0.190 0.190
## .speed 1.000 1.000 1.000 0.392 0.392
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.828 0.046 18.029 0.000 0.738 0.918 2.972 0.558
## sswk (.p2.) 2.129 0.117 18.249 0.000 1.901 2.358 7.641 0.936
## sspc (.p3.) 0.863 0.047 18.387 0.000 0.771 0.955 3.098 0.870
## math =~
## ssar (.p4.) 3.042 0.079 38.620 0.000 2.887 3.196 7.119 0.944
## ssmk (.p5.) 2.464 0.064 38.753 0.000 2.339 2.589 5.767 0.878
## ssmc (.p6.) 0.642 0.035 18.357 0.000 0.573 0.710 1.501 0.280
## electronic =~
## ssgs (.p7.) 0.592 0.028 21.227 0.000 0.537 0.647 2.018 0.379
## ssasi (.p8.) 1.332 0.052 25.423 0.000 1.230 1.435 4.541 0.823
## ssmc (.p9.) 0.946 0.041 23.151 0.000 0.866 1.026 3.225 0.602
## ssei (.10.) 1.212 0.048 25.384 0.000 1.119 1.306 4.131 0.933
## speed =~
## ssno (.11.) 0.509 0.011 46.606 0.000 0.488 0.531 0.845 0.876
## sscs (.12.) 0.465 0.010 45.310 0.000 0.445 0.485 0.771 0.824
## g =~
## verbal (.13.) 3.156 0.182 17.297 0.000 2.798 3.514 0.968 0.968
## math (.14.) 1.918 0.057 33.487 0.000 1.805 2.030 0.902 0.902
## elctrnc 2.683 0.112 23.857 0.000 2.463 2.903 0.866 0.866
## speed (.16.) 1.245 0.034 36.113 0.000 1.177 1.312 0.826 0.826
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 14.719 0.077 191.746 0.000 14.569 14.870 14.719 2.766
## .sswk 27.241 0.156 174.461 0.000 26.935 27.547 27.241 3.339
## .sspc (.34.) 11.113 0.053 211.279 0.000 11.010 11.216 11.113 3.120
## .ssar (.35.) 16.836 0.122 138.397 0.000 16.598 17.075 16.836 2.231
## .ssmk (.36.) 12.849 0.104 123.936 0.000 12.646 13.052 12.849 1.955
## .ssmc (.37.) 11.729 0.073 161.511 0.000 11.587 11.871 11.729 2.190
## .ssasi (.38.) 11.012 0.064 173.283 0.000 10.888 11.137 11.012 1.995
## .ssei 7.758 0.096 80.658 0.000 7.570 7.947 7.758 1.753
## .ssno (.40.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.313
## .sscs 0.157 0.019 8.328 0.000 0.120 0.194 0.157 0.168
## .verbal -1.825 0.081 -22.578 0.000 -1.984 -1.667 -0.509 -0.509
## .math -0.151 0.050 -3.003 0.003 -0.249 -0.052 -0.064 -0.064
## .elctrnc 3.091 0.104 29.624 0.000 2.886 3.295 0.907 0.907
## .speed -0.818 0.043 -18.937 0.000 -0.903 -0.734 -0.493 -0.493
## g 0.313 0.033 9.507 0.000 0.249 0.378 0.285 0.285
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.359 0.161 33.302 0.000 5.043 5.674 5.359 0.189
## .sswk 8.186 0.447 18.311 0.000 7.310 9.062 8.186 0.123
## .sspc 3.088 0.106 29.185 0.000 2.880 3.295 3.088 0.243
## .ssar 6.244 0.386 16.162 0.000 5.487 7.001 6.244 0.110
## .ssmk 9.924 0.331 29.960 0.000 9.275 10.574 9.924 0.230
## .ssmc 8.453 0.247 34.181 0.000 7.968 8.938 8.453 0.295
## .ssasi 9.849 0.330 29.811 0.000 9.202 10.497 9.849 0.323
## .ssei 2.524 0.136 18.505 0.000 2.256 2.791 2.524 0.129
## .ssno 0.216 0.011 19.744 0.000 0.195 0.237 0.216 0.232
## .sscs 0.282 0.014 20.108 0.000 0.254 0.309 0.282 0.321
## .verbal 0.816 0.136 6.013 0.000 0.550 1.082 0.063 0.063
## .math 1.025 0.073 14.043 0.000 0.882 1.168 0.187 0.187
## .electronic 2.898 0.268 10.807 0.000 2.372 3.423 0.249 0.249
## .speed 0.876 0.054 16.302 0.000 0.771 0.982 0.318 0.318
## g 1.211 0.035 34.511 0.000 1.142 1.280 1.000 1.000
strict<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~1"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= 4.916545e-14) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 3353.154 80.000 0.000 0.965 0.087 0.042 504895.663 505260.571
Mc(strict)
## [1] 0.8607847
summary(strict, standardized=T, ci=T) # g -.274 Std.all
## lavaan 0.6-18 ended normally after 129 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 32
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3353.154 1941.895
## Degrees of freedom 80 80
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.727
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1296.762 750.987
## 0 2056.393 1190.908
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.812 0.045 18.001 0.000 0.723 0.900 2.717 0.591
## sswk (.p2.) 2.100 0.116 18.172 0.000 1.874 2.327 7.032 0.927
## sspc (.p3.) 0.853 0.046 18.357 0.000 0.762 0.944 2.854 0.856
## math =~
## ssar (.p4.) 3.029 0.077 39.268 0.000 2.877 3.180 6.575 0.935
## ssmk (.p5.) 2.453 0.062 39.646 0.000 2.331 2.574 5.324 0.866
## ssmc (.p6.) 0.608 0.034 17.873 0.000 0.541 0.674 1.319 0.300
## electronic =~
## ssgs (.p7.) 0.593 0.028 21.088 0.000 0.538 0.648 1.383 0.301
## ssasi (.p8.) 1.343 0.053 25.358 0.000 1.239 1.447 3.133 0.752
## ssmc (.p9.) 0.965 0.041 23.596 0.000 0.885 1.045 2.250 0.511
## ssei (.10.) 1.191 0.049 24.508 0.000 1.096 1.286 2.777 0.824
## speed =~
## ssno (.11.) 0.512 0.010 50.978 0.000 0.493 0.532 0.815 0.871
## sscs (.12.) 0.468 0.010 47.002 0.000 0.449 0.488 0.745 0.803
## g =~
## verbal (.13.) 3.195 0.186 17.180 0.000 2.831 3.560 0.954 0.954
## math (.14.) 1.927 0.057 33.669 0.000 1.815 2.039 0.888 0.888
## elctrnc 2.107 0.093 22.707 0.000 1.925 2.289 0.903 0.903
## speed (.16.) 1.238 0.033 37.697 0.000 1.173 1.302 0.778 0.778
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 14.724 0.077 192.147 0.000 14.574 14.874 14.724 3.202
## .sswk 25.615 0.123 208.263 0.000 25.374 25.856 25.615 3.378
## .sspc (.34.) 11.110 0.053 210.926 0.000 11.007 11.214 11.110 3.334
## .ssar (.35.) 16.838 0.122 138.014 0.000 16.599 17.077 16.838 2.396
## .ssmk (.36.) 12.833 0.104 123.870 0.000 12.630 13.036 12.833 2.088
## .ssmc (.37.) 11.712 0.072 162.052 0.000 11.570 11.853 11.712 2.658
## .ssasi (.38.) 11.036 0.064 173.533 0.000 10.912 11.161 11.036 2.651
## .ssei 9.613 0.062 156.264 0.000 9.492 9.733 9.613 2.852
## .ssno (.40.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.323
## .sscs 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.409
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.17.) 5.369 0.116 46.484 0.000 5.143 5.595 5.369 0.254
## .sswk (.18.) 8.052 0.313 25.717 0.000 7.438 8.665 8.052 0.140
## .sspc (.19.) 2.960 0.071 41.628 0.000 2.821 3.100 2.960 0.267
## .ssar (.20.) 6.171 0.284 21.715 0.000 5.614 6.728 6.171 0.125
## .ssmk (.21.) 9.434 0.237 39.786 0.000 8.969 9.899 9.434 0.250
## .ssmc (.22.) 7.846 0.165 47.537 0.000 7.522 8.169 7.846 0.404
## .ssasi (.23.) 7.518 0.194 38.689 0.000 7.138 7.899 7.518 0.434
## .ssei (.24.) 3.647 0.108 33.719 0.000 3.435 3.859 3.647 0.321
## .ssno (.25.) 0.212 0.009 24.636 0.000 0.195 0.229 0.212 0.242
## .sscs (.26.) 0.307 0.011 28.169 0.000 0.285 0.328 0.307 0.356
## .verbal 1.000 1.000 1.000 0.089 0.089
## .math 1.000 1.000 1.000 0.212 0.212
## .elctrnc 1.000 1.000 1.000 0.184 0.184
## .speed 1.000 1.000 1.000 0.395 0.395
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.812 0.045 18.001 0.000 0.723 0.900 2.957 0.556
## sswk (.p2.) 2.100 0.116 18.172 0.000 1.874 2.327 7.653 0.938
## sspc (.p3.) 0.853 0.046 18.357 0.000 0.762 0.944 3.107 0.875
## math =~
## ssar (.p4.) 3.029 0.077 39.268 0.000 2.877 3.180 7.125 0.944
## ssmk (.p5.) 2.453 0.062 39.646 0.000 2.331 2.574 5.770 0.883
## ssmc (.p6.) 0.608 0.034 17.873 0.000 0.541 0.674 1.430 0.269
## electronic =~
## ssgs (.p7.) 0.593 0.028 21.088 0.000 0.538 0.648 2.045 0.384
## ssasi (.p8.) 1.343 0.053 25.358 0.000 1.239 1.447 4.633 0.861
## ssmc (.p9.) 0.965 0.041 23.596 0.000 0.885 1.045 3.328 0.625
## ssei (.10.) 1.191 0.049 24.508 0.000 1.096 1.286 4.108 0.907
## speed =~
## ssno (.11.) 0.512 0.010 50.978 0.000 0.493 0.532 0.842 0.878
## sscs (.12.) 0.468 0.010 47.002 0.000 0.449 0.488 0.770 0.812
## g =~
## verbal (.13.) 3.195 0.186 17.180 0.000 2.831 3.560 0.965 0.965
## math (.14.) 1.927 0.057 33.669 0.000 1.815 2.039 0.902 0.902
## elctrnc 2.694 0.115 23.523 0.000 2.470 2.919 0.860 0.860
## speed (.16.) 1.238 0.033 37.697 0.000 1.173 1.302 0.829 0.829
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 14.724 0.077 192.147 0.000 14.574 14.874 14.724 2.766
## .sswk 27.227 0.156 174.749 0.000 26.922 27.532 27.227 3.336
## .sspc (.34.) 11.110 0.053 210.926 0.000 11.007 11.214 11.110 3.129
## .ssar (.35.) 16.838 0.122 138.014 0.000 16.599 17.077 16.838 2.231
## .ssmk (.36.) 12.833 0.104 123.870 0.000 12.630 13.036 12.833 1.963
## .ssmc (.37.) 11.712 0.072 162.052 0.000 11.570 11.853 11.712 2.200
## .ssasi (.38.) 11.036 0.064 173.533 0.000 10.912 11.161 11.036 2.050
## .ssei 7.887 0.091 86.901 0.000 7.709 8.065 7.887 1.741
## .ssno (.40.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.315
## .sscs 0.158 0.019 8.335 0.000 0.121 0.195 0.158 0.166
## .verbal -1.805 0.081 -22.367 0.000 -1.964 -1.647 -0.495 -0.495
## .math -0.130 0.050 -2.609 0.009 -0.227 -0.032 -0.055 -0.055
## .elctrnc 3.081 0.104 29.683 0.000 2.878 3.285 0.893 0.893
## .speed -0.799 0.042 -18.822 0.000 -0.883 -0.716 -0.486 -0.486
## g 0.302 0.033 9.115 0.000 0.237 0.367 0.274 0.274
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.17.) 5.369 0.116 46.484 0.000 5.143 5.595 5.369 0.189
## .sswk (.18.) 8.052 0.313 25.717 0.000 7.438 8.665 8.052 0.121
## .sspc (.19.) 2.960 0.071 41.628 0.000 2.821 3.100 2.960 0.235
## .ssar (.20.) 6.171 0.284 21.715 0.000 5.614 6.728 6.171 0.108
## .ssmk (.21.) 9.434 0.237 39.786 0.000 8.969 9.899 9.434 0.221
## .ssmc (.22.) 7.846 0.165 47.537 0.000 7.522 8.169 7.846 0.277
## .ssasi (.23.) 7.518 0.194 38.689 0.000 7.138 7.899 7.518 0.259
## .ssei (.24.) 3.647 0.108 33.719 0.000 3.435 3.859 3.647 0.178
## .ssno (.25.) 0.212 0.009 24.636 0.000 0.195 0.229 0.212 0.230
## .sscs (.26.) 0.307 0.011 28.169 0.000 0.285 0.328 0.307 0.341
## .verbal 0.903 0.136 6.629 0.000 0.636 1.170 0.068 0.068
## .math 1.034 0.067 15.384 0.000 0.902 1.166 0.187 0.187
## .elctrnc 3.102 0.297 10.430 0.000 2.519 3.685 0.261 0.261
## .speed 0.847 0.048 17.755 0.000 0.754 0.941 0.313 0.313
## g 1.212 0.035 34.509 0.000 1.143 1.281 1.000 1.000
latent<-cfa(hof.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~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 (= 3.347973e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(latent, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 3340.736 75.000 0.000 0.965 0.089 0.063 504893.244 505294.643
Mc(latent)
## [1] 0.8610772
summary(latent, standardized=T, ci=T) # g -.138 Std.all
## lavaan 0.6-18 ended normally after 114 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 77
## Number of equality constraints 22
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3340.736 1980.915
## Degrees of freedom 75 75
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.686
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1254.689 743.977
## 0 2086.046 1236.937
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.784 0.038 20.438 0.000 0.709 0.859 2.851 0.601
## sswk (.p2.) 2.026 0.099 20.454 0.000 1.832 2.220 7.364 0.934
## sspc (.p3.) 0.819 0.039 20.841 0.000 0.742 0.896 2.978 0.871
## math =~
## ssar (.p4.) 3.107 0.060 51.430 0.000 2.989 3.226 6.860 0.941
## ssmk (.p5.) 2.514 0.048 51.952 0.000 2.419 2.609 5.550 0.881
## ssmc (.p6.) 0.665 0.032 20.505 0.000 0.601 0.728 1.468 0.326
## electronic =~
## ssgs (.p7.) 0.808 0.026 30.718 0.000 0.757 0.860 1.481 0.312
## ssasi (.p8.) 1.796 0.042 42.556 0.000 1.713 1.879 3.291 0.810
## ssmc (.p9.) 1.272 0.039 32.333 0.000 1.195 1.349 2.331 0.518
## ssei (.10.) 1.654 0.037 44.922 0.000 1.582 1.726 3.031 0.833
## speed =~
## ssno (.11.) 0.495 0.008 59.384 0.000 0.478 0.511 0.829 0.877
## sscs (.12.) 0.452 0.008 56.762 0.000 0.436 0.467 0.757 0.794
## g =~
## verbal (.13.) 3.495 0.182 19.208 0.000 3.139 3.852 0.961 0.961
## math (.14.) 1.968 0.046 42.966 0.000 1.878 2.058 0.892 0.892
## elctrnc 1.536 0.043 35.940 0.000 1.452 1.619 0.838 0.838
## speed (.16.) 1.345 0.031 42.788 0.000 1.284 1.407 0.803 0.803
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 14.710 0.077 191.284 0.000 14.559 14.861 14.710 3.100
## .sswk 25.615 0.123 208.263 0.000 25.374 25.856 25.615 3.250
## .sspc (.34.) 11.118 0.053 211.525 0.000 11.015 11.221 11.118 3.254
## .ssar (.35.) 16.833 0.122 138.199 0.000 16.594 17.072 16.833 2.309
## .ssmk (.36.) 12.851 0.104 123.959 0.000 12.648 13.055 12.851 2.040
## .ssmc (.37.) 11.735 0.073 161.564 0.000 11.593 11.877 11.735 2.609
## .ssasi (.38.) 11.012 0.064 173.125 0.000 10.887 11.136 11.012 2.710
## .ssei 9.613 0.062 156.264 0.000 9.492 9.733 9.613 2.642
## .ssno (.40.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.319
## .sscs 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.399
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.396 0.162 33.391 0.000 5.079 5.712 5.396 0.240
## .sswk 7.899 0.390 20.246 0.000 7.134 8.663 7.899 0.127
## .sspc 2.810 0.094 29.833 0.000 2.625 2.994 2.810 0.241
## .ssar 6.070 0.373 16.251 0.000 5.338 6.802 6.070 0.114
## .ssmk 8.886 0.310 28.666 0.000 8.279 9.494 8.886 0.224
## .ssmc 7.536 0.220 34.221 0.000 7.104 7.967 7.536 0.372
## .ssasi 5.676 0.197 28.824 0.000 5.290 6.062 5.676 0.344
## .ssei 4.050 0.150 26.996 0.000 3.756 4.345 4.050 0.306
## .ssno 0.207 0.011 18.900 0.000 0.185 0.228 0.207 0.231
## .sscs 0.335 0.015 22.779 0.000 0.306 0.364 0.335 0.369
## .verbal 1.000 1.000 1.000 0.076 0.076
## .math 1.000 1.000 1.000 0.205 0.205
## .electronic 1.000 1.000 1.000 0.298 0.298
## .speed 1.000 1.000 1.000 0.356 0.356
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.784 0.038 20.438 0.000 0.709 0.859 2.851 0.552
## sswk (.p2.) 2.026 0.099 20.454 0.000 1.832 2.220 7.364 0.934
## sspc (.p3.) 0.819 0.039 20.841 0.000 0.742 0.896 2.978 0.859
## math =~
## ssar (.p4.) 3.107 0.060 51.430 0.000 2.989 3.226 6.860 0.940
## ssmk (.p5.) 2.514 0.048 51.952 0.000 2.419 2.609 5.550 0.868
## ssmc (.p6.) 0.665 0.032 20.505 0.000 0.601 0.728 1.468 0.282
## electronic =~
## ssgs (.p7.) 0.808 0.026 30.718 0.000 0.757 0.860 1.919 0.371
## ssasi (.p8.) 1.796 0.042 42.556 0.000 1.713 1.879 4.265 0.801
## ssmc (.p9.) 1.272 0.039 32.333 0.000 1.195 1.349 3.021 0.581
## ssei (.10.) 1.654 0.037 44.922 0.000 1.582 1.726 3.927 0.922
## speed =~
## ssno (.11.) 0.495 0.008 59.384 0.000 0.478 0.511 0.829 0.873
## sscs (.12.) 0.452 0.008 56.762 0.000 0.436 0.467 0.757 0.820
## g =~
## verbal (.13.) 3.495 0.182 19.208 0.000 3.139 3.852 0.961 0.961
## math (.14.) 1.968 0.046 42.966 0.000 1.878 2.058 0.892 0.892
## elctrnc 2.154 0.063 34.162 0.000 2.030 2.277 0.907 0.907
## speed (.16.) 1.345 0.031 42.788 0.000 1.284 1.407 0.803 0.803
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 14.710 0.077 191.284 0.000 14.559 14.861 14.710 2.848
## .sswk 27.270 0.157 173.994 0.000 26.963 27.577 27.270 3.459
## .sspc (.34.) 11.118 0.053 211.525 0.000 11.015 11.221 11.118 3.207
## .ssar (.35.) 16.833 0.122 138.199 0.000 16.594 17.072 16.833 2.306
## .ssmk (.36.) 12.851 0.104 123.959 0.000 12.648 13.055 12.851 2.010
## .ssmc (.37.) 11.735 0.073 161.564 0.000 11.593 11.877 11.735 2.255
## .ssasi (.38.) 11.012 0.064 173.125 0.000 10.887 11.136 11.012 2.067
## .ssei 7.706 0.097 79.151 0.000 7.515 7.897 7.706 1.809
## .ssno (.40.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.318
## .sscs 0.157 0.019 8.329 0.000 0.120 0.195 0.157 0.170
## .verbal -1.375 0.050 -27.424 0.000 -1.474 -1.277 -0.378 -0.378
## .math 0.171 0.037 4.636 0.000 0.098 0.243 0.077 0.077
## .elctrnc 2.617 0.071 36.643 0.000 2.477 2.757 1.102 1.102
## .speed -0.626 0.037 -16.757 0.000 -0.700 -0.553 -0.374 -0.374
## g 0.138 0.026 5.360 0.000 0.087 0.188 0.138 0.138
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.328 0.160 33.242 0.000 5.014 5.642 5.328 0.200
## .sswk 7.904 0.410 19.266 0.000 7.100 8.708 7.904 0.127
## .sspc 3.150 0.108 29.116 0.000 2.938 3.362 3.150 0.262
## .ssar 6.237 0.370 16.874 0.000 5.513 6.962 6.237 0.117
## .ssmk 10.069 0.333 30.273 0.000 9.418 10.721 10.069 0.246
## .ssmc 8.627 0.245 35.279 0.000 8.148 9.106 8.627 0.319
## .ssasi 10.182 0.326 31.237 0.000 9.543 10.821 10.182 0.359
## .ssei 2.733 0.130 21.090 0.000 2.479 2.987 2.733 0.151
## .ssno 0.216 0.011 20.023 0.000 0.194 0.237 0.216 0.239
## .sscs 0.280 0.014 19.877 0.000 0.252 0.308 0.280 0.328
## .verbal 1.000 1.000 1.000 0.076 0.076
## .math 1.000 1.000 1.000 0.205 0.205
## .electronic 1.000 1.000 1.000 0.177 0.177
## .speed 1.000 1.000 1.000 0.356 0.356
## g 1.000 1.000 1.000 1.000 1.000
latent2<-cfa(hof.lv, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~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 (= 1.526351e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(latent2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 3002.336 73.000 0.000 0.969 0.086 0.034 504558.844 504974.840
Mc(latent2)
## [1] 0.8744467
summary(latent2, standardized=T, ci=T) # -.264, but -.304 if g variance is constrained
## lavaan 0.6-18 ended normally after 134 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 79
## Number of equality constraints 22
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3002.336 1773.589
## Degrees of freedom 73 73
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.693
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1100.037 649.832
## 0 1902.299 1123.757
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.786 0.038 20.468 0.000 0.711 0.861 2.735 0.595
## sswk (.p2.) 2.020 0.098 20.509 0.000 1.827 2.213 7.029 0.928
## sspc (.p3.) 0.819 0.039 20.861 0.000 0.742 0.896 2.850 0.861
## math =~
## ssar (.p4.) 3.066 0.061 50.050 0.000 2.946 3.186 6.596 0.936
## ssmk (.p5.) 2.483 0.049 50.648 0.000 2.387 2.579 5.342 0.873
## ssmc (.p6.) 0.648 0.033 19.799 0.000 0.584 0.712 1.393 0.319
## electronic =~
## ssgs (.p7.) 0.596 0.028 21.495 0.000 0.541 0.650 1.356 0.295
## ssasi (.p8.) 1.341 0.052 25.886 0.000 1.240 1.443 3.055 0.783
## ssmc (.p9.) 0.952 0.041 23.493 0.000 0.873 1.032 2.168 0.496
## ssei (.10.) 1.221 0.047 25.840 0.000 1.128 1.313 2.780 0.803
## speed =~
## ssno (.11.) 0.492 0.008 59.038 0.000 0.476 0.509 0.803 0.868
## sscs (.12.) 0.449 0.008 56.553 0.000 0.434 0.465 0.734 0.785
## g =~
## verbal (.13.) 3.333 0.175 19.030 0.000 2.990 3.676 0.958 0.958
## math (.14.) 1.905 0.047 40.241 0.000 1.812 1.997 0.885 0.885
## elctrnc 2.046 0.087 23.442 0.000 1.875 2.217 0.898 0.898
## speed (.16.) 1.290 0.032 40.522 0.000 1.227 1.352 0.790 0.790
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 14.720 0.077 191.757 0.000 14.569 14.870 14.720 3.203
## .sswk 25.615 0.123 208.263 0.000 25.374 25.856 25.615 3.380
## .sspc (.34.) 11.113 0.053 211.231 0.000 11.009 11.216 11.113 3.357
## .ssar (.35.) 16.836 0.122 138.234 0.000 16.597 17.075 16.836 2.389
## .ssmk (.36.) 12.849 0.104 123.960 0.000 12.646 13.053 12.849 2.099
## .ssmc (.37.) 11.729 0.073 161.633 0.000 11.587 11.871 11.729 2.685
## .ssasi (.38.) 11.012 0.064 173.185 0.000 10.887 11.136 11.012 2.821
## .ssei 9.613 0.062 156.264 0.000 9.492 9.733 9.613 2.777
## .ssno (.40.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.326
## .sscs 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.407
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.083 0.083
## .math 1.000 1.000 1.000 0.216 0.216
## .speed 1.000 1.000 1.000 0.376 0.376
## .ssgs 5.418 0.162 33.443 0.000 5.101 5.736 5.418 0.257
## .sswk 8.023 0.387 20.730 0.000 7.264 8.781 8.023 0.140
## .sspc 2.837 0.094 30.024 0.000 2.652 3.022 2.837 0.259
## .ssar 6.137 0.370 16.575 0.000 5.411 6.862 6.137 0.124
## .ssmk 8.926 0.308 29.009 0.000 8.323 9.529 8.926 0.238
## .ssmc 7.634 0.220 34.741 0.000 7.203 8.065 7.634 0.400
## .ssasi 5.904 0.196 30.148 0.000 5.520 6.288 5.904 0.388
## .ssei 4.257 0.146 29.199 0.000 3.971 4.543 4.257 0.355
## .ssno 0.211 0.011 19.300 0.000 0.190 0.233 0.211 0.246
## .sscs 0.335 0.015 22.779 0.000 0.306 0.364 0.335 0.384
## .electronic 1.000 1.000 1.000 0.193 0.193
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.786 0.038 20.468 0.000 0.711 0.861 2.980 0.560
## sswk (.p2.) 2.020 0.098 20.509 0.000 1.827 2.213 7.659 0.938
## sspc (.p3.) 0.819 0.039 20.861 0.000 0.742 0.896 3.105 0.870
## math =~
## ssar (.p4.) 3.066 0.061 50.050 0.000 2.946 3.186 7.104 0.943
## ssmk (.p5.) 2.483 0.049 50.648 0.000 2.387 2.579 5.754 0.877
## ssmc (.p6.) 0.648 0.033 19.799 0.000 0.584 0.712 1.501 0.280
## electronic =~
## ssgs (.p7.) 0.596 0.028 21.495 0.000 0.541 0.650 2.016 0.379
## ssasi (.p8.) 1.341 0.052 25.886 0.000 1.240 1.443 4.540 0.823
## ssmc (.p9.) 0.952 0.041 23.493 0.000 0.873 1.032 3.222 0.602
## ssei (.10.) 1.221 0.047 25.840 0.000 1.128 1.313 4.131 0.933
## speed =~
## ssno (.11.) 0.492 0.008 59.038 0.000 0.476 0.509 0.853 0.880
## sscs (.12.) 0.449 0.008 56.553 0.000 0.434 0.465 0.779 0.827
## g =~
## verbal (.13.) 3.333 0.175 19.030 0.000 2.990 3.676 0.965 0.965
## math (.14.) 1.905 0.047 40.241 0.000 1.812 1.997 0.902 0.902
## elctrnc 2.675 0.111 24.181 0.000 2.458 2.892 0.867 0.867
## speed (.16.) 1.290 0.032 40.522 0.000 1.227 1.352 0.817 0.817
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs (.32.) 14.720 0.077 191.757 0.000 14.569 14.870 14.720 2.765
## .sswk 27.239 0.156 174.415 0.000 26.933 27.546 27.239 3.335
## .sspc (.34.) 11.113 0.053 211.231 0.000 11.009 11.216 11.113 3.114
## .ssar (.35.) 16.836 0.122 138.234 0.000 16.597 17.075 16.836 2.236
## .ssmk (.36.) 12.849 0.104 123.960 0.000 12.646 13.053 12.849 1.958
## .ssmc (.37.) 11.729 0.073 161.633 0.000 11.587 11.871 11.729 2.191
## .ssasi (.38.) 11.012 0.064 173.185 0.000 10.887 11.136 11.012 1.995
## .ssei 7.756 0.096 80.525 0.000 7.568 7.945 7.756 1.752
## .ssno (.40.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.312
## .sscs 0.157 0.019 8.330 0.000 0.120 0.194 0.157 0.167
## .verbal -1.847 0.077 -24.041 0.000 -1.998 -1.697 -0.487 -0.487
## .math -0.106 0.048 -2.195 0.028 -0.200 -0.011 -0.046 -0.046
## .elctrnc 3.131 0.106 29.538 0.000 2.923 3.338 0.925 0.925
## .speed -0.817 0.044 -18.704 0.000 -0.903 -0.731 -0.472 -0.472
## g 0.290 0.031 9.487 0.000 0.230 0.350 0.264 0.264
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.070 0.070
## .math 1.000 1.000 1.000 0.186 0.186
## .speed 1.000 1.000 1.000 0.333 0.333
## .ssgs 5.353 0.161 33.327 0.000 5.039 5.668 5.353 0.189
## .sswk 8.050 0.426 18.917 0.000 7.216 8.884 8.050 0.121
## .sspc 3.089 0.106 29.154 0.000 2.882 3.297 3.089 0.243
## .ssar 6.233 0.371 16.811 0.000 5.506 6.960 6.233 0.110
## .ssmk 9.941 0.332 29.924 0.000 9.290 10.592 9.941 0.231
## .ssmc 8.450 0.247 34.165 0.000 7.965 8.935 8.450 0.295
## .ssasi 9.852 0.330 29.817 0.000 9.204 10.500 9.852 0.323
## .ssei 2.524 0.137 18.487 0.000 2.256 2.792 2.524 0.129
## .ssno 0.212 0.011 19.691 0.000 0.191 0.233 0.212 0.225
## .sscs 0.280 0.014 19.863 0.000 0.253 0.308 0.280 0.316
## .electronic 2.840 0.260 10.941 0.000 2.331 3.349 0.248 0.248
## g 1.204 0.035 34.641 0.000 1.136 1.272 1.000 1.000
weak<-cfa(hof.weak, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~1"))
fitMeasures(weak, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 3002.336 74.000 0.000 0.969 0.085 0.034 504556.844 504965.542
Mc(weak)
## [1] 0.8744867
summary(weak, standardized=T, ci=T) # -.214
## lavaan 0.6-18 ended normally after 135 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 78
## Number of equality constraints 22
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3002.336 1797.886
## Degrees of freedom 74 74
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.670
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1100.038 658.734
## 0 1902.299 1139.152
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.786 0.038 20.467 0.000 0.711 0.861 2.735 0.595
## sswk (.p2.) 2.020 0.098 20.508 0.000 1.827 2.213 7.029 0.928
## sspc (.p3.) 0.819 0.039 20.859 0.000 0.742 0.896 2.850 0.861
## math =~
## ssar (.p4.) 3.066 0.061 50.050 0.000 2.946 3.186 6.596 0.936
## ssmk (.p5.) 2.483 0.049 50.648 0.000 2.387 2.579 5.342 0.873
## ssmc (.p6.) 0.648 0.033 19.798 0.000 0.584 0.712 1.393 0.319
## electronic =~
## ssgs (.p7.) 0.596 0.028 21.495 0.000 0.541 0.650 1.356 0.295
## ssasi (.p8.) 1.341 0.052 25.886 0.000 1.240 1.443 3.055 0.783
## ssmc (.p9.) 0.952 0.041 23.494 0.000 0.873 1.032 2.168 0.496
## ssei (.10.) 1.221 0.047 25.840 0.000 1.128 1.313 2.780 0.803
## speed =~
## ssno (.11.) 0.492 0.008 59.038 0.000 0.476 0.509 0.803 0.868
## sscs (.12.) 0.449 0.008 56.553 0.000 0.434 0.465 0.734 0.785
## g =~
## verbal (.13.) 3.333 0.175 19.029 0.000 2.990 3.676 0.958 0.958
## math (.14.) 1.905 0.047 40.241 0.000 1.812 1.997 0.885 0.885
## elctrnc 2.046 0.087 23.443 0.000 1.875 2.217 0.898 0.898
## speed (.16.) 1.290 0.032 40.522 0.000 1.227 1.352 0.790 0.790
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.33.) 14.720 0.077 191.757 0.000 14.569 14.870 14.720 3.203
## .sswk 25.615 0.123 208.263 0.000 25.374 25.856 25.615 3.380
## .sspc (.35.) 11.113 0.053 211.231 0.000 11.009 11.216 11.113 3.357
## .ssar (.36.) 16.836 0.122 138.234 0.000 16.597 17.075 16.836 2.389
## .ssmk (.37.) 12.849 0.104 123.960 0.000 12.646 13.053 12.849 2.099
## .ssmc (.38.) 11.729 0.073 161.633 0.000 11.587 11.871 11.729 2.685
## .ssasi (.39.) 11.012 0.064 173.185 0.000 10.887 11.136 11.012 2.821
## .ssei 9.613 0.062 156.264 0.000 9.492 9.733 9.613 2.777
## .ssno (.41.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.326
## .sscs 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.407
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.083 0.083
## .math 1.000 1.000 1.000 0.216 0.216
## .speed 1.000 1.000 1.000 0.376 0.376
## .ssgs 5.418 0.162 33.443 0.000 5.101 5.736 5.418 0.257
## .sswk 8.023 0.387 20.730 0.000 7.264 8.781 8.023 0.140
## .sspc 2.837 0.094 30.024 0.000 2.652 3.022 2.837 0.259
## .ssar 6.137 0.370 16.575 0.000 5.411 6.862 6.137 0.124
## .ssmk 8.926 0.308 29.009 0.000 8.323 9.529 8.926 0.238
## .ssmc 7.634 0.220 34.741 0.000 7.203 8.065 7.634 0.400
## .ssasi 5.904 0.196 30.148 0.000 5.520 6.288 5.904 0.388
## .ssei 4.257 0.146 29.199 0.000 3.971 4.543 4.257 0.355
## .ssno 0.211 0.011 19.300 0.000 0.190 0.233 0.211 0.246
## .sscs 0.335 0.015 22.779 0.000 0.306 0.364 0.335 0.384
## .electronic 1.000 1.000 1.000 0.193 0.193
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.786 0.038 20.467 0.000 0.711 0.861 2.980 0.560
## sswk (.p2.) 2.020 0.098 20.508 0.000 1.827 2.213 7.659 0.938
## sspc (.p3.) 0.819 0.039 20.859 0.000 0.742 0.896 3.105 0.870
## math =~
## ssar (.p4.) 3.066 0.061 50.050 0.000 2.946 3.186 7.104 0.943
## ssmk (.p5.) 2.483 0.049 50.648 0.000 2.387 2.579 5.754 0.877
## ssmc (.p6.) 0.648 0.033 19.798 0.000 0.584 0.712 1.501 0.280
## electronic =~
## ssgs (.p7.) 0.596 0.028 21.495 0.000 0.541 0.650 2.016 0.379
## ssasi (.p8.) 1.341 0.052 25.886 0.000 1.240 1.443 4.540 0.823
## ssmc (.p9.) 0.952 0.041 23.494 0.000 0.873 1.032 3.222 0.602
## ssei (.10.) 1.221 0.047 25.840 0.000 1.128 1.313 4.131 0.933
## speed =~
## ssno (.11.) 0.492 0.008 59.038 0.000 0.476 0.509 0.853 0.880
## sscs (.12.) 0.449 0.008 56.553 0.000 0.434 0.465 0.779 0.827
## g =~
## verbal (.13.) 3.333 0.175 19.029 0.000 2.990 3.676 0.965 0.965
## math (.14.) 1.905 0.047 40.241 0.000 1.812 1.997 0.902 0.902
## elctrnc 2.675 0.111 24.181 0.000 2.458 2.892 0.867 0.867
## speed (.16.) 1.290 0.032 40.522 0.000 1.227 1.352 0.817 0.817
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.33.) 14.720 0.077 191.757 0.000 14.569 14.870 14.720 2.765
## .sswk 27.239 0.156 174.415 0.000 26.933 27.546 27.239 3.335
## .sspc (.35.) 11.113 0.053 211.231 0.000 11.009 11.216 11.113 3.114
## .ssar (.36.) 16.836 0.122 138.234 0.000 16.597 17.075 16.836 2.236
## .ssmk (.37.) 12.849 0.104 123.960 0.000 12.646 13.053 12.849 1.958
## .ssmc (.38.) 11.729 0.073 161.633 0.000 11.587 11.871 11.729 2.191
## .ssasi (.39.) 11.012 0.064 173.185 0.000 10.887 11.136 11.012 1.995
## .ssei 7.756 0.096 80.525 0.000 7.568 7.945 7.756 1.752
## .ssno (.41.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.312
## .sscs 0.157 0.019 8.330 0.000 0.120 0.194 0.157 0.167
## .verbal -1.662 0.110 -15.156 0.000 -1.877 -1.447 -0.438 -0.438
## .elctrnc 3.279 0.151 21.710 0.000 2.983 3.575 0.969 0.969
## .speed -0.746 0.038 -19.545 0.000 -0.820 -0.671 -0.430 -0.430
## g 0.234 0.031 7.616 0.000 0.174 0.295 0.214 0.214
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.070 0.070
## .math 1.000 1.000 1.000 0.186 0.186
## .speed 1.000 1.000 1.000 0.333 0.333
## .ssgs 5.353 0.161 33.327 0.000 5.039 5.668 5.353 0.189
## .sswk 8.050 0.426 18.917 0.000 7.216 8.884 8.050 0.121
## .sspc 3.089 0.106 29.154 0.000 2.882 3.297 3.089 0.243
## .ssar 6.233 0.371 16.811 0.000 5.506 6.960 6.233 0.110
## .ssmk 9.941 0.332 29.924 0.000 9.290 10.592 9.941 0.231
## .ssmc 8.450 0.247 34.165 0.000 7.965 8.935 8.450 0.295
## .ssasi 9.852 0.330 29.817 0.000 9.204 10.500 9.852 0.323
## .ssei 2.524 0.137 18.487 0.000 2.256 2.792 2.524 0.129
## .ssno 0.212 0.011 19.691 0.000 0.191 0.233 0.212 0.225
## .sscs 0.280 0.014 19.863 0.000 0.253 0.308 0.280 0.316
## .electronic 2.840 0.260 10.941 0.000 2.331 3.349 0.248 0.248
## g 1.204 0.035 34.641 0.000 1.136 1.272 1.000 1.000
standardizedSolution(weak) # get the correct SEs for standardized solution
## lhs op rhs group label est.std se z pvalue ci.lower ci.upper
## 1 verbal =~ ssgs 1 .p1. 0.595 0.009 64.267 0 0.577 0.613
## 2 verbal =~ sswk 1 .p2. 0.928 0.004 247.710 0 0.920 0.935
## 3 verbal =~ sspc 1 .p3. 0.861 0.005 188.570 0 0.852 0.870
## 4 math =~ ssar 1 .p4. 0.936 0.004 240.469 0 0.929 0.944
## 5 math =~ ssmk 1 .p5. 0.873 0.005 182.611 0 0.863 0.882
## 6 math =~ ssmc 1 .p6. 0.319 0.014 23.194 0 0.292 0.346
## 7 electronic =~ ssgs 1 .p7. 0.295 0.009 34.163 0 0.278 0.312
## 8 electronic =~ ssasi 1 .p8. 0.783 0.007 111.021 0 0.769 0.796
## 9 electronic =~ ssmc 1 .p9. 0.496 0.012 40.630 0 0.472 0.520
## 10 electronic =~ ssei 1 .p10. 0.803 0.008 105.901 0 0.788 0.818
## 11 speed =~ ssno 1 .p11. 0.868 0.007 125.477 0 0.855 0.882
## 12 speed =~ sscs 1 .p12. 0.785 0.009 90.581 0 0.768 0.802
## 13 g =~ verbal 1 .p13. 0.958 0.004 230.430 0 0.950 0.966
## 14 g =~ math 1 .p14. 0.885 0.005 186.234 0 0.876 0.895
## 15 g =~ electronic 1 0.898 0.007 121.559 0 0.884 0.913
## 16 g =~ speed 1 .p16. 0.790 0.007 107.913 0 0.776 0.805
## 17 verbal ~~ verbal 1 0.083 0.008 10.371 0 0.067 0.098
## 18 math ~~ math 1 0.216 0.008 25.667 0 0.200 0.233
## 19 speed ~~ speed 1 0.376 0.012 32.444 0 0.353 0.398
## 20 math ~1 1 0.000 0.000 NA NA 0.000 0.000
## 21 ssgs ~~ ssgs 1 0.257 0.008 32.938 0 0.241 0.272
## 22 sswk ~~ sswk 1 0.140 0.007 20.112 0 0.126 0.153
## 23 sspc ~~ sspc 1 0.259 0.008 32.933 0 0.243 0.274
## 24 ssar ~~ ssar 1 0.124 0.007 16.959 0 0.109 0.138
## 25 ssmk ~~ ssmk 1 0.238 0.008 28.558 0 0.222 0.255
## 26 ssmc ~~ ssmc 1 0.400 0.010 40.999 0 0.381 0.419
## 27 ssasi ~~ ssasi 1 0.388 0.011 35.126 0 0.366 0.409
## 28 ssei ~~ ssei 1 0.355 0.012 29.175 0 0.331 0.379
## 29 ssno ~~ ssno 1 0.246 0.012 20.520 0 0.223 0.270
## 30 sscs ~~ sscs 1 0.384 0.014 28.204 0 0.357 0.410
## 31 electronic ~~ electronic 1 0.193 0.013 14.522 0 0.167 0.219
## 32 g ~~ g 1 1.000 0.000 NA NA 1.000 1.000
## 33 ssgs ~1 1 .p33. 3.203 0.033 95.616 0 3.137 3.269
## 34 sswk ~1 1 3.380 0.041 82.110 0 3.299 3.461
## 35 sspc ~1 1 .p35. 3.357 0.044 76.613 0 3.271 3.443
## 36 ssar ~1 1 .p36. 2.389 0.024 99.171 0 2.342 2.437
## 37 ssmk ~1 1 .p37. 2.099 0.021 102.236 0 2.059 2.140
## 38 ssmc ~1 1 .p38. 2.685 0.027 97.955 0 2.631 2.739
## 39 ssasi ~1 1 .p39. 2.821 0.030 93.715 0 2.762 2.880
## 40 ssei ~1 1 2.777 0.029 94.588 0 2.719 2.834
## 41 ssno ~1 1 .p41. 0.326 0.018 18.546 0 0.292 0.361
## 42 sscs ~1 1 0.407 0.018 22.289 0 0.371 0.442
## 43 verbal ~1 1 0.000 0.000 NA NA 0.000 0.000
## 44 electronic ~1 1 0.000 0.000 NA NA 0.000 0.000
## 45 speed ~1 1 0.000 0.000 NA NA 0.000 0.000
## 46 g ~1 1 0.000 0.000 NA NA 0.000 0.000
## 47 verbal =~ ssgs 2 .p1. 0.560 0.009 61.659 0 0.542 0.577
## 48 verbal =~ sswk 2 .p2. 0.938 0.003 276.228 0 0.931 0.944
## 49 verbal =~ sspc 2 .p3. 0.870 0.005 190.620 0 0.861 0.879
## 50 math =~ ssar 2 .p4. 0.943 0.004 268.943 0 0.937 0.950
## 51 math =~ ssmk 2 .p5. 0.877 0.005 194.537 0 0.868 0.886
## 52 math =~ ssmc 2 .p6. 0.280 0.013 22.147 0 0.256 0.305
## 53 electronic =~ ssgs 2 .p7. 0.379 0.010 39.354 0 0.360 0.397
## 54 electronic =~ ssasi 2 .p8. 0.823 0.007 119.802 0 0.809 0.836
## 55 electronic =~ ssmc 2 .p9. 0.602 0.013 44.988 0 0.576 0.628
## 56 electronic =~ ssei 2 .p10. 0.933 0.004 257.307 0 0.926 0.940
## 57 speed =~ ssno 2 .p11. 0.880 0.006 140.056 0 0.868 0.892
## 58 speed =~ sscs 2 .p12. 0.827 0.008 98.575 0 0.811 0.843
## 59 g =~ verbal 2 .p13. 0.965 0.004 274.807 0 0.958 0.971
## 60 g =~ math 2 .p14. 0.902 0.004 215.755 0 0.894 0.910
## 61 g =~ electronic 2 0.867 0.007 120.881 0 0.853 0.881
## 62 g =~ speed 2 .p16. 0.817 0.007 123.341 0 0.804 0.830
## 63 verbal ~~ verbal 2 0.070 0.007 10.271 0 0.056 0.083
## 64 math ~~ math 2 0.186 0.008 24.694 0 0.171 0.201
## 65 speed ~~ speed 2 0.333 0.011 30.795 0 0.312 0.354
## 66 math ~1 2 0.000 0.000 NA NA 0.000 0.000
## 67 ssgs ~~ ssgs 2 0.189 0.006 31.463 0 0.177 0.201
## 68 sswk ~~ sswk 2 0.121 0.006 18.954 0 0.108 0.133
## 69 sspc ~~ sspc 2 0.243 0.008 30.532 0 0.227 0.258
## 70 ssar ~~ ssar 2 0.110 0.007 16.606 0 0.097 0.123
## 71 ssmk ~~ ssmk 2 0.231 0.008 29.208 0 0.215 0.246
## 72 ssmc ~~ ssmc 2 0.295 0.009 31.837 0 0.277 0.313
## 73 ssasi ~~ ssasi 2 0.323 0.011 28.631 0 0.301 0.346
## 74 ssei ~~ ssei 2 0.129 0.007 19.026 0 0.116 0.142
## 75 ssno ~~ ssno 2 0.225 0.011 20.365 0 0.204 0.247
## 76 sscs ~~ sscs 2 0.316 0.014 22.786 0 0.289 0.343
## 77 electronic ~~ electronic 2 0.248 0.012 19.925 0 0.224 0.272
## 78 g ~~ g 2 1.000 0.000 NA NA 1.000 1.000
## 79 ssgs ~1 2 .p33. 2.765 0.028 97.995 0 2.709 2.820
## 80 sswk ~1 2 3.335 0.037 90.877 0 3.263 3.407
## 81 sspc ~1 2 .p35. 3.114 0.034 92.713 0 3.048 3.180
## 82 ssar ~1 2 .p36. 2.236 0.022 103.875 0 2.194 2.278
## 83 ssmk ~1 2 .p37. 1.958 0.018 107.292 0 1.923 1.994
## 84 ssmc ~1 2 .p38. 2.191 0.022 100.720 0 2.149 2.234
## 85 ssasi ~1 2 .p39. 1.995 0.020 97.874 0 1.955 2.035
## 86 ssei ~1 2 1.752 0.027 63.964 0 1.699 1.806
## 87 ssno ~1 2 .p41. 0.312 0.016 19.244 0 0.280 0.343
## 88 sscs ~1 2 0.167 0.020 8.261 0 0.127 0.207
## 89 verbal ~1 2 -0.438 0.019 -22.803 0 -0.476 -0.401
## 90 electronic ~1 2 0.969 0.029 33.484 0 0.912 1.026
## [ reached 'max' / getOption("max.print") -- omitted 2 rows ]
tests<-lavTestLRT(configural, metric2, scalar2, latent2, weak)
## Warning: lavaan->lav_test_diff_SatorraBentler2001():
## scaling factor is negative
Td=tests[2:5,"Chisq diff"]
Td
## [1] 136.004741 103.785824 6.641612 NA
dfd=tests[2:5,"Df diff"]
dfd
## [1] 10 2 3 1
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-5449+ 5469 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04804815 0.09656325 0.01491315 NA
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04105558 0.05538730
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.08124546 0.11280849
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] NA 0.03050019
RMSEA.CI(T=Td[4],df=dfd[4],N=N,G=2)
## [1] NA NA
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 0.343 0.003 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 0.962 0.379
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
## 0.916 0.769 0.000 0.000 0.000 0.000
round(pvals(T=Td[4],df=dfd[4],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## NA NA NA NA NA NA
tests<-lavTestLRT(configural, metric2, scalar2, latent)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 136.0047 103.7858 229.3231
dfd=tests[2:4,"Df diff"]
dfd
## [1] 10 2 5
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-5449+ 5469 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04804815 0.09656325 0.09066407
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.08124546 0.11280849
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.08085696 0.10085883
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 0.962 0.379
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 1.000 0.963 0.066
tests<-lavTestLRT(configural, metric2, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 136.0047 103.7858 187.5479
dfd=tests[2:4,"Df diff"]
dfd
## [1] 10 2 10
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-5449+ 5469 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04804815 0.09656325 0.05703494
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04105558 0.05538730
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.08124546 0.11280849
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.05005450 0.06431334
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 0.343 0.003 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 0.962 0.379
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 0.951 0.259 0.000 0.000
tests<-lavTestLRT(configural, metric2, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 136.0047 820.9512
dfd=tests[2:3,"Df diff"]
dfd
## [1] 10 5
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-5449+ 5469 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.04804815 0.17291407
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04105558 0.05538730
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.1630428 0.1829802
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 0.343 0.003 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)
Td=tests[2,"Chisq diff"]
Td
## [1] 307.5256
dfd=tests[2,"Df diff"]
dfd
## [1] 11
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-5449+ 5469 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.07027778
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.06361947 0.07715784
round(pvals(T=Td[1],df=dfd[1],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 0.994 0.010 0.000
hof.age<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
math~0*1
g ~ age
'
hof.ageq<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
math~0*1
g ~ c(a,a)*age
'
hof.age2<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
math~0*1
g ~ age + age2
'
hof.age2q<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
math~0*1
g ~c(a,a)*age + c(b,b)*age2
'
sem.age<-cfa(hof.age, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~1"))
fitMeasures(sem.age, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 3867.542 92.000 0.000 0.961 0.087 0.039 0.365 504184.603 504607.897
Mc(sem.age)
## [1] 0.8412046
summary(sem.age, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 120 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 80
## Number of equality constraints 22
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3867.542 2306.132
## Degrees of freedom 92 92
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.677
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1595.950 951.630
## 0 2271.593 1354.501
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.783 0.038 20.612 0.000 0.708 0.857 2.734 0.595
## sswk (.p2.) 2.014 0.098 20.653 0.000 1.823 2.205 7.036 0.928
## sspc (.p3.) 0.815 0.039 21.014 0.000 0.739 0.891 2.849 0.860
## math =~
## ssar (.p4.) 3.106 0.061 51.221 0.000 2.987 3.225 6.606 0.937
## ssmk (.p5.) 2.510 0.048 51.811 0.000 2.415 2.604 5.338 0.872
## ssmc (.p6.) 0.656 0.033 19.927 0.000 0.591 0.720 1.394 0.319
## electronic =~
## ssgs (.p7.) 0.588 0.028 21.275 0.000 0.534 0.643 1.355 0.295
## ssasi (.p8.) 1.327 0.052 25.504 0.000 1.225 1.429 3.055 0.783
## ssmc (.p9.) 0.941 0.041 23.196 0.000 0.862 1.021 2.167 0.496
## ssei (.10.) 1.208 0.047 25.474 0.000 1.115 1.301 2.780 0.803
## speed =~
## ssno (.11.) 0.493 0.008 59.192 0.000 0.476 0.509 0.803 0.867
## sscs (.12.) 0.451 0.008 56.709 0.000 0.435 0.466 0.734 0.786
## g =~
## verbal (.13.) 3.307 0.172 19.238 0.000 2.970 3.644 0.958 0.958
## math (.14.) 1.854 0.046 40.081 0.000 1.764 1.945 0.883 0.883
## elctrnc 2.049 0.088 23.209 0.000 1.876 2.222 0.901 0.901
## speed (.16.) 1.270 0.032 39.998 0.000 1.208 1.333 0.789 0.789
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.068 0.008 8.783 0.000 0.053 0.083 0.067 0.155
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.35.) 14.780 0.077 192.916 0.000 14.630 14.930 14.780 3.216
## .sswk 25.720 0.122 211.528 0.000 25.481 25.958 25.720 3.394
## .sspc (.37.) 11.154 0.052 212.641 0.000 11.052 11.257 11.154 3.369
## .ssar (.38.) 16.923 0.123 137.830 0.000 16.682 17.163 16.923 2.401
## .ssmk (.39.) 12.921 0.105 123.266 0.000 12.715 13.126 12.921 2.110
## .ssmc (.40.) 11.778 0.073 161.883 0.000 11.636 11.921 11.778 2.696
## .ssasi (.41.) 11.054 0.063 174.645 0.000 10.930 11.178 11.054 2.832
## .ssei 9.651 0.061 158.423 0.000 9.532 9.771 9.651 2.789
## .ssno (.43.) 0.312 0.015 20.138 0.000 0.282 0.342 0.312 0.337
## .sscs 0.389 0.016 24.814 0.000 0.358 0.420 0.389 0.416
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.082 0.082
## .math 1.000 1.000 1.000 0.221 0.221
## .speed 1.000 1.000 1.000 0.377 0.377
## .ssgs 5.424 0.162 33.484 0.000 5.106 5.741 5.424 0.257
## .sswk 7.926 0.386 20.560 0.000 7.170 8.682 7.926 0.138
## .sspc 2.848 0.095 30.045 0.000 2.662 3.033 2.848 0.260
## .ssar 6.037 0.371 16.292 0.000 5.311 6.764 6.037 0.122
## .ssmk 8.994 0.310 29.028 0.000 8.387 9.601 8.994 0.240
## .ssmc 7.646 0.220 34.777 0.000 7.215 8.077 7.646 0.401
## .ssasi 5.907 0.196 30.210 0.000 5.524 6.291 5.907 0.388
## .ssei 4.247 0.145 29.249 0.000 3.963 4.532 4.247 0.355
## .ssno 0.213 0.011 19.380 0.000 0.191 0.234 0.213 0.248
## .sscs 0.334 0.015 22.666 0.000 0.305 0.363 0.334 0.382
## .electronic 1.000 1.000 1.000 0.189 0.189
## .g 1.000 1.000 1.000 0.976 0.976
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.783 0.038 20.612 0.000 0.708 0.857 2.978 0.559
## sswk (.p2.) 2.014 0.098 20.653 0.000 1.823 2.205 7.664 0.938
## sspc (.p3.) 0.815 0.039 21.014 0.000 0.739 0.891 3.103 0.870
## math =~
## ssar (.p4.) 3.106 0.061 51.221 0.000 2.987 3.225 7.110 0.944
## ssmk (.p5.) 2.510 0.048 51.811 0.000 2.415 2.604 5.745 0.876
## ssmc (.p6.) 0.656 0.033 19.927 0.000 0.591 0.720 1.501 0.280
## electronic =~
## ssgs (.p7.) 0.588 0.028 21.275 0.000 0.534 0.643 2.013 0.378
## ssasi (.p8.) 1.327 0.052 25.504 0.000 1.225 1.429 4.539 0.823
## ssmc (.p9.) 0.941 0.041 23.196 0.000 0.862 1.021 3.220 0.602
## ssei (.10.) 1.208 0.047 25.474 0.000 1.115 1.301 4.132 0.933
## speed =~
## ssno (.11.) 0.493 0.008 59.192 0.000 0.476 0.509 0.852 0.879
## sscs (.12.) 0.451 0.008 56.709 0.000 0.435 0.466 0.780 0.828
## g =~
## verbal (.13.) 3.307 0.172 19.238 0.000 2.970 3.644 0.965 0.965
## math (.14.) 1.854 0.046 40.081 0.000 1.764 1.945 0.900 0.900
## elctrnc 2.681 0.112 23.891 0.000 2.461 2.901 0.870 0.870
## speed (.16.) 1.270 0.032 39.998 0.000 1.208 1.333 0.816 0.816
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.104 0.008 12.967 0.000 0.088 0.120 0.094 0.221
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.35.) 14.780 0.077 192.916 0.000 14.630 14.930 14.780 2.775
## .sswk 27.344 0.156 175.081 0.000 27.038 27.651 27.344 3.348
## .sspc (.37.) 11.154 0.052 212.641 0.000 11.052 11.257 11.154 3.126
## .ssar (.38.) 16.923 0.123 137.830 0.000 16.682 17.163 16.923 2.248
## .ssmk (.39.) 12.921 0.105 123.266 0.000 12.715 13.126 12.921 1.970
## .ssmc (.40.) 11.778 0.073 161.883 0.000 11.636 11.921 11.778 2.201
## .ssasi (.41.) 11.054 0.063 174.645 0.000 10.930 11.178 11.054 2.003
## .ssei 7.793 0.096 81.239 0.000 7.605 7.981 7.793 1.760
## .ssno (.43.) 0.312 0.015 20.138 0.000 0.282 0.342 0.312 0.322
## .sscs 0.167 0.019 8.776 0.000 0.130 0.204 0.167 0.177
## .verbal -1.675 0.110 -15.257 0.000 -1.890 -1.459 -0.440 -0.440
## .elctrnc 3.319 0.155 21.479 0.000 3.016 3.622 0.970 0.970
## .speed -0.747 0.038 -19.587 0.000 -0.821 -0.672 -0.432 -0.432
## .g 0.250 0.031 8.001 0.000 0.189 0.311 0.225 0.225
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.069 0.069
## .math 1.000 1.000 1.000 0.191 0.191
## .speed 1.000 1.000 1.000 0.334 0.334
## .ssgs 5.372 0.161 33.327 0.000 5.056 5.688 5.372 0.189
## .sswk 7.973 0.424 18.810 0.000 7.142 8.804 7.973 0.120
## .sspc 3.102 0.106 29.167 0.000 2.893 3.310 3.102 0.244
## .ssar 6.117 0.371 16.475 0.000 5.389 6.844 6.117 0.108
## .ssmk 10.017 0.334 29.988 0.000 9.362 10.671 10.017 0.233
## .ssmc 8.460 0.247 34.240 0.000 7.976 8.945 8.460 0.295
## .ssasi 9.846 0.330 29.843 0.000 9.199 10.493 9.846 0.323
## .ssei 2.523 0.136 18.600 0.000 2.257 2.789 2.523 0.129
## .ssno 0.213 0.011 19.795 0.000 0.192 0.234 0.213 0.227
## .sscs 0.279 0.014 19.768 0.000 0.252 0.307 0.279 0.315
## .electronic 2.840 0.263 10.793 0.000 2.324 3.355 0.243 0.243
## .g 1.173 0.036 32.600 0.000 1.102 1.243 0.951 0.951
sem.ageq<-cfa(hof.ageq, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~1"))
fitMeasures(sem.ageq, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 3884.270 93.000 0.000 0.960 0.086 0.042 0.366 504199.331 504615.326
Mc(sem.ageq)
## [1] 0.8405989
summary(sem.ageq, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 139 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 80
## Number of equality constraints 23
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3884.270 2318.661
## Degrees of freedom 93 93
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.675
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1603.862 957.403
## 0 2280.408 1361.258
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.779 0.038 20.456 0.000 0.704 0.854 2.754 0.596
## sswk (.p2.) 2.005 0.098 20.485 0.000 1.813 2.197 7.086 0.929
## sspc (.p3.) 0.812 0.039 20.842 0.000 0.735 0.888 2.869 0.862
## math =~
## ssar (.p4.) 3.110 0.061 51.380 0.000 2.991 3.229 6.647 0.938
## ssmk (.p5.) 2.513 0.048 51.954 0.000 2.418 2.608 5.370 0.873
## ssmc (.p6.) 0.657 0.033 19.947 0.000 0.592 0.721 1.403 0.320
## electronic =~
## ssgs (.p7.) 0.587 0.028 21.258 0.000 0.533 0.641 1.362 0.295
## ssasi (.p8.) 1.324 0.052 25.468 0.000 1.222 1.426 3.072 0.784
## ssmc (.p9.) 0.939 0.041 23.165 0.000 0.860 1.019 2.179 0.497
## ssei (.10.) 1.205 0.047 25.431 0.000 1.113 1.298 2.796 0.805
## speed =~
## ssno (.11.) 0.493 0.008 59.219 0.000 0.477 0.509 0.807 0.868
## sscs (.12.) 0.451 0.008 56.734 0.000 0.435 0.467 0.738 0.788
## g =~
## verbal (.13.) 3.326 0.174 19.086 0.000 2.985 3.668 0.959 0.959
## math (.14.) 1.853 0.046 40.131 0.000 1.762 1.943 0.884 0.884
## elctrnc 2.053 0.089 23.181 0.000 1.880 2.227 0.902 0.902
## speed (.16.) 1.271 0.032 39.944 0.000 1.209 1.333 0.792 0.792
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.085 0.006 15.013 0.000 0.074 0.096 0.084 0.194
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.35.) 14.796 0.076 193.549 0.000 14.646 14.945 14.796 3.202
## .sswk 25.747 0.121 213.244 0.000 25.510 25.983 25.747 3.377
## .sspc (.37.) 11.165 0.052 213.351 0.000 11.063 11.268 11.165 3.354
## .ssar (.38.) 16.946 0.123 138.005 0.000 16.705 17.186 16.946 2.392
## .ssmk (.39.) 12.939 0.105 123.054 0.000 12.733 13.145 12.939 2.103
## .ssmc (.40.) 11.791 0.073 162.270 0.000 11.649 11.934 11.791 2.688
## .ssasi (.41.) 11.065 0.063 175.700 0.000 10.941 11.188 11.065 2.825
## .ssei 9.661 0.061 159.634 0.000 9.543 9.780 9.661 2.782
## .ssno (.43.) 0.314 0.015 20.332 0.000 0.284 0.345 0.314 0.338
## .sscs 0.391 0.016 25.079 0.000 0.361 0.422 0.391 0.418
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.080 0.080
## .math 1.000 1.000 1.000 0.219 0.219
## .speed 1.000 1.000 1.000 0.373 0.373
## .ssgs 5.424 0.162 33.482 0.000 5.107 5.742 5.424 0.254
## .sswk 7.914 0.385 20.562 0.000 7.160 8.669 7.914 0.136
## .sspc 2.850 0.095 30.059 0.000 2.664 3.036 2.850 0.257
## .ssar 6.028 0.371 16.268 0.000 5.302 6.754 6.028 0.120
## .ssmk 9.005 0.310 29.028 0.000 8.397 9.613 9.005 0.238
## .ssmc 7.649 0.220 34.783 0.000 7.218 8.080 7.649 0.398
## .ssasi 5.908 0.195 30.227 0.000 5.525 6.291 5.908 0.385
## .ssei 4.245 0.145 29.267 0.000 3.961 4.529 4.245 0.352
## .ssno 0.213 0.011 19.397 0.000 0.191 0.235 0.213 0.247
## .sscs 0.333 0.015 22.649 0.000 0.305 0.362 0.333 0.380
## .electronic 1.000 1.000 1.000 0.186 0.186
## .g 1.000 1.000 1.000 0.962 0.962
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.779 0.038 20.456 0.000 0.704 0.854 2.958 0.558
## sswk (.p2.) 2.005 0.098 20.485 0.000 1.813 2.197 7.612 0.937
## sspc (.p3.) 0.812 0.039 20.842 0.000 0.735 0.888 3.082 0.868
## math =~
## ssar (.p4.) 3.110 0.061 51.380 0.000 2.991 3.229 7.067 0.944
## ssmk (.p5.) 2.513 0.048 51.954 0.000 2.418 2.608 5.710 0.875
## ssmc (.p6.) 0.657 0.033 19.947 0.000 0.592 0.721 1.492 0.280
## electronic =~
## ssgs (.p7.) 0.587 0.028 21.258 0.000 0.533 0.641 2.003 0.378
## ssasi (.p8.) 1.324 0.052 25.468 0.000 1.222 1.426 4.516 0.821
## ssmc (.p9.) 0.939 0.041 23.165 0.000 0.860 1.019 3.203 0.601
## ssei (.10.) 1.205 0.047 25.431 0.000 1.113 1.298 4.111 0.933
## speed =~
## ssno (.11.) 0.493 0.008 59.219 0.000 0.477 0.509 0.848 0.878
## sscs (.12.) 0.451 0.008 56.734 0.000 0.435 0.467 0.776 0.826
## g =~
## verbal (.13.) 3.326 0.174 19.086 0.000 2.985 3.668 0.965 0.965
## math (.14.) 1.853 0.046 40.131 0.000 1.762 1.943 0.898 0.898
## elctrnc 2.689 0.113 23.815 0.000 2.468 2.911 0.868 0.868
## speed (.16.) 1.271 0.032 39.944 0.000 1.209 1.333 0.814 0.814
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.085 0.006 15.013 0.000 0.074 0.096 0.077 0.182
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.35.) 14.796 0.076 193.549 0.000 14.646 14.945 14.796 2.793
## .sswk 27.371 0.156 175.362 0.000 27.066 27.677 27.371 3.371
## .sspc (.37.) 11.165 0.052 213.351 0.000 11.063 11.268 11.165 3.146
## .ssar (.38.) 16.946 0.123 138.005 0.000 16.705 17.186 16.946 2.263
## .ssmk (.39.) 12.939 0.105 123.054 0.000 12.733 13.145 12.939 1.982
## .ssmc (.40.) 11.791 0.073 162.270 0.000 11.649 11.934 11.791 2.212
## .ssasi (.41.) 11.065 0.063 175.700 0.000 10.941 11.188 11.065 2.012
## .ssei 7.802 0.096 81.426 0.000 7.614 7.990 7.802 1.770
## .ssno (.43.) 0.314 0.015 20.332 0.000 0.284 0.345 0.314 0.326
## .sscs 0.169 0.019 8.899 0.000 0.132 0.206 0.169 0.180
## .verbal -1.683 0.111 -15.169 0.000 -1.900 -1.465 -0.443 -0.443
## .elctrnc 3.327 0.155 21.454 0.000 3.023 3.631 0.976 0.976
## .speed -0.746 0.038 -19.587 0.000 -0.821 -0.672 -0.434 -0.434
## .g 0.241 0.031 7.749 0.000 0.180 0.302 0.219 0.219
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.069 0.069
## .math 1.000 1.000 1.000 0.194 0.194
## .speed 1.000 1.000 1.000 0.338 0.338
## .ssgs 5.369 0.161 33.330 0.000 5.053 5.685 5.369 0.191
## .sswk 7.984 0.424 18.840 0.000 7.153 8.814 7.984 0.121
## .sspc 3.101 0.106 29.165 0.000 2.892 3.309 3.101 0.246
## .ssar 6.120 0.372 16.469 0.000 5.392 6.848 6.120 0.109
## .ssmk 10.008 0.334 29.959 0.000 9.353 10.663 10.008 0.235
## .ssmc 8.460 0.247 34.239 0.000 7.976 8.945 8.460 0.298
## .ssasi 9.848 0.330 29.845 0.000 9.201 10.495 9.848 0.326
## .ssei 2.522 0.136 18.582 0.000 2.256 2.788 2.522 0.130
## .ssno 0.213 0.011 19.787 0.000 0.192 0.234 0.213 0.229
## .sscs 0.279 0.014 19.771 0.000 0.252 0.307 0.279 0.317
## .electronic 2.858 0.265 10.791 0.000 2.339 3.377 0.246 0.246
## .g 1.172 0.036 32.528 0.000 1.102 1.243 0.967 0.967
sem.age2<-cfa(hof.age2, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~1"))
fitMeasures(sem.age2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 3926.960 110.000 0.000 0.960 0.080 0.037 0.371 504177.090 504614.981
Mc(sem.age2)
## [1] 0.8396104
summary(sem.age2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 125 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 22
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3926.960 2333.884
## Degrees of freedom 110 110
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.683
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1620.669 963.202
## 0 2306.291 1370.683
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.783 0.038 20.621 0.000 0.708 0.857 2.734 0.595
## sswk (.p2.) 2.014 0.097 20.666 0.000 1.823 2.205 7.036 0.928
## sspc (.p3.) 0.815 0.039 21.028 0.000 0.739 0.892 2.849 0.860
## math =~
## ssar (.p4.) 3.106 0.061 51.224 0.000 2.987 3.225 6.606 0.937
## ssmk (.p5.) 2.510 0.048 51.819 0.000 2.415 2.605 5.338 0.872
## ssmc (.p6.) 0.656 0.033 19.922 0.000 0.591 0.720 1.394 0.319
## electronic =~
## ssgs (.p7.) 0.588 0.028 21.275 0.000 0.534 0.643 1.355 0.295
## ssasi (.p8.) 1.327 0.052 25.504 0.000 1.225 1.429 3.055 0.783
## ssmc (.p9.) 0.941 0.041 23.197 0.000 0.862 1.021 2.167 0.496
## ssei (.10.) 1.208 0.047 25.475 0.000 1.115 1.301 2.780 0.803
## speed =~
## ssno (.11.) 0.493 0.008 59.196 0.000 0.476 0.509 0.803 0.867
## sscs (.12.) 0.451 0.008 56.716 0.000 0.435 0.466 0.734 0.786
## g =~
## verbal (.13.) 3.306 0.172 19.249 0.000 2.970 3.643 0.958 0.958
## math (.14.) 1.854 0.046 40.083 0.000 1.763 1.945 0.883 0.883
## elctrnc 2.049 0.088 23.210 0.000 1.876 2.222 0.901 0.901
## speed (.16.) 1.270 0.032 40.003 0.000 1.208 1.333 0.789 0.789
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.068 0.008 8.597 0.000 0.052 0.083 0.067 0.155
## age2 -0.000 0.003 -0.142 0.887 -0.007 0.006 -0.000 -0.002
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.38.) 14.790 0.102 145.601 0.000 14.591 14.989 14.790 3.218
## .sswk 25.737 0.171 150.536 0.000 25.402 26.072 25.737 3.396
## .sspc (.40.) 11.162 0.071 156.920 0.000 11.022 11.301 11.162 3.371
## .ssar (.41.) 16.938 0.161 105.480 0.000 16.623 17.252 16.938 2.403
## .ssmk (.42.) 12.933 0.134 96.578 0.000 12.670 13.195 12.933 2.112
## .ssmc (.43.) 11.787 0.093 126.690 0.000 11.604 11.969 11.787 2.698
## .ssasi (.44.) 11.061 0.081 136.744 0.000 10.902 11.219 11.061 2.833
## .ssei 9.658 0.076 127.164 0.000 9.509 9.807 9.658 2.791
## .ssno (.46.) 0.314 0.019 16.436 0.000 0.276 0.351 0.314 0.339
## .sscs 0.391 0.019 20.655 0.000 0.353 0.428 0.391 0.418
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.082 0.082
## .math 1.000 1.000 1.000 0.221 0.221
## .speed 1.000 1.000 1.000 0.377 0.377
## .ssgs 5.424 0.162 33.486 0.000 5.106 5.741 5.424 0.257
## .sswk 7.925 0.386 20.558 0.000 7.170 8.681 7.925 0.138
## .sspc 2.848 0.095 30.045 0.000 2.662 3.033 2.848 0.260
## .ssar 6.037 0.371 16.291 0.000 5.311 6.763 6.037 0.122
## .ssmk 8.994 0.310 29.028 0.000 8.387 9.601 8.994 0.240
## .ssmc 7.646 0.220 34.778 0.000 7.215 8.077 7.646 0.401
## .ssasi 5.907 0.196 30.207 0.000 5.524 6.291 5.907 0.388
## .ssei 4.247 0.145 29.249 0.000 3.963 4.532 4.247 0.355
## .ssno 0.213 0.011 19.379 0.000 0.191 0.234 0.213 0.248
## .sscs 0.334 0.015 22.664 0.000 0.305 0.363 0.334 0.382
## .electronic 1.000 1.000 1.000 0.189 0.189
## .g 1.000 1.000 1.000 0.976 0.976
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.783 0.038 20.621 0.000 0.708 0.857 2.978 0.559
## sswk (.p2.) 2.014 0.097 20.666 0.000 1.823 2.205 7.664 0.938
## sspc (.p3.) 0.815 0.039 21.028 0.000 0.739 0.892 3.103 0.870
## math =~
## ssar (.p4.) 3.106 0.061 51.224 0.000 2.987 3.225 7.110 0.944
## ssmk (.p5.) 2.510 0.048 51.819 0.000 2.415 2.605 5.745 0.876
## ssmc (.p6.) 0.656 0.033 19.922 0.000 0.591 0.720 1.501 0.280
## electronic =~
## ssgs (.p7.) 0.588 0.028 21.275 0.000 0.534 0.643 2.013 0.378
## ssasi (.p8.) 1.327 0.052 25.504 0.000 1.225 1.429 4.539 0.823
## ssmc (.p9.) 0.941 0.041 23.197 0.000 0.862 1.021 3.220 0.602
## ssei (.10.) 1.208 0.047 25.475 0.000 1.115 1.301 4.132 0.933
## speed =~
## ssno (.11.) 0.493 0.008 59.196 0.000 0.476 0.509 0.852 0.879
## sscs (.12.) 0.451 0.008 56.716 0.000 0.435 0.466 0.780 0.828
## g =~
## verbal (.13.) 3.306 0.172 19.249 0.000 2.970 3.643 0.965 0.965
## math (.14.) 1.854 0.046 40.083 0.000 1.763 1.945 0.900 0.900
## elctrnc 2.682 0.112 23.890 0.000 2.462 2.902 0.870 0.870
## speed (.16.) 1.270 0.032 40.003 0.000 1.208 1.333 0.816 0.816
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.099 0.008 11.947 0.000 0.083 0.116 0.090 0.211
## age2 -0.010 0.004 -2.736 0.006 -0.017 -0.003 -0.009 -0.047
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.38.) 14.790 0.102 145.601 0.000 14.591 14.989 14.790 2.777
## .sswk 27.362 0.196 139.607 0.000 26.978 27.746 27.362 3.350
## .sspc (.40.) 11.162 0.071 156.920 0.000 11.022 11.301 11.162 3.128
## .ssar (.41.) 16.938 0.161 105.480 0.000 16.623 17.252 16.938 2.250
## .ssmk (.42.) 12.933 0.134 96.578 0.000 12.670 13.195 12.933 1.972
## .ssmc (.43.) 11.787 0.093 126.690 0.000 11.604 11.969 11.787 2.202
## .ssasi (.44.) 11.061 0.081 136.744 0.000 10.902 11.219 11.061 2.004
## .ssei 7.799 0.106 73.475 0.000 7.591 8.007 7.799 1.762
## .ssno (.46.) 0.314 0.019 16.436 0.000 0.276 0.351 0.314 0.324
## .sscs 0.168 0.022 7.779 0.000 0.126 0.211 0.168 0.179
## .verbal -1.674 0.110 -15.262 0.000 -1.889 -1.459 -0.440 -0.440
## .elctrnc 3.321 0.155 21.455 0.000 3.017 3.624 0.971 0.971
## .speed -0.747 0.038 -19.587 0.000 -0.821 -0.672 -0.432 -0.432
## .g 0.303 0.041 7.373 0.000 0.222 0.383 0.273 0.273
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.069 0.069
## .math 1.000 1.000 1.000 0.191 0.191
## .speed 1.000 1.000 1.000 0.334 0.334
## .ssgs 5.372 0.161 33.321 0.000 5.056 5.688 5.372 0.189
## .sswk 7.973 0.423 18.836 0.000 7.143 8.802 7.973 0.120
## .sspc 3.101 0.106 29.160 0.000 2.893 3.310 3.101 0.244
## .ssar 6.120 0.371 16.479 0.000 5.392 6.847 6.120 0.108
## .ssmk 10.015 0.334 29.987 0.000 9.360 10.669 10.015 0.233
## .ssmc 8.461 0.247 34.241 0.000 7.976 8.945 8.461 0.295
## .ssasi 9.845 0.330 29.843 0.000 9.198 10.491 9.845 0.323
## .ssei 2.523 0.136 18.604 0.000 2.257 2.789 2.523 0.129
## .ssno 0.213 0.011 19.797 0.000 0.192 0.234 0.213 0.227
## .sscs 0.279 0.014 19.769 0.000 0.252 0.307 0.279 0.315
## .electronic 2.838 0.263 10.791 0.000 2.322 3.353 0.242 0.242
## .g 1.170 0.036 32.649 0.000 1.100 1.240 0.949 0.949
sem.age2q<-cfa(hof.age2q, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~1"))
fitMeasures(sem.age2q, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 3949.147 112.000 0.000 0.960 0.079 0.041 0.372 504195.277 504618.571
Mc(sem.age2q)
## [1] 0.8388345
summary(sem.age2q, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 137 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 24
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3949.147 2351.922
## Degrees of freedom 112 112
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.679
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1631.230 971.482
## 0 2317.916 1380.440
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.779 0.038 20.462 0.000 0.704 0.854 2.755 0.596
## sswk (.p2.) 2.005 0.098 20.494 0.000 1.813 2.197 7.090 0.930
## sspc (.p3.) 0.812 0.039 20.851 0.000 0.735 0.888 2.871 0.862
## math =~
## ssar (.p4.) 3.111 0.061 51.394 0.000 2.992 3.229 6.650 0.938
## ssmk (.p5.) 2.513 0.048 51.972 0.000 2.419 2.608 5.373 0.873
## ssmc (.p6.) 0.657 0.033 19.947 0.000 0.592 0.721 1.404 0.320
## electronic =~
## ssgs (.p7.) 0.587 0.028 21.254 0.000 0.533 0.641 1.363 0.295
## ssasi (.p8.) 1.324 0.052 25.464 0.000 1.222 1.426 3.073 0.784
## ssmc (.p9.) 0.939 0.041 23.164 0.000 0.860 1.019 2.180 0.497
## ssei (.10.) 1.205 0.047 25.427 0.000 1.112 1.298 2.797 0.805
## speed =~
## ssno (.11.) 0.493 0.008 59.215 0.000 0.477 0.509 0.807 0.868
## sscs (.12.) 0.451 0.008 56.733 0.000 0.435 0.467 0.738 0.788
## g =~
## verbal (.13.) 3.327 0.174 19.094 0.000 2.985 3.668 0.959 0.959
## math (.14.) 1.853 0.046 40.137 0.000 1.763 1.943 0.884 0.884
## elctrnc 2.054 0.089 23.176 0.000 1.880 2.228 0.902 0.902
## speed (.16.) 1.271 0.032 39.946 0.000 1.209 1.334 0.792 0.792
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.083 0.006 14.213 0.000 0.071 0.094 0.081 0.188
## age2 (b) -0.005 0.003 -2.017 0.044 -0.010 -0.000 -0.005 -0.025
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.38.) 14.899 0.090 164.637 0.000 14.722 15.077 14.899 3.223
## .sswk 25.929 0.148 174.865 0.000 25.638 26.219 25.929 3.399
## .sspc (.40.) 11.239 0.062 179.923 0.000 11.117 11.361 11.239 3.375
## .ssar (.41.) 17.103 0.144 118.831 0.000 16.821 17.385 17.103 2.413
## .ssmk (.42.) 13.066 0.121 107.655 0.000 12.828 13.304 13.066 2.123
## .ssmc (.43.) 11.877 0.084 141.316 0.000 11.712 12.042 11.877 2.707
## .ssasi (.44.) 11.139 0.073 152.549 0.000 10.996 11.282 11.139 2.843
## .ssei 9.729 0.069 140.727 0.000 9.593 9.864 9.729 2.800
## .ssno (.46.) 0.332 0.017 19.075 0.000 0.297 0.366 0.332 0.357
## .sscs 0.407 0.017 23.446 0.000 0.373 0.441 0.407 0.434
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.080 0.080
## .math 1.000 1.000 1.000 0.219 0.219
## .speed 1.000 1.000 1.000 0.373 0.373
## .ssgs 5.425 0.162 33.480 0.000 5.107 5.742 5.425 0.254
## .sswk 7.913 0.385 20.554 0.000 7.158 8.667 7.913 0.136
## .sspc 2.850 0.095 30.064 0.000 2.664 3.036 2.850 0.257
## .ssar 6.027 0.370 16.270 0.000 5.301 6.753 6.027 0.120
## .ssmk 9.006 0.310 29.025 0.000 8.397 9.614 9.006 0.238
## .ssmc 7.649 0.220 34.784 0.000 7.218 8.080 7.649 0.397
## .ssasi 5.907 0.195 30.228 0.000 5.524 6.291 5.907 0.385
## .ssei 4.246 0.145 29.272 0.000 3.962 4.530 4.246 0.352
## .ssno 0.213 0.011 19.402 0.000 0.192 0.235 0.213 0.247
## .sscs 0.333 0.015 22.646 0.000 0.305 0.362 0.333 0.379
## .electronic 1.000 1.000 1.000 0.186 0.186
## .g 1.000 1.000 1.000 0.962 0.962
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs (.p1.) 0.779 0.038 20.462 0.000 0.704 0.854 2.956 0.558
## sswk (.p2.) 2.005 0.098 20.494 0.000 1.813 2.197 7.608 0.937
## sspc (.p3.) 0.812 0.039 20.851 0.000 0.735 0.888 3.080 0.868
## math =~
## ssar (.p4.) 3.111 0.061 51.394 0.000 2.992 3.229 7.064 0.944
## ssmk (.p5.) 2.513 0.048 51.972 0.000 2.419 2.608 5.708 0.875
## ssmc (.p6.) 0.657 0.033 19.947 0.000 0.592 0.721 1.491 0.280
## electronic =~
## ssgs (.p7.) 0.587 0.028 21.254 0.000 0.533 0.641 2.002 0.378
## ssasi (.p8.) 1.324 0.052 25.464 0.000 1.222 1.426 4.515 0.821
## ssmc (.p9.) 0.939 0.041 23.164 0.000 0.860 1.019 3.202 0.601
## ssei (.10.) 1.205 0.047 25.427 0.000 1.112 1.298 4.109 0.933
## speed =~
## ssno (.11.) 0.493 0.008 59.215 0.000 0.477 0.509 0.848 0.878
## sscs (.12.) 0.451 0.008 56.733 0.000 0.435 0.467 0.776 0.826
## g =~
## verbal (.13.) 3.327 0.174 19.094 0.000 2.985 3.668 0.965 0.965
## math (.14.) 1.853 0.046 40.137 0.000 1.763 1.943 0.898 0.898
## elctrnc 2.691 0.113 23.808 0.000 2.469 2.912 0.868 0.868
## speed (.16.) 1.271 0.032 39.946 0.000 1.209 1.334 0.814 0.814
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (a) 0.083 0.006 14.213 0.000 0.071 0.094 0.075 0.177
## age2 (b) -0.005 0.003 -2.017 0.044 -0.010 -0.000 -0.005 -0.024
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .math 0.000 0.000 0.000 0.000 0.000
## .ssgs (.38.) 14.899 0.090 164.637 0.000 14.722 15.077 14.899 2.814
## .sswk 27.553 0.178 154.565 0.000 27.204 27.903 27.553 3.395
## .sspc (.40.) 11.239 0.062 179.923 0.000 11.117 11.361 11.239 3.168
## .ssar (.41.) 17.103 0.144 118.831 0.000 16.821 17.385 17.103 2.285
## .ssmk (.42.) 13.066 0.121 107.655 0.000 12.828 13.304 13.066 2.002
## .ssmc (.43.) 11.877 0.084 141.316 0.000 11.712 12.042 11.877 2.229
## .ssasi (.44.) 11.139 0.073 152.549 0.000 10.996 11.282 11.139 2.026
## .ssei 7.870 0.101 77.559 0.000 7.671 8.069 7.870 1.786
## .ssno (.46.) 0.332 0.017 19.075 0.000 0.297 0.366 0.332 0.344
## .sscs 0.185 0.020 9.080 0.000 0.145 0.225 0.185 0.197
## .verbal -1.683 0.111 -15.172 0.000 -1.900 -1.465 -0.443 -0.443
## .elctrnc 3.345 0.156 21.482 0.000 3.040 3.650 0.981 0.981
## .speed -0.747 0.038 -19.588 0.000 -0.821 -0.672 -0.434 -0.434
## .g 0.242 0.031 7.777 0.000 0.181 0.303 0.220 0.220
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .verbal 1.000 1.000 1.000 0.069 0.069
## .math 1.000 1.000 1.000 0.194 0.194
## .speed 1.000 1.000 1.000 0.338 0.338
## .ssgs 5.369 0.161 33.327 0.000 5.054 5.685 5.369 0.192
## .sswk 7.983 0.423 18.853 0.000 7.153 8.813 7.983 0.121
## .sspc 3.101 0.106 29.161 0.000 2.892 3.309 3.101 0.246
## .ssar 6.121 0.372 16.468 0.000 5.392 6.849 6.121 0.109
## .ssmk 10.007 0.334 29.958 0.000 9.353 10.662 10.007 0.235
## .ssmc 8.460 0.247 34.240 0.000 7.976 8.945 8.460 0.298
## .ssasi 9.847 0.330 29.845 0.000 9.201 10.494 9.847 0.326
## .ssei 2.522 0.136 18.586 0.000 2.256 2.788 2.522 0.130
## .ssno 0.213 0.011 19.791 0.000 0.192 0.234 0.213 0.229
## .sscs 0.279 0.014 19.771 0.000 0.252 0.307 0.279 0.317
## .electronic 2.857 0.265 10.788 0.000 2.338 3.376 0.246 0.246
## .g 1.170 0.036 32.559 0.000 1.099 1.240 0.966 0.966
# BIFACTOR (freeing pc intercept alone leads to very good CFI change, but still very bad RMSEAD, thus ar was freed as well)
bf.notworking<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
'
baseline<-cfa(bf.notworking, data=dgroup, meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= -1.077605e-03) is smaller than zero. This may
## be a symptom that the model is not identified.
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2543.836 23.000 0.000 0.973 0.100 0.036 512110.012 512416.535
Mc(baseline)
## [1] 0.890961
summary(baseline, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 51 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 42
##
## Number of observations 10918
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2543.836 1437.362
## Degrees of freedom 23 23
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.770
## Yuan-Bentler correction (Mplus variant)
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal =~
## ssgs 0.401 0.117 3.431 0.001 0.172 0.629 0.401 0.080
## sswk 5.523 1.295 4.265 0.000 2.985 8.061 5.523 0.701
## sspc 0.439 0.122 3.599 0.000 0.200 0.679 0.439 0.127
## math =~
## ssar 2.905 0.110 26.415 0.000 2.689 3.120 2.905 0.396
## ssmk 2.177 0.089 24.503 0.000 2.003 2.351 2.177 0.342
## ssmc 1.127 0.058 19.577 0.000 1.015 1.240 1.127 0.214
## electronic =~
## ssgs 1.146 0.042 27.375 0.000 1.064 1.228 1.146 0.228
## ssasi 3.650 0.056 65.738 0.000 3.541 3.758 3.650 0.665
## ssmc 2.700 0.051 53.163 0.000 2.600 2.799 2.700 0.513
## ssei 2.029 0.040 50.363 0.000 1.950 2.108 2.029 0.477
## speed =~
## ssno 0.433 0.009 49.928 0.000 0.416 0.450 0.433 0.454
## sscs 0.586 0.032 18.260 0.000 0.523 0.649 0.586 0.609
## g =~
## ssgs 4.268 0.046 91.852 0.000 4.177 4.359 4.268 0.848
## ssar 6.223 0.056 110.147 0.000 6.112 6.334 6.223 0.849
## sswk 6.891 0.070 97.747 0.000 6.753 7.029 6.891 0.874
## sspc 2.843 0.032 87.562 0.000 2.779 2.906 2.843 0.821
## ssno 0.669 0.010 67.970 0.000 0.649 0.688 0.669 0.701
## sscs 0.594 0.011 55.483 0.000 0.573 0.615 0.594 0.618
## ssasi 3.171 0.059 53.682 0.000 3.055 3.287 3.171 0.578
## ssmk 5.160 0.052 99.792 0.000 5.059 5.261 5.160 0.810
## ssmc 3.550 0.051 69.297 0.000 3.450 3.651 3.550 0.675
## ssei 3.159 0.039 80.150 0.000 3.082 3.236 3.159 0.742
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## verbal ~~
## math 0.000 0.000 0.000 0.000 0.000
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 15.549 0.060 260.619 0.000 15.432 15.666 15.549 3.089
## .sswk 25.536 0.090 285.179 0.000 25.361 25.712 25.536 3.239
## .sspc 10.746 0.040 268.728 0.000 10.668 10.825 10.746 3.102
## .ssar 17.532 0.090 194.495 0.000 17.355 17.709 17.532 2.393
## .ssmk 13.395 0.080 168.423 0.000 13.239 13.551 13.395 2.102
## .ssmc 13.757 0.065 211.689 0.000 13.629 13.884 13.757 2.614
## .ssasi 13.689 0.067 204.057 0.000 13.558 13.821 13.689 2.496
## .ssei 11.090 0.051 216.290 0.000 10.989 11.190 11.090 2.605
## .ssno 0.191 0.011 16.982 0.000 0.169 0.214 0.191 0.201
## .sscs 0.166 0.012 14.363 0.000 0.143 0.189 0.166 0.173
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssgs 5.640 0.132 42.723 0.000 5.381 5.899 5.640 0.223
## .sswk -15.842 14.458 -1.096 0.273 -44.180 12.496 -15.842 -0.255
## .sspc 3.725 0.101 36.833 0.000 3.527 3.924 3.725 0.310
## .ssar 6.534 0.500 13.071 0.000 5.555 7.514 6.534 0.122
## .ssmk 9.234 0.329 28.086 0.000 8.590 9.879 9.234 0.227
## .ssmc 6.529 0.198 32.936 0.000 6.141 6.918 6.529 0.236
## .ssasi 6.708 0.247 27.209 0.000 6.225 7.191 6.708 0.223
## .ssei 4.031 0.103 39.300 0.000 3.830 4.232 4.031 0.222
## .ssno 0.276 NA NA NA 0.276 0.303
## .sscs 0.229 0.043 5.317 0.000 0.144 0.313 0.229 0.247
## verbal 1.000 1.000 1.000 1.000 1.000
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
bf.model<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
'
bf.lv<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
'
baseline<-cfa(bf.model, data=dgroup, meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= -8.988298e-08) is smaller than zero. This may
## be a symptom that the model is not identified.
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 3083.901 26.000 0.000 0.968 0.104 0.037 512644.077 512928.705
Mc(baseline)
## [1] 0.8693128
summary(baseline, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 31 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 39
##
## Number of observations 10918
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3083.901 1711.703
## Degrees of freedom 26 26
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.802
## Yuan-Bentler correction (Mplus variant)
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar 3.470 0.098 35.367 0.000 3.278 3.663 3.470 0.474
## ssmk 2.613 0.081 32.353 0.000 2.455 2.771 2.613 0.410
## ssmc 1.132 0.049 23.062 0.000 1.035 1.228 1.132 0.217
## electronic =~
## ssgs 1.221 0.040 30.304 0.000 1.142 1.300 1.221 0.242
## ssasi 3.689 0.053 69.699 0.000 3.585 3.792 3.689 0.673
## ssmc 2.696 0.049 55.251 0.000 2.601 2.792 2.696 0.516
## ssei 2.076 0.038 55.009 0.000 2.002 2.150 2.076 0.488
## speed =~
## ssno 0.473 0.010 48.601 0.000 0.454 0.492 0.473 0.495
## sscs 0.561 0.004 133.204 0.000 0.552 0.569 0.561 0.583
## g =~
## ssgs 4.328 0.042 103.306 0.000 4.246 4.410 4.328 0.857
## ssar 5.941 0.055 107.532 0.000 5.833 6.050 5.941 0.811
## sswk 7.283 0.062 117.546 0.000 7.161 7.404 7.283 0.924
## sspc 2.962 0.029 101.692 0.000 2.905 3.019 2.962 0.855
## ssno 0.653 0.010 67.278 0.000 0.634 0.672 0.653 0.684
## sscs 0.591 0.010 56.717 0.000 0.571 0.612 0.591 0.615
## ssasi 3.133 0.056 55.776 0.000 3.023 3.243 3.133 0.571
## ssmk 4.943 0.051 97.610 0.000 4.843 5.042 4.943 0.776
## ssmc 3.473 0.049 70.198 0.000 3.376 3.570 3.473 0.664
## ssei 3.121 0.037 83.347 0.000 3.048 3.195 3.121 0.733
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 17.532 0.090 194.495 0.000 17.355 17.709 17.532 2.393
## .ssmk 13.395 0.080 168.423 0.000 13.239 13.551 13.395 2.102
## .ssmc 13.757 0.065 211.689 0.000 13.629 13.884 13.757 2.632
## .ssgs 15.549 0.060 260.619 0.000 15.432 15.666 15.549 3.078
## .ssasi 13.689 0.067 204.057 0.000 13.558 13.821 13.689 2.496
## .ssei 11.090 0.051 216.290 0.000 10.989 11.190 11.090 2.605
## .ssno 0.191 0.011 16.982 0.000 0.169 0.214 0.191 0.201
## .sscs 0.166 0.012 14.363 0.000 0.143 0.189 0.166 0.173
## .sswk 25.536 0.090 285.179 0.000 25.361 25.712 25.536 3.239
## .sspc 10.746 0.040 268.728 0.000 10.668 10.825 10.746 3.102
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.354 0.579 10.972 0.000 5.219 7.489 6.354 0.118
## .ssmk 9.342 0.373 25.026 0.000 8.610 10.073 9.342 0.230
## .ssmc 6.701 0.185 36.213 0.000 6.339 7.064 6.701 0.245
## .ssgs 5.294 0.117 45.407 0.000 5.066 5.523 5.294 0.207
## .ssasi 6.661 0.244 27.327 0.000 6.183 7.138 6.661 0.221
## .ssei 4.077 0.103 39.713 0.000 3.876 4.278 4.077 0.225
## .ssno 0.261 0.008 32.728 0.000 0.245 0.277 0.261 0.287
## .sscs 0.261 0.010 26.040 0.000 0.242 0.281 0.261 0.282
## .sswk 9.106 0.304 29.924 0.000 8.509 9.702 9.106 0.147
## .sspc 3.227 0.078 41.571 0.000 3.075 3.379 3.227 0.269
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
configural<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= -3.349823e-07) is smaller than zero. This may
## be a symptom that the model is not identified.
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2288.019 52.000 0.000 0.976 0.089 0.026 503886.527 504455.784
Mc(configural)
## [1] 0.9026594
summary(configural, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 36 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 78
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2288.019 1279.672
## Degrees of freedom 52 52
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.788
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 888.789 497.093
## 0 1399.230 782.579
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar 3.385 0.131 25.816 0.000 3.128 3.642 3.385 0.484
## ssmk 2.679 0.114 23.576 0.000 2.456 2.901 2.679 0.437
## ssmc 1.158 0.068 17.107 0.000 1.025 1.291 1.158 0.270
## electronic =~
## ssgs 0.776 0.078 9.903 0.000 0.622 0.929 0.776 0.167
## ssasi 1.455 0.087 16.810 0.000 1.285 1.624 1.455 0.387
## ssmc 1.374 0.094 14.562 0.000 1.189 1.559 1.374 0.320
## ssei 1.070 0.079 13.606 0.000 0.916 1.225 1.070 0.299
## speed =~
## ssno 0.502 0.013 37.930 0.000 0.476 0.528 0.502 0.541
## sscs 0.500 0.007 75.512 0.000 0.487 0.513 0.500 0.532
## g =~
## ssgs 3.969 0.056 71.205 0.000 3.859 4.078 3.969 0.853
## ssar 5.596 0.078 71.821 0.000 5.444 5.749 5.596 0.800
## sswk 7.042 0.085 82.756 0.000 6.875 7.209 7.042 0.922
## sspc 2.800 0.041 67.888 0.000 2.719 2.881 2.800 0.854
## ssno 0.615 0.014 44.519 0.000 0.588 0.642 0.615 0.663
## sscs 0.568 0.015 38.118 0.000 0.539 0.597 0.568 0.604
## ssasi 2.494 0.053 47.216 0.000 2.390 2.597 2.494 0.663
## ssmk 4.646 0.070 66.472 0.000 4.509 4.783 4.646 0.758
## ssmc 2.889 0.058 49.803 0.000 2.775 3.003 2.889 0.673
## ssei 2.682 0.045 59.751 0.000 2.594 2.770 2.682 0.749
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 16.646 0.123 135.820 0.000 16.405 16.886 16.646 2.379
## .ssmk 13.157 0.108 122.070 0.000 12.946 13.369 13.157 2.146
## .ssmc 11.841 0.076 156.606 0.000 11.693 11.989 11.841 2.759
## .ssgs 14.716 0.078 188.083 0.000 14.563 14.869 14.716 3.165
## .ssasi 10.952 0.064 171.593 0.000 10.827 11.077 10.952 2.913
## .ssei 9.613 0.062 156.264 0.000 9.492 9.733 9.613 2.685
## .ssno 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.326
## .sscs 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.404
## .sswk 25.615 0.123 208.263 0.000 25.374 25.856 25.615 3.352
## .sspc 11.115 0.053 210.841 0.000 11.011 11.218 11.115 3.390
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.162 0.743 8.291 0.000 4.705 7.619 6.162 0.126
## .ssmk 8.830 0.526 16.784 0.000 7.799 9.861 8.830 0.235
## .ssmc 6.849 0.282 24.303 0.000 6.297 7.402 6.849 0.372
## .ssgs 5.272 0.171 30.791 0.000 4.936 5.607 5.272 0.244
## .ssasi 5.795 0.237 24.501 0.000 5.332 6.259 5.795 0.410
## .ssei 4.475 0.164 27.269 0.000 4.154 4.797 4.475 0.349
## .ssno 0.231 0.012 19.348 0.000 0.207 0.254 0.231 0.268
## .sscs 0.311 0.014 22.242 0.000 0.284 0.339 0.311 0.352
## .sswk 8.791 0.397 22.141 0.000 8.013 9.569 8.791 0.151
## .sspc 2.910 0.094 30.919 0.000 2.726 3.095 2.910 0.271
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar 3.408 0.149 22.908 0.000 3.116 3.699 3.408 0.452
## ssmk 2.627 0.121 21.743 0.000 2.390 2.864 2.627 0.399
## ssmc 0.956 0.070 13.640 0.000 0.819 1.093 0.956 0.174
## electronic =~
## ssgs 0.807 0.064 12.633 0.000 0.682 0.932 0.807 0.153
## ssasi 3.003 0.081 36.930 0.000 2.844 3.162 3.003 0.537
## ssmc 2.428 0.075 32.279 0.000 2.281 2.575 2.428 0.442
## ssei 1.578 0.059 26.739 0.000 1.463 1.694 1.578 0.361
## speed =~
## ssno 0.473 0.010 48.755 0.000 0.454 0.492 0.473 0.489
## sscs 0.479 0.011 44.467 0.000 0.458 0.501 0.479 0.512
## g =~
## ssgs 4.690 0.058 80.614 0.000 4.576 4.804 4.690 0.887
## ssar 6.256 0.075 83.871 0.000 6.110 6.402 6.256 0.830
## sswk 7.518 0.088 85.874 0.000 7.346 7.689 7.518 0.927
## sspc 3.130 0.039 80.144 0.000 3.053 3.206 3.130 0.870
## ssno 0.686 0.013 51.778 0.000 0.660 0.712 0.686 0.709
## sscs 0.624 0.014 45.873 0.000 0.598 0.651 0.624 0.666
## ssasi 3.864 0.078 49.792 0.000 3.712 4.016 3.864 0.691
## ssmk 5.171 0.072 72.306 0.000 5.030 5.311 5.171 0.785
## ssmc 4.108 0.066 62.045 0.000 3.978 4.238 4.108 0.748
## ssei 3.596 0.050 71.745 0.000 3.497 3.694 3.596 0.822
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 18.393 0.130 141.785 0.000 18.139 18.647 18.393 2.440
## .ssmk 13.626 0.116 116.977 0.000 13.397 13.854 13.626 2.068
## .ssmc 15.617 0.092 169.826 0.000 15.437 15.797 15.617 2.842
## .ssgs 16.358 0.087 188.331 0.000 16.188 16.528 16.358 3.093
## .ssasi 16.348 0.092 177.720 0.000 16.168 16.528 16.348 2.926
## .ssei 12.524 0.072 174.554 0.000 12.384 12.665 12.524 2.865
## .ssno 0.084 0.016 5.181 0.000 0.052 0.116 0.084 0.087
## .sscs -0.042 0.016 -2.602 0.009 -0.073 -0.010 -0.042 -0.045
## .sswk 25.460 0.130 195.905 0.000 25.205 25.715 25.460 3.139
## .sspc 10.389 0.059 175.230 0.000 10.273 10.505 10.389 2.887
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.060 0.895 6.772 0.000 4.306 7.814 6.060 0.107
## .ssmk 9.777 0.583 16.765 0.000 8.634 10.921 9.777 0.225
## .ssmc 6.510 0.285 22.878 0.000 5.952 7.068 6.510 0.216
## .ssgs 5.332 0.162 32.904 0.000 5.014 5.649 5.332 0.191
## .ssasi 7.279 0.364 19.997 0.000 6.565 7.992 7.279 0.233
## .ssei 3.692 0.130 28.407 0.000 3.438 3.947 3.692 0.193
## .ssno 0.241 0.010 24.823 0.000 0.222 0.260 0.241 0.257
## .sscs 0.259 0.013 19.327 0.000 0.233 0.285 0.259 0.295
## .sswk 9.269 0.408 22.711 0.000 8.469 10.069 9.269 0.141
## .sspc 3.156 0.107 29.621 0.000 2.948 3.365 3.156 0.244
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
#modificationIndices(configural, sort=T, maximum.number=30)
metric<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2634.909 67.000 0.000 0.973 0.084 0.053 504203.417 504663.202
Mc(metric)
## [1] 0.8890422
summary(metric, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 62 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 19
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2634.909 1543.380
## Degrees of freedom 67 67
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.707
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1039.285 608.754
## 0 1595.624 934.626
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.379 0.107 31.616 0.000 3.169 3.588 3.379 0.485
## ssmk (.p2.) 2.664 0.091 29.163 0.000 2.485 2.843 2.664 0.436
## ssmc (.p3.) 1.064 0.052 20.285 0.000 0.961 1.167 1.064 0.238
## electronic =~
## ssgs (.p4.) 0.496 0.034 14.597 0.000 0.429 0.562 0.496 0.106
## ssasi (.p5.) 1.614 0.060 27.110 0.000 1.497 1.731 1.614 0.406
## ssmc (.p6.) 1.326 0.054 24.361 0.000 1.219 1.433 1.326 0.297
## ssei (.p7.) 0.885 0.039 22.889 0.000 0.809 0.961 0.885 0.239
## speed =~
## ssno (.p8.) 0.460 0.056 8.164 0.000 0.349 0.570 0.460 0.496
## sscs (.p9.) 0.551 0.076 7.241 0.000 0.402 0.700 0.551 0.589
## g =~
## ssgs (.10.) 4.027 0.048 83.979 0.000 3.933 4.121 4.027 0.862
## ssar (.11.) 5.576 0.067 83.527 0.000 5.445 5.707 5.576 0.800
## sswk (.12.) 6.809 0.080 85.411 0.000 6.653 6.965 6.809 0.911
## sspc (.13.) 2.784 0.035 79.105 0.000 2.715 2.853 2.784 0.851
## ssno (.14.) 0.612 0.010 59.475 0.000 0.591 0.632 0.612 0.660
## sscs (.15.) 0.559 0.010 53.498 0.000 0.539 0.580 0.559 0.598
## ssasi (.16.) 2.817 0.045 61.999 0.000 2.728 2.906 2.817 0.708
## ssmk (.17.) 4.624 0.060 76.447 0.000 4.505 4.742 4.624 0.757
## ssmc (.18.) 3.180 0.046 69.835 0.000 3.090 3.269 3.180 0.712
## ssei (.19.) 2.885 0.036 79.851 0.000 2.815 2.956 2.885 0.778
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 16.646 0.123 135.820 0.000 16.405 16.886 16.646 2.388
## .ssmk 13.157 0.108 122.070 0.000 12.946 13.369 13.157 2.154
## .ssmc 11.841 0.076 156.606 0.000 11.693 11.989 11.841 2.650
## .ssgs 14.716 0.078 188.083 0.000 14.563 14.869 14.716 3.150
## .ssasi 10.952 0.064 171.593 0.000 10.827 11.077 10.952 2.752
## .ssei 9.613 0.062 156.264 0.000 9.492 9.733 9.613 2.593
## .ssno 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.326
## .sscs 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.406
## .sswk 25.615 0.123 208.263 0.000 25.374 25.856 25.615 3.429
## .sspc 11.115 0.053 210.841 0.000 11.011 11.218 11.115 3.396
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.069 0.611 9.940 0.000 4.873 7.266 6.069 0.125
## .ssmk 8.847 0.443 19.991 0.000 7.980 9.715 8.847 0.237
## .ssmc 6.969 0.228 30.523 0.000 6.521 7.416 6.969 0.349
## .ssgs 5.358 0.164 32.688 0.000 5.037 5.679 5.358 0.246
## .ssasi 5.293 0.204 25.977 0.000 4.893 5.692 5.293 0.334
## .ssei 4.638 0.136 34.154 0.000 4.372 4.904 4.638 0.337
## .ssno 0.274 0.054 5.036 0.000 0.167 0.381 0.274 0.319
## .sscs 0.259 0.081 3.193 0.001 0.100 0.419 0.259 0.296
## .sswk 9.442 0.383 24.673 0.000 8.692 10.192 9.442 0.169
## .sspc 2.962 0.095 31.214 0.000 2.776 3.148 2.962 0.276
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.379 0.107 31.616 0.000 3.169 3.588 3.335 0.441
## ssmk (.p2.) 2.664 0.091 29.163 0.000 2.485 2.843 2.629 0.398
## ssmc (.p3.) 1.064 0.052 20.285 0.000 0.961 1.167 1.050 0.203
## electronic =~
## ssgs (.p4.) 0.496 0.034 14.597 0.000 0.429 0.562 0.953 0.184
## ssasi (.p5.) 1.614 0.060 27.110 0.000 1.497 1.731 3.103 0.595
## ssmc (.p6.) 1.326 0.054 24.361 0.000 1.219 1.433 2.549 0.492
## ssei (.p7.) 0.885 0.039 22.889 0.000 0.809 0.961 1.701 0.411
## speed =~
## ssno (.p8.) 0.460 0.056 8.139 0.000 0.349 0.570 0.432 0.447
## sscs (.p9.) 0.551 0.076 7.241 0.000 0.402 0.700 0.518 0.551
## g =~
## ssgs (.10.) 4.027 0.048 83.979 0.000 3.933 4.121 4.544 0.876
## ssar (.11.) 5.576 0.067 83.527 0.000 5.445 5.707 6.291 0.832
## sswk (.12.) 6.809 0.080 85.411 0.000 6.653 6.965 7.682 0.930
## sspc (.13.) 2.784 0.035 79.105 0.000 2.715 2.853 3.141 0.872
## ssno (.14.) 0.612 0.010 59.475 0.000 0.591 0.632 0.690 0.713
## sscs (.15.) 0.559 0.010 53.498 0.000 0.539 0.580 0.631 0.671
## ssasi (.16.) 2.817 0.045 61.999 0.000 2.728 2.906 3.178 0.610
## ssmk (.17.) 4.624 0.060 76.447 0.000 4.505 4.742 5.217 0.789
## ssmc (.18.) 3.180 0.046 69.835 0.000 3.090 3.269 3.587 0.692
## ssei (.19.) 2.885 0.036 79.851 0.000 2.815 2.956 3.255 0.786
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 18.393 0.130 141.785 0.000 18.139 18.647 18.393 2.433
## .ssmk 13.626 0.116 116.977 0.000 13.397 13.854 13.626 2.061
## .ssmc 15.617 0.092 169.826 0.000 15.437 15.797 15.617 3.013
## .ssgs 16.358 0.087 188.331 0.000 16.188 16.528 16.358 3.155
## .ssasi 16.348 0.092 177.720 0.000 16.168 16.528 16.348 3.137
## .ssei 12.524 0.072 174.554 0.000 12.384 12.665 12.524 3.024
## .ssno 0.084 0.016 5.181 0.000 0.052 0.116 0.084 0.087
## .sscs -0.042 0.016 -2.602 0.009 -0.073 -0.010 -0.042 -0.044
## .sswk 25.460 0.130 195.905 0.000 25.205 25.715 25.460 3.082
## .sspc 10.389 0.059 175.230 0.000 10.273 10.505 10.389 2.882
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 6.471 0.633 10.222 0.000 5.231 7.712 6.471 0.113
## .ssmk 9.566 0.444 21.524 0.000 8.695 10.437 9.566 0.219
## .ssmc 6.402 0.272 23.565 0.000 5.869 6.934 6.402 0.238
## .ssgs 5.329 0.160 33.209 0.000 5.015 5.644 5.329 0.198
## .ssasi 7.434 0.351 21.158 0.000 6.745 8.122 7.434 0.274
## .ssei 3.663 0.130 28.181 0.000 3.408 3.917 3.663 0.214
## .ssno 0.274 0.051 5.412 0.000 0.175 0.373 0.274 0.292
## .sscs 0.218 0.067 3.270 0.001 0.087 0.349 0.218 0.247
## .sswk 9.203 0.411 22.400 0.000 8.398 10.008 9.203 0.135
## .sspc 3.122 0.105 29.776 0.000 2.917 3.328 3.122 0.240
## math 0.974 0.056 17.529 0.000 0.865 1.083 1.000 1.000
## electronic 3.696 0.292 12.642 0.000 3.123 4.269 1.000 1.000
## speed 0.885 0.051 17.452 0.000 0.786 0.985 1.000 1.000
## g 1.273 0.037 34.624 0.000 1.201 1.345 1.000 1.000
lavTestScore(metric, release = 1:19)
## 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 341.992 19 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p1. == .p54. 1.262 1 0.261
## 2 .p2. == .p55. 0.239 1 0.625
## 3 .p3. == .p56. 2.785 1 0.095
## 4 .p4. == .p57. 7.829 1 0.005
## 5 .p5. == .p58. 10.609 1 0.001
## 6 .p6. == .p59. 0.032 1 0.857
## 7 .p7. == .p60. 1.890 1 0.169
## 8 .p8. == .p61. 0.000 1 1.000
## 9 .p9. == .p62. 0.000 1 1.000
## 10 .p10. == .p63. 0.355 1 0.552
## 11 .p11. == .p64. 2.522 1 0.112
## 12 .p12. == .p65. 62.661 1 0.000
## 13 .p13. == .p66. 0.199 1 0.655
## 14 .p14. == .p67. 0.066 1 0.798
## 15 .p15. == .p68. 0.831 1 0.362
## 16 .p16. == .p69. 72.114 1 0.000
## 17 .p17. == .p70. 0.955 1 0.329
## 18 .p18. == .p71. 29.831 1 0.000
## 19 .p19. == .p72. 20.152 1 0.000
scalar<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 3074.963 73.000 0.000 0.968 0.087 0.054 504631.471 505047.467
Mc(scalar)
## [1] 0.8715428
summary(scalar, standardized=T, ci=T) # +.090
## lavaan 0.6-18 ended normally after 129 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 29
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3074.963 1837.005
## Degrees of freedom 73 73
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.674
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1248.741 746.007
## 0 1826.222 1090.998
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.972 0.125 31.869 0.000 3.728 4.216 3.972 0.570
## ssmk (.p2.) 2.167 0.084 25.680 0.000 2.002 2.333 2.167 0.356
## ssmc (.p3.) 0.828 0.055 15.068 0.000 0.720 0.935 0.828 0.185
## electronic =~
## ssgs (.p4.) 0.572 0.026 22.246 0.000 0.521 0.622 0.572 0.123
## ssasi (.p5.) 1.658 0.060 27.512 0.000 1.539 1.776 1.658 0.417
## ssmc (.p6.) 1.128 0.044 25.890 0.000 1.043 1.213 1.128 0.252
## ssei (.p7.) 0.928 0.035 26.230 0.000 0.858 0.997 0.928 0.251
## speed =~
## ssno (.p8.) 0.328 0.017 19.215 0.000 0.295 0.362 0.328 0.354
## sscs (.p9.) 0.767 0.041 18.873 0.000 0.688 0.847 0.767 0.820
## g =~
## ssgs (.10.) 4.009 0.048 83.026 0.000 3.914 4.103 4.009 0.860
## ssar (.11.) 5.586 0.067 83.751 0.000 5.456 5.717 5.586 0.802
## sswk (.12.) 6.785 0.081 84.247 0.000 6.628 6.943 6.785 0.909
## sspc (.13.) 2.796 0.034 81.209 0.000 2.728 2.863 2.796 0.849
## ssno (.14.) 0.613 0.010 59.923 0.000 0.593 0.633 0.613 0.661
## sscs (.15.) 0.561 0.010 53.747 0.000 0.540 0.581 0.561 0.599
## ssasi (.16.) 2.799 0.045 61.739 0.000 2.710 2.888 2.799 0.705
## ssmk (.17.) 4.649 0.060 77.206 0.000 4.531 4.767 4.649 0.763
## ssmc (.18.) 3.228 0.045 71.123 0.000 3.139 3.317 3.228 0.722
## ssei (.19.) 2.872 0.036 79.360 0.000 2.801 2.943 2.872 0.775
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 16.662 0.124 134.581 0.000 16.419 16.905 16.662 2.391
## .ssmk (.41.) 13.008 0.103 126.906 0.000 12.807 13.209 13.008 2.134
## .ssmc (.42.) 11.733 0.074 158.524 0.000 11.588 11.878 11.733 2.625
## .ssgs (.43.) 14.768 0.077 192.949 0.000 14.618 14.918 14.768 3.167
## .ssasi (.44.) 10.969 0.064 172.489 0.000 10.844 11.093 10.969 2.761
## .ssei (.45.) 9.638 0.061 159.192 0.000 9.520 9.757 9.638 2.603
## .ssno (.46.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.326
## .sscs (.47.) 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.406
## .sswk (.48.) 25.888 0.120 216.161 0.000 25.654 26.123 25.888 3.467
## .sspc (.49.) 10.895 0.053 207.023 0.000 10.792 10.998 10.895 3.310
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 1.581 0.925 1.708 0.088 -0.233 3.394 1.581 0.033
## .ssmk 10.840 0.381 28.436 0.000 10.093 11.588 10.840 0.292
## .ssmc 7.600 0.223 34.017 0.000 7.162 8.038 7.600 0.380
## .ssgs 5.349 0.164 32.593 0.000 5.027 5.671 5.349 0.246
## .ssasi 5.201 0.204 25.540 0.000 4.802 5.600 5.201 0.330
## .ssei 4.605 0.135 34.111 0.000 4.340 4.870 4.605 0.336
## .ssno 0.376 0.015 25.502 0.000 0.347 0.405 0.376 0.437
## .sscs -0.027 0.063 -0.428 0.668 -0.151 0.097 -0.027 -0.031
## .sswk 9.713 0.395 24.618 0.000 8.940 10.487 9.713 0.174
## .sspc 3.017 0.097 31.075 0.000 2.827 3.207 3.017 0.279
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.972 0.125 31.869 0.000 3.728 4.216 3.950 0.522
## ssmk (.p2.) 2.167 0.084 25.680 0.000 2.002 2.333 2.155 0.326
## ssmc (.p3.) 0.828 0.055 15.068 0.000 0.720 0.935 0.823 0.161
## electronic =~
## ssgs (.p4.) 0.572 0.026 22.246 0.000 0.521 0.622 1.105 0.213
## ssasi (.p5.) 1.658 0.060 27.512 0.000 1.539 1.776 3.204 0.611
## ssmc (.p6.) 1.128 0.044 25.890 0.000 1.043 1.213 2.180 0.427
## ssei (.p7.) 0.928 0.035 26.230 0.000 0.858 0.997 1.793 0.432
## speed =~
## ssno (.p8.) 0.328 0.017 19.215 0.000 0.295 0.362 0.308 0.318
## sscs (.p9.) 0.767 0.041 18.873 0.000 0.688 0.847 0.720 0.765
## g =~
## ssgs (.10.) 4.009 0.048 83.026 0.000 3.914 4.103 4.522 0.870
## ssar (.11.) 5.586 0.067 83.751 0.000 5.456 5.717 6.301 0.833
## sswk (.12.) 6.785 0.081 84.247 0.000 6.628 6.943 7.654 0.928
## sspc (.13.) 2.796 0.034 81.209 0.000 2.728 2.863 3.153 0.871
## ssno (.14.) 0.613 0.010 59.923 0.000 0.593 0.633 0.692 0.715
## sscs (.15.) 0.561 0.010 53.747 0.000 0.540 0.581 0.633 0.673
## ssasi (.16.) 2.799 0.045 61.739 0.000 2.710 2.888 3.157 0.602
## ssmk (.17.) 4.649 0.060 77.206 0.000 4.531 4.767 5.244 0.793
## ssmc (.18.) 3.228 0.045 71.123 0.000 3.139 3.317 3.641 0.712
## ssei (.19.) 2.872 0.036 79.360 0.000 2.801 2.943 3.239 0.779
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 16.662 0.124 134.581 0.000 16.419 16.905 16.662 2.202
## .ssmk (.41.) 13.008 0.103 126.906 0.000 12.807 13.209 13.008 1.968
## .ssmc (.42.) 11.733 0.074 158.524 0.000 11.588 11.878 11.733 2.296
## .ssgs (.43.) 14.768 0.077 192.949 0.000 14.618 14.918 14.768 2.842
## .ssasi (.44.) 10.969 0.064 172.489 0.000 10.844 11.093 10.969 2.093
## .ssei (.45.) 9.638 0.061 159.192 0.000 9.520 9.757 9.638 2.319
## .ssno (.46.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.312
## .sscs (.47.) 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.404
## .sswk (.48.) 25.888 0.120 216.161 0.000 25.654 26.123 25.888 3.138
## .sspc (.49.) 10.895 0.053 207.023 0.000 10.792 10.998 10.895 3.011
## math 0.573 0.031 18.334 0.000 0.512 0.635 0.576 0.576
## elctrnc 3.403 0.135 25.256 0.000 3.139 3.667 1.761 1.761
## speed -0.476 0.036 -13.132 0.000 -0.547 -0.405 -0.507 -0.507
## g -0.101 0.026 -3.859 0.000 -0.153 -0.050 -0.090 -0.090
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 1.941 0.952 2.038 0.042 0.075 3.806 1.941 0.034
## .ssmk 11.531 0.416 27.727 0.000 10.716 12.346 11.531 0.264
## .ssmc 7.431 0.236 31.508 0.000 6.969 7.893 7.431 0.284
## .ssgs 5.337 0.162 33.003 0.000 5.020 5.654 5.337 0.198
## .ssasi 7.237 0.318 22.766 0.000 6.614 7.860 7.237 0.263
## .ssei 3.564 0.128 27.869 0.000 3.313 3.814 3.564 0.206
## .ssno 0.364 0.013 27.874 0.000 0.338 0.389 0.364 0.388
## .sscs -0.034 0.052 -0.651 0.515 -0.135 0.068 -0.034 -0.038
## .sswk 9.474 0.434 21.853 0.000 8.624 10.324 9.474 0.139
## .sspc 3.151 0.109 28.967 0.000 2.938 3.364 3.151 0.241
## math 0.989 0.056 17.696 0.000 0.879 1.099 1.000 1.000
## electronic 3.736 0.304 12.274 0.000 3.139 4.333 1.000 1.000
## speed 0.880 0.051 17.332 0.000 0.780 0.979 1.000 1.000
## g 1.272 0.037 34.769 0.000 1.201 1.344 1.000 1.000
lavTestScore(scalar, release = 20:29)
## 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 420.736 10 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p40. == .p93. 98.866 1 0.000
## 2 .p41. == .p94. 50.174 1 0.000
## 3 .p42. == .p95. 80.606 1 0.000
## 4 .p43. == .p96. 20.125 1 0.000
## 5 .p44. == .p97. 6.888 1 0.009
## 6 .p45. == .p98. 6.494 1 0.011
## 7 .p46. == .p99. 0.000 1 1.000
## 8 .p47. == .p100. 0.000 1 1.000
## 9 .p48. == .p101. 204.649 1 0.000
## 10 .p49. == .p102. 255.609 1 0.000
scalar2<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2817.216 72.000 0.000 0.971 0.084 0.054 504375.725 504799.018
Mc(scalar2)
## [1] 0.8818518
summary(scalar2, standardized=T, ci=T) # +.024
## lavaan 0.6-18 ended normally after 145 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 28
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2817.216 1682.627
## Degrees of freedom 72 72
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.674
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1125.998 672.520
## 0 1691.219 1010.107
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.964 0.138 28.618 0.000 3.692 4.235 3.964 0.569
## ssmk (.p2.) 2.182 0.095 22.913 0.000 1.995 2.369 2.182 0.358
## ssmc (.p3.) 0.845 0.060 14.096 0.000 0.727 0.962 0.845 0.189
## electronic =~
## ssgs (.p4.) 0.529 0.025 21.086 0.000 0.479 0.578 0.529 0.113
## ssasi (.p5.) 1.679 0.061 27.705 0.000 1.560 1.798 1.679 0.423
## ssmc (.p6.) 1.139 0.044 26.052 0.000 1.053 1.224 1.139 0.255
## ssei (.p7.) 0.914 0.035 26.225 0.000 0.846 0.982 0.914 0.247
## speed =~
## ssno (.p8.) 0.354 0.015 23.827 0.000 0.325 0.383 0.354 0.382
## sscs (.p9.) 0.714 0.031 23.089 0.000 0.653 0.774 0.714 0.762
## g =~
## ssgs (.10.) 4.019 0.048 83.532 0.000 3.925 4.113 4.019 0.861
## ssar (.11.) 5.581 0.067 83.774 0.000 5.450 5.711 5.581 0.801
## sswk (.12.) 6.804 0.080 85.485 0.000 6.648 6.960 6.804 0.911
## sspc (.13.) 2.787 0.035 79.665 0.000 2.718 2.855 2.787 0.851
## ssno (.14.) 0.612 0.010 59.860 0.000 0.592 0.632 0.612 0.660
## sscs (.15.) 0.560 0.010 53.715 0.000 0.540 0.580 0.560 0.598
## ssasi (.16.) 2.801 0.045 61.762 0.000 2.712 2.890 2.801 0.705
## ssmk (.17.) 4.639 0.060 77.470 0.000 4.521 4.756 4.639 0.762
## ssmc (.18.) 3.223 0.045 70.914 0.000 3.134 3.312 3.223 0.721
## ssei (.19.) 2.876 0.036 79.525 0.000 2.805 2.947 2.876 0.776
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 16.669 0.125 132.999 0.000 16.423 16.914 16.669 2.392
## .ssmk (.41.) 12.949 0.101 127.984 0.000 12.751 13.147 12.949 2.126
## .ssmc (.42.) 11.738 0.074 159.293 0.000 11.594 11.882 11.738 2.626
## .ssgs (.43.) 14.740 0.077 192.256 0.000 14.590 14.890 14.740 3.158
## .ssasi (.44.) 10.977 0.064 172.503 0.000 10.853 11.102 10.977 2.762
## .ssei (.45.) 9.637 0.060 159.576 0.000 9.519 9.756 9.637 2.601
## .ssno (.46.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.326
## .sscs (.47.) 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.406
## .sswk (.48.) 25.630 0.123 208.921 0.000 25.390 25.871 25.630 3.431
## .sspc 11.115 0.053 210.841 0.000 11.011 11.218 11.115 3.394
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 1.719 1.052 1.633 0.102 -0.344 3.782 1.719 0.035
## .ssmk 10.828 0.415 26.108 0.000 10.015 11.640 10.828 0.292
## .ssmc 7.577 0.226 33.596 0.000 7.135 8.019 7.577 0.379
## .ssgs 5.358 0.164 32.707 0.000 5.037 5.679 5.358 0.246
## .ssasi 5.128 0.205 24.982 0.000 4.726 5.531 5.128 0.325
## .ssei 4.625 0.135 34.258 0.000 4.360 4.889 4.625 0.337
## .ssno 0.359 0.014 25.756 0.000 0.332 0.387 0.359 0.418
## .sscs 0.053 0.045 1.175 0.240 -0.035 0.141 0.053 0.061
## .sswk 9.524 0.385 24.713 0.000 8.769 10.280 9.524 0.171
## .sspc 2.959 0.095 31.257 0.000 2.773 3.144 2.959 0.276
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.964 0.138 28.618 0.000 3.692 4.235 3.941 0.521
## ssmk (.p2.) 2.182 0.095 22.913 0.000 1.995 2.369 2.170 0.329
## ssmc (.p3.) 0.845 0.060 14.096 0.000 0.727 0.962 0.840 0.164
## electronic =~
## ssgs (.p4.) 0.529 0.025 21.086 0.000 0.479 0.578 1.021 0.197
## ssasi (.p5.) 1.679 0.061 27.705 0.000 1.560 1.798 3.243 0.618
## ssmc (.p6.) 1.139 0.044 26.052 0.000 1.053 1.224 2.199 0.430
## ssei (.p7.) 0.914 0.035 26.225 0.000 0.846 0.982 1.766 0.425
## speed =~
## ssno (.p8.) 0.354 0.015 23.827 0.000 0.325 0.383 0.332 0.343
## sscs (.p9.) 0.714 0.031 23.089 0.000 0.653 0.774 0.671 0.713
## g =~
## ssgs (.10.) 4.019 0.048 83.532 0.000 3.925 4.113 4.534 0.874
## ssar (.11.) 5.581 0.067 83.774 0.000 5.450 5.711 6.296 0.832
## sswk (.12.) 6.804 0.080 85.485 0.000 6.648 6.960 7.676 0.929
## sspc (.13.) 2.787 0.035 79.665 0.000 2.718 2.855 3.144 0.873
## ssno (.14.) 0.612 0.010 59.860 0.000 0.592 0.632 0.691 0.714
## sscs (.15.) 0.560 0.010 53.715 0.000 0.540 0.580 0.632 0.672
## ssasi (.16.) 2.801 0.045 61.762 0.000 2.712 2.890 3.160 0.602
## ssmk (.17.) 4.639 0.060 77.470 0.000 4.521 4.756 5.233 0.792
## ssmc (.18.) 3.223 0.045 70.914 0.000 3.134 3.312 3.636 0.711
## ssei (.19.) 2.876 0.036 79.525 0.000 2.805 2.947 3.245 0.781
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 16.669 0.125 132.999 0.000 16.423 16.914 16.669 2.203
## .ssmk (.41.) 12.949 0.101 127.984 0.000 12.751 13.147 12.949 1.961
## .ssmc (.42.) 11.738 0.074 159.293 0.000 11.594 11.882 11.738 2.296
## .ssgs (.43.) 14.740 0.077 192.256 0.000 14.590 14.890 14.740 2.840
## .ssasi (.44.) 10.977 0.064 172.503 0.000 10.853 11.102 10.977 2.091
## .ssei (.45.) 9.637 0.060 159.576 0.000 9.519 9.756 9.637 2.320
## .ssno (.46.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.312
## .sscs (.47.) 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.404
## .sswk (.48.) 25.630 0.123 208.921 0.000 25.390 25.871 25.630 3.103
## .sspc 10.464 0.062 169.596 0.000 10.343 10.585 10.464 2.904
## math 0.466 0.031 14.819 0.000 0.405 0.528 0.469 0.469
## elctrnc 3.223 0.128 25.196 0.000 2.973 3.474 1.669 1.669
## speed -0.570 0.037 -15.547 0.000 -0.642 -0.498 -0.606 -0.606
## g -0.027 0.026 -1.026 0.305 -0.079 0.025 -0.024 -0.024
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 2.096 1.082 1.938 0.053 -0.024 4.217 2.096 0.037
## .ssmk 11.519 0.448 25.727 0.000 10.641 12.397 11.519 0.264
## .ssmc 7.380 0.238 31.029 0.000 6.914 7.847 7.380 0.282
## .ssgs 5.335 0.161 33.200 0.000 5.020 5.650 5.335 0.198
## .ssasi 7.042 0.319 22.046 0.000 6.416 7.668 7.042 0.256
## .ssei 3.604 0.128 28.156 0.000 3.353 3.855 3.604 0.209
## .ssno 0.349 0.012 28.017 0.000 0.325 0.374 0.349 0.373
## .sscs 0.036 0.036 0.992 0.321 -0.035 0.107 0.036 0.041
## .sswk 9.285 0.419 22.145 0.000 8.463 10.107 9.285 0.136
## .sspc 3.099 0.104 29.704 0.000 2.894 3.303 3.099 0.239
## math 0.989 0.056 17.806 0.000 0.880 1.098 1.000 1.000
## electronic 3.731 0.301 12.386 0.000 3.140 4.321 1.000 1.000
## speed 0.883 0.051 17.394 0.000 0.784 0.983 1.000 1.000
## g 1.273 0.037 34.829 0.000 1.201 1.344 1.000 1.000
lavTestScore(scalar2, release = 20:27)
## 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 172.263 8 0
##
## $uni
##
## univariate score tests:
##
## lhs op rhs X2 df p.value
## 1 .p40. == .p93. 129.427 1 0.000
## 2 .p41. == .p94. 80.619 1 0.000
## 3 .p42. == .p95. 68.110 1 0.000
## 4 .p43. == .p96. 4.014 1 0.045
## 5 .p44. == .p97. 15.975 1 0.000
## 6 .p45. == .p98. 5.339 1 0.021
## 7 .p46. == .p99. 0.000 1 1.000
## 8 .p47. == .p100. 0.000 1 1.000
strict<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("sspc~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2923.054 82.000 0.000 0.970 0.080 0.053 504461.562 504811.874
Mc(strict)
## [1] 0.8779895
summary(strict, standardized=T, ci=T) # +.021
## lavaan 0.6-18 ended normally after 89 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 38
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2923.054 1723.193
## Degrees of freedom 82 82
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.696
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1170.442 689.996
## 0 1752.612 1033.196
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.911 0.132 29.654 0.000 3.652 4.169 3.911 0.561
## ssmk (.p2.) 2.183 0.094 23.272 0.000 1.999 2.367 2.183 0.357
## ssmc (.p3.) 0.849 0.060 14.265 0.000 0.733 0.966 0.849 0.191
## electronic =~
## ssgs (.p4.) 0.505 0.024 20.714 0.000 0.457 0.553 0.505 0.108
## ssasi (.p5.) 1.645 0.059 27.723 0.000 1.529 1.762 1.645 0.407
## ssmc (.p6.) 1.094 0.043 25.389 0.000 1.010 1.179 1.094 0.246
## ssei (.p7.) 0.873 0.034 25.492 0.000 0.806 0.940 0.873 0.240
## speed =~
## ssno (.p8.) 0.356 0.015 23.823 0.000 0.327 0.386 0.356 0.385
## sscs (.p9.) 0.722 0.027 26.813 0.000 0.670 0.775 0.722 0.772
## g =~
## ssgs (.10.) 4.019 0.048 83.570 0.000 3.925 4.113 4.019 0.862
## ssar (.11.) 5.582 0.066 84.022 0.000 5.452 5.713 5.582 0.801
## sswk (.12.) 6.803 0.079 86.002 0.000 6.648 6.958 6.803 0.911
## sspc (.13.) 2.786 0.035 79.994 0.000 2.718 2.855 2.786 0.848
## ssno (.14.) 0.612 0.010 59.994 0.000 0.592 0.632 0.612 0.661
## sscs (.15.) 0.560 0.010 53.841 0.000 0.540 0.581 0.560 0.598
## ssasi (.16.) 2.810 0.045 61.836 0.000 2.721 2.899 2.810 0.695
## ssmk (.17.) 4.641 0.060 77.689 0.000 4.524 4.758 4.641 0.759
## ssmc (.18.) 3.219 0.045 71.090 0.000 3.130 3.308 3.219 0.723
## ssei (.19.) 2.867 0.036 79.580 0.000 2.796 2.938 2.867 0.790
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 16.675 0.126 132.641 0.000 16.429 16.922 16.675 2.391
## .ssmk (.41.) 12.934 0.101 127.766 0.000 12.736 13.133 12.934 2.115
## .ssmc (.42.) 11.754 0.074 159.762 0.000 11.609 11.898 11.754 2.642
## .ssgs (.43.) 14.747 0.077 192.467 0.000 14.597 14.897 14.747 3.161
## .ssasi (.44.) 10.955 0.064 171.629 0.000 10.830 11.080 10.955 2.711
## .ssei (.45.) 9.656 0.060 160.807 0.000 9.538 9.773 9.656 2.659
## .ssno (.46.) 0.301 0.015 19.575 0.000 0.271 0.331 0.301 0.325
## .sscs (.47.) 0.380 0.016 24.184 0.000 0.349 0.411 0.380 0.406
## .sswk (.48.) 25.616 0.123 208.353 0.000 25.376 25.857 25.616 3.431
## .sspc 11.115 0.053 210.841 0.000 11.011 11.218 11.115 3.383
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.20.) 2.163 0.998 2.168 0.030 0.208 4.119 2.163 0.044
## .ssmk (.21.) 11.094 0.377 29.391 0.000 10.354 11.834 11.094 0.297
## .ssmc (.22.) 7.516 0.168 44.650 0.000 7.186 7.846 7.516 0.380
## .ssgs (.23.) 5.356 0.117 45.957 0.000 5.127 5.584 5.356 0.246
## .ssasi (.24.) 5.728 0.186 30.854 0.000 5.364 6.092 5.728 0.351
## .ssei (.25.) 4.200 0.095 43.986 0.000 4.013 4.387 4.200 0.319
## .ssno (.26.) 0.355 0.011 32.532 0.000 0.334 0.377 0.355 0.415
## .sscs (.27.) 0.041 0.037 1.121 0.262 -0.031 0.113 0.041 0.047
## .sswk (.28.) 9.467 0.294 32.184 0.000 8.891 10.044 9.467 0.170
## .sspc (.29.) 3.032 0.071 42.933 0.000 2.894 3.171 3.032 0.281
## math 1.000 1.000 1.000 1.000 1.000
## elctrnc 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.911 0.132 29.654 0.000 3.652 4.169 3.926 0.519
## ssmk (.p2.) 2.183 0.094 23.272 0.000 1.999 2.367 2.192 0.333
## ssmc (.p3.) 0.849 0.060 14.265 0.000 0.733 0.966 0.852 0.166
## electronic =~
## ssgs (.p4.) 0.505 0.024 20.714 0.000 0.457 0.553 1.023 0.197
## ssasi (.p5.) 1.645 0.059 27.723 0.000 1.529 1.762 3.333 0.643
## ssmc (.p6.) 1.094 0.043 25.389 0.000 1.010 1.179 2.217 0.432
## ssei (.p7.) 0.873 0.034 25.492 0.000 0.806 0.940 1.768 0.419
## speed =~
## ssno (.p8.) 0.356 0.015 23.823 0.000 0.327 0.386 0.329 0.339
## sscs (.p9.) 0.722 0.027 26.813 0.000 0.670 0.775 0.666 0.709
## g =~
## ssgs (.10.) 4.019 0.048 83.570 0.000 3.925 4.113 4.533 0.873
## ssar (.11.) 5.582 0.066 84.022 0.000 5.452 5.713 6.296 0.832
## sswk (.12.) 6.803 0.079 86.002 0.000 6.648 6.958 7.673 0.928
## sspc (.13.) 2.786 0.035 79.994 0.000 2.718 2.855 3.143 0.875
## ssno (.14.) 0.612 0.010 59.994 0.000 0.592 0.632 0.690 0.712
## sscs (.15.) 0.560 0.010 53.841 0.000 0.540 0.581 0.632 0.672
## ssasi (.16.) 2.810 0.045 61.836 0.000 2.721 2.899 3.169 0.611
## ssmk (.17.) 4.641 0.060 77.689 0.000 4.524 4.758 5.235 0.796
## ssmc (.18.) 3.219 0.045 71.090 0.000 3.130 3.308 3.631 0.707
## ssei (.19.) 2.867 0.036 79.580 0.000 2.796 2.938 3.234 0.767
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 16.675 0.126 132.641 0.000 16.429 16.922 16.675 2.204
## .ssmk (.41.) 12.934 0.101 127.766 0.000 12.736 13.133 12.934 1.966
## .ssmc (.42.) 11.754 0.074 159.762 0.000 11.609 11.898 11.754 2.290
## .ssgs (.43.) 14.747 0.077 192.467 0.000 14.597 14.897 14.747 2.841
## .ssasi (.44.) 10.955 0.064 171.629 0.000 10.830 11.080 10.955 2.113
## .ssei (.45.) 9.656 0.060 160.807 0.000 9.538 9.773 9.656 2.290
## .ssno (.46.) 0.301 0.015 19.575 0.000 0.271 0.331 0.301 0.310
## .sscs (.47.) 0.380 0.016 24.184 0.000 0.349 0.411 0.380 0.404
## .sswk (.48.) 25.616 0.123 208.353 0.000 25.376 25.857 25.616 3.099
## .sspc 10.454 0.062 168.641 0.000 10.332 10.575 10.454 2.909
## math 0.465 0.032 14.662 0.000 0.403 0.527 0.463 0.463
## elctrnc 3.315 0.132 25.113 0.000 3.056 3.574 1.637 1.637
## speed -0.566 0.037 -15.306 0.000 -0.639 -0.494 -0.614 -0.614
## g -0.023 0.026 -0.877 0.380 -0.075 0.029 -0.021 -0.021
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.20.) 2.163 0.998 2.168 0.030 0.208 4.119 2.163 0.038
## .ssmk (.21.) 11.094 0.377 29.391 0.000 10.354 11.834 11.094 0.256
## .ssmc (.22.) 7.516 0.168 44.650 0.000 7.186 7.846 7.516 0.285
## .ssgs (.23.) 5.356 0.117 45.957 0.000 5.127 5.584 5.356 0.199
## .ssasi (.24.) 5.728 0.186 30.854 0.000 5.364 6.092 5.728 0.213
## .ssei (.25.) 4.200 0.095 43.986 0.000 4.013 4.387 4.200 0.236
## .ssno (.26.) 0.355 0.011 32.532 0.000 0.334 0.377 0.355 0.378
## .sscs (.27.) 0.041 0.037 1.121 0.262 -0.031 0.113 0.041 0.046
## .sswk (.28.) 9.467 0.294 32.184 0.000 8.891 10.044 9.467 0.139
## .sspc (.29.) 3.032 0.071 42.933 0.000 2.894 3.171 3.032 0.235
## math 1.008 0.044 23.091 0.000 0.922 1.093 1.000 1.000
## elctrnc 4.104 0.323 12.707 0.000 3.471 4.737 1.000 1.000
## speed 0.850 0.039 21.747 0.000 0.774 0.927 1.000 1.000
## g 1.272 0.036 34.988 0.000 1.201 1.343 1.000 1.000
latent<-cfa(bf.model, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("sspc~1"))
fitMeasures(latent, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 3520.352 76.000 0.000 0.964 0.091 0.129 505070.860 505464.961
Mc(latent)
## [1] 0.8540618
summary(latent, standardized=T, ci=T) # +.030
## lavaan 0.6-18 ended normally after 94 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 28
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3520.352 2115.983
## Degrees of freedom 76 76
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.664
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1612.164 969.026
## 0 1908.188 1146.957
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.028 0.133 30.257 0.000 3.767 4.288 4.028 0.554
## ssmk (.p2.) 2.173 0.090 24.095 0.000 1.996 2.350 2.173 0.344
## ssmc (.p3.) 0.818 0.058 14.193 0.000 0.705 0.931 0.818 0.168
## electronic =~
## ssgs (.p4.) 0.801 0.028 28.735 0.000 0.746 0.856 0.801 0.160
## ssasi (.p5.) 2.483 0.047 52.923 0.000 2.391 2.575 2.483 0.548
## ssmc (.p6.) 1.694 0.042 40.491 0.000 1.612 1.776 1.694 0.348
## ssei (.p7.) 1.385 0.031 45.143 0.000 1.325 1.445 1.385 0.340
## speed =~
## ssno (.p8.) 0.342 0.014 24.309 0.000 0.314 0.370 0.342 0.361
## sscs (.p9.) 0.695 0.029 24.262 0.000 0.639 0.752 0.695 0.730
## g =~
## ssgs (.10.) 4.345 0.040 107.951 0.000 4.266 4.424 4.345 0.870
## ssar (.11.) 5.943 0.054 110.494 0.000 5.837 6.048 5.943 0.817
## sswk (.12.) 7.278 0.061 118.453 0.000 7.157 7.398 7.278 0.923
## sspc (.13.) 2.973 0.028 104.508 0.000 2.918 3.029 2.973 0.868
## ssno (.14.) 0.653 0.010 68.290 0.000 0.634 0.671 0.653 0.689
## sscs (.15.) 0.597 0.010 59.700 0.000 0.578 0.617 0.597 0.627
## ssasi (.16.) 3.154 0.048 65.999 0.000 3.060 3.248 3.154 0.696
## ssmk (.17.) 4.933 0.050 98.416 0.000 4.835 5.031 4.933 0.780
## ssmc (.18.) 3.567 0.046 78.333 0.000 3.477 3.656 3.567 0.732
## ssei (.19.) 3.174 0.034 92.640 0.000 3.107 3.242 3.174 0.779
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 16.662 0.125 133.514 0.000 16.418 16.907 16.662 2.291
## .ssmk (.41.) 12.960 0.101 127.704 0.000 12.761 13.159 12.960 2.050
## .ssmc (.42.) 11.750 0.074 158.780 0.000 11.605 11.895 11.750 2.411
## .ssgs (.43.) 14.731 0.077 192.004 0.000 14.581 14.882 14.731 2.951
## .ssasi (.44.) 10.986 0.064 171.959 0.000 10.861 11.111 10.986 2.425
## .ssei (.45.) 9.611 0.061 158.116 0.000 9.491 9.730 9.611 2.359
## .ssno (.46.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.319
## .sscs (.47.) 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.399
## .sswk (.48.) 25.646 0.123 209.237 0.000 25.406 25.887 25.646 3.253
## .sspc 11.115 0.053 210.841 0.000 11.011 11.218 11.115 3.245
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 1.360 1.082 1.257 0.209 -0.760 3.480 1.360 0.026
## .ssmk 10.913 0.418 26.090 0.000 10.093 11.733 10.913 0.273
## .ssmc 7.492 0.232 32.236 0.000 7.036 7.947 7.492 0.315
## .ssgs 5.396 0.164 32.879 0.000 5.074 5.718 5.396 0.217
## .ssasi 4.411 0.212 20.795 0.000 3.996 4.827 4.411 0.215
## .ssei 4.607 0.140 32.881 0.000 4.332 4.881 4.607 0.278
## .ssno 0.355 0.013 26.364 0.000 0.328 0.381 0.355 0.395
## .sscs 0.067 0.043 1.568 0.117 -0.017 0.150 0.067 0.074
## .sswk 9.193 0.384 23.923 0.000 8.440 9.946 9.193 0.148
## .sspc 2.887 0.093 30.936 0.000 2.704 3.070 2.887 0.246
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 4.028 0.133 30.257 0.000 3.767 4.288 4.028 0.553
## ssmk (.p2.) 2.173 0.090 24.095 0.000 1.996 2.350 2.173 0.340
## ssmc (.p3.) 0.818 0.058 14.193 0.000 0.705 0.931 0.818 0.167
## electronic =~
## ssgs (.p4.) 0.801 0.028 28.735 0.000 0.746 0.856 0.801 0.161
## ssasi (.p5.) 2.483 0.047 52.923 0.000 2.391 2.575 2.483 0.505
## ssmc (.p6.) 1.694 0.042 40.491 0.000 1.612 1.776 1.694 0.345
## ssei (.p7.) 1.385 0.031 45.143 0.000 1.325 1.445 1.385 0.350
## speed =~
## ssno (.p8.) 0.342 0.014 24.309 0.000 0.314 0.370 0.342 0.361
## sscs (.p9.) 0.695 0.029 24.262 0.000 0.639 0.752 0.695 0.752
## g =~
## ssgs (.10.) 4.345 0.040 107.951 0.000 4.266 4.424 4.345 0.872
## ssar (.11.) 5.943 0.054 110.494 0.000 5.837 6.048 5.943 0.816
## sswk (.12.) 7.278 0.061 118.453 0.000 7.157 7.398 7.278 0.924
## sspc (.13.) 2.973 0.028 104.508 0.000 2.918 3.029 2.973 0.858
## ssno (.14.) 0.653 0.010 68.290 0.000 0.634 0.671 0.653 0.688
## sscs (.15.) 0.597 0.010 59.700 0.000 0.578 0.617 0.597 0.646
## ssasi (.16.) 3.154 0.048 65.999 0.000 3.060 3.248 3.154 0.641
## ssmk (.17.) 4.933 0.050 98.416 0.000 4.835 5.031 4.933 0.772
## ssmc (.18.) 3.567 0.046 78.333 0.000 3.477 3.656 3.567 0.727
## ssei (.19.) 3.174 0.034 92.640 0.000 3.107 3.242 3.174 0.803
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 16.662 0.125 133.514 0.000 16.418 16.907 16.662 2.288
## .ssmk (.41.) 12.960 0.101 127.704 0.000 12.761 13.159 12.960 2.028
## .ssmc (.42.) 11.750 0.074 158.780 0.000 11.605 11.895 11.750 2.395
## .ssgs (.43.) 14.731 0.077 192.004 0.000 14.581 14.882 14.731 2.957
## .ssasi (.44.) 10.986 0.064 171.959 0.000 10.861 11.111 10.986 2.234
## .ssei (.45.) 9.611 0.061 158.116 0.000 9.491 9.730 9.611 2.431
## .ssno (.46.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.318
## .sscs (.47.) 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.411
## .sswk (.48.) 25.646 0.123 209.237 0.000 25.406 25.887 25.646 3.255
## .sspc 10.477 0.061 170.436 0.000 10.357 10.598 10.477 3.024
## math 0.469 0.031 15.012 0.000 0.408 0.531 0.469 0.469
## elctrnc 2.174 0.053 41.316 0.000 2.070 2.277 2.174 2.174
## speed -0.581 0.037 -15.524 0.000 -0.654 -0.508 -0.581 -0.581
## g -0.030 0.025 -1.211 0.226 -0.078 0.018 -0.030 -0.030
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar 1.486 1.102 1.348 0.178 -0.674 3.645 1.486 0.028
## .ssmk 11.796 0.447 26.409 0.000 10.921 12.672 11.796 0.289
## .ssmc 7.804 0.240 32.531 0.000 7.333 8.274 7.804 0.324
## .ssgs 5.299 0.160 33.051 0.000 4.985 5.613 5.299 0.213
## .ssasi 8.070 0.322 25.024 0.000 7.438 8.702 8.070 0.334
## .ssei 3.638 0.127 28.584 0.000 3.389 3.888 3.638 0.233
## .ssno 0.357 0.013 27.507 0.000 0.332 0.383 0.357 0.397
## .sscs 0.014 0.038 0.362 0.718 -0.061 0.089 0.014 0.016
## .sswk 9.124 0.389 23.451 0.000 8.361 9.887 9.124 0.147
## .sspc 3.163 0.107 29.683 0.000 2.954 3.372 3.163 0.263
## math 1.000 1.000 1.000 1.000 1.000
## electronic 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
latent2<-cfa(bf.lv, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
fitMeasures(latent2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr aic bic
## 2824.141 74.000 0.000 0.971 0.083 0.054 504378.649 504787.346
Mc(latent2)
## [1] 0.8816529
summary(latent2, standardized=T, ci=T) # +.024
## lavaan 0.6-18 ended normally after 119 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 84
## Number of equality constraints 28
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2824.141 1691.338
## Degrees of freedom 74 74
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.670
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1129.701 676.562
## 0 1694.439 1014.776
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.955 0.130 30.536 0.000 3.702 4.209 3.955 0.568
## ssmk (.p2.) 2.178 0.091 23.965 0.000 1.999 2.356 2.178 0.358
## ssmc (.p3.) 0.842 0.058 14.532 0.000 0.729 0.956 0.842 0.188
## electronic =~
## ssgs (.p4.) 0.529 0.025 21.107 0.000 0.480 0.578 0.529 0.113
## ssasi (.p5.) 1.682 0.060 27.805 0.000 1.563 1.800 1.682 0.423
## ssmc (.p6.) 1.140 0.044 26.138 0.000 1.055 1.226 1.140 0.255
## ssei (.p7.) 0.915 0.035 26.299 0.000 0.847 0.984 0.915 0.247
## speed =~
## ssno (.p8.) 0.343 0.014 24.630 0.000 0.316 0.370 0.343 0.372
## sscs (.p9.) 0.691 0.028 24.530 0.000 0.636 0.747 0.691 0.744
## g =~
## ssgs (.10.) 4.019 0.048 83.553 0.000 3.925 4.113 4.019 0.861
## ssar (.11.) 5.580 0.067 83.802 0.000 5.449 5.710 5.580 0.801
## sswk (.12.) 6.805 0.080 85.513 0.000 6.649 6.961 6.805 0.911
## sspc (.13.) 2.787 0.035 79.652 0.000 2.718 2.855 2.787 0.851
## ssno (.14.) 0.612 0.010 59.733 0.000 0.592 0.632 0.612 0.665
## sscs (.15.) 0.560 0.010 53.608 0.000 0.540 0.580 0.560 0.603
## ssasi (.16.) 2.801 0.045 61.797 0.000 2.713 2.890 2.801 0.705
## ssmk (.17.) 4.638 0.060 77.488 0.000 4.521 4.755 4.638 0.762
## ssmc (.18.) 3.223 0.045 70.912 0.000 3.134 3.312 3.223 0.721
## ssei (.19.) 2.876 0.036 79.570 0.000 2.806 2.947 2.876 0.776
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 16.669 0.125 132.917 0.000 16.423 16.915 16.669 2.393
## .ssmk (.41.) 12.949 0.101 127.808 0.000 12.750 13.148 12.949 2.127
## .ssmc (.42.) 11.738 0.074 159.222 0.000 11.593 11.882 11.738 2.626
## .ssgs (.43.) 14.740 0.077 192.253 0.000 14.590 14.891 14.740 3.157
## .ssasi (.44.) 10.977 0.064 172.503 0.000 10.852 11.102 10.977 2.762
## .ssei (.45.) 9.637 0.060 159.629 0.000 9.519 9.756 9.637 2.600
## .ssno (.46.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.328
## .sscs (.47.) 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.409
## .sswk (.48.) 25.630 0.123 208.869 0.000 25.389 25.870 25.630 3.430
## .sspc 11.115 0.053 210.841 0.000 11.011 11.218 11.115 3.394
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.742 1.036 1.682 0.093 -0.288 3.772 1.742 0.036
## .ssmk 10.819 0.413 26.199 0.000 10.010 11.629 10.819 0.292
## .ssmc 7.576 0.226 33.592 0.000 7.134 8.018 7.576 0.379
## .ssgs 5.366 0.164 32.746 0.000 5.045 5.687 5.366 0.246
## .ssasi 5.124 0.205 24.978 0.000 4.722 5.526 5.124 0.324
## .ssei 4.627 0.135 34.259 0.000 4.363 4.892 4.627 0.337
## .ssno 0.356 0.013 26.536 0.000 0.329 0.382 0.356 0.419
## .sscs 0.071 0.042 1.702 0.089 -0.011 0.153 0.071 0.082
## .sswk 9.542 0.384 24.833 0.000 8.789 10.296 9.542 0.171
## .sspc 2.957 0.094 31.301 0.000 2.772 3.142 2.957 0.276
## electronic 1.000 1.000 1.000 1.000 1.000
## g 1.000 1.000 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.955 0.130 30.536 0.000 3.702 4.209 3.955 0.522
## ssmk (.p2.) 2.178 0.091 23.965 0.000 1.999 2.356 2.178 0.330
## ssmc (.p3.) 0.842 0.058 14.532 0.000 0.729 0.956 0.842 0.165
## electronic =~
## ssgs (.p4.) 0.529 0.025 21.107 0.000 0.480 0.578 1.019 0.196
## ssasi (.p5.) 1.682 0.060 27.805 0.000 1.563 1.800 3.241 0.618
## ssmc (.p6.) 1.140 0.044 26.138 0.000 1.055 1.226 2.198 0.430
## ssei (.p7.) 0.915 0.035 26.299 0.000 0.847 0.984 1.764 0.425
## speed =~
## ssno (.p8.) 0.343 0.014 24.630 0.000 0.316 0.370 0.343 0.352
## sscs (.p9.) 0.691 0.028 24.530 0.000 0.636 0.747 0.691 0.730
## g =~
## ssgs (.10.) 4.019 0.048 83.553 0.000 3.925 4.113 4.534 0.874
## ssar (.11.) 5.580 0.067 83.802 0.000 5.449 5.710 6.294 0.831
## sswk (.12.) 6.805 0.080 85.513 0.000 6.649 6.961 7.676 0.930
## sspc (.13.) 2.787 0.035 79.652 0.000 2.718 2.855 3.144 0.872
## ssno (.14.) 0.612 0.010 59.733 0.000 0.592 0.632 0.691 0.709
## sscs (.15.) 0.560 0.010 53.608 0.000 0.540 0.580 0.632 0.667
## ssasi (.16.) 2.801 0.045 61.797 0.000 2.713 2.890 3.160 0.602
## ssmk (.17.) 4.638 0.060 77.488 0.000 4.521 4.755 5.232 0.792
## ssmc (.18.) 3.223 0.045 70.912 0.000 3.134 3.312 3.636 0.711
## ssei (.19.) 2.876 0.036 79.570 0.000 2.806 2.947 3.245 0.781
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
## g 0.000 0.000 0.000 0.000 0.000
## speed ~~
## g 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.40.) 16.669 0.125 132.917 0.000 16.423 16.915 16.669 2.202
## .ssmk (.41.) 12.949 0.101 127.808 0.000 12.750 13.148 12.949 1.960
## .ssmc (.42.) 11.738 0.074 159.222 0.000 11.593 11.882 11.738 2.296
## .ssgs (.43.) 14.740 0.077 192.253 0.000 14.590 14.891 14.740 2.841
## .ssasi (.44.) 10.977 0.064 172.503 0.000 10.852 11.102 10.977 2.092
## .ssei (.45.) 9.637 0.060 159.629 0.000 9.519 9.756 9.637 2.321
## .ssno (.46.) 0.302 0.015 19.589 0.000 0.272 0.332 0.302 0.310
## .sscs (.47.) 0.380 0.016 24.148 0.000 0.349 0.411 0.380 0.401
## .sswk (.48.) 25.630 0.123 208.869 0.000 25.389 25.870 25.630 3.104
## .sspc 10.464 0.062 169.555 0.000 10.343 10.585 10.464 2.904
## math 0.467 0.032 14.683 0.000 0.405 0.529 0.467 0.467
## elctrnc 3.218 0.127 25.278 0.000 2.969 3.468 1.670 1.670
## speed -0.588 0.038 -15.663 0.000 -0.662 -0.515 -0.588 -0.588
## g -0.027 0.026 -1.023 0.306 -0.079 0.025 -0.024 -0.024
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 2.056 1.063 1.933 0.053 -0.028 4.139 2.056 0.036
## .ssmk 11.536 0.450 25.623 0.000 10.653 12.418 11.536 0.264
## .ssmc 7.383 0.238 31.064 0.000 6.917 7.849 7.383 0.282
## .ssgs 5.328 0.160 33.209 0.000 5.014 5.643 5.328 0.198
## .ssasi 7.045 0.319 22.055 0.000 6.419 7.671 7.045 0.256
## .ssei 3.603 0.128 28.166 0.000 3.352 3.853 3.603 0.209
## .ssno 0.354 0.013 27.332 0.000 0.328 0.379 0.354 0.373
## .sscs 0.019 0.037 0.512 0.609 -0.054 0.093 0.019 0.021
## .sswk 9.231 0.410 22.510 0.000 8.427 10.034 9.231 0.135
## .sspc 3.099 0.104 29.698 0.000 2.895 3.304 3.099 0.239
## electronic 3.714 0.299 12.412 0.000 3.127 4.300 1.000 1.000
## g 1.273 0.037 34.834 0.000 1.201 1.344 1.000 1.000
standardizedSolution(latent2) # get the correct SEs for standardized solution
## lhs op rhs group label est.std se z pvalue ci.lower ci.upper
## 1 math =~ ssar 1 .p1. 0.568 0.019 29.736 0.000 0.530 0.605
## 2 math =~ ssmk 1 .p2. 0.358 0.015 24.365 0.000 0.329 0.386
## 3 math =~ ssmc 1 .p3. 0.188 0.013 14.683 0.000 0.163 0.214
## 4 electronic =~ ssgs 1 .p4. 0.113 0.005 20.753 0.000 0.103 0.124
## 5 electronic =~ ssasi 1 .p5. 0.423 0.014 30.367 0.000 0.396 0.450
## 6 electronic =~ ssmc 1 .p6. 0.255 0.010 26.646 0.000 0.236 0.274
## 7 electronic =~ ssei 1 .p7. 0.247 0.009 26.845 0.000 0.229 0.265
## 8 speed =~ ssno 1 .p8. 0.372 0.015 24.057 0.000 0.342 0.403
## 9 speed =~ sscs 1 .p9. 0.744 0.031 23.632 0.000 0.683 0.806
## 10 g =~ ssgs 1 .p10. 0.861 0.005 190.332 0.000 0.852 0.870
## 11 g =~ ssar 1 .p11. 0.801 0.005 149.959 0.000 0.791 0.811
## 12 g =~ sswk 1 .p12. 0.911 0.004 227.966 0.000 0.903 0.918
## 13 g =~ sspc 1 .p13. 0.851 0.005 176.878 0.000 0.842 0.860
## 14 g =~ ssno 1 .p14. 0.665 0.008 81.374 0.000 0.649 0.681
## 15 g =~ sscs 1 .p15. 0.603 0.009 64.618 0.000 0.585 0.621
## 16 g =~ ssasi 1 .p16. 0.705 0.007 95.222 0.000 0.690 0.719
## 17 g =~ ssmk 1 .p17. 0.762 0.006 123.613 0.000 0.750 0.774
## 18 g =~ ssmc 1 .p18. 0.721 0.006 111.330 0.000 0.708 0.734
## 19 g =~ ssei 1 .p19. 0.776 0.006 138.889 0.000 0.765 0.787
## 20 math ~~ math 1 1.000 0.000 NA NA 1.000 1.000
## 21 speed ~~ speed 1 1.000 0.000 NA NA 1.000 1.000
## 22 ssar ~~ ssar 1 0.036 0.021 1.687 0.092 -0.006 0.078
## 23 ssmk ~~ ssmk 1 0.292 0.011 25.557 0.000 0.269 0.314
## 24 ssmc ~~ ssmc 1 0.379 0.010 39.103 0.000 0.360 0.398
## 25 ssgs ~~ ssgs 1 0.246 0.008 32.453 0.000 0.231 0.261
## 26 ssasi ~~ ssasi 1 0.324 0.012 26.018 0.000 0.300 0.349
## 27 ssei ~~ ssei 1 0.337 0.009 39.284 0.000 0.320 0.354
## 28 ssno ~~ ssno 1 0.419 0.014 29.223 0.000 0.391 0.447
## 29 sscs ~~ sscs 1 0.082 0.048 1.718 0.086 -0.012 0.176
## 30 sswk ~~ sswk 1 0.171 0.007 23.488 0.000 0.157 0.185
## 31 sspc ~~ sspc 1 0.276 0.008 33.675 0.000 0.260 0.292
## 32 electronic ~~ electronic 1 1.000 0.000 NA NA 1.000 1.000
## 33 g ~~ g 1 1.000 0.000 NA NA 1.000 1.000
## 34 math ~~ electronic 1 0.000 0.000 NA NA 0.000 0.000
## 35 math ~~ speed 1 0.000 0.000 NA NA 0.000 0.000
## 36 math ~~ g 1 0.000 0.000 NA NA 0.000 0.000
## 37 electronic ~~ speed 1 0.000 0.000 NA NA 0.000 0.000
## 38 electronic ~~ g 1 0.000 0.000 NA NA 0.000 0.000
## 39 speed ~~ g 1 0.000 0.000 NA NA 0.000 0.000
## 40 ssar ~1 1 .p40. 2.393 0.024 99.731 0.000 2.346 2.440
## 41 ssmk ~1 1 .p41. 2.127 0.021 99.926 0.000 2.085 2.168
## 42 ssmc ~1 1 .p42. 2.626 0.027 97.497 0.000 2.574 2.679
## 43 ssgs ~1 1 .p43. 3.157 0.034 93.757 0.000 3.091 3.223
## 44 ssasi ~1 1 .p44. 2.762 0.031 88.267 0.000 2.700 2.823
## 45 ssei ~1 1 .p45. 2.600 0.027 96.135 0.000 2.547 2.653
## 46 ssno ~1 1 .p46. 0.328 0.018 18.543 0.000 0.293 0.363
## 47 sscs ~1 1 .p47. 0.409 0.018 22.285 0.000 0.373 0.445
## 48 sswk ~1 1 .p48. 3.430 0.042 81.844 0.000 3.347 3.512
## 49 sspc ~1 1 3.394 0.045 75.635 0.000 3.306 3.482
## 50 math ~1 1 0.000 0.000 NA NA 0.000 0.000
## 51 electronic ~1 1 0.000 0.000 NA NA 0.000 0.000
## 52 speed ~1 1 0.000 0.000 NA NA 0.000 0.000
## 53 g ~1 1 0.000 0.000 NA NA 0.000 0.000
## 54 math =~ ssar 2 .p1. 0.522 0.018 29.517 0.000 0.488 0.557
## 55 math =~ ssmk 2 .p2. 0.330 0.014 23.940 0.000 0.303 0.357
## 56 math =~ ssmc 2 .p3. 0.165 0.011 14.529 0.000 0.142 0.187
## 57 electronic =~ ssgs 2 .p4. 0.196 0.007 27.470 0.000 0.182 0.210
## 58 electronic =~ ssasi 2 .p5. 0.618 0.012 53.498 0.000 0.595 0.640
## 59 electronic =~ ssmc 2 .p6. 0.430 0.011 38.791 0.000 0.408 0.452
## 60 electronic =~ ssei 2 .p7. 0.425 0.010 42.412 0.000 0.405 0.444
## 61 speed =~ ssno 2 .p8. 0.352 0.015 24.277 0.000 0.324 0.381
## 62 speed =~ sscs 2 .p9. 0.730 0.029 24.910 0.000 0.673 0.788
## 63 g =~ ssgs 2 .p10. 0.874 0.004 219.822 0.000 0.866 0.882
## 64 g =~ ssar 2 .p11. 0.831 0.005 169.296 0.000 0.822 0.841
## 65 g =~ sswk 2 .p12. 0.930 0.003 285.658 0.000 0.923 0.936
## 66 g =~ sspc 2 .p13. 0.872 0.004 197.896 0.000 0.864 0.881
## 67 g =~ ssno 2 .p14. 0.709 0.008 92.277 0.000 0.694 0.724
## 68 g =~ sscs 2 .p15. 0.667 0.009 72.335 0.000 0.649 0.685
## 69 g =~ ssasi 2 .p16. 0.602 0.010 60.449 0.000 0.583 0.622
## 70 g =~ ssmk 2 .p17. 0.792 0.005 150.052 0.000 0.782 0.802
## 71 g =~ ssmc 2 .p18. 0.711 0.008 90.024 0.000 0.696 0.727
## 72 g =~ ssei 2 .p19. 0.781 0.007 115.644 0.000 0.768 0.795
## 73 math ~~ math 2 1.000 0.000 NA NA 1.000 1.000
## 74 speed ~~ speed 2 1.000 0.000 NA NA 1.000 1.000
## 75 ssar ~~ ssar 2 0.036 0.018 1.939 0.052 0.000 0.072
## 76 ssmk ~~ ssmk 2 0.264 0.010 25.263 0.000 0.244 0.285
## 77 ssmc ~~ ssmc 2 0.282 0.009 31.445 0.000 0.265 0.300
## 78 ssgs ~~ ssgs 2 0.198 0.006 31.474 0.000 0.186 0.210
## 79 ssasi ~~ ssasi 2 0.256 0.011 23.517 0.000 0.235 0.277
## 80 ssei ~~ ssei 2 0.209 0.007 28.611 0.000 0.195 0.223
## 81 ssno ~~ ssno 2 0.373 0.013 28.553 0.000 0.347 0.399
## 82 sscs ~~ sscs 2 0.021 0.042 0.512 0.609 -0.060 0.103
## 83 sswk ~~ sswk 2 0.135 0.006 22.374 0.000 0.124 0.147
## 84 sspc ~~ sspc 2 0.239 0.008 31.032 0.000 0.224 0.254
## 85 electronic ~~ electronic 2 1.000 0.000 NA NA 1.000 1.000
## 86 g ~~ g 2 1.000 0.000 NA NA 1.000 1.000
## 87 math ~~ electronic 2 0.000 0.000 NA NA 0.000 0.000
## 88 math ~~ speed 2 0.000 0.000 NA NA 0.000 0.000
## 89 math ~~ g 2 0.000 0.000 NA NA 0.000 0.000
## 90 electronic ~~ speed 2 0.000 0.000 NA NA 0.000 0.000
## [ reached 'max' / getOption("max.print") -- omitted 16 rows ]
tests<-lavTestLRT(configural, metric, scalar2, latent2)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 243.034287 147.862335 4.595506
dfd=tests[2:4,"Df diff"]
dfd
## [1] 15 5 2
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-5449+ 5469 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.05277615 0.07235309 0.01541982
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04704534 0.05871794
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.06256854 0.08262127
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] NA 0.03451587
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 0.792 0.022 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 0.981 0.112 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
## 0.900 0.771 0.001 0.000 0.000 0.000
tests<-lavTestLRT(configural, metric, scalar2, latent)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 243.0343 147.8623 477.3863
dfd=tests[2:4,"Df diff"]
dfd
## [1] 15 5 4
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-5449+ 5469 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.05277615 0.07235309 0.14725196
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.06256854 0.08262127
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.1362503 0.1585489
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 0.981 0.112 0.000
round(pvals(T=Td[3],df=dfd[3],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1 1 1 1 1 1
tests<-lavTestLRT(configural, metric, scalar2, strict)
Td=tests[2:4,"Chisq diff"]
Td
## [1] 243.03429 147.86233 57.06334
dfd=tests[2:4,"Df diff"]
dfd
## [1] 15 5 10
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-5449+ 5469 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.05277615 0.07235309 0.02936463
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04704534 0.05871794
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.06256854 0.08262127
RMSEA.CI(T=Td[3],df=dfd[3],N=N,G=2)
## [1] 0.02222937 0.03698418
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 0.792 0.022 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 0.981 0.112 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
tests<-lavTestLRT(configural, metric, scalar)
Td=tests[2:3,"Chisq diff"]
Td
## [1] 243.0343 338.0623
dfd=tests[2:3,"Df diff"]
dfd
## [1] 15 6
lambda<-Td-dfd
ld<-lambda/dfd
G<-2 # number of groups
N<-5449+ 5469 # sample size
RMSEAD<-sqrt((ld)*G/(N-G))
RMSEAD
## [1] 0.05277615 0.10069720
RMSEA.CI(T=Td[1],df=dfd[1],N=N,G=2)
## [1] 0.04704534 0.05871794
RMSEA.CI(T=Td[2],df=dfd[2],N=N,G=2)
## [1] 0.09171843 0.10996486
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 0.792 0.022 0.000 0.000
round(pvals(T=Td[2],df=dfd[2],N=N,G=2),3)
## RMSEA>0 RMSEA>.01 RMSEA>.05 RMSEA>.06 RMSEA>.08 RMSEA>.10
## 1.000 1.000 1.000 1.000 1.000 0.561
bf.age<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
g ~ age
'
bf.ageq<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
g ~ c(b,b)*age
'
bf.age2<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
g ~ age + age2
'
bf.age2q<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
g ~ c(b,b)*age+c(c,c)*age2
'
sem.age<-sem(bf.age, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
fitMeasures(sem.age, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 3704.105 92.000 0.000 0.962 0.085 0.055 0.350 504021.166 504444.460
Mc(sem.age)
## [1] 0.8475251
summary(sem.age, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 115 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 28
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3704.105 2208.880
## Degrees of freedom 92 92
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.677
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1619.995 966.056
## 0 2084.110 1242.823
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.963 0.130 30.601 0.000 3.710 4.217 3.963 0.569
## ssmk (.p2.) 2.195 0.092 23.973 0.000 2.016 2.375 2.195 0.361
## ssmc (.p3.) 0.846 0.058 14.541 0.000 0.732 0.960 0.846 0.189
## electronic =~
## ssgs (.p4.) 0.525 0.025 20.971 0.000 0.476 0.574 0.525 0.112
## ssasi (.p5.) 1.673 0.061 27.584 0.000 1.554 1.792 1.673 0.421
## ssmc (.p6.) 1.136 0.044 25.937 0.000 1.050 1.222 1.136 0.254
## ssei (.p7.) 0.910 0.035 26.120 0.000 0.842 0.978 0.910 0.245
## speed =~
## ssno (.p8.) 0.343 0.014 24.667 0.000 0.316 0.371 0.343 0.373
## sscs (.p9.) 0.691 0.028 24.578 0.000 0.636 0.747 0.691 0.744
## g =~
## ssgs (.10.) 3.967 0.049 80.895 0.000 3.871 4.063 4.019 0.861
## ssar (.11.) 5.503 0.068 80.556 0.000 5.369 5.637 5.575 0.800
## sswk (.12.) 6.722 0.081 82.888 0.000 6.563 6.881 6.809 0.911
## sspc (.13.) 2.749 0.036 76.577 0.000 2.679 2.820 2.785 0.850
## ssno (.14.) 0.604 0.010 58.039 0.000 0.583 0.624 0.612 0.664
## sscs (.15.) 0.553 0.010 52.856 0.000 0.532 0.573 0.560 0.603
## ssasi (.16.) 2.773 0.045 61.711 0.000 2.685 2.861 2.809 0.706
## ssmk (.17.) 4.567 0.062 73.775 0.000 4.446 4.688 4.627 0.760
## ssmc (.18.) 3.182 0.046 69.758 0.000 3.093 3.272 3.224 0.721
## ssei (.19.) 2.844 0.036 79.271 0.000 2.774 2.914 2.881 0.777
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.070 0.008 9.206 0.000 0.055 0.085 0.069 0.160
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.39.) 16.759 0.126 132.867 0.000 16.511 17.006 16.759 2.406
## .ssmk (.40.) 13.020 0.102 127.106 0.000 12.819 13.220 13.020 2.138
## .ssmc (.41.) 11.787 0.074 159.394 0.000 11.642 11.932 11.787 2.637
## .ssgs (.42.) 14.806 0.076 193.804 0.000 14.656 14.956 14.806 3.171
## .ssasi (.43.) 11.022 0.063 174.219 0.000 10.898 11.146 11.022 2.771
## .ssei (.44.) 9.684 0.060 162.118 0.000 9.567 9.801 9.684 2.612
## .ssno (.45.) 0.312 0.015 20.143 0.000 0.282 0.342 0.312 0.339
## .sscs (.46.) 0.389 0.016 24.824 0.000 0.358 0.420 0.389 0.419
## .sswk (.47.) 25.736 0.121 211.858 0.000 25.498 25.974 25.736 3.445
## .sspc 11.159 0.053 212.148 0.000 11.056 11.262 11.159 3.408
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.740 1.039 1.675 0.094 -0.296 3.775 1.740 0.036
## .ssmk 10.851 0.417 25.999 0.000 10.033 11.669 10.851 0.293
## .ssmc 7.580 0.226 33.576 0.000 7.138 8.023 7.580 0.379
## .ssgs 5.370 0.164 32.777 0.000 5.049 5.691 5.370 0.246
## .ssasi 5.132 0.205 25.025 0.000 4.730 5.534 5.132 0.324
## .ssei 4.616 0.135 34.271 0.000 4.352 4.880 4.616 0.336
## .ssno 0.356 0.013 26.553 0.000 0.330 0.383 0.356 0.420
## .sscs 0.071 0.042 1.697 0.090 -0.011 0.153 0.071 0.082
## .sswk 9.455 0.383 24.701 0.000 8.705 10.205 9.455 0.169
## .sspc 2.966 0.095 31.303 0.000 2.781 3.152 2.966 0.277
## electronic 1.000 1.000 1.000 1.000 1.000
## .g 1.000 1.000 1.000 0.974 0.974
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.963 0.130 30.601 0.000 3.710 4.217 3.963 0.524
## ssmk (.p2.) 2.195 0.092 23.973 0.000 2.016 2.375 2.195 0.332
## ssmc (.p3.) 0.846 0.058 14.541 0.000 0.732 0.960 0.846 0.165
## electronic =~
## ssgs (.p4.) 0.525 0.025 20.971 0.000 0.476 0.574 1.011 0.195
## ssasi (.p5.) 1.673 0.061 27.584 0.000 1.554 1.792 3.224 0.615
## ssmc (.p6.) 1.136 0.044 25.937 0.000 1.050 1.222 2.189 0.428
## ssei (.p7.) 0.910 0.035 26.120 0.000 0.842 0.978 1.753 0.422
## speed =~
## ssno (.p8.) 0.343 0.014 24.667 0.000 0.316 0.371 0.343 0.353
## sscs (.p9.) 0.691 0.028 24.578 0.000 0.636 0.747 0.691 0.730
## g =~
## ssgs (.10.) 3.967 0.049 80.895 0.000 3.871 4.063 4.535 0.874
## ssar (.11.) 5.503 0.068 80.556 0.000 5.369 5.637 6.290 0.831
## sswk (.12.) 6.722 0.081 82.888 0.000 6.563 6.881 7.683 0.930
## sspc (.13.) 2.749 0.036 76.577 0.000 2.679 2.820 3.142 0.872
## ssno (.14.) 0.604 0.010 58.039 0.000 0.583 0.624 0.690 0.709
## sscs (.15.) 0.553 0.010 52.856 0.000 0.532 0.573 0.632 0.667
## ssasi (.16.) 2.773 0.045 61.711 0.000 2.685 2.861 3.169 0.604
## ssmk (.17.) 4.567 0.062 73.775 0.000 4.446 4.688 5.220 0.790
## ssmc (.18.) 3.182 0.046 69.758 0.000 3.093 3.272 3.637 0.712
## ssei (.19.) 2.844 0.036 79.271 0.000 2.774 2.914 3.251 0.783
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.101 0.008 12.221 0.000 0.085 0.117 0.088 0.208
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.39.) 16.759 0.126 132.867 0.000 16.511 17.006 16.759 2.214
## .ssmk (.40.) 13.020 0.102 127.106 0.000 12.819 13.220 13.020 1.971
## .ssmc (.41.) 11.787 0.074 159.394 0.000 11.642 11.932 11.787 2.306
## .ssgs (.42.) 14.806 0.076 193.804 0.000 14.656 14.956 14.806 2.853
## .ssasi (.43.) 11.022 0.063 174.219 0.000 10.898 11.146 11.022 2.102
## .ssei (.44.) 9.684 0.060 162.118 0.000 9.567 9.801 9.684 2.332
## .ssno (.45.) 0.312 0.015 20.143 0.000 0.282 0.342 0.312 0.320
## .sscs (.46.) 0.389 0.016 24.824 0.000 0.358 0.420 0.389 0.411
## .sswk (.47.) 25.736 0.121 211.858 0.000 25.498 25.974 25.736 3.117
## .sspc 10.507 0.061 171.395 0.000 10.387 10.627 10.507 2.916
## math 0.465 0.032 14.635 0.000 0.403 0.527 0.465 0.465
## elctrnc 3.234 0.129 25.113 0.000 2.981 3.486 1.678 1.678
## speed -0.589 0.038 -15.686 0.000 -0.662 -0.515 -0.589 -0.589
## .g -0.017 0.026 -0.658 0.511 -0.069 0.034 -0.015 -0.015
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 2.036 1.066 1.909 0.056 -0.054 4.126 2.036 0.036
## .ssmk 11.571 0.454 25.468 0.000 10.681 12.462 11.571 0.265
## .ssmc 7.384 0.238 31.039 0.000 6.918 7.851 7.384 0.283
## .ssgs 5.349 0.161 33.213 0.000 5.033 5.664 5.349 0.199
## .ssasi 7.066 0.319 22.123 0.000 6.440 7.691 7.066 0.257
## .ssei 3.597 0.128 28.187 0.000 3.347 3.847 3.597 0.209
## .ssno 0.354 0.013 27.356 0.000 0.329 0.380 0.354 0.374
## .sscs 0.019 0.037 0.509 0.610 -0.054 0.092 0.019 0.021
## .sswk 9.165 0.408 22.477 0.000 8.366 9.965 9.165 0.134
## .sspc 3.109 0.105 29.712 0.000 2.904 3.314 3.109 0.239
## electronic 3.712 0.301 12.322 0.000 3.122 4.303 1.000 1.000
## .g 1.250 0.038 33.261 0.000 1.176 1.323 0.957 0.957
sem.ageq<-sem(bf.ageq, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
fitMeasures(sem.ageq, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 3716.215 93.000 0.000 0.962 0.084 0.059 0.351 504031.276 504447.272
Mc(sem.ageq)
## [1] 0.8470939
summary(sem.ageq, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 117 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 86
## Number of equality constraints 29
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3716.215 2218.478
## Degrees of freedom 93 93
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.675
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1624.482 969.771
## 0 2091.733 1248.707
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.963 0.129 30.637 0.000 3.710 4.217 3.963 0.567
## ssmk (.p2.) 2.197 0.092 24.002 0.000 2.018 2.376 2.197 0.359
## ssmc (.p3.) 0.847 0.058 14.560 0.000 0.733 0.960 0.847 0.189
## electronic =~
## ssgs (.p4.) 0.524 0.025 20.972 0.000 0.475 0.574 0.524 0.112
## ssasi (.p5.) 1.672 0.061 27.560 0.000 1.553 1.791 1.672 0.419
## ssmc (.p6.) 1.135 0.044 25.911 0.000 1.049 1.221 1.135 0.253
## ssei (.p7.) 0.909 0.035 26.104 0.000 0.841 0.978 0.909 0.244
## speed =~
## ssno (.p8.) 0.343 0.014 24.667 0.000 0.316 0.371 0.343 0.372
## sscs (.p9.) 0.692 0.028 24.576 0.000 0.636 0.747 0.692 0.743
## g =~
## ssgs (.10.) 3.969 0.049 80.579 0.000 3.873 4.066 4.044 0.862
## ssar (.11.) 5.506 0.069 80.145 0.000 5.371 5.641 5.610 0.802
## sswk (.12.) 6.727 0.081 82.582 0.000 6.567 6.886 6.854 0.913
## sspc (.13.) 2.751 0.036 76.281 0.000 2.680 2.822 2.803 0.852
## ssno (.14.) 0.604 0.010 57.877 0.000 0.584 0.624 0.615 0.666
## sscs (.15.) 0.553 0.010 52.735 0.000 0.533 0.574 0.564 0.606
## ssasi (.16.) 2.773 0.045 61.563 0.000 2.685 2.861 2.825 0.708
## ssmk (.17.) 4.569 0.062 73.466 0.000 4.447 4.691 4.656 0.762
## ssmc (.18.) 3.183 0.046 69.547 0.000 3.093 3.273 3.243 0.723
## ssei (.19.) 2.845 0.036 79.043 0.000 2.775 2.916 2.899 0.779
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (b) 0.084 0.006 14.806 0.000 0.073 0.095 0.083 0.192
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.39.) 16.777 0.126 133.244 0.000 16.530 17.024 16.777 2.399
## .ssmk (.40.) 13.034 0.103 126.857 0.000 12.833 13.236 13.034 2.133
## .ssmc (.41.) 11.797 0.074 159.644 0.000 11.653 11.942 11.797 2.631
## .ssgs (.42.) 14.819 0.076 194.472 0.000 14.670 14.968 14.819 3.159
## .ssasi (.43.) 11.032 0.063 175.172 0.000 10.908 11.155 11.032 2.766
## .ssei (.44.) 9.694 0.059 163.316 0.000 9.577 9.810 9.694 2.605
## .ssno (.45.) 0.314 0.015 20.301 0.000 0.284 0.344 0.314 0.340
## .sscs (.46.) 0.391 0.016 25.042 0.000 0.360 0.421 0.391 0.420
## .sswk (.47.) 25.759 0.121 213.151 0.000 25.522 25.996 25.759 3.430
## .sspc 11.168 0.053 212.692 0.000 11.065 11.271 11.168 3.395
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.744 1.037 1.681 0.093 -0.289 3.777 1.744 0.036
## .ssmk 10.855 0.418 25.987 0.000 10.037 11.674 10.855 0.291
## .ssmc 7.581 0.226 33.574 0.000 7.139 8.024 7.581 0.377
## .ssgs 5.371 0.164 32.778 0.000 5.050 5.692 5.371 0.244
## .ssasi 5.133 0.205 25.034 0.000 4.731 5.535 5.133 0.323
## .ssei 4.614 0.135 34.280 0.000 4.350 4.878 4.614 0.333
## .ssno 0.356 0.013 26.553 0.000 0.330 0.383 0.356 0.418
## .sscs 0.071 0.042 1.692 0.091 -0.011 0.152 0.071 0.082
## .sswk 9.435 0.382 24.710 0.000 8.687 10.184 9.435 0.167
## .sspc 2.968 0.095 31.302 0.000 2.782 3.154 2.968 0.274
## electronic 1.000 1.000 1.000 1.000 1.000
## .g 1.000 1.000 1.000 0.963 0.963
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.963 0.129 30.637 0.000 3.710 4.217 3.963 0.526
## ssmk (.p2.) 2.197 0.092 24.002 0.000 2.018 2.376 2.197 0.334
## ssmc (.p3.) 0.847 0.058 14.560 0.000 0.733 0.960 0.847 0.166
## electronic =~
## ssgs (.p4.) 0.524 0.025 20.972 0.000 0.475 0.574 1.012 0.196
## ssasi (.p5.) 1.672 0.061 27.560 0.000 1.553 1.791 3.227 0.617
## ssmc (.p6.) 1.135 0.044 25.911 0.000 1.049 1.221 2.191 0.430
## ssei (.p7.) 0.909 0.035 26.104 0.000 0.841 0.978 1.755 0.424
## speed =~
## ssno (.p8.) 0.343 0.014 24.667 0.000 0.316 0.371 0.343 0.354
## sscs (.p9.) 0.692 0.028 24.576 0.000 0.636 0.747 0.692 0.732
## g =~
## ssgs (.10.) 3.969 0.049 80.579 0.000 3.873 4.066 4.507 0.872
## ssar (.11.) 5.506 0.069 80.145 0.000 5.371 5.641 6.252 0.829
## sswk (.12.) 6.727 0.081 82.582 0.000 6.567 6.886 7.637 0.930
## sspc (.13.) 2.751 0.036 76.281 0.000 2.680 2.822 3.123 0.871
## ssno (.14.) 0.604 0.010 57.877 0.000 0.584 0.624 0.686 0.706
## sscs (.15.) 0.553 0.010 52.735 0.000 0.533 0.574 0.628 0.665
## ssasi (.16.) 2.773 0.045 61.563 0.000 2.685 2.861 3.148 0.602
## ssmk (.17.) 4.569 0.062 73.466 0.000 4.447 4.691 5.188 0.788
## ssmc (.18.) 3.183 0.046 69.547 0.000 3.093 3.273 3.614 0.709
## ssei (.19.) 2.845 0.036 79.043 0.000 2.775 2.916 3.230 0.781
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (b) 0.084 0.006 14.806 0.000 0.073 0.095 0.074 0.175
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.39.) 16.777 0.126 133.244 0.000 16.530 17.024 16.777 2.225
## .ssmk (.40.) 13.034 0.103 126.857 0.000 12.833 13.236 13.034 1.981
## .ssmc (.41.) 11.797 0.074 159.644 0.000 11.653 11.942 11.797 2.315
## .ssgs (.42.) 14.819 0.076 194.472 0.000 14.670 14.968 14.819 2.869
## .ssasi (.43.) 11.032 0.063 175.172 0.000 10.908 11.155 11.032 2.108
## .ssei (.44.) 9.694 0.059 163.316 0.000 9.577 9.810 9.694 2.343
## .ssno (.45.) 0.314 0.015 20.301 0.000 0.284 0.344 0.314 0.323
## .sscs (.46.) 0.391 0.016 25.042 0.000 0.360 0.421 0.391 0.414
## .sswk (.47.) 25.759 0.121 213.151 0.000 25.522 25.996 25.759 3.135
## .sspc 10.516 0.061 172.301 0.000 10.396 10.636 10.516 2.932
## math 0.465 0.032 14.633 0.000 0.403 0.527 0.465 0.465
## elctrnc 3.236 0.129 25.092 0.000 2.983 3.489 1.677 1.677
## speed -0.589 0.038 -15.683 0.000 -0.662 -0.515 -0.589 -0.589
## .g -0.025 0.026 -0.952 0.341 -0.076 0.026 -0.022 -0.022
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 2.051 1.065 1.926 0.054 -0.036 4.138 2.051 0.036
## .ssmk 11.562 0.454 25.454 0.000 10.672 12.452 11.562 0.267
## .ssmc 7.383 0.238 31.037 0.000 6.917 7.850 7.383 0.284
## .ssgs 5.346 0.161 33.220 0.000 5.030 5.661 5.346 0.200
## .ssasi 7.061 0.319 22.108 0.000 6.435 7.687 7.061 0.258
## .ssei 3.598 0.128 28.185 0.000 3.348 3.848 3.598 0.210
## .ssno 0.354 0.013 27.352 0.000 0.329 0.380 0.354 0.376
## .sscs 0.019 0.037 0.509 0.611 -0.054 0.092 0.019 0.021
## .sswk 9.167 0.408 22.467 0.000 8.367 9.966 9.167 0.136
## .sspc 3.107 0.105 29.707 0.000 2.902 3.312 3.107 0.242
## electronic 3.725 0.302 12.320 0.000 3.132 4.318 1.000 1.000
## .g 1.250 0.038 33.227 0.000 1.176 1.323 0.969 0.969
sem.age2<-sem(bf.age2, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
fitMeasures(sem.age2, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 3764.394 110.000 0.000 0.962 0.078 0.052 0.356 504014.524 504452.414
Mc(sem.age2)
## [1] 0.8458851
summary(sem.age2, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 120 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 88
## Number of equality constraints 28
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3764.394 2237.430
## Degrees of freedom 110 110
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.682
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1644.854 977.646
## 0 2119.539 1259.783
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.963 0.130 30.603 0.000 3.710 4.217 3.963 0.569
## ssmk (.p2.) 2.195 0.092 23.971 0.000 2.016 2.375 2.195 0.361
## ssmc (.p3.) 0.846 0.058 14.542 0.000 0.732 0.960 0.846 0.189
## electronic =~
## ssgs (.p4.) 0.525 0.025 20.968 0.000 0.476 0.574 0.525 0.112
## ssasi (.p5.) 1.673 0.061 27.583 0.000 1.554 1.792 1.673 0.421
## ssmc (.p6.) 1.136 0.044 25.936 0.000 1.050 1.222 1.136 0.254
## ssei (.p7.) 0.910 0.035 26.119 0.000 0.842 0.978 0.910 0.245
## speed =~
## ssno (.p8.) 0.343 0.014 24.667 0.000 0.316 0.371 0.343 0.373
## sscs (.p9.) 0.691 0.028 24.579 0.000 0.636 0.747 0.691 0.744
## g =~
## ssgs (.10.) 3.967 0.049 80.896 0.000 3.871 4.063 4.019 0.861
## ssar (.11.) 5.503 0.068 80.556 0.000 5.369 5.637 5.575 0.800
## sswk (.12.) 6.722 0.081 82.888 0.000 6.563 6.880 6.809 0.911
## sspc (.13.) 2.749 0.036 76.575 0.000 2.679 2.820 2.785 0.850
## ssno (.14.) 0.604 0.010 58.042 0.000 0.583 0.624 0.612 0.664
## sscs (.15.) 0.553 0.010 52.857 0.000 0.532 0.573 0.560 0.603
## ssasi (.16.) 2.773 0.045 61.711 0.000 2.685 2.861 2.809 0.706
## ssmk (.17.) 4.567 0.062 73.774 0.000 4.446 4.688 4.627 0.760
## ssmc (.18.) 3.182 0.046 69.754 0.000 3.093 3.272 3.224 0.721
## ssei (.19.) 2.844 0.036 79.273 0.000 2.774 2.914 2.881 0.777
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.070 0.008 9.042 0.000 0.055 0.085 0.069 0.160
## age2 -0.000 0.003 -0.072 0.942 -0.007 0.006 -0.000 -0.001
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.42.) 16.766 0.159 105.297 0.000 16.454 17.078 16.766 2.407
## .ssmk (.43.) 13.025 0.130 100.474 0.000 12.771 13.280 13.025 2.139
## .ssmc (.44.) 11.791 0.094 125.497 0.000 11.607 11.975 11.791 2.638
## .ssgs (.45.) 14.811 0.103 144.180 0.000 14.610 15.013 14.811 3.172
## .ssasi (.46.) 11.026 0.081 135.888 0.000 10.867 11.185 11.026 2.772
## .ssei (.47.) 9.688 0.079 123.274 0.000 9.534 9.842 9.688 2.613
## .ssno (.48.) 0.313 0.019 16.681 0.000 0.276 0.349 0.313 0.340
## .sscs (.49.) 0.390 0.019 20.929 0.000 0.353 0.426 0.390 0.420
## .sswk (.50.) 25.745 0.170 151.505 0.000 25.412 26.078 25.745 3.446
## .sspc 11.163 0.071 156.336 0.000 11.023 11.303 11.163 3.409
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.740 1.039 1.676 0.094 -0.295 3.776 1.740 0.036
## .ssmk 10.851 0.417 25.999 0.000 10.033 11.669 10.851 0.293
## .ssmc 7.580 0.226 33.575 0.000 7.138 8.023 7.580 0.379
## .ssgs 5.370 0.164 32.779 0.000 5.049 5.691 5.370 0.246
## .ssasi 5.132 0.205 25.026 0.000 4.730 5.534 5.132 0.324
## .ssei 4.616 0.135 34.270 0.000 4.352 4.880 4.616 0.336
## .ssno 0.356 0.013 26.553 0.000 0.330 0.383 0.356 0.420
## .sscs 0.071 0.042 1.698 0.090 -0.011 0.153 0.071 0.082
## .sswk 9.455 0.383 24.701 0.000 8.705 10.205 9.455 0.169
## .sspc 2.966 0.095 31.303 0.000 2.781 3.152 2.966 0.277
## electronic 1.000 1.000 1.000 1.000 1.000
## .g 1.000 1.000 1.000 0.974 0.974
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.963 0.130 30.603 0.000 3.710 4.217 3.963 0.524
## ssmk (.p2.) 2.195 0.092 23.971 0.000 2.016 2.375 2.195 0.332
## ssmc (.p3.) 0.846 0.058 14.542 0.000 0.732 0.960 0.846 0.165
## electronic =~
## ssgs (.p4.) 0.525 0.025 20.968 0.000 0.476 0.574 1.011 0.195
## ssasi (.p5.) 1.673 0.061 27.583 0.000 1.554 1.792 3.223 0.615
## ssmc (.p6.) 1.136 0.044 25.936 0.000 1.050 1.222 2.189 0.428
## ssei (.p7.) 0.910 0.035 26.119 0.000 0.842 0.978 1.753 0.422
## speed =~
## ssno (.p8.) 0.343 0.014 24.667 0.000 0.316 0.371 0.343 0.353
## sscs (.p9.) 0.691 0.028 24.579 0.000 0.636 0.747 0.691 0.730
## g =~
## ssgs (.10.) 3.967 0.049 80.896 0.000 3.871 4.063 4.535 0.874
## ssar (.11.) 5.503 0.068 80.556 0.000 5.369 5.637 6.290 0.831
## sswk (.12.) 6.722 0.081 82.888 0.000 6.563 6.880 7.683 0.930
## sspc (.13.) 2.749 0.036 76.575 0.000 2.679 2.820 3.142 0.872
## ssno (.14.) 0.604 0.010 58.042 0.000 0.583 0.624 0.690 0.709
## sscs (.15.) 0.553 0.010 52.857 0.000 0.532 0.573 0.632 0.667
## ssasi (.16.) 2.773 0.045 61.711 0.000 2.685 2.861 3.170 0.604
## ssmk (.17.) 4.567 0.062 73.774 0.000 4.446 4.688 5.220 0.790
## ssmc (.18.) 3.182 0.046 69.754 0.000 3.093 3.272 3.637 0.712
## ssei (.19.) 2.844 0.036 79.273 0.000 2.774 2.914 3.251 0.783
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age 0.096 0.009 11.272 0.000 0.080 0.113 0.084 0.199
## age2 -0.010 0.004 -2.618 0.009 -0.017 -0.003 -0.009 -0.045
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.42.) 16.766 0.159 105.297 0.000 16.454 17.078 16.766 2.215
## .ssmk (.43.) 13.025 0.130 100.474 0.000 12.771 13.280 13.025 1.972
## .ssmc (.44.) 11.791 0.094 125.497 0.000 11.607 11.975 11.791 2.307
## .ssgs (.45.) 14.811 0.103 144.180 0.000 14.610 15.013 14.811 2.854
## .ssasi (.46.) 11.026 0.081 135.888 0.000 10.867 11.185 11.026 2.103
## .ssei (.47.) 9.688 0.079 123.274 0.000 9.534 9.842 9.688 2.333
## .ssno (.48.) 0.313 0.019 16.681 0.000 0.276 0.349 0.313 0.321
## .sscs (.49.) 0.390 0.019 20.929 0.000 0.353 0.426 0.390 0.412
## .sswk (.50.) 25.745 0.170 151.505 0.000 25.412 26.078 25.745 3.118
## .sspc 10.510 0.078 134.535 0.000 10.357 10.663 10.510 2.917
## math 0.465 0.032 14.633 0.000 0.403 0.527 0.465 0.465
## elctrnc 3.234 0.129 25.113 0.000 2.981 3.486 1.679 1.679
## speed -0.589 0.038 -15.686 0.000 -0.662 -0.515 -0.589 -0.589
## .g 0.036 0.037 0.975 0.329 -0.037 0.109 0.032 0.032
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 2.038 1.066 1.911 0.056 -0.052 4.128 2.038 0.036
## .ssmk 11.570 0.454 25.467 0.000 10.680 12.460 11.570 0.265
## .ssmc 7.384 0.238 31.036 0.000 6.918 7.851 7.384 0.283
## .ssgs 5.350 0.161 33.207 0.000 5.034 5.666 5.350 0.199
## .ssasi 7.067 0.319 22.127 0.000 6.441 7.693 7.067 0.257
## .ssei 3.597 0.128 28.186 0.000 3.347 3.847 3.597 0.209
## .ssno 0.354 0.013 27.359 0.000 0.329 0.380 0.354 0.374
## .sscs 0.019 0.037 0.510 0.610 -0.054 0.092 0.019 0.021
## .sswk 9.166 0.407 22.516 0.000 8.368 9.964 9.166 0.134
## .sspc 3.108 0.105 29.705 0.000 2.903 3.314 3.108 0.239
## electronic 3.711 0.301 12.320 0.000 3.120 4.301 1.000 1.000
## .g 1.247 0.037 33.334 0.000 1.174 1.321 0.955 0.955
sem.age2q<-sem(bf.age2q, data=dgroup, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
fitMeasures(sem.age2q, c("chisq", "df", "pvalue", "cfi", "rmsea", "srmr", "ecvi", "aic", "bic"))
## chisq df pvalue cfi rmsea srmr ecvi aic bic
## 3781.967 112.000 0.000 0.962 0.077 0.057 0.357 504028.097 504451.390
Mc(sem.age2q)
## [1] 0.845282
summary(sem.age2q, standardized=T, ci=T)
## lavaan 0.6-18 ended normally after 123 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 88
## Number of equality constraints 30
##
## Number of observations per group:
## 1 5449
## 0 5469
## Sampling weights variable sweight
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3781.967 2252.421
## Degrees of freedom 112 112
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.679
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 1651.781 983.749
## 0 2130.186 1268.672
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.963 0.129 30.639 0.000 3.710 4.217 3.963 0.566
## ssmk (.p2.) 2.197 0.092 24.002 0.000 2.018 2.377 2.197 0.359
## ssmc (.p3.) 0.847 0.058 14.560 0.000 0.733 0.961 0.847 0.189
## electronic =~
## ssgs (.p4.) 0.524 0.025 20.968 0.000 0.475 0.573 0.524 0.112
## ssasi (.p5.) 1.672 0.061 27.558 0.000 1.553 1.791 1.672 0.419
## ssmc (.p6.) 1.135 0.044 25.910 0.000 1.049 1.221 1.135 0.253
## ssei (.p7.) 0.909 0.035 26.101 0.000 0.841 0.978 0.909 0.244
## speed =~
## ssno (.p8.) 0.343 0.014 24.666 0.000 0.316 0.371 0.343 0.372
## sscs (.p9.) 0.692 0.028 24.577 0.000 0.636 0.747 0.692 0.743
## g =~
## ssgs (.10.) 3.970 0.049 80.585 0.000 3.874 4.067 4.046 0.862
## ssar (.11.) 5.507 0.069 80.168 0.000 5.373 5.642 5.613 0.802
## sswk (.12.) 6.728 0.081 82.587 0.000 6.569 6.888 6.857 0.913
## sspc (.13.) 2.752 0.036 76.244 0.000 2.681 2.822 2.804 0.852
## ssno (.14.) 0.604 0.010 57.887 0.000 0.584 0.625 0.616 0.667
## sscs (.15.) 0.553 0.010 52.751 0.000 0.533 0.574 0.564 0.606
## ssasi (.16.) 2.774 0.045 61.531 0.000 2.686 2.862 2.827 0.709
## ssmk (.17.) 4.570 0.062 73.474 0.000 4.448 4.692 4.658 0.762
## ssmc (.18.) 3.184 0.046 69.523 0.000 3.094 3.274 3.245 0.723
## ssei (.19.) 2.846 0.036 79.017 0.000 2.775 2.916 2.900 0.779
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (b) 0.082 0.006 14.057 0.000 0.070 0.093 0.080 0.186
## age2 (c) -0.005 0.003 -1.867 0.062 -0.010 0.000 -0.005 -0.024
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.42.) 16.917 0.145 116.595 0.000 16.632 17.201 16.917 2.418
## .ssmk (.43.) 13.150 0.119 110.945 0.000 12.918 13.382 13.150 2.151
## .ssmc (.44.) 11.878 0.085 139.056 0.000 11.711 12.045 11.878 2.648
## .ssgs (.45.) 14.920 0.092 162.905 0.000 14.740 15.099 14.920 3.179
## .ssasi (.46.) 11.102 0.074 150.996 0.000 10.958 11.246 11.102 2.782
## .ssei (.47.) 9.766 0.071 138.316 0.000 9.627 9.904 9.766 2.624
## .ssno (.48.) 0.329 0.017 19.070 0.000 0.295 0.363 0.329 0.356
## .sscs (.49.) 0.405 0.017 23.455 0.000 0.371 0.439 0.405 0.435
## .sswk (.50.) 25.929 0.149 174.347 0.000 25.638 26.221 25.929 3.451
## .sspc 11.238 0.063 177.992 0.000 11.114 11.362 11.238 3.415
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 1.743 1.037 1.681 0.093 -0.290 3.777 1.743 0.036
## .ssmk 10.856 0.418 25.983 0.000 10.037 11.675 10.856 0.290
## .ssmc 7.581 0.226 33.574 0.000 7.139 8.024 7.581 0.377
## .ssgs 5.371 0.164 32.774 0.000 5.050 5.692 5.371 0.244
## .ssasi 5.133 0.205 25.035 0.000 4.731 5.535 5.133 0.322
## .ssei 4.615 0.135 34.284 0.000 4.351 4.879 4.615 0.333
## .ssno 0.356 0.013 26.556 0.000 0.330 0.383 0.356 0.418
## .sscs 0.071 0.042 1.693 0.091 -0.011 0.152 0.071 0.081
## .sswk 9.434 0.382 24.700 0.000 8.685 10.183 9.434 0.167
## .sspc 2.968 0.095 31.307 0.000 2.782 3.154 2.968 0.274
## electronic 1.000 1.000 1.000 1.000 1.000
## .g 1.000 1.000 1.000 0.963 0.963
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math =~
## ssar (.p1.) 3.963 0.129 30.639 0.000 3.710 4.217 3.963 0.526
## ssmk (.p2.) 2.197 0.092 24.002 0.000 2.018 2.377 2.197 0.334
## ssmc (.p3.) 0.847 0.058 14.560 0.000 0.733 0.961 0.847 0.166
## electronic =~
## ssgs (.p4.) 0.524 0.025 20.968 0.000 0.475 0.573 1.012 0.196
## ssasi (.p5.) 1.672 0.061 27.558 0.000 1.553 1.791 3.227 0.617
## ssmc (.p6.) 1.135 0.044 25.910 0.000 1.049 1.221 2.191 0.430
## ssei (.p7.) 0.909 0.035 26.101 0.000 0.841 0.978 1.755 0.424
## speed =~
## ssno (.p8.) 0.343 0.014 24.666 0.000 0.316 0.371 0.343 0.354
## sscs (.p9.) 0.692 0.028 24.577 0.000 0.636 0.747 0.692 0.732
## g =~
## ssgs (.10.) 3.970 0.049 80.585 0.000 3.874 4.067 4.505 0.872
## ssar (.11.) 5.507 0.069 80.168 0.000 5.373 5.642 6.248 0.829
## sswk (.12.) 6.728 0.081 82.587 0.000 6.569 6.888 7.633 0.930
## sspc (.13.) 2.752 0.036 76.244 0.000 2.681 2.822 3.122 0.871
## ssno (.14.) 0.604 0.010 57.887 0.000 0.584 0.625 0.685 0.706
## sscs (.15.) 0.553 0.010 52.751 0.000 0.533 0.574 0.628 0.665
## ssasi (.16.) 2.774 0.045 61.531 0.000 2.686 2.862 3.147 0.601
## ssmk (.17.) 4.570 0.062 73.474 0.000 4.448 4.692 5.185 0.788
## ssmc (.18.) 3.184 0.046 69.523 0.000 3.094 3.274 3.612 0.709
## ssei (.19.) 2.846 0.036 79.017 0.000 2.775 2.916 3.229 0.781
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## g ~
## age (b) 0.082 0.006 14.057 0.000 0.070 0.093 0.072 0.170
## age2 (c) -0.005 0.003 -1.867 0.062 -0.010 0.000 -0.004 -0.022
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math ~~
## electronic 0.000 0.000 0.000 0.000 0.000
## speed 0.000 0.000 0.000 0.000 0.000
## electronic ~~
## speed 0.000 0.000 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## .ssar (.42.) 16.917 0.145 116.595 0.000 16.632 17.201 16.917 2.245
## .ssmk (.43.) 13.150 0.119 110.945 0.000 12.918 13.382 13.150 1.999
## .ssmc (.44.) 11.878 0.085 139.056 0.000 11.711 12.045 11.878 2.332
## .ssgs (.45.) 14.920 0.092 162.905 0.000 14.740 15.099 14.920 2.889
## .ssasi (.46.) 11.102 0.074 150.996 0.000 10.958 11.246 11.102 2.122
## .ssei (.47.) 9.766 0.071 138.316 0.000 9.627 9.904 9.766 2.361
## .ssno (.48.) 0.329 0.017 19.070 0.000 0.295 0.363 0.329 0.339
## .sscs (.49.) 0.405 0.017 23.455 0.000 0.371 0.439 0.405 0.429
## .sswk (.50.) 25.929 0.149 174.347 0.000 25.638 26.221 25.929 3.158
## .sspc 10.586 0.070 151.290 0.000 10.449 10.723 10.586 2.953
## math 0.465 0.032 14.633 0.000 0.403 0.527 0.465 0.465
## elctrnc 3.236 0.129 25.089 0.000 2.984 3.489 1.677 1.677
## speed -0.589 0.038 -15.683 0.000 -0.662 -0.515 -0.589 -0.589
## .g -0.024 0.026 -0.921 0.357 -0.075 0.027 -0.021 -0.021
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
## math 1.000 1.000 1.000 1.000 1.000
## speed 1.000 1.000 1.000 1.000 1.000
## .ssar 2.051 1.065 1.926 0.054 -0.036 4.138 2.051 0.036
## .ssmk 11.562 0.454 25.453 0.000 10.671 12.452 11.562 0.267
## .ssmc 7.383 0.238 31.036 0.000 6.917 7.849 7.383 0.285
## .ssgs 5.346 0.161 33.217 0.000 5.031 5.661 5.346 0.201
## .ssasi 7.062 0.319 22.110 0.000 6.436 7.688 7.062 0.258
## .ssei 3.598 0.128 28.184 0.000 3.348 3.848 3.598 0.210
## .ssno 0.354 0.013 27.354 0.000 0.329 0.380 0.354 0.376
## .sscs 0.019 0.037 0.510 0.610 -0.054 0.092 0.019 0.021
## .sswk 9.167 0.408 22.485 0.000 8.368 9.966 9.167 0.136
## .sspc 3.107 0.105 29.703 0.000 2.902 3.312 3.107 0.242
## electronic 3.725 0.302 12.319 0.000 3.132 4.318 1.000 1.000
## .g 1.247 0.037 33.280 0.000 1.174 1.321 0.969 0.969
# CROSS VALIDATION
set.seed(123) # For reproducibility, set seed if needed
split_indices <- sample(1:nrow(dgroup), size = nrow(dgroup) / 2)
dhalf1 <- dgroup[split_indices, ]
dhalf2 <- dgroup[-split_indices, ]
# ALL RACE GROUP
# CORRELATED FACTOR MODEL
cf.model<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
'
cf.lv<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
verbal~~1*verbal
math~~1*math
speed~~1*speed
'
baseline<-cfa(cf.model, data=dhalf1, meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1329.668 27.000 0.000 0.972 0.888 0.094 0.030 256144.510 256395.501
configural<-cfa(cf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 928.923 54.000 0.000 0.981 0.923 0.077 0.020 251886.082 252388.063
metric<-cfa(cf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1017.633 62.000 0.000 0.980 0.916 0.075 0.026 251958.791 252407.933
scalar<-cfa(cf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1799.083 68.000 0.000 0.963 0.853 0.097 0.046 252728.241 253137.752
scalar2<-cfa(cf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("ssei~1", "sswk~1", "sscs~1"))
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1164.491 65.000 0.000 0.977 0.904 0.079 0.029 252099.650 252528.976
strict<-cfa(cf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("ssei~1", "sswk~1", "sscs~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1356.579 75.000 0.000 0.973 0.889 0.079 0.037 252271.737 252635.013
cf.cov<-cfa(cf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("ssei~1", "sswk~1", "sscs~1"))
fitMeasures(cf.cov, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1376.539 71.000 0.000 0.972 0.887 0.082 0.105 252299.697 252689.393
cf.vcov<-cfa(cf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances", "lv.variances"), group.partial=c("ssei~1", "sswk~1", "sscs~1"))
fitMeasures(cf.vcov, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1644.278 75.000 0.000 0.966 0.866 0.088 0.126 252559.436 252922.712
cf.cov2<-cfa(cf.lv, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("ssei~1", "sswk~1", "sscs~1"))
fitMeasures(cf.cov2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1409.731 74.000 0.000 0.971 0.885 0.081 0.104 252326.889 252696.770
baseline<-cfa(cf.model, data=dhalf2, meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1363.763 27.000 0.000 0.972 0.885 0.095 0.029 256072.369 256323.360
configural<-cfa(cf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 913.551 54.000 0.000 0.982 0.924 0.076 0.019 251490.562 251992.544
metric<-cfa(cf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1057.927 62.000 0.000 0.979 0.913 0.077 0.028 251618.938 252068.079
scalar<-cfa(cf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1883.486 68.000 0.000 0.962 0.847 0.099 0.047 252432.497 252842.008
scalar2<-cfa(cf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("ssei~1", "sswk~1", "sscs~1"))
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1164.009 65.000 0.000 0.977 0.904 0.079 0.030 251719.020 252148.346
strict<-cfa(cf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("ssei~1", "sswk~1", "sscs~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1338.495 75.000 0.000 0.973 0.891 0.079 0.039 251873.506 252236.782
cf.cov<-cfa(cf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("ssei~1", "sswk~1", "sscs~1"))
fitMeasures(cf.cov, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1357.242 71.000 0.000 0.973 0.889 0.081 0.113 251900.253 252289.949
cf.vcov<-cfa(cf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances", "lv.variances"), group.partial=c("ssei~1", "sswk~1", "sscs~1"))
fitMeasures(cf.vcov, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1554.958 75.000 0.000 0.969 0.873 0.085 0.128 252089.969 252453.245
cf.cov2<-cfa(cf.lv, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.covariances"), group.partial=c("ssei~1", "sswk~1", "sscs~1"))
fitMeasures(cf.cov2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1377.823 74.000 0.000 0.973 0.887 0.080 0.112 251914.834 252284.715
# HIGH ORDER FACTOR
hof.model<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
'
hof.lv<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
'
hof.weak<-'
verbal =~ ssgs + sswk + sspc
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ verbal + math + electronic + speed
verbal~~1*verbal
math~~1*math
speed~~1*speed
math~0*1
'
baseline<-cfa(hof.model, data=dhalf1, meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1949.011 29.000 0.000 0.959 0.839 0.110 0.044 256759.854 256997.635
configural<-cfa(hof.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1348.802 58.000 0.000 0.972 0.888 0.090 0.028 252297.961 252773.522
metric<-cfa(hof.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1569.506 69.000 0.000 0.968 0.872 0.089 0.054 252496.664 252899.571
metric2<-cfa(hof.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"), group.partial=c("g=~electronic"))
fitMeasures(metric2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1430.656 68.000 0.000 0.971 0.883 0.086 0.033 252359.815 252769.326
scalar<-cfa(hof.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= 6.945956e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 2193.549 73.000 0.000 0.955 0.823 0.103 0.052 253112.708 253489.194
scalar2<-cfa(hof.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~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 (= 5.418587e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1575.855 70.000 0.000 0.968 0.871 0.089 0.036 252501.014 252897.315
strict<-cfa(hof.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~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 (= 9.336031e-14) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1769.107 80.000 0.000 0.964 0.857 0.088 0.043 252674.265 253004.516
latent<-cfa(hof.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~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 (= 8.308293e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(latent, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1786.424 75.000 0.000 0.963 0.855 0.091 0.059 252701.582 253064.859
latent2<-cfa(hof.lv, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~1"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= 4.373136e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(latent2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1585.016 73.000 0.000 0.968 0.871 0.087 0.036 252504.174 252880.660
weak<-cfa(hof.weak, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~1"))
fitMeasures(weak, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1585.016 74.000 0.000 0.968 0.871 0.086 0.036 252502.174 252872.055
baseline<-cfa(hof.model, data=dhalf2, meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1931.559 29.000 0.000 0.960 0.840 0.110 0.043 256636.166 256873.946
configural<-cfa(hof.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight")
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1283.972 58.000 0.000 0.974 0.894 0.088 0.026 251852.983 252328.545
metric<-cfa(hof.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1528.494 69.000 0.000 0.969 0.875 0.088 0.052 252075.505 252478.411
metric2<-cfa(hof.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings"), group.partial=c("g=~electronic"))
fitMeasures(metric2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1418.607 68.000 0.000 0.972 0.884 0.085 0.034 251967.618 252377.129
scalar<-cfa(hof.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= 3.311871e-14) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 2225.474 73.000 0.000 0.955 0.821 0.104 0.052 252764.485 253140.971
scalar2<-cfa(hof.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~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 (= 5.913766e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1522.811 70.000 0.000 0.969 0.875 0.087 0.036 252067.822 252464.123
strict<-cfa(hof.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~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 (= 1.505217e-13) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1696.723 80.000 0.000 0.966 0.862 0.086 0.044 252221.734 252551.985
latent<-cfa(hof.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~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 (= 8.925379e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(latent, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1672.176 75.000 0.000 0.966 0.864 0.088 0.070 252207.187 252570.463
latent2<-cfa(hof.lv, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~1"))
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= 4.522227e-15) is close to zero. This may be a
## symptom that the model is not identified.
fitMeasures(latent2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1530.611 73.000 0.000 0.969 0.875 0.086 0.036 252069.622 252446.109
weak<-cfa(hof.weak, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", group.equal=c("loadings", "intercepts"), group.partial=c("g=~electronic", "ssei~1", "sswk~1", "sscs~1"))
fitMeasures(weak, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1530.611 74.000 0.000 0.969 0.875 0.085 0.036 252067.622 252437.504
# BIFACTOR
bf.model<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
'
bf.lv<-'
math =~ ssar + ssmk + ssmc
electronic =~ ssgs + ssasi + ssmc + ssei
speed =~ ssno + sscs
g =~ ssgs + ssar + sswk + sspc + ssno + sscs + ssasi + ssmk + ssmc + ssei
math~~1*math
speed~~1*speed
'
baseline<-cfa(bf.model, data=dhalf1, meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= -2.225220e+00) is smaller than zero. This may
## be a symptom that the model is not identified.
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1539.467 26.000 0.000 0.968 0.871 0.103 0.037 256356.309 256613.905
configural<-cfa(bf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= -2.137122e-07) is smaller than zero. This may
## be a symptom that the model is not identified.
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1185.160 52.000 0.000 0.976 0.901 0.089 0.027 252146.318 252661.510
metric<-cfa(bf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1364.976 67.000 0.000 0.972 0.888 0.084 0.056 252296.135 252712.251
scalar<-cfa(bf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"))
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1601.017 73.000 0.000 0.967 0.869 0.088 0.056 252520.175 252896.662
scalar2<-cfa(bf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1473.100 72.000 0.000 0.970 0.880 0.084 0.056 252394.259 252777.350
strict<-cfa(bf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("sspc~1"))
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1531.117 82.000 0.000 0.969 0.876 0.080 0.055 252432.275 252749.316
latent<-cfa(bf.model, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("sspc~1"))
fitMeasures(latent, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1865.455 76.000 0.000 0.962 0.849 0.093 0.128 252778.613 253135.284
latent2<-cfa(bf.lv, data=dhalf1, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
fitMeasures(latent2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1475.255 74.000 0.000 0.970 0.880 0.083 0.056 252392.413 252762.295
baseline<-cfa(bf.model, data=dhalf2, meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
fitMeasures(baseline, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1597.891 26.000 0.000 0.967 0.866 0.105 0.037 256308.497 256566.093
configural<-cfa(bf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not appear to be
## positive definite! The smallest eigenvalue (= -5.641903e-08) is smaller than zero. This may
## be a symptom that the model is not identified.
fitMeasures(configural, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1186.628 52.000 0.000 0.976 0.901 0.089 0.025 251767.639 252282.830
metric<-cfa(bf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings"))
fitMeasures(metric, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1374.446 67.000 0.000 0.973 0.887 0.085 0.053 251925.457 252341.573
scalar<-cfa(bf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(scalar, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1583.172 73.000 0.000 0.968 0.871 0.087 0.054 252122.182 252498.669
scalar2<-cfa(bf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(scalar2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1453.871 72.000 0.000 0.971 0.881 0.084 0.053 251994.882 252377.973
strict<-cfa(bf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts", "residuals"), group.partial=c("sspc~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(strict, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1513.006 82.000 0.000 0.970 0.877 0.080 0.054 252034.016 252351.057
latent<-cfa(bf.model, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts", "lv.variances"), group.partial=c("sspc~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(latent, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1770.962 76.000 0.000 0.964 0.856 0.090 0.130 252303.973 252660.644
latent2<-cfa(bf.lv, data=dhalf2, group="sex", meanstructure=T, std.lv=T, sampling.weights="sweight", orthogonal=T, group.equal=c("loadings", "intercepts"), group.partial=c("sspc~1"))
## Warning: lavaan->lav_object_post_check():
## some estimated ov variances are negative
fitMeasures(latent2, c("chisq", "df", "pvalue", "cfi", "mfi", "rmsea", "srmr", "aic", "bic"))
## chisq df pvalue cfi mfi rmsea srmr aic bic
## 1460.573 74.000 0.000 0.971 0.881 0.083 0.053 251997.583 252367.465
# Testing for selection effect?
dw<- filter(dk, bhw==3)
dw$sexage<- dw$sex*dw$age
dw$sexmomeduc<- dw$sex*dw$momeduc
dw$agemomeduc<- dw$age*dw$momeduc
dw$momeduc<- dw$momeduc-12
dw$sexagemomeduc<- dw$sex*dw$age*dw$momeduc
dw$sexdadeduc<- dw$sex*dw$dadeduc
dw$agedadeduc<- dw$age*dw$dadeduc
dw$dadeduc<- dw$dadeduc-12
dw$sexagedadeduc<- dw$sex*dw$age*dw$dadeduc
fit<-lm(efa ~ sex + age + momeduc + sexage + sexmomeduc + agemomeduc + sexagemomeduc, data=dw, weights=dw$sweight)
summary(fit)
##
## Call:
## lm(formula = efa ~ sex + age + momeduc + sexage + sexmomeduc +
## agemomeduc + sexagemomeduc, data = dw, weights = dw$sweight)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -34510 -3707 101 3758 21584
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 110.22225 0.20392 540.528 < 2e-16 ***
## sex -1.82848 1.46399 -1.249 0.211725
## age 2.54360 0.44001 5.781 7.82e-09 ***
## momeduc 2.19427 0.08457 25.945 < 2e-16 ***
## sexage -0.43873 0.12384 -3.543 0.000399 ***
## sexmomeduc -0.20146 0.11910 -1.692 0.090788 .
## agemomeduc -0.09825 0.03579 -2.746 0.006060 **
## sexagemomeduc 0.09477 0.04987 1.900 0.057459 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6777 on 5817 degrees of freedom
## (254 observations deleted due to missingness)
## Multiple R-squared: 0.2425, Adjusted R-squared: 0.2416
## F-statistic: 266 on 7 and 5817 DF, p-value: < 2.2e-16
fit<-lm(efa ~ sex + age + dadeduc + sexage + sexdadeduc + agedadeduc + sexagedadeduc, data=dw, weights=dw$sweight)
summary(fit)
##
## Call:
## lm(formula = efa ~ sex + age + dadeduc + sexage + sexdadeduc +
## agedadeduc + sexagedadeduc, data = dw, weights = dw$sweight)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -36242 -3645 177 3715 23290
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 109.95878 0.20588 534.085 < 2e-16 ***
## sex -2.28037 1.12728 -2.023 0.0431 *
## age 2.22715 0.32498 6.853 7.99e-12 ***
## dadeduc 1.57443 0.06064 25.963 < 2e-16 ***
## sexage -0.55490 0.12544 -4.424 9.88e-06 ***
## sexdadeduc -0.17177 0.08791 -1.954 0.0508 .
## agedadeduc -0.06181 0.02540 -2.433 0.0150 *
## sexagedadeduc 0.03844 0.03701 1.039 0.2990
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6732 on 5620 degrees of freedom
## (456 observations deleted due to missingness)
## Multiple R-squared: 0.2396, Adjusted R-squared: 0.2386
## F-statistic: 252.9 on 7 and 5620 DF, p-value: < 2.2e-16
fit<-lm(momeduc~ sex + age + sexage, data=dw, weights=dw$sweight)
summary(fit)
##
## Call:
## lm(formula = momeduc ~ sex + age + sexage, data = dw, weights = dw$sweight)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -10587.8 -489.7 -29.5 38.2 6536.6
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.10585 0.04487 2.359 0.0184 *
## sex -0.12099 0.06398 -1.891 0.0587 .
## age 0.03282 0.01893 1.734 0.0830 .
## sexage -0.06125 0.02727 -2.246 0.0247 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1494 on 5821 degrees of freedom
## (254 observations deleted due to missingness)
## Multiple R-squared: 0.001368, Adjusted R-squared: 0.0008536
## F-statistic: 2.658 on 3 and 5821 DF, p-value: 0.04662
fit<-lm(dadeduc ~ sex + age + sexage, data=dw, weights=dw$sweight)
summary(fit)
##
## Call:
## lm(formula = dadeduc ~ sex + age + sexage, data = dw, weights = dw$sweight)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -10710.7 -977.8 -255.9 546.3 7341.1
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.42514 0.06212 6.844 8.51e-12 ***
## sex -0.06896 0.08883 -0.776 0.438
## age -0.02638 0.02625 -1.005 0.315
## sexage -0.01742 0.03792 -0.459 0.646
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2047 on 5624 degrees of freedom
## (456 observations deleted due to missingness)
## Multiple R-squared: 0.0007308, Adjusted R-squared: 0.0001978
## F-statistic: 1.371 on 3 and 5624 DF, p-value: 0.2496
da<- dk
da$sexage<- da$sex*da$age
da$sexmomeduc<- da$sex*da$momeduc
da$agemomeduc<- da$age*da$momeduc
da$momeduc<- da$momeduc-12
da$sexagemomeduc<- da$sex*da$age*da$momeduc
da$sexdadeduc<- da$sex*da$dadeduc
da$agedadeduc<- da$age*da$dadeduc
da$dadeduc<- da$dadeduc-12
da$sexagedadeduc<- da$sex*da$age*da$dadeduc
fit<-lm(efa ~ sex + age + momeduc + sexage + sexmomeduc + agemomeduc + sexagemomeduc, data=da, weights=da$sweight)
summary(fit)
##
## Call:
## lm(formula = efa ~ sex + age + momeduc + sexage + sexmomeduc +
## agemomeduc + sexagemomeduc, data = da, weights = da$sweight)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -31050.2 -4609.3 -553.1 3098.7 25205.2
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 107.513848 0.177404 606.039 < 2e-16 ***
## sex -1.747194 1.072591 -1.629 0.1034
## age 1.444684 0.326518 4.425 9.77e-06 ***
## momeduc 2.395023 0.063825 37.525 < 2e-16 ***
## sexage -0.475432 0.108088 -4.399 1.10e-05 ***
## sexmomeduc -0.183457 0.089610 -2.047 0.0407 *
## agemomeduc -0.004453 0.027182 -0.164 0.8699
## sexagemomeduc 0.018171 0.038024 0.478 0.6327
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6571 on 10098 degrees of freedom
## (663 observations deleted due to missingness)
## Multiple R-squared: 0.2538, Adjusted R-squared: 0.2533
## F-statistic: 490.7 on 7 and 10098 DF, p-value: < 2.2e-16
fit<-lm(efa ~ sex + age + dadeduc + sexage + sexdadeduc + agedadeduc + sexagedadeduc, data=da, weights=da$sweight)
summary(fit)
##
## Call:
## lm(formula = efa ~ sex + age + dadeduc + sexage + sexdadeduc +
## agedadeduc + sexagedadeduc, data = da, weights = da$sweight)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -33296 -4474 -387 3087 26377
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 107.60989 0.17861 602.492 < 2e-16 ***
## sex -1.76268 0.87137 -2.023 0.0431 *
## age 1.62152 0.25786 6.288 3.35e-10 ***
## dadeduc 1.87474 0.04925 38.066 < 2e-16 ***
## sexage -0.55593 0.10865 -5.117 3.17e-07 ***
## sexdadeduc -0.19600 0.07012 -2.795 0.0052 **
## agedadeduc -0.01299 0.02074 -0.626 0.5311
## sexagedadeduc 0.01643 0.02969 0.553 0.5801
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6490 on 9214 degrees of freedom
## (1566 observations deleted due to missingness)
## Multiple R-squared: 0.2652, Adjusted R-squared: 0.2646
## F-statistic: 475 on 7 and 9214 DF, p-value: < 2.2e-16
fit<-lm(momeduc~ sex + age + sexage, data=da, weights=da$sweight)
summary(fit)
##
## Call:
## lm(formula = momeduc ~ sex + age + sexage, data = da, weights = da$sweight)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -10244.8 -793.7 83.1 271.2 6888.4
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.27869 0.03928 -7.096 1.38e-12 ***
## sex -0.17239 0.05577 -3.091 0.0020 **
## age 0.02920 0.01661 1.759 0.0787 .
## sexage -0.05689 0.02379 -2.391 0.0168 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1462 on 10102 degrees of freedom
## (663 observations deleted due to missingness)
## Multiple R-squared: 0.001374, Adjusted R-squared: 0.001078
## F-statistic: 4.634 on 3 and 10102 DF, p-value: 0.003054
fit<-lm(dadeduc ~ sex + age + sexage, data=da, weights=da$sweight)
summary(fit)
##
## Call:
## lm(formula = dadeduc ~ sex + age + sexage, data = da, weights = da$sweight)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -10298.1 -1248.0 0.0 183.3 7797.1
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.04499 0.05312 -0.847 0.3970
## sex -0.13021 0.07568 -1.721 0.0854 .
## age -0.02823 0.02245 -1.257 0.2088
## sexage -0.02245 0.03229 -0.695 0.4868
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1931 on 9218 degrees of freedom
## (1566 observations deleted due to missingness)
## Multiple R-squared: 0.000989, Adjusted R-squared: 0.0006639
## F-statistic: 3.042 on 3 and 9218 DF, p-value: 0.02772
dgroup<- dplyr::select(d, id, starts_with("ss"), afqt, efa, educ2000, momeduc, dadeduc, age, age2, sex, agesex, bhw, sweight, weight2000, cweight, asvabweight)
dgroup$sexage<- dgroup$sex*dgroup$age
# momeduc or dadeduc being not mean centered only changes the intercept, nothing else
fit<-lm(momeduc~ sex + age + sexage, data=dgroup, weights=dgroup$sweight)
summary(fit)
##
## Call:
## lm(formula = momeduc ~ sex + age + sexage, data = dgroup, weights = dgroup$sweight)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -6412.5 -1088.4 59.4 179.0 5638.0
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.773428 0.084831 138.787 <2e-16 ***
## sex -0.025962 0.121775 -0.213 0.831
## age -0.003619 0.038605 -0.094 0.925
## sexage 0.065932 0.055793 1.182 0.237
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1500 on 2004 degrees of freedom
## (112 observations deleted due to missingness)
## Multiple R-squared: 0.00128, Adjusted R-squared: -0.0002151
## F-statistic: 0.8561 on 3 and 2004 DF, p-value: 0.4632
fit<-lm(dadeduc ~ sex + age + sexage, data=dgroup, weights=dgroup$sweight)
summary(fit)
##
## Call:
## lm(formula = dadeduc ~ sex + age + sexage, data = dgroup, weights = dgroup$sweight)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -6098.9 -1616.3 -112.4 206.7 7585.2
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.09500 0.11921 101.457 <2e-16 ***
## sex -0.10106 0.17045 -0.593 0.5533
## age -0.03700 0.05382 -0.687 0.4919
## sexage 0.13628 0.07776 1.753 0.0798 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2071 on 1878 degrees of freedom
## (237 observations deleted due to missingness)
## Multiple R-squared: 0.002304, Adjusted R-squared: 0.00071
## F-statistic: 1.446 on 3 and 1878 DF, p-value: 0.2277