library(tidyverse)
library(magrittr)
library(kableExtra)
library(haven)
library(visdat)
library(ggplot2)
library(tidyverse)
library(lavaan)
library(psych)
fitstats <- \(x) fitmeasures(x, c("df","rmsea.robust", "cfi.robust", "srmr"))
### function that generates syntax
get_model <- function(vars=1:5, equal.loadings=F,
which.intercepts=1){
basemodel <- paste0("F1=~ NA*x1_",vars[1],"+a*x1_",vars[1],"+", paste0("x1_", vars[-1], collapse="+"), "\n",
"F2=~ NA*x2_",vars[1],"+a*x2_",vars[1],"+", paste0("x2_", vars[-1], collapse="+"), "\n",
"F3=~ NA*x3_",vars[1],"+a*x3_",vars[1],"+", paste0("x3_", vars[-1], collapse="+"), "\n") %>%
paste0("\nF1 ~ 0*1; F2 ~ 1; F3~1; F1~~1*F1")
metricmodel <- paste0("F1=~ NA*x1_",vars[1],"+", paste0(letters[vars],"*x1_", vars , collapse="+"), "\n",
"F2=~NA*x2_",vars[1],"+", paste0(letters[vars],"*x2_", vars , collapse="+"), "\n",
"F3=~NA*x3_",vars[1],"+", paste0(letters[vars],"*x3_", vars , collapse="+"), "\n") %>%
paste0("\nF1 ~ 0*1; F2 ~ 1; F3~1; F1~~1*F1")
errs <-sapply(vars,\(v){
paste0("\nx1_",v,"~~ x2_",v, "+x3_",v,"; x2_",v,"~~ x3_",v)
}) %>% paste0(collapse="")
ints <- sapply(which.intercepts,\(v){
paste0("x1_", vars[v],"+x2_", vars[v], "+x3_",vars[v],"~i", vars[v], "*1\n")
}) %>% paste0(collapse="")
if(equal.loadings)
return(paste(metricmodel,"\n", ints, "\n",errs))
else
return(paste(basemodel,"\n", ints, "\n",errs))
}
#load data
mydata <- readRDS("finaldata_cutoff25_40.rds")
#sc items
sc2items <- strsplit("s2_scr8 + s2_scr9 + s2_scr12 + s2_scr13 + s2_scr15", split=" \\+ ", "fixed=T") %>% unlist
sc3items <- strsplit("s3_scr8 + s3_scr9 + s3_scr12 + s3_scr13 + s3_scr15", split=" \\+ ", "fixed=T") %>% unlist
sc4items <- strsplit("s4_scr8 + s4_scr9 + s4_scr12 + s4_scr13 + s4_scr15", split=" \\+ ", "fixed=T") %>% unlist
dd <- mydata # or alldata?
df <- cbind(select(dd, all_of(sc2items)),
select(dd, all_of(sc3items)),
select(dd, all_of(sc4items)))
df[df==-990] <- NA
colnames(df) <- c(paste0("x1_", 1:5),paste0("x2_", 1:5),paste0("x3_", 1:5))Measurement Invariance of Self Concept Scale
descriptives univariate
Five items across three grades in two groups
df$group <- dd$group
ll <- pivot_longer(df, 1:15)
ll$grade <- str_extract_all(ll$name, "x(\\d)") %>% unlist %>% str_remove_all("x")
ll$item <- str_extract_all(ll$name, "_(\\d)") %>% unlist %>% str_remove_all("_")
ggplot(ll, aes(x=value,fill=group))+geom_bar(position="dodge2")+facet_grid(grade~item)
Correlations
Grade 1
psych::cor.plot(cor(df[, 1:5]))
GGally::ggpairs(cor(df[, 1:5]))
Grade 2
psych::cor.plot(cor(df[, 6:10], use="pairwise.complete.obs" ))
Grade 3
psych::cor.plot(cor(df[, 11:15], use="pairwise.complete.obs"))
psych::cor.plot(psych::polychoric(df[, 11:15])$rho)
Testing for measurement invariance across groups
Criterion: For sample sizes with adequate power, equal group sizes, and mixed invariance (i.e., some loadings are higher and some lower in the first group), Chen (2007) also suggested a criterion of a -.01 change in CFI, paired with changes in RMSEA of .015 and SRMR of .030 (for metric invariance) or .015 (for scalar or residual invariance)
df$group <- dd$group
# full model all grades
mod <- "F1=~ x1_1+x1_4+x1_5+x1_2+x1_3
F2=~ x2_1+x2_4+x2_5+x3_2+x3_3
F3=~ x3_1+x3_4+x3_5+x3_2+x3_3"
# configural invariance
fit1 <- cfa(mod, data=df, estimator="MLM", group="group")
# weak invariance
fit2 <- cfa(mod, data=df, estimator="MLM", group="group", group.equal="loadings")
# strong invariance
fit3 <- cfa(mod, data=df, estimator="MLM", group="group", group.equal=c("intercepts", "loadings"))
lavTestLRT(fit1, fit2, fit3)
Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
lavaan->lavTestLRT(): lavaan NOTE: The "Chisq" column contains
standard test statistics, not the robust test that should be reported per
model. A robust difference test is a function of two standard (not robust)
statistics.
Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
fit1 120 34162 34602 239.53
fit2 132 34148 34528 250.02 9.208 12 0.685
fit3 142 34177 34508 299.15 53.314 10 6.511e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1data.frame(conf=fitstats(fit1), weak=fitstats(fit2), strong=fitstats(fit3)) %>%
round(3) %>% kable(caption=paste("MI across groups"))| conf | weak | strong | |
|---|---|---|---|
| df | 120.000 | 132.000 | 142.000 |
| rmsea.robust | 0.039 | 0.037 | 0.042 |
| cfi.robust | 0.959 | 0.960 | 0.944 |
| srmr | 0.035 | 0.037 | 0.044 |
df$group <- NULLWe have moderate support for group invariance
Testing for longitudinal invariance
Metric/weak invariance holds, but strong invariance is not present:
## STEP 1 CONFIGURAL
confmod <- get_model()
fit_conf <- cfa(confmod, data = df, estimator="MLM")
## STEP 2 METRIC
metrmod <- get_model(equal.loadings = T)
fit_metr <- cfa(metrmod, data = df, estimator="MLM")
## STEP 3 SCALAR
scalmod <- get_model(equal.loadings=T, which.intercepts = 1:5)
fit_scal <- cfa(scalmod, data = df, estimator="MLM")
data.frame(configural=fitstats(fit_conf), metric=fitstats(fit_metr), strong=fitstats(fit_scal)) %>%
round(3) %>% kable()| configural | metric | strong | |
|---|---|---|---|
| df | 72.000 | 80.000 | 88.000 |
| rmsea.robust | 0.024 | 0.029 | 0.071 |
| cfi.robust | 0.987 | 0.979 | 0.863 |
| srmr | 0.024 | 0.035 | 0.060 |
Inspect the mean values of each item across time occasions in order to understand the source of invariance. The mean values look similar across grades 2 and 3, but are different in grade 1.
tmp <- data.frame(mean=colMeans(df, na.rm=T))
tmp$grade <- factor(rep(1:3, each=5))
tmp$item <- rep(1:5, 3)
ggplot(tmp, aes(item, mean, fill=grade))+geom_col()+facet_wrap(grade~ .)
ggplot(tmp, aes(item, mean, color=grade, group=grade))+geom_point()+geom_line()
Let us test for longitudinal invariance across grades 2 and 3
confmod <- "F2=~ NA*x2_1+a*x2_1+x2_2+x2_3+x2_4+x2_5
F3=~ NA*x3_1+a*x3_1+x3_2+x3_3+x3_4+x3_5
F2 ~ 0*1; F3~1
x2_1+x3_1~i1*1
x2_1~~ x3_1
x2_2~~ x3_2
x2_3~~ x3_3
x2_4~~ x3_4
x2_5~~ x3_5"
metrmod <- "F2=~ NA*x2_1+a*x2_1+b*x2_2+c*x2_3+d*x2_4+e*x2_5
F3=~ NA*x3_1+a*x3_1+b*x3_2+c*x3_3+d*x3_4+e*x3_5
F2 ~ 0*1; F3~1
x2_1+x3_1~i1*1
x2_1~~ x3_1
x2_2~~ x3_2
x2_3~~ x3_3
x2_4~~ x3_4
x2_5~~ x3_5"
scalmod <- "F2=~ NA*x2_1+a*x2_1+b*x2_2+c*x2_3+d*x2_4+e*x2_5
F3=~ NA*x3_1+a*x3_1+b*x3_2+c*x3_3+d*x3_4+e*x3_5
F2 ~ 0*1; F3~1
x2_1+x3_1~i1*1
x2_2+x3_2~i2*1
x2_3+x3_3~i3*1
x2_4+x3_4~i4*1
x2_5+x3_5~i5*1
x2_1~~ x3_1
x2_2~~ x3_2
x2_3~~ x3_3
x2_4~~ x3_4
x2_5~~ x3_5"
fit_conf <- cfa(confmod, data = df, estimator="MLM")
fit_metr <- cfa(metrmod, data = df, estimator="MLM")
fit_scal <- cfa(scalmod, data = df, estimator="MLM")
data.frame(configural=fitstats(fit_conf), metric=fitstats(fit_metr), strong=fitstats(fit_scal)) %>%
round(3) %>% kable()| configural | metric | strong | |
|---|---|---|---|
| df | 28.000 | 32.000 | 36.000 |
| rmsea.robust | 0.039 | 0.037 | 0.048 |
| cfi.robust | 0.980 | 0.980 | 0.962 |
| srmr | 0.025 | 0.029 | 0.034 |
The evidence against strong invariance has been weakened but is still not negligible.
Partial Invariance Model
To specify a partial invariance model we free up the intercepts of items that do not behave similarly across grades. We fix intercepts of item 1 and 4 to be equal across grades. We see that we could equally well have fixed items 2 and 5.
confmod <- get_model()
fit_conf <- cfa(confmod, data = df, estimator="MLM")
metrmod <- get_model(equal.loadings = T)
fit_metr <- cfa(metrmod, data = df, estimator="MLM")
# a model which does not constraint intercepts
scalmod <- get_model(equal.loadings = T, which.intercepts=c(2,5))
fit_scal25 <- cfa(scalmod, data = df, estimator="MLM")
scalmod <- get_model(equal.loadings = T, which.intercepts=c(1,4))
fit_scal14 <- cfa(scalmod, data = df, estimator="MLM")
data.frame(configural=fitstats(fit_conf), metric=fitstats(fit_metr), strong25=fitstats(fit_scal25),strong14=fitstats(fit_scal14)) %>%
round(3) %>% kable()| configural | metric | strong25 | strong14 | |
|---|---|---|---|---|
| df | 72.000 | 80.000 | 82.000 | 82.000 |
| rmsea.robust | 0.024 | 0.029 | 0.028 | 0.028 |
| cfi.robust | 0.987 | 0.979 | 0.980 | 0.980 |
| srmr | 0.024 | 0.035 | 0.035 | 0.035 |
Full longitudinal invariance for subsets of items
Let us restrict our measurement model for SC to items 1, 4 and 5. Then we have strong invariance and excellent fit.
items <- c(1,4,5)
confmod <- get_model(vars=items)
fit_conf <- cfa(confmod, data = df, estimator="MLM")
metrmod <- get_model(vars=items, equal.loadings = T)
fit_metr <- cfa(metrmod, data = df, estimator="MLM")
scalmod <- get_model(vars=items, equal.loadings = T, which.intercepts=1:2)
fit_scal <- cfa(scalmod, data = df, estimator="MLM")
data.frame(configural=fitstats(fit_conf), metric=fitstats(fit_metr), strong=fitstats(fit_scal)) %>%
round(3) %>% kable(caption=paste("Only items", paste(items, collapse=" and ")))| configural | metric | strong | |
|---|---|---|---|
| df | 15.000 | 19.000 | 21.000 |
| rmsea.robust | 0.022 | 0.026 | 0.026 |
| cfi.robust | 0.995 | 0.991 | 0.990 |
| srmr | 0.017 | 0.028 | 0.028 |
We have weak/moderate support for strict invariance across groups in the three-item model.
Growth curve model for MI items compared to all 5 items
All five items
df$group <- factor(dd$group, labels=c("Risk Decod", "Risk Compr"))
df$gender <- dd$s0_gend
items <- 1:5
df$sc3 <- rowSums(select(df, paste0("x3_", items)))
df$sc2 <- rowSums(select(df, paste0("x2_", items)))
df$sc1 <- rowSums(select(df, paste0("x1_", items)))
model0 <- ' i =~ 1*sc1 + 1*sc2 + 1*sc3
s =~ 0*sc1 + 1*sc2 + 2*sc3
i ~ gender + group
s ~ gender+group'
fit_growth <- growth(model0, df, estimator="MLM")
fitstats(fit_growth) df rmsea.robust cfi.robust srmr
3.000 0.051 0.988 0.016 summary(fit_growth)lavaan 0.6-18.2090 ended normally after 74 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 12
Used Total
Number of observations 1097 1205
Model Test User Model:
Standard Scaled
Test Statistic 11.353 11.532
Degrees of freedom 3 3
P-value (Chi-square) 0.010 0.009
Scaling correction factor 0.984
Satorra-Bentler correction
Parameter Estimates:
Standard errors Robust.sem
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
i =~
sc1 1.000
sc2 1.000
sc3 1.000
s =~
sc1 0.000
sc2 1.000
sc3 2.000
Regressions:
Estimate Std.Err z-value P(>|z|)
i ~
gender -0.094 0.182 -0.515 0.607
group 1.942 0.181 10.746 0.000
s ~
gender 0.263 0.106 2.481 0.013
group -0.288 0.106 -2.715 0.007
Covariances:
Estimate Std.Err z-value P(>|z|)
.i ~~
.s -0.650 0.322 -2.021 0.043
Intercepts:
Estimate Std.Err z-value P(>|z|)
.i 16.464 0.375 43.921 0.000
.s -0.386 0.219 -1.758 0.079
Variances:
Estimate Std.Err z-value P(>|z|)
.sc1 7.083 0.575 12.316 0.000
.sc2 3.933 0.285 13.811 0.000
.sc3 2.973 0.478 6.222 0.000
.i 3.909 0.595 6.572 0.000
.s 0.738 0.257 2.874 0.004standardizedsolution(fit_growth) %>% filter(op=="~") %>% select(c(1:5,7)) lhs op rhs est.std se pvalue
1 i ~ gender -0.021 0.041 0.606
2 i ~ group 0.440 0.042 0.000
3 s ~ gender 0.149 0.062 0.015
4 s ~ group -0.163 0.065 0.012Only items 1,4,5
items <- c(1,4,5)
df$sc3 <- rowSums(select(df, paste0("x3_", items)))
df$sc2 <- rowSums(select(df, paste0("x2_", items)))
df$sc1 <- rowSums(select(df, paste0("x1_", items)))
model0 <- ' i =~ 1*sc1 + 1*sc2 + 1*sc3
s =~ 0*sc1 + 1*sc2 + 2*sc3
i ~ gender + group
s ~ gender+group'
fit_growth <- growth(model0, df, estimator="MLM")
fitstats(fit_growth) df rmsea.robust cfi.robust srmr
3.000 0.051 0.983 0.017 summary(fit_growth)lavaan 0.6-18.2090 ended normally after 63 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 12
Used Total
Number of observations 1097 1205
Model Test User Model:
Standard Scaled
Test Statistic 11.545 11.724
Degrees of freedom 3 3
P-value (Chi-square) 0.009 0.008
Scaling correction factor 0.985
Satorra-Bentler correction
Parameter Estimates:
Standard errors Robust.sem
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
i =~
sc1 1.000
sc2 1.000
sc3 1.000
s =~
sc1 0.000
sc2 1.000
sc3 2.000
Regressions:
Estimate Std.Err z-value P(>|z|)
i ~
gender 0.148 0.118 1.257 0.209
group 0.982 0.117 8.397 0.000
s ~
gender 0.136 0.072 1.898 0.058
group -0.122 0.072 -1.705 0.088
Covariances:
Estimate Std.Err z-value P(>|z|)
.i ~~
.s -0.353 0.137 -2.582 0.010
Intercepts:
Estimate Std.Err z-value P(>|z|)
.i 10.322 0.236 43.766 0.000
.s -0.210 0.145 -1.452 0.146
Variances:
Estimate Std.Err z-value P(>|z|)
.sc1 2.952 0.252 11.703 0.000
.sc2 1.929 0.134 14.344 0.000
.sc3 1.398 0.196 7.149 0.000
.i 1.539 0.248 6.210 0.000
.s 0.368 0.110 3.344 0.001growth curves for individual items sc
sc1
model0 <- ' i =~ 1*x1_1 + 1*x2_1 + 1*x3_1
s =~ 0*x1_1+ 1*x2_1 + 2*x3_1
i ~ gender + group
s ~ gender+group'
fit_growth <- growth(model0, df, estimator="MLM")
fitstats(fit_growth) df rmsea.robust cfi.robust srmr
3.000 0.033 0.992 0.013 summary(fit_growth)lavaan 0.6-18.2090 ended normally after 37 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 12
Used Total
Number of observations 1097 1205
Model Test User Model:
Standard Scaled
Test Statistic 6.552 6.646
Degrees of freedom 3 3
P-value (Chi-square) 0.088 0.084
Scaling correction factor 0.986
Satorra-Bentler correction
Parameter Estimates:
Standard errors Robust.sem
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
i =~
x1_1 1.000
x2_1 1.000
x3_1 1.000
s =~
x1_1 0.000
x2_1 1.000
x3_1 2.000
Regressions:
Estimate Std.Err z-value P(>|z|)
i ~
gender -0.064 0.046 -1.397 0.162
group 0.407 0.045 9.017 0.000
s ~
gender 0.047 0.031 1.530 0.126
group -0.012 0.030 -0.399 0.690
Covariances:
Estimate Std.Err z-value P(>|z|)
.i ~~
.s -0.050 0.023 -2.218 0.027
Intercepts:
Estimate Std.Err z-value P(>|z|)
.i 3.831 0.094 40.849 0.000
.s -0.158 0.061 -2.611 0.009
Variances:
Estimate Std.Err z-value P(>|z|)
.x1_1 0.453 0.042 10.844 0.000
.x2_1 0.349 0.025 13.999 0.000
.x3_1 0.302 0.044 6.891 0.000
.i 0.210 0.036 5.807 0.000
.s 0.067 0.019 3.540 0.000standardizedsolution(fit_growth) %>% filter(op=="~") %>% select(c(1:5,7)) lhs op rhs est.std se pvalue
1 i ~ gender -0.064 0.045 0.160
2 i ~ group 0.405 0.046 0.000
3 s ~ gender 0.090 0.059 0.131
4 s ~ group -0.023 0.058 0.690sc2
model0 <- ' i =~ 1*x1_2 + 1*x2_2 + 1*x3_2
s =~ 0*x1_2+ 1*x2_2 + 2*x3_2
i ~ gender + group
s ~ gender+group'
fit_growth <- growth(model0, df, estimator="MLM")
fitstats(fit_growth) df rmsea.robust cfi.robust srmr
3.000 0.000 1.000 0.008 summary(fit_growth)lavaan 0.6-18.2090 ended normally after 41 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 12
Used Total
Number of observations 1097 1205
Model Test User Model:
Standard Scaled
Test Statistic 2.406 2.422
Degrees of freedom 3 3
P-value (Chi-square) 0.492 0.490
Scaling correction factor 0.993
Satorra-Bentler correction
Parameter Estimates:
Standard errors Robust.sem
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
i =~
x1_2 1.000
x2_2 1.000
x3_2 1.000
s =~
x1_2 0.000
x2_2 1.000
x3_2 2.000
Regressions:
Estimate Std.Err z-value P(>|z|)
i ~
gender -0.176 0.060 -2.910 0.004
group 0.590 0.060 9.850 0.000
s ~
gender 0.066 0.037 1.768 0.077
group -0.119 0.037 -3.204 0.001
Covariances:
Estimate Std.Err z-value P(>|z|)
.i ~~
.s -0.029 0.037 -0.785 0.432
Intercepts:
Estimate Std.Err z-value P(>|z|)
.i 2.827 0.127 22.313 0.000
.s 0.133 0.080 1.667 0.096
Variances:
Estimate Std.Err z-value P(>|z|)
.x1_2 0.975 0.075 13.043 0.000
.x2_2 0.548 0.030 18.246 0.000
.x3_2 0.449 0.055 8.130 0.000
.i 0.281 0.064 4.424 0.000
.s 0.043 0.031 1.386 0.166standardizedsolution(fit_growth) %>% filter(op=="~") %>% select(c(1:5,7)) lhs op rhs est.std se pvalue
1 i ~ gender -0.144 0.050 0.004
2 i ~ group 0.482 0.054 0.000
3 s ~ gender 0.151 0.098 0.124
4 s ~ group -0.272 0.115 0.019sc3 bad fit
sc4
model0 <- ' i =~ 1*x1_4 + 1*x2_4 + 1*x3_4
s =~ 0*x1_4+ 1*x2_4 + 2*x3_4
i ~ gender + group
s ~ gender+group'
fit_growth <- growth(model0, df, estimator="MLM")
fitstats(fit_growth) df rmsea.robust cfi.robust srmr
3.000 0.036 0.989 0.015 summary(fit_growth)lavaan 0.6-18.2090 ended normally after 41 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 12
Used Total
Number of observations 1097 1205
Model Test User Model:
Standard Scaled
Test Statistic 7.121 7.196
Degrees of freedom 3 3
P-value (Chi-square) 0.068 0.066
Scaling correction factor 0.990
Satorra-Bentler correction
Parameter Estimates:
Standard errors Robust.sem
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
i =~
x1_4 1.000
x2_4 1.000
x3_4 1.000
s =~
x1_4 0.000
x2_4 1.000
x3_4 2.000
Regressions:
Estimate Std.Err z-value P(>|z|)
i ~
gender 0.063 0.055 1.144 0.253
group 0.452 0.055 8.281 0.000
s ~
gender 0.054 0.035 1.539 0.124
group -0.046 0.035 -1.306 0.191
Covariances:
Estimate Std.Err z-value P(>|z|)
.i ~~
.s -0.056 0.034 -1.663 0.096
Intercepts:
Estimate Std.Err z-value P(>|z|)
.i 3.297 0.117 28.088 0.000
.s -0.120 0.075 -1.590 0.112
Variances:
Estimate Std.Err z-value P(>|z|)
.x1_4 0.767 0.068 11.207 0.000
.x2_4 0.539 0.027 19.935 0.000
.x3_4 0.345 0.052 6.696 0.000
.i 0.238 0.059 4.044 0.000
.s 0.078 0.028 2.821 0.005standardizedsolution(fit_growth) %>% filter(op=="~") %>% select(c(1:5,7)) lhs op rhs est.std se pvalue
1 i ~ gender 0.058 0.051 0.256
2 i ~ group 0.418 0.058 0.000
3 s ~ gender 0.096 0.063 0.127
4 s ~ group -0.082 0.064 0.203sc5
model0 <- ' i =~ 1*x1_5 + 1*x2_5 + 1*x3_5
s =~ 0*x1_5+ 1*x2_5 + 2*x3_5
i ~ gender + group
s ~ gender+group'
fit_growth <- growth(model0, df, estimator="MLM")
fitstats(fit_growth) df rmsea.robust cfi.robust srmr
3.000 0.023 0.986 0.013 summary(fit_growth)lavaan 0.6-18.2090 ended normally after 44 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 12
Used Total
Number of observations 1097 1205
Model Test User Model:
Standard Scaled
Test Statistic 4.687 4.696
Degrees of freedom 3 3
P-value (Chi-square) 0.196 0.195
Scaling correction factor 0.998
Satorra-Bentler correction
Parameter Estimates:
Standard errors Robust.sem
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
i =~
x1_5 1.000
x2_5 1.000
x3_5 1.000
s =~
x1_5 0.000
x2_5 1.000
x3_5 2.000
Regressions:
Estimate Std.Err z-value P(>|z|)
i ~
gender 0.151 0.058 2.588 0.010
group 0.118 0.059 2.003 0.045
s ~
gender 0.034 0.037 0.910 0.363
group -0.061 0.037 -1.636 0.102
Covariances:
Estimate Std.Err z-value P(>|z|)
.i ~~
.s -0.077 0.034 -2.247 0.025
Intercepts:
Estimate Std.Err z-value P(>|z|)
.i 3.194 0.119 26.924 0.000
.s 0.069 0.074 0.924 0.355
Variances:
Estimate Std.Err z-value P(>|z|)
.x1_5 0.979 0.071 13.728 0.000
.x2_5 0.524 0.028 18.732 0.000
.x3_5 0.402 0.044 9.133 0.000
.i 0.230 0.058 4.000 0.000
.s 0.054 0.028 1.949 0.051standardizedsolution(fit_growth) %>% filter(op=="~") %>% select(c(1:5,7)) lhs op rhs est.std se pvalue
1 i ~ gender 0.154 0.061 0.012
2 i ~ group 0.120 0.061 0.048
3 s ~ gender 0.072 0.080 0.368
4 s ~ group -0.130 0.085 0.125combining 2 and 5
df$x1_25 <- rowMeans(select(df, all_of(c("x1_2", "x1_5"))), na.rm=T)
df$x2_25 <- rowMeans(select(df, all_of(c("x2_2", "x2_5"))), na.rm=T)
df$x3_25 <- rowMeans(select(df, all_of(c("x3_2", "x3_5"))), na.rm=T)
model0 <- ' i =~ 1*x1_25 + 1*x2_25 + 1*x3_25
s =~ 0*x1_25+ 1*x2_25 + 2*x3_25
i ~ gender + group
s ~ gender+group'
fit_growth <- growth(model0, df, estimator="MLM")
fitstats(fit_growth) df rmsea.robust cfi.robust srmr
3.000 0.029 0.992 0.013 summary(fit_growth)lavaan 0.6-18.2090 ended normally after 40 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 12
Used Total
Number of observations 1097 1205
Model Test User Model:
Standard Scaled
Test Statistic 5.723 5.754
Degrees of freedom 3 3
P-value (Chi-square) 0.126 0.124
Scaling correction factor 0.995
Satorra-Bentler correction
Parameter Estimates:
Standard errors Robust.sem
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
i =~
x1_25 1.000
x2_25 1.000
x3_25 1.000
s =~
x1_25 0.000
x2_25 1.000
x3_25 2.000
Regressions:
Estimate Std.Err z-value P(>|z|)
i ~
gender -0.011 0.048 -0.231 0.817
group 0.354 0.048 7.321 0.000
s ~
gender 0.049 0.029 1.687 0.092
group -0.090 0.029 -3.093 0.002
Covariances:
Estimate Std.Err z-value P(>|z|)
.i ~~
.s -0.055 0.023 -2.449 0.014
Intercepts:
Estimate Std.Err z-value P(>|z|)
.i 3.009 0.099 30.472 0.000
.s 0.102 0.059 1.731 0.084
Variances:
Estimate Std.Err z-value P(>|z|)
.x1_25 0.567 0.044 12.771 0.000
.x2_25 0.302 0.018 16.927 0.000
.x3_25 0.233 0.030 7.830 0.000
.i 0.232 0.040 5.864 0.000
.s 0.043 0.018 2.347 0.019standardizedsolution(fit_growth) %>% filter(op=="~") %>% select(c(1:5,7)) lhs op rhs est.std se pvalue
1 i ~ gender -0.011 0.047 0.817
2 i ~ group 0.344 0.048 0.000
3 s ~ gender 0.114 0.070 0.104
4 s ~ group -0.210 0.076 0.006combining 1 and 4
df$x1_14 <- rowMeans(select(df, all_of(c("x1_1", "x1_4"))), na.rm=T)
df$x2_14 <- rowMeans(select(df, all_of(c("x2_1", "x2_4"))), na.rm=T)
df$x3_14 <- rowMeans(select(df, all_of(c("x3_1", "x3_4"))), na.rm=T)
model0 <- ' i =~ 1*x1_14 + 1*x2_14 + 1*x3_14
s =~ 0*x1_14+ 1*x2_14 + 2*x3_14
i ~ gender + group
s ~ gender+group'
fit_growth <- growth(model0, df, estimator="MLM")
fitstats(fit_growth) df rmsea.robust cfi.robust srmr
3.000 0.048 0.987 0.016 summary(fit_growth)lavaan 0.6-18.2090 ended normally after 38 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 12
Used Total
Number of observations 1097 1205
Model Test User Model:
Standard Scaled
Test Statistic 10.572 10.726
Degrees of freedom 3 3
P-value (Chi-square) 0.014 0.013
Scaling correction factor 0.986
Satorra-Bentler correction
Parameter Estimates:
Standard errors Robust.sem
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
i =~
x1_14 1.000
x2_14 1.000
x3_14 1.000
s =~
x1_14 0.000
x2_14 1.000
x3_14 2.000
Regressions:
Estimate Std.Err z-value P(>|z|)
i ~
gender -0.001 0.042 -0.023 0.982
group 0.430 0.042 10.335 0.000
s ~
gender 0.050 0.027 1.868 0.062
group -0.029 0.027 -1.103 0.270
Covariances:
Estimate Std.Err z-value P(>|z|)
.i ~~
.s -0.041 0.017 -2.463 0.014
Intercepts:
Estimate Std.Err z-value P(>|z|)
.i 3.564 0.087 40.881 0.000
.s -0.139 0.056 -2.493 0.013
Variances:
Estimate Std.Err z-value P(>|z|)
.x1_14 0.377 0.033 11.353 0.000
.x2_14 0.283 0.018 16.140 0.000
.x3_14 0.179 0.030 6.025 0.000
.i 0.188 0.030 6.168 0.000
.s 0.064 0.015 4.267 0.000standardizedsolution(fit_growth) %>% filter(op=="~") %>% select(c(1:5,7)) lhs op rhs est.std se pvalue
1 i ~ gender -0.001 0.043 0.982
2 i ~ group 0.444 0.044 0.000
3 s ~ gender 0.099 0.053 0.062
4 s ~ group -0.058 0.053 0.275