Suporte Gerencial
- 1 Preparing Data
- 2 Descriptive Statistics
- 3 Splitting Data for Analysis
- 4 Method 1 - bootEGA Method from EFAShiny
- 5 Method 2 - ega.object from Cleyton’s paper (need to completed)
- 6 Method 3 - original boot.ega function with parallel processing
- 7 Confirmatory Factor Analysis
- 8 Item Reponse Theory
- 8.1 Subsetting Data
- 8.2 Descriptives
- 8.3 Alpha - per excluded item
- 8.4 Correlation Itens
- 8.5 Empirical Plots - Total Raw Score and Responses
- 8.6 Firts Constrained Model
- 8.7 Unconstrained Model
- 8.8 Comparisons Constrained and Uconstrained
- 8.9 Unconstrained Model
- 8.10 Item Response Category Characteristic Curves
1 Preparing Data
1.0.0.0.1 Loading Libraries and function using auxiliary file
source("funlibs.R")1.0.0.0.2 Loading database
TDados <- read.spss(file = "Base Integrada - Servidores - Trabalho Remoto Covid-19 (dados completos)_27dez15h30.sav", to.data.frame = TRUE, use.value.labels = FALSE)
TDados<-as.data.frame(TDados)
#view(TDados)
# Criei um banco só com os itens de Suporte Gerencial
Itens <- na.omit(TDados[c(89:94)])1.0.0.0.3 Subsetting AEC itens
data<-data.matrix(TDados[,c(89:94)])2 Descriptive Statistics
2.0.0.0.1 Summary Statistics
psych::describe(data)## vars n mean sd median trimmed mad min max range skew
## SupG_Feed 1 7608 3.79 1.04 4 3.92 1.48 1 5 4 -0.89
## SupG_Meta 2 7608 4.10 0.82 4 4.20 0.00 1 5 4 -1.17
## SupG_Ori 3 7608 4.35 0.76 4 4.47 1.48 1 5 4 -1.42
## SupG_Mon 4 7608 4.33 0.75 4 4.45 1.48 1 5 4 -1.35
## SupG_Infra 5 7608 3.53 1.13 4 3.62 1.48 1 5 4 -0.54
## SupG_Bestar 6 7608 3.95 1.03 4 4.10 1.48 1 5 4 -1.03
## kurtosis se
## SupG_Feed 0.42 0.01
## SupG_Meta 1.99 0.01
## SupG_Ori 2.95 0.01
## SupG_Mon 2.87 0.01
## SupG_Infra -0.35 0.01
## SupG_Bestar 0.74 0.012.1 Relative Frequencies
data<-as.matrix(data)
dsc<-descript(data)
porcentagem<-as.data.frame(round(dsc$perc,2)*100)
names(porcentagem)<-c("% lv1","% lv2","% lv3","% lv4","% lv5")
porcentagem## % lv1 % lv2 % lv3 % lv4 % lv5
## SupG_Feed 4 7 18 44 25
## SupG_Meta 1 4 10 54 31
## SupG_Ori 1 2 6 44 48
## SupG_Mon 1 2 7 45 46
## SupG_Infra 7 10 28 34 21
## SupG_Bestar 4 5 17 40 342.1.0.0.1 Plotting Itens as Likert
lbs <- c("lv1","lv2","lv3","lv4","lv5")
survey <- TDados[,c(89:94)] %>%
dplyr::mutate_if(is.numeric, factor, levels = 1:5, labels = lbs)
plot(likert(survey[,1:6]), ordered = F, wrap= 60)
2.1.0.0.2 Histogram
dta_long <- melt(as.data.frame(data))
colnames(dta_long) <- c("Item", "Response")
Histogram <- ggplot(dta_long, aes(x = Response, fill = Item))+
geom_histogram(bins = 5)+
facet_wrap(~Item)+
theme_default()
Histogram
2.1.0.0.3 Density Plot
DensityPlot <- ggplot(dta_long, aes(x = Response, fill = Item))+
geom_density()+
facet_wrap(~Item)+
theme_default()
DensityPlot 
2.1.0.0.4 Correlation Matrix
CorMat <- psych::polychoric(data, correct=T, smooth=T,global=T)$rho2.1.0.0.5 Plotting
corrplot(CorMat,order="hclust",type="upper",method="ellipse",
tl.pos = "lt",mar = c(2,2,2,2))
corrplot(CorMat,order="hclust",type="lower",method="number",
diag=FALSE,tl.pos="n", cl.pos="n",add=TRUE,mar = c(2,2,2,2))
2.1.0.0.6 Ggcorplot
#ggcorrplot(CorMat, hc.order = T,type = "lower", lab = TRUE,
#colors = c("#E46726", "white", "#6D9EC2"))3 Splitting Data for Analysis
3.0.0.0.1 Random sampling training and test data for EFA and CFA
# Sorteio Aleatório
ss <- sample(1:2,size=nrow(TDados),replace=T,prob=c(0.3,0.7))
banco_EFA <- TDados[ss==1,]
banco_CFA <- TDados[ss==2,]3.0.0.0.2 EFA of Criativity Auto-Efficacy
data<-as.data.frame(banco_EFA)3.0.0.1 Subsetting
data<-data[,89:94]3.0.0.1.1 Polychoric Correlation
CorMat <- psych::polychoric(data, correct=T, smooth=T,global=T)$rho3.0.0.1.2 Bartlett Sphericity
bartlett<-psych::cortest.bartlett(CorMat, n = nrow(data),diag=TRUE)
#bartlett3.0.0.1.3 Kayser Meyer - Sample Adequacy
kmo <-psych::KMO(CorMat)
#kmoIt was observed that the six items of CAEFF grouped a latent factor, Bartlett’s chi-square test 7964.06; df= 15; p< 0 and KMO = 0.88
3.0.0.1.4 Parallel Analysis using unweighted least square
parallel<-pa.plot(CorMat,n.obs = nrow(data), fm="uls", cor="poly",n.iter=1000)## Parallel analysis suggests that the number of factors = 2 and the number of components = 1print(parallel)## [[1]]
##
## [[2]]
## [1] 2#parallel[[2]][1]Number of factor by parallel analysis is equal to 2
3.0.0.1.5 Numeric Rules - Very Simples Structure based on parallel number of factor plus one
NumericRule <- VSS(CorMat,n =parallel[[2]][1]+1, plot = F, n.obs =nrow(data),rotate="promax",cor="poly", fm="uls")
temp1 <- data.frame(nFactor = row.names(NumericRule$vss.stats),
VSS1 = NumericRule$cfit.1, VSS2 = NumericRule$cfit.2,
MAP = NumericRule$map)
temp2 <- NumericRule$vss.stats[,c(6:8,11)]
NumericRule <- cbind(temp1,temp2)
NumericRule## nFactor VSS1 VSS2 MAP RMSEA BIC SABIC SRMR
## 1 1 0.9383 0.0000 0.07033 0.17515 537.631 566.23 0.055433
## 2 2 0.6282 0.7207 0.11965 0.05953 3.971 16.68 0.009464
## 3 3 0.4602 0.6296 0.23577 NA NA NA 0.0004403.0.0.1.6 Exploratory Graph Analysis (EGA)
4 Method 1 - bootEGA Method from EFAShiny
EGArst <- bootEGA(data = data, n = 1000, medianStructure = TRUE, plot.MedianStructure = TRUE, ncores = 4, layout = "spring")## Note: bootnet will store only the following statistics: edge, strength, outStrength, inStrength## model set to 'GGM'## Estimating sample network...## Estimating Network. Using package::function:
## - qgraph::EBICglasso for EBIC model selection
## - using glasso::glasso## Note: Network with lowest lambda selected as best network: assumption of sparsity might be violated.## Warning in EBICglassoCore(S = S, n = n, gamma = gamma, penalize.diagonal =
## penalize.diagonal, : A dense regularized network was selected (lambda < 0.1 *
## lambda.max). Recent work indicates a possible drop in specificity. Interpret the
## presence of the smallest edges with care. Setting threshold = TRUE will enforce
## higher specificity, at the cost of sensitivity.## Bootstrapping...## Computing statistics...## Warning: `tbl_df()` was deprecated in dplyr 1.0.0.
## Please use `tibble::as_tibble()` instead.
5 Method 2 - ega.object from Cleyton’s paper (need to completed)
ega1 <- ega.object(CorMat,data)## Note: Network with lowest lambda selected as best network: assumption of sparsity might be violated.6 Method 3 - original boot.ega function with parallel processing
# BootEGA Function
boot.ega <- bootnet(data, nBoot = 1000, default = "EBICglasso",computeCentrality = T, type = "parametric", nCores = 4)## Note: bootnet will store only the following statistics: edge, strength, outStrength, inStrength## model set to 'GGM'## Estimating sample network...## Estimating Network. Using package::function:
## - qgraph::EBICglasso for EBIC model selection
## - using glasso::glasso## Note: Network with lowest lambda selected as best network: assumption of sparsity might be violated.## Warning in EBICglassoCore(S = S, n = n, gamma = gamma, penalize.diagonal =
## penalize.diagonal, : A dense regularized network was selected (lambda < 0.1 *
## lambda.max). Recent work indicates a possible drop in specificity. Interpret the
## presence of the smallest edges with care. Setting threshold = TRUE will enforce
## higher specificity, at the cost of sensitivity.## Bootstrapping...## Computing statistics...boot.ega## === bootnet Results ===
## Number of nodes: 6
## Number of non-zero edges in sample: 15 / 15
## Mean weight of sample: 0.1671
## Number of bootstrapped networks: 1000
## Results of original sample stored in x$sample
## Table of all statistics from original sample stored in x$sampleTable
## Results of bootstraps stored in x$boots
## Table of all statistics from bootstraps stored in x$bootTable
##
## Use plot(x$sample) to plot estimated network of original sample
## Use summary(x) to inspect summarized statistics (see ?summary.bootnet for details)
## Use plot(x) to plot summarized statistics (see ?plot.bootnet for details)
##
## Relevant references:
##
## Friedman, J. H., Hastie, T., & Tibshirani, R. (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9 (3), 432-441.
## Foygel, R., & Drton, M. (2010). Extended Bayesian information criteria for Gaussian graphical models.
## Friedman, J. H., Hastie, T., & Tibshirani, R. (2014). glasso: Graphical lasso estimation of gaussian graphical models. Retrieved from https://CRAN.R-project.org/package=glasso
## Epskamp, S., Cramer, A., Waldorp, L., Schmittmann, V. D., & Borsboom, D. (2012). qgraph: Network visualizations of relationships in psychometric data. Journal of Statistical Software, 48 (1), 1-18.
## Epskamp, S., Borsboom, D., & Fried, E. I. (2016). Estimating psychological networks and their accuracy: a tutorial paper. arXiv preprint, arXiv:1604.08462.6.0.0.0.1 Estimated network of original sample
plot(boot.ega$sample)
##### Summarized statistics
summary(boot.ega)## Warning: `select_()` was deprecated in dplyr 0.7.0.
## Please use `select()` instead.## Warning: `mutate_()` was deprecated in dplyr 0.7.0.
## Please use `mutate()` instead.
## See vignette('programming') for more help## Warning: `summarise_()` was deprecated in dplyr 0.7.0.
## Please use `summarise()` instead.## Warning: `group_by_()` was deprecated in dplyr 0.7.0.
## Please use `group_by()` instead.
## See vignette('programming') for more help## Warning: `filter_()` was deprecated in dplyr 0.7.0.
## Please use `filter()` instead.
## See vignette('programming') for more help## # A tibble: 21 x 17
## # Groups: type, node1, node2 [21]
## type id node1 node2 sample mean sd CIlower CIupper q2.5 q97.5
## <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 edge SupG_F… SupG… SupG… 0.171 0.170 0.0209 0.129 0.213 0.130 0.213
## 2 edge SupG_F… SupG… SupG… 0.165 0.165 0.0204 0.124 0.206 0.123 0.206
## 3 edge SupG_F… SupG… SupG… 0.138 0.136 0.0203 0.0971 0.178 0.0930 0.176
## 4 edge SupG_F… SupG… SupG… 0.210 0.210 0.0206 0.169 0.251 0.167 0.250
## 5 edge SupG_F… SupG… SupG… 0.145 0.144 0.0204 0.104 0.185 0.103 0.184
## 6 edge SupG_I… SupG… SupG… 0.467 0.462 0.0161 0.435 0.499 0.430 0.493
## 7 edge SupG_M… SupG… SupG… 0.0368 0.0380 0.0205 -0.00434 0.0779 0 0.0770
## 8 edge SupG_M… SupG… SupG… 0.0658 0.0653 0.0203 0.0253 0.106 0.0265 0.104
## 9 edge SupG_M… SupG… SupG… 0.152 0.152 0.0202 0.111 0.192 0.112 0.191
## 10 edge SupG_M… SupG… SupG… 0.176 0.174 0.0204 0.135 0.217 0.133 0.213
## # … with 11 more rows, and 6 more variables: q2.5_non0 <dbl>, mean_non0 <dbl>,
## # q97.5_non0 <dbl>, var_non0 <dbl>, sd_non0 <dbl>, prop0 <dbl>6.0.0.1 Plot from summarized statistics
plot(boot.ega)## Warning: `arrange_()` was deprecated in dplyr 0.7.0.
## Please use `arrange()` instead.
## See vignette('programming') for more help
6.0.0.2 Method 3 - New EGA package from Golino and XXX
# Estimate EGA
EGA(data =CorMat,n=nrow(data), plot.EGA = T,uni.method = "LE")## Warning in EGA(data = CorMat, n = nrow(data), plot.EGA = T, uni.method =
## "LE"): Previous versions of EGAnet (<= 0.9.8) checked unidimensionality using
## [4;muni.method = "expand"[0m as the default## Network estimated with:
## • gamma = 0.5
## • lambda.min.ratio = 0.1
## EGA Results:
##
## Number of Dimensions:
## [1] 1
##
## Items per Dimension:
## items dimension
## SupG_Feed SupG_Feed 1
## SupG_Meta SupG_Meta 1
## SupG_Ori SupG_Ori 1
## SupG_Mon SupG_Mon 1
## SupG_Infra SupG_Infra 1
## SupG_Bestar SupG_Bestar 16.0.0.3 Factorial Exploratory Analysis
EFArst <- psych::fa(as.matrix(CorMat),1,n.obs=nrow(data), rotate = "promax",fm = "uls", n.iter =1000, alpha = T,correct = T)The communalities were observed between 0.451 and 0.733, and the factor loadings between 0.671and 0.856 Table2. A factor was retained, with an eigenvalue of 3.66 that explained 0.61% of the variance.
6.0.0.3.1 Complete results from EFA
EFArst## Factor Analysis with confidence intervals using method = psych::fa(r = as.matrix(CorMat), nfactors = 1, n.obs = nrow(data),
## n.iter = 1000, rotate = "promax", fm = "uls", alpha = T,
## correct = T)
## Factor Analysis using method = uls
## Call: psych::fa(r = as.matrix(CorMat), nfactors = 1, n.obs = nrow(data),
## n.iter = 1000, rotate = "promax", fm = "uls", alpha = T,
## correct = T)
## Standardized loadings (pattern matrix) based upon correlation matrix
## ULS1 h2 u2 com
## SupG_Feed 0.78 0.61 0.39 1
## SupG_Meta 0.67 0.45 0.55 1
## SupG_Ori 0.84 0.71 0.29 1
## SupG_Mon 0.86 0.73 0.27 1
## SupG_Infra 0.74 0.55 0.45 1
## SupG_Bestar 0.78 0.60 0.40 1
##
## ULS1
## SS loadings 3.66
## Proportion Var 0.61
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 15 and the objective function was 3.69 with Chi Square of 7964
## The degrees of freedom for the model are 9 and the objective function was 0.28
##
## The root mean square of the residuals (RMSR) is 0.06
## The df corrected root mean square of the residuals is 0.07
##
## The harmonic number of observations is 2165 with the empirical chi square 199.6 with prob < 0.000000000000000000000000000000000000041
## The total number of observations was 2165 with Likelihood Chi Square = 606.8 with prob < 7.4e-125
##
## Tucker Lewis Index of factoring reliability = 0.875
## RMSEA index = 0.175 and the 0 % confidence intervals are NA 0.175
## BIC = 537.6
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## ULS1
## Correlation of (regression) scores with factors 0.95
## Multiple R square of scores with factors 0.91
## Minimum correlation of possible factor scores 0.82
##
## Coefficients and bootstrapped confidence intervals
## low ULS1 upper
## SupG_Feed 0.76 0.78 0.80
## SupG_Meta 0.65 0.67 0.70
## SupG_Ori 0.83 0.84 0.86
## SupG_Mon 0.84 0.86 0.87
## SupG_Infra 0.72 0.74 0.76
## SupG_Bestar 0.76 0.78 0.806.0.0.4 Exploratory Fator Analysis using semTools and a Lavaan engine
#fa_mod1 <- efaUnrotate(data=data, nf = 1, estimator = "ULSMV",ordered=T,missing="pairwise",std.lv=T)
#fa_mod2 <- efaUnrotate(data, nf = 1, estimator = "MLR",ordered=F,missing="FIML")7 Confirmatory Factor Analysis
7.0.0.1 Changing data
data<-banco_CFA7.1 Structure Validity - Dimensionality
7.1.0.1 Model
model <- 'SupG =~ SupG_Feed + SupG_Meta + SupG_Ori + SupG_Mon + SupG_Infra + SupG_Bestar'7.1.0.2 Fitting
fit <- lavaan::cfa(model, data =data,estimator="ULSMV",ordered=T,missing="pairwise",std.lv=T)7.1.0.3 General Summary
summary(fit,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 9 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 30
##
## Number of observations 5443
## Number of missing patterns 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 184.060 914.458
## Degrees of freedom 9 9
## P-value (Unknown) NA 0.000
## Scaling correction factor 0.201
## Shift parameter 0.557
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 31844.214 37805.641
## Degrees of freedom 15 15
## P-value NA 0.000
## Scaling correction factor 0.842
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.995 0.976
## Tucker-Lewis Index (TLI) 0.991 0.960
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.060 0.136
## 90 Percent confidence interval - lower 0.052 0.129
## 90 Percent confidence interval - upper 0.067 0.143
## P-value RMSEA <= 0.05 0.015 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.040 0.040
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 0.798 0.007 121.204 0.000 0.798 0.798
## SupG_Meta 0.693 0.008 82.107 0.000 0.693 0.693
## SupG_Ori 0.846 0.006 146.456 0.000 0.846 0.846
## SupG_Mon 0.827 0.006 133.870 0.000 0.827 0.827
## SupG_Infra 0.769 0.007 111.458 0.000 0.769 0.769
## SupG_Bestar 0.796 0.006 123.043 0.000 0.796 0.796
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -1.711 0.030 -57.090 0.000 -1.711 -1.711
## SupG_Feed|t2 -1.197 0.022 -53.819 0.000 -1.197 -1.197
## SupG_Feed|t3 -0.521 0.018 -29.189 0.000 -0.521 -0.521
## SupG_Feed|t4 0.653 0.018 35.519 0.000 0.653 0.653
## SupG_Meta|t1 -2.247 0.047 -48.009 0.000 -2.247 -2.247
## SupG_Meta|t2 -1.610 0.028 -57.510 0.000 -1.610 -1.610
## SupG_Meta|t3 -1.039 0.021 -50.002 0.000 -1.039 -1.039
## SupG_Meta|t4 0.483 0.018 27.245 0.000 0.483 0.483
## SupG_Ori|t1 -2.422 0.056 -43.359 0.000 -2.422 -2.422
## SupG_Ori|t2 -1.871 0.034 -55.477 0.000 -1.871 -1.871
## SupG_Ori|t3 -1.337 0.024 -56.080 0.000 -1.337 -1.337
## SupG_Ori|t4 0.057 0.017 3.375 0.001 0.057 0.057
## SupG_Mon|t1 -2.358 0.052 -45.120 0.000 -2.358 -2.358
## SupG_Mon|t2 -1.942 0.036 -54.427 0.000 -1.942 -1.942
## SupG_Mon|t3 -1.305 0.023 -55.656 0.000 -1.305 -1.305
## SupG_Mon|t4 0.100 0.017 5.895 0.000 0.100 0.100
## SupG_Infra|t1 -1.494 0.026 -57.374 0.000 -1.494 -1.494
## SupG_Infra|t2 -0.949 0.020 -47.261 0.000 -0.949 -0.949
## SupG_Infra|t3 -0.136 0.017 -7.953 0.000 -0.136 -0.136
## SupG_Infra|t4 0.789 0.019 41.388 0.000 0.789 0.789
## SupG_Bestar|t1 -1.783 0.032 -56.500 0.000 -1.783 -1.783
## SupG_Bestar|t2 -1.333 0.024 -56.024 0.000 -1.333 -1.333
## SupG_Bestar|t3 -0.643 0.018 -35.074 0.000 -0.643 -0.643
## SupG_Bestar|t4 0.404 0.018 23.096 0.000 0.404 0.404
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.363 0.363 0.363
## .SupG_Meta 0.520 0.520 0.520
## .SupG_Ori 0.284 0.284 0.284
## .SupG_Mon 0.316 0.316 0.316
## .SupG_Infra 0.409 0.409 0.409
## .SupG_Bestar 0.366 0.366 0.366
## SupG 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 1.000 1.000 1.000
## SupG_Meta 1.000 1.000 1.000
## SupG_Ori 1.000 1.000 1.000
## SupG_Mon 1.000 1.000 1.000
## SupG_Infra 1.000 1.000 1.000
## SupG_Bestar 1.000 1.000 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.637
## SupG_Meta 0.480
## SupG_Ori 0.716
## SupG_Mon 0.684
## SupG_Infra 0.591
## SupG_Bestar 0.6347.1.0.4 Selected Robust and Scaled Fit Measures
lavaan::fitMeasures(fit,c("chisq.scaled","df.scaled","pvalue.scaled","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue.scaled
## 914.458 9.000 0.000
## srmr cfi.scaled tli.scaled
## 0.040 0.976 0.960
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.136 0.129 0.1437.1.0.5 Factor Loadings
parameters<-lavaan::standardizedSolution(fit)
loadings<-parameters[parameters$op=="=~",]
loadings## lhs op rhs est.std se z pvalue ci.lower ci.upper
## 1 SupG =~ SupG_Feed 0.798 0.007 121.20 0 0.785 0.811
## 2 SupG =~ SupG_Meta 0.693 0.008 82.11 0 0.676 0.709
## 3 SupG =~ SupG_Ori 0.846 0.006 146.46 0 0.835 0.857
## 4 SupG =~ SupG_Mon 0.827 0.006 133.87 0 0.815 0.839
## 5 SupG =~ SupG_Infra 0.769 0.007 111.46 0 0.755 0.783
## 6 SupG =~ SupG_Bestar 0.796 0.006 123.04 0 0.784 0.8097.1.0.6 Modificantion Indices considering very bad RMSEA
modificationindices(fit, sort.=T)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 65 SupG_Infra ~~ SupG_Bestar 140.700 0.206 0.206 0.534 0.534
## 60 SupG_Ori ~~ SupG_Mon 40.100 0.116 0.116 0.388 0.388
## 61 SupG_Ori ~~ SupG_Infra 33.097 -0.103 -0.103 -0.301 -0.301
## 64 SupG_Mon ~~ SupG_Bestar 29.655 -0.097 -0.097 -0.287 -0.287
## 58 SupG_Meta ~~ SupG_Infra 16.442 -0.067 -0.067 -0.146 -0.146
## 56 SupG_Meta ~~ SupG_Ori 14.683 0.066 0.066 0.171 0.171
## 59 SupG_Meta ~~ SupG_Bestar 9.444 -0.052 -0.052 -0.119 -0.119
## 62 SupG_Ori ~~ SupG_Bestar 8.880 -0.054 -0.054 -0.167 -0.167
## 63 SupG_Mon ~~ SupG_Infra 8.312 -0.051 -0.051 -0.142 -0.142
## 57 SupG_Meta ~~ SupG_Mon 3.930 0.034 0.034 0.083 0.083
## 52 SupG_Feed ~~ SupG_Ori 1.837 -0.025 -0.025 -0.076 -0.076
## 51 SupG_Feed ~~ SupG_Meta 1.035 0.017 0.017 0.039 0.039
## 54 SupG_Feed ~~ SupG_Infra 0.544 0.013 0.013 0.033 0.033
## 55 SupG_Feed ~~ SupG_Bestar 0.022 -0.003 -0.003 -0.007 -0.007
## 53 SupG_Feed ~~ SupG_Mon 0.009 -0.002 -0.002 -0.005 -0.0057.1.0.7 Ordinal Alpha and Omega
semTools::reliability(fit)## For constructs with categorical indicators, Zumbo et al.`s (2007) "ordinal alpha" is calculated in addition to the standard alpha, which treats ordinal variables as numeric. See Chalmers (2018) for a critique of "alpha.ord". Likewise, average variance extracted is calculated from polychoric (polyserial) not Pearson correlations.## SupG
## alpha 0.8621
## alpha.ord 0.9076
## omega 0.8710
## omega2 0.8710
## omega3 0.8691
## avevar 0.62377.1.0.8 Modified Model
model <-
'
SupG =~ SupG_Feed + SupG_Meta + SupG_Ori + SupG_Mon + SupG_Infra + SupG_Bestar
SupG_Infra ~~ SupG_Bestar
'7.1.0.9 Fitting
fit <- lavaan::cfa(model, data =data,estimator="ULSMV",ordered=T,missing="pairwise",std.lv=T)7.1.0.10 General Summary
summary(fit,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 15 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 31
##
## Number of observations 5443
## Number of missing patterns 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 43.268 227.316
## Degrees of freedom 8 8
## P-value (Unknown) NA 0.000
## Scaling correction factor 0.191
## Shift parameter 0.410
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 31844.214 37805.641
## Degrees of freedom 15 15
## P-value NA 0.000
## Scaling correction factor 0.842
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.999 0.994
## Tucker-Lewis Index (TLI) 0.998 0.989
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.028 0.071
## 90 Percent confidence interval - lower 0.020 0.063
## 90 Percent confidence interval - upper 0.037 0.079
## P-value RMSEA <= 0.05 1.000 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.019 0.019
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 0.809 0.007 121.452 0.000 0.809 0.809
## SupG_Meta 0.703 0.008 83.304 0.000 0.703 0.703
## SupG_Ori 0.861 0.006 151.329 0.000 0.861 0.861
## SupG_Mon 0.842 0.006 137.055 0.000 0.842 0.842
## SupG_Infra 0.718 0.008 87.082 0.000 0.718 0.718
## SupG_Bestar 0.746 0.008 97.156 0.000 0.746 0.746
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.202 0.009 23.807 0.000 0.202 0.436
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -1.711 0.030 -57.090 0.000 -1.711 -1.711
## SupG_Feed|t2 -1.197 0.022 -53.819 0.000 -1.197 -1.197
## SupG_Feed|t3 -0.521 0.018 -29.189 0.000 -0.521 -0.521
## SupG_Feed|t4 0.653 0.018 35.519 0.000 0.653 0.653
## SupG_Meta|t1 -2.247 0.047 -48.009 0.000 -2.247 -2.247
## SupG_Meta|t2 -1.610 0.028 -57.510 0.000 -1.610 -1.610
## SupG_Meta|t3 -1.039 0.021 -50.002 0.000 -1.039 -1.039
## SupG_Meta|t4 0.483 0.018 27.245 0.000 0.483 0.483
## SupG_Ori|t1 -2.422 0.056 -43.359 0.000 -2.422 -2.422
## SupG_Ori|t2 -1.871 0.034 -55.477 0.000 -1.871 -1.871
## SupG_Ori|t3 -1.337 0.024 -56.080 0.000 -1.337 -1.337
## SupG_Ori|t4 0.057 0.017 3.375 0.001 0.057 0.057
## SupG_Mon|t1 -2.358 0.052 -45.120 0.000 -2.358 -2.358
## SupG_Mon|t2 -1.942 0.036 -54.427 0.000 -1.942 -1.942
## SupG_Mon|t3 -1.305 0.023 -55.656 0.000 -1.305 -1.305
## SupG_Mon|t4 0.100 0.017 5.895 0.000 0.100 0.100
## SupG_Infra|t1 -1.494 0.026 -57.374 0.000 -1.494 -1.494
## SupG_Infra|t2 -0.949 0.020 -47.261 0.000 -0.949 -0.949
## SupG_Infra|t3 -0.136 0.017 -7.953 0.000 -0.136 -0.136
## SupG_Infra|t4 0.789 0.019 41.388 0.000 0.789 0.789
## SupG_Bestar|t1 -1.783 0.032 -56.500 0.000 -1.783 -1.783
## SupG_Bestar|t2 -1.333 0.024 -56.024 0.000 -1.333 -1.333
## SupG_Bestar|t3 -0.643 0.018 -35.074 0.000 -0.643 -0.643
## SupG_Bestar|t4 0.404 0.018 23.096 0.000 0.404 0.404
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.345 0.345 0.345
## .SupG_Meta 0.506 0.506 0.506
## .SupG_Ori 0.258 0.258 0.258
## .SupG_Mon 0.292 0.292 0.292
## .SupG_Infra 0.485 0.485 0.485
## .SupG_Bestar 0.444 0.444 0.444
## SupG 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 1.000 1.000 1.000
## SupG_Meta 1.000 1.000 1.000
## SupG_Ori 1.000 1.000 1.000
## SupG_Mon 1.000 1.000 1.000
## SupG_Infra 1.000 1.000 1.000
## SupG_Bestar 1.000 1.000 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.655
## SupG_Meta 0.494
## SupG_Ori 0.742
## SupG_Mon 0.708
## SupG_Infra 0.515
## SupG_Bestar 0.5567.1.0.11 Selected Robust and Scaled Fit Measures
lavaan::fitMeasures(fit,c("chisq.scaled","df.scaled","pvalue.scaled","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue.scaled
## 227.316 8.000 0.000
## srmr cfi.scaled tli.scaled
## 0.019 0.994 0.989
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.071 0.063 0.0797.1.0.12 Factor Loadings
parameters<-lavaan::standardizedSolution(fit)
loadings<-parameters[parameters$op=="=~",]
loadings## lhs op rhs est.std se z pvalue ci.lower ci.upper
## 1 SupG =~ SupG_Feed 0.809 0.007 121.45 0 0.796 0.822
## 2 SupG =~ SupG_Meta 0.703 0.008 83.30 0 0.686 0.719
## 3 SupG =~ SupG_Ori 0.861 0.006 151.33 0 0.850 0.872
## 4 SupG =~ SupG_Mon 0.842 0.006 137.06 0 0.830 0.854
## 5 SupG =~ SupG_Infra 0.718 0.008 87.08 0 0.701 0.734
## 6 SupG =~ SupG_Bestar 0.746 0.008 97.16 0 0.731 0.7617.1.0.13 Modificantion Indices considering very bad RMSEA
modificationindices(fit, sort.=T)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 61 SupG_Ori ~~ SupG_Mon 15.939 0.077 0.077 0.279 0.279
## 55 SupG_Feed ~~ SupG_Infra 15.601 0.070 0.070 0.171 0.171
## 53 SupG_Feed ~~ SupG_Ori 13.097 -0.068 -0.068 -0.228 -0.228
## 56 SupG_Feed ~~ SupG_Bestar 8.889 0.053 0.053 0.137 0.137
## 62 SupG_Ori ~~ SupG_Infra 7.134 -0.049 -0.049 -0.138 -0.138
## 65 SupG_Mon ~~ SupG_Bestar 6.188 -0.045 -0.045 -0.126 -0.126
## 54 SupG_Feed ~~ SupG_Mon 4.807 -0.041 -0.041 -0.128 -0.128
## 57 SupG_Meta ~~ SupG_Ori 4.246 0.036 0.036 0.101 0.101
## 59 SupG_Meta ~~ SupG_Infra 2.327 -0.026 -0.026 -0.052 -0.052
## 60 SupG_Meta ~~ SupG_Bestar 0.347 -0.010 -0.010 -0.021 -0.021
## 52 SupG_Feed ~~ SupG_Meta 0.206 -0.008 -0.008 -0.019 -0.019
## 58 SupG_Meta ~~ SupG_Mon 0.061 0.004 0.004 0.011 0.011
## 64 SupG_Mon ~~ SupG_Infra 0.041 0.004 0.004 0.010 0.010
## 63 SupG_Ori ~~ SupG_Bestar 0.009 0.002 0.002 0.005 0.0057.1.0.14 Ordinal Alpha and Omega
semTools::reliability(fit)## For constructs with categorical indicators, Zumbo et al.`s (2007) "ordinal alpha" is calculated in addition to the standard alpha, which treats ordinal variables as numeric. See Chalmers (2018) for a critique of "alpha.ord". Likewise, average variance extracted is calculated from polychoric (polyserial) not Pearson correlations.## SupG
## alpha 0.8621
## alpha.ord 0.9076
## omega 0.8414
## omega2 0.8414
## omega3 0.8403
## avevar 0.61177.1.0.15 Graphical Representation
semPaths(object=fit,whatLabels ="stand",residuals = F, thresholds = F,ThreshAtSide=F, cardinal = c("exogenous covariances", border.color = ("black")), layout="circle",intercept=F, edge.label.cex = 1)
7.1.1 Internal Validity
7.1.1.1 Organizing Sex
data$Gen<-car::recode(data$Gen,"0=NA")
data$SexoR<-as.factor(data$Gen)7.1.1.2 Sex Invariance Model
model <-
'
SupG =~ SupG_Feed + SupG_Meta + SupG_Ori + SupG_Mon + SupG_Infra + SupG_Bestar
SupG_Infra ~~ SupG_Bestar
'7.1.1.3 Fitting
invariance<- measurementInvarianceCat(model = model, data = data, group = "SexoR",parameterization = "theta", estimator = "ULSMV",ordered =T,missing="pairwise",std.lv=T)## Warning: The measurementInvarianceCat function is deprecated, and it will cease
## to be included in future versions of semTools. See help('semTools-deprecated)
## for details.## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'SexoR' contains missing values
## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'SexoR' contains missing values
## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'SexoR' contains missing values
## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'SexoR' contains missing values
## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'SexoR' contains missing values##
## Measurement invariance models:
##
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.thresholds
## Model 4 : fit.means
##
## Scaled Chi-Squared Difference Test (method = "satorra.2000")
##
## 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)
## fit.configural 16 47.5
## fit.loadings 21 66.2 8.07 5 0.152
## fit.thresholds 38 134.6 31.10 17 0.019 *
## fit.means 39 144.8 1.10 1 0.295
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Fit measures:
##
## cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural 0.994 0.073 NA NA
## fit.loadings 0.998 0.033 0.004 0.040
## fit.thresholds 0.998 0.024 0.000 0.008
## fit.means 0.999 0.022 0.000 0.0037.1.1.3.1 Configural
summary(invariance$fit.configural,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 130 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 69
## Number of equality constraints 7
##
## Number of observations per group:
## 2 2240
## 1 3199
## Number of missing patterns per group:
## 2 1
## 1 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 47.519 248.570
## Degrees of freedom 16 16
## P-value (Unknown) NA 0.000
## Scaling correction factor 0.192
## Shift parameter for each group:
## 2 0.413
## 1 0.589
## simple second-order correction
## Test statistic for each group:
## 2 16.779 87.830
## 1 30.740 160.740
##
## Model Test Baseline Model:
##
## Test statistic 31830.796 38247.598
## Degrees of freedom 30 30
## P-value NA 0.000
## Scaling correction factor 0.833
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.999 0.994
## Tucker-Lewis Index (TLI) 0.998 0.989
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.027 0.073
## 90 Percent confidence interval - lower 0.018 0.065
## 90 Percent confidence interval - upper 0.036 0.081
## P-value RMSEA <= 0.05 1.000 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.020 0.020
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
##
## Group 1 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.431 0.053 26.961 0.000 1.431 0.820
## SupG_Meta 1.066 0.037 28.894 0.000 1.066 0.729
## SupG_Ori 1.739 0.067 25.869 0.000 1.739 0.867
## SupG_Mon 1.520 0.056 26.956 0.000 1.520 0.835
## SupG_Infra 1.063 0.038 27.857 0.000 1.063 0.728
## SupG_Bestar 1.126 0.040 27.957 0.000 1.126 0.748
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.443 0.019 22.749 0.000 0.443 0.443
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.984 0.081 -36.873 0.000 -2.984 -1.709
## SupG_Feed|t2 -2.051 0.065 -31.721 0.000 -2.051 -1.175
## SupG_Feed|t3 -0.893 0.051 -17.538 0.000 -0.893 -0.512
## SupG_Feed|t4 1.200 0.053 22.590 0.000 1.200 0.687
## SupG_Meta|t1 -3.201 0.100 -32.080 0.000 -3.201 -2.189
## SupG_Meta|t2 -2.386 0.065 -36.591 0.000 -2.386 -1.632
## SupG_Meta|t3 -1.526 0.049 -30.852 0.000 -1.526 -1.044
## SupG_Meta|t4 0.667 0.040 16.869 0.000 0.667 0.456
## SupG_Ori|t1 -4.714 0.154 -30.534 0.000 -4.714 -2.350
## SupG_Ori|t2 -3.616 0.110 -32.879 0.000 -3.616 -1.803
## SupG_Ori|t3 -2.472 0.084 -29.370 0.000 -2.472 -1.232
## SupG_Ori|t4 0.241 0.052 4.603 0.000 0.241 0.120
## SupG_Mon|t1 -4.186 0.138 -30.364 0.000 -4.186 -2.300
## SupG_Mon|t2 -3.580 0.110 -32.660 0.000 -3.580 -1.968
## SupG_Mon|t3 -2.393 0.077 -30.884 0.000 -2.393 -1.315
## SupG_Mon|t4 0.257 0.048 5.418 0.000 0.257 0.141
## SupG_Infra|t1 -2.110 0.059 -36.062 0.000 -2.110 -1.446
## SupG_Infra|t2 -1.354 0.047 -28.884 0.000 -1.354 -0.928
## SupG_Infra|t3 -0.218 0.039 -5.601 0.000 -0.218 -0.149
## SupG_Infra|t4 1.140 0.044 26.020 0.000 1.140 0.781
## SupG_Bestar|t1 -2.750 0.076 -36.165 0.000 -2.750 -1.826
## SupG_Bestar|t2 -2.018 0.058 -34.677 0.000 -2.018 -1.340
## SupG_Bestar|t3 -0.945 0.044 -21.417 0.000 -0.945 -0.627
## SupG_Bestar|t4 0.630 0.041 15.407 0.000 0.630 0.418
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.000 1.000 0.328
## .SupG_Meta 1.000 1.000 0.468
## .SupG_Ori 1.000 1.000 0.249
## .SupG_Mon 1.000 1.000 0.302
## .SupG_Infra 1.000 1.000 0.470
## .SupG_Bestar 1.000 1.000 0.441
## SupG 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.573 0.573 1.000
## SupG_Meta 0.684 0.684 1.000
## SupG_Ori 0.499 0.499 1.000
## SupG_Mon 0.550 0.550 1.000
## SupG_Infra 0.685 0.685 1.000
## SupG_Bestar 0.664 0.664 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.672
## SupG_Meta 0.532
## SupG_Ori 0.751
## SupG_Mon 0.698
## SupG_Infra 0.530
## SupG_Bestar 0.559
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.497 0.146 10.263 0.000 1.497 0.801
## SupG_Meta 0.993 0.069 14.317 0.000 0.993 0.683
## SupG_Ori 1.708 0.133 12.862 0.000 1.708 0.858
## SupG_Mon 1.547 0.117 13.226 0.000 1.547 0.847
## SupG_Infra 1.048 0.089 11.716 0.000 1.048 0.709
## SupG_Bestar 1.244 0.102 12.228 0.000 1.244 0.745
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.505 0.084 5.977 0.000 0.505 0.435
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.149 0.152 0.980 0.327 0.149 0.149
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.984 0.081 -36.873 0.000 -2.984 -1.596
## SupG_Feed|t2 -2.051 0.065 -31.721 0.000 -2.051 -1.097
## SupG_Feed|t3 -0.767 0.158 -4.857 0.000 -0.767 -0.410
## SupG_Feed|t4 1.397 0.355 3.934 0.000 1.397 0.747
## SupG_Meta|t1 -3.201 0.100 -32.080 0.000 -3.201 -2.202
## SupG_Meta|t2 -2.175 0.101 -21.531 0.000 -2.175 -1.496
## SupG_Meta|t3 -1.358 0.105 -12.947 0.000 -1.358 -0.934
## SupG_Meta|t4 0.878 0.199 4.400 0.000 0.878 0.604
## SupG_Ori|t1 -4.714 0.154 -30.534 0.000 -4.714 -2.370
## SupG_Ori|t2 -3.583 0.166 -21.599 0.000 -3.583 -1.801
## SupG_Ori|t3 -2.579 0.161 -16.048 0.000 -2.579 -1.296
## SupG_Ori|t4 0.282 0.277 1.018 0.309 0.282 0.142
## SupG_Mon|t1 -4.186 0.138 -30.364 0.000 -4.186 -2.291
## SupG_Mon|t2 -3.293 0.149 -22.126 0.000 -3.293 -1.802
## SupG_Mon|t3 -2.143 0.149 -14.361 0.000 -2.143 -1.173
## SupG_Mon|t4 0.362 0.257 1.407 0.160 0.362 0.198
## SupG_Infra|t1 -2.110 0.059 -36.062 0.000 -2.110 -1.428
## SupG_Infra|t2 -1.271 0.077 -16.409 0.000 -1.271 -0.861
## SupG_Infra|t3 -0.032 0.158 -0.205 0.838 -0.032 -0.022
## SupG_Infra|t4 1.328 0.264 5.039 0.000 1.328 0.899
## SupG_Bestar|t1 -2.750 0.076 -36.165 0.000 -2.750 -1.647
## SupG_Bestar|t2 -2.034 0.083 -24.548 0.000 -2.034 -1.218
## SupG_Bestar|t3 -0.908 0.131 -6.940 0.000 -0.908 -0.544
## SupG_Bestar|t4 0.844 0.251 3.360 0.001 0.844 0.505
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.254 0.235 5.329 0.000 1.254 0.359
## .SupG_Meta 1.128 0.146 7.714 0.000 1.128 0.534
## .SupG_Ori 1.042 0.157 6.633 0.000 1.042 0.263
## .SupG_Mon 0.945 0.138 6.848 0.000 0.945 0.283
## .SupG_Infra 1.084 0.181 5.998 0.000 1.084 0.497
## .SupG_Bestar 1.241 0.196 6.324 0.000 1.241 0.445
## SupG 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.535 0.535 1.000
## SupG_Meta 0.688 0.688 1.000
## SupG_Ori 0.503 0.503 1.000
## SupG_Mon 0.547 0.547 1.000
## SupG_Infra 0.677 0.677 1.000
## SupG_Bestar 0.599 0.599 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.641
## SupG_Meta 0.466
## SupG_Ori 0.737
## SupG_Mon 0.717
## SupG_Infra 0.503
## SupG_Bestar 0.555lavaan::fitMeasures(invariance$fit.configural,c("chisq.scaled","df.scaled","pvalue.scaled","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue.scaled
## 248.570 16.000 0.000
## srmr cfi.scaled tli.scaled
## 0.020 0.994 0.989
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.073 0.065 0.081modificationindices(invariance$fit.configural, sort.=T)## lhs op rhs block group level mi epc sepc.lv sepc.all
## 133 SupG_Ori ~~ SupG_Mon 2 2 1 13.242 0.335 0.335 0.337
## 125 SupG_Feed ~~ SupG_Ori 2 2 1 9.924 -0.287 -0.287 -0.251
## 127 SupG_Feed ~~ SupG_Infra 2 2 1 9.820 0.200 0.200 0.171
## 113 SupG_Feed ~~ SupG_Infra 1 1 1 5.776 0.170 0.170 0.170
## 134 SupG_Ori ~~ SupG_Infra 2 2 1 5.518 -0.165 -0.165 -0.155
## 126 SupG_Feed ~~ SupG_Mon 2 2 1 5.227 -0.190 -0.190 -0.175
## 128 SupG_Feed ~~ SupG_Bestar 2 2 1 5.196 0.167 0.167 0.134
## 114 SupG_Feed ~~ SupG_Bestar 1 1 1 3.823 0.144 0.144 0.144
## 111 SupG_Feed ~~ SupG_Ori 1 1 1 3.757 -0.199 -0.199 -0.199
## 119 SupG_Ori ~~ SupG_Mon 1 1 1 3.692 0.207 0.207 0.207
## 115 SupG_Meta ~~ SupG_Ori 1 1 1 3.620 0.155 0.155 0.155
## 137 SupG_Mon ~~ SupG_Bestar 2 2 1 3.603 -0.139 -0.139 -0.129
## 123 SupG_Mon ~~ SupG_Bestar 1 1 1 2.847 -0.130 -0.130 -0.130
## 110 SupG_Feed ~~ SupG_Meta 1 1 1 2.090 -0.100 -0.100 -0.100
## 120 SupG_Ori ~~ SupG_Infra 1 1 1 1.839 -0.113 -0.113 -0.113
## 117 SupG_Meta ~~ SupG_Infra 1 1 1 1.369 -0.066 -0.066 -0.066
## 129 SupG_Meta ~~ SupG_Ori 2 2 1 1.145 0.071 0.071 0.065
## 132 SupG_Meta ~~ SupG_Bestar 2 2 1 1.144 -0.057 -0.057 -0.048
## 131 SupG_Meta ~~ SupG_Infra 2 2 1 1.045 -0.048 -0.048 -0.043
## 124 SupG_Feed ~~ SupG_Meta 2 2 1 0.464 0.041 0.041 0.035
## 112 SupG_Feed ~~ SupG_Mon 1 1 1 0.438 -0.060 -0.060 -0.060
## 135 SupG_Ori ~~ SupG_Bestar 2 2 1 0.385 0.050 0.050 0.044
## 121 SupG_Ori ~~ SupG_Bestar 1 1 1 0.341 -0.051 -0.051 -0.051
## 118 SupG_Meta ~~ SupG_Bestar 1 1 1 0.142 0.022 0.022 0.022
## 136 SupG_Mon ~~ SupG_Infra 2 2 1 0.048 0.014 0.014 0.014
## 116 SupG_Meta ~~ SupG_Mon 1 1 1 0.038 0.014 0.014 0.014
## 130 SupG_Meta ~~ SupG_Mon 2 2 1 0.018 0.008 0.008 0.008
## 122 SupG_Mon ~~ SupG_Infra 1 1 1 0.007 0.006 0.006 0.006
## sepc.nox
## 133 0.337
## 125 -0.251
## 127 0.171
## 113 0.170
## 134 -0.155
## 126 -0.175
## 128 0.134
## 114 0.144
## 111 -0.199
## 119 0.207
## 115 0.155
## 137 -0.129
## 123 -0.130
## 110 -0.100
## 120 -0.113
## 117 -0.066
## 129 0.065
## 132 -0.048
## 131 -0.043
## 124 0.035
## 112 -0.060
## 135 0.044
## 121 -0.051
## 118 0.022
## 136 0.014
## 116 0.014
## 130 0.008
## 122 0.006semTools::reliability(invariance$fit.configural)## For constructs with categorical indicators, Zumbo et al.`s (2007) "ordinal alpha" is calculated in addition to the standard alpha, which treats ordinal variables as numeric. See Chalmers (2018) for a critique of "alpha.ord". Likewise, average variance extracted is calculated from polychoric (polyserial) not Pearson correlations.## $`2`
## SupG
## alpha 0.8694
## alpha.ord 0.9121
## omega 0.8480
## omega2 0.8480
## omega3 0.8471
## avevar 0.6454
##
## $`1`
## SupG
## alpha 0.8562
## alpha.ord 0.9043
## omega 0.8396
## omega2 0.8396
## omega3 0.8385
## avevar 0.62557.1.1.3.2 Loadings
summary(invariance$fit.loadings,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 123 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 70
## Number of equality constraints 13
##
## Number of observations per group:
## 2 2240
## 1 3199
## Number of missing patterns per group:
## 2 1
## 1 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 66.250 82.456
## Degrees of freedom 21 21
## P-value (Unknown) NA 0.000
## Scaling correction factor 0.850
## Shift parameter for each group:
## 2 1.868
## 1 2.668
## simple second-order correction
## Test statistic for each group:
## 2 27.561 34.283
## 1 38.690 48.172
##
## Model Test Baseline Model:
##
## Test statistic 31830.796 38247.598
## Degrees of freedom 30 30
## P-value NA 0.000
## Scaling correction factor 0.833
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.999 0.998
## Tucker-Lewis Index (TLI) 0.998 0.998
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.028 0.033
## 90 Percent confidence interval - lower 0.021 0.026
## 90 Percent confidence interval - upper 0.036 0.040
## P-value RMSEA <= 0.05 1.000 1.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.023 0.023
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
##
## Group 1 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.456 0.057 25.398 0.000 1.456 0.824
## SupG_Meta 1.005 0.041 24.742 0.000 1.005 0.709
## SupG_Ori 1.682 0.099 17.069 0.000 1.682 0.860
## SupG_Mon 1.556 0.080 19.383 0.000 1.556 0.841
## SupG_Infra 1.040 0.036 28.778 0.000 1.040 0.721
## SupG_Bestar 1.223 0.049 24.914 0.000 1.223 0.774
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.428 0.025 16.891 0.000 0.428 0.428
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.991 0.099 -30.362 0.000 -2.991 -1.694
## SupG_Feed|t2 -2.098 0.077 -27.229 0.000 -2.098 -1.188
## SupG_Feed|t3 -0.904 0.053 -17.151 0.000 -0.904 -0.512
## SupG_Feed|t4 1.214 0.055 21.997 0.000 1.214 0.687
## SupG_Meta|t1 -3.129 0.114 -27.480 0.000 -3.129 -2.207
## SupG_Meta|t2 -2.314 0.077 -30.099 0.000 -2.314 -1.632
## SupG_Meta|t3 -1.480 0.054 -27.604 0.000 -1.480 -1.044
## SupG_Meta|t4 0.647 0.039 16.626 0.000 0.647 0.456
## SupG_Ori|t1 -4.609 0.267 -17.236 0.000 -4.609 -2.355
## SupG_Ori|t2 -3.527 0.176 -20.058 0.000 -3.527 -1.803
## SupG_Ori|t3 -2.411 0.118 -20.452 0.000 -2.411 -1.232
## SupG_Ori|t4 0.235 0.052 4.532 0.000 0.235 0.120
## SupG_Mon|t1 -4.244 0.217 -19.576 0.000 -4.244 -2.294
## SupG_Mon|t2 -3.640 0.171 -21.242 0.000 -3.640 -1.968
## SupG_Mon|t3 -2.433 0.107 -22.821 0.000 -2.433 -1.315
## SupG_Mon|t4 0.262 0.049 5.372 0.000 0.262 0.141
## SupG_Infra|t1 -2.107 0.063 -33.676 0.000 -2.107 -1.460
## SupG_Infra|t2 -1.339 0.050 -26.710 0.000 -1.339 -0.928
## SupG_Infra|t3 -0.216 0.039 -5.567 0.000 -0.216 -0.149
## SupG_Infra|t4 1.127 0.043 26.056 0.000 1.127 0.781
## SupG_Bestar|t1 -2.844 0.102 -27.826 0.000 -2.844 -1.800
## SupG_Bestar|t2 -2.116 0.076 -27.860 0.000 -2.116 -1.340
## SupG_Bestar|t3 -0.991 0.050 -19.871 0.000 -0.991 -0.627
## SupG_Bestar|t4 0.660 0.044 15.125 0.000 0.660 0.418
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.000 1.000 0.321
## .SupG_Meta 1.000 1.000 0.497
## .SupG_Ori 1.000 1.000 0.261
## .SupG_Mon 1.000 1.000 0.292
## .SupG_Infra 1.000 1.000 0.480
## .SupG_Bestar 1.000 1.000 0.401
## SupG 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.566 0.566 1.000
## SupG_Meta 0.705 0.705 1.000
## SupG_Ori 0.511 0.511 1.000
## SupG_Mon 0.541 0.541 1.000
## SupG_Infra 0.693 0.693 1.000
## SupG_Bestar 0.633 0.633 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.679
## SupG_Meta 0.503
## SupG_Ori 0.739
## SupG_Mon 0.708
## SupG_Infra 0.520
## SupG_Bestar 0.599
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.456 0.057 25.398 0.000 1.376 0.798
## SupG_Meta 1.005 0.041 24.742 0.000 0.950 0.698
## SupG_Ori 1.682 0.099 17.069 0.000 1.589 0.863
## SupG_Mon 1.556 0.080 19.383 0.000 1.471 0.842
## SupG_Infra 1.040 0.036 28.778 0.000 0.983 0.715
## SupG_Bestar 1.223 0.049 24.914 0.000 1.156 0.725
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.471 0.068 6.924 0.000 0.471 0.446
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG -0.010 0.134 -0.076 0.940 -0.011 -0.011
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.991 0.099 -30.362 0.000 -2.991 -1.734
## SupG_Feed|t2 -2.098 0.077 -27.229 0.000 -2.098 -1.216
## SupG_Feed|t3 -0.928 0.133 -6.976 0.000 -0.928 -0.538
## SupG_Feed|t4 1.068 0.274 3.901 0.000 1.068 0.619
## SupG_Meta|t1 -3.129 0.114 -27.480 0.000 -3.129 -2.299
## SupG_Meta|t2 -2.185 0.098 -22.263 0.000 -2.185 -1.606
## SupG_Meta|t3 -1.420 0.088 -16.155 0.000 -1.420 -1.044
## SupG_Meta|t4 0.673 0.178 3.775 0.000 0.673 0.494
## SupG_Ori|t1 -4.609 0.267 -17.236 0.000 -4.609 -2.504
## SupG_Ori|t2 -3.567 0.240 -14.841 0.000 -3.567 -1.938
## SupG_Ori|t3 -2.639 0.193 -13.691 0.000 -2.639 -1.433
## SupG_Ori|t4 0.008 0.228 0.036 0.972 0.008 0.004
## SupG_Mon|t1 -4.244 0.217 -19.576 0.000 -4.244 -2.431
## SupG_Mon|t2 -3.383 0.198 -17.066 0.000 -3.383 -1.938
## SupG_Mon|t3 -2.285 0.155 -14.701 0.000 -2.285 -1.308
## SupG_Mon|t4 0.109 0.217 0.503 0.615 0.109 0.063
## SupG_Infra|t1 -2.107 0.063 -33.676 0.000 -2.107 -1.532
## SupG_Infra|t2 -1.340 0.074 -18.144 0.000 -1.340 -0.974
## SupG_Infra|t3 -0.186 0.130 -1.433 0.152 -0.186 -0.135
## SupG_Infra|t4 1.080 0.210 5.146 0.000 1.080 0.786
## SupG_Bestar|t1 -2.844 0.102 -27.826 0.000 -2.844 -1.784
## SupG_Bestar|t2 -2.131 0.097 -22.013 0.000 -2.131 -1.337
## SupG_Bestar|t3 -1.056 0.118 -8.984 0.000 -1.056 -0.663
## SupG_Bestar|t4 0.616 0.200 3.078 0.002 0.616 0.387
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.083 0.183 5.918 0.000 1.083 0.364
## .SupG_Meta 0.950 0.146 6.517 0.000 0.950 0.513
## .SupG_Ori 0.862 0.202 4.266 0.000 0.862 0.255
## .SupG_Mon 0.885 0.184 4.800 0.000 0.885 0.290
## .SupG_Infra 0.925 0.132 7.011 0.000 0.925 0.489
## .SupG_Bestar 1.205 0.169 7.145 0.000 1.205 0.474
## SupG 0.893 0.127 7.056 0.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.580 0.580 1.000
## SupG_Meta 0.735 0.735 1.000
## SupG_Ori 0.543 0.543 1.000
## SupG_Mon 0.573 0.573 1.000
## SupG_Infra 0.727 0.727 1.000
## SupG_Bestar 0.627 0.627 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.636
## SupG_Meta 0.487
## SupG_Ori 0.745
## SupG_Mon 0.710
## SupG_Infra 0.511
## SupG_Bestar 0.526lavaan::fitMeasures(invariance$fit.loadings,c("chisq.scaled","df.scaled","pvalue.scaled","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue.scaled
## 82.456 21.000 0.000
## srmr cfi.scaled tli.scaled
## 0.023 0.998 0.998
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.033 0.026 0.040modificationindices(invariance$fit.loadings, sort.=T)## lhs op rhs block group level mi epc sepc.lv
## 134 SupG_Feed ~~ SupG_Bestar 2 2 1 11.316 0.200 0.200
## 101 SupG_Bestar ~1 2 2 1 10.835 -0.295 -0.295
## 95 SupG_Bestar ~*~ SupG_Bestar 2 2 1 10.835 -0.065 -0.065
## 44 SupG_Bestar ~*~ SupG_Bestar 1 1 1 10.835 0.066 0.066
## 50 SupG_Bestar ~1 1 1 1 10.835 0.295 0.295
## 139 SupG_Ori ~~ SupG_Mon 2 2 1 10.420 0.236 0.236
## 129 SupG_Mon ~~ SupG_Bestar 1 1 1 9.070 -0.222 -0.222
## 121 SupG_Meta ~~ SupG_Ori 1 1 1 9.049 0.209 0.209
## 131 SupG_Feed ~~ SupG_Ori 2 2 1 8.670 -0.207 -0.207
## 133 SupG_Feed ~~ SupG_Infra 2 2 1 8.030 0.147 0.147
## 140 SupG_Ori ~~ SupG_Infra 2 2 1 7.381 -0.150 -0.150
## 46 SupG_Meta ~1 1 1 1 7.358 -0.268 -0.268
## 91 SupG_Meta ~*~ SupG_Meta 2 2 1 7.358 0.063 0.063
## 40 SupG_Meta ~*~ SupG_Meta 1 1 1 7.358 -0.060 -0.060
## 97 SupG_Meta ~1 2 2 1 7.358 0.268 0.268
## 119 SupG_Feed ~~ SupG_Infra 1 1 1 5.776 0.158 0.158
## 137 SupG_Meta ~~ SupG_Infra 2 2 1 3.649 -0.073 -0.073
## 125 SupG_Ori ~~ SupG_Mon 1 1 1 3.057 0.164 0.164
## 132 SupG_Feed ~~ SupG_Mon 2 2 1 2.679 -0.108 -0.108
## 100 SupG_Infra ~1 2 2 1 2.661 0.119 0.119
## 43 SupG_Infra ~*~ SupG_Infra 1 1 1 2.661 -0.039 -0.039
## 94 SupG_Infra ~*~ SupG_Infra 2 2 1 2.661 0.041 0.041
## 49 SupG_Infra ~1 1 1 1 2.661 -0.119 -0.119
## 117 SupG_Feed ~~ SupG_Ori 1 1 1 2.482 -0.140 -0.140
## 141 SupG_Ori ~~ SupG_Bestar 2 2 1 2.235 0.095 0.095
## 127 SupG_Ori ~~ SupG_Bestar 1 1 1 2.234 -0.117 -0.117
## 118 SupG_Feed ~~ SupG_Mon 1 1 1 1.161 -0.090 -0.090
## 48 SupG_Mon ~1 1 1 1 0.833 0.110 0.110
## 42 SupG_Mon ~*~ SupG_Mon 1 1 1 0.833 0.014 0.014
## 99 SupG_Mon ~1 2 2 1 0.833 -0.110 -0.110
## 93 SupG_Mon ~*~ SupG_Mon 2 2 1 0.833 -0.015 -0.015
## 122 SupG_Meta ~~ SupG_Mon 1 1 1 0.820 0.059 0.059
## 138 SupG_Meta ~~ SupG_Bestar 2 2 1 0.670 -0.037 -0.037
## 90 SupG_Feed ~*~ SupG_Feed 2 2 1 0.596 -0.016 -0.016
## 39 SupG_Feed ~*~ SupG_Feed 1 1 1 0.593 0.015 0.015
## 98 SupG_Ori ~1 2 2 1 0.525 0.094 0.094
## 41 SupG_Ori ~*~ SupG_Ori 1 1 1 0.525 -0.010 -0.010
## 47 SupG_Ori ~1 1 1 1 0.525 -0.094 -0.094
## 92 SupG_Ori ~*~ SupG_Ori 2 2 1 0.525 0.011 0.011
## 116 SupG_Feed ~~ SupG_Meta 1 1 1 0.303 -0.033 -0.033
## 136 SupG_Meta ~~ SupG_Mon 2 2 1 0.295 -0.028 -0.028
## 126 SupG_Ori ~~ SupG_Infra 1 1 1 0.290 -0.038 -0.038
## 120 SupG_Feed ~~ SupG_Bestar 1 1 1 0.126 0.025 0.025
## 143 SupG_Mon ~~ SupG_Bestar 2 2 1 0.102 -0.019 -0.019
## 96 SupG_Feed ~1 2 2 1 0.074 -0.031 -0.031
## 45 SupG_Feed ~1 1 1 1 0.074 0.031 0.031
## 128 SupG_Mon ~~ SupG_Infra 1 1 1 0.033 0.012 0.012
## 124 SupG_Meta ~~ SupG_Bestar 1 1 1 0.027 0.009 0.009
## 135 SupG_Meta ~~ SupG_Ori 2 2 1 0.017 -0.007 -0.007
## 142 SupG_Mon ~~ SupG_Infra 2 2 1 0.010 0.005 0.005
## 123 SupG_Meta ~~ SupG_Infra 1 1 1 0.001 0.001 0.001
## 130 SupG_Feed ~~ SupG_Meta 2 2 1 0.000 -0.001 -0.001
## sepc.all sepc.nox
## 134 0.175 0.175
## 101 -0.185 -0.185
## 95 -1.000 -1.000
## 44 1.000 1.000
## 50 0.187 0.187
## 139 0.270 0.270
## 129 -0.222 -0.222
## 121 0.209 0.209
## 131 -0.215 -0.215
## 133 0.147 0.147
## 140 -0.168 -0.168
## 46 -0.189 -0.189
## 91 1.000 1.000
## 40 -1.000 -1.000
## 97 0.197 0.197
## 119 0.158 0.158
## 137 -0.078 -0.078
## 125 0.164 0.164
## 132 -0.111 -0.111
## 100 0.087 0.087
## 43 -1.000 -1.000
## 94 1.000 1.000
## 49 -0.083 -0.083
## 117 -0.140 -0.140
## 141 0.094 0.094
## 127 -0.117 -0.117
## 118 -0.090 -0.090
## 48 0.059 0.059
## 42 1.000 1.000
## 99 -0.063 -0.063
## 93 -1.000 -1.000
## 122 0.059 0.059
## 138 -0.034 -0.034
## 90 -1.000 -1.000
## 39 1.000 1.000
## 98 0.051 0.051
## 41 -1.000 -1.000
## 47 -0.048 -0.048
## 92 1.000 1.000
## 116 -0.033 -0.033
## 136 -0.030 -0.030
## 126 -0.038 -0.038
## 120 0.025 0.025
## 143 -0.019 -0.019
## 96 -0.018 -0.018
## 45 0.018 0.018
## 128 0.012 0.012
## 124 0.009 0.009
## 135 -0.008 -0.008
## 142 0.006 0.006
## 123 0.001 0.001
## 130 -0.001 -0.001semTools::reliability(invariance$fit.loadings)## For constructs with categorical indicators, Zumbo et al.`s (2007) "ordinal alpha" is calculated in addition to the standard alpha, which treats ordinal variables as numeric. See Chalmers (2018) for a critique of "alpha.ord". Likewise, average variance extracted is calculated from polychoric (polyserial) not Pearson correlations.## $`2`
## SupG
## alpha 0.8694
## alpha.ord 0.9121
## omega 0.8502
## omega2 0.8502
## omega3 0.8494
## avevar 0.6462
##
## $`1`
## SupG
## alpha 0.8562
## alpha.ord 0.9043
## omega 0.8339
## omega2 0.8339
## omega3 0.8322
## avevar 0.62357.1.1.3.3 Thresholds
summary(invariance$fit.thresholds,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 96 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 70
## Number of equality constraints 30
##
## Number of observations per group:
## 2 2240
## 1 3199
## Number of missing patterns per group:
## 2 1
## 1 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 134.582 99.465
## Degrees of freedom 38 38
## P-value (Unknown) NA 0.000
## Scaling correction factor 1.453
## Shift parameter for each group:
## 2 2.813
## 1 4.017
## simple second-order correction
## Test statistic for each group:
## 2 68.323 49.841
## 1 66.258 49.624
##
## Model Test Baseline Model:
##
## Test statistic 31830.796 38247.598
## Degrees of freedom 30 30
## P-value NA 0.000
## Scaling correction factor 0.833
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.997 0.998
## Tucker-Lewis Index (TLI) 0.998 0.999
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.031 0.024
## 90 Percent confidence interval - lower 0.025 0.019
## 90 Percent confidence interval - upper 0.036 0.030
## P-value RMSEA <= 0.05 1.000 1.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.023 0.023
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
##
## Group 1 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.461 0.059 24.825 0.000 1.461 0.825
## SupG_Meta 1.014 0.038 26.877 0.000 1.014 0.712
## SupG_Ori 1.609 0.077 20.981 0.000 1.609 0.849
## SupG_Mon 1.633 0.081 20.095 0.000 1.633 0.853
## SupG_Infra 1.035 0.036 29.040 0.000 1.035 0.719
## SupG_Bestar 1.206 0.045 26.662 0.000 1.206 0.770
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.434 0.025 17.313 0.000 0.434 0.434
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -3.013 0.100 -30.101 0.000 -3.013 -1.702
## SupG_Feed|t2 -2.101 0.075 -28.033 0.000 -2.101 -1.187
## SupG_Feed|t3 -0.899 0.049 -18.526 0.000 -0.899 -0.508
## SupG_Feed|t4 1.186 0.056 21.305 0.000 1.186 0.670
## SupG_Meta|t1 -3.181 0.103 -30.772 0.000 -3.181 -2.234
## SupG_Meta|t2 -2.267 0.075 -30.255 0.000 -2.267 -1.592
## SupG_Meta|t3 -1.455 0.053 -27.594 0.000 -1.455 -1.022
## SupG_Meta|t4 0.705 0.037 19.219 0.000 0.705 0.495
## SupG_Ori|t1 -4.433 0.202 -21.964 0.000 -4.433 -2.340
## SupG_Ori|t2 -3.407 0.156 -21.908 0.000 -3.407 -1.798
## SupG_Ori|t3 -2.435 0.115 -21.222 0.000 -2.435 -1.285
## SupG_Ori|t4 0.135 0.044 3.068 0.002 0.135 0.071
## SupG_Mon|t1 -4.485 0.213 -21.105 0.000 -4.485 -2.343
## SupG_Mon|t2 -3.676 0.178 -20.684 0.000 -3.676 -1.920
## SupG_Mon|t3 -2.458 0.121 -20.347 0.000 -2.458 -1.284
## SupG_Mon|t4 0.223 0.045 4.926 0.000 0.223 0.116
## SupG_Infra|t1 -2.103 0.059 -35.615 0.000 -2.103 -1.462
## SupG_Infra|t2 -1.327 0.044 -29.989 0.000 -1.327 -0.922
## SupG_Infra|t3 -0.173 0.031 -5.551 0.000 -0.173 -0.120
## SupG_Infra|t4 1.138 0.041 27.814 0.000 1.138 0.791
## SupG_Bestar|t1 -2.818 0.093 -30.440 0.000 -2.818 -1.799
## SupG_Bestar|t2 -2.098 0.070 -29.971 0.000 -2.098 -1.339
## SupG_Bestar|t3 -1.000 0.045 -22.204 0.000 -1.000 -0.638
## SupG_Bestar|t4 0.665 0.039 16.997 0.000 0.665 0.425
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.000 1.000 0.319
## .SupG_Meta 1.000 1.000 0.493
## .SupG_Ori 1.000 1.000 0.279
## .SupG_Mon 1.000 1.000 0.273
## .SupG_Infra 1.000 1.000 0.483
## .SupG_Bestar 1.000 1.000 0.408
## SupG 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.565 0.565 1.000
## SupG_Meta 0.702 0.702 1.000
## SupG_Ori 0.528 0.528 1.000
## SupG_Mon 0.522 0.522 1.000
## SupG_Infra 0.695 0.695 1.000
## SupG_Bestar 0.638 0.638 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.681
## SupG_Meta 0.507
## SupG_Ori 0.721
## SupG_Mon 0.727
## SupG_Infra 0.517
## SupG_Bestar 0.592
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.461 0.059 24.825 0.000 1.418 0.797
## SupG_Meta 1.014 0.038 26.877 0.000 0.984 0.695
## SupG_Ori 1.609 0.077 20.981 0.000 1.562 0.872
## SupG_Mon 1.633 0.081 20.095 0.000 1.585 0.834
## SupG_Infra 1.035 0.036 29.040 0.000 1.004 0.716
## SupG_Bestar 1.206 0.045 26.662 0.000 1.170 0.728
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.479 0.046 10.366 0.000 0.479 0.443
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.033 0.031 1.049 0.294 0.034 0.034
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -3.013 0.100 -30.101 0.000 -3.013 -1.693
## SupG_Feed|t2 -2.101 0.075 -28.033 0.000 -2.101 -1.181
## SupG_Feed|t3 -0.899 0.049 -18.526 0.000 -0.899 -0.505
## SupG_Feed|t4 1.186 0.056 21.305 0.000 1.186 0.667
## SupG_Meta|t1 -3.181 0.103 -30.772 0.000 -3.181 -2.249
## SupG_Meta|t2 -2.267 0.075 -30.255 0.000 -2.267 -1.602
## SupG_Meta|t3 -1.455 0.053 -27.594 0.000 -1.455 -1.028
## SupG_Meta|t4 0.705 0.037 19.219 0.000 0.705 0.498
## SupG_Ori|t1 -4.433 0.202 -21.964 0.000 -4.433 -2.475
## SupG_Ori|t2 -3.407 0.156 -21.908 0.000 -3.407 -1.902
## SupG_Ori|t3 -2.435 0.115 -21.222 0.000 -2.435 -1.360
## SupG_Ori|t4 0.135 0.044 3.068 0.002 0.135 0.075
## SupG_Mon|t1 -4.485 0.213 -21.105 0.000 -4.485 -2.360
## SupG_Mon|t2 -3.676 0.178 -20.684 0.000 -3.676 -1.934
## SupG_Mon|t3 -2.458 0.121 -20.347 0.000 -2.458 -1.293
## SupG_Mon|t4 0.223 0.045 4.926 0.000 0.223 0.117
## SupG_Infra|t1 -2.103 0.059 -35.615 0.000 -2.103 -1.499
## SupG_Infra|t2 -1.327 0.044 -29.989 0.000 -1.327 -0.946
## SupG_Infra|t3 -0.173 0.031 -5.551 0.000 -0.173 -0.123
## SupG_Infra|t4 1.138 0.041 27.814 0.000 1.138 0.811
## SupG_Bestar|t1 -2.818 0.093 -30.440 0.000 -2.818 -1.753
## SupG_Bestar|t2 -2.098 0.070 -29.971 0.000 -2.098 -1.305
## SupG_Bestar|t3 -1.000 0.045 -22.204 0.000 -1.000 -0.622
## SupG_Bestar|t4 0.665 0.039 16.997 0.000 0.665 0.414
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.154 0.106 10.900 0.000 1.154 0.365
## .SupG_Meta 1.034 0.093 11.099 0.000 1.034 0.517
## .SupG_Ori 0.769 0.119 6.467 0.000 0.769 0.240
## .SupG_Mon 1.101 0.158 6.992 0.000 1.101 0.305
## .SupG_Infra 0.961 0.067 14.363 0.000 0.961 0.488
## .SupG_Bestar 1.214 0.103 11.747 0.000 1.214 0.470
## SupG 0.942 0.055 17.016 0.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.562 0.562 1.000
## SupG_Meta 0.707 0.707 1.000
## SupG_Ori 0.558 0.558 1.000
## SupG_Mon 0.526 0.526 1.000
## SupG_Infra 0.713 0.713 1.000
## SupG_Bestar 0.622 0.622 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.635
## SupG_Meta 0.483
## SupG_Ori 0.760
## SupG_Mon 0.695
## SupG_Infra 0.512
## SupG_Bestar 0.530lavaan::fitMeasures(invariance$fit.thresholds,c("chisq.scaled","df.scaled","pvalue.scaled","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue.scaled
## 99.465 38.000 0.000
## srmr cfi.scaled tli.scaled
## 0.023 0.998 0.999
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.024 0.019 0.030modificationindices(invariance$fit.thresholds, sort.=T)## lhs op rhs block group level mi epc sepc.lv
## 47 SupG_Ori ~1 1 1 1 20.460 -0.199 -0.199
## 98 SupG_Ori ~1 2 2 1 20.460 0.199 0.199
## 148 SupG_Feed ~~ SupG_Ori 2 2 1 11.138 -0.232 -0.232
## 146 SupG_Mon ~~ SupG_Bestar 1 1 1 10.651 -0.244 -0.244
## 156 SupG_Ori ~~ SupG_Mon 2 2 1 10.042 0.238 0.238
## 138 SupG_Meta ~~ SupG_Ori 1 1 1 10.011 0.207 0.207
## 157 SupG_Ori ~~ SupG_Infra 2 2 1 9.964 -0.171 -0.171
## 151 SupG_Feed ~~ SupG_Bestar 2 2 1 9.880 0.189 0.189
## 150 SupG_Feed ~~ SupG_Infra 2 2 1 7.299 0.142 0.142
## 95 SupG_Bestar ~*~ SupG_Bestar 2 2 1 7.136 -0.049 -0.049
## 44 SupG_Bestar ~*~ SupG_Bestar 1 1 1 7.136 0.051 0.051
## 97 SupG_Meta ~1 2 2 1 6.515 -0.074 -0.074
## 46 SupG_Meta ~1 1 1 1 6.514 0.074 0.074
## 136 SupG_Feed ~~ SupG_Infra 1 1 1 5.445 0.146 0.146
## 42 SupG_Mon ~*~ SupG_Mon 1 1 1 4.648 0.030 0.030
## 93 SupG_Mon ~*~ SupG_Mon 2 2 1 4.607 -0.029 -0.029
## 40 SupG_Meta ~*~ SupG_Meta 1 1 1 4.311 -0.041 -0.041
## 92 SupG_Ori ~*~ SupG_Ori 2 2 1 4.060 0.029 0.029
## 91 SupG_Meta ~*~ SupG_Meta 2 2 1 3.880 0.039 0.039
## 41 SupG_Ori ~*~ SupG_Ori 1 1 1 3.616 -0.026 -0.026
## 154 SupG_Meta ~~ SupG_Infra 2 2 1 3.260 -0.073 -0.073
## 135 SupG_Feed ~~ SupG_Mon 1 1 1 2.688 -0.140 -0.140
## 142 SupG_Ori ~~ SupG_Mon 1 1 1 2.675 0.150 0.150
## 43 SupG_Infra ~*~ SupG_Infra 1 1 1 2.530 -0.035 -0.035
## 94 SupG_Infra ~*~ SupG_Infra 2 2 1 2.326 0.034 0.034
## 134 SupG_Feed ~~ SupG_Ori 1 1 1 1.242 -0.094 -0.094
## 149 SupG_Feed ~~ SupG_Mon 2 2 1 1.201 -0.080 -0.080
## 100 SupG_Infra ~1 2 2 1 1.124 -0.026 -0.026
## 49 SupG_Infra ~1 1 1 1 1.124 0.026 0.026
## 50 SupG_Bestar ~1 1 1 1 1.108 0.033 0.033
## 101 SupG_Bestar ~1 2 2 1 1.108 -0.033 -0.033
## 158 SupG_Ori ~~ SupG_Bestar 2 2 1 0.777 0.055 0.055
## 155 SupG_Meta ~~ SupG_Bestar 2 2 1 0.667 -0.038 -0.038
## 144 SupG_Ori ~~ SupG_Bestar 1 1 1 0.666 -0.060 -0.060
## 96 SupG_Feed ~1 2 2 1 0.590 0.025 0.025
## 45 SupG_Feed ~1 1 1 1 0.590 -0.025 -0.025
## 133 SupG_Feed ~~ SupG_Meta 1 1 1 0.510 -0.043 -0.043
## 39 SupG_Feed ~*~ SupG_Feed 1 1 1 0.492 0.011 0.011
## 90 SupG_Feed ~*~ SupG_Feed 2 2 1 0.437 -0.010 -0.010
## 99 SupG_Mon ~1 2 2 1 0.415 -0.029 -0.029
## 48 SupG_Mon ~1 1 1 1 0.415 0.029 0.029
## 137 SupG_Feed ~~ SupG_Bestar 1 1 1 0.256 0.035 0.035
## 159 SupG_Mon ~~ SupG_Infra 2 2 1 0.224 0.027 0.027
## 152 SupG_Meta ~~ SupG_Ori 2 2 1 0.135 -0.020 -0.020
## 139 SupG_Meta ~~ SupG_Mon 1 1 1 0.093 0.020 0.020
## 141 SupG_Meta ~~ SupG_Bestar 1 1 1 0.043 0.011 0.011
## 145 SupG_Mon ~~ SupG_Infra 1 1 1 0.036 -0.013 -0.013
## 147 SupG_Feed ~~ SupG_Meta 2 2 1 0.021 0.007 0.007
## 160 SupG_Mon ~~ SupG_Bestar 2 2 1 0.003 -0.004 -0.004
## 143 SupG_Ori ~~ SupG_Infra 1 1 1 0.001 -0.002 -0.002
## 153 SupG_Meta ~~ SupG_Mon 2 2 1 0.000 0.001 0.001
## 140 SupG_Meta ~~ SupG_Infra 1 1 1 0.000 -0.001 -0.001
## sepc.all sepc.nox
## 47 -0.105 -0.105
## 98 0.111 0.111
## 148 -0.246 -0.246
## 146 -0.244 -0.244
## 156 0.259 0.259
## 138 0.207 0.207
## 157 -0.199 -0.199
## 151 0.159 0.159
## 150 0.135 0.135
## 95 -1.000 -1.000
## 44 1.000 1.000
## 97 -0.052 -0.052
## 46 0.052 0.052
## 136 0.146 0.146
## 42 1.000 1.000
## 93 -1.000 -1.000
## 40 -1.000 -1.000
## 92 1.000 1.000
## 91 1.000 1.000
## 41 -1.000 -1.000
## 154 -0.073 -0.073
## 135 -0.140 -0.140
## 142 0.150 0.150
## 43 -1.000 -1.000
## 94 1.000 1.000
## 134 -0.094 -0.094
## 149 -0.071 -0.071
## 100 -0.018 -0.018
## 49 0.018 0.018
## 50 0.021 0.021
## 101 -0.020 -0.020
## 158 0.057 0.057
## 155 -0.034 -0.034
## 144 -0.060 -0.060
## 96 0.014 0.014
## 45 -0.014 -0.014
## 133 -0.043 -0.043
## 39 1.000 1.000
## 90 -1.000 -1.000
## 99 -0.015 -0.015
## 48 0.015 0.015
## 137 0.035 0.035
## 159 0.026 0.026
## 152 -0.022 -0.022
## 139 0.020 0.020
## 141 0.011 0.011
## 145 -0.013 -0.013
## 147 0.007 0.007
## 160 -0.003 -0.003
## 143 -0.002 -0.002
## 153 0.001 0.001
## 140 -0.001 -0.001semTools::reliability(invariance$fit.thresholds)## For constructs with categorical indicators, Zumbo et al.`s (2007) "ordinal alpha" is calculated in addition to the standard alpha, which treats ordinal variables as numeric. See Chalmers (2018) for a critique of "alpha.ord". Likewise, average variance extracted is calculated from polychoric (polyserial) not Pearson correlations.## $`2`
## SupG
## alpha 0.8694
## alpha.ord 0.9121
## omega 0.8498
## omega2 0.8498
## omega3 0.8487
## avevar 0.6458
##
## $`1`
## SupG
## alpha 0.8562
## alpha.ord 0.9043
## omega 0.8351
## omega2 0.8351
## omega3 0.8335
## avevar 0.62317.1.1.4 Partial Invariance - Sex Means
summary(invariance$fit.means,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 95 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 69
## Number of equality constraints 30
##
## Number of observations per group:
## 2 2240
## 1 3199
## Number of missing patterns per group:
## 2 1
## 1 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 144.821 89.182
## Degrees of freedom 39 39
## P-value (Unknown) NA 0.000
## Scaling correction factor 1.800
## Shift parameter for each group:
## 2 3.593
## 1 5.131
## simple second-order correction
## Test statistic for each group:
## 2 75.169 45.354
## 1 69.653 43.828
##
## Model Test Baseline Model:
##
## Test statistic 31830.796 38247.598
## Degrees of freedom 30 30
## P-value NA 0.000
## Scaling correction factor 0.833
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.997 0.999
## Tucker-Lewis Index (TLI) 0.997 0.999
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.032 0.022
## 90 Percent confidence interval - lower 0.026 0.016
## 90 Percent confidence interval - upper 0.037 0.028
## P-value RMSEA <= 0.05 1.000 1.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.023 0.023
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
##
## Group 1 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.458 0.059 24.743 0.000 1.458 0.825
## SupG_Meta 1.017 0.038 26.856 0.000 1.017 0.713
## SupG_Ori 1.603 0.076 21.046 0.000 1.603 0.848
## SupG_Mon 1.632 0.081 20.063 0.000 1.632 0.853
## SupG_Infra 1.038 0.036 29.081 0.000 1.038 0.720
## SupG_Bestar 1.205 0.045 26.503 0.000 1.205 0.769
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.433 0.025 17.215 0.000 0.433 0.433
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -3.010 0.101 -29.950 0.000 -3.010 -1.703
## SupG_Feed|t2 -2.108 0.073 -28.757 0.000 -2.108 -1.192
## SupG_Feed|t3 -0.918 0.042 -21.764 0.000 -0.918 -0.519
## SupG_Feed|t4 1.146 0.047 24.261 0.000 1.146 0.648
## SupG_Meta|t1 -3.184 0.104 -30.698 0.000 -3.184 -2.233
## SupG_Meta|t2 -2.274 0.074 -30.634 0.000 -2.274 -1.594
## SupG_Meta|t3 -1.466 0.051 -29.032 0.000 -1.466 -1.028
## SupG_Meta|t4 0.682 0.031 22.101 0.000 0.682 0.478
## SupG_Ori|t1 -4.415 0.202 -21.907 0.000 -4.415 -2.336
## SupG_Ori|t2 -3.400 0.155 -21.961 0.000 -3.400 -1.800
## SupG_Ori|t3 -2.440 0.113 -21.534 0.000 -2.440 -1.291
## SupG_Ori|t4 0.101 0.031 3.270 0.001 0.101 0.053
## SupG_Mon|t1 -4.479 0.213 -20.989 0.000 -4.479 -2.340
## SupG_Mon|t2 -3.675 0.178 -20.648 0.000 -3.675 -1.920
## SupG_Mon|t3 -2.468 0.120 -20.583 0.000 -2.468 -1.289
## SupG_Mon|t4 0.189 0.033 5.775 0.000 0.189 0.099
## SupG_Infra|t1 -2.112 0.058 -36.660 0.000 -2.112 -1.465
## SupG_Infra|t2 -1.340 0.041 -32.734 0.000 -1.340 -0.930
## SupG_Infra|t3 -0.192 0.024 -7.850 0.000 -0.192 -0.133
## SupG_Infra|t4 1.111 0.036 30.659 0.000 1.111 0.771
## SupG_Bestar|t1 -2.815 0.094 -30.043 0.000 -2.815 -1.798
## SupG_Bestar|t2 -2.101 0.069 -30.298 0.000 -2.101 -1.342
## SupG_Bestar|t3 -1.014 0.040 -25.047 0.000 -1.014 -0.648
## SupG_Bestar|t4 0.637 0.033 19.580 0.000 0.637 0.407
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.000 1.000 0.320
## .SupG_Meta 1.000 1.000 0.492
## .SupG_Ori 1.000 1.000 0.280
## .SupG_Mon 1.000 1.000 0.273
## .SupG_Infra 1.000 1.000 0.482
## .SupG_Bestar 1.000 1.000 0.408
## SupG 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.566 0.566 1.000
## SupG_Meta 0.701 0.701 1.000
## SupG_Ori 0.529 0.529 1.000
## SupG_Mon 0.522 0.522 1.000
## SupG_Infra 0.694 0.694 1.000
## SupG_Bestar 0.639 0.639 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.680
## SupG_Meta 0.508
## SupG_Ori 0.720
## SupG_Mon 0.727
## SupG_Infra 0.518
## SupG_Bestar 0.592
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.458 0.059 24.743 0.000 1.396 0.797
## SupG_Meta 1.017 0.038 26.856 0.000 0.973 0.695
## SupG_Ori 1.603 0.076 21.046 0.000 1.535 0.872
## SupG_Mon 1.632 0.081 20.063 0.000 1.563 0.834
## SupG_Infra 1.038 0.036 29.081 0.000 0.993 0.715
## SupG_Bestar 1.205 0.045 26.503 0.000 1.153 0.729
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.466 0.047 10.005 0.000 0.466 0.443
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -3.010 0.101 -29.950 0.000 -3.010 -1.719
## SupG_Feed|t2 -2.108 0.073 -28.757 0.000 -2.108 -1.204
## SupG_Feed|t3 -0.918 0.042 -21.764 0.000 -0.918 -0.524
## SupG_Feed|t4 1.146 0.047 24.261 0.000 1.146 0.655
## SupG_Meta|t1 -3.184 0.104 -30.698 0.000 -3.184 -2.274
## SupG_Meta|t2 -2.274 0.074 -30.634 0.000 -2.274 -1.624
## SupG_Meta|t3 -1.466 0.051 -29.032 0.000 -1.466 -1.047
## SupG_Meta|t4 0.682 0.031 22.101 0.000 0.682 0.487
## SupG_Ori|t1 -4.415 0.202 -21.907 0.000 -4.415 -2.507
## SupG_Ori|t2 -3.400 0.155 -21.961 0.000 -3.400 -1.931
## SupG_Ori|t3 -2.440 0.113 -21.534 0.000 -2.440 -1.386
## SupG_Ori|t4 0.101 0.031 3.270 0.001 0.101 0.057
## SupG_Mon|t1 -4.479 0.213 -20.989 0.000 -4.479 -2.390
## SupG_Mon|t2 -3.675 0.178 -20.648 0.000 -3.675 -1.961
## SupG_Mon|t3 -2.468 0.120 -20.583 0.000 -2.468 -1.317
## SupG_Mon|t4 0.189 0.033 5.775 0.000 0.189 0.101
## SupG_Infra|t1 -2.112 0.058 -36.660 0.000 -2.112 -1.521
## SupG_Infra|t2 -1.340 0.041 -32.734 0.000 -1.340 -0.965
## SupG_Infra|t3 -0.192 0.024 -7.850 0.000 -0.192 -0.138
## SupG_Infra|t4 1.111 0.036 30.659 0.000 1.111 0.800
## SupG_Bestar|t1 -2.815 0.094 -30.043 0.000 -2.815 -1.778
## SupG_Bestar|t2 -2.101 0.069 -30.298 0.000 -2.101 -1.327
## SupG_Bestar|t3 -1.014 0.040 -25.047 0.000 -1.014 -0.640
## SupG_Bestar|t4 0.637 0.033 19.580 0.000 0.637 0.402
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.117 0.106 10.552 0.000 1.117 0.364
## .SupG_Meta 1.013 0.093 10.935 0.000 1.013 0.517
## .SupG_Ori 0.746 0.115 6.482 0.000 0.746 0.240
## .SupG_Mon 1.070 0.154 6.964 0.000 1.070 0.305
## .SupG_Infra 0.942 0.068 13.836 0.000 0.942 0.488
## .SupG_Bestar 1.176 0.107 10.993 0.000 1.176 0.469
## SupG 0.917 0.054 17.018 0.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.571 0.571 1.000
## SupG_Meta 0.714 0.714 1.000
## SupG_Ori 0.568 0.568 1.000
## SupG_Mon 0.534 0.534 1.000
## SupG_Infra 0.720 0.720 1.000
## SupG_Bestar 0.632 0.632 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.636
## SupG_Meta 0.483
## SupG_Ori 0.760
## SupG_Mon 0.695
## SupG_Infra 0.512
## SupG_Bestar 0.531lavaan::fitMeasures(invariance$fit.means,c("chisq.scaled","df.scaled","pvalue.scaled","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue.scaled
## 89.182 39.000 0.000
## srmr cfi.scaled tli.scaled
## 0.023 0.999 0.999
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.022 0.016 0.028modificationindices(invariance$fit.means, sort.=T)## lhs op rhs block group level mi epc sepc.lv
## 47 SupG_Ori ~1 1 1 1 28.264 -0.220 -0.220
## 98 SupG_Ori ~1 2 2 1 28.264 0.220 0.220
## 148 SupG_Feed ~~ SupG_Ori 2 2 1 11.149 -0.225 -0.225
## 146 SupG_Mon ~~ SupG_Bestar 1 1 1 10.520 -0.242 -0.242
## 51 SupG ~1 1 1 1 10.220 -0.033 -0.033
## 102 SupG ~1 2 2 1 10.219 0.033 0.034
## 156 SupG_Ori ~~ SupG_Mon 2 2 1 10.132 0.233 0.233
## 138 SupG_Meta ~~ SupG_Ori 1 1 1 9.889 0.205 0.205
## 157 SupG_Ori ~~ SupG_Infra 2 2 1 9.785 -0.165 -0.165
## 151 SupG_Feed ~~ SupG_Bestar 2 2 1 9.654 0.181 0.181
## 150 SupG_Feed ~~ SupG_Infra 2 2 1 7.347 0.139 0.139
## 95 SupG_Bestar ~*~ SupG_Bestar 2 2 1 6.767 -0.049 -0.049
## 44 SupG_Bestar ~*~ SupG_Bestar 1 1 1 6.767 0.049 0.049
## 136 SupG_Feed ~~ SupG_Infra 1 1 1 5.328 0.144 0.144
## 45 SupG_Feed ~1 1 1 1 4.636 -0.063 -0.063
## 96 SupG_Feed ~1 2 2 1 4.636 0.063 0.063
## 93 SupG_Mon ~*~ SupG_Mon 2 2 1 4.559 -0.030 -0.030
## 42 SupG_Mon ~*~ SupG_Mon 1 1 1 4.559 0.029 0.029
## 41 SupG_Ori ~*~ SupG_Ori 1 1 1 3.946 -0.027 -0.027
## 92 SupG_Ori ~*~ SupG_Ori 2 2 1 3.946 0.029 0.029
## 91 SupG_Meta ~*~ SupG_Meta 2 2 1 3.747 0.039 0.039
## 40 SupG_Meta ~*~ SupG_Meta 1 1 1 3.747 -0.038 -0.038
## 154 SupG_Meta ~~ SupG_Infra 2 2 1 3.170 -0.070 -0.070
## 142 SupG_Ori ~~ SupG_Mon 1 1 1 2.812 0.153 0.153
## 135 SupG_Feed ~~ SupG_Mon 1 1 1 2.582 -0.136 -0.136
## 43 SupG_Infra ~*~ SupG_Infra 1 1 1 2.161 -0.032 -0.032
## 94 SupG_Infra ~*~ SupG_Infra 2 2 1 2.161 0.033 0.033
## 97 SupG_Meta ~1 2 2 1 1.854 -0.037 -0.037
## 46 SupG_Meta ~1 1 1 1 1.854 0.037 0.037
## 149 SupG_Feed ~~ SupG_Mon 2 2 1 1.251 -0.079 -0.079
## 134 SupG_Feed ~~ SupG_Ori 1 1 1 1.098 -0.088 -0.088
## 158 SupG_Ori ~~ SupG_Bestar 2 2 1 0.746 0.052 0.052
## 155 SupG_Meta ~~ SupG_Bestar 2 2 1 0.689 -0.037 -0.037
## 144 SupG_Ori ~~ SupG_Bestar 1 1 1 0.589 -0.056 -0.056
## 133 SupG_Feed ~~ SupG_Meta 1 1 1 0.547 -0.045 -0.045
## 90 SupG_Feed ~*~ SupG_Feed 2 2 1 0.398 -0.010 -0.010
## 39 SupG_Feed ~*~ SupG_Feed 1 1 1 0.398 0.010 0.010
## 137 SupG_Feed ~~ SupG_Bestar 1 1 1 0.291 0.037 0.037
## 49 SupG_Infra ~1 1 1 1 0.279 -0.011 -0.011
## 100 SupG_Infra ~1 2 2 1 0.279 0.011 0.011
## 159 SupG_Mon ~~ SupG_Infra 2 2 1 0.233 0.027 0.027
## 99 SupG_Mon ~1 2 2 1 0.183 0.018 0.018
## 48 SupG_Mon ~1 1 1 1 0.183 -0.018 -0.018
## 152 SupG_Meta ~~ SupG_Ori 2 2 1 0.113 -0.017 -0.017
## 139 SupG_Meta ~~ SupG_Mon 1 1 1 0.067 0.017 0.017
## 145 SupG_Mon ~~ SupG_Infra 1 1 1 0.054 -0.016 -0.016
## 101 SupG_Bestar ~1 2 2 1 0.051 0.007 0.007
## 50 SupG_Bestar ~1 1 1 1 0.051 -0.007 -0.007
## 141 SupG_Meta ~~ SupG_Bestar 1 1 1 0.030 0.009 0.009
## 147 SupG_Feed ~~ SupG_Meta 2 2 1 0.022 0.008 0.008
## 160 SupG_Mon ~~ SupG_Bestar 2 2 1 0.009 -0.006 -0.006
## 140 SupG_Meta ~~ SupG_Infra 1 1 1 0.009 -0.005 -0.005
## 143 SupG_Ori ~~ SupG_Infra 1 1 1 0.002 -0.003 -0.003
## 153 SupG_Meta ~~ SupG_Mon 2 2 1 0.001 0.002 0.002
## sepc.all sepc.nox
## 47 -0.116 -0.116
## 98 0.125 0.125
## 148 -0.247 -0.247
## 146 -0.242 -0.242
## 51 -0.033 -0.033
## 102 0.034 0.034
## 156 0.260 0.260
## 138 0.205 0.205
## 157 -0.197 -0.197
## 151 0.158 0.158
## 150 0.135 0.135
## 95 -1.000 -1.000
## 44 1.000 1.000
## 136 0.144 0.144
## 45 -0.036 -0.036
## 96 0.036 0.036
## 93 -1.000 -1.000
## 42 1.000 1.000
## 41 -1.000 -1.000
## 92 1.000 1.000
## 91 1.000 1.000
## 40 -1.000 -1.000
## 154 -0.072 -0.072
## 142 0.153 0.153
## 135 -0.136 -0.136
## 43 -1.000 -1.000
## 94 1.000 1.000
## 97 -0.026 -0.026
## 46 0.026 0.026
## 149 -0.072 -0.072
## 134 -0.088 -0.088
## 158 0.055 0.055
## 155 -0.034 -0.034
## 144 -0.056 -0.056
## 133 -0.045 -0.045
## 90 -1.000 -1.000
## 39 1.000 1.000
## 137 0.037 0.037
## 49 -0.008 -0.008
## 100 0.008 0.008
## 159 0.027 0.027
## 99 0.010 0.010
## 48 -0.009 -0.009
## 152 -0.020 -0.020
## 139 0.017 0.017
## 145 -0.016 -0.016
## 101 0.004 0.004
## 50 -0.004 -0.004
## 141 0.009 0.009
## 147 0.007 0.007
## 160 -0.005 -0.005
## 140 -0.005 -0.005
## 143 -0.003 -0.003
## 153 0.002 0.002semTools::reliability(invariance$fit.means)## For constructs with categorical indicators, Zumbo et al.`s (2007) "ordinal alpha" is calculated in addition to the standard alpha, which treats ordinal variables as numeric. See Chalmers (2018) for a critique of "alpha.ord". Likewise, average variance extracted is calculated from polychoric (polyserial) not Pearson correlations.## $`2`
## SupG
## alpha 0.8694
## alpha.ord 0.9121
## omega 0.8497
## omega2 0.8497
## omega3 0.8488
## avevar 0.6454
##
## $`1`
## SupG
## alpha 0.8562
## alpha.ord 0.9043
## omega 0.8345
## omega2 0.8345
## omega3 0.8329
## avevar 0.62287.1.1.4.1 Checking Latent Differences
partial<-partialInvarianceCat(invariance,type="means",return.fit = F)## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'SexoR' contains missing values
## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'SexoR' contains missing valuespartial## $estimates
## poolest mean:2 mean:1 std:2 std:1 diff_std:1 vs. 2
## SupG~1 0 0 0.03275 0 0.03333 0.03333
##
## $results
## free.chi free.df free.p free.cfi fix.chi fix.df fix.p fix.cfi
## SupG~1 0.6831 1 0.4085 -0.0002906 0.6831 1 0.4085 -0.0002906
## wald.chi wald.df wald.p
## SupG~1 NA NA NA7.1.1.5 Organizing Education
data$Esc<-car::recode(data$Esc,"5=4")
data$EscClasseR<-as.factor(data$Esc)7.1.1.6 Education Invariance Model
model <-
'
SupG =~ SupG_Feed + SupG_Meta + SupG_Ori + SupG_Mon + SupG_Infra + SupG_Bestar
SupG_Infra ~~ SupG_Bestar
'7.1.1.7 Fitting
invariance<- measurementInvarianceCat(model = model, data = data, group = "EscClasseR",parameterization = "theta", estimator = "ULSMV",ordered = T,missing="pairwise",std.lv=T)## Warning: The measurementInvarianceCat function is deprecated, and it will cease
## to be included in future versions of semTools. See help('semTools-deprecated)
## for details.##
## Measurement invariance models:
##
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.thresholds
## Model 4 : fit.means
##
## Scaled Chi-Squared Difference Test (method = "satorra.2000")
##
## lavaan NOTE:
## The "Chisq" column contains standard test statistics, not the
## robust test that should be reported per model. A robust difference
## test is a function of two standard (not robust) statistics.
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## fit.configural 32 52.1
## fit.loadings 47 104.0 17.9 15 0.268
## fit.thresholds 98 306.9 67.0 51 0.066 .
## fit.means 101 400.9 5.4 3 0.143
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Fit measures:
##
## cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural 0.994 0.075 NA NA
## fit.loadings 0.999 0.029 0.005 0.046
## fit.thresholds 0.998 0.026 0.001 0.003
## fit.means 0.997 0.027 0.000 0.0017.1.1.7.1 Configural
summary(invariance$fit.configural,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 411 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 145
## Number of equality constraints 21
##
## Number of observations per group:
## 2 1807
## 3 2851
## 1 356
## 4 429
## Number of missing patterns per group:
## 2 1
## 3 1
## 1 1
## 4 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 52.088 275.532
## Degrees of freedom 32 32
## P-value (Unknown) NA 0.000
## Scaling correction factor 0.191
## Shift parameter for each group:
## 2 0.831
## 3 1.310
## 1 0.164
## 4 0.197
## simple second-order correction
## Test statistic for each group:
## 2 11.493 61.072
## 3 22.903 121.364
## 1 11.123 58.468
## 4 6.569 34.628
##
## Model Test Baseline Model:
##
## Test statistic 31849.655 38983.303
## Degrees of freedom 60 60
## P-value NA 0.000
## Scaling correction factor 0.818
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.999 0.994
## Tucker-Lewis Index (TLI) 0.999 0.988
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.021 0.075
## 90 Percent confidence interval - lower 0.010 0.067
## 90 Percent confidence interval - upper 0.032 0.083
## P-value RMSEA <= 0.05 1.000 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.021 0.021
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
##
## Group 1 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.266 0.053 23.825 0.000 1.266 0.785
## SupG_Meta 0.926 0.038 24.387 0.000 0.926 0.679
## SupG_Ori 1.724 0.079 21.775 0.000 1.724 0.865
## SupG_Mon 1.629 0.073 22.246 0.000 1.629 0.852
## SupG_Infra 1.033 0.043 24.128 0.000 1.033 0.718
## SupG_Bestar 1.131 0.046 24.610 0.000 1.131 0.749
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.424 0.022 18.978 0.000 0.424 0.424
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.828 0.085 -33.361 0.000 -2.828 -1.752
## SupG_Feed|t2 -1.968 0.067 -29.261 0.000 -1.968 -1.220
## SupG_Feed|t3 -0.906 0.053 -17.027 0.000 -0.906 -0.562
## SupG_Feed|t4 1.113 0.054 20.524 0.000 1.113 0.690
## SupG_Meta|t1 -2.980 0.102 -29.120 0.000 -2.980 -2.187
## SupG_Meta|t2 -2.187 0.067 -32.695 0.000 -2.187 -1.605
## SupG_Meta|t3 -1.432 0.051 -27.892 0.000 -1.432 -1.051
## SupG_Meta|t4 0.644 0.041 15.614 0.000 0.644 0.473
## SupG_Ori|t1 -4.726 0.188 -25.077 0.000 -4.726 -2.372
## SupG_Ori|t2 -3.890 0.142 -27.385 0.000 -3.890 -1.952
## SupG_Ori|t3 -2.760 0.106 -26.012 0.000 -2.760 -1.385
## SupG_Ori|t4 0.093 0.058 1.591 0.112 0.093 0.046
## SupG_Mon|t1 -4.626 0.194 -23.852 0.000 -4.626 -2.421
## SupG_Mon|t2 -3.928 0.142 -27.692 0.000 -3.928 -2.055
## SupG_Mon|t3 -2.534 0.096 -26.269 0.000 -2.534 -1.326
## SupG_Mon|t4 0.225 0.056 4.031 0.000 0.225 0.117
## SupG_Infra|t1 -2.225 0.069 -32.106 0.000 -2.225 -1.547
## SupG_Infra|t2 -1.437 0.053 -27.057 0.000 -1.437 -0.999
## SupG_Infra|t3 -0.319 0.043 -7.400 0.000 -0.319 -0.222
## SupG_Infra|t4 1.051 0.047 22.239 0.000 1.051 0.731
## SupG_Bestar|t1 -2.738 0.087 -31.517 0.000 -2.738 -1.814
## SupG_Bestar|t2 -2.125 0.068 -31.215 0.000 -2.125 -1.407
## SupG_Bestar|t3 -1.031 0.051 -20.410 0.000 -1.031 -0.683
## SupG_Bestar|t4 0.590 0.045 12.981 0.000 0.590 0.390
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.000 1.000 0.384
## .SupG_Meta 1.000 1.000 0.538
## .SupG_Ori 1.000 1.000 0.252
## .SupG_Mon 1.000 1.000 0.274
## .SupG_Infra 1.000 1.000 0.484
## .SupG_Bestar 1.000 1.000 0.439
## SupG 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.620 0.620 1.000
## SupG_Meta 0.734 0.734 1.000
## SupG_Ori 0.502 0.502 1.000
## SupG_Mon 0.523 0.523 1.000
## SupG_Infra 0.696 0.696 1.000
## SupG_Bestar 0.662 0.662 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.616
## SupG_Meta 0.462
## SupG_Ori 0.748
## SupG_Mon 0.726
## SupG_Infra 0.516
## SupG_Bestar 0.561
##
##
## Group 2 [3]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.394 0.149 9.382 0.000 1.394 0.819
## SupG_Meta 0.958 0.073 13.162 0.000 0.958 0.723
## SupG_Ori 1.602 0.133 12.039 0.000 1.602 0.850
## SupG_Mon 1.667 0.144 11.608 0.000 1.667 0.831
## SupG_Infra 1.083 0.103 10.533 0.000 1.083 0.709
## SupG_Bestar 1.157 0.100 11.528 0.000 1.157 0.742
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.490 0.089 5.506 0.000 0.490 0.435
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.033 0.171 0.191 0.849 0.033 0.033
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.828 0.085 -33.361 0.000 -2.828 -1.662
## SupG_Feed|t2 -1.968 0.067 -29.261 0.000 -1.968 -1.157
## SupG_Feed|t3 -0.777 0.161 -4.823 0.000 -0.777 -0.457
## SupG_Feed|t4 1.150 0.354 3.247 0.001 1.150 0.676
## SupG_Meta|t1 -2.980 0.102 -29.120 0.000 -2.980 -2.247
## SupG_Meta|t2 -2.112 0.103 -20.493 0.000 -2.112 -1.593
## SupG_Meta|t3 -1.348 0.109 -12.391 0.000 -1.348 -1.017
## SupG_Meta|t4 0.681 0.206 3.301 0.001 0.681 0.513
## SupG_Ori|t1 -4.726 0.188 -25.077 0.000 -4.726 -2.508
## SupG_Ori|t2 -3.422 0.187 -18.303 0.000 -3.422 -1.816
## SupG_Ori|t3 -2.425 0.179 -13.562 0.000 -2.425 -1.287
## SupG_Ori|t4 0.187 0.286 0.655 0.513 0.187 0.099
## SupG_Mon|t1 -4.626 0.194 -23.852 0.000 -4.626 -2.306
## SupG_Mon|t2 -3.778 0.188 -20.101 0.000 -3.778 -1.883
## SupG_Mon|t3 -2.525 0.177 -14.296 0.000 -2.525 -1.259
## SupG_Mon|t4 0.262 0.304 0.863 0.388 0.262 0.131
## SupG_Infra|t1 -2.225 0.069 -32.106 0.000 -2.225 -1.457
## SupG_Infra|t2 -1.363 0.087 -15.625 0.000 -1.363 -0.892
## SupG_Infra|t3 -0.063 0.181 -0.350 0.726 -0.063 -0.042
## SupG_Infra|t4 1.329 0.302 4.394 0.000 1.329 0.870
## SupG_Bestar|t1 -2.738 0.087 -31.517 0.000 -2.738 -1.756
## SupG_Bestar|t2 -1.955 0.091 -21.503 0.000 -1.955 -1.254
## SupG_Bestar|t3 -0.893 0.138 -6.490 0.000 -0.893 -0.573
## SupG_Bestar|t4 0.725 0.255 2.848 0.004 0.725 0.465
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.951 0.197 4.832 0.000 0.951 0.329
## .SupG_Meta 0.840 0.122 6.905 0.000 0.840 0.478
## .SupG_Ori 0.985 0.160 6.162 0.000 0.985 0.277
## .SupG_Mon 1.247 0.206 6.045 0.000 1.247 0.310
## .SupG_Infra 1.159 0.215 5.388 0.000 1.159 0.497
## .SupG_Bestar 1.094 0.184 5.939 0.000 1.094 0.450
## SupG 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.588 0.588 1.000
## SupG_Meta 0.754 0.754 1.000
## SupG_Ori 0.531 0.531 1.000
## SupG_Mon 0.498 0.498 1.000
## SupG_Infra 0.655 0.655 1.000
## SupG_Bestar 0.641 0.641 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.671
## SupG_Meta 0.522
## SupG_Ori 0.723
## SupG_Mon 0.690
## SupG_Infra 0.503
## SupG_Bestar 0.550
##
##
## Group 3 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.344 0.316 4.249 0.000 1.344 0.796
## SupG_Meta 0.998 0.184 5.437 0.000 0.998 0.707
## SupG_Ori 2.027 0.434 4.673 0.000 2.027 0.887
## SupG_Mon 1.879 0.375 5.006 0.000 1.879 0.884
## SupG_Infra 1.094 0.239 4.578 0.000 1.094 0.758
## SupG_Bestar 1.023 0.190 5.385 0.000 1.023 0.706
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.309 0.127 2.440 0.015 0.309 0.320
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.243 0.379 0.640 0.522 0.243 0.243
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.828 0.085 -33.361 0.000 -2.828 -1.674
## SupG_Feed|t2 -1.968 0.067 -29.261 0.000 -1.968 -1.166
## SupG_Feed|t3 -0.828 0.320 -2.584 0.010 -0.828 -0.490
## SupG_Feed|t4 1.363 0.812 1.678 0.093 1.363 0.807
## SupG_Meta|t1 -2.980 0.102 -29.120 0.000 -2.980 -2.111
## SupG_Meta|t2 -2.288 0.217 -10.526 0.000 -2.288 -1.621
## SupG_Meta|t3 -1.451 0.243 -5.969 0.000 -1.451 -1.028
## SupG_Meta|t4 0.992 0.521 1.904 0.057 0.992 0.703
## SupG_Ori|t1 -4.726 0.188 -25.077 0.000 -4.726 -2.067
## SupG_Ori|t2 -3.978 0.330 -12.066 0.000 -3.978 -1.740
## SupG_Ori|t3 -2.831 0.389 -7.273 0.000 -2.831 -1.238
## SupG_Ori|t4 0.557 0.875 0.636 0.525 0.557 0.243
## SupG_Mon|t1 -4.626 0.194 -23.852 0.000 -4.626 -2.175
## SupG_Mon|t2 -4.214 0.328 -12.863 0.000 -4.214 -1.981
## SupG_Mon|t3 -2.635 0.430 -6.131 0.000 -2.635 -1.239
## SupG_Mon|t4 0.681 0.829 0.822 0.411 0.681 0.320
## SupG_Infra|t1 -2.225 0.069 -32.106 0.000 -2.225 -1.542
## SupG_Infra|t2 -1.486 0.156 -9.501 0.000 -1.486 -1.030
## SupG_Infra|t3 -0.431 0.336 -1.281 0.200 -0.431 -0.299
## SupG_Infra|t4 1.264 0.670 1.887 0.059 1.264 0.876
## SupG_Bestar|t1 -2.738 0.087 -31.517 0.000 -2.738 -1.889
## SupG_Bestar|t2 -1.983 0.169 -11.761 0.000 -1.983 -1.368
## SupG_Bestar|t3 -1.034 0.246 -4.194 0.000 -1.034 -0.713
## SupG_Bestar|t4 0.748 0.506 1.479 0.139 0.748 0.516
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.044 0.473 2.206 0.027 1.044 0.366
## .SupG_Meta 0.997 0.314 3.174 0.002 0.997 0.500
## .SupG_Ori 1.119 0.467 2.394 0.017 1.119 0.214
## .SupG_Mon 0.990 0.358 2.767 0.006 0.990 0.219
## .SupG_Infra 0.884 0.370 2.391 0.017 0.884 0.425
## .SupG_Bestar 1.053 0.361 2.914 0.004 1.053 0.501
## SupG 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.592 0.592 1.000
## SupG_Meta 0.708 0.708 1.000
## SupG_Ori 0.437 0.437 1.000
## SupG_Mon 0.470 0.470 1.000
## SupG_Infra 0.693 0.693 1.000
## SupG_Bestar 0.690 0.690 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.634
## SupG_Meta 0.500
## SupG_Ori 0.786
## SupG_Mon 0.781
## SupG_Infra 0.575
## SupG_Bestar 0.499
##
##
## Group 4 [4]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.414 0.264 5.353 0.000 1.414 0.837
## SupG_Meta 0.832 0.106 7.849 0.000 0.832 0.676
## SupG_Ori 1.851 0.264 7.001 0.000 1.851 0.896
## SupG_Mon 1.665 0.211 7.893 0.000 1.665 0.847
## SupG_Infra 1.250 0.211 5.918 0.000 1.250 0.747
## SupG_Bestar 1.315 0.205 6.405 0.000 1.315 0.783
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.641 0.225 2.850 0.004 0.641 0.551
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG -0.101 0.286 -0.354 0.723 -0.101 -0.101
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.828 0.085 -33.361 0.000 -2.828 -1.675
## SupG_Feed|t2 -1.968 0.067 -29.261 0.000 -1.968 -1.166
## SupG_Feed|t3 -0.947 0.235 -4.025 0.000 -0.947 -0.561
## SupG_Feed|t4 0.796 0.537 1.481 0.139 0.796 0.471
## SupG_Meta|t1 -2.980 0.102 -29.120 0.000 -2.980 -2.421
## SupG_Meta|t2 -1.901 0.179 -10.629 0.000 -1.901 -1.545
## SupG_Meta|t3 -1.160 0.178 -6.521 0.000 -1.160 -0.942
## SupG_Meta|t4 0.462 0.279 1.657 0.098 0.462 0.375
## SupG_Ori|t1 -4.726 0.188 -25.077 0.000 -4.726 -2.288
## SupG_Ori|t2 -3.704 0.278 -13.322 0.000 -3.704 -1.794
## SupG_Ori|t3 -2.700 0.308 -8.758 0.000 -2.700 -1.307
## SupG_Ori|t4 -0.121 0.516 -0.234 0.815 -0.121 -0.059
## SupG_Mon|t1 -4.626 0.194 -23.852 0.000 -4.626 -2.354
## SupG_Mon|t2 -3.421 0.293 -11.689 0.000 -3.421 -1.741
## SupG_Mon|t3 -2.608 0.309 -8.441 0.000 -2.608 -1.327
## SupG_Mon|t4 -0.163 0.463 -0.352 0.725 -0.163 -0.083
## SupG_Infra|t1 -2.225 0.069 -32.106 0.000 -2.225 -1.330
## SupG_Infra|t2 -1.450 0.155 -9.383 0.000 -1.450 -0.867
## SupG_Infra|t3 -0.083 0.350 -0.236 0.813 -0.083 -0.049
## SupG_Infra|t4 1.118 0.536 2.088 0.037 1.118 0.668
## SupG_Bestar|t1 -2.738 0.087 -31.517 0.000 -2.738 -1.629
## SupG_Bestar|t2 -2.263 0.130 -17.403 0.000 -2.263 -1.346
## SupG_Bestar|t3 -1.150 0.229 -5.020 0.000 -1.150 -0.684
## SupG_Bestar|t4 0.329 0.422 0.781 0.435 0.329 0.196
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.852 0.285 2.987 0.003 0.852 0.299
## .SupG_Meta 0.823 0.193 4.272 0.000 0.823 0.543
## .SupG_Ori 0.838 0.239 3.503 0.000 0.838 0.197
## .SupG_Mon 1.089 0.284 3.832 0.000 1.089 0.282
## .SupG_Infra 1.236 0.429 2.882 0.004 1.236 0.442
## .SupG_Bestar 1.095 0.345 3.176 0.001 1.095 0.388
## SupG 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.592 0.592 1.000
## SupG_Meta 0.812 0.812 1.000
## SupG_Ori 0.484 0.484 1.000
## SupG_Mon 0.509 0.509 1.000
## SupG_Infra 0.598 0.598 1.000
## SupG_Bestar 0.595 0.595 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.701
## SupG_Meta 0.457
## SupG_Ori 0.803
## SupG_Mon 0.718
## SupG_Infra 0.558
## SupG_Bestar 0.612lavaan::fitMeasures(invariance$fit.configural,c("chisq.scaled","df.scaled","pvalue.scaled","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue.scaled
## 275.532 32.000 0.000
## srmr cfi.scaled tli.scaled
## 0.021 0.994 0.988
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.075 0.067 0.083modificationindices(invariance$fit.configural, sort.=T)## lhs op rhs block group level mi epc sepc.lv sepc.all
## 249 SupG_Ori ~~ SupG_Mon 2 2 1 7.765 0.276 0.276 0.249
## 243 SupG_Feed ~~ SupG_Infra 2 2 1 7.303 0.172 0.172 0.164
## 244 SupG_Feed ~~ SupG_Bestar 2 2 1 5.310 0.152 0.152 0.149
## 257 SupG_Feed ~~ SupG_Infra 3 3 1 5.232 0.386 0.386 0.401
## 250 SupG_Ori ~~ SupG_Infra 2 2 1 5.165 -0.163 -0.163 -0.153
## 253 SupG_Mon ~~ SupG_Bestar 2 2 1 5.139 -0.178 -0.178 -0.152
## 241 SupG_Feed ~~ SupG_Ori 2 2 1 5.046 -0.187 -0.187 -0.193
## 227 SupG_Feed ~~ SupG_Ori 1 1 1 4.714 -0.226 -0.226 -0.226
## 263 SupG_Ori ~~ SupG_Mon 3 3 1 4.301 0.780 0.780 0.741
## 235 SupG_Ori ~~ SupG_Mon 1 1 1 4.250 0.266 0.266 0.266
## 256 SupG_Feed ~~ SupG_Mon 3 3 1 4.117 -0.531 -0.531 -0.522
## 229 SupG_Feed ~~ SupG_Infra 1 1 1 3.203 0.127 0.127 0.127
## 245 SupG_Meta ~~ SupG_Ori 2 2 1 2.413 0.095 0.095 0.105
## 271 SupG_Feed ~~ SupG_Infra 4 4 1 2.064 0.260 0.260 0.253
## 272 SupG_Feed ~~ SupG_Bestar 4 4 1 2.048 0.264 0.264 0.273
## 255 SupG_Feed ~~ SupG_Ori 3 3 1 1.956 -0.394 -0.394 -0.364
## 236 SupG_Ori ~~ SupG_Infra 1 1 1 1.812 -0.123 -0.123 -0.123
## 240 SupG_Feed ~~ SupG_Meta 2 2 1 1.603 -0.069 -0.069 -0.077
## 269 SupG_Feed ~~ SupG_Ori 4 4 1 1.550 -0.296 -0.296 -0.350
## 231 SupG_Meta ~~ SupG_Ori 1 1 1 1.388 0.098 0.098 0.098
## 270 SupG_Feed ~~ SupG_Mon 4 4 1 1.284 -0.248 -0.248 -0.258
## 261 SupG_Meta ~~ SupG_Infra 3 3 1 1.239 -0.150 -0.150 -0.160
## 264 SupG_Ori ~~ SupG_Infra 3 3 1 1.221 -0.265 -0.265 -0.267
## 242 SupG_Feed ~~ SupG_Mon 2 2 1 1.190 -0.096 -0.096 -0.088
## 277 SupG_Ori ~~ SupG_Mon 4 4 1 1.148 0.298 0.298 0.312
## 230 SupG_Feed ~~ SupG_Bestar 1 1 1 1.069 0.078 0.078 0.078
## 258 SupG_Feed ~~ SupG_Bestar 3 3 1 1.068 0.172 0.172 0.164
## 233 SupG_Meta ~~ SupG_Infra 1 1 1 1.033 -0.058 -0.058 -0.058
## 274 SupG_Meta ~~ SupG_Mon 4 4 1 1.024 0.149 0.149 0.157
## 239 SupG_Mon ~~ SupG_Bestar 1 1 1 0.992 -0.092 -0.092 -0.092
## 228 SupG_Feed ~~ SupG_Mon 1 1 1 0.970 -0.098 -0.098 -0.098
## 276 SupG_Meta ~~ SupG_Bestar 4 4 1 0.888 -0.117 -0.117 -0.123
## 232 SupG_Meta ~~ SupG_Mon 1 1 1 0.598 -0.061 -0.061 -0.061
## 273 SupG_Meta ~~ SupG_Ori 4 4 1 0.533 0.115 0.115 0.139
## 226 SupG_Feed ~~ SupG_Meta 1 1 1 0.533 0.047 0.047 0.047
## 275 SupG_Meta ~~ SupG_Infra 4 4 1 0.448 -0.082 -0.082 -0.081
## 267 SupG_Mon ~~ SupG_Bestar 3 3 1 0.335 -0.127 -0.127 -0.124
## 247 SupG_Meta ~~ SupG_Infra 2 2 1 0.323 -0.027 -0.027 -0.027
## 254 SupG_Feed ~~ SupG_Meta 3 3 1 0.297 0.086 0.086 0.085
## 238 SupG_Mon ~~ SupG_Infra 1 1 1 0.281 0.046 0.046 0.046
## 260 SupG_Meta ~~ SupG_Mon 3 3 1 0.240 0.102 0.102 0.103
## 280 SupG_Mon ~~ SupG_Infra 4 4 1 0.225 -0.100 -0.100 -0.086
## 281 SupG_Mon ~~ SupG_Bestar 4 4 1 0.201 -0.097 -0.097 -0.088
## 262 SupG_Meta ~~ SupG_Bestar 3 3 1 0.164 -0.054 -0.054 -0.053
## 278 SupG_Ori ~~ SupG_Infra 4 4 1 0.132 -0.083 -0.083 -0.082
## 259 SupG_Meta ~~ SupG_Ori 3 3 1 0.117 0.077 0.077 0.072
## 268 SupG_Feed ~~ SupG_Meta 4 4 1 0.078 -0.035 -0.035 -0.042
## 246 SupG_Meta ~~ SupG_Mon 2 2 1 0.062 0.016 0.016 0.016
## 234 SupG_Meta ~~ SupG_Bestar 1 1 1 0.055 -0.014 -0.014 -0.014
## 237 SupG_Ori ~~ SupG_Bestar 1 1 1 0.044 0.020 0.020 0.020
## 279 SupG_Ori ~~ SupG_Bestar 4 4 1 0.023 -0.035 -0.035 -0.037
## 252 SupG_Mon ~~ SupG_Infra 2 2 1 0.020 0.011 0.011 0.009
## 266 SupG_Mon ~~ SupG_Infra 3 3 1 0.007 -0.018 -0.018 -0.019
## 248 SupG_Meta ~~ SupG_Bestar 2 2 1 0.004 -0.003 -0.003 -0.003
## 265 SupG_Ori ~~ SupG_Bestar 3 3 1 0.002 -0.010 -0.010 -0.009
## 251 SupG_Ori ~~ SupG_Bestar 2 2 1 0.002 0.003 0.003 0.003
## sepc.nox
## 249 0.249
## 243 0.164
## 244 0.149
## 257 0.401
## 250 -0.153
## 253 -0.152
## 241 -0.193
## 227 -0.226
## 263 0.741
## 235 0.266
## 256 -0.522
## 229 0.127
## 245 0.105
## 271 0.253
## 272 0.273
## 255 -0.364
## 236 -0.123
## 240 -0.077
## 269 -0.350
## 231 0.098
## 270 -0.258
## 261 -0.160
## 264 -0.267
## 242 -0.088
## 277 0.312
## 230 0.078
## 258 0.164
## 233 -0.058
## 274 0.157
## 239 -0.092
## 228 -0.098
## 276 -0.123
## 232 -0.061
## 273 0.139
## 226 0.047
## 275 -0.081
## 267 -0.124
## 247 -0.027
## 254 0.085
## 238 0.046
## 260 0.103
## 280 -0.086
## 281 -0.088
## 262 -0.053
## 278 -0.082
## 259 0.072
## 268 -0.042
## 246 0.016
## 234 -0.014
## 237 0.020
## 279 -0.037
## 252 0.009
## 266 -0.019
## 248 -0.003
## 265 -0.009
## 251 0.003semTools::reliability(invariance$fit.configural)## For constructs with categorical indicators, Zumbo et al.`s (2007) "ordinal alpha" is calculated in addition to the standard alpha, which treats ordinal variables as numeric. See Chalmers (2018) for a critique of "alpha.ord". Likewise, average variance extracted is calculated from polychoric (polyserial) not Pearson correlations.## $`2`
## SupG
## alpha 0.8551
## alpha.ord 0.9046
## omega 0.8364
## omega2 0.8364
## omega3 0.8355
## avevar 0.6348
##
## $`3`
## SupG
## alpha 0.8629
## alpha.ord 0.9073
## omega 0.8423
## omega2 0.8423
## omega3 0.8413
## avevar 0.6307
##
## $`1`
## SupG
## alpha 0.8700
## alpha.ord 0.9117
## omega 0.8539
## omega2 0.8539
## omega3 0.8514
## avevar 0.6758
##
## $`4`
## SupG
## alpha 0.8764
## alpha.ord 0.9178
## omega 0.8530
## omega2 0.8530
## omega3 0.8518
## avevar 0.67247.1.1.7.2 Loadings
summary(invariance$fit.loadings,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 313 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 148
## Number of equality constraints 39
##
## Number of observations per group:
## 2 1807
## 3 2851
## 1 356
## 4 429
## Number of missing patterns per group:
## 2 1
## 3 1
## 1 1
## 4 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 104.041 100.872
## Degrees of freedom 47 47
## P-value (Unknown) NA 0.000
## Scaling correction factor 1.234
## Shift parameter for each group:
## 2 5.505
## 3 8.686
## 1 1.085
## 4 1.307
## simple second-order correction
## Test statistic for each group:
## 2 17.870 19.983
## 3 34.874 36.939
## 1 25.910 22.076
## 4 25.386 21.874
##
## Model Test Baseline Model:
##
## Test statistic 31849.655 38983.303
## Degrees of freedom 60 60
## P-value NA 0.000
## Scaling correction factor 0.818
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.998 0.999
## Tucker-Lewis Index (TLI) 0.998 0.998
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.030 0.029
## 90 Percent confidence interval - lower 0.022 0.021
## 90 Percent confidence interval - upper 0.038 0.037
## P-value RMSEA <= 0.05 1.000 1.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.026 0.026
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
##
## Group 1 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.328 0.059 22.410 0.000 1.328 0.799
## SupG_Meta 0.931 0.044 21.216 0.000 0.931 0.681
## SupG_Ori 1.543 0.095 16.239 0.000 1.543 0.839
## SupG_Mon 1.665 0.104 16.024 0.000 1.665 0.857
## SupG_Infra 1.055 0.042 24.903 0.000 1.055 0.726
## SupG_Bestar 1.129 0.049 22.855 0.000 1.129 0.749
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.417 0.030 13.997 0.000 0.417 0.417
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.869 0.106 -26.950 0.000 -2.869 -1.726
## SupG_Feed|t2 -2.056 0.084 -24.473 0.000 -2.056 -1.237
## SupG_Feed|t3 -0.934 0.057 -16.422 0.000 -0.934 -0.562
## SupG_Feed|t4 1.147 0.058 19.916 0.000 1.147 0.690
## SupG_Meta|t1 -2.985 0.125 -23.884 0.000 -2.985 -2.185
## SupG_Meta|t2 -2.193 0.085 -25.955 0.000 -2.193 -1.605
## SupG_Meta|t3 -1.436 0.058 -24.562 0.000 -1.436 -1.051
## SupG_Meta|t4 0.646 0.042 15.364 0.000 0.646 0.473
## SupG_Ori|t1 -4.397 0.272 -16.180 0.000 -4.397 -2.391
## SupG_Ori|t2 -3.589 0.193 -18.571 0.000 -3.589 -1.952
## SupG_Ori|t3 -2.547 0.129 -19.706 0.000 -2.547 -1.385
## SupG_Ori|t4 0.085 0.054 1.584 0.113 0.085 0.046
## SupG_Mon|t1 -4.693 0.313 -14.978 0.000 -4.693 -2.416
## SupG_Mon|t2 -3.992 0.235 -17.013 0.000 -3.992 -2.055
## SupG_Mon|t3 -2.575 0.138 -18.637 0.000 -2.575 -1.326
## SupG_Mon|t4 0.228 0.057 3.996 0.000 0.228 0.117
## SupG_Infra|t1 -2.240 0.079 -28.301 0.000 -2.240 -1.541
## SupG_Infra|t2 -1.453 0.060 -24.339 0.000 -1.453 -0.999
## SupG_Infra|t3 -0.322 0.044 -7.300 0.000 -0.322 -0.222
## SupG_Infra|t4 1.062 0.048 22.107 0.000 1.062 0.731
## SupG_Bestar|t1 -2.739 0.106 -25.881 0.000 -2.739 -1.816
## SupG_Bestar|t2 -2.122 0.084 -25.210 0.000 -2.122 -1.407
## SupG_Bestar|t3 -1.030 0.055 -18.861 0.000 -1.030 -0.683
## SupG_Bestar|t4 0.589 0.046 12.858 0.000 0.589 0.390
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.000 1.000 0.362
## .SupG_Meta 1.000 1.000 0.536
## .SupG_Ori 1.000 1.000 0.296
## .SupG_Mon 1.000 1.000 0.265
## .SupG_Infra 1.000 1.000 0.473
## .SupG_Bestar 1.000 1.000 0.440
## SupG 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.602 0.602 1.000
## SupG_Meta 0.732 0.732 1.000
## SupG_Ori 0.544 0.544 1.000
## SupG_Mon 0.515 0.515 1.000
## SupG_Infra 0.688 0.688 1.000
## SupG_Bestar 0.663 0.663 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.638
## SupG_Meta 0.464
## SupG_Ori 0.704
## SupG_Mon 0.735
## SupG_Infra 0.527
## SupG_Bestar 0.560
##
##
## Group 2 [3]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.328 0.059 22.410 0.000 1.242 0.806
## SupG_Meta 0.931 0.044 21.216 0.000 0.871 0.706
## SupG_Ori 1.543 0.095 16.239 0.000 1.443 0.880
## SupG_Mon 1.665 0.104 16.024 0.000 1.557 0.828
## SupG_Infra 1.055 0.042 24.903 0.000 0.987 0.711
## SupG_Bestar 1.129 0.049 22.855 0.000 1.056 0.741
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.405 0.067 6.067 0.000 0.405 0.434
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG -0.180 0.147 -1.223 0.221 -0.192 -0.192
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.869 0.106 -26.950 0.000 -2.869 -1.862
## SupG_Feed|t2 -2.056 0.084 -24.473 0.000 -2.056 -1.334
## SupG_Feed|t3 -0.984 0.138 -7.146 0.000 -0.984 -0.639
## SupG_Feed|t4 0.762 0.275 2.770 0.006 0.762 0.494
## SupG_Meta|t1 -2.985 0.125 -23.884 0.000 -2.985 -2.420
## SupG_Meta|t2 -2.161 0.105 -20.647 0.000 -2.161 -1.752
## SupG_Meta|t3 -1.451 0.094 -15.454 0.000 -1.451 -1.176
## SupG_Meta|t4 0.437 0.179 2.446 0.014 0.437 0.354
## SupG_Ori|t1 -4.397 0.272 -16.180 0.000 -4.397 -2.682
## SupG_Ori|t2 -3.300 0.233 -14.169 0.000 -3.300 -2.013
## SupG_Ori|t3 -2.432 0.186 -13.043 0.000 -2.432 -1.484
## SupG_Ori|t4 -0.160 0.236 -0.678 0.498 -0.160 -0.097
## SupG_Mon|t1 -4.693 0.313 -14.978 0.000 -4.693 -2.495
## SupG_Mon|t2 -3.892 0.275 -14.167 0.000 -3.892 -2.069
## SupG_Mon|t3 -2.718 0.206 -13.200 0.000 -2.718 -1.445
## SupG_Mon|t4 -0.105 0.259 -0.404 0.686 -0.105 -0.056
## SupG_Infra|t1 -2.240 0.079 -28.301 0.000 -2.240 -1.614
## SupG_Infra|t2 -1.460 0.086 -16.894 0.000 -1.460 -1.052
## SupG_Infra|t3 -0.279 0.150 -1.864 0.062 -0.279 -0.201
## SupG_Infra|t4 0.986 0.242 4.069 0.000 0.986 0.710
## SupG_Bestar|t1 -2.739 0.106 -25.881 0.000 -2.739 -1.923
## SupG_Bestar|t2 -2.023 0.102 -19.903 0.000 -2.023 -1.420
## SupG_Bestar|t3 -1.053 0.124 -8.458 0.000 -1.053 -0.739
## SupG_Bestar|t4 0.425 0.208 2.040 0.041 0.425 0.298
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.833 0.156 5.321 0.000 0.833 0.351
## .SupG_Meta 0.763 0.127 6.026 0.000 0.763 0.502
## .SupG_Ori 0.607 0.156 3.887 0.000 0.607 0.226
## .SupG_Mon 1.115 0.262 4.250 0.000 1.115 0.315
## .SupG_Infra 0.953 0.157 6.089 0.000 0.953 0.495
## .SupG_Bestar 0.914 0.143 6.403 0.000 0.914 0.451
## SupG 0.874 0.141 6.189 0.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.649 0.649 1.000
## SupG_Meta 0.811 0.811 1.000
## SupG_Ori 0.610 0.610 1.000
## SupG_Mon 0.532 0.532 1.000
## SupG_Infra 0.720 0.720 1.000
## SupG_Bestar 0.702 0.702 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.649
## SupG_Meta 0.498
## SupG_Ori 0.774
## SupG_Mon 0.685
## SupG_Infra 0.505
## SupG_Bestar 0.549
##
##
## Group 3 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.328 0.059 22.410 0.000 1.523 0.807
## SupG_Meta 0.931 0.044 21.216 0.000 1.068 0.715
## SupG_Ori 1.543 0.095 16.239 0.000 1.769 0.815
## SupG_Mon 1.665 0.104 16.024 0.000 1.909 0.849
## SupG_Infra 1.055 0.042 24.903 0.000 1.210 0.776
## SupG_Bestar 1.129 0.049 22.855 0.000 1.295 0.797
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.164 0.131 1.249 0.212 0.164 0.170
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.436 0.445 0.980 0.327 0.381 0.381
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.869 0.106 -26.950 0.000 -2.869 -1.521
## SupG_Feed|t2 -2.056 0.084 -24.473 0.000 -2.056 -1.090
## SupG_Feed|t3 -0.710 0.344 -2.066 0.039 -0.710 -0.376
## SupG_Feed|t4 1.737 0.814 2.134 0.033 1.737 0.921
## SupG_Meta|t1 -2.985 0.125 -23.884 0.000 -2.985 -1.999
## SupG_Meta|t2 -2.270 0.209 -10.873 0.000 -2.270 -1.521
## SupG_Meta|t3 -1.385 0.216 -6.414 0.000 -1.385 -0.927
## SupG_Meta|t4 1.199 0.551 2.176 0.030 1.199 0.803
## SupG_Ori|t1 -4.397 0.272 -16.180 0.000 -4.397 -2.026
## SupG_Ori|t2 -3.569 0.327 -10.913 0.000 -3.569 -1.645
## SupG_Ori|t3 -2.481 0.326 -7.619 0.000 -2.481 -1.143
## SupG_Ori|t4 0.734 0.698 1.052 0.293 0.734 0.338
## SupG_Mon|t1 -4.693 0.313 -14.978 0.000 -4.693 -2.088
## SupG_Mon|t2 -4.209 0.378 -11.142 0.000 -4.209 -1.873
## SupG_Mon|t3 -2.541 0.361 -7.044 0.000 -2.541 -1.130
## SupG_Mon|t4 0.964 0.792 1.217 0.224 0.964 0.429
## SupG_Infra|t1 -2.240 0.079 -28.301 0.000 -2.240 -1.437
## SupG_Infra|t2 -1.432 0.172 -8.341 0.000 -1.432 -0.919
## SupG_Infra|t3 -0.292 0.344 -0.850 0.395 -0.292 -0.187
## SupG_Infra|t4 1.539 0.661 2.330 0.020 1.539 0.988
## SupG_Bestar|t1 -2.739 0.106 -25.881 0.000 -2.739 -1.686
## SupG_Bestar|t2 -2.009 0.200 -10.061 0.000 -2.009 -1.237
## SupG_Bestar|t3 -0.944 0.292 -3.235 0.001 -0.944 -0.581
## SupG_Bestar|t4 1.053 0.592 1.779 0.075 1.053 0.648
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.241 0.542 2.291 0.022 1.241 0.349
## .SupG_Meta 1.090 0.390 2.793 0.005 1.090 0.489
## .SupG_Ori 1.579 0.664 2.380 0.017 1.579 0.335
## .SupG_Mon 1.408 0.712 1.978 0.048 1.408 0.279
## .SupG_Infra 0.965 0.365 2.648 0.008 0.965 0.397
## .SupG_Bestar 0.963 0.356 2.704 0.007 0.963 0.365
## SupG 1.315 0.496 2.652 0.008 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.530 0.530 1.000
## SupG_Meta 0.670 0.670 1.000
## SupG_Ori 0.461 0.461 1.000
## SupG_Mon 0.445 0.445 1.000
## SupG_Infra 0.642 0.642 1.000
## SupG_Bestar 0.616 0.616 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.651
## SupG_Meta 0.511
## SupG_Ori 0.665
## SupG_Mon 0.721
## SupG_Infra 0.603
## SupG_Bestar 0.635
##
##
## Group 4 [4]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.328 0.059 22.410 0.000 1.206 0.855
## SupG_Meta 0.931 0.044 21.216 0.000 0.845 0.755
## SupG_Ori 1.543 0.095 16.239 0.000 1.401 0.851
## SupG_Mon 1.665 0.104 16.024 0.000 1.511 0.867
## SupG_Infra 1.055 0.042 24.903 0.000 0.958 0.706
## SupG_Bestar 1.129 0.049 22.855 0.000 1.025 0.734
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.558 0.137 4.082 0.000 0.558 0.612
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG -0.458 0.189 -2.421 0.015 -0.505 -0.505
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.869 0.106 -26.950 0.000 -2.869 -2.035
## SupG_Feed|t2 -2.056 0.084 -24.473 0.000 -2.056 -1.459
## SupG_Feed|t3 -1.279 0.171 -7.488 0.000 -1.279 -0.908
## SupG_Feed|t4 0.176 0.332 0.529 0.597 0.176 0.125
## SupG_Meta|t1 -2.985 0.125 -23.884 0.000 -2.985 -2.665
## SupG_Meta|t2 -2.080 0.149 -14.005 0.000 -2.080 -1.857
## SupG_Meta|t3 -1.405 0.127 -11.021 0.000 -1.405 -1.254
## SupG_Meta|t4 0.070 0.233 0.302 0.762 0.070 0.063
## SupG_Ori|t1 -4.397 0.272 -16.180 0.000 -4.397 -2.672
## SupG_Ori|t2 -3.509 0.274 -12.821 0.000 -3.509 -2.132
## SupG_Ori|t3 -2.709 0.244 -11.094 0.000 -2.709 -1.646
## SupG_Ori|t4 -0.654 0.303 -2.161 0.031 -0.654 -0.397
## SupG_Mon|t1 -4.693 0.313 -14.978 0.000 -4.693 -2.692
## SupG_Mon|t2 -3.647 0.307 -11.875 0.000 -3.647 -2.093
## SupG_Mon|t3 -2.926 0.275 -10.658 0.000 -2.926 -1.679
## SupG_Mon|t4 -0.757 0.321 -2.358 0.018 -0.757 -0.435
## SupG_Infra|t1 -2.240 0.079 -28.301 0.000 -2.240 -1.651
## SupG_Infra|t2 -1.557 0.116 -13.444 0.000 -1.557 -1.147
## SupG_Infra|t3 -0.448 0.208 -2.149 0.032 -0.448 -0.330
## SupG_Infra|t4 0.526 0.305 1.727 0.084 0.526 0.388
## SupG_Bestar|t1 -2.739 0.106 -25.881 0.000 -2.739 -1.962
## SupG_Bestar|t2 -2.286 0.121 -18.882 0.000 -2.286 -1.638
## SupG_Bestar|t3 -1.361 0.156 -8.730 0.000 -1.361 -0.975
## SupG_Bestar|t4 -0.133 0.253 -0.526 0.599 -0.133 -0.095
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.533 0.158 3.362 0.001 0.533 0.268
## .SupG_Meta 0.540 0.181 2.985 0.003 0.540 0.430
## .SupG_Ori 0.746 0.265 2.820 0.005 0.746 0.276
## .SupG_Mon 0.754 0.325 2.317 0.020 0.754 0.248
## .SupG_Infra 0.924 0.218 4.237 0.000 0.924 0.502
## .SupG_Bestar 0.898 0.204 4.405 0.000 0.898 0.461
## SupG 0.824 0.183 4.491 0.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.710 0.710 1.000
## SupG_Meta 0.893 0.893 1.000
## SupG_Ori 0.608 0.608 1.000
## SupG_Mon 0.574 0.574 1.000
## SupG_Infra 0.737 0.737 1.000
## SupG_Bestar 0.716 0.716 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.732
## SupG_Meta 0.570
## SupG_Ori 0.724
## SupG_Mon 0.752
## SupG_Infra 0.498
## SupG_Bestar 0.539lavaan::fitMeasures(invariance$fit.loadings,c("chisq.scaled","df.scaled","pvalue.scaled","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue.scaled
## 100.872 47.000 0.000
## srmr cfi.scaled tli.scaled
## 0.026 0.999 0.998
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.029 0.021 0.037modificationindices(invariance$fit.loadings, sort.=T)## lhs op rhs block group level mi epc sepc.lv
## 98 SupG_Ori ~1 2 2 1 21.990 0.552 0.552
## 92 SupG_Ori ~*~ SupG_Ori 2 2 1 21.990 0.082 0.082
## 199 SupG_Meta ~1 4 4 1 14.028 0.538 0.538
## 193 SupG_Meta ~*~ SupG_Meta 4 4 1 14.026 0.188 0.188
## 268 SupG_Ori ~~ SupG_Infra 2 2 1 12.712 -0.186 -0.186
## 281 SupG_Ori ~~ SupG_Mon 3 3 1 12.627 1.041 1.041
## 261 SupG_Feed ~~ SupG_Infra 2 2 1 9.586 0.153 0.153
## 146 SupG_Bestar ~*~ SupG_Bestar 3 3 1 8.923 0.109 0.109
## 152 SupG_Bestar ~1 3 3 1 8.922 0.570 0.570
## 259 SupG_Feed ~~ SupG_Ori 2 2 1 8.245 -0.170 -0.170
## 97 SupG_Meta ~1 2 2 1 7.940 -0.254 -0.254
## 91 SupG_Meta ~*~ SupG_Meta 2 2 1 7.940 -0.073 -0.073
## 262 SupG_Feed ~~ SupG_Bestar 2 2 1 7.894 0.141 0.141
## 253 SupG_Ori ~~ SupG_Mon 1 1 1 6.943 0.267 0.267
## 143 SupG_Ori ~*~ SupG_Ori 3 3 1 6.209 -0.064 -0.064
## 149 SupG_Ori ~1 3 3 1 6.207 -0.701 -0.701
## 41 SupG_Ori ~*~ SupG_Ori 1 1 1 6.151 -0.039 -0.039
## 47 SupG_Ori ~1 1 1 1 6.151 -0.318 -0.318
## 90 SupG_Feed ~*~ SupG_Feed 2 2 1 6.085 -0.057 -0.057
## 96 SupG_Feed ~1 2 2 1 5.871 -0.248 -0.248
## 194 SupG_Ori ~*~ SupG_Ori 4 4 1 4.959 -0.070 -0.070
## 200 SupG_Ori ~1 4 4 1 4.958 -0.426 -0.426
## 286 SupG_Feed ~~ SupG_Meta 4 4 1 4.363 -0.178 -0.178
## 198 SupG_Feed ~1 4 4 1 3.823 0.317 0.317
## 290 SupG_Feed ~~ SupG_Bestar 4 4 1 3.550 0.207 0.207
## 271 SupG_Mon ~~ SupG_Bestar 2 2 1 3.475 -0.113 -0.113
## 289 SupG_Feed ~~ SupG_Infra 4 4 1 3.333 0.200 0.200
## 249 SupG_Meta ~~ SupG_Ori 1 1 1 3.329 0.125 0.125
## 280 SupG_Meta ~~ SupG_Bestar 3 3 1 3.290 -0.255 -0.255
## 288 SupG_Feed ~~ SupG_Mon 4 4 1 3.015 -0.239 -0.239
## 203 SupG_Bestar ~1 4 4 1 2.858 -0.224 -0.224
## 197 SupG_Bestar ~*~ SupG_Bestar 4 4 1 2.858 -0.072 -0.072
## 39 SupG_Feed ~*~ SupG_Feed 1 1 1 2.807 0.036 0.036
## 246 SupG_Feed ~~ SupG_Mon 1 1 1 2.742 -0.149 -0.149
## 297 SupG_Ori ~~ SupG_Bestar 4 4 1 2.734 0.206 0.206
## 285 SupG_Mon ~~ SupG_Bestar 3 3 1 2.523 -0.343 -0.343
## 275 SupG_Feed ~~ SupG_Infra 3 3 1 2.464 0.290 0.290
## 202 SupG_Infra ~1 4 4 1 2.221 -0.175 -0.175
## 196 SupG_Infra ~*~ SupG_Infra 4 4 1 2.220 -0.073 -0.073
## 245 SupG_Feed ~~ SupG_Ori 1 1 1 2.038 -0.120 -0.120
## 294 SupG_Meta ~~ SupG_Bestar 4 4 1 2.011 -0.118 -0.118
## 295 SupG_Ori ~~ SupG_Mon 4 4 1 1.942 0.225 0.225
## 269 SupG_Ori ~~ SupG_Bestar 2 2 1 1.935 -0.075 -0.075
## 279 SupG_Meta ~~ SupG_Infra 3 3 1 1.821 -0.181 -0.181
## 296 SupG_Ori ~~ SupG_Infra 4 4 1 1.708 0.158 0.158
## 274 SupG_Feed ~~ SupG_Mon 3 3 1 1.611 -0.319 -0.319
## 264 SupG_Meta ~~ SupG_Mon 2 2 1 1.581 0.065 0.065
## 45 SupG_Feed ~1 1 1 1 1.553 0.140 0.140
## 293 SupG_Meta ~~ SupG_Infra 4 4 1 1.518 -0.100 -0.100
## 251 SupG_Meta ~~ SupG_Infra 1 1 1 1.497 -0.064 -0.064
## 277 SupG_Meta ~~ SupG_Ori 3 3 1 1.480 0.234 0.234
## 255 SupG_Ori ~~ SupG_Bestar 1 1 1 1.334 0.088 0.088
## 267 SupG_Ori ~~ SupG_Mon 2 2 1 1.091 0.077 0.077
## 292 SupG_Meta ~~ SupG_Mon 4 4 1 1.044 -0.111 -0.111
## 257 SupG_Mon ~~ SupG_Bestar 1 1 1 1.027 -0.082 -0.082
## 263 SupG_Meta ~~ SupG_Ori 2 2 1 0.986 0.046 0.046
## 144 SupG_Mon ~*~ SupG_Mon 3 3 1 0.971 -0.024 -0.024
## 150 SupG_Mon ~1 3 3 1 0.971 -0.291 -0.291
## 250 SupG_Meta ~~ SupG_Mon 1 1 1 0.907 -0.069 -0.069
## 192 SupG_Feed ~*~ SupG_Feed 4 4 1 0.819 0.042 0.042
## 247 SupG_Feed ~~ SupG_Infra 1 1 1 0.711 0.058 0.058
## 276 SupG_Feed ~~ SupG_Bestar 3 3 1 0.677 -0.153 -0.153
## 278 SupG_Meta ~~ SupG_Mon 3 3 1 0.634 0.159 0.159
## 266 SupG_Meta ~~ SupG_Bestar 2 2 1 0.533 0.028 0.028
## 195 SupG_Mon ~*~ SupG_Mon 4 4 1 0.442 0.020 0.020
## 201 SupG_Mon ~1 4 4 1 0.442 0.135 0.135
## 43 SupG_Infra ~*~ SupG_Infra 1 1 1 0.430 0.016 0.016
## 49 SupG_Infra ~1 1 1 1 0.430 0.052 0.052
## 142 SupG_Meta ~*~ SupG_Meta 3 3 1 0.301 0.023 0.023
## 148 SupG_Meta ~1 3 3 1 0.301 0.114 0.114
## 48 SupG_Mon ~1 1 1 1 0.300 0.075 0.075
## 42 SupG_Mon ~*~ SupG_Mon 1 1 1 0.300 0.008 0.008
## 254 SupG_Ori ~~ SupG_Infra 1 1 1 0.288 -0.039 -0.039
## 283 SupG_Ori ~~ SupG_Bestar 3 3 1 0.280 -0.109 -0.109
## 99 SupG_Mon ~1 2 2 1 0.249 -0.063 -0.063
## 93 SupG_Mon ~*~ SupG_Mon 2 2 1 0.249 -0.008 -0.008
## 141 SupG_Feed ~*~ SupG_Feed 3 3 1 0.240 0.017 0.017
## 287 SupG_Feed ~~ SupG_Ori 4 4 1 0.233 -0.062 -0.062
## 94 SupG_Infra ~*~ SupG_Infra 2 2 1 0.179 0.011 0.011
## 100 SupG_Infra ~1 2 2 1 0.179 0.031 0.031
## 248 SupG_Feed ~~ SupG_Bestar 1 1 1 0.178 0.029 0.029
## 258 SupG_Feed ~~ SupG_Meta 2 2 1 0.091 0.013 0.013
## 252 SupG_Meta ~~ SupG_Bestar 1 1 1 0.070 -0.014 -0.014
## 40 SupG_Meta ~*~ SupG_Meta 1 1 1 0.066 0.006 0.006
## 46 SupG_Meta ~1 1 1 1 0.065 0.025 0.025
## 151 SupG_Infra ~1 3 3 1 0.058 -0.041 -0.041
## 145 SupG_Infra ~*~ SupG_Infra 3 3 1 0.058 -0.010 -0.010
## 299 SupG_Mon ~~ SupG_Bestar 4 4 1 0.058 0.032 0.032
## 50 SupG_Bestar ~1 1 1 1 0.049 -0.020 -0.020
## 44 SupG_Bestar ~*~ SupG_Bestar 1 1 1 0.049 -0.005 -0.005
## 291 SupG_Meta ~~ SupG_Ori 4 4 1 0.048 -0.022 -0.022
## 270 SupG_Mon ~~ SupG_Infra 2 2 1 0.038 0.012 0.012
## 272 SupG_Feed ~~ SupG_Meta 3 3 1 0.033 0.029 0.029
## 284 SupG_Mon ~~ SupG_Infra 3 3 1 0.027 0.034 0.034
## 265 SupG_Meta ~~ SupG_Infra 2 2 1 0.018 0.005 0.005
## 273 SupG_Feed ~~ SupG_Ori 3 3 1 0.017 -0.031 -0.031
## 244 SupG_Feed ~~ SupG_Meta 1 1 1 0.014 0.007 0.007
## 147 SupG_Feed ~1 3 3 1 0.012 0.027 0.027
## 298 SupG_Mon ~~ SupG_Infra 4 4 1 0.008 0.012 0.012
## 260 SupG_Feed ~~ SupG_Mon 2 2 1 0.004 -0.004 -0.004
## 282 SupG_Ori ~~ SupG_Infra 3 3 1 0.004 -0.013 -0.013
## 101 SupG_Bestar ~1 2 2 1 0.001 -0.003 -0.003
## 95 SupG_Bestar ~*~ SupG_Bestar 2 2 1 0.001 -0.001 -0.001
## 256 SupG_Mon ~~ SupG_Infra 1 1 1 0.001 -0.003 -0.003
## sepc.all sepc.nox
## 98 0.337 0.337
## 92 1.000 1.000
## 199 0.480 0.480
## 193 1.000 1.000
## 268 -0.245 -0.245
## 281 0.698 0.698
## 261 0.172 0.172
## 146 1.000 1.000
## 152 0.351 0.351
## 259 -0.240 -0.240
## 97 -0.206 -0.206
## 91 -1.000 -1.000
## 262 0.162 0.162
## 253 0.267 0.267
## 143 -1.000 -1.000
## 149 -0.323 -0.323
## 41 -1.000 -1.000
## 47 -0.173 -0.173
## 90 -1.000 -1.000
## 96 -0.161 -0.161
## 194 -1.000 -1.000
## 200 -0.259 -0.259
## 286 -0.331 -0.331
## 198 0.225 0.225
## 290 0.300 0.300
## 271 -0.112 -0.112
## 289 0.285 0.285
## 249 0.125 0.125
## 280 -0.249 -0.249
## 288 -0.377 -0.377
## 203 -0.161 -0.161
## 197 -1.000 -1.000
## 39 1.000 1.000
## 246 -0.149 -0.149
## 297 0.252 0.252
## 285 -0.294 -0.294
## 275 0.265 0.265
## 202 -0.129 -0.129
## 196 -1.000 -1.000
## 245 -0.120 -0.120
## 294 -0.170 -0.170
## 295 0.300 0.300
## 269 -0.101 -0.101
## 279 -0.176 -0.176
## 296 0.191 0.191
## 274 -0.241 -0.241
## 264 0.071 0.071
## 45 0.084 0.084
## 293 -0.141 -0.141
## 251 -0.064 -0.064
## 277 0.178 0.178
## 255 0.088 0.088
## 267 0.093 0.093
## 292 -0.174 -0.174
## 257 -0.082 -0.082
## 263 0.068 0.068
## 144 -1.000 -1.000
## 150 -0.130 -0.130
## 250 -0.069 -0.069
## 192 1.000 1.000
## 247 0.058 0.058
## 276 -0.140 -0.140
## 278 0.129 0.129
## 266 0.034 0.034
## 195 1.000 1.000
## 201 0.077 0.077
## 43 1.000 1.000
## 49 0.036 0.036
## 142 1.000 1.000
## 148 0.077 0.077
## 48 0.038 0.038
## 42 1.000 1.000
## 254 -0.039 -0.039
## 283 -0.089 -0.089
## 99 -0.033 -0.033
## 93 -1.000 -1.000
## 141 1.000 1.000
## 287 -0.099 -0.099
## 94 1.000 1.000
## 100 0.022 0.022
## 248 0.029 0.029
## 258 0.016 0.016
## 252 -0.014 -0.014
## 40 1.000 1.000
## 46 0.018 0.018
## 151 -0.027 -0.027
## 145 -1.000 -1.000
## 299 0.039 0.039
## 50 -0.013 -0.013
## 44 -1.000 -1.000
## 291 -0.035 -0.035
## 270 0.011 0.011
## 272 0.025 0.025
## 284 0.029 0.029
## 265 0.006 0.006
## 273 -0.022 -0.022
## 244 0.007 0.007
## 147 0.014 0.014
## 298 0.014 0.014
## 260 -0.005 -0.005
## 282 -0.011 -0.011
## 101 -0.002 -0.002
## 95 -1.000 -1.000
## 256 -0.003 -0.003semTools::reliability(invariance$fit.loadings)## For constructs with categorical indicators, Zumbo et al.`s (2007) "ordinal alpha" is calculated in addition to the standard alpha, which treats ordinal variables as numeric. See Chalmers (2018) for a critique of "alpha.ord". Likewise, average variance extracted is calculated from polychoric (polyserial) not Pearson correlations.## $`2`
## SupG
## alpha 0.8551
## alpha.ord 0.9046
## omega 0.8381
## omega2 0.8381
## omega3 0.8389
## avevar 0.6290
##
## $`3`
## SupG
## alpha 0.8629
## alpha.ord 0.9073
## omega 0.8358
## omega2 0.8358
## omega3 0.8328
## avevar 0.6317
##
## $`1`
## SupG
## alpha 0.8700
## alpha.ord 0.9117
## omega 0.8682
## omega2 0.8682
## omega3 0.8703
## avevar 0.6485
##
## $`4`
## SupG
## alpha 0.8764
## alpha.ord 0.9178
## omega 0.8274
## omega2 0.8274
## omega3 0.8235
## avevar 0.65607.1.1.7.3 Thresholds
summary(invariance$fit.thresholds,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 145 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 148
## Number of equality constraints 90
##
## Number of observations per group:
## 2 1807
## 3 2851
## 1 356
## 4 429
## Number of missing patterns per group:
## 2 1
## 3 1
## 1 1
## 4 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 306.914 189.994
## Degrees of freedom 98 98
## P-value (Unknown) NA 0.000
## Scaling correction factor 1.932
## Shift parameter for each group:
## 2 10.345
## 3 16.322
## 1 2.038
## 4 2.456
## simple second-order correction
## Test statistic for each group:
## 2 64.216 43.578
## 3 76.210 55.762
## 1 86.255 46.676
## 4 80.233 43.978
##
## Model Test Baseline Model:
##
## Test statistic 31849.655 38983.303
## Degrees of freedom 60 60
## P-value NA 0.000
## Scaling correction factor 0.818
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.993 0.998
## Tucker-Lewis Index (TLI) 0.996 0.999
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.040 0.026
## 90 Percent confidence interval - lower 0.035 0.021
## 90 Percent confidence interval - upper 0.045 0.032
## P-value RMSEA <= 0.05 1.000 1.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.025 0.025
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
##
## Group 1 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.354 0.061 22.076 0.000 1.354 0.804
## SupG_Meta 0.919 0.038 24.205 0.000 0.919 0.677
## SupG_Ori 1.590 0.087 18.217 0.000 1.590 0.847
## SupG_Mon 1.614 0.090 18.015 0.000 1.614 0.850
## SupG_Infra 1.045 0.041 25.599 0.000 1.045 0.723
## SupG_Bestar 1.134 0.047 24.189 0.000 1.134 0.750
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.419 0.030 13.920 0.000 0.419 0.419
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.943 0.111 -26.608 0.000 -2.943 -1.748
## SupG_Feed|t2 -2.072 0.083 -25.107 0.000 -2.072 -1.231
## SupG_Feed|t3 -0.925 0.052 -17.836 0.000 -0.925 -0.550
## SupG_Feed|t4 1.065 0.057 18.715 0.000 1.065 0.633
## SupG_Meta|t1 -3.003 0.110 -27.423 0.000 -3.003 -2.211
## SupG_Meta|t2 -2.162 0.079 -27.378 0.000 -2.162 -1.592
## SupG_Meta|t3 -1.406 0.055 -25.385 0.000 -1.406 -1.035
## SupG_Meta|t4 0.610 0.037 16.580 0.000 0.610 0.449
## SupG_Ori|t1 -4.603 0.245 -18.788 0.000 -4.603 -2.450
## SupG_Ori|t2 -3.549 0.195 -18.233 0.000 -3.549 -1.889
## SupG_Ori|t3 -2.548 0.140 -18.149 0.000 -2.548 -1.356
## SupG_Ori|t4 0.056 0.048 1.173 0.241 0.056 0.030
## SupG_Mon|t1 -4.619 0.259 -17.809 0.000 -4.619 -2.433
## SupG_Mon|t2 -3.841 0.215 -17.826 0.000 -3.841 -2.023
## SupG_Mon|t3 -2.578 0.144 -17.953 0.000 -2.578 -1.358
## SupG_Mon|t4 0.148 0.050 2.976 0.003 0.148 0.078
## SupG_Infra|t1 -2.224 0.073 -30.539 0.000 -2.224 -1.537
## SupG_Infra|t2 -1.424 0.053 -26.989 0.000 -1.424 -0.985
## SupG_Infra|t3 -0.235 0.034 -6.829 0.000 -0.235 -0.163
## SupG_Infra|t4 1.122 0.046 24.499 0.000 1.122 0.776
## SupG_Bestar|t1 -2.780 0.100 -27.833 0.000 -2.780 -1.839
## SupG_Bestar|t2 -2.082 0.079 -26.468 0.000 -2.082 -1.377
## SupG_Bestar|t3 -1.022 0.049 -20.699 0.000 -1.022 -0.676
## SupG_Bestar|t4 0.588 0.040 14.643 0.000 0.588 0.389
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.000 1.000 0.353
## .SupG_Meta 1.000 1.000 0.542
## .SupG_Ori 1.000 1.000 0.283
## .SupG_Mon 1.000 1.000 0.277
## .SupG_Infra 1.000 1.000 0.478
## .SupG_Bestar 1.000 1.000 0.438
## SupG 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.594 0.594 1.000
## SupG_Meta 0.736 0.736 1.000
## SupG_Ori 0.532 0.532 1.000
## SupG_Mon 0.527 0.527 1.000
## SupG_Infra 0.691 0.691 1.000
## SupG_Bestar 0.662 0.662 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.647
## SupG_Meta 0.458
## SupG_Ori 0.717
## SupG_Mon 0.723
## SupG_Infra 0.522
## SupG_Bestar 0.562
##
##
## Group 2 [3]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.354 0.061 22.076 0.000 1.353 0.804
## SupG_Meta 0.919 0.038 24.205 0.000 0.919 0.710
## SupG_Ori 1.590 0.087 18.217 0.000 1.590 0.873
## SupG_Mon 1.614 0.090 18.015 0.000 1.613 0.832
## SupG_Infra 1.045 0.041 25.599 0.000 1.045 0.716
## SupG_Bestar 1.134 0.047 24.189 0.000 1.133 0.738
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.456 0.048 9.592 0.000 0.456 0.432
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG -0.068 0.034 -1.987 0.047 -0.068 -0.068
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.943 0.111 -26.608 0.000 -2.943 -1.748
## SupG_Feed|t2 -2.072 0.083 -25.107 0.000 -2.072 -1.230
## SupG_Feed|t3 -0.925 0.052 -17.836 0.000 -0.925 -0.549
## SupG_Feed|t4 1.065 0.057 18.715 0.000 1.065 0.633
## SupG_Meta|t1 -3.003 0.110 -27.423 0.000 -3.003 -2.320
## SupG_Meta|t2 -2.162 0.079 -27.378 0.000 -2.162 -1.670
## SupG_Meta|t3 -1.406 0.055 -25.385 0.000 -1.406 -1.086
## SupG_Meta|t4 0.610 0.037 16.580 0.000 0.610 0.471
## SupG_Ori|t1 -4.603 0.245 -18.788 0.000 -4.603 -2.528
## SupG_Ori|t2 -3.549 0.195 -18.233 0.000 -3.549 -1.949
## SupG_Ori|t3 -2.548 0.140 -18.149 0.000 -2.548 -1.399
## SupG_Ori|t4 0.056 0.048 1.173 0.241 0.056 0.031
## SupG_Mon|t1 -4.619 0.259 -17.809 0.000 -4.619 -2.382
## SupG_Mon|t2 -3.841 0.215 -17.826 0.000 -3.841 -1.981
## SupG_Mon|t3 -2.578 0.144 -17.953 0.000 -2.578 -1.330
## SupG_Mon|t4 0.148 0.050 2.976 0.003 0.148 0.076
## SupG_Infra|t1 -2.224 0.073 -30.539 0.000 -2.224 -1.524
## SupG_Infra|t2 -1.424 0.053 -26.989 0.000 -1.424 -0.976
## SupG_Infra|t3 -0.235 0.034 -6.829 0.000 -0.235 -0.161
## SupG_Infra|t4 1.122 0.046 24.499 0.000 1.122 0.769
## SupG_Bestar|t1 -2.780 0.100 -27.833 0.000 -2.780 -1.810
## SupG_Bestar|t2 -2.082 0.079 -26.468 0.000 -2.082 -1.355
## SupG_Bestar|t3 -1.022 0.049 -20.699 0.000 -1.022 -0.665
## SupG_Bestar|t4 0.588 0.040 14.643 0.000 0.588 0.383
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.004 0.099 10.160 0.000 1.004 0.354
## .SupG_Meta 0.831 0.080 10.361 0.000 0.831 0.496
## .SupG_Ori 0.789 0.134 5.881 0.000 0.789 0.238
## .SupG_Mon 1.156 0.179 6.462 0.000 1.156 0.308
## .SupG_Infra 1.037 0.081 12.858 0.000 1.037 0.487
## .SupG_Bestar 1.076 0.098 10.981 0.000 1.076 0.456
## SupG 0.999 0.065 15.291 0.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.594 0.594 1.000
## SupG_Meta 0.773 0.773 1.000
## SupG_Ori 0.549 0.549 1.000
## SupG_Mon 0.516 0.516 1.000
## SupG_Infra 0.685 0.685 1.000
## SupG_Bestar 0.651 0.651 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.646
## SupG_Meta 0.504
## SupG_Ori 0.762
## SupG_Mon 0.692
## SupG_Infra 0.513
## SupG_Bestar 0.544
##
##
## Group 3 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.354 0.061 22.076 0.000 1.358 0.822
## SupG_Meta 0.919 0.038 24.205 0.000 0.922 0.704
## SupG_Ori 1.590 0.087 18.217 0.000 1.595 0.809
## SupG_Mon 1.614 0.090 18.015 0.000 1.618 0.844
## SupG_Infra 1.045 0.041 25.599 0.000 1.048 0.789
## SupG_Bestar 1.134 0.047 24.189 0.000 1.137 0.793
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.110 0.097 1.131 0.258 0.110 0.154
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.114 0.066 1.724 0.085 0.113 0.113
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.943 0.111 -26.608 0.000 -2.943 -1.783
## SupG_Feed|t2 -2.072 0.083 -25.107 0.000 -2.072 -1.255
## SupG_Feed|t3 -0.925 0.052 -17.836 0.000 -0.925 -0.560
## SupG_Feed|t4 1.065 0.057 18.715 0.000 1.065 0.645
## SupG_Meta|t1 -3.003 0.110 -27.423 0.000 -3.003 -2.293
## SupG_Meta|t2 -2.162 0.079 -27.378 0.000 -2.162 -1.650
## SupG_Meta|t3 -1.406 0.055 -25.385 0.000 -1.406 -1.073
## SupG_Meta|t4 0.610 0.037 16.580 0.000 0.610 0.465
## SupG_Ori|t1 -4.603 0.245 -18.788 0.000 -4.603 -2.334
## SupG_Ori|t2 -3.549 0.195 -18.233 0.000 -3.549 -1.800
## SupG_Ori|t3 -2.548 0.140 -18.149 0.000 -2.548 -1.292
## SupG_Ori|t4 0.056 0.048 1.173 0.241 0.056 0.028
## SupG_Mon|t1 -4.619 0.259 -17.809 0.000 -4.619 -2.408
## SupG_Mon|t2 -3.841 0.215 -17.826 0.000 -3.841 -2.002
## SupG_Mon|t3 -2.578 0.144 -17.953 0.000 -2.578 -1.344
## SupG_Mon|t4 0.148 0.050 2.976 0.003 0.148 0.077
## SupG_Infra|t1 -2.224 0.073 -30.539 0.000 -2.224 -1.673
## SupG_Infra|t2 -1.424 0.053 -26.989 0.000 -1.424 -1.072
## SupG_Infra|t3 -0.235 0.034 -6.829 0.000 -0.235 -0.177
## SupG_Infra|t4 1.122 0.046 24.499 0.000 1.122 0.844
## SupG_Bestar|t1 -2.780 0.100 -27.833 0.000 -2.780 -1.940
## SupG_Bestar|t2 -2.082 0.079 -26.468 0.000 -2.082 -1.453
## SupG_Bestar|t3 -1.022 0.049 -20.699 0.000 -1.022 -0.713
## SupG_Bestar|t4 0.588 0.040 14.643 0.000 0.588 0.410
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.881 0.175 5.031 0.000 0.881 0.323
## .SupG_Meta 0.866 0.148 5.842 0.000 0.866 0.505
## .SupG_Ori 1.346 0.298 4.516 0.000 1.346 0.346
## .SupG_Mon 1.061 0.343 3.090 0.002 1.061 0.288
## .SupG_Infra 0.668 0.117 5.690 0.000 0.668 0.378
## .SupG_Bestar 0.761 0.158 4.829 0.000 0.761 0.371
## SupG 1.005 0.136 7.409 0.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.606 0.606 1.000
## SupG_Meta 0.763 0.763 1.000
## SupG_Ori 0.507 0.507 1.000
## SupG_Mon 0.521 0.521 1.000
## SupG_Infra 0.752 0.752 1.000
## SupG_Bestar 0.698 0.698 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.677
## SupG_Meta 0.495
## SupG_Ori 0.654
## SupG_Mon 0.712
## SupG_Infra 0.622
## SupG_Bestar 0.629
##
##
## Group 4 [4]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.354 0.061 22.076 0.000 1.529 0.828
## SupG_Meta 0.919 0.038 24.205 0.000 1.038 0.755
## SupG_Ori 1.590 0.087 18.217 0.000 1.796 0.875
## SupG_Mon 1.614 0.090 18.015 0.000 1.823 0.863
## SupG_Infra 1.045 0.041 25.599 0.000 1.181 0.700
## SupG_Bestar 1.134 0.047 24.189 0.000 1.280 0.751
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.826 0.150 5.507 0.000 0.826 0.608
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG -0.029 0.068 -0.431 0.666 -0.026 -0.026
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.943 0.111 -26.608 0.000 -2.943 -1.594
## SupG_Feed|t2 -2.072 0.083 -25.107 0.000 -2.072 -1.122
## SupG_Feed|t3 -0.925 0.052 -17.836 0.000 -0.925 -0.501
## SupG_Feed|t4 1.065 0.057 18.715 0.000 1.065 0.577
## SupG_Meta|t1 -3.003 0.110 -27.423 0.000 -3.003 -2.183
## SupG_Meta|t2 -2.162 0.079 -27.378 0.000 -2.162 -1.571
## SupG_Meta|t3 -1.406 0.055 -25.385 0.000 -1.406 -1.022
## SupG_Meta|t4 0.610 0.037 16.580 0.000 0.610 0.443
## SupG_Ori|t1 -4.603 0.245 -18.788 0.000 -4.603 -2.242
## SupG_Ori|t2 -3.549 0.195 -18.233 0.000 -3.549 -1.728
## SupG_Ori|t3 -2.548 0.140 -18.149 0.000 -2.548 -1.241
## SupG_Ori|t4 0.056 0.048 1.173 0.241 0.056 0.027
## SupG_Mon|t1 -4.619 0.259 -17.809 0.000 -4.619 -2.186
## SupG_Mon|t2 -3.841 0.215 -17.826 0.000 -3.841 -1.817
## SupG_Mon|t3 -2.578 0.144 -17.953 0.000 -2.578 -1.220
## SupG_Mon|t4 0.148 0.050 2.976 0.003 0.148 0.070
## SupG_Infra|t1 -2.224 0.073 -30.539 0.000 -2.224 -1.318
## SupG_Infra|t2 -1.424 0.053 -26.989 0.000 -1.424 -0.844
## SupG_Infra|t3 -0.235 0.034 -6.829 0.000 -0.235 -0.140
## SupG_Infra|t4 1.122 0.046 24.499 0.000 1.122 0.665
## SupG_Bestar|t1 -2.780 0.100 -27.833 0.000 -2.780 -1.630
## SupG_Bestar|t2 -2.082 0.079 -26.468 0.000 -2.082 -1.221
## SupG_Bestar|t3 -1.022 0.049 -20.699 0.000 -1.022 -0.599
## SupG_Bestar|t4 0.588 0.040 14.643 0.000 0.588 0.345
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.070 0.199 5.367 0.000 1.070 0.314
## .SupG_Meta 0.815 0.178 4.566 0.000 0.815 0.431
## .SupG_Ori 0.989 0.288 3.434 0.001 0.989 0.235
## .SupG_Mon 1.141 0.350 3.266 0.001 1.141 0.256
## .SupG_Infra 1.451 0.188 7.701 0.000 1.451 0.510
## .SupG_Bestar 1.270 0.199 6.399 0.000 1.270 0.437
## SupG 1.276 0.136 9.349 0.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.542 0.542 1.000
## SupG_Meta 0.727 0.727 1.000
## SupG_Ori 0.487 0.487 1.000
## SupG_Mon 0.473 0.473 1.000
## SupG_Infra 0.593 0.593 1.000
## SupG_Bestar 0.586 0.586 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.686
## SupG_Meta 0.569
## SupG_Ori 0.765
## SupG_Mon 0.744
## SupG_Infra 0.490
## SupG_Bestar 0.563lavaan::fitMeasures(invariance$fit.thresholds,c("chisq.scaled","df.scaled","pvalue.scaled","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue.scaled
## 189.994 98.000 0.000
## srmr cfi.scaled tli.scaled
## 0.025 0.998 0.999
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.026 0.021 0.032modificationindices(invariance$fit.thresholds, sort.=T)## lhs op rhs block group level mi epc sepc.lv
## 49 SupG_Infra ~1 1 1 1 17.499 0.109 0.109
## 100 SupG_Infra ~1 2 2 1 16.724 -0.101 -0.101
## 151 SupG_Infra ~1 3 3 1 14.525 0.184 0.184
## 202 SupG_Infra ~1 4 4 1 14.017 -0.191 -0.191
## 332 SupG_Ori ~~ SupG_Mon 3 3 1 13.061 0.787 0.787
## 319 SupG_Ori ~~ SupG_Infra 2 2 1 12.211 -0.210 -0.210
## 193 SupG_Meta ~*~ SupG_Meta 4 4 1 10.853 0.118 0.118
## 92 SupG_Ori ~*~ SupG_Ori 2 2 1 10.842 0.047 0.047
## 313 SupG_Feed ~~ SupG_Bestar 2 2 1 9.032 0.172 0.172
## 312 SupG_Feed ~~ SupG_Infra 2 2 1 7.745 0.151 0.151
## 146 SupG_Bestar ~*~ SupG_Bestar 3 3 1 6.757 0.102 0.102
## 304 SupG_Ori ~~ SupG_Mon 1 1 1 6.433 0.249 0.249
## 143 SupG_Ori ~*~ SupG_Ori 3 3 1 6.194 -0.065 -0.065
## 99 SupG_Mon ~1 2 2 1 5.393 0.105 0.105
## 310 SupG_Feed ~~ SupG_Ori 2 2 1 5.357 -0.163 -0.163
## 48 SupG_Mon ~1 1 1 1 5.306 -0.110 -0.110
## 90 SupG_Feed ~*~ SupG_Feed 2 2 1 5.210 -0.038 -0.038
## 340 SupG_Feed ~~ SupG_Infra 4 4 1 4.949 0.366 0.366
## 150 SupG_Mon ~1 3 3 1 4.729 -0.204 -0.204
## 296 SupG_Feed ~~ SupG_Ori 1 1 1 3.721 -0.166 -0.166
## 341 SupG_Feed ~~ SupG_Bestar 4 4 1 3.714 0.322 0.322
## 39 SupG_Feed ~*~ SupG_Feed 1 1 1 3.680 0.033 0.033
## 91 SupG_Meta ~*~ SupG_Meta 2 2 1 3.565 -0.041 -0.041
## 148 SupG_Meta ~1 3 3 1 3.544 -0.104 -0.104
## 322 SupG_Mon ~~ SupG_Bestar 2 2 1 3.459 -0.124 -0.124
## 101 SupG_Bestar ~1 2 2 1 3.420 -0.055 -0.055
## 45 SupG_Feed ~1 1 1 1 3.364 -0.061 -0.061
## 203 SupG_Bestar ~1 4 4 1 3.199 0.107 0.107
## 201 SupG_Mon ~1 4 4 1 3.108 0.156 0.156
## 149 SupG_Ori ~1 3 3 1 3.056 -0.168 -0.168
## 300 SupG_Meta ~~ SupG_Ori 1 1 1 2.934 0.115 0.115
## 96 SupG_Feed ~1 2 2 1 2.762 0.052 0.052
## 345 SupG_Meta ~~ SupG_Bestar 4 4 1 2.761 -0.203 -0.203
## 41 SupG_Ori ~*~ SupG_Ori 1 1 1 2.661 -0.024 -0.024
## 196 SupG_Infra ~*~ SupG_Infra 4 4 1 2.658 -0.056 -0.056
## 337 SupG_Feed ~~ SupG_Meta 4 4 1 2.492 -0.211 -0.211
## 297 SupG_Feed ~~ SupG_Mon 1 1 1 2.477 -0.137 -0.137
## 331 SupG_Meta ~~ SupG_Bestar 3 3 1 2.356 -0.163 -0.163
## 97 SupG_Meta ~1 2 2 1 2.308 0.040 0.040
## 328 SupG_Meta ~~ SupG_Ori 3 3 1 2.056 0.209 0.209
## 325 SupG_Feed ~~ SupG_Mon 3 3 1 2.002 -0.260 -0.260
## 336 SupG_Mon ~~ SupG_Bestar 3 3 1 1.956 -0.222 -0.222
## 330 SupG_Meta ~~ SupG_Infra 3 3 1 1.761 -0.131 -0.131
## 152 SupG_Bestar ~1 3 3 1 1.564 0.075 0.075
## 94 SupG_Infra ~*~ SupG_Infra 2 2 1 1.476 0.026 0.026
## 318 SupG_Ori ~~ SupG_Mon 2 2 1 1.293 0.093 0.093
## 344 SupG_Meta ~~ SupG_Infra 4 4 1 1.230 -0.134 -0.134
## 194 SupG_Ori ~*~ SupG_Ori 4 4 1 1.173 -0.025 -0.025
## 144 SupG_Mon ~*~ SupG_Mon 3 3 1 1.123 -0.028 -0.028
## 314 SupG_Meta ~~ SupG_Ori 2 2 1 1.109 0.055 0.055
## 339 SupG_Feed ~~ SupG_Mon 4 4 1 1.087 -0.218 -0.218
## 329 SupG_Meta ~~ SupG_Mon 3 3 1 1.057 0.146 0.146
## 347 SupG_Ori ~~ SupG_Infra 4 4 1 1.026 0.187 0.187
## 98 SupG_Ori ~1 2 2 1 0.998 0.044 0.044
## 326 SupG_Feed ~~ SupG_Infra 3 3 1 0.991 0.127 0.127
## 141 SupG_Feed ~*~ SupG_Feed 3 3 1 0.970 0.032 0.032
## 327 SupG_Feed ~~ SupG_Bestar 3 3 1 0.947 -0.133 -0.133
## 302 SupG_Meta ~~ SupG_Infra 1 1 1 0.904 -0.048 -0.048
## 346 SupG_Ori ~~ SupG_Mon 4 4 1 0.901 0.222 0.222
## 348 SupG_Ori ~~ SupG_Bestar 4 4 1 0.809 0.168 0.168
## 343 SupG_Meta ~~ SupG_Mon 4 4 1 0.801 -0.137 -0.137
## 197 SupG_Bestar ~*~ SupG_Bestar 4 4 1 0.696 -0.026 -0.026
## 320 SupG_Ori ~~ SupG_Bestar 2 2 1 0.677 -0.052 -0.052
## 315 SupG_Meta ~~ SupG_Mon 2 2 1 0.673 0.045 0.045
## 306 SupG_Ori ~~ SupG_Bestar 1 1 1 0.670 0.063 0.063
## 308 SupG_Mon ~~ SupG_Bestar 1 1 1 0.624 -0.061 -0.061
## 298 SupG_Feed ~~ SupG_Infra 1 1 1 0.526 0.047 0.047
## 46 SupG_Meta ~1 1 1 1 0.492 -0.020 -0.020
## 317 SupG_Meta ~~ SupG_Bestar 2 2 1 0.485 0.030 0.030
## 95 SupG_Bestar ~*~ SupG_Bestar 2 2 1 0.464 -0.013 -0.013
## 305 SupG_Ori ~~ SupG_Infra 1 1 1 0.439 -0.049 -0.049
## 342 SupG_Meta ~~ SupG_Ori 4 4 1 0.377 -0.092 -0.092
## 198 SupG_Feed ~1 4 4 1 0.276 0.032 0.032
## 301 SupG_Meta ~~ SupG_Mon 1 1 1 0.245 -0.034 -0.034
## 192 SupG_Feed ~*~ SupG_Feed 4 4 1 0.211 -0.013 -0.013
## 195 SupG_Mon ~*~ SupG_Mon 4 4 1 0.169 0.009 0.009
## 147 SupG_Feed ~1 3 3 1 0.167 -0.026 -0.026
## 338 SupG_Feed ~~ SupG_Ori 4 4 1 0.151 -0.079 -0.079
## 50 SupG_Bestar ~1 1 1 1 0.124 0.011 0.011
## 307 SupG_Mon ~~ SupG_Infra 1 1 1 0.124 0.026 0.026
## 334 SupG_Ori ~~ SupG_Bestar 3 3 1 0.123 -0.057 -0.057
## 43 SupG_Infra ~*~ SupG_Infra 1 1 1 0.091 0.007 0.007
## 321 SupG_Mon ~~ SupG_Infra 2 2 1 0.090 -0.019 -0.019
## 316 SupG_Meta ~~ SupG_Infra 2 2 1 0.078 -0.011 -0.011
## 324 SupG_Feed ~~ SupG_Ori 3 3 1 0.075 -0.051 -0.051
## 349 SupG_Mon ~~ SupG_Infra 4 4 1 0.073 0.051 0.051
## 40 SupG_Meta ~*~ SupG_Meta 1 1 1 0.062 -0.005 -0.005
## 309 SupG_Feed ~~ SupG_Meta 2 2 1 0.037 0.009 0.009
## 145 SupG_Infra ~*~ SupG_Infra 3 3 1 0.035 0.008 0.008
## 311 SupG_Feed ~~ SupG_Mon 2 2 1 0.035 -0.014 -0.014
## 93 SupG_Mon ~*~ SupG_Mon 2 2 1 0.032 0.002 0.002
## 333 SupG_Ori ~~ SupG_Infra 3 3 1 0.027 -0.025 -0.025
## 299 SupG_Feed ~~ SupG_Bestar 1 1 1 0.025 0.011 0.011
## 42 SupG_Mon ~*~ SupG_Mon 1 1 1 0.023 -0.002 -0.002
## 323 SupG_Feed ~~ SupG_Meta 3 3 1 0.021 0.018 0.018
## 47 SupG_Ori ~1 1 1 1 0.019 -0.006 -0.006
## 303 SupG_Meta ~~ SupG_Bestar 1 1 1 0.019 -0.007 -0.007
## 200 SupG_Ori ~1 4 4 1 0.018 -0.012 -0.012
## 295 SupG_Feed ~~ SupG_Meta 1 1 1 0.015 0.007 0.007
## 199 SupG_Meta ~1 4 4 1 0.007 0.004 0.004
## 142 SupG_Meta ~*~ SupG_Meta 3 3 1 0.006 0.003 0.003
## 44 SupG_Bestar ~*~ SupG_Bestar 1 1 1 0.002 -0.001 -0.001
## 335 SupG_Mon ~~ SupG_Infra 3 3 1 0.001 0.006 0.006
## 350 SupG_Mon ~~ SupG_Bestar 4 4 1 0.000 -0.003 -0.003
## sepc.all sepc.nox
## 49 0.075 0.075
## 100 -0.069 -0.069
## 151 0.138 0.138
## 202 -0.113 -0.113
## 332 0.659 0.659
## 319 -0.232 -0.232
## 193 1.000 1.000
## 92 1.000 1.000
## 313 0.166 0.166
## 312 0.148 0.148
## 146 1.000 1.000
## 304 0.249 0.249
## 143 -1.000 -1.000
## 99 0.054 0.054
## 310 -0.183 -0.183
## 48 -0.058 -0.058
## 90 -1.000 -1.000
## 340 0.294 0.294
## 150 -0.106 -0.106
## 296 -0.166 -0.166
## 341 0.276 0.276
## 39 1.000 1.000
## 91 -1.000 -1.000
## 148 -0.079 -0.079
## 322 -0.111 -0.111
## 101 -0.036 -0.036
## 45 -0.036 -0.036
## 203 0.063 0.063
## 201 0.074 0.074
## 149 -0.085 -0.085
## 300 0.115 0.115
## 96 0.031 0.031
## 345 -0.200 -0.200
## 41 -1.000 -1.000
## 196 -1.000 -1.000
## 337 -0.226 -0.226
## 297 -0.137 -0.137
## 331 -0.201 -0.201
## 97 0.031 0.031
## 328 0.193 0.193
## 325 -0.268 -0.268
## 336 -0.247 -0.247
## 330 -0.172 -0.172
## 152 0.052 0.052
## 94 1.000 1.000
## 318 0.097 0.097
## 344 -0.123 -0.123
## 194 -1.000 -1.000
## 144 -1.000 -1.000
## 314 0.068 0.068
## 339 -0.198 -0.198
## 329 0.153 0.153
## 347 0.156 0.156
## 98 0.024 0.024
## 326 0.165 0.165
## 141 1.000 1.000
## 327 -0.162 -0.162
## 302 -0.048 -0.048
## 346 0.209 0.209
## 348 0.150 0.150
## 343 -0.142 -0.142
## 197 -1.000 -1.000
## 320 -0.057 -0.057
## 315 0.046 0.046
## 306 0.063 0.063
## 308 -0.061 -0.061
## 298 0.047 0.047
## 46 -0.015 -0.015
## 317 0.032 0.032
## 95 -1.000 -1.000
## 305 -0.049 -0.049
## 342 -0.102 -0.102
## 198 0.018 0.018
## 301 -0.034 -0.034
## 192 -1.000 -1.000
## 195 1.000 1.000
## 147 -0.016 -0.016
## 338 -0.077 -0.077
## 50 0.007 0.007
## 307 0.026 0.026
## 334 -0.056 -0.056
## 43 1.000 1.000
## 321 -0.017 -0.017
## 316 -0.012 -0.012
## 324 -0.047 -0.047
## 349 0.040 0.040
## 40 -1.000 -1.000
## 309 0.010 0.010
## 145 1.000 1.000
## 311 -0.013 -0.013
## 93 1.000 1.000
## 333 -0.026 -0.026
## 299 0.011 0.011
## 42 -1.000 -1.000
## 323 0.020 0.020
## 47 -0.003 -0.003
## 303 -0.007 -0.007
## 200 -0.006 -0.006
## 295 0.007 0.007
## 199 0.003 0.003
## 142 1.000 1.000
## 44 -1.000 -1.000
## 335 0.007 0.007
## 350 -0.002 -0.002semTools::reliability(invariance$fit.thresholds)## For constructs with categorical indicators, Zumbo et al.`s (2007) "ordinal alpha" is calculated in addition to the standard alpha, which treats ordinal variables as numeric. See Chalmers (2018) for a critique of "alpha.ord". Likewise, average variance extracted is calculated from polychoric (polyserial) not Pearson correlations.## $`2`
## SupG
## alpha 0.8551
## alpha.ord 0.9046
## omega 0.8394
## omega2 0.8394
## omega3 0.8402
## avevar 0.6294
##
## $`3`
## SupG
## alpha 0.8629
## alpha.ord 0.9073
## omega 0.8383
## omega2 0.8383
## omega3 0.8357
## avevar 0.6334
##
## $`1`
## SupG
## alpha 0.8700
## alpha.ord 0.9117
## omega 0.8703
## omega2 0.8703
## omega3 0.8741
## avevar 0.6473
##
## $`4`
## SupG
## alpha 0.8764
## alpha.ord 0.9178
## omega 0.8417
## omega2 0.8417
## omega3 0.8359
## avevar 0.65877.1.1.7.4 Partial Invariance - Means
summary(invariance$fit.means,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 139 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 145
## Number of equality constraints 90
##
## Number of observations per group:
## 2 1807
## 3 2851
## 1 356
## 4 429
## Number of missing patterns per group:
## 2 1
## 3 1
## 1 1
## 4 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 400.862 202.952
## Degrees of freedom 101 101
## P-value (Unknown) NA 0.000
## Scaling correction factor 2.390
## Shift parameter for each group:
## 2 11.704
## 3 18.467
## 1 2.306
## 4 2.779
## simple second-order correction
## Test statistic for each group:
## 2 72.584 42.069
## 3 109.195 64.147
## 1 137.927 60.006
## 4 81.157 36.730
##
## Model Test Baseline Model:
##
## Test statistic 31849.655 38983.303
## Degrees of freedom 60 60
## P-value NA 0.000
## Scaling correction factor 0.818
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.991 0.997
## Tucker-Lewis Index (TLI) 0.994 0.998
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.047 0.027
## 90 Percent confidence interval - lower 0.042 0.022
## 90 Percent confidence interval - upper 0.052 0.033
## P-value RMSEA <= 0.05 0.865 1.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.025 0.025
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
##
## Group 1 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.360 0.062 21.998 0.000 1.360 0.806
## SupG_Meta 0.918 0.038 24.370 0.000 0.918 0.676
## SupG_Ori 1.598 0.088 18.134 0.000 1.598 0.848
## SupG_Mon 1.624 0.091 17.915 0.000 1.624 0.852
## SupG_Infra 1.034 0.040 26.013 0.000 1.034 0.719
## SupG_Bestar 1.131 0.047 24.147 0.000 1.131 0.749
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.423 0.030 14.314 0.000 0.423 0.423
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.948 0.111 -26.617 0.000 -2.948 -1.747
## SupG_Feed|t2 -2.064 0.080 -25.744 0.000 -2.064 -1.223
## SupG_Feed|t3 -0.900 0.044 -20.378 0.000 -0.900 -0.533
## SupG_Feed|t4 1.123 0.049 22.695 0.000 1.123 0.665
## SupG_Meta|t1 -3.004 0.109 -27.520 0.000 -3.004 -2.213
## SupG_Meta|t2 -2.156 0.077 -27.837 0.000 -2.156 -1.588
## SupG_Meta|t3 -1.391 0.052 -26.607 0.000 -1.391 -1.025
## SupG_Meta|t4 0.646 0.031 21.044 0.000 0.646 0.475
## SupG_Ori|t1 -4.627 0.248 -18.678 0.000 -4.627 -2.454
## SupG_Ori|t2 -3.559 0.196 -18.152 0.000 -3.559 -1.888
## SupG_Ori|t3 -2.541 0.140 -18.207 0.000 -2.541 -1.348
## SupG_Ori|t4 0.109 0.032 3.372 0.001 0.109 0.058
## SupG_Mon|t1 -4.646 0.262 -17.704 0.000 -4.646 -2.436
## SupG_Mon|t2 -3.857 0.217 -17.744 0.000 -3.857 -2.023
## SupG_Mon|t3 -2.572 0.143 -18.008 0.000 -2.572 -1.349
## SupG_Mon|t4 0.199 0.035 5.754 0.000 0.199 0.104
## SupG_Infra|t1 -2.204 0.069 -31.858 0.000 -2.204 -1.533
## SupG_Infra|t2 -1.402 0.047 -29.589 0.000 -1.402 -0.975
## SupG_Infra|t3 -0.209 0.026 -8.113 0.000 -0.209 -0.146
## SupG_Infra|t4 1.155 0.041 28.397 0.000 1.155 0.803
## SupG_Bestar|t1 -2.778 0.100 -27.675 0.000 -2.778 -1.840
## SupG_Bestar|t2 -2.074 0.077 -26.930 0.000 -2.074 -1.374
## SupG_Bestar|t3 -1.002 0.043 -23.152 0.000 -1.002 -0.664
## SupG_Bestar|t4 0.626 0.033 18.823 0.000 0.626 0.415
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.000 1.000 0.351
## .SupG_Meta 1.000 1.000 0.543
## .SupG_Ori 1.000 1.000 0.281
## .SupG_Mon 1.000 1.000 0.275
## .SupG_Infra 1.000 1.000 0.483
## .SupG_Bestar 1.000 1.000 0.439
## SupG 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.592 0.592 1.000
## SupG_Meta 0.737 0.737 1.000
## SupG_Ori 0.530 0.530 1.000
## SupG_Mon 0.524 0.524 1.000
## SupG_Infra 0.695 0.695 1.000
## SupG_Bestar 0.662 0.662 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.649
## SupG_Meta 0.457
## SupG_Ori 0.719
## SupG_Mon 0.725
## SupG_Infra 0.517
## SupG_Bestar 0.561
##
##
## Group 2 [3]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.360 0.062 21.998 0.000 1.397 0.804
## SupG_Meta 0.918 0.038 24.370 0.000 0.943 0.712
## SupG_Ori 1.598 0.088 18.134 0.000 1.642 0.873
## SupG_Mon 1.624 0.091 17.915 0.000 1.669 0.833
## SupG_Infra 1.034 0.040 26.013 0.000 1.062 0.715
## SupG_Bestar 1.131 0.047 24.147 0.000 1.162 0.735
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.485 0.052 9.289 0.000 0.485 0.436
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.948 0.111 -26.617 0.000 -2.948 -1.695
## SupG_Feed|t2 -2.064 0.080 -25.744 0.000 -2.064 -1.187
## SupG_Feed|t3 -0.900 0.044 -20.378 0.000 -0.900 -0.517
## SupG_Feed|t4 1.123 0.049 22.695 0.000 1.123 0.646
## SupG_Meta|t1 -3.004 0.109 -27.520 0.000 -3.004 -2.268
## SupG_Meta|t2 -2.156 0.077 -27.837 0.000 -2.156 -1.627
## SupG_Meta|t3 -1.391 0.052 -26.607 0.000 -1.391 -1.050
## SupG_Meta|t4 0.646 0.031 21.044 0.000 0.646 0.487
## SupG_Ori|t1 -4.627 0.248 -18.678 0.000 -4.627 -2.460
## SupG_Ori|t2 -3.559 0.196 -18.152 0.000 -3.559 -1.893
## SupG_Ori|t3 -2.541 0.140 -18.207 0.000 -2.541 -1.351
## SupG_Ori|t4 0.109 0.032 3.372 0.001 0.109 0.058
## SupG_Mon|t1 -4.646 0.262 -17.704 0.000 -4.646 -2.319
## SupG_Mon|t2 -3.857 0.217 -17.744 0.000 -3.857 -1.926
## SupG_Mon|t3 -2.572 0.143 -18.008 0.000 -2.572 -1.284
## SupG_Mon|t4 0.199 0.035 5.754 0.000 0.199 0.099
## SupG_Infra|t1 -2.204 0.069 -31.858 0.000 -2.204 -1.483
## SupG_Infra|t2 -1.402 0.047 -29.589 0.000 -1.402 -0.944
## SupG_Infra|t3 -0.209 0.026 -8.113 0.000 -0.209 -0.141
## SupG_Infra|t4 1.155 0.041 28.397 0.000 1.155 0.777
## SupG_Bestar|t1 -2.778 0.100 -27.675 0.000 -2.778 -1.758
## SupG_Bestar|t2 -2.074 0.077 -26.930 0.000 -2.074 -1.312
## SupG_Bestar|t3 -1.002 0.043 -23.152 0.000 -1.002 -0.634
## SupG_Bestar|t4 0.626 0.033 18.823 0.000 0.626 0.396
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.072 0.109 9.830 0.000 1.072 0.354
## .SupG_Meta 0.865 0.085 10.208 0.000 0.865 0.493
## .SupG_Ori 0.840 0.144 5.852 0.000 0.840 0.238
## .SupG_Mon 1.228 0.191 6.422 0.000 1.228 0.306
## .SupG_Infra 1.081 0.086 12.503 0.000 1.081 0.489
## .SupG_Bestar 1.148 0.112 10.298 0.000 1.148 0.460
## SupG 1.056 0.068 15.429 0.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.575 0.575 1.000
## SupG_Meta 0.755 0.755 1.000
## SupG_Ori 0.532 0.532 1.000
## SupG_Mon 0.499 0.499 1.000
## SupG_Infra 0.673 0.673 1.000
## SupG_Bestar 0.633 0.633 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.646
## SupG_Meta 0.507
## SupG_Ori 0.762
## SupG_Mon 0.694
## SupG_Infra 0.511
## SupG_Bestar 0.540
##
##
## Group 3 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.360 0.062 21.998 0.000 1.305 0.827
## SupG_Meta 0.918 0.038 24.370 0.000 0.881 0.700
## SupG_Ori 1.598 0.088 18.134 0.000 1.534 0.812
## SupG_Mon 1.624 0.091 17.915 0.000 1.558 0.847
## SupG_Infra 1.034 0.040 26.013 0.000 0.992 0.777
## SupG_Bestar 1.131 0.047 24.147 0.000 1.085 0.795
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.114 0.089 1.280 0.201 0.114 0.172
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.948 0.111 -26.617 0.000 -2.948 -1.868
## SupG_Feed|t2 -2.064 0.080 -25.744 0.000 -2.064 -1.308
## SupG_Feed|t3 -0.900 0.044 -20.378 0.000 -0.900 -0.570
## SupG_Feed|t4 1.123 0.049 22.695 0.000 1.123 0.712
## SupG_Meta|t1 -3.004 0.109 -27.520 0.000 -3.004 -2.388
## SupG_Meta|t2 -2.156 0.077 -27.837 0.000 -2.156 -1.713
## SupG_Meta|t3 -1.391 0.052 -26.607 0.000 -1.391 -1.106
## SupG_Meta|t4 0.646 0.031 21.044 0.000 0.646 0.513
## SupG_Ori|t1 -4.627 0.248 -18.678 0.000 -4.627 -2.449
## SupG_Ori|t2 -3.559 0.196 -18.152 0.000 -3.559 -1.884
## SupG_Ori|t3 -2.541 0.140 -18.207 0.000 -2.541 -1.345
## SupG_Ori|t4 0.109 0.032 3.372 0.001 0.109 0.058
## SupG_Mon|t1 -4.646 0.262 -17.704 0.000 -4.646 -2.525
## SupG_Mon|t2 -3.857 0.217 -17.744 0.000 -3.857 -2.096
## SupG_Mon|t3 -2.572 0.143 -18.008 0.000 -2.572 -1.398
## SupG_Mon|t4 0.199 0.035 5.754 0.000 0.199 0.108
## SupG_Infra|t1 -2.204 0.069 -31.858 0.000 -2.204 -1.726
## SupG_Infra|t2 -1.402 0.047 -29.589 0.000 -1.402 -1.098
## SupG_Infra|t3 -0.209 0.026 -8.113 0.000 -0.209 -0.164
## SupG_Infra|t4 1.155 0.041 28.397 0.000 1.155 0.904
## SupG_Bestar|t1 -2.778 0.100 -27.675 0.000 -2.778 -2.036
## SupG_Bestar|t2 -2.074 0.077 -26.930 0.000 -2.074 -1.520
## SupG_Bestar|t3 -1.002 0.043 -23.152 0.000 -1.002 -0.735
## SupG_Bestar|t4 0.626 0.033 18.823 0.000 0.626 0.459
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.788 0.162 4.859 0.000 0.788 0.316
## .SupG_Meta 0.807 0.138 5.829 0.000 0.807 0.510
## .SupG_Ori 1.216 0.275 4.424 0.000 1.216 0.341
## .SupG_Mon 0.958 0.314 3.053 0.002 0.958 0.283
## .SupG_Infra 0.647 0.110 5.864 0.000 0.647 0.397
## .SupG_Bestar 0.684 0.149 4.582 0.000 0.684 0.368
## SupG 0.921 0.123 7.497 0.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.634 0.634 1.000
## SupG_Meta 0.795 0.795 1.000
## SupG_Ori 0.529 0.529 1.000
## SupG_Mon 0.543 0.543 1.000
## SupG_Infra 0.783 0.783 1.000
## SupG_Bestar 0.733 0.733 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.684
## SupG_Meta 0.490
## SupG_Ori 0.659
## SupG_Mon 0.717
## SupG_Infra 0.603
## SupG_Bestar 0.632
##
##
## Group 4 [4]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG =~
## SupG_Feed 1.360 0.062 21.998 0.000 1.554 0.829
## SupG_Meta 0.918 0.038 24.370 0.000 1.049 0.755
## SupG_Ori 1.598 0.088 18.134 0.000 1.827 0.876
## SupG_Mon 1.624 0.091 17.915 0.000 1.856 0.864
## SupG_Infra 1.034 0.040 26.013 0.000 1.181 0.698
## SupG_Bestar 1.131 0.047 24.147 0.000 1.293 0.749
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Infra ~~
## .SupG_Bestar 0.847 0.160 5.305 0.000 0.847 0.611
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 0.000 0.000 0.000
## .SupG_Meta 0.000 0.000 0.000
## .SupG_Ori 0.000 0.000 0.000
## .SupG_Mon 0.000 0.000 0.000
## .SupG_Infra 0.000 0.000 0.000
## .SupG_Bestar 0.000 0.000 0.000
## SupG 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed|t1 -2.948 0.111 -26.617 0.000 -2.948 -1.572
## SupG_Feed|t2 -2.064 0.080 -25.744 0.000 -2.064 -1.100
## SupG_Feed|t3 -0.900 0.044 -20.378 0.000 -0.900 -0.480
## SupG_Feed|t4 1.123 0.049 22.695 0.000 1.123 0.599
## SupG_Meta|t1 -3.004 0.109 -27.520 0.000 -3.004 -2.162
## SupG_Meta|t2 -2.156 0.077 -27.837 0.000 -2.156 -1.551
## SupG_Meta|t3 -1.391 0.052 -26.607 0.000 -1.391 -1.001
## SupG_Meta|t4 0.646 0.031 21.044 0.000 0.646 0.465
## SupG_Ori|t1 -4.627 0.248 -18.678 0.000 -4.627 -2.218
## SupG_Ori|t2 -3.559 0.196 -18.152 0.000 -3.559 -1.706
## SupG_Ori|t3 -2.541 0.140 -18.207 0.000 -2.541 -1.218
## SupG_Ori|t4 0.109 0.032 3.372 0.001 0.109 0.052
## SupG_Mon|t1 -4.646 0.262 -17.704 0.000 -4.646 -2.162
## SupG_Mon|t2 -3.857 0.217 -17.744 0.000 -3.857 -1.795
## SupG_Mon|t3 -2.572 0.143 -18.008 0.000 -2.572 -1.197
## SupG_Mon|t4 0.199 0.035 5.754 0.000 0.199 0.093
## SupG_Infra|t1 -2.204 0.069 -31.858 0.000 -2.204 -1.302
## SupG_Infra|t2 -1.402 0.047 -29.589 0.000 -1.402 -0.828
## SupG_Infra|t3 -0.209 0.026 -8.113 0.000 -0.209 -0.124
## SupG_Infra|t4 1.155 0.041 28.397 0.000 1.155 0.682
## SupG_Bestar|t1 -2.778 0.100 -27.675 0.000 -2.778 -1.610
## SupG_Bestar|t2 -2.074 0.077 -26.930 0.000 -2.074 -1.202
## SupG_Bestar|t3 -1.002 0.043 -23.152 0.000 -1.002 -0.581
## SupG_Bestar|t4 0.626 0.033 18.823 0.000 0.626 0.363
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SupG_Feed 1.102 0.213 5.182 0.000 1.102 0.313
## .SupG_Meta 0.829 0.183 4.543 0.000 0.829 0.430
## .SupG_Ori 1.015 0.300 3.386 0.001 1.015 0.233
## .SupG_Mon 1.172 0.365 3.212 0.001 1.172 0.254
## .SupG_Infra 1.473 0.200 7.374 0.000 1.473 0.513
## .SupG_Bestar 1.306 0.223 5.847 0.000 1.306 0.439
## SupG 1.306 0.141 9.254 0.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SupG_Feed 0.533 0.533 1.000
## SupG_Meta 0.720 0.720 1.000
## SupG_Ori 0.479 0.479 1.000
## SupG_Mon 0.465 0.465 1.000
## SupG_Infra 0.590 0.590 1.000
## SupG_Bestar 0.580 0.580 1.000
##
## R-Square:
## Estimate
## SupG_Feed 0.687
## SupG_Meta 0.570
## SupG_Ori 0.767
## SupG_Mon 0.746
## SupG_Infra 0.487
## SupG_Bestar 0.561lavaan::fitMeasures(invariance$fit.means,c("chisq.scaled","df.scaled","pvalue.scaled","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue.scaled
## 202.952 101.000 0.000
## srmr cfi.scaled tli.scaled
## 0.025 0.997 0.998
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.027 0.022 0.033modificationindices(invariance$fit.means, sort.=T)## lhs op rhs block group level mi epc sepc.lv
## 102 SupG ~1 2 2 1 61.802 -0.082 -0.080
## 153 SupG ~1 3 3 1 57.312 0.147 0.153
## 100 SupG_Infra ~1 2 2 1 55.237 -0.162 -0.162
## 151 SupG_Infra ~1 3 3 1 49.353 0.274 0.274
## 49 SupG_Infra ~1 1 1 1 29.213 0.124 0.124
## 101 SupG_Bestar ~1 2 2 1 22.125 -0.131 -0.131
## 152 SupG_Bestar ~1 3 3 1 16.523 0.205 0.205
## 51 SupG ~1 1 1 1 15.979 0.044 0.044
## 332 SupG_Ori ~~ SupG_Mon 3 3 1 12.359 0.705 0.705
## 202 SupG_Infra ~1 4 4 1 11.882 -0.159 -0.159
## 319 SupG_Ori ~~ SupG_Infra 2 2 1 11.617 -0.215 -0.215
## 193 SupG_Meta ~*~ SupG_Meta 4 4 1 10.990 0.118 0.118
## 92 SupG_Ori ~*~ SupG_Ori 2 2 1 10.499 0.044 0.044
## 313 SupG_Feed ~~ SupG_Bestar 2 2 1 9.770 0.190 0.190
## 147 SupG_Feed ~1 3 3 1 9.587 0.163 0.163
## 312 SupG_Feed ~~ SupG_Infra 2 2 1 8.187 0.163 0.163
## 146 SupG_Bestar ~*~ SupG_Bestar 3 3 1 7.733 0.115 0.115
## 304 SupG_Ori ~~ SupG_Mon 1 1 1 5.919 0.241 0.241
## 143 SupG_Ori ~*~ SupG_Ori 3 3 1 5.796 -0.066 -0.066
## 310 SupG_Feed ~~ SupG_Ori 2 2 1 5.330 -0.173 -0.173
## 90 SupG_Feed ~*~ SupG_Feed 2 2 1 5.215 -0.036 -0.036
## 340 SupG_Feed ~~ SupG_Infra 4 4 1 5.124 0.380 0.380
## 96 SupG_Feed ~1 2 2 1 4.447 -0.059 -0.059
## 39 SupG_Feed ~*~ SupG_Feed 1 1 1 4.204 0.036 0.036
## 296 SupG_Feed ~~ SupG_Ori 1 1 1 4.135 -0.177 -0.177
## 341 SupG_Feed ~~ SupG_Bestar 4 4 1 3.788 0.334 0.334
## 322 SupG_Mon ~~ SupG_Bestar 2 2 1 3.124 -0.125 -0.125
## 50 SupG_Bestar ~1 1 1 1 3.055 0.051 0.051
## 196 SupG_Infra ~*~ SupG_Infra 4 4 1 2.946 -0.059 -0.059
## 300 SupG_Meta ~~ SupG_Ori 1 1 1 2.868 0.114 0.114
## 201 SupG_Mon ~1 4 4 1 2.864 0.144 0.144
## 297 SupG_Feed ~~ SupG_Mon 1 1 1 2.846 -0.148 -0.148
## 345 SupG_Meta ~~ SupG_Bestar 4 4 1 2.719 -0.206 -0.206
## 203 SupG_Bestar ~1 4 4 1 2.603 0.091 0.091
## 337 SupG_Feed ~~ SupG_Meta 4 4 1 2.549 -0.219 -0.219
## 41 SupG_Ori ~*~ SupG_Ori 1 1 1 2.406 -0.023 -0.023
## 325 SupG_Feed ~~ SupG_Mon 3 3 1 2.402 -0.261 -0.261
## 91 SupG_Meta ~*~ SupG_Meta 2 2 1 2.387 -0.032 -0.032
## 98 SupG_Ori ~1 2 2 1 2.337 -0.064 -0.064
## 331 SupG_Meta ~~ SupG_Bestar 3 3 1 2.282 -0.147 -0.147
## 336 SupG_Mon ~~ SupG_Bestar 3 3 1 2.218 -0.217 -0.217
## 328 SupG_Meta ~~ SupG_Ori 3 3 1 2.089 0.194 0.194
## 47 SupG_Ori ~1 1 1 1 1.711 0.058 0.058
## 141 SupG_Feed ~*~ SupG_Feed 3 3 1 1.349 0.039 0.039
## 326 SupG_Feed ~~ SupG_Infra 3 3 1 1.273 0.132 0.132
## 330 SupG_Meta ~~ SupG_Infra 3 3 1 1.218 -0.100 -0.100
## 327 SupG_Feed ~~ SupG_Bestar 3 3 1 1.170 -0.135 -0.135
## 97 SupG_Meta ~1 2 2 1 1.165 -0.027 -0.027
## 344 SupG_Meta ~~ SupG_Infra 4 4 1 1.161 -0.132 -0.132
## 339 SupG_Feed ~~ SupG_Mon 4 4 1 1.144 -0.232 -0.232
## 318 SupG_Ori ~~ SupG_Mon 2 2 1 1.133 0.092 0.092
## 194 SupG_Ori ~*~ SupG_Ori 4 4 1 1.120 -0.024 -0.024
## 94 SupG_Infra ~*~ SupG_Infra 2 2 1 1.120 0.022 0.022
## 347 SupG_Ori ~~ SupG_Infra 4 4 1 1.101 0.197 0.197
## 329 SupG_Meta ~~ SupG_Mon 3 3 1 1.086 0.137 0.137
## 144 SupG_Mon ~*~ SupG_Mon 3 3 1 0.934 -0.027 -0.027
## 95 SupG_Bestar ~*~ SupG_Bestar 2 2 1 0.896 -0.018 -0.018
## 343 SupG_Meta ~~ SupG_Mon 4 4 1 0.857 -0.146 -0.146
## 314 SupG_Meta ~~ SupG_Ori 2 2 1 0.836 0.050 0.050
## 348 SupG_Ori ~~ SupG_Bestar 4 4 1 0.835 0.175 0.175
## 346 SupG_Ori ~~ SupG_Mon 4 4 1 0.835 0.221 0.221
## 197 SupG_Bestar ~*~ SupG_Bestar 4 4 1 0.755 -0.027 -0.027
## 298 SupG_Feed ~~ SupG_Infra 1 1 1 0.697 0.054 0.054
## 308 SupG_Mon ~~ SupG_Bestar 1 1 1 0.662 -0.064 -0.064
## 302 SupG_Meta ~~ SupG_Infra 1 1 1 0.661 -0.041 -0.041
## 306 SupG_Ori ~~ SupG_Bestar 1 1 1 0.651 0.062 0.062
## 48 SupG_Mon ~1 1 1 1 0.637 -0.036 -0.036
## 46 SupG_Meta ~1 1 1 1 0.500 0.019 0.019
## 317 SupG_Meta ~~ SupG_Bestar 2 2 1 0.488 0.031 0.031
## 320 SupG_Ori ~~ SupG_Bestar 2 2 1 0.483 -0.047 -0.047
## 148 SupG_Meta ~1 3 3 1 0.455 0.033 0.033
## 149 SupG_Ori ~1 3 3 1 0.444 0.056 0.056
## 315 SupG_Meta ~~ SupG_Mon 2 2 1 0.435 0.038 0.038
## 342 SupG_Meta ~~ SupG_Ori 4 4 1 0.408 -0.098 -0.098
## 305 SupG_Ori ~~ SupG_Infra 1 1 1 0.296 -0.040 -0.040
## 301 SupG_Meta ~~ SupG_Mon 1 1 1 0.276 -0.036 -0.036
## 198 SupG_Feed ~1 4 4 1 0.226 0.026 0.026
## 307 SupG_Mon ~~ SupG_Infra 1 1 1 0.216 0.034 0.034
## 195 SupG_Mon ~*~ SupG_Mon 4 4 1 0.200 0.010 0.010
## 192 SupG_Feed ~*~ SupG_Feed 4 4 1 0.197 -0.012 -0.012
## 334 SupG_Ori ~~ SupG_Bestar 3 3 1 0.191 -0.065 -0.065
## 338 SupG_Feed ~~ SupG_Ori 4 4 1 0.168 -0.086 -0.086
## 324 SupG_Feed ~~ SupG_Ori 3 3 1 0.161 -0.069 -0.069
## 150 SupG_Mon ~1 3 3 1 0.134 0.030 0.030
## 316 SupG_Meta ~~ SupG_Infra 2 2 1 0.096 -0.013 -0.013
## 40 SupG_Meta ~*~ SupG_Meta 1 1 1 0.093 -0.007 -0.007
## 349 SupG_Mon ~~ SupG_Infra 4 4 1 0.091 0.058 0.058
## 99 SupG_Mon ~1 2 2 1 0.083 -0.012 -0.012
## 93 SupG_Mon ~*~ SupG_Mon 2 2 1 0.077 0.004 0.004
## 321 SupG_Mon ~~ SupG_Infra 2 2 1 0.068 -0.017 -0.017
## 45 SupG_Feed ~1 1 1 1 0.053 0.007 0.007
## 145 SupG_Infra ~*~ SupG_Infra 3 3 1 0.052 -0.010 -0.010
## 311 SupG_Feed ~~ SupG_Mon 2 2 1 0.050 -0.018 -0.018
## 335 SupG_Mon ~~ SupG_Infra 3 3 1 0.038 0.027 0.027
## 299 SupG_Feed ~~ SupG_Bestar 1 1 1 0.020 0.010 0.010
## 323 SupG_Feed ~~ SupG_Meta 3 3 1 0.020 0.016 0.016
## 199 SupG_Meta ~1 4 4 1 0.016 0.006 0.006
## 303 SupG_Meta ~~ SupG_Bestar 1 1 1 0.010 -0.005 -0.005
## 295 SupG_Feed ~~ SupG_Meta 1 1 1 0.009 0.006 0.006
## 309 SupG_Feed ~~ SupG_Meta 2 2 1 0.008 0.004 0.004
## 142 SupG_Meta ~*~ SupG_Meta 3 3 1 0.006 -0.003 -0.003
## 200 SupG_Ori ~1 4 4 1 0.006 -0.006 -0.006
## 42 SupG_Mon ~*~ SupG_Mon 1 1 1 0.001 -0.001 -0.001
## 43 SupG_Infra ~*~ SupG_Infra 1 1 1 0.001 -0.001 -0.001
## 44 SupG_Bestar ~*~ SupG_Bestar 1 1 1 0.001 -0.001 -0.001
## 333 SupG_Ori ~~ SupG_Infra 3 3 1 0.000 -0.002 -0.002
## 350 SupG_Mon ~~ SupG_Bestar 4 4 1 0.000 -0.001 -0.001
## 204 SupG ~1 4 4 1 0.000 0.000 0.000
## sepc.all sepc.nox
## 102 -0.080 -0.080
## 153 0.153 0.153
## 100 -0.109 -0.109
## 151 0.215 0.215
## 49 0.086 0.086
## 101 -0.083 -0.083
## 152 0.151 0.151
## 51 0.044 0.044
## 332 0.654 0.654
## 202 -0.094 -0.094
## 319 -0.225 -0.225
## 193 1.000 1.000
## 92 1.000 1.000
## 313 0.171 0.171
## 147 0.103 0.103
## 312 0.152 0.152
## 146 1.000 1.000
## 304 0.241 0.241
## 143 -1.000 -1.000
## 310 -0.182 -0.182
## 90 -1.000 -1.000
## 340 0.298 0.298
## 96 -0.034 -0.034
## 39 1.000 1.000
## 296 -0.177 -0.177
## 341 0.278 0.278
## 322 -0.105 -0.105
## 50 0.034 0.034
## 196 -1.000 -1.000
## 300 0.114 0.114
## 201 0.067 0.067
## 297 -0.148 -0.148
## 345 -0.198 -0.198
## 203 0.053 0.053
## 337 -0.229 -0.229
## 41 -1.000 -1.000
## 325 -0.301 -0.301
## 91 -1.000 -1.000
## 98 -0.034 -0.034
## 331 -0.198 -0.198
## 336 -0.268 -0.268
## 328 0.196 0.196
## 47 0.031 0.031
## 141 1.000 1.000
## 326 0.185 0.185
## 330 -0.139 -0.139
## 327 -0.184 -0.184
## 97 -0.021 -0.021
## 344 -0.119 -0.119
## 339 -0.204 -0.204
## 318 0.091 0.091
## 194 -1.000 -1.000
## 94 1.000 1.000
## 347 0.161 0.161
## 329 0.156 0.156
## 144 -1.000 -1.000
## 95 -1.000 -1.000
## 343 -0.148 -0.148
## 314 0.059 0.059
## 348 0.152 0.152
## 346 0.203 0.203
## 197 -1.000 -1.000
## 298 0.054 0.054
## 308 -0.064 -0.064
## 302 -0.041 -0.041
## 306 0.062 0.062
## 48 -0.019 -0.019
## 46 0.014 0.014
## 317 0.032 0.032
## 320 -0.047 -0.047
## 148 0.026 0.026
## 149 0.030 0.030
## 315 0.037 0.037
## 342 -0.107 -0.107
## 305 -0.040 -0.040
## 301 -0.036 -0.036
## 198 0.014 0.014
## 307 0.034 0.034
## 195 1.000 1.000
## 192 -1.000 -1.000
## 334 -0.071 -0.071
## 338 -0.082 -0.082
## 324 -0.071 -0.071
## 150 0.016 0.016
## 316 -0.014 -0.014
## 40 -1.000 -1.000
## 349 0.044 0.044
## 99 -0.006 -0.006
## 93 1.000 1.000
## 321 -0.015 -0.015
## 45 0.004 0.004
## 145 -1.000 -1.000
## 311 -0.015 -0.015
## 335 0.034 0.034
## 299 0.010 0.010
## 323 0.020 0.020
## 199 0.004 0.004
## 303 -0.005 -0.005
## 295 0.006 0.006
## 309 0.005 0.005
## 142 -1.000 -1.000
## 200 -0.003 -0.003
## 42 -1.000 -1.000
## 43 -1.000 -1.000
## 44 -1.000 -1.000
## 333 -0.003 -0.003
## 350 -0.001 -0.001
## 204 0.000 0.000semTools::reliability(invariance$fit.means)## For constructs with categorical indicators, Zumbo et al.`s (2007) "ordinal alpha" is calculated in addition to the standard alpha, which treats ordinal variables as numeric. See Chalmers (2018) for a critique of "alpha.ord". Likewise, average variance extracted is calculated from polychoric (polyserial) not Pearson correlations.## $`2`
## SupG
## alpha 0.8551
## alpha.ord 0.9046
## omega 0.8389
## omega2 0.8389
## omega3 0.8395
## avevar 0.6304
##
## $`3`
## SupG
## alpha 0.8629
## alpha.ord 0.9073
## omega 0.8390
## omega2 0.8390
## omega3 0.8362
## avevar 0.6341
##
## $`1`
## SupG
## alpha 0.8700
## alpha.ord 0.9117
## omega 0.8674
## omega2 0.8674
## omega3 0.8706
## avevar 0.6488
##
## $`4`
## SupG
## alpha 0.8764
## alpha.ord 0.9178
## omega 0.8419
## omega2 0.8419
## omega3 0.8359
## avevar 0.65967.1.1.7.5 Checking Latent Differences
partial<-partialInvarianceCat(invariance,type="means",return.fit = F)
partial## $estimates
## poolest mean:2 mean:3 mean:1 mean:4 std:2 std:3 std:1 std:4
## SupG~1 0 0 -0.06791 0.1136 -0.02939 0 -0.06719 0.1124 -0.02908
## diff_std:3 vs. 2 diff_std:1 vs. 2 diff_std:4 vs. 2
## SupG~1 -0.06719 0.1124 -0.02908
##
## $results
## free.chi free.df free.p free.cfi fix.chi fix.df fix.p fix.cfi
## SupG~1 5.413 3 0.1439 -0.002861 5.413 3 0.1439 -0.002861
## wald.chi wald.df wald.p
## SupG~1 NA NA NA7.1.2 Predicting Latent as Factor Scores
data_predict <- predict(fit)
data <- cbind(data,data_predict)
write.csv(data,"data.csv")
#names(data)8 Item Reponse Theory
8.1 Subsetting Data
data<-data.matrix(TDados[,c(89:94)])8.2 Descriptives
dsc<-descript(data)8.3 Alpha - per excluded item
dsc$alpha## value
## All Items 0.8600
## Excluding SupG_Feed 0.8314
## Excluding SupG_Meta 0.8533
## Excluding SupG_Ori 0.8340
## Excluding SupG_Mon 0.8355
## Excluding SupG_Infra 0.8359
## Excluding SupG_Bestar 0.82768.4 Correlation Itens
rcor.test(data, method = "kendall")##
## SupG_Feed SupG_Meta SupG_Ori SupG_Mon SupG_Infra SupG_Bestar
## SupG_Feed ***** 0.443 0.497 0.507 0.475 0.485
## SupG_Meta <0.001 ***** 0.497 0.482 0.358 0.385
## SupG_Ori <0.001 <0.001 ***** 0.655 0.426 0.492
## SupG_Mon <0.001 <0.001 <0.001 ***** 0.449 0.470
## SupG_Infra <0.001 <0.001 <0.001 <0.001 ***** 0.583
## SupG_Bestar <0.001 <0.001 <0.001 <0.001 <0.001 *****
##
## upper diagonal part contains correlation coefficient estimates
## lower diagonal part contains corresponding p-values8.5 Empirical Plots - Total Raw Score and Responses
empirical_plot(data, c(1,2,3,4,5,6), smooth = TRUE)
8.6 Firts Constrained Model
fit1<-ltm::grm(data,constrained = T, Hessian=T,IRT.param=T)
fit1##
## Call:
## ltm::grm(data = data, constrained = T, IRT.param = T, Hessian = T)
##
## Coefficients:
## Extrmt1 Extrmt2 Extrmt3 Extrmt4 Dscrmn
## SupG_Feed -2.116 -1.448 -0.650 0.798 2.384
## SupG_Meta -2.728 -1.894 -1.238 0.579 2.384
## SupG_Ori -3.064 -2.300 -1.609 0.070 2.384
## SupG_Mon -2.996 -2.359 -1.556 0.126 2.384
## SupG_Infra -1.827 -1.155 -0.197 0.964 2.384
## SupG_Bestar -2.185 -1.604 -0.774 0.496 2.384
##
## Log.Lik: -45613margins(fit1)##
## Call:
## ltm::grm(data = data, constrained = T, IRT.param = T, Hessian = T)
##
## Fit on the Two-Way Margins
##
## SupG_Feed SupG_Meta SupG_Ori SupG_Mon SupG_Infra SupG_Bestar
## SupG_Feed - 927.15 671.07 531.04 338.59 265.87
## SupG_Meta *** - 580.61 557.31 762.42 599.88
## SupG_Ori *** *** - 881.66 556.79 403.31
## SupG_Mon *** *** *** - 609.26 409.83
## SupG_Infra *** *** *** *** - 909.38
## SupG_Bestar *** *** *** *** *** -
##
## '***' denotes pairs of items with lack-of-fitmargins(fit1, "three")##
## Call:
## ltm::grm(data = data, constrained = T, IRT.param = T, Hessian = T)
##
## Fit on the Three-Way Margins
##
## Item i Item j Item k (O-E)^2/E
## 1 1 2 3 3291 ***
## 2 1 2 4 2756 ***
## 3 1 2 5 2747 ***
## 4 1 2 6 2256 ***
## 5 1 3 4 2399 ***
## 6 1 3 5 1875 ***
## 7 1 3 6 1575 ***
## 8 1 4 5 1716 ***
## 9 1 4 6 1474 ***
## 10 1 5 6 1659 ***
## 11 2 3 4 5560 ***
## 12 2 3 5 2629 ***
## 13 2 3 6 2188 ***
## 14 2 4 5 2422 ***
## 15 2 4 6 2029 ***
## 16 2 5 6 3473 ***
## 17 3 4 5 2610 ***
## 18 3 4 6 2213 ***
## 19 3 5 6 2213 ***
## 20 4 5 6 2421 ***
##
## '***' denotes triplets of items with lack-of-fit8.7 Unconstrained Model
fit2<-grm(data,constrained = F, Hessian=T,IRT.param=T)
fit2##
## Call:
## grm(data = data, constrained = F, IRT.param = T, Hessian = T)
##
## Coefficients:
## Extrmt1 Extrmt2 Extrmt3 Extrmt4 Dscrmn
## SupG_Feed -2.110 -1.444 -0.647 0.809 2.370
## SupG_Meta -3.147 -2.162 -1.390 0.669 1.812
## SupG_Ori -2.736 -2.062 -1.456 0.056 3.204
## SupG_Mon -2.710 -2.139 -1.423 0.110 3.073
## SupG_Infra -1.914 -1.206 -0.199 1.023 2.118
## SupG_Bestar -2.169 -1.595 -0.770 0.502 2.377
##
## Log.Lik: -45394margins(fit2)##
## Call:
## grm(data = data, constrained = F, IRT.param = T, Hessian = T)
##
## Fit on the Two-Way Margins
##
## SupG_Feed SupG_Meta SupG_Ori SupG_Mon SupG_Infra SupG_Bestar
## SupG_Feed - 713.75 726.12 553.25 318.87 266.27
## SupG_Meta *** - 587.88 522.35 385.22 360.88
## SupG_Ori *** *** - 648.21 611.74 459.19
## SupG_Mon *** *** *** - 631.18 507.61
## SupG_Infra *** *** *** *** - 1016.62
## SupG_Bestar *** *** *** *** *** -
##
## '***' denotes pairs of items with lack-of-fitmargins(fit2, "three")##
## Call:
## grm(data = data, constrained = F, IRT.param = T, Hessian = T)
##
## Fit on the Three-Way Margins
##
## Item i Item j Item k (O-E)^2/E
## 1 1 2 3 2282 ***
## 2 1 2 4 2107 ***
## 3 1 2 5 1649 ***
## 4 1 2 6 1421 ***
## 5 1 3 4 2849 ***
## 6 1 3 5 2397 ***
## 7 1 3 6 2007 ***
## 8 1 4 5 2002 ***
## 9 1 4 6 2026 ***
## 10 1 5 6 1728 ***
## 11 2 3 4 2352 ***
## 12 2 3 5 1825 ***
## 13 2 3 6 1577 ***
## 14 2 4 5 1826 ***
## 15 2 4 6 1782 ***
## 16 2 5 6 2090 ***
## 17 3 4 5 2469 ***
## 18 3 4 6 2505 ***
## 19 3 5 6 3414 ***
## 20 4 5 6 3695 ***
##
## '***' denotes triplets of items with lack-of-fit8.8 Comparisons Constrained and Uconstrained
anova(fit1,fit2)##
## Likelihood Ratio Table
## AIC BIC log.Lik LRT df p.value
## fit1 91276 91449 -45613
## fit2 90848 91056 -45394 438.16 5 <0.0018.9 Unconstrained Model
8.9.1 Coeficients
coef(fit2, simplify = TRUE,standardized=T,prob=T,order=T)## Extrmt1 Extrmt2 Extrmt3 Extrmt4 Dscrmn
## SupG_Feed -2.110 -1.444 -0.647 0.809 2.370
## SupG_Meta -3.147 -2.162 -1.390 0.669 1.812
## SupG_Ori -2.736 -2.062 -1.456 0.056 3.204
## SupG_Mon -2.710 -2.139 -1.423 0.110 3.073
## SupG_Infra -1.914 -1.206 -0.199 1.023 2.118
## SupG_Bestar -2.169 -1.595 -0.770 0.502 2.3778.9.2 Information
information(fit2, c(-4, 4), items = c(1:6))##
## Call:
## grm(data = data, constrained = F, IRT.param = T, Hessian = T)
##
## Total Information = 44.07
## Information in (-4, 4) = 43.55 (98.81%)
## Based on items 1, 2, 3, 4, 5, 68.10 Item Response Category Characteristic Curves
op <- par(mfrow = c(2,2))
plot(fit2, lwd = 2, legend = TRUE, ncol = 2)
8.10.1 Item Information Curve
plot(fit2, type = "IIC")
8.10.2 Item Information Curve
plot(fit2, type = "IIC",item=0,zrange = c(-4, 4))
8.10.3 Item Information Curve - Standard Error of Measurement
vals <- plot(fit2, type = "IIC", items = 0, plot = FALSE)
plot(vals[,1], 1 / sqrt(vals[, 2]), type = "l", lwd = 2,
xlab = "Ability", ylab = "Standard Error",
main = "Standard Error of Measurement")
8.10.4 Operational Characteristic Curve itens (upper)
op <- par(mfrow = c(2,2))
plot(fit2, type = "OCCu")
8.10.5 Operational Characteristic Curve itens (lower)
op <- par(mfrow = c(2,2))
plot(fit2,type='OCCl')
8.10.6 Person Parameters Factor Score
f.scores<-ltm::factor.scores(fit2)
plot(f.scores, main = "KDE for Person Parameters")