Autoeficácia Criativa
- 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
- 6 Method 3 - original boot.ega function with parallel processing
- 7 Confirmatory Factor Analysis
- 8 External Relationships - Convergent and Concurrent Valididity
- 9 Item Reponse Theory
- 9.1 Subsetting Data
- 9.2 Descriptives
- 9.3 Alpha - per excluded item
- 9.4 Correlation Itens
- 9.5 Empirical Plots - Total Raw Score and Responses
- 9.6 Firts Constrained Model
- 9.7 Unconstrained Model
- 9.8 Comparisons Constrained and Uconstrained
- 9.9 Unconstrained Model
- 9.10 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 = "Banco de Dados AEC_Clarissa 07NOV_BanTod11.04.19.Mis.sav", to.data.frame = TRUE, use.value.labels = FALSE)
TDados<-as.data.frame(TDados)1.0.0.0.3 Subsetting AEC itens
data<-data.matrix(TDados[,c(234:237)])2 Descriptive Statistics
2.0.0.0.1 Summary Statistics
psych::describe(data)## vars n mean sd median trimmed mad min max range skew kurtosis se
## AEC01 1 789 4.08 1.25 4 4.05 1.48 1 7 6 0.16 0.43 0.04
## AEC02 2 789 4.28 1.25 4 4.25 1.48 1 7 6 0.14 0.31 0.04
## AEC03 3 789 4.03 1.27 4 4.00 1.48 1 7 6 0.24 0.19 0.05
## AEC04 4 789 4.13 1.24 4 4.09 1.48 1 7 6 0.21 0.26 0.042.1 Relative Frequencies
data<-as.matrix(data)
dsc<-descript(data)
porcentagem<-as.data.frame(round(dsc$perc,2)*100)
names(porcentagem)<-c("% lv1","% lv2","% lv3","% lv4","% lv5","% lv6","% lv7")
porcentagem## % lv1 % lv2 % lv3 % lv4 % lv5 % lv6 % lv7
## AEC01 2 6 20 39 22 5 5
## AEC02 2 6 14 41 23 7 7
## AEC03 2 7 23 35 21 5 5
## AEC04 2 6 21 37 23 6 52.1.0.0.1 Plotting Itens as Likert
lbs <- c("lv1","lv2","lv3","lv4","lv5","lv6","lv7")
survey <- TDados[,c(234:237)] %>%
dplyr::mutate_if(is.numeric, factor, levels = 1:7, labels = lbs)
plot(likert(survey[,1:4]), ordered = F, wrap= 60)
2.1.0.1 Recoding just as a test
#TDados[,c(234)]<-car::Recode(TDados[,c(234)],"1=1;2=1;3=2;4=3;5=4;6=5;7=5")
#TDados[,c(235)]<-car::Recode(TDados[,c(235)],"1=1;2=1;3=2;4=3;5=4;6=5;7=5")
#TDados[,c(236)]<-car::Recode(TDados[,c(236)],"1=1;2=1;3=2;4=3;5=4;6=5;7=5")
#TDados[,c(237)]<-car::Recode(TDados[,c(237)],"1=1;2=1;3=2;4=3;5=4;6=5;7=5")
#data<-data.matrix(TDados[,c(234:237)])2.1.0.1.1 Histogram
dta_long <- melt(as.data.frame(data))
colnames(dta_long) <- c("Item", "Response")
Histogram <- ggplot(dta_long, aes(x = Response, fill = Item))+
geom_histogram(bins = 5)+
facet_wrap(~Item)+
theme_default()
Histogram
2.1.0.1.2 Density Plot
DensityPlot <- ggplot(dta_long, aes(x = Response, fill = Item))+
geom_density()+
facet_wrap(~Item)+
theme_default()
DensityPlot 
2.1.0.1.3 Correlation Matrix
CorMat <- psych::polychoric(data, correct=T, smooth=T,global=T)$rho2.1.0.1.4 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))
2.1.0.1.5 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 Recoding into five levels
#data[,c(234)]<-car::Recode(data[,c(234)],"1=1;2=1;3=2;4=3;5=4;6=5;7=5")
#data[,c(235)]<-car::Recode(data[,c(235)],"1=1;2=1;3=2;4=3;5=4;6=5;7=5")
#data[,c(236)]<-car::Recode(data[,c(236)],"1=1;2=1;3=2;4=3;5=4;6=5;7=5")
#data[,c(237)]<-car::Recode(data[,c(237)],"1=1;2=1;3=2;4=3;5=4;6=5;7=5")
#data<-data.matrix(data[,c(234:237)])3.0.0.2 Subsetting
data<-data[,234:237]3.0.0.2.1 Polychoric Correlation
CorMat <- psych::polychoric(data, correct=T, smooth=T,global=T)$rho3.0.0.2.2 Bartlett Sphericity
bartlett<-psych::cortest.bartlett(CorMat, n = nrow(data),diag=TRUE)
#bartlett3.0.0.2.3 Kayser Meyer - Sample Adequacy
kmo <-psych::KMO(CorMat)
#kmoIt was observed that the six items of CAEFF grouped a latent factor, Bartlett’s chi-square test 963.89; df= 6; p< 0 and KMO = 0.85
3.0.0.2.4 Parallel Analysis using unweighted least square
parallel<-pa.plot(CorMat,n.obs = nrow(data), fm="uls", cor="poly",n.iter=1000)## Parallel analysis suggests that the number of factors = 1 and the number of components = 1print(parallel)## [[1]]
##
## [[2]]
## [1] 1#parallel[[2]][1]Number of factor by parallel analysis is equal to 1
3.0.0.2.5 Numeric Rules - Very Simples Structure based on parallel number of factor plus one
NumericRule <- VSS(CorMat,n =parallel[[2]][1]+1, plot = F, n.obs =nrow(data),rotate="promax",cor="poly", fm="uls")
temp1 <- data.frame(nFactor = row.names(NumericRule$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 0.9795 0.0000 0.1289 0.06531 -6.896 -0.5557 0.009646985
## 2 2 0.4045 0.7538 0.3695 NA NA NA 0.0000016153.0.0.2.6 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
#Figures
ega1 <- ega.object(CorMat,data)## Note: Network with lowest lambda selected as best network: assumption of sparsity might be violated.###
dim1 <- ega1$dim.variables
one <- which(dim1$dimension==1)
dim1$dimension[one] <- rep("AEC01",length(one))
two <- which(dim1$dimension==2)
dim1$dimension[two] <- rep("AEC02",length(two))
three <-which(dim1$dimension==3)
dim1$dimension[three] <- rep("AEC03",length(three))
four <-which(dim1$dimension==4)
dim1$dimension[four] <- rep("AEC04",length(four))6 Method 3 - original boot.ega function with parallel processing
# BootEGA Function
boot.ega <- bootnet(data, nBoot = 1000, default = "EBICglasso",computeCentrality = T, type = "parametric", nCores = 4)## Note: bootnet will store only the following statistics: edge, strength, outStrength, inStrength## model set to 'GGM'## Estimating sample network...## Estimating Network. Using package::function:
## - qgraph::EBICglasso for EBIC model selection
## - using glasso::glasso## Note: Network with lowest lambda selected as best network: assumption of sparsity might be violated.## Warning in EBICglassoCore(S = S, n = n, gamma = gamma, penalize.diagonal =
## penalize.diagonal, : A dense regularized network was selected (lambda < 0.1 *
## lambda.max). Recent work indicates a possible drop in specificity. Interpret the
## presence of the smallest edges with care. Setting threshold = TRUE will enforce
## higher specificity, at the cost of sensitivity.## Bootstrapping...## Computing statistics...boot.ega## === bootnet Results ===
## Number of nodes: 4
## Number of non-zero edges in sample: 6 / 6
## Mean weight of sample: 0.2915
## Number of bootstrapped networks: 1000
## Results of original sample stored in x$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: 10 x 17
## # Groups: type, node1, node2 [10]
## 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 AEC01-… AEC01 "AEC… 0.422 0.417 0.0481 0.326 0.519 3.18e-1 0.508
## 2 edge AEC01-… AEC01 "AEC… 0.184 0.184 0.0595 0.0649 0.303 5.97e-2 0.299
## 3 edge AEC01-… AEC01 "AEC… 0.291 0.292 0.0539 0.183 0.399 1.85e-1 0.392
## 4 edge AEC02-… AEC02 "AEC… 0.115 0.120 0.0589 -0.00318 0.233 2.18e-5 0.233
## 5 edge AEC02-… AEC02 "AEC… 0.460 0.453 0.0459 0.368 0.551 3.59e-1 0.537
## 6 edge AEC03-… AEC03 "AEC… 0.278 0.275 0.0539 0.170 0.385 1.69e-1 0.377
## 7 stren… AEC01 AEC01 "" 0.897 0.892 0.0589 0.779 1.01 7.82e-1 1.01
## 8 stren… AEC02 AEC02 "" 0.997 0.989 0.0609 0.875 1.12 8.66e-1 1.12
## 9 stren… AEC03 AEC03 "" 0.576 0.579 0.0449 0.487 0.666 4.86e-1 0.669
## 10 stren… AEC04 AEC04 "" 1.03 1.02 0.0602 0.908 1.15 9.01e-1 1.13
## # … with 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
## AEC01 AEC01 1
## AEC02 AEC02 1
## AEC03 AEC03 1
## AEC04 AEC04 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 0.582 and 0.874, and the factor loadings between 0.763and 0.935 Table2. A factor was retained, with an eigenvalue of 3.16 that explained 0.79% 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
## AEC01 0.91 0.84 0.16 1
## AEC02 0.94 0.87 0.13 1
## AEC03 0.76 0.58 0.42 1
## AEC04 0.93 0.87 0.13 1
##
## ULS1
## SS loadings 3.16
## Proportion Var 0.79
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 6 and the objective function was 3.77 with Chi Square of 963.9
## The degrees of freedom for the model are 2 and the objective function was 0.02
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.02
##
## The harmonic number of observations is 259 with the empirical chi square 0.29 with prob < 0.87
## The total number of observations was 259 with Likelihood Chi Square = 4.22 with prob < 0.12
##
## Tucker Lewis Index of factoring reliability = 0.993
## RMSEA index = 0.065 and the 0 % confidence intervals are NA 0.078
## BIC = -6.9
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## ULS1
## Correlation of (regression) scores with factors 0.98
## Multiple R square of scores with factors 0.95
## Minimum correlation of possible factor scores 0.91
##
## Coefficients and bootstrapped confidence intervals
## low ULS1 upper
## AEC01 0.89 0.91 0.94
## AEC02 0.91 0.94 0.96
## AEC03 0.71 0.76 0.82
## AEC04 0.91 0.93 0.966.0.0.4 Exploratory Fator Analysis using semTools and a Lavaan engine
#fa_mod1 <- efaUnrotate(datas[,c(234:237)], nf = 1, estimator = "WLSMV",ordered=T,missing="pairwise")
#fa_mod1 <- efaUnrotate(data[,c(234:237)], nf = 1, estimator = "MLR",ordered=F,missing="MLR")7 Confirmatory Factor Analysis
7.0.0.1 Changing data
data<-banco_CFA7.0.0.2 Recoding into five levels
#data[,c(234)]<-car::Recode(data[,c(234)],"1=1;2=1;3=2;4=3;5=4;6=5;7=5")
#data[,c(235)]<-car::Recode(data[,c(235)],"1=1;2=1;3=2;4=3;5=4;6=5;7=5")
#data[,c(236)]<-car::Recode(data[,c(236)],"1=1;2=1;3=2;4=3;5=4;6=5;7=5")
#data[,c(237)]<-car::Recode(data[,c(237)],"1=1;2=1;3=2;4=3;5=4;6=5;7=5")
#data<-data.matrix(data[,c(234:237)])7.1 Structure Validity - Dimensionality
7.1.0.1 Model
model <- 'AEC =~ AEC04 + AEC02 + AEC03 + AEC01'7.1.0.2 Fitting
fit <- lavaan::cfa(model, data =data,estimator="ULSMV",ordered=T,missing="pairwise")7.1.0.3 General Summary
summary(fit,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 12 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 28
##
## Number of observations 530
## Number of missing patterns 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 1.567 38.796
## Degrees of freedom 2 2
## P-value (Unknown) NA 0.000
## Scaling correction factor 0.041
## Shift parameter 0.223
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 2004.344 8789.031
## Degrees of freedom 6 6
## P-value NA 0.000
## Scaling correction factor 0.228
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 0.996
## Tucker-Lewis Index (TLI) 1.001 0.987
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000 0.186
## 90 Percent confidence interval - lower 0.000 0.138
## 90 Percent confidence interval - upper 0.080 0.240
## P-value RMSEA <= 0.05 0.779 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.017 0.017
##
## 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
## AEC =~
## AEC04 1.000 0.975 0.975
## AEC02 0.950 0.008 120.057 0.000 0.926 0.926
## AEC03 0.788 0.016 48.010 0.000 0.768 0.768
## AEC01 0.913 0.010 87.304 0.000 0.890 0.890
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## AEC 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -2.348 0.166 -14.151 0.000 -2.348 -2.348
## AEC04|t2 -1.436 0.081 -17.787 0.000 -1.436 -1.436
## AEC04|t3 -0.591 0.058 -10.169 0.000 -0.591 -0.591
## AEC04|t4 0.383 0.056 6.839 0.000 0.383 0.383
## AEC04|t5 1.153 0.070 16.485 0.000 1.153 1.153
## AEC04|t6 1.521 0.085 17.917 0.000 1.521 1.521
## AEC02|t1 -2.220 0.146 -15.179 0.000 -2.220 -2.220
## AEC02|t2 -1.521 0.085 -17.917 0.000 -1.521 -1.521
## AEC02|t3 -0.835 0.062 -13.469 0.000 -0.835 -0.835
## AEC02|t4 0.337 0.056 6.064 0.000 0.337 0.337
## AEC02|t5 1.040 0.067 15.601 0.000 1.040 1.040
## AEC02|t6 1.450 0.081 17.815 0.000 1.450 1.450
## AEC03|t1 -2.168 0.139 -15.568 0.000 -2.168 -2.168
## AEC03|t2 -1.292 0.075 -17.294 0.000 -1.292 -1.292
## AEC03|t3 -0.424 0.056 -7.527 0.000 -0.424 -0.424
## AEC03|t4 0.439 0.056 7.784 0.000 0.439 0.439
## AEC03|t5 1.190 0.071 16.734 0.000 1.190 1.190
## AEC03|t6 1.552 0.087 17.936 0.000 1.552 1.552
## AEC01|t1 -2.121 0.133 -15.900 0.000 -2.121 -2.121
## AEC01|t2 -1.326 0.076 -17.439 0.000 -1.326 -1.326
## AEC01|t3 -0.596 0.058 -10.253 0.000 -0.596 -0.596
## AEC01|t4 0.476 0.057 8.383 0.000 0.476 0.476
## AEC01|t5 1.200 0.071 16.795 0.000 1.200 1.200
## AEC01|t6 1.521 0.085 17.917 0.000 1.521 1.521
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.049 0.049 0.049
## .AEC02 0.142 0.142 0.142
## .AEC03 0.410 0.410 0.410
## .AEC01 0.207 0.207 0.207
## AEC 0.951 0.010 97.740 0.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 1.000 1.000 1.000
## AEC02 1.000 1.000 1.000
## AEC03 1.000 1.000 1.000
## AEC01 1.000 1.000 1.000
##
## R-Square:
## Estimate
## AEC04 0.951
## AEC02 0.858
## AEC03 0.590
## AEC01 0.7937.1.0.4 Selected Robust and Scaled Fit Measures
lavaan::fitMeasures(fit,c("chisq.scaled","df.scaled","pvalue","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue
## 38.796 2.000 NA
## srmr cfi.scaled tli.scaled
## 0.017 0.996 0.987
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.186 0.138 0.2407.1.0.5 Factor Loadings
parameters<-lavaan::standardizedSolution(fit)
loadings<-parameters[parameters$op=="=~",]
loadings## lhs op rhs est.std se z pvalue ci.lower ci.upper
## 1 AEC =~ AEC04 0.975 0.005 195.48 0 0.965 0.985
## 2 AEC =~ AEC02 0.926 0.006 142.80 0 0.913 0.939
## 3 AEC =~ AEC03 0.768 0.016 48.20 0 0.737 0.800
## 4 AEC =~ AEC01 0.890 0.009 98.06 0 0.873 0.9087.1.0.6 Modificantion Indices considering very bad RMSEA
modificationindices(fit, sort.=T)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 44 AEC04 ~~ AEC03 1.239 0.080 0.080 0.567 0.567
## 47 AEC02 ~~ AEC01 1.239 0.088 0.088 0.515 0.515
## 46 AEC02 ~~ AEC03 1.113 -0.073 -0.073 -0.301 -0.301
## 45 AEC04 ~~ AEC01 1.113 -0.089 -0.089 -0.879 -0.879
## 43 AEC04 ~~ AEC02 0.004 -0.006 -0.006 -0.066 -0.066
## 48 AEC03 ~~ AEC01 0.004 -0.004 -0.004 -0.014 -0.0147.1.0.7 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.## AEC
## alpha 0.9261
## alpha.ord 0.9378
## omega 0.9202
## omega2 0.9202
## omega3 0.9201
## avevar 0.79807.1.1 Internal Validity
7.1.1.1 Sex Invariance Model
data$SexoR<-as.factor(data$Sexo)
model <- 'AEC =~ AEC04 + AEC01 + AEC02 + AEC03'7.1.1.2 Fitting
invariance<- measurementInvarianceCat(model = model, data = data, group = "SexoR",parameterization = "theta", estimator = "ULSMV",ordered = c("AEC01", "AEC02", "AEC03", "AEC04"),missing="pairwise")## 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_object_post_check(object): lavaan WARNING: some estimated ov
## variances are negative##
## 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 4 2.54
## fit.loadings 7 3.71 2.05 3 0.5613
## fit.thresholds 26 31.82 17.17 19 0.5784
## fit.means 27 296.44 7.75 1 0.0054 **
## ---
## 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 0.219 NA NA
## fit.loadings 1.000 0.024 0.006 0.195
## fit.thresholds 1.000 0.000 0.000 0.024
## fit.means 0.994 0.081 0.006 0.0817.1.1.2.1 Configural
summary(invariance$fit.configural,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 378 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 61
## Number of equality constraints 5
##
## Number of observations per group:
## 2 371
## 1 159
## Number of missing patterns per group:
## 2 1
## 1 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 2.536 54.492
## Degrees of freedom 4 4
## P-value (Unknown) NA 0.000
## Scaling correction factor 0.047
## Shift parameter for each group:
## 2 0.397
## 1 0.170
## simple second-order correction
## Test statistic for each group:
## 2 1.904 40.883
## 1 0.632 13.609
##
## Model Test Baseline Model:
##
## Test statistic 1975.357 8140.340
## Degrees of freedom 12 12
## P-value NA 0.000
## Scaling correction factor 0.243
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 0.994
## Tucker-Lewis Index (TLI) 1.002 0.981
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000 0.219
## 90 Percent confidence interval - lower 0.000 0.169
## 90 Percent confidence interval - upper 0.075 0.272
## P-value RMSEA <= 0.05 0.845 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.022 0.022
##
## 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
## AEC =~
## AEC04 1.000 4.663 0.978
## AEC01 0.436 0.075 5.801 0.000 2.033 0.897
## AEC02 0.486 0.081 5.996 0.000 2.264 0.915
## AEC03 0.244 0.039 6.348 0.000 1.140 0.752
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## AEC 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -10.958 2.028 -5.403 0.000 -10.958 -2.298
## AEC04|t2 -6.346 0.930 -6.825 0.000 -6.346 -1.331
## AEC04|t3 -2.292 0.403 -5.690 0.000 -2.292 -0.481
## AEC04|t4 2.256 0.474 4.765 0.000 2.256 0.473
## AEC04|t5 6.046 0.880 6.871 0.000 6.046 1.268
## AEC04|t6 7.788 1.064 7.320 0.000 7.788 1.633
## AEC01|t1 -4.708 0.307 -15.353 0.000 -4.708 -2.078
## AEC01|t2 -2.873 0.202 -14.215 0.000 -2.873 -1.268
## AEC01|t3 -1.176 0.162 -7.273 0.000 -1.176 -0.519
## AEC01|t4 1.229 0.155 7.934 0.000 1.229 0.542
## AEC01|t5 3.091 0.216 14.313 0.000 3.091 1.364
## AEC01|t6 3.760 0.255 14.761 0.000 3.760 1.659
## AEC02|t1 -5.476 0.440 -12.444 0.000 -5.476 -2.212
## AEC02|t2 -3.603 0.272 -13.229 0.000 -3.603 -1.455
## AEC02|t3 -1.771 0.188 -9.431 0.000 -1.771 -0.715
## AEC02|t4 1.115 0.173 6.446 0.000 1.115 0.451
## AEC02|t5 2.893 0.205 14.122 0.000 2.893 1.169
## AEC02|t6 3.863 0.206 18.745 0.000 3.863 1.561
## AEC03|t1 -3.245 0.215 -15.092 0.000 -3.245 -2.140
## AEC03|t2 -1.772 0.120 -14.705 0.000 -1.772 -1.169
## AEC03|t3 -0.506 0.101 -5.003 0.000 -0.506 -0.334
## AEC03|t4 0.787 0.102 7.706 0.000 0.787 0.519
## AEC03|t5 1.993 0.128 15.511 0.000 1.993 1.314
## AEC03|t6 2.601 0.163 15.921 0.000 2.601 1.716
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 1.000 1.000 0.044
## .AEC01 1.000 1.000 0.195
## .AEC02 1.000 1.000 0.163
## .AEC03 1.000 1.000 0.435
## AEC 21.739 6.675 3.257 0.001 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.210 0.210 1.000
## AEC01 0.441 0.441 1.000
## AEC02 0.404 0.404 1.000
## AEC03 0.660 0.660 1.000
##
## R-Square:
## Estimate
## AEC04 0.956
## AEC01 0.805
## AEC02 0.837
## AEC03 0.565
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC =~
## AEC04 1.000 6.200 0.965
## AEC01 0.432 0.104 4.145 0.000 2.681 0.870
## AEC02 0.573 0.119 4.806 0.000 3.553 0.949
## AEC03 0.255 0.062 4.140 0.000 1.579 0.779
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## AEC 5.076 6.084 0.834 0.404 0.819 0.819
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -10.958 2.028 -5.403 0.000 -10.958 -1.706
## AEC04|t2 -6.346 0.930 -6.825 0.000 -6.346 -0.988
## AEC04|t3 -0.596 3.177 -0.188 0.851 -0.596 -0.093
## AEC04|t4 6.247 6.692 0.934 0.351 6.247 0.972
## AEC04|t5 11.053 9.225 1.198 0.231 11.053 1.720
## AEC04|t6 13.521 10.537 1.283 0.199 13.521 2.104
## AEC01|t1 -4.708 0.307 -15.353 0.000 -4.708 -1.527
## AEC01|t2 -2.374 0.575 -4.129 0.000 -2.374 -0.770
## AEC01|t3 -0.251 1.402 -0.179 0.858 -0.251 -0.081
## AEC01|t4 3.209 2.858 1.123 0.261 3.209 1.041
## AEC01|t5 4.989 3.624 1.377 0.169 4.989 1.618
## AEC01|t6 6.135 4.123 1.488 0.137 6.135 1.990
## AEC02|t1 -5.476 0.440 -12.444 0.000 -5.476 -1.462
## AEC02|t2 -3.479 0.651 -5.343 0.000 -3.479 -0.929
## AEC02|t3 -1.501 1.369 -1.096 0.273 -1.501 -0.401
## AEC02|t4 3.233 3.396 0.952 0.341 3.233 0.863
## AEC02|t5 5.879 4.576 1.285 0.199 5.879 1.570
## AEC02|t6 7.563 5.338 1.417 0.157 7.563 2.020
## AEC03|t1 -3.245 0.215 -15.092 0.000 -3.245 -1.601
## AEC03|t2 -2.164 0.362 -5.986 0.000 -2.164 -1.068
## AEC03|t3 -0.024 0.926 -0.026 0.979 -0.024 -0.012
## AEC03|t4 1.826 1.596 1.144 0.253 1.826 0.901
## AEC03|t5 3.228 2.132 1.514 0.130 3.228 1.593
## AEC03|t6 3.883 2.390 1.625 0.104 3.883 1.916
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 2.837 3.102 0.915 0.360 2.837 0.069
## .AEC01 2.317 2.042 1.135 0.256 2.317 0.244
## .AEC02 1.401 1.313 1.067 0.286 1.401 0.100
## .AEC03 1.613 1.243 1.298 0.194 1.613 0.393
## AEC 38.444 41.068 0.936 0.349 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.156 0.156 1.000
## AEC01 0.324 0.324 1.000
## AEC02 0.267 0.267 1.000
## AEC03 0.493 0.493 1.000
##
## R-Square:
## Estimate
## AEC04 0.931
## AEC01 0.756
## AEC02 0.900
## AEC03 0.607lavaan::fitMeasures(invariance$fit.configural,c("chisq.scaled","df.scaled","pvalue","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue
## 54.492 4.000 NA
## srmr cfi.scaled tli.scaled
## 0.022 0.994 0.981
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.219 0.169 0.272modificationindices(invariance$fit.configural, sort.=T)## lhs op rhs block group level mi epc sepc.lv sepc.all sepc.nox
## 92 AEC04 ~~ AEC03 1 1 1 1.856 0.845 0.845 0.845 0.845
## 93 AEC01 ~~ AEC02 1 1 1 1.856 0.732 0.732 0.732 0.732
## 90 AEC04 ~~ AEC01 1 1 1 0.752 -0.965 -0.965 -0.965 -0.965
## 95 AEC02 ~~ AEC03 1 1 1 0.752 -0.263 -0.263 -0.263 -0.263
## 97 AEC04 ~~ AEC02 2 2 1 0.474 2.687 2.687 1.348 1.348
## 100 AEC01 ~~ AEC03 2 2 1 0.474 0.516 0.516 0.267 0.267
## 96 AEC04 ~~ AEC01 2 2 1 0.465 -1.989 -1.989 -0.776 -0.776
## 101 AEC02 ~~ AEC03 2 2 1 0.465 -0.671 -0.671 -0.447 -0.447
## 94 AEC01 ~~ AEC03 1 1 1 0.254 -0.137 -0.137 -0.137 -0.137
## 91 AEC04 ~~ AEC02 1 1 1 0.254 -0.626 -0.626 -0.626 -0.626
## 99 AEC01 ~~ AEC02 2 2 1 0.000 -0.001 -0.001 0.000 0.000
## 98 AEC04 ~~ AEC03 2 2 1 0.000 -0.001 -0.001 0.000 0.000semTools::reliability(invariance$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`
## AEC
## alpha 0.9189
## alpha.ord 0.9347
## omega 0.9174
## omega2 0.9174
## omega3 0.9174
## avevar 0.8898
##
## $`1`
## AEC
## alpha 0.9351
## alpha.ord 0.9382
## omega 0.9197
## omega2 0.9197
## omega3 0.9194
## avevar 0.88157.1.1.2.2 Loadings
summary(invariance$fit.loadings,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 322 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 61
## Number of equality constraints 8
##
## Number of observations per group:
## 2 371
## 1 159
## Number of missing patterns per group:
## 2 1
## 1 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 3.706 8.074
## Degrees of freedom 7 7
## P-value (Unknown) NA 0.326
## Scaling correction factor 0.645
## Shift parameter for each group:
## 2 1.633
## 1 0.700
## simple second-order correction
## Test statistic for each group:
## 2 2.099 4.886
## 1 1.606 3.189
##
## Model Test Baseline Model:
##
## Test statistic 1975.357 8140.340
## Degrees of freedom 12 12
## P-value NA 0.000
## Scaling correction factor 0.243
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 1.000
## Tucker-Lewis Index (TLI) 1.003 1.000
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000 0.024
## 90 Percent confidence interval - lower 0.000 0.000
## 90 Percent confidence interval - upper 0.047 0.082
## P-value RMSEA <= 0.05 0.958 0.702
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower 0.000
## 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
## AEC =~
## AEC04 1.000 4.049 0.971
## AEC01 0.485 0.155 3.119 0.002 1.962 0.891
## AEC02 0.619 0.201 3.081 0.002 2.507 0.929
## AEC03 0.281 0.087 3.229 0.001 1.137 0.751
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## AEC 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -9.600 2.865 -3.351 0.001 -9.600 -2.302
## AEC04|t2 -5.550 1.509 -3.678 0.000 -5.550 -1.331
## AEC04|t3 -2.005 0.579 -3.462 0.001 -2.005 -0.481
## AEC04|t4 1.973 0.603 3.273 0.001 1.973 0.473
## AEC04|t5 5.288 1.423 3.716 0.000 5.288 1.268
## AEC04|t6 6.812 1.809 3.765 0.000 6.812 1.633
## AEC01|t1 -4.586 0.397 -11.557 0.000 -4.586 -2.082
## AEC01|t2 -2.792 0.238 -11.723 0.000 -2.792 -1.268
## AEC01|t3 -1.143 0.165 -6.929 0.000 -1.143 -0.519
## AEC01|t4 1.194 0.160 7.481 0.000 1.194 0.542
## AEC01|t5 3.004 0.247 12.179 0.000 3.004 1.364
## AEC01|t6 3.655 0.293 12.478 0.000 3.655 1.659
## AEC02|t1 -5.947 0.774 -7.680 0.000 -5.947 -2.204
## AEC02|t2 -3.928 0.484 -8.118 0.000 -3.928 -1.455
## AEC02|t3 -1.931 0.275 -7.015 0.000 -1.931 -0.715
## AEC02|t4 1.216 0.220 5.517 0.000 1.216 0.451
## AEC02|t5 3.154 0.368 8.573 0.000 3.154 1.169
## AEC02|t6 4.212 0.447 9.418 0.000 4.212 1.561
## AEC03|t1 -3.241 0.233 -13.910 0.000 -3.241 -2.141
## AEC03|t2 -1.769 0.127 -13.941 0.000 -1.769 -1.169
## AEC03|t3 -0.505 0.102 -4.967 0.000 -0.505 -0.334
## AEC03|t4 0.786 0.103 7.648 0.000 0.786 0.519
## AEC03|t5 1.990 0.133 14.908 0.000 1.990 1.314
## AEC03|t6 2.597 0.170 15.288 0.000 2.597 1.716
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 1.000 1.000 0.057
## .AEC01 1.000 1.000 0.206
## .AEC02 1.000 1.000 0.137
## .AEC03 1.000 1.000 0.436
## AEC 16.397 9.346 1.754 0.079 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.240 0.240 1.000
## AEC01 0.454 0.454 1.000
## AEC02 0.371 0.371 1.000
## AEC03 0.661 0.661 1.000
##
## R-Square:
## Estimate
## AEC04 0.943
## AEC01 0.794
## AEC02 0.863
## AEC03 0.564
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC =~
## AEC04 1.000 5.660 0.987
## AEC01 0.485 0.155 3.119 0.002 2.743 0.892
## AEC02 0.619 0.201 3.081 0.002 3.504 0.901
## AEC03 0.281 0.087 3.229 0.001 1.589 0.782
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## AEC 4.646 5.726 0.811 0.417 0.821 0.821
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -9.600 2.865 -3.351 0.001 -9.600 -1.674
## AEC04|t2 -5.550 1.509 -3.678 0.000 -5.550 -0.968
## AEC04|t3 -0.417 2.629 -0.159 0.874 -0.417 -0.073
## AEC04|t4 5.692 6.386 0.891 0.373 5.692 0.992
## AEC04|t5 9.983 9.154 1.091 0.275 9.983 1.740
## AEC04|t6 12.187 10.585 1.151 0.250 12.187 2.124
## AEC01|t1 -4.586 0.397 -11.557 0.000 -4.586 -1.492
## AEC01|t2 -2.305 0.579 -3.979 0.000 -2.305 -0.750
## AEC01|t3 -0.187 1.362 -0.137 0.891 -0.187 -0.061
## AEC01|t4 3.263 2.815 1.159 0.246 3.263 1.061
## AEC01|t5 5.038 3.585 1.405 0.160 5.038 1.639
## AEC01|t6 6.181 4.086 1.513 0.130 6.181 2.010
## AEC02|t1 -5.947 0.774 -7.680 0.000 -5.947 -1.529
## AEC02|t2 -3.759 0.962 -3.908 0.000 -3.759 -0.966
## AEC02|t3 -1.704 1.384 -1.232 0.218 -1.704 -0.438
## AEC02|t4 3.214 3.049 1.054 0.292 3.214 0.826
## AEC02|t5 5.962 4.092 1.457 0.145 5.962 1.533
## AEC02|t6 7.712 4.774 1.615 0.106 7.712 1.982
## AEC03|t1 -3.241 0.233 -13.910 0.000 -3.241 -1.596
## AEC03|t2 -2.160 0.361 -5.993 0.000 -2.160 -1.064
## AEC03|t3 -0.016 0.907 -0.018 0.986 -0.016 -0.008
## AEC03|t4 1.839 1.567 1.173 0.241 1.839 0.905
## AEC03|t5 3.244 2.096 1.548 0.122 3.244 1.597
## AEC03|t6 3.900 2.351 1.659 0.097 3.900 1.920
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.868 4.064 0.213 0.831 0.868 0.026
## .AEC01 1.930 1.995 0.967 0.334 1.930 0.204
## .AEC02 2.856 2.651 1.077 0.281 2.856 0.189
## .AEC03 1.601 1.185 1.352 0.177 1.601 0.388
## AEC 32.037 39.548 0.810 0.418 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.174 0.174 1.000
## AEC01 0.325 0.325 1.000
## AEC02 0.257 0.257 1.000
## AEC03 0.492 0.492 1.000
##
## R-Square:
## Estimate
## AEC04 0.974
## AEC01 0.796
## AEC02 0.811
## AEC03 0.612lavaan::fitMeasures(invariance$fit.loadings,c("chisq.scaled","df.scaled","pvalue","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue
## 8.074 7.000 NA
## srmr cfi.scaled tli.scaled
## 0.025 1.000 1.000
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.024 0.000 0.082modificationindices(invariance$fit.loadings, sort.=T)## lhs op rhs block group level mi epc sepc.lv sepc.all sepc.nox
## 95 AEC04 ~~ AEC03 1 1 1 2.021 0.704 0.704 0.704 0.704
## 99 AEC04 ~~ AEC01 2 2 1 1.283 -2.036 -2.036 -1.573 -1.573
## 98 AEC02 ~~ AEC03 1 1 1 1.187 -0.338 -0.338 -0.338 -0.338
## 36 AEC02 ~*~ AEC02 1 1 1 1.076 0.057 0.057 1.000 1.000
## 40 AEC02 ~1 1 1 1 1.076 0.909 0.909 0.337 0.337
## 78 AEC02 ~*~ AEC02 2 2 1 1.076 -0.026 -0.026 -1.000 -1.000
## 82 AEC02 ~1 2 2 1 1.075 -0.909 -0.909 -0.234 -0.234
## 96 AEC01 ~~ AEC02 1 1 1 1.034 0.523 0.523 0.523 0.523
## 100 AEC04 ~~ AEC02 2 2 1 0.748 1.970 1.970 1.251 1.251
## 94 AEC04 ~~ AEC02 1 1 1 0.485 -0.728 -0.728 -0.728 -0.728
## 81 AEC01 ~1 2 2 1 0.277 0.358 0.358 0.117 0.117
## 35 AEC01 ~*~ AEC01 1 1 1 0.277 -0.035 -0.035 -1.000 -1.000
## 39 AEC01 ~1 1 1 1 0.277 -0.358 -0.358 -0.163 -0.163
## 77 AEC01 ~*~ AEC01 2 2 1 0.277 0.017 0.017 1.000 1.000
## 80 AEC04 ~1 2 2 1 0.232 0.708 0.708 0.123 0.123
## 38 AEC04 ~1 1 1 1 0.232 -0.708 -0.708 -0.170 -0.170
## 76 AEC04 ~*~ AEC04 2 2 1 0.222 0.008 0.008 1.000 1.000
## 1 AEC =~ AEC04 1 1 1 0.215 0.068 0.276 0.066 0.066
## 34 AEC04 ~*~ AEC04 1 1 1 0.215 -0.016 -0.016 -1.000 -1.000
## 43 AEC =~ AEC04 2 2 1 0.215 -0.068 -0.386 -0.067 -0.067
## 93 AEC04 ~~ AEC01 1 1 1 0.118 -0.283 -0.283 -0.283 -0.283
## 102 AEC01 ~~ AEC02 2 2 1 0.108 0.381 0.381 0.162 0.162
## 97 AEC01 ~~ AEC03 1 1 1 0.100 -0.078 -0.078 -0.078 -0.078
## 101 AEC04 ~~ AEC03 2 2 1 0.091 -0.337 -0.337 -0.286 -0.286
## 103 AEC01 ~~ AEC03 2 2 1 0.057 0.141 0.141 0.080 0.080
## 37 AEC03 ~*~ AEC03 1 1 1 0.002 -0.005 -0.005 -1.000 -1.000
## 83 AEC03 ~1 2 2 1 0.002 0.024 0.024 0.012 0.012
## 41 AEC03 ~1 1 1 1 0.002 -0.024 -0.024 -0.016 -0.016
## 79 AEC03 ~*~ AEC03 2 2 1 0.002 0.003 0.003 1.000 1.000
## 104 AEC02 ~~ AEC03 2 2 1 0.001 0.017 0.017 0.008 0.008semTools::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`
## AEC
## alpha 0.9189
## alpha.ord 0.9347
## omega 0.9172
## omega2 0.9172
## omega3 0.9171
## avevar 0.8743
##
## $`1`
## AEC
## alpha 0.9351
## alpha.ord 0.9382
## omega 0.9190
## omega2 0.9190
## omega3 0.9182
## avevar 0.88237.1.1.2.3 Thresholds
summary(invariance$fit.thresholds,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 191 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 61
## Number of equality constraints 27
##
## Number of observations per group:
## 2 371
## 1 159
## Number of missing patterns per group:
## 2 1
## 1 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 31.817 22.649
## Degrees of freedom 26 26
## P-value (Unknown) NA 0.653
## Scaling correction factor 2.583
## Shift parameter for each group:
## 2 7.233
## 1 3.100
## simple second-order correction
## Test statistic for each group:
## 2 10.422 11.267
## 1 21.395 11.382
##
## Model Test Baseline Model:
##
## Test statistic 1975.357 8140.340
## Degrees of freedom 12 12
## P-value NA 0.000
## Scaling correction factor 0.243
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.997 1.000
## Tucker-Lewis Index (TLI) 0.999 1.000
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.029 0.000
## 90 Percent confidence interval - lower 0.000 0.000
## 90 Percent confidence interval - upper 0.059 0.041
## P-value RMSEA <= 0.05 0.853 0.985
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower 0.000
## 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
## AEC =~
## AEC04 1.000 3.399 0.959
## AEC01 0.573 0.120 4.766 0.000 1.948 0.890
## AEC02 0.716 0.146 4.904 0.000 2.432 0.925
## AEC03 0.354 0.066 5.399 0.000 1.203 0.769
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## AEC 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -8.017 1.446 -5.544 0.000 -8.017 -2.263
## AEC04|t2 -4.837 0.850 -5.688 0.000 -4.837 -1.365
## AEC04|t3 -1.765 0.384 -4.591 0.000 -1.765 -0.498
## AEC04|t4 1.746 0.354 4.936 0.000 1.746 0.493
## AEC04|t5 4.525 0.772 5.859 0.000 4.525 1.277
## AEC04|t6 5.845 0.968 6.040 0.000 5.845 1.650
## AEC01|t1 -4.546 0.352 -12.903 0.000 -4.546 -2.076
## AEC01|t2 -2.771 0.226 -12.252 0.000 -2.771 -1.266
## AEC01|t3 -1.138 0.159 -7.175 0.000 -1.138 -0.520
## AEC01|t4 1.271 0.155 8.188 0.000 1.271 0.580
## AEC01|t5 2.950 0.249 11.844 0.000 2.950 1.347
## AEC01|t6 3.658 0.296 12.361 0.000 3.658 1.671
## AEC02|t1 -5.688 0.562 -10.118 0.000 -5.688 -2.163
## AEC02|t2 -3.836 0.376 -10.202 0.000 -3.836 -1.459
## AEC02|t3 -2.020 0.243 -8.326 0.000 -2.020 -0.768
## AEC02|t4 1.174 0.188 6.258 0.000 1.174 0.446
## AEC02|t5 3.085 0.293 10.510 0.000 3.085 1.173
## AEC02|t6 4.178 0.372 11.236 0.000 4.178 1.589
## AEC03|t1 -3.293 0.215 -15.300 0.000 -3.293 -2.106
## AEC03|t2 -1.964 0.126 -15.580 0.000 -1.964 -1.255
## AEC03|t3 -0.545 0.100 -5.433 0.000 -0.545 -0.348
## AEC03|t4 0.828 0.100 8.272 0.000 0.828 0.530
## AEC03|t5 2.035 0.140 14.548 0.000 2.035 1.301
## AEC03|t6 2.632 0.175 15.061 0.000 2.632 1.683
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 1.000 1.000 0.080
## .AEC01 1.000 1.000 0.209
## .AEC02 1.000 1.000 0.145
## .AEC03 1.000 1.000 0.409
## AEC 11.553 4.010 2.881 0.004 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.282 0.282 1.000
## AEC01 0.457 0.457 1.000
## AEC02 0.380 0.380 1.000
## AEC03 0.639 0.639 1.000
##
## R-Square:
## Estimate
## AEC04 0.920
## AEC01 0.791
## AEC02 0.855
## AEC03 0.591
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC =~
## AEC04 1.000 3.569 0.992
## AEC01 0.573 0.120 4.766 0.000 2.045 0.871
## AEC02 0.716 0.146 4.904 0.000 2.554 0.915
## AEC03 0.354 0.066 5.399 0.000 1.263 0.784
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## AEC 1.260 0.398 3.166 0.002 0.353 0.353
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -8.017 1.446 -5.544 0.000 -8.017 -2.229
## AEC04|t2 -4.837 0.850 -5.688 0.000 -4.837 -1.345
## AEC04|t3 -1.765 0.384 -4.591 0.000 -1.765 -0.491
## AEC04|t4 1.746 0.354 4.936 0.000 1.746 0.486
## AEC04|t5 4.525 0.772 5.859 0.000 4.525 1.258
## AEC04|t6 5.845 0.968 6.040 0.000 5.845 1.625
## AEC01|t1 -4.546 0.352 -12.903 0.000 -4.546 -1.935
## AEC01|t2 -2.771 0.226 -12.252 0.000 -2.771 -1.180
## AEC01|t3 -1.138 0.159 -7.175 0.000 -1.138 -0.484
## AEC01|t4 1.271 0.155 8.188 0.000 1.271 0.541
## AEC01|t5 2.950 0.249 11.844 0.000 2.950 1.256
## AEC01|t6 3.658 0.296 12.361 0.000 3.658 1.557
## AEC02|t1 -5.688 0.562 -10.118 0.000 -5.688 -2.038
## AEC02|t2 -3.836 0.376 -10.202 0.000 -3.836 -1.374
## AEC02|t3 -2.020 0.243 -8.326 0.000 -2.020 -0.723
## AEC02|t4 1.174 0.188 6.258 0.000 1.174 0.420
## AEC02|t5 3.085 0.293 10.510 0.000 3.085 1.105
## AEC02|t6 4.178 0.372 11.236 0.000 4.178 1.496
## AEC03|t1 -3.293 0.215 -15.300 0.000 -3.293 -2.045
## AEC03|t2 -1.964 0.126 -15.580 0.000 -1.964 -1.220
## AEC03|t3 -0.545 0.100 -5.433 0.000 -0.545 -0.338
## AEC03|t4 0.828 0.100 8.272 0.000 0.828 0.514
## AEC03|t5 2.035 0.140 14.548 0.000 2.035 1.264
## AEC03|t6 2.632 0.175 15.061 0.000 2.632 1.634
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.198 0.943 0.210 0.834 0.198 0.015
## .AEC01 1.335 0.409 3.260 0.001 1.335 0.242
## .AEC02 1.272 0.580 2.191 0.028 1.272 0.163
## .AEC03 0.998 0.231 4.313 0.000 0.998 0.385
## AEC 12.738 4.725 2.696 0.007 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.278 0.278 1.000
## AEC01 0.426 0.426 1.000
## AEC02 0.358 0.358 1.000
## AEC03 0.621 0.621 1.000
##
## R-Square:
## Estimate
## AEC04 0.985
## AEC01 0.758
## AEC02 0.837
## AEC03 0.615lavaan::fitMeasures(invariance$fit.thresholds,c("chisq.scaled","df.scaled","pvalue","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue
## 22.649 26.000 NA
## srmr cfi.scaled tli.scaled
## 0.026 1.000 1.000
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.000 0.000 0.041modificationindices(invariance$fit.thresholds, sort.=T)## lhs op rhs block group level mi epc sepc.lv sepc.all sepc.nox
## 83 AEC03 ~1 2 2 1 3.105 0.128 0.128 0.080 0.080
## 41 AEC03 ~1 1 1 1 3.105 -0.128 -0.128 -0.082 -0.082
## 117 AEC02 ~~ AEC03 1 1 1 1.881 -0.398 -0.398 -0.398 -0.398
## 114 AEC04 ~~ AEC03 1 1 1 1.145 0.426 0.426 0.426 0.426
## 115 AEC01 ~~ AEC02 1 1 1 1.068 0.455 0.455 0.455 0.455
## 37 AEC03 ~*~ AEC03 1 1 1 0.881 0.059 0.059 1.000 1.000
## 34 AEC04 ~*~ AEC04 1 1 1 0.814 -0.024 -0.024 -1.000 -1.000
## 1 AEC =~ AEC04 1 1 1 0.814 0.086 0.292 0.083 0.083
## 43 AEC =~ AEC04 2 2 1 0.814 -0.086 -0.307 -0.085 -0.085
## 118 AEC04 ~~ AEC01 2 2 1 0.730 -0.722 -0.722 -1.404 -1.404
## 78 AEC02 ~*~ AEC02 2 2 1 0.520 -0.026 -0.026 -1.000 -1.000
## 116 AEC01 ~~ AEC03 1 1 1 0.466 -0.161 -0.161 -0.161 -0.161
## 39 AEC01 ~1 1 1 1 0.428 0.072 0.072 0.033 0.033
## 81 AEC01 ~1 2 2 1 0.428 -0.072 -0.072 -0.030 -0.030
## 76 AEC04 ~*~ AEC04 2 2 1 0.317 0.016 0.016 1.000 1.000
## 119 AEC04 ~~ AEC02 2 2 1 0.312 0.572 0.572 1.139 1.139
## 38 AEC04 ~1 1 1 1 0.298 0.098 0.098 0.028 0.028
## 80 AEC04 ~1 2 2 1 0.298 -0.098 -0.098 -0.027 -0.027
## 35 AEC01 ~*~ AEC01 1 1 1 0.208 -0.020 -0.020 -1.000 -1.000
## 122 AEC01 ~~ AEC03 2 2 1 0.207 0.160 0.160 0.139 0.139
## 36 AEC02 ~*~ AEC02 1 1 1 0.197 0.016 0.016 1.000 1.000
## 121 AEC01 ~~ AEC02 2 2 1 0.192 0.279 0.279 0.214 0.214
## 120 AEC04 ~~ AEC03 2 2 1 0.161 -0.225 -0.225 -0.505 -0.505
## 82 AEC02 ~1 2 2 1 0.159 -0.054 -0.054 -0.019 -0.019
## 40 AEC02 ~1 1 1 1 0.159 0.054 0.054 0.020 0.020
## 113 AEC04 ~~ AEC02 1 1 1 0.029 -0.128 -0.128 -0.128 -0.128
## 123 AEC02 ~~ AEC03 2 2 1 0.029 -0.072 -0.072 -0.064 -0.064
## 79 AEC03 ~*~ AEC03 2 2 1 0.014 0.008 0.008 1.000 1.000
## 77 AEC01 ~*~ AEC01 2 2 1 0.002 0.002 0.002 1.000 1.000
## 112 AEC04 ~~ AEC01 1 1 1 0.001 0.021 0.021 0.021 0.021semTools::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`
## AEC
## alpha 0.9189
## alpha.ord 0.9347
## omega 0.9162
## omega2 0.9162
## omega3 0.9171
## avevar 0.8502
##
## $`1`
## AEC
## alpha 0.9351
## alpha.ord 0.9382
## omega 0.9217
## omega2 0.9217
## omega3 0.9209
## avevar 0.86827.1.1.3 Partial Invariance - Sex Means
summary(invariance$fit.means,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 194 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 60
## Number of equality constraints 27
##
## Number of observations per group:
## 2 371
## 1 159
## Number of missing patterns per group:
## 2 1
## 1 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 296.443 73.466
## Degrees of freedom 27 27
## P-value (Unknown) NA 0.000
## Scaling correction factor 4.932
## Shift parameter for each group:
## 2 9.350
## 1 4.007
## simple second-order correction
## Test statistic for each group:
## 2 88.835 27.363
## 1 207.607 46.103
##
## Model Test Baseline Model:
##
## Test statistic 1975.357 8140.340
## Degrees of freedom 12 12
## P-value NA 0.000
## Scaling correction factor 0.243
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.863 0.994
## Tucker-Lewis Index (TLI) 0.939 0.997
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.194 0.081
## 90 Percent confidence interval - lower 0.175 0.059
## 90 Percent confidence interval - upper 0.215 0.103
## P-value RMSEA <= 0.05 0.000 0.012
##
## 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
## AEC =~
## AEC04 1.000 3.536 0.962
## AEC01 0.573 0.132 4.358 0.000 2.027 0.897
## AEC02 0.683 0.146 4.691 0.000 2.414 0.924
## AEC03 0.330 0.069 4.808 0.000 1.167 0.759
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## AEC 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -8.599 1.682 -5.113 0.000 -8.599 -2.340
## AEC04|t2 -5.349 1.015 -5.268 0.000 -5.349 -1.456
## AEC04|t3 -2.199 0.450 -4.886 0.000 -2.199 -0.599
## AEC04|t4 1.402 0.338 4.149 0.000 1.402 0.382
## AEC04|t5 4.249 0.825 5.148 0.000 4.249 1.156
## AEC04|t6 5.602 1.061 5.280 0.000 5.602 1.524
## AEC01|t1 -4.863 0.383 -12.681 0.000 -4.863 -2.152
## AEC01|t2 -3.044 0.242 -12.557 0.000 -3.044 -1.347
## AEC01|t3 -1.370 0.156 -8.781 0.000 -1.370 -0.606
## AEC01|t4 1.100 0.142 7.749 0.000 1.100 0.487
## AEC01|t5 2.818 0.235 11.995 0.000 2.818 1.247
## AEC01|t6 3.545 0.285 12.418 0.000 3.545 1.568
## AEC02|t1 -5.818 0.573 -10.153 0.000 -5.818 -2.227
## AEC02|t2 -4.009 0.392 -10.236 0.000 -4.009 -1.534
## AEC02|t3 -2.234 0.237 -9.414 0.000 -2.234 -0.855
## AEC02|t4 0.897 0.164 5.489 0.000 0.897 0.343
## AEC02|t5 2.770 0.269 10.306 0.000 2.770 1.060
## AEC02|t6 3.842 0.341 11.264 0.000 3.842 1.471
## AEC03|t1 -3.347 0.214 -15.660 0.000 -3.347 -2.178
## AEC03|t2 -2.048 0.119 -17.248 0.000 -2.048 -1.333
## AEC03|t3 -0.660 0.090 -7.325 0.000 -0.660 -0.429
## AEC03|t4 0.684 0.089 7.672 0.000 0.684 0.445
## AEC03|t5 1.863 0.127 14.722 0.000 1.863 1.212
## AEC03|t6 2.446 0.161 15.208 0.000 2.446 1.592
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 1.000 1.000 0.074
## .AEC01 1.000 1.000 0.196
## .AEC02 1.000 1.000 0.146
## .AEC03 1.000 1.000 0.423
## AEC 12.504 4.771 2.621 0.009 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.272 0.272 1.000
## AEC01 0.442 0.442 1.000
## AEC02 0.383 0.383 1.000
## AEC03 0.651 0.651 1.000
##
## R-Square:
## Estimate
## AEC04 0.926
## AEC01 0.804
## AEC02 0.854
## AEC03 0.577
##
##
## Group 2 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC =~
## AEC04 1.000 3.588 1.001
## AEC01 0.573 0.132 4.358 0.000 2.056 0.870
## AEC02 0.683 0.146 4.691 0.000 2.449 0.928
## AEC03 0.330 0.069 4.808 0.000 1.184 0.761
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## AEC 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -8.599 1.682 -5.113 0.000 -8.599 -2.399
## AEC04|t2 -5.349 1.015 -5.268 0.000 -5.349 -1.492
## AEC04|t3 -2.199 0.450 -4.886 0.000 -2.199 -0.614
## AEC04|t4 1.402 0.338 4.149 0.000 1.402 0.391
## AEC04|t5 4.249 0.825 5.148 0.000 4.249 1.185
## AEC04|t6 5.602 1.061 5.280 0.000 5.602 1.563
## AEC01|t1 -4.863 0.383 -12.681 0.000 -4.863 -2.058
## AEC01|t2 -3.044 0.242 -12.557 0.000 -3.044 -1.288
## AEC01|t3 -1.370 0.156 -8.781 0.000 -1.370 -0.580
## AEC01|t4 1.100 0.142 7.749 0.000 1.100 0.465
## AEC01|t5 2.818 0.235 11.995 0.000 2.818 1.193
## AEC01|t6 3.545 0.285 12.418 0.000 3.545 1.501
## AEC02|t1 -5.818 0.573 -10.153 0.000 -5.818 -2.205
## AEC02|t2 -4.009 0.392 -10.236 0.000 -4.009 -1.519
## AEC02|t3 -2.234 0.237 -9.414 0.000 -2.234 -0.847
## AEC02|t4 0.897 0.164 5.489 0.000 0.897 0.340
## AEC02|t5 2.770 0.269 10.306 0.000 2.770 1.050
## AEC02|t6 3.842 0.341 11.264 0.000 3.842 1.456
## AEC03|t1 -3.347 0.214 -15.660 0.000 -3.347 -2.150
## AEC03|t2 -2.048 0.119 -17.248 0.000 -2.048 -1.316
## AEC03|t3 -0.660 0.090 -7.325 0.000 -0.660 -0.424
## AEC03|t4 0.684 0.089 7.672 0.000 0.684 0.439
## AEC03|t5 1.863 0.127 14.722 0.000 1.863 1.197
## AEC03|t6 2.446 0.161 15.208 0.000 2.446 1.571
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 -0.028 0.727 -0.039 0.969 -0.028 -0.002
## .AEC01 1.352 0.423 3.197 0.001 1.352 0.242
## .AEC02 0.965 0.497 1.941 0.052 0.965 0.139
## .AEC03 1.022 0.221 4.618 0.000 1.022 0.422
## AEC 12.872 5.270 2.443 0.015 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.279 0.279 1.000
## AEC01 0.423 0.423 1.000
## AEC02 0.379 0.379 1.000
## AEC03 0.642 0.642 1.000
##
## R-Square:
## Estimate
## AEC04 NA
## AEC01 0.758
## AEC02 0.861
## AEC03 0.578lavaan::fitMeasures(invariance$fit.means,c("chisq.scaled","df.scaled","pvalue","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue
## 73.466 27.000 NA
## srmr cfi.scaled tli.scaled
## 0.025 0.994 0.997
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.081 0.059 0.103modificationindices(invariance$fit.means, sort.=T)## lhs op rhs block group level mi epc sepc.lv sepc.all sepc.nox
## 42 AEC ~1 1 1 1 262.788 -1.270 -0.359 -0.359 -0.359
## 84 AEC ~1 2 2 1 262.787 1.270 0.354 0.354 0.354
## 83 AEC03 ~1 2 2 1 74.972 0.521 0.521 0.335 0.335
## 41 AEC03 ~1 1 1 1 74.971 -0.521 -0.521 -0.339 -0.339
## 38 AEC04 ~1 1 1 1 72.205 -1.202 -1.202 -0.327 -0.327
## 80 AEC04 ~1 2 2 1 72.204 1.202 1.202 0.335 0.335
## 40 AEC02 ~1 1 1 1 62.927 -0.825 -0.825 -0.316 -0.316
## 82 AEC02 ~1 2 2 1 62.927 0.825 0.825 0.313 0.313
## 81 AEC01 ~1 2 2 1 55.898 0.678 0.678 0.287 0.287
## 39 AEC01 ~1 1 1 1 55.898 -0.678 -0.678 -0.300 -0.300
## 114 AEC04 ~~ AEC03 1 1 1 1.631 0.527 0.527 0.527 0.527
## 117 AEC02 ~~ AEC03 1 1 1 1.287 -0.325 -0.325 -0.325 -0.325
## 118 AEC04 ~~ AEC01 2 2 1 0.991 -0.863 -0.863 -4.413 -4.413
## 115 AEC01 ~~ AEC02 1 1 1 0.809 0.419 0.419 0.419 0.419
## 43 AEC =~ AEC04 2 2 1 0.630 -0.082 -0.296 -0.082 -0.082
## 76 AEC04 ~*~ AEC04 2 2 1 0.630 0.023 0.023 1.000 1.000
## 1 AEC =~ AEC04 1 1 1 0.630 0.082 0.291 0.079 0.079
## 34 AEC04 ~*~ AEC04 1 1 1 0.630 -0.022 -0.022 -1.000 -1.000
## 122 AEC01 ~~ AEC03 2 2 1 0.587 0.263 0.263 0.224 0.224
## 116 AEC01 ~~ AEC03 1 1 1 0.376 -0.150 -0.150 -0.150 -0.150
## 79 AEC03 ~*~ AEC03 2 2 1 0.207 -0.031 -0.031 -1.000 -1.000
## 37 AEC03 ~*~ AEC03 1 1 1 0.207 0.031 0.031 1.000 1.000
## 36 AEC02 ~*~ AEC02 1 1 1 0.185 0.017 0.017 1.000 1.000
## 78 AEC02 ~*~ AEC02 2 2 1 0.185 -0.017 -0.017 -1.000 -1.000
## 121 AEC01 ~~ AEC02 2 2 1 0.073 0.167 0.167 0.146 0.146
## 112 AEC04 ~~ AEC01 1 1 1 0.062 -0.167 -0.167 -0.167 -0.167
## 113 AEC04 ~~ AEC02 1 1 1 0.053 -0.182 -0.182 -0.182 -0.182
## 119 AEC04 ~~ AEC02 2 2 1 0.049 0.220 0.220 1.330 1.330
## 120 AEC04 ~~ AEC03 2 2 1 0.021 -0.079 -0.079 -0.463 -0.463
## 35 AEC01 ~*~ AEC01 1 1 1 0.008 -0.004 -0.004 -1.000 -1.000
## 77 AEC01 ~*~ AEC01 2 2 1 0.008 0.004 0.004 1.000 1.000
## 123 AEC02 ~~ AEC03 2 2 1 0.000 0.001 0.001 0.001 0.001semTools::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`
## AEC
## alpha 0.9189
## alpha.ord 0.9347
## omega 0.9169
## omega2 0.9169
## omega3 0.9173
## avevar 0.8561
##
## $`1`
## AEC
## alpha 0.9351
## alpha.ord 0.9382
## omega 0.9235
## omega2 0.9235
## omega3 0.9215
## avevar 0.88097.1.1.3.1 Checking Latent Differences
partial<-partialInvarianceCat(invariance,type="means",return.fit = F)## Warning in lav_object_post_check(object): lavaan WARNING: some estimated ov
## variances are negativepartial## $estimates
## poolest mean:2 mean:1 std:2 std:1 diff_std:1 vs. 2
## AEC~1 0 0 1.26 0 0.3652 0.3652
##
## $results
## free.chi free.df free.p free.cfi fix.chi fix.df fix.p fix.cfi wald.chi
## AEC~1 4.01 1 0.04524 -0.1343 4.01 1 0.04524 -0.1343 NA
## wald.df wald.p
## AEC~1 NA NA7.1.1.4 Education Invariance Model
data$EscClasseR<-as.factor(data$EscClasse)
model <- 'AEC =~ AEC04 + AEC02 + AEC03 + AEC01'7.1.1.5 Fitting
invariance<- measurementInvarianceCat(model = model, data = data, group = "EscClasseR",parameterization = "theta", estimator = "ULSMV",ordered = c("AEC01", "AEC02", "AEC03", "AEC04"),missing="pairwise")## Warning: The measurementInvarianceCat function is deprecated, and it will cease
## to be included in future versions of semTools. See help('semTools-deprecated)
## for details.## Warning in lav_object_post_check(object): lavaan WARNING: some estimated ov
## variances are negative##
## Measurement invariance models:
##
## Model 1 : fit.configural
## Model 2 : fit.loadings
## Model 3 : fit.thresholds
## Model 4 : fit.means
##
## Scaled Chi-Squared Difference Test (method = "satorra.2000")
##
## lavaan NOTE:
## The "Chisq" column contains standard test statistics, not the
## robust test that should be reported per model. A robust difference
## test is a function of two standard (not robust) statistics.
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## fit.configural 6 2.26
## fit.loadings 12 5.35 4.5 6 0.61
## fit.thresholds 50 60.30 34.5 38 0.63
## fit.means 52 108.21 2.0 2 0.37
##
##
## Fit measures:
##
## cfi.scaled rmsea.scaled cfi.scaled.delta rmsea.scaled.delta
## fit.configural 0.995 0.2 NA NA
## fit.loadings 1.000 0.0 0.005 0.2
## fit.thresholds 1.000 0.0 0.000 0.0
## fit.means 1.000 0.0 0.000 0.07.1.1.5.1 Configural
summary(invariance$fit.configural,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 453 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 94
## Number of equality constraints 10
##
## Number of observations per group:
## 1 90
## 2 190
## 3 250
## Number of missing patterns per group:
## 1 1
## 2 1
## 3 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 2.257 48.158
## Degrees of freedom 6 6
## P-value (Unknown) NA 0.000
## Scaling correction factor 0.048
## Shift parameter for each group:
## 1 0.151
## 2 0.320
## 3 0.421
## simple second-order correction
## Test statistic for each group:
## 1 1.200 25.281
## 2 0.218 4.890
## 3 0.839 17.986
##
## Model Test Baseline Model:
##
## Test statistic 2009.846 8858.756
## Degrees of freedom 18 18
## P-value NA 0.000
## Scaling correction factor 0.227
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 0.995
## Tucker-Lewis Index (TLI) 1.006 0.986
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000 0.200
## 90 Percent confidence interval - lower 0.000 0.150
## 90 Percent confidence interval - upper 0.044 0.254
## P-value RMSEA <= 0.05 0.960 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
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC =~
## AEC04 1.000 3.657 0.965
## AEC02 0.721 0.182 3.965 0.000 2.636 0.935
## AEC03 0.321 0.076 4.227 0.000 1.174 0.761
## AEC01 0.538 0.122 4.407 0.000 1.969 0.892
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## AEC 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -6.953 1.763 -3.944 0.000 -6.953 -1.834
## AEC04|t2 -4.628 1.047 -4.418 0.000 -4.628 -1.221
## AEC04|t3 -1.070 0.475 -2.254 0.024 -1.070 -0.282
## AEC04|t4 1.868 0.646 2.891 0.004 1.868 0.493
## AEC04|t5 4.859 1.040 4.671 0.000 4.859 1.282
## AEC04|t6 5.691 1.141 4.986 0.000 5.691 1.501
## AEC02|t1 -5.666 0.996 -5.686 0.000 -5.666 -2.010
## AEC02|t2 -3.613 0.640 -5.643 0.000 -3.613 -1.282
## AEC02|t3 -1.569 0.424 -3.700 0.000 -1.569 -0.557
## AEC02|t4 1.044 0.401 2.602 0.009 1.044 0.370
## AEC02|t5 2.727 0.459 5.939 0.000 2.727 0.967
## AEC02|t6 4.232 0.415 10.206 0.000 4.232 1.501
## AEC03|t1 -2.624 0.268 -9.789 0.000 -2.624 -1.701
## AEC03|t2 -1.977 0.225 -8.792 0.000 -1.977 -1.282
## AEC03|t3 -0.303 0.207 -1.459 0.144 -0.303 -0.196
## AEC03|t4 0.809 0.209 3.879 0.000 0.809 0.524
## AEC03|t5 1.636 0.245 6.676 0.000 1.636 1.061
## AEC03|t6 2.079 0.278 7.478 0.000 2.079 1.348
## AEC01|t1 -4.439 0.653 -6.801 0.000 -4.439 -2.010
## AEC01|t2 -2.237 0.353 -6.329 0.000 -2.237 -1.013
## AEC01|t3 -0.752 0.299 -2.513 0.012 -0.752 -0.341
## AEC01|t4 1.019 0.310 3.286 0.001 1.019 0.461
## AEC01|t5 2.696 0.376 7.166 0.000 2.696 1.221
## AEC01|t6 3.757 0.404 9.305 0.000 3.757 1.701
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 1.000 1.000 0.070
## .AEC02 1.000 1.000 0.126
## .AEC03 1.000 1.000 0.420
## .AEC01 1.000 1.000 0.205
## AEC 13.374 5.839 2.291 0.022 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.264 0.264 1.000
## AEC02 0.355 0.355 1.000
## AEC03 0.648 0.648 1.000
## AEC01 0.453 0.453 1.000
##
## R-Square:
## Estimate
## AEC04 0.930
## AEC02 0.874
## AEC03 0.580
## AEC01 0.795
##
##
## Group 2 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC =~
## AEC04 1.000 1.926 0.978
## AEC02 0.884 0.211 4.184 0.000 1.703 0.922
## AEC03 0.344 0.081 4.242 0.000 0.662 0.777
## AEC01 0.688 0.151 4.552 0.000 1.326 0.864
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## AEC -1.916 1.506 -1.272 0.203 -0.995 -0.995
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -6.953 1.763 -3.944 0.000 -6.953 -3.531
## AEC04|t2 -4.628 1.047 -4.418 0.000 -4.628 -2.350
## AEC04|t3 -3.163 1.101 -2.874 0.004 -3.163 -1.606
## AEC04|t4 -1.309 1.759 -0.744 0.457 -1.309 -0.665
## AEC04|t5 0.103 2.420 0.043 0.966 0.103 0.052
## AEC04|t6 1.095 2.915 0.376 0.707 1.095 0.556
## AEC02|t1 -5.666 0.996 -5.686 0.000 -5.666 -3.066
## AEC02|t2 -4.443 0.809 -5.491 0.000 -4.443 -2.404
## AEC02|t3 -3.082 0.936 -3.294 0.001 -3.082 -1.668
## AEC02|t4 -1.099 1.629 -0.674 0.500 -1.099 -0.594
## AEC02|t5 0.201 2.181 0.092 0.927 0.201 0.109
## AEC02|t6 1.131 2.594 0.436 0.663 1.131 0.612
## AEC03|t1 -2.624 0.268 -9.789 0.000 -2.624 -3.080
## AEC03|t2 -1.725 0.304 -5.675 0.000 -1.725 -2.025
## AEC03|t3 -1.017 0.478 -2.126 0.034 -1.017 -1.194
## AEC03|t4 -0.336 0.699 -0.480 0.631 -0.336 -0.394
## AEC03|t5 0.274 0.910 0.301 0.763 0.274 0.322
## AEC03|t6 0.644 1.043 0.618 0.537 0.644 0.756
## AEC01|t1 -4.439 0.653 -6.801 0.000 -4.439 -2.892
## AEC01|t2 -3.433 0.536 -6.407 0.000 -3.433 -2.237
## AEC01|t3 -2.267 0.741 -3.061 0.002 -2.267 -1.477
## AEC01|t4 -0.443 1.442 -0.308 0.758 -0.443 -0.289
## AEC01|t5 0.517 1.853 0.279 0.780 0.517 0.337
## AEC01|t6 1.028 2.077 0.495 0.621 1.028 0.670
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.168 0.190 0.885 0.376 0.168 0.043
## .AEC02 0.515 0.477 1.080 0.280 0.515 0.151
## .AEC03 0.288 0.211 1.364 0.173 0.288 0.397
## .AEC01 0.598 0.532 1.123 0.261 0.598 0.254
## AEC 3.709 3.975 0.933 0.351 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.508 0.508 1.000
## AEC02 0.541 0.541 1.000
## AEC03 1.174 1.174 1.000
## AEC01 0.651 0.651 1.000
##
## R-Square:
## Estimate
## AEC04 0.957
## AEC02 0.849
## AEC03 0.603
## AEC01 0.746
##
##
## Group 3 [3]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC =~
## AEC04 1.000 2.139 0.978
## AEC02 0.847 0.204 4.148 0.000 1.810 0.929
## AEC03 0.334 0.082 4.071 0.000 0.714 0.769
## AEC01 0.690 0.151 4.577 0.000 1.475 0.914
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## AEC -1.151 1.874 -0.614 0.539 -0.538 -0.538
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -6.953 1.763 -3.944 0.000 -6.953 -3.178
## AEC04|t2 -4.628 1.047 -4.418 0.000 -4.628 -2.115
## AEC04|t3 -2.640 1.266 -2.085 0.037 -2.640 -1.207
## AEC04|t4 -0.272 2.291 -0.119 0.905 -0.272 -0.125
## AEC04|t5 1.509 3.196 0.472 0.637 1.509 0.690
## AEC04|t6 2.179 3.548 0.614 0.539 2.179 0.996
## AEC02|t1 -5.666 0.996 -5.686 0.000 -5.666 -2.909
## AEC02|t2 -4.217 0.810 -5.204 0.000 -4.217 -2.165
## AEC02|t3 -2.976 0.938 -3.173 0.002 -2.976 -1.528
## AEC02|t4 -0.318 1.918 -0.166 0.868 -0.318 -0.163
## AEC02|t5 1.130 2.553 0.443 0.658 1.130 0.580
## AEC02|t6 1.711 2.815 0.608 0.543 1.711 0.878
## AEC03|t1 -2.624 0.268 -9.789 0.000 -2.624 -2.822
## AEC03|t2 -1.620 0.324 -5.003 0.000 -1.620 -1.742
## AEC03|t3 -0.861 0.524 -1.643 0.100 -0.861 -0.927
## AEC03|t4 0.040 0.825 0.048 0.961 0.040 0.043
## AEC03|t5 0.851 1.116 0.762 0.446 0.851 0.915
## AEC03|t6 1.163 1.231 0.945 0.345 1.163 1.251
## AEC01|t1 -4.439 0.653 -6.801 0.000 -4.439 -2.749
## AEC01|t2 -3.107 0.561 -5.538 0.000 -3.107 -1.924
## AEC01|t3 -1.893 0.892 -2.122 0.034 -1.893 -1.173
## AEC01|t4 -0.128 1.620 -0.079 0.937 -0.128 -0.079
## AEC01|t5 1.136 2.183 0.520 0.603 1.136 0.703
## AEC01|t6 1.565 2.379 0.658 0.511 1.565 0.969
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.212 0.236 0.900 0.368 0.212 0.044
## .AEC02 0.516 0.488 1.057 0.290 0.516 0.136
## .AEC03 0.354 0.264 1.341 0.180 0.354 0.409
## .AEC01 0.430 0.405 1.064 0.287 0.430 0.165
## AEC 4.574 5.011 0.913 0.361 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.457 0.457 1.000
## AEC02 0.513 0.513 1.000
## AEC03 1.076 1.076 1.000
## AEC01 0.619 0.619 1.000
##
## R-Square:
## Estimate
## AEC04 0.956
## AEC02 0.864
## AEC03 0.591
## AEC01 0.835lavaan::fitMeasures(invariance$fit.configural,c("chisq.scaled","df.scaled","pvalue","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue
## 48.158 6.000 NA
## srmr cfi.scaled tli.scaled
## 0.019 0.995 0.986
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.200 0.150 0.254modificationindices(invariance$fit.configural, sort.=T)## lhs op rhs block group level mi epc sepc.lv sepc.all sepc.nox
## 141 AEC02 ~~ AEC01 1 1 1 1.185 1.329 1.329 1.329 1.329
## 138 AEC04 ~~ AEC03 1 1 1 1.185 1.099 1.099 1.099 1.099
## 151 AEC04 ~~ AEC01 3 3 1 0.754 -0.380 -0.380 -1.258 -1.258
## 152 AEC02 ~~ AEC03 3 3 1 0.754 -0.156 -0.156 -0.365 -0.365
## 150 AEC04 ~~ AEC03 3 3 1 0.468 0.144 0.144 0.527 0.527
## 153 AEC02 ~~ AEC01 3 3 1 0.468 0.252 0.252 0.535 0.535
## 139 AEC04 ~~ AEC01 1 1 1 0.339 -0.988 -0.988 -0.988 -0.988
## 140 AEC02 ~~ AEC03 1 1 1 0.339 -0.425 -0.425 -0.425 -0.425
## 142 AEC03 ~~ AEC01 1 1 1 0.262 -0.281 -0.281 -0.281 -0.281
## 137 AEC04 ~~ AEC02 1 1 1 0.262 -1.170 -1.170 -1.170 -1.170
## 146 AEC02 ~~ AEC03 2 2 1 0.201 -0.082 -0.082 -0.214 -0.214
## 145 AEC04 ~~ AEC01 2 2 1 0.201 -0.187 -0.187 -0.588 -0.588
## 143 AEC04 ~~ AEC02 2 2 1 0.109 0.178 0.178 0.605 0.605
## 148 AEC03 ~~ AEC01 2 2 1 0.109 0.048 0.048 0.115 0.115
## 149 AEC04 ~~ AEC02 3 3 1 0.033 0.098 0.098 0.296 0.296
## 154 AEC03 ~~ AEC01 3 3 1 0.033 0.027 0.027 0.068 0.068
## 144 AEC04 ~~ AEC03 2 2 1 0.014 0.025 0.025 0.113 0.113
## 147 AEC02 ~~ AEC01 2 2 1 0.014 0.044 0.044 0.079 0.079semTools::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.## $`1`
## AEC
## alpha 0.9251
## alpha.ord 0.9365
## omega 0.9198
## omega2 0.9198
## omega3 0.9198
## avevar 0.8648
##
## $`2`
## AEC
## alpha 0.9191
## alpha.ord 0.9347
## omega 0.9134
## omega2 0.9134
## omega3 0.9133
## avevar 0.8487
##
## $`3`
## AEC
## alpha 0.9327
## alpha.ord 0.9423
## omega 0.9233
## omega2 0.9233
## omega3 0.9232
## avevar 0.87457.1.1.5.2 Loadings
summary(invariance$fit.loadings,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 363 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 94
## Number of equality constraints 16
##
## Number of observations per group:
## 1 90
## 2 190
## 3 250
## Number of missing patterns per group:
## 1 1
## 2 1
## 3 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 5.353 11.559
## Degrees of freedom 12 12
## P-value (Unknown) NA 0.482
## Scaling correction factor 0.602
## Shift parameter for each group:
## 1 0.453
## 2 0.957
## 3 1.259
## simple second-order correction
## Test statistic for each group:
## 1 3.739 6.662
## 2 0.525 1.828
## 3 1.089 3.069
##
## Model Test Baseline Model:
##
## Test statistic 2009.846 8858.756
## Degrees of freedom 18 18
## P-value NA 0.000
## Scaling correction factor 0.227
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 1.000
## Tucker-Lewis Index (TLI) 1.005 1.000
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000 0.000
## 90 Percent confidence interval - lower 0.000 0.000
## 90 Percent confidence interval - upper 0.012 0.075
## P-value RMSEA <= 0.05 0.990 0.797
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower 0.000
## 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 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC =~
## AEC04 1.000 1.854 0.880
## AEC02 2.238 1.664 1.345 0.179 4.150 0.972
## AEC03 0.564 0.161 3.500 0.000 1.045 0.723
## AEC01 2.093 1.471 1.423 0.155 3.881 0.968
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## AEC 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -3.951 0.872 -4.533 0.000 -3.951 -1.876
## AEC04|t2 -2.614 0.589 -4.440 0.000 -2.614 -1.241
## AEC04|t3 -0.595 0.296 -2.005 0.045 -0.595 -0.282
## AEC04|t4 1.038 0.338 3.073 0.002 1.038 0.493
## AEC04|t5 2.700 0.569 4.745 0.000 2.700 1.282
## AEC04|t6 3.162 0.645 4.901 0.000 3.162 1.501
## AEC02|t1 -8.479 5.547 -1.529 0.126 -8.479 -1.986
## AEC02|t2 -5.471 3.324 -1.646 0.100 -5.471 -1.282
## AEC02|t3 -2.376 1.485 -1.600 0.110 -2.376 -0.557
## AEC02|t4 1.581 1.101 1.436 0.151 1.581 0.370
## AEC02|t5 4.130 2.464 1.676 0.094 4.130 0.967
## AEC02|t6 6.408 3.656 1.753 0.080 6.408 1.501
## AEC03|t1 -2.501 0.336 -7.444 0.000 -2.501 -1.729
## AEC03|t2 -1.854 0.288 -6.429 0.000 -1.854 -1.282
## AEC03|t3 -0.284 0.196 -1.452 0.147 -0.284 -0.196
## AEC03|t4 0.759 0.202 3.749 0.000 0.759 0.524
## AEC03|t5 1.534 0.249 6.158 0.000 1.534 1.061
## AEC03|t6 1.950 0.287 6.791 0.000 1.950 1.348
## AEC01|t1 -7.843 4.663 -1.682 0.093 -7.843 -1.957
## AEC01|t2 -4.059 2.238 -1.814 0.070 -4.059 -1.013
## AEC01|t3 -1.365 0.873 -1.564 0.118 -1.365 -0.341
## AEC01|t4 1.850 1.114 1.660 0.097 1.850 0.461
## AEC01|t5 4.892 2.570 1.903 0.057 4.892 1.221
## AEC01|t6 6.818 3.432 1.986 0.047 6.818 1.701
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 1.000 1.000 0.225
## .AEC02 1.000 1.000 0.055
## .AEC03 1.000 1.000 0.478
## .AEC01 1.000 1.000 0.062
## AEC 3.438 1.579 2.177 0.029 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.475 0.475 1.000
## AEC02 0.234 0.234 1.000
## AEC03 0.691 0.691 1.000
## AEC01 0.250 0.250 1.000
##
## R-Square:
## Estimate
## AEC04 0.775
## AEC02 0.945
## AEC03 0.522
## AEC01 0.938
##
##
## Group 2 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC =~
## AEC04 1.000 1.143 1.001
## AEC02 2.238 1.664 1.345 0.179 2.558 0.901
## AEC03 0.564 0.161 3.500 0.000 0.644 0.777
## AEC01 2.093 1.471 1.423 0.155 2.392 0.860
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## AEC -1.044 0.814 -1.283 0.199 -0.914 -0.914
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -3.951 0.872 -4.533 0.000 -3.951 -3.463
## AEC04|t2 -2.614 0.589 -4.440 0.000 -2.614 -2.291
## AEC04|t3 -1.767 0.617 -2.863 0.004 -1.767 -1.549
## AEC04|t4 -0.693 0.939 -0.737 0.461 -0.693 -0.607
## AEC04|t5 0.126 1.273 0.099 0.921 0.126 0.110
## AEC04|t6 0.700 1.527 0.458 0.647 0.700 0.614
## AEC02|t1 -8.479 5.547 -1.529 0.126 -8.479 -2.985
## AEC02|t2 -6.563 4.279 -1.534 0.125 -6.563 -2.311
## AEC02|t3 -4.470 2.974 -1.503 0.133 -4.470 -1.574
## AEC02|t4 -1.423 2.229 -0.638 0.523 -1.423 -0.501
## AEC02|t5 0.574 2.991 0.192 0.848 0.574 0.202
## AEC02|t6 2.005 3.874 0.517 0.605 2.005 0.706
## AEC03|t1 -2.501 0.336 -7.444 0.000 -2.501 -3.017
## AEC03|t2 -1.627 0.302 -5.387 0.000 -1.627 -1.962
## AEC03|t3 -0.938 0.411 -2.279 0.023 -0.938 -1.131
## AEC03|t4 -0.275 0.594 -0.464 0.643 -0.275 -0.332
## AEC03|t5 0.319 0.778 0.409 0.682 0.319 0.384
## AEC03|t6 0.678 0.898 0.756 0.450 0.678 0.819
## AEC01|t1 -7.843 4.663 -1.682 0.093 -7.843 -2.820
## AEC01|t2 -6.016 3.553 -1.693 0.090 -6.016 -2.163
## AEC01|t3 -3.903 2.382 -1.639 0.101 -3.903 -1.404
## AEC01|t4 -0.600 2.255 -0.266 0.790 -0.600 -0.216
## AEC01|t5 1.141 3.149 0.362 0.717 1.141 0.410
## AEC01|t6 2.066 3.735 0.553 0.580 2.066 0.743
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 -0.004 0.108 -0.035 0.972 -0.004 -0.003
## .AEC02 1.524 2.551 0.597 0.550 1.524 0.189
## .AEC03 0.272 0.192 1.414 0.157 0.272 0.396
## .AEC01 2.013 3.175 0.634 0.526 2.013 0.260
## AEC 1.306 1.220 1.070 0.284 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.876 0.876 1.000
## AEC02 0.352 0.352 1.000
## AEC03 1.206 1.206 1.000
## AEC01 0.360 0.360 1.000
##
## R-Square:
## Estimate
## AEC04 NA
## AEC02 0.811
## AEC03 0.604
## AEC01 0.740
##
##
## Group 3 [3]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC =~
## AEC04 1.000 1.232 0.982
## AEC02 2.238 1.664 1.345 0.179 2.758 0.936
## AEC03 0.564 0.161 3.500 0.000 0.695 0.777
## AEC01 2.093 1.471 1.423 0.155 2.579 0.895
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## AEC -0.623 0.981 -0.635 0.526 -0.505 -0.505
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -3.951 0.872 -4.533 0.000 -3.951 -3.148
## AEC04|t2 -2.614 0.589 -4.440 0.000 -2.614 -2.083
## AEC04|t3 -1.477 0.687 -2.150 0.032 -1.477 -1.177
## AEC04|t4 -0.119 1.189 -0.100 0.920 -0.119 -0.095
## AEC04|t5 0.903 1.646 0.549 0.583 0.903 0.720
## AEC04|t6 1.287 1.824 0.706 0.480 1.287 1.026
## AEC02|t1 -8.479 5.547 -1.529 0.126 -8.479 -2.878
## AEC02|t2 -6.298 4.141 -1.521 0.128 -6.298 -2.138
## AEC02|t3 -4.422 2.962 -1.493 0.135 -4.422 -1.501
## AEC02|t4 -0.401 2.579 -0.155 0.877 -0.401 -0.136
## AEC02|t5 1.789 3.821 0.468 0.640 1.789 0.607
## AEC02|t6 2.668 4.428 0.603 0.547 2.668 0.906
## AEC03|t1 -2.501 0.336 -7.444 0.000 -2.501 -2.796
## AEC03|t2 -1.539 0.315 -4.881 0.000 -1.539 -1.721
## AEC03|t3 -0.810 0.455 -1.781 0.075 -0.810 -0.906
## AEC03|t4 0.057 0.712 0.080 0.936 0.057 0.064
## AEC03|t5 0.837 0.971 0.862 0.389 0.837 0.936
## AEC03|t6 1.138 1.075 1.058 0.290 1.138 1.272
## AEC01|t1 -7.843 4.663 -1.682 0.093 -7.843 -2.722
## AEC01|t2 -5.432 3.165 -1.716 0.086 -5.432 -1.885
## AEC01|t3 -3.266 2.140 -1.526 0.127 -3.266 -1.133
## AEC01|t4 -0.115 2.530 -0.045 0.964 -0.115 -0.040
## AEC01|t5 2.141 3.853 0.556 0.578 2.141 0.743
## AEC01|t6 2.907 4.370 0.665 0.506 2.907 1.009
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.057 0.137 0.416 0.678 0.057 0.036
## .AEC02 1.074 1.863 0.576 0.564 1.074 0.124
## .AEC03 0.317 0.225 1.411 0.158 0.317 0.397
## .AEC01 1.654 2.541 0.651 0.515 1.654 0.199
## AEC 1.518 1.452 1.045 0.296 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.797 0.797 1.000
## AEC02 0.339 0.339 1.000
## AEC03 1.118 1.118 1.000
## AEC01 0.347 0.347 1.000
##
## R-Square:
## Estimate
## AEC04 0.964
## AEC02 0.876
## AEC03 0.603
## AEC01 0.801lavaan::fitMeasures(invariance$fit.loadings,c("chisq.scaled","df.scaled","pvalue","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue
## 11.559 12.000 NA
## srmr cfi.scaled tli.scaled
## 0.025 1.000 1.000
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.000 0.000 0.075modificationindices(invariance$fit.loadings, sort.=T)## lhs op rhs block group level mi epc sepc.lv sepc.all sepc.nox
## 144 AEC04 ~~ AEC03 1 1 1 3.347 0.677 0.677 0.677 0.677
## 38 AEC04 ~1 1 1 1 1.837 -0.703 -0.703 -0.334 -0.334
## 34 AEC04 ~*~ AEC04 1 1 1 1.508 -0.078 -0.078 -1.000 -1.000
## 1 AEC =~ AEC04 1 1 1 1.508 0.164 0.304 0.144 0.144
## 37 AEC01 ~*~ AEC01 1 1 1 1.504 0.041 0.041 1.000 1.000
## 41 AEC01 ~1 1 1 1 1.504 1.283 1.283 0.320 0.320
## 158 AEC02 ~~ AEC03 3 3 1 0.961 -0.212 -0.212 -0.363 -0.363
## 159 AEC02 ~~ AEC01 3 3 1 0.569 0.555 0.555 0.416 0.416
## 121 AEC01 ~*~ AEC01 3 3 1 0.447 -0.023 -0.023 -1.000 -1.000
## 125 AEC01 ~1 3 3 1 0.447 -0.425 -0.425 -0.148 -0.148
## 80 AEC04 ~1 2 2 1 0.425 0.207 0.207 0.182 0.182
## 151 AEC04 ~~ AEC01 2 2 1 0.423 -0.211 -0.211 -2.407 -2.407
## 148 AEC03 ~~ AEC01 1 1 1 0.404 -0.464 -0.464 -0.464 -0.464
## 43 AEC =~ AEC04 2 2 1 0.398 -0.052 -0.059 -0.052 -0.052
## 76 AEC04 ~*~ AEC04 2 2 1 0.384 0.060 0.060 1.000 1.000
## 36 AEC03 ~*~ AEC03 1 1 1 0.368 -0.061 -0.061 -1.000 -1.000
## 40 AEC03 ~1 1 1 1 0.368 -0.219 -0.219 -0.151 -0.151
## 81 AEC02 ~1 2 2 1 0.336 -0.400 -0.400 -0.141 -0.141
## 77 AEC02 ~*~ AEC02 2 2 1 0.336 -0.023 -0.023 -1.000 -1.000
## 39 AEC02 ~1 1 1 1 0.310 0.628 0.628 0.147 0.147
## 35 AEC02 ~*~ AEC02 1 1 1 0.310 0.017 0.017 1.000 1.000
## 147 AEC02 ~~ AEC01 1 1 1 0.307 -1.302 -1.302 -1.302 -1.302
## 153 AEC02 ~~ AEC01 2 2 1 0.231 0.366 0.366 0.209 0.209
## 146 AEC02 ~~ AEC03 1 1 1 0.111 -0.260 -0.260 -0.260 -0.260
## 124 AEC03 ~1 3 3 1 0.110 0.072 0.072 0.081 0.081
## 120 AEC03 ~*~ AEC03 3 3 1 0.110 0.037 0.037 1.000 1.000
## 154 AEC03 ~~ AEC01 2 2 1 0.100 0.066 0.066 0.089 0.089
## 156 AEC04 ~~ AEC03 3 3 1 0.099 0.029 0.029 0.218 0.218
## 157 AEC04 ~~ AEC01 3 3 1 0.090 -0.097 -0.097 -0.317 -0.317
## 145 AEC04 ~~ AEC01 1 1 1 0.085 -0.330 -0.330 -0.330 -0.330
## 160 AEC03 ~~ AEC01 3 3 1 0.085 0.060 0.060 0.083 0.083
## 150 AEC04 ~~ AEC03 2 2 1 0.062 -0.023 -0.023 -0.708 -0.708
## 123 AEC02 ~1 3 3 1 0.056 0.163 0.163 0.055 0.055
## 119 AEC02 ~*~ AEC02 3 3 1 0.056 0.008 0.008 1.000 1.000
## 143 AEC04 ~~ AEC02 1 1 1 0.053 0.276 0.276 0.276 0.276
## 149 AEC04 ~~ AEC02 2 2 1 0.049 0.075 0.075 0.983 0.983
## 122 AEC04 ~1 3 3 1 0.031 0.056 0.056 0.044 0.044
## 85 AEC =~ AEC04 3 3 1 0.014 -0.010 -0.012 -0.010 -0.010
## 118 AEC04 ~*~ AEC04 3 3 1 0.012 0.008 0.008 1.000 1.000
## 155 AEC04 ~~ AEC02 3 3 1 0.011 -0.036 -0.036 -0.144 -0.144
## 152 AEC02 ~~ AEC03 2 2 1 0.006 -0.018 -0.018 -0.027 -0.027
## 83 AEC01 ~1 2 2 1 0.006 -0.050 -0.050 -0.018 -0.018
## 79 AEC01 ~*~ AEC01 2 2 1 0.006 -0.003 -0.003 -1.000 -1.000
## 78 AEC03 ~*~ AEC03 2 2 1 0.001 0.004 0.004 1.000 1.000
## 82 AEC03 ~1 2 2 1 0.001 0.007 0.007 0.009 0.009semTools::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.## $`1`
## AEC
## alpha 0.9251
## alpha.ord 0.9365
## omega 0.9193
## omega2 0.9193
## omega3 0.9145
## avevar 0.9020
##
## $`2`
## AEC
## alpha 0.9191
## alpha.ord 0.9347
## omega 0.9175
## omega2 0.9175
## omega3 0.9170
## avevar 0.7861
##
## $`3`
## AEC
## alpha 0.9327
## alpha.ord 0.9423
## omega 0.9233
## omega2 0.9233
## omega3 0.9231
## avevar 0.83987.1.1.5.3 Thresholds
summary(invariance$fit.thresholds,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 200 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 94
## Number of equality constraints 54
##
## Number of observations per group:
## 1 90
## 2 190
## 3 250
## Number of missing patterns per group:
## 1 1
## 2 1
## 3 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 60.295 42.772
## Degrees of freedom 50 50
## P-value (Unknown) NA 0.756
## Scaling correction factor 2.735
## Shift parameter for each group:
## 1 3.520
## 2 7.431
## 3 9.778
## simple second-order correction
## Test statistic for each group:
## 1 28.927 14.095
## 2 18.803 14.305
## 3 12.565 14.372
##
## Model Test Baseline Model:
##
## Test statistic 2009.846 8858.756
## Degrees of freedom 18 18
## P-value NA 0.000
## Scaling correction factor 0.227
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.995 1.000
## Tucker-Lewis Index (TLI) 0.998 1.000
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.034 0.000
## 90 Percent confidence interval - lower 0.000 0.000
## 90 Percent confidence interval - upper 0.062 0.036
## P-value RMSEA <= 0.05 0.799 0.992
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower 0.000
## 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 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC =~
## AEC04 1.000 2.822 0.943
## AEC02 0.997 0.452 2.206 0.027 2.814 0.942
## AEC03 0.366 0.126 2.894 0.004 1.033 0.718
## AEC01 1.010 0.522 1.935 0.053 2.851 0.944
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## AEC 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -6.005 1.843 -3.259 0.001 -6.005 -2.006
## AEC04|t2 -3.328 1.140 -2.919 0.004 -3.328 -1.111
## AEC04|t3 -1.127 0.513 -2.197 0.028 -1.127 -0.377
## AEC04|t4 1.416 0.559 2.533 0.011 1.416 0.473
## AEC04|t5 3.415 1.145 2.983 0.003 3.415 1.141
## AEC04|t6 4.353 1.423 3.059 0.002 4.353 1.454
## AEC02|t1 -5.732 1.461 -3.924 0.000 -5.732 -1.920
## AEC02|t2 -3.786 1.019 -3.714 0.000 -3.786 -1.268
## AEC02|t3 -1.917 0.622 -3.080 0.002 -1.917 -0.642
## AEC02|t4 1.344 0.423 3.180 0.001 1.344 0.450
## AEC02|t5 3.272 0.780 4.196 0.000 3.272 1.096
## AEC02|t6 4.381 1.019 4.298 0.000 4.381 1.467
## AEC03|t1 -2.583 0.255 -10.114 0.000 -2.583 -1.797
## AEC03|t2 -1.404 0.180 -7.801 0.000 -1.404 -0.976
## AEC03|t3 -0.366 0.134 -2.721 0.007 -0.366 -0.254
## AEC03|t4 0.689 0.155 4.447 0.000 0.689 0.480
## AEC03|t5 1.618 0.212 7.641 0.000 1.618 1.125
## AEC03|t6 2.057 0.246 8.346 0.000 2.057 1.431
## AEC01|t1 -5.711 1.525 -3.746 0.000 -5.711 -1.890
## AEC01|t2 -3.437 0.968 -3.550 0.000 -3.437 -1.138
## AEC01|t3 -1.309 0.506 -2.587 0.010 -1.309 -0.433
## AEC01|t4 1.790 0.541 3.306 0.001 1.790 0.592
## AEC01|t5 3.866 1.016 3.807 0.000 3.866 1.280
## AEC01|t6 4.795 1.250 3.836 0.000 4.795 1.587
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 1.000 1.000 0.112
## .AEC02 1.000 1.000 0.112
## .AEC03 1.000 1.000 0.484
## .AEC01 1.000 1.000 0.110
## AEC 7.964 5.379 1.481 0.139 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.334 0.334 1.000
## AEC02 0.335 0.335 1.000
## AEC03 0.696 0.696 1.000
## AEC01 0.331 0.331 1.000
##
## R-Square:
## Estimate
## AEC04 0.888
## AEC02 0.888
## AEC03 0.516
## AEC01 0.890
##
##
## Group 2 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC =~
## AEC04 1.000 2.557 0.982
## AEC02 0.997 0.452 2.206 0.027 2.549 0.909
## AEC03 0.366 0.126 2.894 0.004 0.935 0.762
## AEC01 1.010 0.522 1.935 0.053 2.583 0.886
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## AEC 0.429 0.408 1.051 0.293 0.168 0.168
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -6.005 1.843 -3.259 0.001 -6.005 -2.307
## AEC04|t2 -3.328 1.140 -2.919 0.004 -3.328 -1.278
## AEC04|t3 -1.127 0.513 -2.197 0.028 -1.127 -0.433
## AEC04|t4 1.416 0.559 2.533 0.011 1.416 0.544
## AEC04|t5 3.415 1.145 2.983 0.003 3.415 1.312
## AEC04|t6 4.353 1.423 3.059 0.002 4.353 1.672
## AEC02|t1 -5.732 1.461 -3.924 0.000 -5.732 -2.044
## AEC02|t2 -3.786 1.019 -3.714 0.000 -3.786 -1.350
## AEC02|t3 -1.917 0.622 -3.080 0.002 -1.917 -0.683
## AEC02|t4 1.344 0.423 3.180 0.001 1.344 0.479
## AEC02|t5 3.272 0.780 4.196 0.000 3.272 1.167
## AEC02|t6 4.381 1.019 4.298 0.000 4.381 1.562
## AEC03|t1 -2.583 0.255 -10.114 0.000 -2.583 -2.104
## AEC03|t2 -1.404 0.180 -7.801 0.000 -1.404 -1.143
## AEC03|t3 -0.366 0.134 -2.721 0.007 -0.366 -0.298
## AEC03|t4 0.689 0.155 4.447 0.000 0.689 0.561
## AEC03|t5 1.618 0.212 7.641 0.000 1.618 1.317
## AEC03|t6 2.057 0.246 8.346 0.000 2.057 1.675
## AEC01|t1 -5.711 1.525 -3.746 0.000 -5.711 -1.960
## AEC01|t2 -3.437 0.968 -3.550 0.000 -3.437 -1.180
## AEC01|t3 -1.309 0.506 -2.587 0.010 -1.309 -0.449
## AEC01|t4 1.790 0.541 3.306 0.001 1.790 0.614
## AEC01|t5 3.866 1.016 3.807 0.000 3.866 1.327
## AEC01|t6 4.795 1.250 3.836 0.000 4.795 1.646
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.241 0.437 0.552 0.581 0.241 0.036
## .AEC02 1.371 0.838 1.636 0.102 1.371 0.174
## .AEC03 0.633 0.171 3.708 0.000 0.633 0.420
## .AEC01 1.818 1.151 1.579 0.114 1.818 0.214
## AEC 6.537 4.239 1.542 0.123 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.384 0.384 1.000
## AEC02 0.357 0.357 1.000
## AEC03 0.814 0.814 1.000
## AEC01 0.343 0.343 1.000
##
## R-Square:
## Estimate
## AEC04 0.964
## AEC02 0.826
## AEC03 0.580
## AEC01 0.786
##
##
## Group 3 [3]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC =~
## AEC04 1.000 2.439 0.993
## AEC02 0.997 0.452 2.206 0.027 2.432 0.932
## AEC03 0.366 0.126 2.894 0.004 0.893 0.781
## AEC01 1.010 0.522 1.935 0.053 2.464 0.883
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## AEC 0.540 0.409 1.322 0.186 0.222 0.222
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -6.005 1.843 -3.259 0.001 -6.005 -2.444
## AEC04|t2 -3.328 1.140 -2.919 0.004 -3.328 -1.354
## AEC04|t3 -1.127 0.513 -2.197 0.028 -1.127 -0.459
## AEC04|t4 1.416 0.559 2.533 0.011 1.416 0.576
## AEC04|t5 3.415 1.145 2.983 0.003 3.415 1.390
## AEC04|t6 4.353 1.423 3.059 0.002 4.353 1.771
## AEC02|t1 -5.732 1.461 -3.924 0.000 -5.732 -2.198
## AEC02|t2 -3.786 1.019 -3.714 0.000 -3.786 -1.452
## AEC02|t3 -1.917 0.622 -3.080 0.002 -1.917 -0.735
## AEC02|t4 1.344 0.423 3.180 0.001 1.344 0.515
## AEC02|t5 3.272 0.780 4.196 0.000 3.272 1.255
## AEC02|t6 4.381 1.019 4.298 0.000 4.381 1.680
## AEC03|t1 -2.583 0.255 -10.114 0.000 -2.583 -2.262
## AEC03|t2 -1.404 0.180 -7.801 0.000 -1.404 -1.229
## AEC03|t3 -0.366 0.134 -2.721 0.007 -0.366 -0.320
## AEC03|t4 0.689 0.155 4.447 0.000 0.689 0.603
## AEC03|t5 1.618 0.212 7.641 0.000 1.618 1.416
## AEC03|t6 2.057 0.246 8.346 0.000 2.057 1.801
## AEC01|t1 -5.711 1.525 -3.746 0.000 -5.711 -2.046
## AEC01|t2 -3.437 0.968 -3.550 0.000 -3.437 -1.231
## AEC01|t3 -1.309 0.506 -2.587 0.010 -1.309 -0.469
## AEC01|t4 1.790 0.541 3.306 0.001 1.790 0.641
## AEC01|t5 3.866 1.016 3.807 0.000 3.866 1.385
## AEC01|t6 4.795 1.250 3.836 0.000 4.795 1.717
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.088 0.300 0.293 0.770 0.088 0.015
## .AEC02 0.888 0.526 1.688 0.091 0.888 0.130
## .AEC03 0.508 0.127 4.013 0.000 0.508 0.389
## .AEC01 1.722 0.934 1.844 0.065 1.722 0.221
## AEC 5.951 3.845 1.548 0.122 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.407 0.407 1.000
## AEC02 0.383 0.383 1.000
## AEC03 0.875 0.875 1.000
## AEC01 0.358 0.358 1.000
##
## R-Square:
## Estimate
## AEC04 0.985
## AEC02 0.870
## AEC03 0.611
## AEC01 0.779lavaan::fitMeasures(invariance$fit.thresholds,c("chisq.scaled","df.scaled","pvalue","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue
## 42.772 50.000 NA
## srmr cfi.scaled tli.scaled
## 0.025 1.000 1.000
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.000 0.000 0.036modificationindices(invariance$fit.thresholds, sort.=T)## lhs op rhs block group level mi epc sepc.lv sepc.all sepc.nox
## 124 AEC03 ~1 3 3 1 5.708 -0.115 -0.115 -0.101 -0.101
## 81 AEC02 ~1 2 2 1 4.955 -0.271 -0.271 -0.096 -0.096
## 80 AEC04 ~1 2 2 1 3.699 0.224 0.224 0.086 0.086
## 38 AEC04 ~1 1 1 1 3.190 -0.294 -0.294 -0.098 -0.098
## 82 AEC03 ~1 2 2 1 2.906 0.086 0.086 0.070 0.070
## 123 AEC02 ~1 3 3 1 2.119 0.169 0.169 0.065 0.065
## 182 AEC04 ~~ AEC03 1 1 1 1.907 0.719 0.719 0.719 0.719
## 125 AEC01 ~1 3 3 1 1.789 0.159 0.159 0.057 0.057
## 83 AEC01 ~1 2 2 1 1.734 -0.164 -0.164 -0.056 -0.056
## 40 AEC03 ~1 1 1 1 1.311 0.083 0.083 0.058 0.058
## 197 AEC02 ~~ AEC01 3 3 1 1.097 0.646 0.646 0.523 0.523
## 121 AEC01 ~*~ AEC01 3 3 1 1.081 -0.035 -0.035 -1.000 -1.000
## 196 AEC02 ~~ AEC03 3 3 1 0.985 -0.238 -0.238 -0.354 -0.354
## 39 AEC02 ~1 1 1 1 0.909 0.158 0.158 0.053 0.053
## 37 AEC01 ~*~ AEC01 1 1 1 0.670 0.034 0.034 1.000 1.000
## 189 AEC04 ~~ AEC01 2 2 1 0.602 -0.563 -0.563 -0.850 -0.850
## 183 AEC04 ~~ AEC01 1 1 1 0.518 -0.854 -0.854 -0.854 -0.854
## 36 AEC03 ~*~ AEC03 1 1 1 0.500 -0.065 -0.065 -1.000 -1.000
## 85 AEC =~ AEC04 3 3 1 0.477 -0.062 -0.151 -0.062 -0.062
## 122 AEC04 ~1 3 3 1 0.403 -0.071 -0.071 -0.029 -0.029
## 79 AEC01 ~*~ AEC01 2 2 1 0.382 0.021 0.021 1.000 1.000
## 43 AEC =~ AEC04 2 2 1 0.309 0.052 0.134 0.051 0.051
## 120 AEC03 ~*~ AEC03 3 3 1 0.239 0.041 0.041 1.000 1.000
## 118 AEC04 ~*~ AEC04 3 3 1 0.185 0.016 0.016 1.000 1.000
## 78 AEC03 ~*~ AEC03 2 2 1 0.183 -0.035 -0.035 -1.000 -1.000
## 198 AEC03 ~~ AEC01 3 3 1 0.154 0.099 0.099 0.105 0.105
## 187 AEC04 ~~ AEC02 2 2 1 0.143 0.267 0.267 0.464 0.464
## 186 AEC03 ~~ AEC01 1 1 1 0.141 -0.197 -0.197 -0.197 -0.197
## 77 AEC02 ~*~ AEC02 2 2 1 0.100 -0.011 -0.011 -1.000 -1.000
## 188 AEC04 ~~ AEC03 2 2 1 0.082 0.082 0.082 0.211 0.211
## 193 AEC04 ~~ AEC02 3 3 1 0.063 -0.144 -0.144 -0.517 -0.517
## 195 AEC04 ~~ AEC01 3 3 1 0.058 -0.145 -0.145 -0.372 -0.372
## 34 AEC04 ~*~ AEC04 1 1 1 0.052 -0.010 -0.010 -1.000 -1.000
## 1 AEC =~ AEC04 1 1 1 0.052 0.029 0.082 0.028 0.028
## 192 AEC03 ~~ AEC01 2 2 1 0.036 0.059 0.059 0.055 0.055
## 181 AEC04 ~~ AEC02 1 1 1 0.024 -0.180 -0.180 -0.180 -0.180
## 119 AEC02 ~*~ AEC02 3 3 1 0.017 0.005 0.005 1.000 1.000
## 76 AEC04 ~*~ AEC04 2 2 1 0.014 0.004 0.004 1.000 1.000
## 41 AEC01 ~1 1 1 1 0.012 -0.018 -0.018 -0.006 -0.006
## 35 AEC02 ~*~ AEC02 1 1 1 0.009 0.004 0.004 1.000 1.000
## 191 AEC02 ~~ AEC01 2 2 1 0.007 -0.061 -0.061 -0.039 -0.039
## 185 AEC02 ~~ AEC01 1 1 1 0.007 0.095 0.095 0.095 0.095
## 190 AEC02 ~~ AEC03 2 2 1 0.003 0.016 0.016 0.017 0.017
## 184 AEC02 ~~ AEC03 1 1 1 0.002 -0.022 -0.022 -0.022 -0.022
## 194 AEC04 ~~ AEC03 3 3 1 0.002 0.010 0.010 0.046 0.046semTools::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.## $`1`
## AEC
## alpha 0.9251
## alpha.ord 0.9365
## omega 0.9183
## omega2 0.9183
## omega3 0.9138
## avevar 0.8624
##
## $`2`
## AEC
## alpha 0.9191
## alpha.ord 0.9347
## omega 0.9169
## omega2 0.9169
## omega3 0.9162
## avevar 0.8351
##
## $`3`
## AEC
## alpha 0.9327
## alpha.ord 0.9423
## omega 0.9246
## omega2 0.9246
## omega3 0.9242
## avevar 0.85397.1.1.5.4 Partial Invariance - Means
summary(invariance$fit.means,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 167 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 92
## Number of equality constraints 54
##
## Number of observations per group:
## 1 90
## 2 190
## 3 250
## Number of missing patterns per group:
## 1 1
## 2 1
## 3 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 108.205 47.965
## Degrees of freedom 52 52
## P-value (Unknown) NA 0.633
## Scaling correction factor 5.025
## Shift parameter for each group:
## 1 4.488
## 2 9.475
## 3 12.467
## simple second-order correction
## Test statistic for each group:
## 1 67.255 17.873
## 2 18.063 13.070
## 3 22.886 17.022
##
## Model Test Baseline Model:
##
## Test statistic 2009.846 8858.756
## Degrees of freedom 18 18
## P-value NA 0.000
## Scaling correction factor 0.227
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.972 1.000
## Tucker-Lewis Index (TLI) 0.990 1.000
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.078 0.000
## 90 Percent confidence interval - lower 0.057 0.000
## 90 Percent confidence interval - upper 0.099 0.042
## P-value RMSEA <= 0.05 0.015 0.984
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower 0.000
## 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 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC =~
## AEC04 1.000 2.564 0.932
## AEC02 1.075 0.435 2.474 0.013 2.757 0.940
## AEC03 0.417 0.127 3.282 0.001 1.070 0.731
## AEC01 1.139 0.547 2.083 0.037 2.920 0.946
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## AEC 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -5.778 1.451 -3.982 0.000 -5.778 -2.099
## AEC04|t2 -3.375 0.929 -3.631 0.000 -3.375 -1.226
## AEC04|t3 -1.402 0.405 -3.466 0.001 -1.402 -0.510
## AEC04|t4 0.881 0.277 3.176 0.001 0.881 0.320
## AEC04|t5 2.673 0.756 3.533 0.000 2.673 0.971
## AEC04|t6 3.514 0.976 3.600 0.000 3.514 1.277
## AEC02|t1 -5.917 1.455 -4.066 0.000 -5.917 -2.018
## AEC02|t2 -4.048 1.002 -4.039 0.000 -4.048 -1.380
## AEC02|t3 -2.253 0.573 -3.929 0.000 -2.253 -0.768
## AEC02|t4 0.883 0.262 3.371 0.001 0.883 0.301
## AEC02|t5 2.736 0.687 3.982 0.000 2.736 0.933
## AEC02|t6 3.799 0.940 4.040 0.000 3.799 1.295
## AEC03|t1 -2.772 0.277 -10.011 0.000 -2.772 -1.893
## AEC03|t2 -1.580 0.173 -9.117 0.000 -1.580 -1.079
## AEC03|t3 -0.531 0.085 -6.280 0.000 -0.531 -0.363
## AEC03|t4 0.535 0.086 6.208 0.000 0.535 0.365
## AEC03|t5 1.473 0.163 9.044 0.000 1.473 1.006
## AEC03|t6 1.917 0.205 9.337 0.000 1.917 1.309
## AEC01|t1 -6.187 1.663 -3.721 0.000 -6.187 -2.004
## AEC01|t2 -3.896 1.057 -3.687 0.000 -3.896 -1.262
## AEC01|t3 -1.749 0.497 -3.518 0.000 -1.749 -0.567
## AEC01|t4 1.377 0.395 3.486 0.000 1.377 0.446
## AEC01|t5 3.471 0.946 3.670 0.000 3.471 1.124
## AEC01|t6 4.407 1.199 3.674 0.000 4.407 1.428
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 1.000 1.000 0.132
## .AEC02 1.000 1.000 0.116
## .AEC03 1.000 1.000 0.466
## .AEC01 1.000 1.000 0.105
## AEC 6.575 3.761 1.748 0.080 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.363 0.363 1.000
## AEC02 0.341 0.341 1.000
## AEC03 0.683 0.683 1.000
## AEC01 0.324 0.324 1.000
##
## R-Square:
## Estimate
## AEC04 0.868
## AEC02 0.884
## AEC03 0.534
## AEC01 0.895
##
##
## Group 2 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC =~
## AEC04 1.000 2.282 0.977
## AEC02 1.075 0.435 2.474 0.013 2.454 0.910
## AEC03 0.417 0.127 3.282 0.001 0.952 0.767
## AEC01 1.139 0.547 2.083 0.037 2.599 0.885
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## AEC 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -5.778 1.451 -3.982 0.000 -5.778 -2.475
## AEC04|t2 -3.375 0.929 -3.631 0.000 -3.375 -1.445
## AEC04|t3 -1.402 0.405 -3.466 0.001 -1.402 -0.601
## AEC04|t4 0.881 0.277 3.176 0.001 0.881 0.377
## AEC04|t5 2.673 0.756 3.533 0.000 2.673 1.145
## AEC04|t6 3.514 0.976 3.600 0.000 3.514 1.505
## AEC02|t1 -5.917 1.455 -4.066 0.000 -5.917 -2.195
## AEC02|t2 -4.048 1.002 -4.039 0.000 -4.048 -1.502
## AEC02|t3 -2.253 0.573 -3.929 0.000 -2.253 -0.836
## AEC02|t4 0.883 0.262 3.371 0.001 0.883 0.328
## AEC02|t5 2.736 0.687 3.982 0.000 2.736 1.015
## AEC02|t6 3.799 0.940 4.040 0.000 3.799 1.410
## AEC03|t1 -2.772 0.277 -10.011 0.000 -2.772 -2.232
## AEC03|t2 -1.580 0.173 -9.117 0.000 -1.580 -1.272
## AEC03|t3 -0.531 0.085 -6.280 0.000 -0.531 -0.428
## AEC03|t4 0.535 0.086 6.208 0.000 0.535 0.431
## AEC03|t5 1.473 0.163 9.044 0.000 1.473 1.186
## AEC03|t6 1.917 0.205 9.337 0.000 1.917 1.544
## AEC01|t1 -6.187 1.663 -3.721 0.000 -6.187 -2.107
## AEC01|t2 -3.896 1.057 -3.687 0.000 -3.896 -1.327
## AEC01|t3 -1.749 0.497 -3.518 0.000 -1.749 -0.596
## AEC01|t4 1.377 0.395 3.486 0.000 1.377 0.469
## AEC01|t5 3.471 0.946 3.670 0.000 3.471 1.182
## AEC01|t6 4.407 1.199 3.674 0.000 4.407 1.501
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.243 0.363 0.669 0.503 0.243 0.045
## .AEC02 1.244 0.786 1.583 0.113 1.244 0.171
## .AEC03 0.636 0.177 3.600 0.000 0.636 0.412
## .AEC01 1.869 1.227 1.523 0.128 1.869 0.217
## AEC 5.209 2.896 1.798 0.072 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.428 0.428 1.000
## AEC02 0.371 0.371 1.000
## AEC03 0.805 0.805 1.000
## AEC01 0.341 0.341 1.000
##
## R-Square:
## Estimate
## AEC04 0.955
## AEC02 0.829
## AEC03 0.588
## AEC01 0.783
##
##
## Group 3 [3]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC =~
## AEC04 1.000 2.168 0.989
## AEC02 1.075 0.435 2.474 0.013 2.331 0.935
## AEC03 0.417 0.127 3.282 0.001 0.904 0.785
## AEC01 1.139 0.547 2.083 0.037 2.469 0.880
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## AEC 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -5.778 1.451 -3.982 0.000 -5.778 -2.636
## AEC04|t2 -3.375 0.929 -3.631 0.000 -3.375 -1.539
## AEC04|t3 -1.402 0.405 -3.466 0.001 -1.402 -0.640
## AEC04|t4 0.881 0.277 3.176 0.001 0.881 0.402
## AEC04|t5 2.673 0.756 3.533 0.000 2.673 1.219
## AEC04|t6 3.514 0.976 3.600 0.000 3.514 1.603
## AEC02|t1 -5.917 1.455 -4.066 0.000 -5.917 -2.375
## AEC02|t2 -4.048 1.002 -4.039 0.000 -4.048 -1.625
## AEC02|t3 -2.253 0.573 -3.929 0.000 -2.253 -0.904
## AEC02|t4 0.883 0.262 3.371 0.001 0.883 0.354
## AEC02|t5 2.736 0.687 3.982 0.000 2.736 1.098
## AEC02|t6 3.799 0.940 4.040 0.000 3.799 1.525
## AEC03|t1 -2.772 0.277 -10.011 0.000 -2.772 -2.408
## AEC03|t2 -1.580 0.173 -9.117 0.000 -1.580 -1.372
## AEC03|t3 -0.531 0.085 -6.280 0.000 -0.531 -0.461
## AEC03|t4 0.535 0.086 6.208 0.000 0.535 0.464
## AEC03|t5 1.473 0.163 9.044 0.000 1.473 1.279
## AEC03|t6 1.917 0.205 9.337 0.000 1.917 1.665
## AEC01|t1 -6.187 1.663 -3.721 0.000 -6.187 -2.205
## AEC01|t2 -3.896 1.057 -3.687 0.000 -3.896 -1.388
## AEC01|t3 -1.749 0.497 -3.518 0.000 -1.749 -0.623
## AEC01|t4 1.377 0.395 3.486 0.000 1.377 0.491
## AEC01|t5 3.471 0.946 3.670 0.000 3.471 1.237
## AEC01|t6 4.407 1.199 3.674 0.000 4.407 1.570
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.107 0.234 0.457 0.647 0.107 0.022
## .AEC02 0.776 0.486 1.597 0.110 0.776 0.125
## .AEC03 0.508 0.130 3.920 0.000 0.508 0.383
## .AEC01 1.779 1.010 1.761 0.078 1.779 0.226
## AEC 4.700 2.603 1.806 0.071 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 0.456 0.456 1.000
## AEC02 0.401 0.401 1.000
## AEC03 0.868 0.868 1.000
## AEC01 0.356 0.356 1.000
##
## R-Square:
## Estimate
## AEC04 0.978
## AEC02 0.875
## AEC03 0.617
## AEC01 0.774lavaan::fitMeasures(invariance$fit.means,c("chisq.scaled","df.scaled","pvalue","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue
## 47.965 52.000 NA
## srmr cfi.scaled tli.scaled
## 0.025 1.000 1.000
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.000 0.000 0.042modificationindices(invariance$fit.means, sort.=T)## lhs op rhs block group level mi epc sepc.lv sepc.all sepc.nox
## 42 AEC ~1 1 1 1 43.429 -0.444 -0.173 -0.173 -0.173
## 38 AEC04 ~1 1 1 1 24.934 -0.639 -0.639 -0.232 -0.232
## 126 AEC ~1 3 3 1 20.067 0.204 0.094 0.094 0.094
## 123 AEC02 ~1 3 3 1 13.045 0.345 0.345 0.138 0.138
## 41 AEC01 ~1 1 1 1 12.745 -0.517 -0.517 -0.168 -0.168
## 125 AEC01 ~1 3 3 1 12.341 0.363 0.363 0.129 0.129
## 39 AEC02 ~1 1 1 1 6.995 -0.367 -0.367 -0.125 -0.125
## 81 AEC02 ~1 2 2 1 3.582 -0.190 -0.190 -0.071 -0.071
## 122 AEC04 ~1 3 3 1 3.300 0.152 0.152 0.069 0.069
## 40 AEC03 ~1 1 1 1 2.791 -0.113 -0.113 -0.077 -0.077
## 80 AEC04 ~1 2 2 1 2.257 0.131 0.131 0.056 0.056
## 82 AEC03 ~1 2 2 1 2.082 0.066 0.066 0.053 0.053
## 182 AEC04 ~~ AEC03 1 1 1 1.810 0.657 0.657 0.657 0.657
## 121 AEC01 ~*~ AEC01 3 3 1 1.354 -0.039 -0.039 -1.000 -1.000
## 196 AEC02 ~~ AEC03 3 3 1 1.257 -0.261 -0.261 -0.416 -0.416
## 197 AEC02 ~~ AEC01 3 3 1 1.111 0.628 0.628 0.535 0.535
## 83 AEC01 ~1 2 2 1 1.031 -0.110 -0.110 -0.037 -0.037
## 37 AEC01 ~*~ AEC01 1 1 1 0.699 0.035 0.035 1.000 1.000
## 189 AEC04 ~~ AEC01 2 2 1 0.458 -0.444 -0.444 -0.659 -0.659
## 120 AEC03 ~*~ AEC03 3 3 1 0.409 0.053 0.053 1.000 1.000
## 183 AEC04 ~~ AEC01 1 1 1 0.390 -0.694 -0.694 -0.694 -0.694
## 79 AEC01 ~*~ AEC01 2 2 1 0.326 0.019 0.019 1.000 1.000
## 186 AEC03 ~~ AEC01 1 1 1 0.271 -0.286 -0.286 -0.286 -0.286
## 36 AEC03 ~*~ AEC03 1 1 1 0.241 -0.044 -0.044 -1.000 -1.000
## 187 AEC04 ~~ AEC02 2 2 1 0.181 0.259 0.259 0.471 0.471
## 34 AEC04 ~*~ AEC04 1 1 1 0.175 -0.019 -0.019 -1.000 -1.000
## 1 AEC =~ AEC04 1 1 1 0.175 0.053 0.137 0.050 0.050
## 198 AEC03 ~~ AEC01 3 3 1 0.137 0.095 0.095 0.100 0.100
## 118 AEC04 ~*~ AEC04 3 3 1 0.094 0.013 0.013 1.000 1.000
## 85 AEC =~ AEC04 3 3 1 0.094 -0.029 -0.063 -0.029 -0.029
## 78 AEC03 ~*~ AEC03 2 2 1 0.087 -0.024 -0.024 -1.000 -1.000
## 124 AEC03 ~1 3 3 1 0.087 -0.013 -0.013 -0.011 -0.011
## 77 AEC02 ~*~ AEC02 2 2 1 0.080 -0.010 -0.010 -1.000 -1.000
## 188 AEC04 ~~ AEC03 2 2 1 0.070 0.069 0.069 0.177 0.177
## 193 AEC04 ~~ AEC02 3 3 1 0.056 -0.117 -0.117 -0.407 -0.407
## 119 AEC02 ~*~ AEC02 3 3 1 0.051 0.009 0.009 1.000 1.000
## 184 AEC02 ~~ AEC03 1 1 1 0.023 -0.078 -0.078 -0.078 -0.078
## 192 AEC03 ~~ AEC01 2 2 1 0.019 0.044 0.044 0.040 0.040
## 195 AEC04 ~~ AEC01 3 3 1 0.011 -0.057 -0.057 -0.131 -0.131
## 191 AEC02 ~~ AEC01 2 2 1 0.007 -0.061 -0.061 -0.040 -0.040
## 185 AEC02 ~~ AEC01 1 1 1 0.006 0.093 0.093 0.093 0.093
## 35 AEC02 ~*~ AEC02 1 1 1 0.003 0.003 0.003 1.000 1.000
## 190 AEC02 ~~ AEC03 2 2 1 0.002 -0.012 -0.012 -0.014 -0.014
## 194 AEC04 ~~ AEC03 3 3 1 0.001 0.005 0.005 0.023 0.023
## 84 AEC ~1 2 2 1 0.001 -0.001 -0.001 -0.001 -0.001
## 181 AEC04 ~~ AEC02 1 1 1 0.000 -0.011 -0.011 -0.011 -0.011
## 43 AEC =~ AEC04 2 2 1 0.000 0.000 -0.001 0.000 0.000
## 76 AEC04 ~*~ AEC04 2 2 1 0.000 0.000 0.000 1.000 1.000semTools::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.## $`1`
## AEC
## alpha 0.9251
## alpha.ord 0.9365
## omega 0.9189
## omega2 0.9189
## omega3 0.9154
## avevar 0.8564
##
## $`2`
## AEC
## alpha 0.9191
## alpha.ord 0.9347
## omega 0.9168
## omega2 0.9168
## omega3 0.9164
## avevar 0.8256
##
## $`3`
## AEC
## alpha 0.9327
## alpha.ord 0.9423
## omega 0.9241
## omega2 0.9241
## omega3 0.9238
## avevar 0.84327.1.1.5.5 Checking Latent Differences
partial<-partialInvarianceCat(invariance,type="means",return.fit = F)
partial## $estimates
## poolest mean:1 mean:2 mean:3 std:1 std:2 std:3 diff_std:2 vs. 1
## AEC~1 0 0 0.4292 0.5404 0 0.1683 0.212 0.1683
## diff_std:3 vs. 1
## AEC~1 0.212
##
## $results
## free.chi free.df free.p free.cfi fix.chi fix.df fix.p fix.cfi wald.chi
## AEC~1 0.7696 2 0.6806 -0.02305 0.7696 2 0.6806 -0.02305 NA
## wald.df wald.p
## AEC~1 NA NA8 External Relationships - Convergent and Concurrent Valididity
8.1 First Step CFA for each construct - with all cases
data<-TDados8.2 AEG
model <- 'AEG =~ AEG01 + AEG02 + AEG03 + AEG04 + AEG05 + AEG06 + AEG07 + AEG08 + AEG09 + AEG10' 8.2.0.1 Fitting
fit <- lavaan::cfa(model, data =data,estimator="ULSMV",ordered=T,missing="pairwise")## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: some cases are empty and will be ignored:
## 1 12 13 14 15 16 17 18 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 7898.2.0.2 General Summary
summary(fit,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 17 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 40
##
## Used Total
## Number of observations 586 789
## Number of missing patterns 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 95.335 241.884
## Degrees of freedom 35 35
## P-value (Unknown) NA 0.000
## Scaling correction factor 0.402
## Shift parameter 4.927
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 7763.930 5152.575
## Degrees of freedom 45 45
## P-value NA 0.000
## Scaling correction factor 1.514
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.992 0.959
## Tucker-Lewis Index (TLI) 0.990 0.948
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.054 0.101
## 90 Percent confidence interval - lower 0.041 0.089
## 90 Percent confidence interval - upper 0.067 0.113
## P-value RMSEA <= 0.05 0.278 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.054 0.054
##
## 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
## AEG =~
## AEG01 1.000 0.754 0.754
## AEG02 0.852 0.048 17.899 0.000 0.642 0.642
## AEG03 1.077 0.044 24.544 0.000 0.812 0.812
## AEG04 1.023 0.049 20.828 0.000 0.771 0.771
## AEG05 1.001 0.048 20.668 0.000 0.754 0.754
## AEG06 0.969 0.047 20.612 0.000 0.731 0.731
## AEG07 0.857 0.048 17.816 0.000 0.646 0.646
## AEG08 1.045 0.044 23.539 0.000 0.788 0.788
## AEG09 0.850 0.045 18.820 0.000 0.641 0.641
## AEG10 1.043 0.044 23.499 0.000 0.786 0.786
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEG01 0.000 0.000 0.000
## .AEG02 0.000 0.000 0.000
## .AEG03 0.000 0.000 0.000
## .AEG04 0.000 0.000 0.000
## .AEG05 0.000 0.000 0.000
## .AEG06 0.000 0.000 0.000
## .AEG07 0.000 0.000 0.000
## .AEG08 0.000 0.000 0.000
## .AEG09 0.000 0.000 0.000
## .AEG10 0.000 0.000 0.000
## AEG 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEG01|t1 -2.568 0.200 -12.850 0.000 -2.568 -2.568
## AEG01|t2 -1.780 0.096 -18.534 0.000 -1.780 -1.780
## AEG01|t3 -0.026 0.052 -0.495 0.620 -0.026 -0.026
## AEG02|t1 -2.259 0.144 -15.645 0.000 -2.259 -2.259
## AEG02|t2 -1.213 0.068 -17.743 0.000 -1.213 -1.213
## AEG02|t3 0.499 0.054 9.202 0.000 0.499 0.499
## AEG03|t1 -2.080 0.122 -17.005 0.000 -2.080 -2.080
## AEG03|t2 -1.120 0.066 -17.086 0.000 -1.120 -1.120
## AEG03|t3 0.470 0.054 8.714 0.000 0.470 0.470
## AEG04|t1 -2.466 0.179 -13.808 0.000 -2.466 -2.466
## AEG04|t2 -1.702 0.091 -18.736 0.000 -1.702 -1.702
## AEG04|t3 -0.060 0.052 -1.156 0.248 -0.060 -0.060
## AEG05|t1 -1.979 0.112 -17.637 0.000 -1.979 -1.979
## AEG05|t2 -1.088 0.065 -16.829 0.000 -1.088 -1.088
## AEG05|t3 0.437 0.054 8.144 0.000 0.437 0.437
## AEG06|t1 -2.161 0.132 -16.424 0.000 -2.161 -2.161
## AEG06|t2 -1.370 0.074 -18.511 0.000 -1.370 -1.370
## AEG06|t3 0.220 0.052 4.207 0.000 0.220 0.220
## AEG07|t1 -1.633 0.087 -18.838 0.000 -1.633 -1.633
## AEG07|t2 -0.938 0.061 -15.375 0.000 -0.938 -0.938
## AEG07|t3 0.381 0.053 7.164 0.000 0.381 0.381
## AEG08|t1 -2.044 0.119 -17.243 0.000 -2.044 -2.044
## AEG08|t2 -0.979 0.062 -15.806 0.000 -0.979 -0.979
## AEG08|t3 0.578 0.055 10.495 0.000 0.578 0.578
## AEG09|t1 -1.502 0.080 -18.822 0.000 -1.502 -1.502
## AEG09|t2 -0.504 0.054 -9.283 0.000 -0.504 -0.504
## AEG09|t3 0.721 0.057 12.642 0.000 0.721 0.721
## AEG10|t1 -1.823 0.099 -18.384 0.000 -1.823 -1.823
## AEG10|t2 -0.789 0.058 -13.575 0.000 -0.789 -0.789
## AEG10|t3 0.710 0.057 12.485 0.000 0.710 0.710
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEG01 0.432 0.432 0.432
## .AEG02 0.588 0.588 0.588
## .AEG03 0.340 0.340 0.340
## .AEG04 0.405 0.405 0.405
## .AEG05 0.431 0.431 0.431
## .AEG06 0.466 0.466 0.466
## .AEG07 0.582 0.582 0.582
## .AEG08 0.379 0.379 0.379
## .AEG09 0.589 0.589 0.589
## .AEG10 0.382 0.382 0.382
## AEG 0.568 0.042 13.487 0.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEG01 1.000 1.000 1.000
## AEG02 1.000 1.000 1.000
## AEG03 1.000 1.000 1.000
## AEG04 1.000 1.000 1.000
## AEG05 1.000 1.000 1.000
## AEG06 1.000 1.000 1.000
## AEG07 1.000 1.000 1.000
## AEG08 1.000 1.000 1.000
## AEG09 1.000 1.000 1.000
## AEG10 1.000 1.000 1.000
##
## R-Square:
## Estimate
## AEG01 0.568
## AEG02 0.412
## AEG03 0.660
## AEG04 0.595
## AEG05 0.569
## AEG06 0.534
## AEG07 0.418
## AEG08 0.621
## AEG09 0.411
## AEG10 0.6188.2.0.3 Selected Robust and Scaled Fit Measures
lavaan::fitMeasures(fit,c("chisq.scaled","df.scaled","pvalue","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue
## 241.884 35.000 NA
## srmr cfi.scaled tli.scaled
## 0.054 0.959 0.948
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.101 0.089 0.1138.2.0.4 Factor Loadings
parameters<-lavaan::standardizedSolution(fit)
loadings<-parameters[parameters$op=="=~",]
loadings## lhs op rhs est.std se z pvalue ci.lower ci.upper
## 1 AEG =~ AEG01 0.754 0.028 26.97 0 0.699 0.809
## 2 AEG =~ AEG02 0.642 0.029 22.25 0 0.586 0.699
## 3 AEG =~ AEG03 0.812 0.018 44.55 0 0.776 0.848
## 4 AEG =~ AEG04 0.771 0.025 30.40 0 0.721 0.821
## 5 AEG =~ AEG05 0.754 0.024 31.97 0 0.708 0.800
## 6 AEG =~ AEG06 0.731 0.027 27.46 0 0.679 0.783
## 7 AEG =~ AEG07 0.646 0.030 21.68 0 0.588 0.705
## 8 AEG =~ AEG08 0.788 0.020 38.94 0 0.748 0.828
## 9 AEG =~ AEG09 0.641 0.027 23.61 0 0.588 0.694
## 10 AEG =~ AEG10 0.786 0.020 38.73 0 0.746 0.8268.2.0.5 Modificantion Indices considering very bad RMSEA
modificationindices(fit, sort.=T)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 98 AEG04 ~~ AEG06 25.998 0.241 0.241 0.553 0.553
## 88 AEG02 ~~ AEG09 11.988 -0.157 -0.157 -0.266 -0.266
## 117 AEG09 ~~ AEG10 10.863 0.153 0.153 0.323 0.323
## 110 AEG06 ~~ AEG09 10.770 -0.151 -0.151 -0.288 -0.288
## 115 AEG08 ~~ AEG09 7.608 0.128 0.128 0.271 0.271
## 94 AEG03 ~~ AEG08 6.982 0.128 0.128 0.355 0.355
## 95 AEG03 ~~ AEG09 6.833 0.122 0.122 0.273 0.273
## 100 AEG04 ~~ AEG08 5.832 -0.115 -0.115 -0.294 -0.294
## 86 AEG02 ~~ AEG07 4.277 0.094 0.094 0.160 0.160
## 101 AEG04 ~~ AEG09 4.252 -0.096 -0.096 -0.195 -0.195
## 97 AEG04 ~~ AEG05 3.446 0.088 0.088 0.211 0.211
## 90 AEG03 ~~ AEG04 2.846 -0.081 -0.081 -0.218 -0.218
## 103 AEG05 ~~ AEG06 2.382 0.073 0.073 0.162 0.162
## 91 AEG03 ~~ AEG05 2.180 -0.071 -0.071 -0.185 -0.185
## 92 AEG03 ~~ AEG06 1.957 -0.067 -0.067 -0.167 -0.167
## 111 AEG06 ~~ AEG10 1.895 -0.065 -0.065 -0.154 -0.154
## 109 AEG06 ~~ AEG08 1.613 -0.060 -0.060 -0.143 -0.143
## 104 AEG05 ~~ AEG07 1.570 -0.058 -0.058 -0.116 -0.116
## 82 AEG02 ~~ AEG03 1.491 0.057 0.057 0.128 0.128
## 102 AEG04 ~~ AEG10 1.350 -0.056 -0.056 -0.141 -0.141
## 73 AEG01 ~~ AEG02 1.243 0.051 0.051 0.102 0.102
## 87 AEG02 ~~ AEG08 1.207 -0.051 -0.051 -0.108 -0.108
## 96 AEG03 ~~ AEG10 0.835 -0.044 -0.044 -0.122 -0.122
## 79 AEG01 ~~ AEG08 0.345 -0.028 -0.028 -0.069 -0.069
## 108 AEG06 ~~ AEG07 0.331 0.026 0.026 0.051 0.051
## 93 AEG03 ~~ AEG07 0.265 -0.024 -0.024 -0.054 -0.054
## 80 AEG01 ~~ AEG09 0.264 -0.024 -0.024 -0.047 -0.047
## 75 AEG01 ~~ AEG04 0.241 0.023 0.023 0.056 0.056
## 106 AEG05 ~~ AEG09 0.149 -0.018 -0.018 -0.035 -0.035
## 114 AEG07 ~~ AEG10 0.146 -0.018 -0.018 -0.038 -0.038
## 107 AEG05 ~~ AEG10 0.128 0.017 0.017 0.042 0.042
## 116 AEG08 ~~ AEG10 0.123 0.017 0.017 0.044 0.044
## 84 AEG02 ~~ AEG05 0.115 -0.016 -0.016 -0.031 -0.031
## 105 AEG05 ~~ AEG08 0.085 -0.014 -0.014 -0.034 -0.034
## 77 AEG01 ~~ AEG06 0.041 -0.010 -0.010 -0.021 -0.021
## 113 AEG07 ~~ AEG09 0.030 0.008 0.008 0.013 0.013
## 81 AEG01 ~~ AEG10 0.029 0.008 0.008 0.020 0.020
## 76 AEG01 ~~ AEG05 0.027 -0.008 -0.008 -0.018 -0.018
## 99 AEG04 ~~ AEG07 0.025 -0.007 -0.007 -0.015 -0.015
## 83 AEG02 ~~ AEG04 0.017 0.006 0.006 0.013 0.013
## 74 AEG01 ~~ AEG03 0.016 -0.006 -0.006 -0.016 -0.016
## 78 AEG01 ~~ AEG07 0.012 -0.005 -0.005 -0.010 -0.010
## 89 AEG02 ~~ AEG10 0.006 0.004 0.004 0.008 0.008
## 85 AEG02 ~~ AEG06 0.002 0.002 0.002 0.004 0.004
## 112 AEG07 ~~ AEG08 0.002 -0.002 -0.002 -0.004 -0.0048.2.0.6 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.## AEG
## alpha NA
## alpha.ord 0.9204
## omega 0.8824
## omega2 0.8824
## omega3 0.8817
## avevar 0.54058.3 AEO
model <- 'AEO =~ AEO01 + AEO02 + AEO03 + AEO04 + AEO05 + AEO06'8.3.0.1 Fitting
fit <- lavaan::cfa(model, data =data,estimator="ULSMV",ordered=T,missing="pairwise")## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: some cases are empty and will be ignored:
## 13 110 132 133 134 135 241 242 252 253 258 261 262 275 404 417 738 739 749 750 761 7808.3.0.2 General Summary
summary(fit,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 12 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 30
##
## Used Total
## Number of observations 767 789
## Number of missing patterns 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 52.580 152.110
## Degrees of freedom 9 9
## P-value (Unknown) NA 0.000
## Scaling correction factor 0.348
## Shift parameter 0.826
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 3321.827 2868.879
## Degrees of freedom 15 15
## P-value NA 0.000
## Scaling correction factor 1.160
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.987 0.950
## Tucker-Lewis Index (TLI) 0.978 0.916
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.080 0.144
## 90 Percent confidence interval - lower 0.060 0.124
## 90 Percent confidence interval - upper 0.101 0.165
## P-value RMSEA <= 0.05 0.009 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.057 0.057
##
## 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
## AEO =~
## AEO01 1.000 0.718 0.718
## AEO02 1.102 0.041 27.054 0.000 0.792 0.792
## AEO03 1.107 0.040 27.824 0.000 0.795 0.795
## AEO04 0.854 0.042 20.153 0.000 0.613 0.613
## AEO05 0.974 0.040 24.422 0.000 0.700 0.700
## AEO06 1.049 0.040 26.366 0.000 0.754 0.754
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEO01 0.000 0.000 0.000
## .AEO02 0.000 0.000 0.000
## .AEO03 0.000 0.000 0.000
## .AEO04 0.000 0.000 0.000
## .AEO05 0.000 0.000 0.000
## .AEO06 0.000 0.000 0.000
## AEO 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEO01|t1 -2.091 0.108 -19.369 0.000 -2.091 -2.091
## AEO01|t2 -1.137 0.058 -19.703 0.000 -1.137 -1.137
## AEO01|t3 -0.741 0.050 -14.783 0.000 -0.741 -0.741
## AEO01|t4 0.502 0.047 10.594 0.000 0.502 0.502
## AEO02|t1 -2.310 0.133 -17.404 0.000 -2.310 -2.310
## AEO02|t2 -1.408 0.066 -21.320 0.000 -1.408 -1.408
## AEO02|t3 -0.848 0.052 -16.396 0.000 -0.848 -0.848
## AEO02|t4 0.540 0.048 11.302 0.000 0.540 0.540
## AEO03|t1 -2.225 0.122 -18.219 0.000 -2.225 -2.225
## AEO03|t2 -1.195 0.059 -20.173 0.000 -1.195 -1.195
## AEO03|t3 -0.605 0.048 -12.498 0.000 -0.605 -0.605
## AEO03|t4 0.732 0.050 14.646 0.000 0.732 0.732
## AEO04|t1 -1.881 0.091 -20.762 0.000 -1.881 -1.881
## AEO04|t2 -1.349 0.064 -21.094 0.000 -1.349 -1.349
## AEO04|t3 -0.749 0.050 -14.919 0.000 -0.749 -0.749
## AEO04|t4 0.044 0.045 0.974 0.330 0.044 0.044
## AEO05|t1 -2.036 0.103 -19.787 0.000 -2.036 -2.036
## AEO05|t2 -1.302 0.062 -20.863 0.000 -1.302 -1.302
## AEO05|t3 -0.724 0.050 -14.509 0.000 -0.724 -0.724
## AEO05|t4 0.521 0.048 10.948 0.000 0.521 0.521
## AEO06|t1 -2.188 0.118 -18.556 0.000 -2.188 -2.188
## AEO06|t2 -1.399 0.066 -21.291 0.000 -1.399 -1.399
## AEO06|t3 -0.926 0.053 -17.435 0.000 -0.926 -0.926
## AEO06|t4 0.219 0.046 4.796 0.000 0.219 0.219
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEO01 0.484 0.484 0.484
## .AEO02 0.373 0.373 0.373
## .AEO03 0.368 0.368 0.368
## .AEO04 0.624 0.624 0.624
## .AEO05 0.510 0.510 0.510
## .AEO06 0.432 0.432 0.432
## AEO 0.516 0.033 15.616 0.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEO01 1.000 1.000 1.000
## AEO02 1.000 1.000 1.000
## AEO03 1.000 1.000 1.000
## AEO04 1.000 1.000 1.000
## AEO05 1.000 1.000 1.000
## AEO06 1.000 1.000 1.000
##
## R-Square:
## Estimate
## AEO01 0.516
## AEO02 0.627
## AEO03 0.632
## AEO04 0.376
## AEO05 0.490
## AEO06 0.5688.3.0.3 Selected Robust and Scaled Fit Measures
lavaan::fitMeasures(fit,c("chisq.scaled","df.scaled","pvalue","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue
## 152.110 9.000 NA
## srmr cfi.scaled tli.scaled
## 0.057 0.950 0.916
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.144 0.124 0.1658.3.0.4 Factor Loadings
parameters<-lavaan::standardizedSolution(fit)
loadings<-parameters[parameters$op=="=~",]
loadings## lhs op rhs est.std se z pvalue ci.lower ci.upper
## 1 AEO =~ AEO01 0.718 0.023 31.23 0 0.673 0.764
## 2 AEO =~ AEO02 0.792 0.019 40.95 0 0.754 0.830
## 3 AEO =~ AEO03 0.795 0.018 44.15 0 0.760 0.830
## 4 AEO =~ AEO04 0.613 0.028 21.76 0 0.558 0.669
## 5 AEO =~ AEO05 0.700 0.023 30.94 0 0.656 0.744
## 6 AEO =~ AEO06 0.754 0.021 35.55 0 0.712 0.7958.3.0.5 Modificantion Indices considering very bad RMSEA
modificationindices(fit, sort.=T)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 65 AEO05 ~~ AEO06 25.384 0.234 0.234 0.499 0.499
## 56 AEO02 ~~ AEO03 9.623 0.155 0.155 0.419 0.419
## 59 AEO02 ~~ AEO06 7.941 -0.138 -0.138 -0.343 -0.343
## 51 AEO01 ~~ AEO02 7.679 0.133 0.133 0.312 0.312
## 63 AEO04 ~~ AEO05 7.303 0.118 0.118 0.209 0.209
## 54 AEO01 ~~ AEO05 7.127 -0.122 -0.122 -0.245 -0.245
## 58 AEO02 ~~ AEO05 6.231 -0.118 -0.118 -0.271 -0.271
## 61 AEO03 ~~ AEO05 4.631 -0.102 -0.102 -0.236 -0.236
## 52 AEO01 ~~ AEO03 3.486 0.090 0.090 0.212 0.212
## 60 AEO03 ~~ AEO04 2.791 -0.076 -0.076 -0.159 -0.159
## 62 AEO03 ~~ AEO06 2.182 -0.072 -0.072 -0.181 -0.181
## 55 AEO01 ~~ AEO06 1.692 -0.061 -0.061 -0.133 -0.133
## 53 AEO01 ~~ AEO04 1.141 -0.047 -0.047 -0.085 -0.085
## 64 AEO04 ~~ AEO06 0.988 0.044 0.044 0.085 0.085
## 57 AEO02 ~~ AEO04 0.602 -0.035 -0.035 -0.073 -0.0738.3.0.6 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.## AEO
## alpha NA
## alpha.ord 0.8714
## omega 0.8312
## omega2 0.8312
## omega3 0.8304
## avevar 0.53498.4 WAMI
model <- 'WAMI =~ WAMI01 + WAMI02 + WAMI03 + WAMI04 + WAMI05 + WAMI06 + WAMI07 + WAMI08 + WAMI09 + WAMI10' 8.4.0.1 Fitting
fit <- lavaan::cfa(model, data =data,estimator="ULSMV",ordered=T,missing="pairwise")## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: some cases are empty and will be ignored:
## 12 13 15 16 105 109 110 119 132 133 134 135 241 242 252 253 258 261 262 263 275 282 404 410 413 417 715 733 738 739 744 749 750 751 761 767 778 779 780 781 7868.4.0.2 General Summary
summary(fit,rsquare=T,fit=T,standardized=T)## lavaan 0.6-8 ended normally after 23 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 50
##
## Used Total
## Number of observations 748 789
## Number of missing patterns 1
##
## Model Test User Model:
## Standard Robust
## Test Statistic 65.674 528.629
## Degrees of freedom 35 35
## P-value (Unknown) NA 0.000
## Scaling correction factor 0.126
## Shift parameter 8.928
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 17411.711 17316.740
## Degrees of freedom 45 45
## P-value NA 0.000
## Scaling correction factor 1.007
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.998 0.971
## Tucker-Lewis Index (TLI) 0.998 0.963
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.034 0.137
## 90 Percent confidence interval - lower 0.021 0.127
## 90 Percent confidence interval - upper 0.047 0.148
## P-value RMSEA <= 0.05 0.981 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
## WAMI =~
## WAMI01 1.000 0.875 0.875
## WAMI02 0.974 0.016 61.902 0.000 0.852 0.852
## WAMI03 -0.770 0.027 -28.778 0.000 -0.674 -0.674
## WAMI04 1.016 0.014 72.576 0.000 0.889 0.889
## WAMI05 1.014 0.014 70.252 0.000 0.887 0.887
## WAMI06 0.963 0.016 60.277 0.000 0.843 0.843
## WAMI07 0.925 0.017 53.914 0.000 0.809 0.809
## WAMI08 1.066 0.013 80.601 0.000 0.933 0.933
## WAMI09 0.955 0.016 57.910 0.000 0.836 0.836
## WAMI10 0.980 0.015 65.929 0.000 0.857 0.857
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .WAMI01 0.000 0.000 0.000
## .WAMI02 0.000 0.000 0.000
## .WAMI03 0.000 0.000 0.000
## .WAMI04 0.000 0.000 0.000
## .WAMI05 0.000 0.000 0.000
## .WAMI06 0.000 0.000 0.000
## .WAMI07 0.000 0.000 0.000
## .WAMI08 0.000 0.000 0.000
## .WAMI09 0.000 0.000 0.000
## .WAMI10 0.000 0.000 0.000
## WAMI 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## WAMI01|t1 -1.576 0.074 -21.319 0.000 -1.576 -1.576
## WAMI01|t2 -1.194 0.060 -19.911 0.000 -1.194 -1.194
## WAMI01|t3 -0.581 0.049 -11.903 0.000 -0.581 -0.581
## WAMI01|t4 0.352 0.047 7.511 0.000 0.352 0.352
## WAMI02|t1 -1.851 0.090 -20.650 0.000 -1.851 -1.851
## WAMI02|t2 -1.479 0.070 -21.233 0.000 -1.479 -1.479
## WAMI02|t3 -0.966 0.055 -17.705 0.000 -0.966 -0.966
## WAMI02|t4 0.000 0.046 0.000 1.000 0.000 0.000
## WAMI03|t1 0.158 0.046 3.433 0.001 0.158 0.158
## WAMI03|t2 0.743 0.051 14.642 0.000 0.743 0.743
## WAMI03|t3 1.311 0.063 20.650 0.000 1.311 1.311
## WAMI03|t4 1.781 0.085 20.939 0.000 1.781 1.781
## WAMI04|t1 -1.749 0.083 -21.045 0.000 -1.749 -1.749
## WAMI04|t2 -1.243 0.061 -20.255 0.000 -1.243 -1.243
## WAMI04|t3 -0.621 0.049 -12.613 0.000 -0.621 -0.621
## WAMI04|t4 0.327 0.047 7.003 0.000 0.327 0.327
## WAMI05|t1 -1.870 0.091 -20.559 0.000 -1.870 -1.870
## WAMI05|t2 -1.369 0.065 -20.912 0.000 -1.369 -1.369
## WAMI05|t3 -0.798 0.052 -15.465 0.000 -0.798 -0.798
## WAMI05|t4 0.168 0.046 3.652 0.000 0.168 0.168
## WAMI06|t1 -1.749 0.083 -21.045 0.000 -1.749 -1.749
## WAMI06|t2 -1.369 0.065 -20.912 0.000 -1.369 -1.369
## WAMI06|t3 -0.683 0.050 -13.669 0.000 -0.683 -0.683
## WAMI06|t4 0.138 0.046 2.995 0.003 0.138 0.138
## WAMI07|t1 -1.510 0.071 -21.279 0.000 -1.510 -1.510
## WAMI07|t2 -1.122 0.058 -19.323 0.000 -1.122 -1.122
## WAMI07|t3 -0.414 0.047 -8.743 0.000 -0.414 -0.414
## WAMI07|t4 0.443 0.048 9.321 0.000 0.443 0.443
## WAMI08|t1 -1.404 0.067 -21.039 0.000 -1.404 -1.404
## WAMI08|t2 -1.009 0.055 -18.205 0.000 -1.009 -1.009
## WAMI08|t3 -0.545 0.048 -11.261 0.000 -0.545 -0.545
## WAMI08|t4 0.392 0.047 8.309 0.000 0.392 0.392
## WAMI09|t1 -1.637 0.077 -21.283 0.000 -1.637 -1.637
## WAMI09|t2 -1.173 0.059 -19.756 0.000 -1.173 -1.173
## WAMI09|t3 -0.621 0.049 -12.613 0.000 -0.621 -0.621
## WAMI09|t4 0.306 0.047 6.567 0.000 0.306 0.306
## WAMI10|t1 -1.460 0.069 -21.193 0.000 -1.460 -1.460
## WAMI10|t2 -1.085 0.057 -18.982 0.000 -1.085 -1.085
## WAMI10|t3 -0.473 0.048 -9.898 0.000 -0.473 -0.473
## WAMI10|t4 0.282 0.047 6.058 0.000 0.282 0.282
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .WAMI01 0.234 0.234 0.234
## .WAMI02 0.274 0.274 0.274
## .WAMI03 0.546 0.546 0.546
## .WAMI04 0.210 0.210 0.210
## .WAMI05 0.213 0.213 0.213
## .WAMI06 0.290 0.290 0.290
## .WAMI07 0.345 0.345 0.345
## .WAMI08 0.129 0.129 0.129
## .WAMI09 0.301 0.301 0.301
## .WAMI10 0.265 0.265 0.265
## WAMI 0.766 0.019 40.098 0.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## WAMI01 1.000 1.000 1.000
## WAMI02 1.000 1.000 1.000
## WAMI03 1.000 1.000 1.000
## WAMI04 1.000 1.000 1.000
## WAMI05 1.000 1.000 1.000
## WAMI06 1.000 1.000 1.000
## WAMI07 1.000 1.000 1.000
## WAMI08 1.000 1.000 1.000
## WAMI09 1.000 1.000 1.000
## WAMI10 1.000 1.000 1.000
##
## R-Square:
## Estimate
## WAMI01 0.766
## WAMI02 0.726
## WAMI03 0.454
## WAMI04 0.790
## WAMI05 0.787
## WAMI06 0.710
## WAMI07 0.655
## WAMI08 0.871
## WAMI09 0.699
## WAMI10 0.7358.4.0.3 Selected Robust and Scaled Fit Measures
lavaan::fitMeasures(fit,c("chisq.scaled","df.scaled","pvalue","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue
## 528.629 35.000 NA
## srmr cfi.scaled tli.scaled
## 0.040 0.971 0.963
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.137 0.127 0.1488.4.0.4 Factor Loadings
parameters<-lavaan::standardizedSolution(fit)
loadings<-parameters[parameters$op=="=~",]
loadings## lhs op rhs est.std se z pvalue ci.lower ci.upper
## 1 WAMI =~ WAMI01 0.875 0.011 80.20 0 0.854 0.896
## 2 WAMI =~ WAMI02 0.852 0.013 63.49 0 0.826 0.879
## 3 WAMI =~ WAMI03 -0.674 0.023 -29.04 0 -0.719 -0.628
## 4 WAMI =~ WAMI04 0.889 0.010 86.12 0 0.869 0.909
## 5 WAMI =~ WAMI05 0.887 0.011 82.78 0 0.866 0.908
## 6 WAMI =~ WAMI06 0.843 0.013 63.71 0 0.817 0.869
## 7 WAMI =~ WAMI07 0.809 0.015 55.74 0 0.781 0.838
## 8 WAMI =~ WAMI08 0.933 0.007 137.14 0 0.920 0.946
## 9 WAMI =~ WAMI09 0.836 0.013 62.31 0 0.810 0.862
## 10 WAMI =~ WAMI10 0.857 0.012 73.24 0 0.834 0.8808.4.0.5 Modificantion Indices considering very bad RMSEA
modificationindices(fit, sort.=T)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 102 WAMI03 ~~ WAMI06 12.497 -0.142 -0.142 -0.358 -0.358
## 123 WAMI07 ~~ WAMI09 12.258 0.144 0.144 0.446 0.446
## 83 WAMI01 ~~ WAMI02 9.615 0.129 0.129 0.511 0.511
## 103 WAMI03 ~~ WAMI07 6.151 0.099 0.099 0.229 0.229
## 121 WAMI06 ~~ WAMI10 4.313 0.086 0.086 0.311 0.311
## 118 WAMI06 ~~ WAMI07 3.685 -0.079 -0.079 -0.250 -0.250
## 107 WAMI04 ~~ WAMI05 3.518 0.079 0.079 0.374 0.374
## 127 WAMI09 ~~ WAMI10 3.115 0.073 0.073 0.259 0.259
## 90 WAMI01 ~~ WAMI09 2.931 -0.071 -0.071 -0.268 -0.268
## 113 WAMI05 ~~ WAMI06 2.485 0.066 0.066 0.265 0.265
## 95 WAMI02 ~~ WAMI06 2.251 -0.062 -0.062 -0.221 -0.221
## 99 WAMI02 ~~ WAMI10 2.006 -0.059 -0.059 -0.218 -0.218
## 89 WAMI01 ~~ WAMI08 1.883 0.058 0.058 0.334 0.334
## 87 WAMI01 ~~ WAMI06 1.773 -0.055 -0.055 -0.213 -0.213
## 94 WAMI02 ~~ WAMI05 1.418 -0.050 -0.050 -0.206 -0.206
## 116 WAMI05 ~~ WAMI09 1.202 -0.046 -0.046 -0.180 -0.180
## 88 WAMI01 ~~ WAMI07 1.178 -0.045 -0.045 -0.158 -0.158
## 91 WAMI01 ~~ WAMI10 1.102 -0.044 -0.044 -0.176 -0.176
## 106 WAMI03 ~~ WAMI10 1.063 -0.042 -0.042 -0.109 -0.109
## 112 WAMI04 ~~ WAMI10 1.006 -0.042 -0.042 -0.178 -0.178
## 105 WAMI03 ~~ WAMI09 0.783 0.036 0.036 0.088 0.088
## 100 WAMI03 ~~ WAMI04 0.778 0.036 0.036 0.106 0.106
## 114 WAMI05 ~~ WAMI07 0.759 -0.036 -0.036 -0.133 -0.133
## 122 WAMI07 ~~ WAMI08 0.727 0.036 0.036 0.169 0.169
## 96 WAMI02 ~~ WAMI07 0.688 0.034 0.034 0.111 0.111
## 109 WAMI04 ~~ WAMI07 0.648 0.033 0.033 0.124 0.124
## 119 WAMI06 ~~ WAMI08 0.634 -0.034 -0.034 -0.173 -0.173
## 120 WAMI06 ~~ WAMI09 0.565 -0.031 -0.031 -0.105 -0.105
## 117 WAMI05 ~~ WAMI10 0.363 -0.025 -0.025 -0.106 -0.106
## 92 WAMI02 ~~ WAMI03 0.298 -0.022 -0.022 -0.057 -0.057
## 104 WAMI03 ~~ WAMI08 0.281 0.022 0.022 0.082 0.082
## 111 WAMI04 ~~ WAMI09 0.241 -0.020 -0.020 -0.081 -0.081
## 86 WAMI01 ~~ WAMI05 0.168 0.017 0.017 0.077 0.077
## 85 WAMI01 ~~ WAMI04 0.157 0.017 0.017 0.075 0.075
## 84 WAMI01 ~~ WAMI03 0.150 0.016 0.016 0.044 0.044
## 126 WAMI08 ~~ WAMI10 0.129 -0.015 -0.015 -0.082 -0.082
## 110 WAMI04 ~~ WAMI08 0.109 -0.014 -0.014 -0.085 -0.085
## 108 WAMI04 ~~ WAMI06 0.082 -0.012 -0.012 -0.048 -0.048
## 93 WAMI02 ~~ WAMI04 0.071 -0.011 -0.011 -0.047 -0.047
## 115 WAMI05 ~~ WAMI08 0.052 -0.010 -0.010 -0.059 -0.059
## 125 WAMI08 ~~ WAMI09 0.025 -0.007 -0.007 -0.034 -0.034
## 124 WAMI07 ~~ WAMI10 0.010 -0.004 -0.004 -0.013 -0.013
## 97 WAMI02 ~~ WAMI08 0.009 0.004 0.004 0.022 0.022
## 98 WAMI02 ~~ WAMI09 0.009 -0.004 -0.004 -0.014 -0.014
## 101 WAMI03 ~~ WAMI05 0.002 -0.002 -0.002 -0.005 -0.0058.4.0.6 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.## WAMI
## alpha NA
## alpha.ord 0.9028
## omega 0.9282
## omega2 0.9282
## omega3 0.9274
## avevar 0.71928.5 Final Model with suggested error correlated by modificiation indices from previous analysis
model <- '
# Recurso Pessoal - Autoeficácia Criativa (Variavel a ser validada)
AEC =~ AEC04 + AEC01 + AEC02 + AEC03
# Recurso Pessoal - Autoeficacia Geral (Concorrente)
AEG =~ AEG01 + AEG02 + AEG03 + AEG04 + AEG05 + AEG06 + AEG07 + AEG08 + AEG09 + AEG10
AEG04 ~~ AEG06
# Recurso Pessoal - Autoeficácia Ocupacional (Concorrente)
AEO =~ AEO01 + AEO02 + AEO03 + AEO04 + AEO05 + AEO06
# Recurso Pessoal - Sentido do Trabalho (Convergente)
WAMI =~ WAMI01 + WAMI02 + WAMI03 + WAMI04 + WAMI05 + WAMI06 + WAMI07 + WAMI08 + WAMI09 + WAMI10
# Desfecho do Trabalho - Indicador de bem-estar no trabalho (Convergente)
Engaj =~ UWES01Vi + UWES02Vi + UWES03De + UWES04.De + UWES05Vi + UWES06Ab + UWES07De + UWES08Ab + UWES09Ab
UWES01Vi ~~ UWES02Vi
### remove
#Recurso do Trabalho - Motivação Intrinseca no Trabalho (Convergente) - VAI FICAR DE FORA
#MotIntr =~ Flow09MI + Flow10MI + Flow11MI + Flow12MI + Flow13MI
'8.5.0.0.1 Fitting using standardization from latent insted of indicators
fit <- cfa(model=model, data = data, ordered=T,estimator = "ULSMV",missing="pairwise",std.lv=T)8.5.0.0.2 General Summary
summary(fit, fit.measures=TRUE, standardized = TRUE)## lavaan 0.6-8 ended normally after 43 iterations
##
## Estimator ULS
## Optimization method NLMINB
## Number of model parameters 223
##
## Number of observations 789
## Number of missing patterns 5
##
## Model Test User Model:
## Standard Robust
## Test Statistic 1193.504 1352.810
## Degrees of freedom 690 690
## P-value (Unknown) NA 0.000
## Scaling correction factor 1.271
## Shift parameter 413.844
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 118211.061 22639.296
## Degrees of freedom 741 741
## P-value NA 0.000
## Scaling correction factor 5.364
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.996 0.970
## Tucker-Lewis Index (TLI) 0.995 0.967
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.030 0.035
## 90 Percent confidence interval - lower 0.028 0.032
## 90 Percent confidence interval - upper 0.033 0.038
## 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 0.044 0.044
##
## 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
## AEC =~
## AEC04 0.966 0.017 55.779 0.000 0.966 0.966
## AEC01 0.865 0.021 41.574 0.000 0.865 0.865
## AEC02 0.972 0.020 48.461 0.000 0.972 0.972
## AEC03 0.749 0.026 28.398 0.000 0.749 0.749
## AEG =~
## AEG01 0.816 0.033 24.877 0.000 0.816 0.816
## AEG02 0.590 0.036 16.523 0.000 0.590 0.590
## AEG03 0.795 0.023 33.864 0.000 0.795 0.795
## AEG04 0.679 0.037 18.221 0.000 0.679 0.679
## AEG05 0.768 0.031 24.676 0.000 0.768 0.768
## AEG06 0.648 0.035 18.472 0.000 0.648 0.648
## AEG07 0.717 0.033 22.030 0.000 0.717 0.717
## AEG08 0.801 0.025 32.549 0.000 0.801 0.801
## AEG09 0.689 0.031 22.512 0.000 0.689 0.689
## AEG10 0.760 0.027 28.574 0.000 0.760 0.760
## AEO =~
## AEO01 0.749 0.025 29.885 0.000 0.749 0.749
## AEO02 0.814 0.021 39.124 0.000 0.814 0.814
## AEO03 0.774 0.020 39.274 0.000 0.774 0.774
## AEO04 0.672 0.029 22.823 0.000 0.672 0.672
## AEO05 0.661 0.028 23.866 0.000 0.661 0.661
## AEO06 0.699 0.025 27.890 0.000 0.699 0.699
## WAMI =~
## WAMI01 0.939 0.012 79.117 0.000 0.939 0.939
## WAMI02 0.865 0.015 56.351 0.000 0.865 0.865
## WAMI03 -0.631 0.029 -21.533 0.000 -0.631 -0.631
## WAMI04 0.912 0.012 74.491 0.000 0.912 0.912
## WAMI05 0.900 0.015 60.739 0.000 0.900 0.900
## WAMI06 0.805 0.019 43.200 0.000 0.805 0.805
## WAMI07 0.798 0.018 44.426 0.000 0.798 0.798
## WAMI08 0.949 0.010 93.562 0.000 0.949 0.949
## WAMI09 0.805 0.018 44.928 0.000 0.805 0.805
## WAMI10 0.828 0.017 49.081 0.000 0.828 0.828
## Engaj =~
## UWES01Vi 0.846 0.014 62.292 0.000 0.846 0.846
## UWES02Vi 0.879 0.012 75.089 0.000 0.879 0.879
## UWES03De 0.932 0.008 113.835 0.000 0.932 0.932
## UWES04.De 0.953 0.009 108.837 0.000 0.953 0.953
## UWES05Vi 0.885 0.012 74.127 0.000 0.885 0.885
## UWES06Ab 0.819 0.016 51.531 0.000 0.819 0.819
## UWES07De 0.922 0.011 83.012 0.000 0.922 0.922
## UWES08Ab 0.933 0.011 88.631 0.000 0.933 0.933
## UWES09Ab 0.607 0.026 23.491 0.000 0.607 0.607
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEG04 ~~
## .AEG06 0.309 0.036 8.490 0.000 0.309 0.552
## .UWES01Vi ~~
## .UWES02Vi 0.225 0.019 11.755 0.000 0.225 0.886
## AEC ~~
## AEG 0.586 0.035 16.773 0.000 0.586 0.586
## AEO 0.447 0.030 15.146 0.000 0.447 0.447
## WAMI 0.264 0.034 7.783 0.000 0.264 0.264
## Engaj 0.257 0.034 7.581 0.000 0.257 0.257
## AEG ~~
## AEO 0.854 0.021 40.476 0.000 0.854 0.854
## WAMI 0.433 0.037 11.634 0.000 0.433 0.433
## Engaj 0.464 0.035 13.372 0.000 0.464 0.464
## AEO ~~
## WAMI 0.533 0.030 17.588 0.000 0.533 0.533
## Engaj 0.594 0.027 21.830 0.000 0.594 0.594
## WAMI ~~
## Engaj 0.794 0.014 55.422 0.000 0.794 0.794
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.000 0.000 0.000
## .AEC01 0.000 0.000 0.000
## .AEC02 0.000 0.000 0.000
## .AEC03 0.000 0.000 0.000
## .AEG01 0.000 0.000 0.000
## .AEG02 0.000 0.000 0.000
## .AEG03 0.000 0.000 0.000
## .AEG04 0.000 0.000 0.000
## .AEG05 0.000 0.000 0.000
## .AEG06 0.000 0.000 0.000
## .AEG07 0.000 0.000 0.000
## .AEG08 0.000 0.000 0.000
## .AEG09 0.000 0.000 0.000
## .AEG10 0.000 0.000 0.000
## .AEO01 0.000 0.000 0.000
## .AEO02 0.000 0.000 0.000
## .AEO03 0.000 0.000 0.000
## .AEO04 0.000 0.000 0.000
## .AEO05 0.000 0.000 0.000
## .AEO06 0.000 0.000 0.000
## .WAMI01 0.000 0.000 0.000
## .WAMI02 0.000 0.000 0.000
## .WAMI03 0.000 0.000 0.000
## .WAMI04 0.000 0.000 0.000
## .WAMI05 0.000 0.000 0.000
## .WAMI06 0.000 0.000 0.000
## .WAMI07 0.000 0.000 0.000
## .WAMI08 0.000 0.000 0.000
## .WAMI09 0.000 0.000 0.000
## .WAMI10 0.000 0.000 0.000
## .UWES01Vi 0.000 0.000 0.000
## .UWES02Vi 0.000 0.000 0.000
## .UWES03De 0.000 0.000 0.000
## .UWES04.De 0.000 0.000 0.000
## .UWES05Vi 0.000 0.000 0.000
## .UWES06Ab 0.000 0.000 0.000
## .UWES07De 0.000 0.000 0.000
## .UWES08Ab 0.000 0.000 0.000
## .UWES09Ab 0.000 0.000 0.000
## AEC 0.000 0.000 0.000
## AEG 0.000 0.000 0.000
## AEO 0.000 0.000 0.000
## WAMI 0.000 0.000 0.000
## Engaj 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04|t1 -2.133 0.110 -19.303 0.000 -2.133 -2.133
## AEC04|t2 -1.415 0.065 -21.645 0.000 -1.415 -1.415
## AEC04|t3 -0.571 0.047 -12.053 0.000 -0.571 -0.571
## AEC04|t4 0.403 0.046 8.763 0.000 0.403 0.403
## AEC04|t5 1.212 0.059 20.586 0.000 1.212 1.212
## AEC04|t6 1.603 0.073 21.889 0.000 1.603 1.603
## AEC01|t1 -1.976 0.096 -20.492 0.000 -1.976 -1.976
## AEC01|t2 -1.349 0.063 -21.393 0.000 -1.349 -1.349
## AEC01|t3 -0.571 0.047 -12.053 0.000 -0.571 -0.571
## AEC01|t4 0.462 0.046 9.958 0.000 0.462 0.462
## AEC01|t5 1.274 0.061 20.998 0.000 1.274 1.274
## AEC01|t6 1.614 0.074 21.881 0.000 1.614 1.614
## AEC02|t1 -2.165 0.114 -19.028 0.000 -2.165 -2.165
## AEC02|t2 -1.441 0.066 -21.722 0.000 -1.441 -1.441
## AEC02|t3 -0.796 0.050 -15.865 0.000 -0.796 -0.796
## AEC02|t4 0.322 0.045 7.068 0.000 0.322 0.322
## AEC02|t5 1.083 0.056 19.479 0.000 1.083 1.083
## AEC02|t6 1.497 0.069 21.837 0.000 1.497 1.497
## AEC03|t1 -2.048 0.102 -19.982 0.000 -2.048 -2.048
## AEC03|t2 -1.318 0.062 -21.244 0.000 -1.318 -1.318
## AEC03|t3 -0.445 0.046 -9.607 0.000 -0.445 -0.445
## AEC03|t4 0.469 0.046 10.099 0.000 0.469 0.469
## AEC03|t5 1.252 0.060 20.866 0.000 1.252 1.252
## AEC03|t6 1.638 0.075 21.858 0.000 1.638 1.638
## AEG01|t1 -2.568 0.200 -12.853 0.000 -2.568 -2.568
## AEG01|t2 -1.780 0.096 -18.538 0.000 -1.780 -1.780
## AEG01|t3 -0.026 0.052 -0.495 0.620 -0.026 -0.026
## AEG02|t1 -2.259 0.144 -15.649 0.000 -2.259 -2.259
## AEG02|t2 -1.213 0.068 -17.747 0.000 -1.213 -1.213
## AEG02|t3 0.499 0.054 9.204 0.000 0.499 0.499
## AEG03|t1 -2.080 0.122 -17.009 0.000 -2.080 -2.080
## AEG03|t2 -1.120 0.066 -17.089 0.000 -1.120 -1.120
## AEG03|t3 0.470 0.054 8.716 0.000 0.470 0.470
## AEG04|t1 -2.466 0.179 -13.811 0.000 -2.466 -2.466
## AEG04|t2 -1.702 0.091 -18.740 0.000 -1.702 -1.702
## AEG04|t3 -0.060 0.052 -1.156 0.248 -0.060 -0.060
## AEG05|t1 -1.979 0.112 -17.641 0.000 -1.979 -1.979
## AEG05|t2 -1.088 0.065 -16.833 0.000 -1.088 -1.088
## AEG05|t3 0.437 0.054 8.146 0.000 0.437 0.437
## AEG06|t1 -2.161 0.132 -16.427 0.000 -2.161 -2.161
## AEG06|t2 -1.370 0.074 -18.516 0.000 -1.370 -1.370
## AEG06|t3 0.220 0.052 4.208 0.000 0.220 0.220
## AEG07|t1 -1.633 0.087 -18.842 0.000 -1.633 -1.633
## AEG07|t2 -0.938 0.061 -15.379 0.000 -0.938 -0.938
## AEG07|t3 0.381 0.053 7.165 0.000 0.381 0.381
## AEG08|t1 -2.044 0.119 -17.247 0.000 -2.044 -2.044
## AEG08|t2 -0.979 0.062 -15.809 0.000 -0.979 -0.979
## AEG08|t3 0.578 0.055 10.497 0.000 0.578 0.578
## AEG09|t1 -1.502 0.080 -18.826 0.000 -1.502 -1.502
## AEG09|t2 -0.504 0.054 -9.285 0.000 -0.504 -0.504
## AEG09|t3 0.721 0.057 12.645 0.000 0.721 0.721
## AEG10|t1 -1.823 0.099 -18.388 0.000 -1.823 -1.823
## AEG10|t2 -0.789 0.058 -13.578 0.000 -0.789 -0.789
## AEG10|t3 0.710 0.057 12.488 0.000 0.710 0.710
## AEO01|t1 -2.091 0.108 -19.369 0.000 -2.091 -2.091
## AEO01|t2 -1.137 0.058 -19.703 0.000 -1.137 -1.137
## AEO01|t3 -0.741 0.050 -14.783 0.000 -0.741 -0.741
## AEO01|t4 0.502 0.047 10.594 0.000 0.502 0.502
## AEO02|t1 -2.310 0.133 -17.404 0.000 -2.310 -2.310
## AEO02|t2 -1.408 0.066 -21.321 0.000 -1.408 -1.408
## AEO02|t3 -0.848 0.052 -16.396 0.000 -0.848 -0.848
## AEO02|t4 0.540 0.048 11.302 0.000 0.540 0.540
## AEO03|t1 -2.225 0.122 -18.219 0.000 -2.225 -2.225
## AEO03|t2 -1.195 0.059 -20.174 0.000 -1.195 -1.195
## AEO03|t3 -0.605 0.048 -12.498 0.000 -0.605 -0.605
## AEO03|t4 0.732 0.050 14.646 0.000 0.732 0.732
## AEO04|t1 -1.881 0.091 -20.762 0.000 -1.881 -1.881
## AEO04|t2 -1.349 0.064 -21.094 0.000 -1.349 -1.349
## AEO04|t3 -0.749 0.050 -14.919 0.000 -0.749 -0.749
## AEO04|t4 0.044 0.045 0.974 0.330 0.044 0.044
## AEO05|t1 -2.036 0.103 -19.787 0.000 -2.036 -2.036
## AEO05|t2 -1.302 0.062 -20.863 0.000 -1.302 -1.302
## AEO05|t3 -0.724 0.050 -14.509 0.000 -0.724 -0.724
## AEO05|t4 0.521 0.048 10.948 0.000 0.521 0.521
## AEO06|t1 -2.188 0.118 -18.557 0.000 -2.188 -2.188
## AEO06|t2 -1.399 0.066 -21.292 0.000 -1.399 -1.399
## AEO06|t3 -0.926 0.053 -17.435 0.000 -0.926 -0.926
## AEO06|t4 0.219 0.046 4.796 0.000 0.219 0.219
## WAMI01|t1 -1.576 0.074 -21.319 0.000 -1.576 -1.576
## WAMI01|t2 -1.194 0.060 -19.912 0.000 -1.194 -1.194
## WAMI01|t3 -0.581 0.049 -11.903 0.000 -0.581 -0.581
## WAMI01|t4 0.352 0.047 7.511 0.000 0.352 0.352
## WAMI02|t1 -1.851 0.090 -20.651 0.000 -1.851 -1.851
## WAMI02|t2 -1.479 0.070 -21.233 0.000 -1.479 -1.479
## WAMI02|t3 -0.966 0.055 -17.706 0.000 -0.966 -0.966
## WAMI02|t4 0.000 0.046 0.000 1.000 0.000 0.000
## WAMI03|t1 0.158 0.046 3.433 0.001 0.158 0.158
## WAMI03|t2 0.743 0.051 14.643 0.000 0.743 0.743
## WAMI03|t3 1.311 0.063 20.651 0.000 1.311 1.311
## WAMI03|t4 1.781 0.085 20.940 0.000 1.781 1.781
## WAMI04|t1 -1.749 0.083 -21.046 0.000 -1.749 -1.749
## WAMI04|t2 -1.243 0.061 -20.255 0.000 -1.243 -1.243
## WAMI04|t3 -0.621 0.049 -12.613 0.000 -0.621 -0.621
## WAMI04|t4 0.327 0.047 7.003 0.000 0.327 0.327
## WAMI05|t1 -1.870 0.091 -20.559 0.000 -1.870 -1.870
## WAMI05|t2 -1.369 0.065 -20.913 0.000 -1.369 -1.369
## WAMI05|t3 -0.798 0.052 -15.465 0.000 -0.798 -0.798
## WAMI05|t4 0.168 0.046 3.652 0.000 0.168 0.168
## WAMI06|t1 -1.749 0.083 -21.046 0.000 -1.749 -1.749
## WAMI06|t2 -1.369 0.065 -20.913 0.000 -1.369 -1.369
## WAMI06|t3 -0.683 0.050 -13.669 0.000 -0.683 -0.683
## WAMI06|t4 0.138 0.046 2.995 0.003 0.138 0.138
## WAMI07|t1 -1.510 0.071 -21.280 0.000 -1.510 -1.510
## WAMI07|t2 -1.122 0.058 -19.324 0.000 -1.122 -1.122
## WAMI07|t3 -0.414 0.047 -8.743 0.000 -0.414 -0.414
## WAMI07|t4 0.443 0.048 9.321 0.000 0.443 0.443
## WAMI08|t1 -1.404 0.067 -21.040 0.000 -1.404 -1.404
## WAMI08|t2 -1.009 0.055 -18.205 0.000 -1.009 -1.009
## WAMI08|t3 -0.545 0.048 -11.261 0.000 -0.545 -0.545
## WAMI08|t4 0.392 0.047 8.309 0.000 0.392 0.392
## WAMI09|t1 -1.637 0.077 -21.284 0.000 -1.637 -1.637
## WAMI09|t2 -1.173 0.059 -19.757 0.000 -1.173 -1.173
## WAMI09|t3 -0.621 0.049 -12.613 0.000 -0.621 -0.621
## WAMI09|t4 0.306 0.047 6.567 0.000 0.306 0.306
## WAMI10|t1 -1.460 0.069 -21.194 0.000 -1.460 -1.460
## WAMI10|t2 -1.085 0.057 -18.982 0.000 -1.085 -1.085
## WAMI10|t3 -0.473 0.048 -9.898 0.000 -0.473 -0.473
## WAMI10|t4 0.282 0.047 6.058 0.000 0.282 0.282
## UWES01Vi|t1 -1.817 0.087 -20.843 0.000 -1.817 -1.817
## UWES01Vi|t2 -1.313 0.063 -20.704 0.000 -1.313 -1.313
## UWES01Vi|t3 -0.867 0.053 -16.479 0.000 -0.867 -0.867
## UWES01Vi|t4 -0.428 0.047 -9.051 0.000 -0.428 -0.428
## UWES01Vi|t5 -0.022 0.046 -0.474 0.635 -0.022 -0.022
## UWES01Vi|t6 1.217 0.060 20.119 0.000 1.217 1.217
## UWES02Vi|t1 -1.853 0.090 -20.684 0.000 -1.853 -1.853
## UWES02Vi|t2 -1.305 0.063 -20.663 0.000 -1.305 -1.305
## UWES02Vi|t3 -0.876 0.053 -16.611 0.000 -0.876 -0.876
## UWES02Vi|t4 -0.410 0.047 -8.690 0.000 -0.410 -0.410
## UWES02Vi|t5 -0.015 0.046 -0.328 0.743 -0.015 -0.015
## UWES02Vi|t6 1.224 0.061 20.168 0.000 1.224 1.224
## UWES03De|t1 -1.652 0.078 -21.308 0.000 -1.652 -1.652
## UWES03De|t2 -1.137 0.058 -19.494 0.000 -1.137 -1.137
## UWES03De|t3 -0.760 0.051 -14.926 0.000 -0.760 -0.760
## UWES03De|t4 -0.381 0.047 -8.112 0.000 -0.381 -0.381
## UWES03De|t5 -0.018 0.046 -0.401 0.688 -0.018 -0.018
## UWES03De|t6 0.947 0.054 17.520 0.000 0.947 0.947
## UWES04.De|t1 -1.567 0.073 -21.362 0.000 -1.567 -1.567
## UWES04.De|t2 -1.130 0.058 -19.439 0.000 -1.130 -1.130
## UWES04.De|t3 -0.778 0.051 -15.200 0.000 -0.778 -0.778
## UWES04.De|t4 -0.447 0.047 -9.411 0.000 -0.447 -0.447
## UWES04.De|t5 -0.062 0.046 -1.349 0.177 -0.062 -0.062
## UWES04.De|t6 0.751 0.051 14.788 0.000 0.751 0.751
## UWES05Vi|t1 -1.275 0.062 -20.493 0.000 -1.275 -1.275
## UWES05Vi|t2 -0.819 0.052 -15.810 0.000 -0.819 -0.819
## UWES05Vi|t3 -0.553 0.048 -11.418 0.000 -0.553 -0.553
## UWES05Vi|t4 -0.265 0.046 -5.719 0.000 -0.265 -0.265
## UWES05Vi|t5 0.089 0.046 1.933 0.053 0.089 0.089
## UWES05Vi|t6 0.995 0.055 18.086 0.000 0.995 0.995
## UWES06Ab|t1 -1.406 0.067 -21.089 0.000 -1.406 -1.406
## UWES06Ab|t2 -1.081 0.057 -18.987 0.000 -1.081 -1.081
## UWES06Ab|t3 -0.787 0.051 -15.336 0.000 -0.787 -0.787
## UWES06Ab|t4 -0.392 0.047 -8.329 0.000 -0.392 -0.392
## UWES06Ab|t5 -0.015 0.046 -0.328 0.743 -0.015 -0.015
## UWES06Ab|t6 0.787 0.051 15.336 0.000 0.787 0.787
## UWES07De|t1 -1.652 0.078 -21.308 0.000 -1.652 -1.652
## UWES07De|t2 -1.329 0.064 -20.783 0.000 -1.329 -1.329
## UWES07De|t3 -0.952 0.054 -17.583 0.000 -0.952 -0.952
## UWES07De|t4 -0.620 0.049 -12.625 0.000 -0.620 -0.620
## UWES07De|t5 -0.244 0.046 -5.283 0.000 -0.244 -0.244
## UWES07De|t6 0.461 0.048 9.699 0.000 0.461 0.461
## UWES08Ab|t1 -1.736 0.082 -21.128 0.000 -1.736 -1.736
## UWES08Ab|t2 -1.397 0.066 -21.060 0.000 -1.397 -1.397
## UWES08Ab|t3 -1.029 0.056 -18.453 0.000 -1.029 -1.029
## UWES08Ab|t4 -0.738 0.051 -14.582 0.000 -0.738 -0.738
## UWES08Ab|t5 -0.335 0.047 -7.171 0.000 -0.335 -0.335
## UWES08Ab|t6 0.356 0.047 7.605 0.000 0.356 0.356
## UWES09Ab|t1 -1.481 0.070 -21.280 0.000 -1.481 -1.481
## UWES09Ab|t2 -1.034 0.056 -18.513 0.000 -1.034 -1.034
## UWES09Ab|t3 -0.690 0.050 -13.818 0.000 -0.690 -0.690
## UWES09Ab|t4 -0.324 0.047 -6.953 0.000 -0.324 -0.324
## UWES09Ab|t5 0.075 0.046 1.641 0.101 0.075 0.075
## UWES09Ab|t6 0.916 0.053 17.134 0.000 0.916 0.916
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AEC04 0.067 0.067 0.067
## .AEC01 0.252 0.252 0.252
## .AEC02 0.055 0.055 0.055
## .AEC03 0.439 0.439 0.439
## .AEG01 0.333 0.333 0.333
## .AEG02 0.652 0.652 0.652
## .AEG03 0.368 0.368 0.368
## .AEG04 0.539 0.539 0.539
## .AEG05 0.411 0.411 0.411
## .AEG06 0.581 0.581 0.581
## .AEG07 0.486 0.486 0.486
## .AEG08 0.358 0.358 0.358
## .AEG09 0.525 0.525 0.525
## .AEG10 0.422 0.422 0.422
## .AEO01 0.439 0.439 0.439
## .AEO02 0.337 0.337 0.337
## .AEO03 0.401 0.401 0.401
## .AEO04 0.549 0.549 0.549
## .AEO05 0.564 0.564 0.564
## .AEO06 0.511 0.511 0.511
## .WAMI01 0.118 0.118 0.118
## .WAMI02 0.252 0.252 0.252
## .WAMI03 0.601 0.601 0.601
## .WAMI04 0.168 0.168 0.168
## .WAMI05 0.190 0.190 0.190
## .WAMI06 0.353 0.353 0.353
## .WAMI07 0.363 0.363 0.363
## .WAMI08 0.099 0.099 0.099
## .WAMI09 0.352 0.352 0.352
## .WAMI10 0.314 0.314 0.314
## .UWES01Vi 0.285 0.285 0.285
## .UWES02Vi 0.227 0.227 0.227
## .UWES03De 0.131 0.131 0.131
## .UWES04.De 0.092 0.092 0.092
## .UWES05Vi 0.216 0.216 0.216
## .UWES06Ab 0.330 0.330 0.330
## .UWES07De 0.149 0.149 0.149
## .UWES08Ab 0.129 0.129 0.129
## .UWES09Ab 0.632 0.632 0.632
## AEC 1.000 1.000 1.000
## AEG 1.000 1.000 1.000
## AEO 1.000 1.000 1.000
## WAMI 1.000 1.000 1.000
## Engaj 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AEC04 1.000 1.000 1.000
## AEC01 1.000 1.000 1.000
## AEC02 1.000 1.000 1.000
## AEC03 1.000 1.000 1.000
## AEG01 1.000 1.000 1.000
## AEG02 1.000 1.000 1.000
## AEG03 1.000 1.000 1.000
## AEG04 1.000 1.000 1.000
## AEG05 1.000 1.000 1.000
## AEG06 1.000 1.000 1.000
## AEG07 1.000 1.000 1.000
## AEG08 1.000 1.000 1.000
## AEG09 1.000 1.000 1.000
## AEG10 1.000 1.000 1.000
## AEO01 1.000 1.000 1.000
## AEO02 1.000 1.000 1.000
## AEO03 1.000 1.000 1.000
## AEO04 1.000 1.000 1.000
## AEO05 1.000 1.000 1.000
## AEO06 1.000 1.000 1.000
## WAMI01 1.000 1.000 1.000
## WAMI02 1.000 1.000 1.000
## WAMI03 1.000 1.000 1.000
## WAMI04 1.000 1.000 1.000
## WAMI05 1.000 1.000 1.000
## WAMI06 1.000 1.000 1.000
## WAMI07 1.000 1.000 1.000
## WAMI08 1.000 1.000 1.000
## WAMI09 1.000 1.000 1.000
## WAMI10 1.000 1.000 1.000
## UWES01Vi 1.000 1.000 1.000
## UWES02Vi 1.000 1.000 1.000
## UWES03De 1.000 1.000 1.000
## UWES04.De 1.000 1.000 1.000
## UWES05Vi 1.000 1.000 1.000
## UWES06Ab 1.000 1.000 1.000
## UWES07De 1.000 1.000 1.000
## UWES08Ab 1.000 1.000 1.000
## UWES09Ab 1.000 1.000 1.0008.5.0.1 Robust and Scaled Fit Measures
lavaan::fitMeasures(fit,c("chisq.scaled","df.scaled","pvalue","srmr","cfi.scaled","tli.scaled","rmsea.scaled","rmsea.ci.lower.scaled","rmsea.ci.upper.scaled"))## chisq.scaled df.scaled pvalue
## 1352.810 690.000 NA
## srmr cfi.scaled tli.scaled
## 0.044 0.970 0.967
## rmsea.scaled rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.035 0.032 0.0388.5.0.2 Factor Loadings - Standardized
parameters<-lavaan::standardizedSolution(fit)
loadings<-parameters[parameters$op=="=~",]
loadings## lhs op rhs est.std se z pvalue ci.lower ci.upper
## 1 AEC =~ AEC04 0.966 0.017 55.78 0 0.932 1.000
## 2 AEC =~ AEC01 0.865 0.021 41.57 0 0.824 0.906
## 3 AEC =~ AEC02 0.972 0.020 48.46 0 0.933 1.012
## 4 AEC =~ AEC03 0.749 0.026 28.40 0 0.697 0.801
## 5 AEG =~ AEG01 0.816 0.033 24.88 0 0.752 0.881
## 6 AEG =~ AEG02 0.590 0.036 16.52 0 0.520 0.660
## 7 AEG =~ AEG03 0.795 0.023 33.86 0 0.749 0.841
## 8 AEG =~ AEG04 0.679 0.037 18.22 0 0.606 0.752
## 9 AEG =~ AEG05 0.768 0.031 24.68 0 0.707 0.829
## 10 AEG =~ AEG06 0.648 0.035 18.47 0 0.579 0.716
## 11 AEG =~ AEG07 0.717 0.033 22.03 0 0.653 0.781
## 12 AEG =~ AEG08 0.801 0.025 32.55 0 0.753 0.849
## 13 AEG =~ AEG09 0.689 0.031 22.51 0 0.629 0.749
## 14 AEG =~ AEG10 0.760 0.027 28.57 0 0.708 0.812
## 16 AEO =~ AEO01 0.749 0.025 29.89 0 0.700 0.798
## 17 AEO =~ AEO02 0.814 0.021 39.12 0 0.773 0.855
## 18 AEO =~ AEO03 0.774 0.020 39.27 0 0.735 0.812
## 19 AEO =~ AEO04 0.672 0.029 22.82 0 0.614 0.730
## 20 AEO =~ AEO05 0.661 0.028 23.87 0 0.606 0.715
## 21 AEO =~ AEO06 0.699 0.025 27.89 0 0.650 0.749
## 22 WAMI =~ WAMI01 0.939 0.012 79.12 0 0.916 0.962
## 23 WAMI =~ WAMI02 0.865 0.015 56.35 0 0.835 0.895
## 24 WAMI =~ WAMI03 -0.631 0.029 -21.53 0 -0.689 -0.574
## 25 WAMI =~ WAMI04 0.912 0.012 74.49 0 0.888 0.936
## 26 WAMI =~ WAMI05 0.900 0.015 60.74 0 0.871 0.929
## 27 WAMI =~ WAMI06 0.805 0.019 43.20 0 0.768 0.841
## 28 WAMI =~ WAMI07 0.798 0.018 44.43 0 0.763 0.833
## 29 WAMI =~ WAMI08 0.949 0.010 93.56 0 0.929 0.969
## 30 WAMI =~ WAMI09 0.805 0.018 44.93 0 0.770 0.840
## 31 WAMI =~ WAMI10 0.828 0.017 49.08 0 0.795 0.861
## 32 Engaj =~ UWES01Vi 0.846 0.014 62.29 0 0.819 0.872
## 33 Engaj =~ UWES02Vi 0.879 0.012 75.09 0 0.856 0.902
## 34 Engaj =~ UWES03De 0.932 0.008 113.83 0 0.916 0.948
## 35 Engaj =~ UWES04.De 0.953 0.009 108.84 0 0.936 0.970
## 36 Engaj =~ UWES05Vi 0.885 0.012 74.13 0 0.862 0.909
## 37 Engaj =~ UWES06Ab 0.819 0.016 51.53 0 0.788 0.850
## 38 Engaj =~ UWES07De 0.922 0.011 83.01 0 0.901 0.944
## 39 Engaj =~ UWES08Ab 0.933 0.011 88.63 0 0.912 0.954
## 40 Engaj =~ UWES09Ab 0.607 0.026 23.49 0 0.556 0.6588.5.0.3 Covariances Standardized Correlations
parameters<-lavaan::standardizedSolution(fit)
corr<-parameters[parameters$op=="~~",]
corr## lhs op rhs est.std se z pvalue ci.lower ci.upper
## 15 AEG04 ~~ AEG06 0.552 0.040 13.710 0.000 0.473 0.631
## 41 UWES01Vi ~~ UWES02Vi 0.886 0.012 75.913 0.000 0.863 0.909
## 214 AEC04 ~~ AEC04 0.067 0.033 2.008 0.045 0.002 0.133
## 215 AEC01 ~~ AEC01 0.252 0.036 7.011 0.000 0.182 0.323
## 216 AEC02 ~~ AEC02 0.055 0.039 1.403 0.161 -0.022 0.131
## 217 AEC03 ~~ AEC03 0.439 0.039 11.118 0.000 0.362 0.517
## 218 AEG01 ~~ AEG01 0.333 0.054 6.220 0.000 0.228 0.438
## 219 AEG02 ~~ AEG02 0.652 0.042 15.495 0.000 0.570 0.735
## 220 AEG03 ~~ AEG03 0.368 0.037 9.878 0.000 0.295 0.442
## 221 AEG04 ~~ AEG04 0.539 0.051 10.668 0.000 0.440 0.638
## 222 AEG05 ~~ AEG05 0.411 0.048 8.595 0.000 0.317 0.504
## 223 AEG06 ~~ AEG06 0.581 0.045 12.786 0.000 0.492 0.670
## 224 AEG07 ~~ AEG07 0.486 0.047 10.415 0.000 0.395 0.577
## 225 AEG08 ~~ AEG08 0.358 0.039 9.081 0.000 0.281 0.435
## 226 AEG09 ~~ AEG09 0.525 0.042 12.451 0.000 0.443 0.608
## 227 AEG10 ~~ AEG10 0.422 0.040 10.435 0.000 0.343 0.501
## 228 AEO01 ~~ AEO01 0.439 0.038 11.679 0.000 0.365 0.512
## 229 AEO02 ~~ AEO02 0.337 0.034 9.945 0.000 0.271 0.403
## 230 AEO03 ~~ AEO03 0.401 0.030 13.170 0.000 0.342 0.461
## 231 AEO04 ~~ AEO04 0.549 0.040 13.867 0.000 0.471 0.626
## 232 AEO05 ~~ AEO05 0.564 0.037 15.405 0.000 0.492 0.635
## 233 AEO06 ~~ AEO06 0.511 0.035 14.562 0.000 0.442 0.580
## 234 WAMI01 ~~ WAMI01 0.118 0.022 5.296 0.000 0.074 0.162
## 235 WAMI02 ~~ WAMI02 0.252 0.027 9.492 0.000 0.200 0.304
## 236 WAMI03 ~~ WAMI03 0.601 0.037 16.243 0.000 0.529 0.674
## 237 WAMI04 ~~ WAMI04 0.168 0.022 7.505 0.000 0.124 0.212
## 238 WAMI05 ~~ WAMI05 0.190 0.027 7.127 0.000 0.138 0.242
## 239 WAMI06 ~~ WAMI06 0.353 0.030 11.761 0.000 0.294 0.411
## 240 WAMI07 ~~ WAMI07 0.363 0.029 12.658 0.000 0.307 0.419
## 241 WAMI08 ~~ WAMI08 0.099 0.019 5.137 0.000 0.061 0.137
## 242 WAMI09 ~~ WAMI09 0.352 0.029 12.212 0.000 0.296 0.409
## 243 WAMI10 ~~ WAMI10 0.314 0.028 11.233 0.000 0.259 0.369
## 244 UWES01Vi ~~ UWES01Vi 0.285 0.023 12.401 0.000 0.240 0.330
## 245 UWES02Vi ~~ UWES02Vi 0.227 0.021 11.026 0.000 0.187 0.267
## 246 UWES03De ~~ UWES03De 0.131 0.015 8.563 0.000 0.101 0.161
## 247 UWES04.De ~~ UWES04.De 0.092 0.017 5.491 0.000 0.059 0.124
## 248 UWES05Vi ~~ UWES05Vi 0.216 0.021 10.207 0.000 0.174 0.257
## 249 UWES06Ab ~~ UWES06Ab 0.330 0.026 12.662 0.000 0.278 0.381
## 250 UWES07De ~~ UWES07De 0.149 0.021 7.274 0.000 0.109 0.189
## 251 UWES08Ab ~~ UWES08Ab 0.129 0.020 6.591 0.000 0.091 0.168
## 252 UWES09Ab ~~ UWES09Ab 0.632 0.031 20.132 0.000 0.570 0.693
## 253 AEC ~~ AEC 1.000 0.000 NA NA 1.000 1.000
## 254 AEG ~~ AEG 1.000 0.000 NA NA 1.000 1.000
## 255 AEO ~~ AEO 1.000 0.000 NA NA 1.000 1.000
## 256 WAMI ~~ WAMI 1.000 0.000 NA NA 1.000 1.000
## 257 Engaj ~~ Engaj 1.000 0.000 NA NA 1.000 1.000
## 258 AEC ~~ AEG 0.586 0.035 16.773 0.000 0.518 0.655
## 259 AEC ~~ AEO 0.447 0.030 15.146 0.000 0.389 0.505
## 260 AEC ~~ WAMI 0.264 0.034 7.783 0.000 0.197 0.330
## 261 AEC ~~ Engaj 0.257 0.034 7.581 0.000 0.190 0.323
## 262 AEG ~~ AEO 0.854 0.021 40.476 0.000 0.812 0.895
## 263 AEG ~~ WAMI 0.433 0.037 11.634 0.000 0.360 0.506
## 264 AEG ~~ Engaj 0.464 0.035 13.372 0.000 0.396 0.532
## 265 AEO ~~ WAMI 0.533 0.030 17.588 0.000 0.473 0.592
## 266 AEO ~~ Engaj 0.594 0.027 21.830 0.000 0.541 0.647
## 267 WAMI ~~ Engaj 0.794 0.014 55.422 0.000 0.766 0.8228.5.0.4 Modification Indices
modificationindices(fit, sort.=T)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 452 WAMI =~ AEG01 84.739 0.158 0.158 0.158 0.158
## 481 Engaj =~ AEG01 81.596 0.161 0.161 0.161 0.161
## 465 WAMI =~ AEO04 65.004 0.169 0.169 0.169 0.169
## 497 Engaj =~ WAMI01 51.262 0.371 0.371 0.371 0.371
## 897 AEG09 ~~ AEO01 50.759 0.264 0.264 0.550 0.550
## 425 AEO =~ AEG07 49.709 0.416 0.416 0.416 0.416
## 419 AEO =~ AEG01 48.178 0.421 0.421 0.421 0.421
## 494 Engaj =~ AEO04 44.992 0.151 0.151 0.151 0.151
## 458 WAMI =~ AEG07 42.445 0.109 0.109 0.109 0.109
## 420 AEO =~ AEG02 38.974 -0.359 -0.359 -0.359 -0.359
## 1037 AEO05 ~~ AEO06 37.820 0.232 0.232 0.432 0.432
## 482 Engaj =~ AEG02 37.564 -0.104 -0.104 -0.104 -0.104
## 453 WAMI =~ AEG02 36.096 -0.099 -0.099 -0.099 -0.099
## 487 Engaj =~ AEG07 35.412 0.104 0.104 0.104 0.104
## 486 Engaj =~ AEG06 31.570 -0.097 -0.097 -0.097 -0.097
## 457 WAMI =~ AEG06 30.941 -0.093 -0.093 -0.093 -0.093
## 1113 WAMI03 ~~ WAMI06 26.906 -0.193 -0.193 -0.419 -0.419
## 362 AEC =~ AEO02 25.262 0.148 0.148 0.148 0.148
## 427 AEO =~ AEG09 24.704 0.292 0.292 0.292 0.292
## 393 AEG =~ AEO04 22.621 -0.290 -0.290 -0.290 -0.290
## 391 AEG =~ AEO02 20.910 0.292 0.292 0.292 0.292
## 502 Engaj =~ WAMI06 20.725 -0.228 -0.228 -0.228 -0.228
## 1170 WAMI07 ~~ WAMI09 19.268 0.165 0.165 0.462 0.462
## 365 AEC =~ AEO05 18.464 -0.121 -0.121 -0.121 -0.121
## 461 WAMI =~ AEG10 18.186 -0.072 -0.072 -0.072 -0.072
## 471 WAMI =~ UWES04.De 17.046 0.216 0.216 0.216 0.216
## 490 Engaj =~ AEG10 15.796 -0.070 -0.070 -0.070 -0.070
## 455 WAMI =~ AEG04 15.735 -0.067 -0.067 -0.067 -0.067
## 499 Engaj =~ WAMI03 14.845 0.186 0.186 0.186 0.186
## 422 AEO =~ AEG04 14.675 -0.227 -0.227 -0.227 -0.227
## 489 Engaj =~ AEG09 14.547 0.066 0.066 0.066 0.066
## 752 AEG04 ~~ AEG05 14.283 0.142 0.142 0.302 0.302
## 424 AEO =~ AEG06 13.657 -0.217 -0.217 -0.217 -0.217
## 484 Engaj =~ AEG04 13.515 -0.064 -0.064 -0.064 -0.064
## 693 AEG02 ~~ AEG09 13.439 -0.136 -0.136 -0.232 -0.232
## 1159 WAMI06 ~~ WAMI10 13.307 0.137 0.137 0.413 0.413
## 463 WAMI =~ AEO02 11.355 -0.074 -0.074 -0.074 -0.074
## 505 Engaj =~ WAMI09 11.331 -0.168 -0.168 -0.168 -0.168
## 474 WAMI =~ UWES07De 11.313 0.174 0.174 0.174 0.174
## 355 AEC =~ AEG05 10.737 0.110 0.110 0.110 0.110
## 782 AEG05 ~~ AEG06 10.593 0.122 0.122 0.250 0.250
## 492 Engaj =~ AEO02 10.572 -0.077 -0.077 -0.077 -0.077
## 783 AEG05 ~~ AEG07 10.545 -0.122 -0.122 -0.274 -0.274
## 1192 WAMI09 ~~ WAMI10 10.063 0.120 0.120 0.359 0.359
## 450 WAMI =~ AEC02 10.058 0.053 0.053 0.053 0.053
## 428 AEO =~ AEG10 9.927 -0.188 -0.188 -0.188 -0.188
## 442 AEO =~ UWES04.De 9.851 -0.075 -0.075 -0.075 -0.075
## 378 AEC =~ UWES02Vi 9.785 0.063 0.063 0.063 0.063
## 1088 WAMI01 ~~ UWES04.De 9.453 0.115 0.115 1.108 1.108
## 930 AEG10 ~~ WAMI03 9.447 0.111 0.111 0.219 0.219
## 440 AEO =~ UWES02Vi 9.404 0.073 0.073 0.073 0.073
## 658 AEG01 ~~ AEG07 9.305 -0.115 -0.115 -0.287 -0.287
## 409 AEG =~ UWES04.De 9.167 -0.059 -0.059 -0.059 -0.059
## 896 AEG09 ~~ AEG10 9.020 0.113 0.113 0.240 0.240
## 460 WAMI =~ AEG09 8.950 0.050 0.050 0.050 0.050
## 521 AEC04 ~~ AEO02 8.783 0.111 0.111 0.737 0.737
## 407 AEG =~ UWES02Vi 8.734 0.057 0.057 0.057 0.057
## 394 AEG =~ AEO05 8.724 -0.179 -0.179 -0.179 -0.179
## 814 AEG06 ~~ AEG09 8.609 -0.109 -0.109 -0.198 -0.198
## 660 AEG01 ~~ AEG09 8.573 -0.111 -0.111 -0.264 -0.264
## 479 Engaj =~ AEC02 8.530 0.049 0.049 0.049 0.049
## 688 AEG02 ~~ AEG04 8.520 0.108 0.108 0.182 0.182
## 506 Engaj =~ WAMI10 8.505 -0.147 -0.147 -0.147 -0.147
## 724 AEG03 ~~ AEG08 8.441 0.111 0.111 0.305 0.305
## 1211 UWES01Vi ~~ UWES03De 8.420 0.111 0.111 0.576 0.576
## 1242 UWES06Ab ~~ UWES09Ab 8.316 0.107 0.107 0.235 0.235
## 687 AEG02 ~~ AEG03 8.271 0.108 0.108 0.219 0.219
## 359 AEC =~ AEG09 8.219 -0.095 -0.095 -0.095 -0.095
## 682 AEG01 ~~ UWES05Vi 8.025 0.103 0.103 0.383 0.383
## 949 AEO01 ~~ AEO04 7.981 -0.107 -0.107 -0.219 -0.219
## 357 AEC =~ AEG07 7.755 -0.092 -0.092 -0.092 -0.092
## 790 AEG05 ~~ AEO04 7.674 -0.103 -0.103 -0.216 -0.216
## 668 AEG01 ~~ WAMI01 7.669 0.101 0.101 0.507 0.507
## 1092 WAMI01 ~~ UWES08Ab 7.630 0.103 0.103 0.837 0.837
## 1091 WAMI01 ~~ UWES07De 7.593 0.103 0.103 0.777 0.777
## 431 AEO =~ WAMI03 7.576 0.058 0.058 0.058 0.058
## 925 AEG10 ~~ AEO04 7.317 -0.100 -0.100 -0.208 -0.208
## 1164 WAMI06 ~~ UWES05Vi 7.315 -0.100 -0.100 -0.363 -0.363
## 836 AEG06 ~~ UWES05Vi 7.310 -0.098 -0.098 -0.276 -0.276
## 1019 AEO04 ~~ WAMI02 7.267 0.098 0.098 0.263 0.263
## 380 AEC =~ UWES04.De 7.217 -0.054 -0.054 -0.054 -0.054
## 383 AEC =~ UWES07De 7.010 0.053 0.053 0.053 0.053
## 1161 WAMI06 ~~ UWES02Vi 6.971 -0.098 -0.098 -0.346 -0.346
## 414 AEG =~ UWES09Ab 6.919 -0.048 -0.048 -0.048 -0.048
## 1218 UWES02Vi ~~ UWES03De 6.915 0.101 0.101 0.586 0.586
## 1105 WAMI02 ~~ UWES04.De 6.908 0.098 0.098 0.645 0.645
## 369 AEC =~ WAMI03 6.869 0.050 0.050 0.050 0.050
## 1024 AEO04 ~~ WAMI07 6.782 0.094 0.094 0.212 0.212
## 690 AEG02 ~~ AEG06 6.764 0.096 0.096 0.156 0.156
## 1117 WAMI03 ~~ WAMI10 6.746 -0.097 -0.097 -0.223 -0.223
## 848 AEG07 ~~ AEO05 6.532 0.094 0.094 0.180 0.180
## 855 AEG07 ~~ WAMI06 6.529 0.092 0.092 0.223 0.223
## 708 AEG02 ~~ WAMI08 6.509 -0.092 -0.092 -0.363 -0.363
## 433 AEO =~ WAMI05 6.496 0.056 0.056 0.056 0.056
## 447 AEO =~ UWES09Ab 6.479 -0.058 -0.058 -0.058 -0.058
## 972 AEO02 ~~ AEO04 6.401 -0.097 -0.097 -0.226 -0.226
## 1160 WAMI06 ~~ UWES01Vi 6.383 -0.093 -0.093 -0.295 -0.295
## 852 AEG07 ~~ WAMI03 6.346 -0.091 -0.091 -0.167 -0.167
## 667 AEG01 ~~ AEO06 6.164 -0.092 -0.092 -0.224 -0.224
## 971 AEO02 ~~ AEO03 6.078 0.096 0.096 0.261 0.261
## 659 AEG01 ~~ AEG08 5.975 -0.093 -0.093 -0.270 -0.270
## 711 AEG02 ~~ UWES01Vi 5.966 -0.088 -0.088 -0.204 -0.204
## 900 AEG09 ~~ AEO04 5.923 -0.090 -0.090 -0.167 -0.167
## 475 WAMI =~ UWES08Ab 5.866 0.126 0.126 0.126 0.126
## 483 Engaj =~ AEG03 5.812 -0.043 -0.043 -0.043 -0.043
## 397 AEG =~ WAMI02 5.783 -0.044 -0.044 -0.044 -0.044
## 994 AEO03 ~~ AEO04 5.783 -0.092 -0.092 -0.195 -0.195
## 714 AEG02 ~~ UWES04.De 5.747 -0.087 -0.087 -0.355 -0.355
## 379 AEC =~ UWES03De 5.721 -0.048 -0.048 -0.048 -0.048
## 1025 AEO04 ~~ WAMI08 5.702 0.087 0.087 0.374 0.374
## 1083 WAMI01 ~~ WAMI09 5.693 -0.091 -0.091 -0.445 -0.445
## 469 WAMI =~ UWES02Vi 5.626 -0.124 -0.124 -0.124 -0.124
## 417 AEO =~ AEC02 5.589 0.067 0.067 0.067 0.067
## 597 AEC02 ~~ AEO05 5.537 -0.087 -0.087 -0.494 -0.494
## 398 AEG =~ WAMI03 5.525 0.041 0.041 0.041 0.041
## 352 AEC =~ AEG02 5.505 0.076 0.076 0.076 0.076
## 924 AEG10 ~~ AEO03 5.497 0.087 0.087 0.212 0.212
## 1021 AEO04 ~~ WAMI04 5.462 0.085 0.085 0.281 0.281
## 622 AEC03 ~~ AEG05 5.459 0.086 0.086 0.203 0.203
## 430 AEO =~ WAMI02 5.393 -0.051 -0.051 -0.051 -0.051
## 839 AEG06 ~~ UWES08Ab 5.392 -0.084 -0.084 -0.307 -0.307
## 400 AEG =~ WAMI05 5.325 0.042 0.042 0.042 0.042
## 1081 WAMI01 ~~ WAMI07 5.268 -0.087 -0.087 -0.422 -0.422
## 822 AEG06 ~~ WAMI01 5.223 -0.083 -0.083 -0.316 -0.316
## 351 AEC =~ AEG01 5.166 -0.077 -0.077 -0.077 -0.077
## 1245 UWES08Ab ~~ UWES09Ab 5.148 0.085 0.085 0.297 0.297
## 817 AEG06 ~~ AEO02 5.145 0.084 0.084 0.190 0.190
## 454 WAMI =~ AEG03 5.074 -0.038 -0.038 -0.038 -0.038
## 451 WAMI =~ AEC03 5.072 -0.033 -0.033 -0.033 -0.033
## 665 AEG01 ~~ AEO04 5.048 -0.084 -0.084 -0.195 -0.195
## 673 AEG01 ~~ WAMI06 5.016 0.081 0.081 0.236 0.236
## 504 Engaj =~ WAMI08 5.011 0.116 0.116 0.116 0.116
## 1142 WAMI05 ~~ WAMI06 4.911 0.084 0.084 0.325 0.325
## 999 AEO03 ~~ WAMI03 4.877 0.080 0.080 0.163 0.163
## 672 AEG01 ~~ WAMI05 4.863 0.080 0.080 0.318 0.318
## 514 AEC04 ~~ AEG05 4.845 0.082 0.082 0.495 0.495
## 683 AEG01 ~~ UWES06Ab 4.809 0.079 0.079 0.240 0.240
## 619 AEC03 ~~ AEG02 4.754 0.079 0.079 0.149 0.149
## 854 AEG07 ~~ WAMI05 4.707 0.078 0.078 0.258 0.258
## 842 AEG07 ~~ AEG09 4.667 -0.081 -0.081 -0.160 -0.160
## 1186 WAMI08 ~~ UWES04.De 4.630 0.081 0.081 0.848 0.848
## 561 AEC01 ~~ AEO05 4.572 -0.078 -0.078 -0.208 -0.208
## 1087 WAMI01 ~~ UWES03De 4.520 0.080 0.080 0.641 0.641
## 421 AEO =~ AEG03 4.484 -0.128 -0.128 -0.128 -0.128
## 751 AEG03 ~~ UWES09Ab 4.440 -0.076 -0.076 -0.157 -0.157
## 1165 WAMI06 ~~ UWES06Ab 4.426 -0.078 -0.078 -0.228 -0.228
## 480 Engaj =~ AEC03 4.370 -0.031 -0.031 -0.031 -0.031
## 1023 AEO04 ~~ WAMI06 4.291 0.075 0.075 0.171 0.171
## 441 AEO =~ UWES03De 4.272 -0.049 -0.049 -0.049 -0.049
## 671 AEG01 ~~ WAMI04 4.243 0.075 0.075 0.316 0.316
## 691 AEG02 ~~ AEG07 4.243 0.077 0.077 0.136 0.136
## 950 AEO01 ~~ AEO05 4.169 -0.077 -0.077 -0.156 -0.156
## 498 Engaj =~ WAMI02 4.161 0.104 0.104 0.104 0.104
## 725 AEG03 ~~ AEG09 4.154 0.077 0.077 0.175 0.175
## 825 AEG06 ~~ WAMI04 4.138 -0.073 -0.073 -0.235 -0.235
## 1215 UWES01Vi ~~ UWES07De 4.137 -0.078 -0.078 -0.377 -0.377
## 464 WAMI =~ AEO03 4.106 -0.044 -0.044 -0.044 -0.044
## 408 AEG =~ UWES03De 4.099 -0.039 -0.039 -0.039 -0.039
## 1078 WAMI01 ~~ WAMI04 4.052 -0.077 -0.077 -0.550 -0.550
## 765 AEG04 ~~ WAMI03 4.002 0.072 0.072 0.126 0.126
## 1048 AEO05 ~~ UWES01Vi 3.979 0.073 0.073 0.181 0.181
## 1089 WAMI01 ~~ UWES05Vi 3.958 0.074 0.074 0.465 0.465
## 841 AEG07 ~~ AEG08 3.952 -0.075 -0.075 -0.180 -0.180
## 412 AEG =~ UWES07De 3.942 0.038 0.038 0.038 0.038
## 1026 AEO04 ~~ WAMI09 3.942 0.072 0.072 0.164 0.164
## 1236 UWES05Vi ~~ UWES06Ab 3.922 0.075 0.075 0.281 0.281
## 685 AEG01 ~~ UWES08Ab 3.917 0.072 0.072 0.347 0.347
## 388 AEG =~ AEC02 3.914 0.072 0.072 0.072 0.072
## 472 WAMI =~ UWES05Vi 3.905 -0.101 -0.101 -0.101 -0.101
## 1022 AEO04 ~~ WAMI05 3.888 0.072 0.072 0.222 0.222
## 1016 AEO04 ~~ AEO05 3.863 0.074 0.074 0.133 0.133
## 818 AEG06 ~~ AEO03 3.849 0.073 0.073 0.151 0.151
## 445 AEO =~ UWES07De 3.817 0.047 0.047 0.047 0.047
## 500 Engaj =~ WAMI04 3.796 0.100 0.100 0.100 0.100
## 1213 UWES01Vi ~~ UWES05Vi 3.750 0.074 0.074 0.297 0.297
## 656 AEG01 ~~ AEG05 3.712 -0.073 -0.073 -0.198 -0.198
## 1070 AEO06 ~~ UWES04.De 3.704 -0.071 -0.071 -0.326 -0.326
## 713 AEG02 ~~ UWES03De 3.693 -0.069 -0.069 -0.238 -0.238
## 675 AEG01 ~~ WAMI08 3.691 0.070 0.070 0.384 0.384
## 858 AEG07 ~~ WAMI09 3.658 0.069 0.069 0.167 0.167
## 1202 WAMI10 ~~ UWES01Vi 3.642 -0.071 -0.071 -0.236 -0.236
## 723 AEG03 ~~ AEG07 3.601 -0.072 -0.072 -0.169 -0.169
## 1108 WAMI02 ~~ UWES07De 3.567 0.070 0.070 0.363 0.363
## 468 WAMI =~ UWES01Vi 3.560 -0.098 -0.098 -0.098 -0.098
## 701 AEG02 ~~ WAMI01 3.554 -0.068 -0.068 -0.245 -0.245
## 1119 WAMI03 ~~ UWES02Vi 3.467 0.068 0.068 0.185 0.185
## 632 AEC03 ~~ AEO05 3.453 -0.068 -0.068 -0.136 -0.136
## 1084 WAMI01 ~~ WAMI10 3.426 -0.071 -0.071 -0.367 -0.367
## 766 AEG04 ~~ WAMI04 3.417 -0.067 -0.067 -0.222 -0.222
## 823 AEG06 ~~ WAMI02 3.408 -0.067 -0.067 -0.174 -0.174
## 917 AEG09 ~~ UWES05Vi 3.398 0.067 0.067 0.198 0.198
## 476 WAMI =~ UWES09Ab 3.396 -0.089 -0.089 -0.089 -0.089
## 1222 UWES02Vi ~~ UWES07De 3.361 -0.070 -0.070 -0.382 -0.382
## 555 AEC01 ~~ AEG09 3.359 -0.068 -0.068 -0.186 -0.186
## 1080 WAMI01 ~~ WAMI06 3.356 -0.070 -0.070 -0.342 -0.342
## 699 AEG02 ~~ AEO05 3.355 0.067 0.067 0.111 0.111
## 953 AEO01 ~~ WAMI02 3.299 -0.066 -0.066 -0.199 -0.199
## 776 AEG04 ~~ UWES04.De 3.283 -0.066 -0.066 -0.295 -0.295
## 929 AEG10 ~~ WAMI02 3.279 -0.066 -0.066 -0.201 -0.201
## 1096 WAMI02 ~~ WAMI05 3.274 -0.069 -0.069 -0.315 -0.315
## 528 AEC04 ~~ WAMI03 3.245 0.065 0.065 0.323 0.323
## 670 AEG01 ~~ WAMI03 3.224 -0.065 -0.065 -0.144 -0.144
## 976 AEO02 ~~ WAMI02 3.211 -0.065 -0.065 -0.225 -0.225
## 835 AEG06 ~~ UWES04.De 3.198 -0.065 -0.065 -0.281 -0.281
## 508 AEC04 ~~ AEC02 3.172 -0.082 -0.082 -1.361 -1.361
## 366 AEC =~ AEO06 3.171 0.051 0.051 0.051 0.051
## 669 AEG01 ~~ WAMI02 3.168 0.064 0.064 0.222 0.222
## 1203 WAMI10 ~~ UWES02Vi 3.167 -0.066 -0.066 -0.247 -0.247
## 1220 UWES02Vi ~~ UWES05Vi 3.166 0.068 0.068 0.307 0.307
## 785 AEG05 ~~ AEG09 3.139 -0.067 -0.067 -0.143 -0.143
## 695 AEG02 ~~ AEO01 3.137 -0.065 -0.065 -0.122 -0.122
## 648 AEC03 ~~ UWES05Vi 3.112 -0.064 -0.064 -0.207 -0.207
## 473 WAMI =~ UWES06Ab 3.096 -0.089 -0.089 -0.089 -0.089
## 895 AEG08 ~~ UWES09Ab 3.089 -0.063 -0.063 -0.133 -0.133
## 694 AEG02 ~~ AEG10 3.064 0.065 0.065 0.124 0.124
## 847 AEG07 ~~ AEO04 3.062 0.065 0.065 0.125 0.125
## 1162 WAMI06 ~~ UWES03De 3.059 -0.065 -0.065 -0.303 -0.303
## 370 AEC =~ WAMI04 3.010 0.034 0.034 0.034 0.034
## 496 Engaj =~ AEO06 2.984 -0.039 -0.039 -0.039 -0.039
## 615 AEC02 ~~ UWES07De 2.971 0.063 0.063 0.697 0.697
## 705 AEG02 ~~ WAMI05 2.937 -0.062 -0.062 -0.176 -0.176
## 558 AEC01 ~~ AEO02 2.912 0.063 0.063 0.217 0.217
## 594 AEC02 ~~ AEO02 2.901 0.064 0.064 0.469 0.469
## 770 AEG04 ~~ WAMI08 2.900 -0.062 -0.062 -0.267 -0.267
## 1228 UWES03De ~~ UWES07De 2.870 -0.065 -0.065 -0.466 -0.466
## 1079 WAMI01 ~~ WAMI05 2.847 -0.065 -0.065 -0.432 -0.432
## 1237 UWES05Vi ~~ UWES07De 2.834 -0.064 -0.064 -0.359 -0.359
## 418 AEO =~ AEC03 2.821 -0.040 -0.040 -0.040 -0.040
## 516 AEC04 ~~ AEG07 2.800 -0.062 -0.062 -0.344 -0.344
## 629 AEC03 ~~ AEO02 2.797 0.062 0.062 0.160 0.160
## 367 AEC =~ WAMI01 2.795 -0.033 -0.033 -0.033 -0.033
## 946 AEG10 ~~ UWES09Ab 2.741 -0.060 -0.060 -0.115 -0.115
## 1069 AEO06 ~~ UWES03De 2.732 -0.061 -0.061 -0.234 -0.234
## 432 AEO =~ WAMI04 2.730 0.036 0.036 0.036 0.036
## 933 AEG10 ~~ WAMI06 2.702 -0.059 -0.059 -0.154 -0.154
## 605 AEC02 ~~ WAMI07 2.695 0.060 0.060 0.423 0.423
## 680 AEG01 ~~ UWES03De 2.664 0.059 0.059 0.284 0.284
## 781 AEG04 ~~ UWES09Ab 2.628 -0.058 -0.058 -0.100 -0.100
## 869 AEG08 ~~ AEG09 2.620 0.061 0.061 0.141 0.141
## 1071 AEO06 ~~ UWES05Vi 2.619 -0.059 -0.059 -0.178 -0.178
## 702 AEG02 ~~ WAMI02 2.592 -0.058 -0.058 -0.143 -0.143
## 1123 WAMI03 ~~ UWES06Ab 2.581 0.059 0.059 0.132 0.132
## 853 AEG07 ~~ WAMI04 2.572 0.058 0.058 0.203 0.203
## 712 AEG02 ~~ UWES02Vi 2.548 -0.058 -0.058 -0.150 -0.150
## 945 AEG10 ~~ UWES08Ab 2.521 -0.058 -0.058 -0.247 -0.247
## 977 AEO02 ~~ WAMI03 2.504 0.057 0.057 0.127 0.127
## 973 AEO02 ~~ AEO05 2.502 -0.061 -0.061 -0.139 -0.139
## 503 Engaj =~ WAMI07 2.488 -0.079 -0.079 -0.079 -0.079
## 834 AEG06 ~~ UWES03De 2.484 -0.057 -0.057 -0.207 -0.207
## 591 AEC02 ~~ AEG09 2.480 -0.058 -0.058 -0.344 -0.344
## 387 AEG =~ AEC01 2.457 -0.052 -0.052 -0.052 -0.052
## 734 AEG03 ~~ WAMI02 2.389 -0.056 -0.056 -0.184 -0.184
## 518 AEC04 ~~ AEG09 2.366 -0.057 -0.057 -0.304 -0.304
## 791 AEG05 ~~ AEO05 2.356 -0.057 -0.057 -0.118 -0.118
## 574 AEC01 ~~ UWES02Vi 2.356 0.056 0.056 0.233 0.233
## 1226 UWES03De ~~ UWES05Vi 2.353 0.059 0.059 0.350 0.350
## 684 AEG01 ~~ UWES07De 2.352 0.056 0.056 0.250 0.250
## 511 AEC04 ~~ AEG02 2.336 0.056 0.056 0.269 0.269
## 696 AEG02 ~~ AEO02 2.318 -0.056 -0.056 -0.120 -0.120
## 874 AEG08 ~~ AEO04 2.306 -0.056 -0.056 -0.127 -0.127
## 624 AEC03 ~~ AEG07 2.305 -0.056 -0.056 -0.121 -0.121
## 618 AEC03 ~~ AEG01 2.294 -0.056 -0.056 -0.146 -0.146
## 843 AEG07 ~~ AEG10 2.283 -0.057 -0.057 -0.126 -0.126
## 363 AEC =~ AEO03 2.282 -0.044 -0.044 -0.044 -0.044
## 1223 UWES02Vi ~~ UWES08Ab 2.265 -0.058 -0.058 -0.337 -0.337
## 721 AEG03 ~~ AEG05 2.262 -0.057 -0.057 -0.147 -0.147
## 385 AEC =~ UWES09Ab 2.258 -0.029 -0.029 -0.029 -0.029
## 1020 AEO04 ~~ WAMI03 2.249 -0.054 -0.054 -0.094 -0.094
## 401 AEG =~ WAMI06 2.247 0.027 0.027 0.027 0.027
## 1118 WAMI03 ~~ UWES01Vi 2.218 0.055 0.055 0.132 0.132
## 922 AEG10 ~~ AEO01 2.214 0.055 0.055 0.129 0.129
## 562 AEC01 ~~ AEO06 2.214 0.055 0.055 0.152 0.152
## 610 AEC02 ~~ UWES02Vi 2.199 0.054 0.054 0.485 0.485
## 676 AEG01 ~~ WAMI09 2.195 0.054 0.054 0.156 0.156
## 1216 UWES01Vi ~~ UWES08Ab 2.165 -0.056 -0.056 -0.293 -0.293
## 974 AEO02 ~~ AEO06 2.139 -0.056 -0.056 -0.136 -0.136
## 755 AEG04 ~~ AEG09 2.114 -0.054 -0.054 -0.102 -0.102
## 787 AEG05 ~~ AEO01 2.105 -0.054 -0.054 -0.127 -0.127
## 756 AEG04 ~~ AEG10 2.092 0.054 0.054 0.114 0.114
## 1233 UWES04.De ~~ UWES07De 2.091 -0.056 -0.056 -0.477 -0.477
## 1194 WAMI09 ~~ UWES02Vi 2.085 -0.054 -0.054 -0.189 -0.189
## 364 AEC =~ AEO04 2.049 -0.040 -0.040 -0.040 -0.040
## 1229 UWES03De ~~ UWES08Ab 2.042 -0.055 -0.055 -0.423 -0.423
## 1130 WAMI04 ~~ WAMI08 2.036 -0.055 -0.055 -0.426 -0.426
## 403 AEG =~ WAMI08 2.030 -0.026 -0.026 -0.026 -0.026
## 390 AEG =~ AEO01 2.008 0.088 0.088 0.088 0.088
## 859 AEG07 ~~ WAMI10 1.991 0.051 0.051 0.130 0.130
## 904 AEG09 ~~ WAMI02 1.969 -0.051 -0.051 -0.139 -0.139
## 399 AEG =~ WAMI04 1.965 0.026 0.026 0.026 0.026
## 374 AEC =~ WAMI08 1.957 -0.028 -0.028 -0.028 -0.028
## 681 AEG01 ~~ UWES04.De 1.953 0.051 0.051 0.291 0.291
## 794 AEG05 ~~ WAMI02 1.936 -0.050 -0.050 -0.156 -0.156
## 493 Engaj =~ AEO03 1.936 -0.032 -0.032 -0.032 -0.032
## 434 AEO =~ WAMI06 1.904 0.030 0.030 0.030 0.030
## 819 AEG06 ~~ AEO04 1.896 0.051 0.051 0.090 0.090
## 448 WAMI =~ AEC04 1.877 -0.023 -0.023 -0.023 -0.023
## 582 AEC02 ~~ AEC03 1.870 -0.058 -0.058 -0.375 -0.375
## 1034 AEO04 ~~ UWES07De 1.865 0.050 0.050 0.175 0.175
## 679 AEG01 ~~ UWES02Vi 1.853 0.049 0.049 0.180 0.180
## 1094 WAMI02 ~~ WAMI03 1.845 -0.051 -0.051 -0.130 -0.130
## 634 AEC03 ~~ WAMI01 1.841 -0.049 -0.049 -0.216 -0.216
## 358 AEC =~ AEG08 1.841 0.046 0.046 0.046 0.046
## 485 Engaj =~ AEG05 1.837 0.024 0.024 0.024 0.024
## 875 AEG08 ~~ AEO05 1.832 -0.050 -0.050 -0.112 -0.112
## 829 AEG06 ~~ WAMI08 1.828 -0.049 -0.049 -0.204 -0.204
## 636 AEC03 ~~ WAMI03 1.828 0.049 0.049 0.094 0.094
## 526 AEC04 ~~ WAMI01 1.817 -0.049 -0.049 -0.553 -0.553
## 373 AEC =~ WAMI07 1.816 0.026 0.026 0.026 0.026
## 1049 AEO05 ~~ UWES02Vi 1.814 0.049 0.049 0.137 0.137
## 957 AEO01 ~~ WAMI06 1.808 0.049 0.049 0.124 0.124
## 1056 AEO05 ~~ UWES09Ab 1.803 0.049 0.049 0.081 0.081
## 923 AEG10 ~~ AEO02 1.794 0.050 0.050 0.133 0.133
## 546 AEC01 ~~ AEC03 1.792 0.055 0.055 0.165 0.165
## 655 AEG01 ~~ AEG04 1.789 0.051 0.051 0.119 0.119
## 621 AEC03 ~~ AEG04 1.778 0.049 0.049 0.100 0.100
## 547 AEC01 ~~ AEG01 1.769 -0.050 -0.050 -0.171 -0.171
## 1061 AEO06 ~~ WAMI05 1.767 0.048 0.048 0.155 0.155
## 935 AEG10 ~~ WAMI08 1.743 -0.048 -0.048 -0.234 -0.234
## 1189 WAMI08 ~~ UWES07De 1.721 0.049 0.049 0.404 0.404
## 988 AEO02 ~~ UWES04.De 1.719 -0.048 -0.048 -0.275 -0.275
## 881 AEG08 ~~ WAMI05 1.718 0.048 0.048 0.182 0.182
## 1065 AEO06 ~~ WAMI09 1.713 -0.048 -0.048 -0.112 -0.112
## 509 AEC04 ~~ AEC03 1.710 0.055 0.055 0.323 0.323
## 866 AEG07 ~~ UWES07De 1.708 0.047 0.047 0.176 0.176
## 1244 UWES07De ~~ UWES09Ab 1.706 0.049 0.049 0.159 0.159
## 371 AEC =~ WAMI05 1.706 0.026 0.026 0.026 0.026
## 1006 AEO03 ~~ WAMI10 1.704 -0.048 -0.048 -0.134 -0.134
## 792 AEG05 ~~ AEO06 1.699 -0.048 -0.048 -0.106 -0.106
## 1136 WAMI04 ~~ UWES04.De 1.693 0.049 0.049 0.393 0.393
## 763 AEG04 ~~ WAMI01 1.686 -0.047 -0.047 -0.186 -0.186
## 653 AEG01 ~~ AEG02 1.683 0.049 0.049 0.104 0.104
## 602 AEC02 ~~ WAMI04 1.681 0.047 0.047 0.494 0.494
## 948 AEO01 ~~ AEO03 1.658 0.050 0.050 0.118 0.118
## 1060 AEO06 ~~ WAMI04 1.656 0.047 0.047 0.160 0.160
## 467 WAMI =~ AEO06 1.653 -0.027 -0.027 -0.027 -0.027
## 719 AEG02 ~~ UWES09Ab 1.613 -0.046 -0.046 -0.071 -0.071
## 998 AEO03 ~~ WAMI02 1.611 -0.046 -0.046 -0.146 -0.146
## 1190 WAMI08 ~~ UWES08Ab 1.608 0.048 0.048 0.420 0.420
## 477 Engaj =~ AEC04 1.599 -0.021 -0.021 -0.021 -0.021
## 559 AEC01 ~~ AEO03 1.587 -0.047 -0.047 -0.146 -0.146
## 937 AEG10 ~~ WAMI10 1.585 -0.045 -0.045 -0.125 -0.125
## 1093 WAMI01 ~~ UWES09Ab 1.580 0.046 0.046 0.169 0.169
## 965 AEO01 ~~ UWES04.De 1.572 -0.046 -0.046 -0.230 -0.230
## 941 AEG10 ~~ UWES04.De 1.562 -0.045 -0.045 -0.231 -0.231
## 439 AEO =~ UWES01Vi 1.554 0.030 0.030 0.030 0.030
## 867 AEG07 ~~ UWES08Ab 1.552 0.045 0.045 0.180 0.180
## 816 AEG06 ~~ AEO01 1.547 -0.046 -0.046 -0.091 -0.091
## 600 AEC02 ~~ WAMI02 1.543 0.045 0.045 0.385 0.385
## 654 AEG01 ~~ AEG03 1.528 -0.047 -0.047 -0.135 -0.135
## 920 AEG09 ~~ UWES08Ab 1.521 0.045 0.045 0.171 0.171
## 1043 AEO05 ~~ WAMI06 1.515 0.045 0.045 0.100 0.100
## 470 WAMI =~ UWES03De 1.514 -0.064 -0.064 -0.064 -0.064
## 788 AEG05 ~~ AEO02 1.506 0.046 0.046 0.124 0.124
## 630 AEC03 ~~ AEO03 1.505 -0.045 -0.045 -0.107 -0.107
## 1114 WAMI03 ~~ WAMI07 1.489 0.045 0.045 0.097 0.097
## 919 AEG09 ~~ UWES07De 1.483 0.044 0.044 0.158 0.158
## 566 AEC01 ~~ WAMI04 1.482 0.044 0.044 0.215 0.215
## 677 AEG01 ~~ WAMI10 1.461 0.044 0.044 0.135 0.135
## 733 AEG03 ~~ WAMI01 1.454 -0.044 -0.044 -0.210 -0.210
## 1095 WAMI02 ~~ WAMI04 1.449 -0.046 -0.046 -0.223 -0.223
## 1055 AEO05 ~~ UWES08Ab 1.449 0.044 0.044 0.163 0.163
## 1126 WAMI03 ~~ UWES09Ab 1.446 0.044 0.044 0.071 0.071
## 646 AEC03 ~~ UWES03De 1.440 -0.043 -0.043 -0.181 -0.181
## 1068 AEO06 ~~ UWES02Vi 1.419 0.044 0.044 0.128 0.128
## 1046 AEO05 ~~ WAMI09 1.417 -0.043 -0.043 -0.097 -0.097
## 587 AEC02 ~~ AEG05 1.416 0.044 0.044 0.296 0.296
## 524 AEC04 ~~ AEO05 1.409 -0.044 -0.044 -0.225 -0.225
## 411 AEG =~ UWES06Ab 1.385 0.022 0.022 0.022 0.022
## 899 AEG09 ~~ AEO03 1.374 0.044 0.044 0.095 0.095
## 943 AEG10 ~~ UWES06Ab 1.369 0.042 0.042 0.114 0.114
## 778 AEG04 ~~ UWES06Ab 1.368 0.042 0.042 0.100 0.100
## 707 AEG02 ~~ WAMI07 1.354 -0.042 -0.042 -0.086 -0.086
## 902 AEG09 ~~ AEO06 1.332 -0.043 -0.043 -0.082 -0.082
## 1085 WAMI01 ~~ UWES01Vi 1.325 0.043 0.043 0.234 0.234
## 989 AEO02 ~~ UWES05Vi 1.308 -0.042 -0.042 -0.156 -0.156
## 436 AEO =~ WAMI08 1.299 -0.025 -0.025 -0.025 -0.025
## 960 AEO01 ~~ WAMI09 1.295 -0.041 -0.041 -0.105 -0.105
## 1197 WAMI09 ~~ UWES05Vi 1.293 -0.042 -0.042 -0.153 -0.153
## 565 AEC01 ~~ WAMI03 1.288 0.041 0.041 0.105 0.105
## 959 AEO01 ~~ WAMI08 1.283 -0.041 -0.041 -0.199 -0.199
## 838 AEG06 ~~ UWES07De 1.274 -0.041 -0.041 -0.139 -0.139
## 826 AEG06 ~~ WAMI05 1.269 -0.041 -0.041 -0.122 -0.122
## 1058 AEO06 ~~ WAMI02 1.266 -0.041 -0.041 -0.114 -0.114
## 666 AEG01 ~~ AEO05 1.263 -0.042 -0.042 -0.096 -0.096
## 1027 AEO04 ~~ WAMI10 1.260 0.041 0.041 0.098 0.098
## 495 Engaj =~ AEO05 1.235 0.025 0.025 0.025 0.025
## 804 AEG05 ~~ UWES02Vi 1.234 0.040 0.040 0.132 0.132
## 856 AEG07 ~~ WAMI07 1.234 0.040 0.040 0.095 0.095
## 883 AEG08 ~~ WAMI07 1.230 0.040 0.040 0.111 0.111
## 525 AEC04 ~~ AEO06 1.216 0.041 0.041 0.220 0.220
## 914 AEG09 ~~ UWES02Vi 1.209 0.040 0.040 0.115 0.115
## 381 AEC =~ UWES05Vi 1.201 -0.022 -0.022 -0.022 -0.022
## 553 AEC01 ~~ AEG07 1.192 -0.040 -0.040 -0.115 -0.115
## 1198 WAMI09 ~~ UWES06Ab 1.188 -0.040 -0.040 -0.118 -0.118
## 1199 WAMI09 ~~ UWES07De 1.178 -0.040 -0.040 -0.176 -0.176
## 456 WAMI =~ AEG05 1.173 0.018 0.018 0.018 0.018
## 913 AEG09 ~~ UWES01Vi 1.172 0.039 0.039 0.101 0.101
## 1109 WAMI02 ~~ UWES08Ab 1.158 0.040 0.040 0.222 0.222
## 851 AEG07 ~~ WAMI02 1.151 0.039 0.039 0.111 0.111
## 865 AEG07 ~~ UWES06Ab 1.149 0.039 0.039 0.097 0.097
## 550 AEC01 ~~ AEG04 1.146 -0.039 -0.039 -0.107 -0.107
## 1018 AEO04 ~~ WAMI01 1.142 0.039 0.039 0.153 0.153
## 849 AEG07 ~~ AEO06 1.136 0.039 0.039 0.079 0.079
## 1005 AEO03 ~~ WAMI09 1.106 -0.038 -0.038 -0.102 -0.102
## 947 AEO01 ~~ AEO02 1.103 0.041 0.041 0.106 0.106
## 1040 AEO05 ~~ WAMI03 1.099 0.038 0.038 0.065 0.065
## 1207 WAMI10 ~~ UWES06Ab 1.094 -0.039 -0.039 -0.120 -0.120
## 598 AEC02 ~~ AEO06 1.090 0.039 0.039 0.231 0.231
## 962 AEO01 ~~ UWES01Vi 1.075 0.038 0.038 0.107 0.107
## 538 AEC04 ~~ UWES03De 1.071 -0.038 -0.038 -0.403 -0.403
## 1195 WAMI09 ~~ UWES03De 1.061 -0.038 -0.038 -0.178 -0.178
## 1151 WAMI05 ~~ UWES05Vi 1.054 -0.038 -0.038 -0.189 -0.189
## 1075 AEO06 ~~ UWES09Ab 1.047 -0.037 -0.037 -0.065 -0.065
## 1144 WAMI05 ~~ WAMI08 1.036 -0.039 -0.039 -0.285 -0.285
## 512 AEC04 ~~ AEG03 1.035 0.038 0.038 0.242 0.242
## 1234 UWES04.De ~~ UWES08Ab 1.033 -0.039 -0.039 -0.360 -0.360
## 928 AEG10 ~~ WAMI01 1.020 -0.037 -0.037 -0.164 -0.164
## 1206 WAMI10 ~~ UWES05Vi 1.016 -0.037 -0.037 -0.144 -0.144
## 1241 UWES06Ab ~~ UWES08Ab 1.012 -0.038 -0.038 -0.185 -0.185
## 1044 AEO05 ~~ WAMI07 1.011 -0.036 -0.036 -0.081 -0.081
## 915 AEG09 ~~ UWES03De 1.008 0.036 0.036 0.139 0.139
## 1173 WAMI07 ~~ UWES02Vi 1.003 -0.037 -0.037 -0.129 -0.129
## 517 AEC04 ~~ AEG08 1.000 0.037 0.037 0.241 0.241
## 1076 WAMI01 ~~ WAMI02 0.993 0.038 0.038 0.221 0.221
## 764 AEG04 ~~ WAMI02 0.992 -0.036 -0.036 -0.098 -0.098
## 444 AEO =~ UWES06Ab 0.992 0.023 0.023 0.023 0.023
## 368 AEC =~ WAMI02 0.984 -0.019 -0.019 -0.019 -0.019
## 647 AEC03 ~~ UWES04.De 0.984 -0.036 -0.036 -0.179 -0.179
## 901 AEG09 ~~ AEO05 0.980 -0.036 -0.036 -0.067 -0.067
## 389 AEG =~ AEC03 0.975 -0.030 -0.030 -0.030 -0.030
## 590 AEC02 ~~ AEG08 0.967 0.037 0.037 0.263 0.263
## 757 AEG04 ~~ AEO01 0.958 -0.036 -0.036 -0.075 -0.075
## 1041 AEO05 ~~ WAMI04 0.957 0.036 0.036 0.116 0.116
## 1238 UWES05Vi ~~ UWES08Ab 0.956 -0.037 -0.037 -0.224 -0.224
## 1168 WAMI06 ~~ UWES09Ab 0.954 -0.036 -0.036 -0.076 -0.076
## 808 AEG05 ~~ UWES06Ab 0.951 0.035 0.035 0.096 0.096
## 579 AEC01 ~~ UWES07De 0.950 0.035 0.035 0.183 0.183
## 678 AEG01 ~~ UWES01Vi 0.950 0.035 0.035 0.115 0.115
## 1059 AEO06 ~~ WAMI03 0.949 0.035 0.035 0.063 0.063
## 975 AEO02 ~~ WAMI01 0.945 -0.036 -0.036 -0.179 -0.179
## 510 AEC04 ~~ AEG01 0.936 -0.036 -0.036 -0.242 -0.242
## 1082 WAMI01 ~~ WAMI08 0.930 -0.037 -0.037 -0.344 -0.344
## 1158 WAMI06 ~~ WAMI09 0.928 0.036 0.036 0.103 0.103
## 815 AEG06 ~~ AEG10 0.923 0.036 0.036 0.073 0.073
## 1042 AEO05 ~~ WAMI05 0.923 0.035 0.035 0.107 0.107
## 641 AEC03 ~~ WAMI08 0.922 -0.035 -0.035 -0.167 -0.167
## 1193 WAMI09 ~~ UWES01Vi 0.918 -0.035 -0.035 -0.112 -0.112
## 1180 WAMI07 ~~ UWES09Ab 0.908 -0.035 -0.035 -0.073 -0.073
## 800 AEG05 ~~ WAMI08 0.905 0.035 0.035 0.171 0.171
## 777 AEG04 ~~ UWES05Vi 0.896 -0.034 -0.034 -0.100 -0.100
## 402 AEG =~ WAMI07 0.892 0.017 0.017 0.017 0.017
## 1210 WAMI10 ~~ UWES09Ab 0.891 -0.035 -0.035 -0.078 -0.078
## 1101 WAMI02 ~~ WAMI10 0.882 -0.036 -0.036 -0.126 -0.126
## 784 AEG05 ~~ AEG08 0.875 -0.036 -0.036 -0.093 -0.093
## 627 AEC03 ~~ AEG10 0.871 0.034 0.034 0.080 0.080
## 1120 WAMI03 ~~ UWES03De 0.868 0.034 0.034 0.122 0.122
## 462 WAMI =~ AEO01 0.840 -0.020 -0.020 -0.020 -0.020
## 970 AEO01 ~~ UWES09Ab 0.833 -0.033 -0.033 -0.063 -0.063
## 583 AEC02 ~~ AEG01 0.829 -0.034 -0.034 -0.253 -0.253
## 1112 WAMI03 ~~ WAMI05 0.823 -0.034 -0.034 -0.100 -0.100
## 892 AEG08 ~~ UWES06Ab 0.821 -0.033 -0.033 -0.096 -0.096
## 944 AEG10 ~~ UWES07De 0.818 -0.033 -0.033 -0.131 -0.131
## 1107 WAMI02 ~~ UWES06Ab 0.814 0.033 0.033 0.116 0.116
## 789 AEG05 ~~ AEO03 0.813 -0.034 -0.034 -0.083 -0.083
## 907 AEG09 ~~ WAMI05 0.807 0.032 0.032 0.103 0.103
## 1053 AEO05 ~~ UWES06Ab 0.803 -0.033 -0.033 -0.076 -0.076
## 811 AEG05 ~~ UWES09Ab 0.801 0.032 0.032 0.063 0.063
## 745 AEG03 ~~ UWES03De 0.798 -0.032 -0.032 -0.148 -0.148
## 1174 WAMI07 ~~ UWES03De 0.797 -0.033 -0.033 -0.152 -0.152
## 759 AEG04 ~~ AEO03 0.795 -0.033 -0.033 -0.071 -0.071
## 908 AEG09 ~~ WAMI06 0.795 0.032 0.032 0.075 0.075
## 984 AEO02 ~~ WAMI10 0.790 -0.032 -0.032 -0.100 -0.100
## 593 AEC02 ~~ AEO01 0.790 -0.033 -0.033 -0.213 -0.213
## 1086 WAMI01 ~~ UWES02Vi 0.783 0.033 0.033 0.202 0.202
## 423 AEO =~ AEG05 0.781 -0.053 -0.053 -0.053 -0.053
## 446 AEO =~ UWES08Ab 0.780 0.021 0.021 0.021 0.021
## 416 AEO =~ AEC01 0.778 -0.023 -0.023 -0.023 -0.023
## 406 AEG =~ UWES01Vi 0.774 0.017 0.017 0.017 0.017
## 542 AEC04 ~~ UWES07De 0.769 0.032 0.032 0.320 0.320
## 871 AEG08 ~~ AEO01 0.764 0.033 0.033 0.082 0.082
## 372 AEC =~ WAMI06 0.762 0.017 0.017 0.017 0.017
## 1171 WAMI07 ~~ WAMI10 0.759 0.033 0.033 0.097 0.097
## 1033 AEO04 ~~ UWES06Ab 0.756 0.032 0.032 0.074 0.074
## 1062 AEO06 ~~ WAMI06 0.743 0.031 0.031 0.074 0.074
## 812 AEG06 ~~ AEG07 0.742 0.032 0.032 0.061 0.061
## 1204 WAMI10 ~~ UWES03De 0.736 -0.032 -0.032 -0.158 -0.158
## 769 AEG04 ~~ WAMI07 0.736 -0.031 -0.031 -0.070 -0.070
## 898 AEG09 ~~ AEO02 0.735 0.032 0.032 0.076 0.076
## 1200 WAMI09 ~~ UWES08Ab 0.735 -0.032 -0.032 -0.149 -0.149
## 797 AEG05 ~~ WAMI05 0.731 0.031 0.031 0.111 0.111
## 740 AEG03 ~~ WAMI08 0.723 -0.031 -0.031 -0.162 -0.162
## 1104 WAMI02 ~~ UWES03De 0.721 0.032 0.032 0.174 0.174
## 1143 WAMI05 ~~ WAMI07 0.718 -0.032 -0.032 -0.122 -0.122
## 722 AEG03 ~~ AEG06 0.717 0.032 0.032 0.069 0.069
## 645 AEC03 ~~ UWES02Vi 0.715 0.031 0.031 0.097 0.097
## 589 AEC02 ~~ AEG07 0.713 -0.031 -0.031 -0.192 -0.192
## 652 AEC03 ~~ UWES09Ab 0.710 0.030 0.030 0.057 0.057
## 857 AEG07 ~~ WAMI08 0.710 0.031 0.031 0.139 0.139
## 1205 WAMI10 ~~ UWES04.De 0.710 0.031 0.031 0.185 0.185
## 1176 WAMI07 ~~ UWES05Vi 0.706 -0.031 -0.031 -0.111 -0.111
## 1225 UWES03De ~~ UWES04.De 0.690 0.032 0.032 0.293 0.293
## 861 AEG07 ~~ UWES02Vi 0.686 0.030 0.030 0.090 0.090
## 940 AEG10 ~~ UWES03De 0.682 -0.030 -0.030 -0.128 -0.128
## 1232 UWES04.De ~~ UWES06Ab 0.677 -0.031 -0.031 -0.181 -0.181
## 1127 WAMI04 ~~ WAMI05 0.674 0.031 0.031 0.176 0.176
## 963 AEO01 ~~ UWES02Vi 0.668 0.030 0.030 0.095 0.095
## 539 AEC04 ~~ UWES04.De 0.665 -0.030 -0.030 -0.380 -0.380
## 384 AEC =~ UWES08Ab 0.664 0.016 0.016 0.016 0.016
## 1045 AEO05 ~~ WAMI08 0.662 -0.030 -0.030 -0.126 -0.126
## 882 AEG08 ~~ WAMI06 0.661 0.029 0.029 0.083 0.083
## 674 AEG01 ~~ WAMI07 0.655 0.029 0.029 0.084 0.084
## 775 AEG04 ~~ UWES03De 0.654 -0.029 -0.029 -0.110 -0.110
## 413 AEG =~ UWES08Ab 0.653 0.016 0.016 0.016 0.016
## 607 AEC02 ~~ WAMI09 0.644 0.029 0.029 0.210 0.210
## 1124 WAMI03 ~~ UWES07De 0.641 -0.029 -0.029 -0.098 -0.098
## 720 AEG03 ~~ AEG04 0.641 0.030 0.030 0.068 0.068
## 612 AEC02 ~~ UWES04.De 0.639 -0.029 -0.029 -0.413 -0.413
## 1015 AEO03 ~~ UWES09Ab 0.619 -0.029 -0.029 -0.057 -0.057
## 1098 WAMI02 ~~ WAMI07 0.619 0.030 0.030 0.098 0.098
## 1001 AEO03 ~~ WAMI05 0.618 0.029 0.029 0.104 0.104
## 760 AEG04 ~~ AEO04 0.617 -0.029 -0.029 -0.053 -0.053
## 735 AEG03 ~~ WAMI03 0.616 -0.028 -0.028 -0.060 -0.060
## 1154 WAMI05 ~~ UWES08Ab 0.610 0.029 0.029 0.186 0.186
## 443 AEO =~ UWES05Vi 0.609 -0.018 -0.018 -0.018 -0.018
## 879 AEG08 ~~ WAMI03 0.609 -0.028 -0.028 -0.061 -0.061
## 958 AEO01 ~~ WAMI07 0.604 -0.028 -0.028 -0.071 -0.071
## 377 AEC =~ UWES01Vi 0.604 0.015 0.015 0.015 0.015
## 1132 WAMI04 ~~ WAMI10 0.604 -0.030 -0.030 -0.129 -0.129
## 1097 WAMI02 ~~ WAMI06 0.603 -0.029 -0.029 -0.098 -0.098
## 809 AEG05 ~~ UWES07De 0.600 0.028 0.028 0.114 0.114
## 1139 WAMI04 ~~ UWES07De 0.596 0.029 0.029 0.182 0.182
## 620 AEC03 ~~ AEG03 0.586 -0.028 -0.028 -0.070 -0.070
## 761 AEG04 ~~ AEO05 0.583 0.028 0.028 0.051 0.051
## 608 AEC02 ~~ WAMI10 0.580 0.028 0.028 0.211 0.211
## 1047 AEO05 ~~ WAMI10 0.580 -0.028 -0.028 -0.066 -0.066
## 575 AEC01 ~~ UWES03De 0.569 -0.027 -0.027 -0.151 -0.151
## 1177 WAMI07 ~~ UWES06Ab 0.567 -0.028 -0.028 -0.080 -0.080
## 541 AEC04 ~~ UWES06Ab 0.556 -0.027 -0.027 -0.182 -0.182
## 1116 WAMI03 ~~ WAMI09 0.555 -0.028 -0.028 -0.060 -0.060
## 1169 WAMI07 ~~ WAMI08 0.551 0.028 0.028 0.149 0.149
## 595 AEC02 ~~ AEO03 0.549 -0.028 -0.028 -0.186 -0.186
## 807 AEG05 ~~ UWES05Vi 0.549 0.027 0.027 0.090 0.090
## 1110 WAMI02 ~~ UWES09Ab 0.548 0.027 0.027 0.068 0.068
## 727 AEG03 ~~ AEO01 0.544 0.028 0.028 0.068 0.068
## 573 AEC01 ~~ UWES01Vi 0.536 0.027 0.027 0.099 0.099
## 611 AEC02 ~~ UWES03De 0.536 -0.027 -0.027 -0.316 -0.316
## 873 AEG08 ~~ AEO03 0.534 0.027 0.027 0.072 0.072
## 918 AEG09 ~~ UWES06Ab 0.531 0.026 0.026 0.063 0.063
## 638 AEC03 ~~ WAMI05 0.531 -0.026 -0.026 -0.091 -0.091
## 603 AEC02 ~~ WAMI05 0.527 0.026 0.026 0.259 0.259
## 1122 WAMI03 ~~ UWES05Vi 0.520 0.026 0.026 0.074 0.074
## 537 AEC04 ~~ UWES02Vi 0.519 0.026 0.026 0.213 0.213
## 831 AEG06 ~~ WAMI10 0.513 -0.026 -0.026 -0.060 -0.060
## 986 AEO02 ~~ UWES02Vi 0.509 0.026 0.026 0.095 0.095
## 1008 AEO03 ~~ UWES02Vi 0.508 0.026 0.026 0.087 0.087
## 743 AEG03 ~~ UWES01Vi 0.505 -0.026 -0.026 -0.080 -0.080
## 912 AEG09 ~~ WAMI10 0.503 0.026 0.026 0.063 0.063
## 426 AEO =~ AEG08 0.501 -0.043 -0.043 -0.043 -0.043
## 578 AEC01 ~~ UWES06Ab 0.495 -0.025 -0.025 -0.088 -0.088
## 730 AEG03 ~~ AEO04 0.494 -0.026 -0.026 -0.058 -0.058
## 700 AEG02 ~~ AEO06 0.480 0.025 0.025 0.044 0.044
## 1141 WAMI04 ~~ UWES09Ab 0.478 -0.025 -0.025 -0.078 -0.078
## 438 AEO =~ WAMI10 0.477 -0.015 -0.015 -0.015 -0.015
## 868 AEG07 ~~ UWES09Ab 0.475 -0.025 -0.025 -0.045 -0.045
## 870 AEG08 ~~ AEG10 0.474 0.026 0.026 0.067 0.067
## 1090 WAMI01 ~~ UWES06Ab 0.473 0.026 0.026 0.130 0.130
## 540 AEC04 ~~ UWES05Vi 0.473 -0.025 -0.025 -0.208 -0.208
## 1240 UWES06Ab ~~ UWES07De 0.469 -0.026 -0.026 -0.118 -0.118
## 1099 WAMI02 ~~ WAMI08 0.468 -0.026 -0.026 -0.166 -0.166
## 1029 AEO04 ~~ UWES02Vi 0.466 0.025 0.025 0.071 0.071
## 990 AEO02 ~~ UWES06Ab 0.456 -0.025 -0.025 -0.074 -0.074
## 1067 AEO06 ~~ UWES01Vi 0.454 0.025 0.025 0.065 0.065
## 1156 WAMI06 ~~ WAMI07 0.451 -0.025 -0.025 -0.071 -0.071
## 1175 WAMI07 ~~ UWES04.De 0.449 0.025 0.025 0.137 0.137
## 754 AEG04 ~~ AEG08 0.447 -0.025 -0.025 -0.057 -0.057
## 616 AEC02 ~~ UWES08Ab 0.445 0.024 0.024 0.290 0.290
## 786 AEG05 ~~ AEG10 0.442 0.025 0.025 0.060 0.060
## 1035 AEO04 ~~ UWES08Ab 0.442 0.024 0.024 0.091 0.091
## 491 Engaj =~ AEO01 0.436 -0.015 -0.015 -0.015 -0.015
## 650 AEC03 ~~ UWES07De 0.434 0.024 0.024 0.093 0.093
## 1140 WAMI04 ~~ UWES08Ab 0.432 0.025 0.025 0.167 0.167
## 798 AEG05 ~~ WAMI06 0.430 -0.024 -0.024 -0.062 -0.062
## 661 AEG01 ~~ AEG10 0.428 -0.025 -0.025 -0.066 -0.066
## 1243 UWES07De ~~ UWES08Ab 0.428 0.025 0.025 0.181 0.181
## 978 AEO02 ~~ WAMI04 0.427 -0.024 -0.024 -0.101 -0.101
## 926 AEG10 ~~ AEO05 0.424 -0.024 -0.024 -0.049 -0.049
## 703 AEG02 ~~ WAMI03 0.419 0.023 0.023 0.037 0.037
## 891 AEG08 ~~ UWES05Vi 0.418 -0.023 -0.023 -0.084 -0.084
## 435 AEO =~ WAMI07 0.417 0.014 0.014 0.014 0.014
## 1187 WAMI08 ~~ UWES05Vi 0.416 0.024 0.024 0.165 0.165
## 1214 UWES01Vi ~~ UWES06Ab 0.413 0.024 0.024 0.079 0.079
## 501 Engaj =~ WAMI05 0.409 0.033 0.033 0.033 0.033
## 850 AEG07 ~~ WAMI01 0.405 0.023 0.023 0.096 0.096
## 1004 AEO03 ~~ WAMI08 0.404 -0.023 -0.023 -0.117 -0.117
## 1017 AEO04 ~~ AEO06 0.403 0.024 0.024 0.045 0.045
## 982 AEO02 ~~ WAMI08 0.400 -0.023 -0.023 -0.127 -0.127
## 827 AEG06 ~~ WAMI06 0.395 -0.023 -0.023 -0.050 -0.050
## 1185 WAMI08 ~~ UWES03De 0.386 0.023 0.023 0.205 0.205
## 1051 AEO05 ~~ UWES04.De 0.375 -0.022 -0.022 -0.099 -0.099
## 576 AEC01 ~~ UWES04.De 0.374 -0.022 -0.022 -0.146 -0.146
## 1010 AEO03 ~~ UWES04.De 0.371 -0.022 -0.022 -0.117 -0.117
## 936 AEG10 ~~ WAMI09 0.369 0.022 0.022 0.057 0.057
## 1003 AEO03 ~~ WAMI07 0.369 -0.022 -0.022 -0.058 -0.058
## 563 AEC01 ~~ WAMI01 0.368 -0.022 -0.022 -0.128 -0.128
## 376 AEC =~ WAMI10 0.367 0.012 0.012 0.012 0.012
## 890 AEG08 ~~ UWES04.De 0.363 -0.022 -0.022 -0.121 -0.121
## 580 AEC01 ~~ UWES08Ab 0.362 0.022 0.022 0.121 0.121
## 885 AEG08 ~~ WAMI09 0.360 0.022 0.022 0.061 0.061
## 916 AEG09 ~~ UWES04.De 0.357 0.022 0.022 0.099 0.099
## 548 AEC01 ~~ AEG02 0.357 0.022 0.022 0.054 0.054
## 396 AEG =~ WAMI01 0.356 -0.011 -0.011 -0.011 -0.011
## 1152 WAMI05 ~~ UWES06Ab 0.352 -0.022 -0.022 -0.088 -0.088
## 1066 AEO06 ~~ WAMI10 0.348 -0.021 -0.021 -0.054 -0.054
## 938 AEG10 ~~ UWES01Vi 0.344 -0.021 -0.021 -0.061 -0.061
## 609 AEC02 ~~ UWES01Vi 0.343 0.021 0.021 0.171 0.171
## 985 AEO02 ~~ UWES01Vi 0.341 0.021 0.021 0.069 0.069
## 731 AEG03 ~~ AEO05 0.339 -0.022 -0.022 -0.047 -0.047
## 968 AEO01 ~~ UWES07De 0.330 0.021 0.021 0.082 0.082
## 639 AEC03 ~~ WAMI06 0.328 -0.021 -0.021 -0.052 -0.052
## 631 AEC03 ~~ AEO04 0.322 -0.021 -0.021 -0.042 -0.042
## 886 AEG08 ~~ WAMI10 0.319 -0.020 -0.020 -0.061 -0.061
## 706 AEG02 ~~ WAMI06 0.319 -0.020 -0.020 -0.042 -0.042
## 951 AEO01 ~~ AEO06 0.319 -0.022 -0.022 -0.045 -0.045
## 689 AEG02 ~~ AEG05 0.316 0.021 0.021 0.041 0.041
## 996 AEO03 ~~ AEO06 0.314 0.021 0.021 0.047 0.047
## 992 AEO02 ~~ UWES08Ab 0.310 -0.021 -0.021 -0.098 -0.098
## 533 AEC04 ~~ WAMI08 0.307 -0.020 -0.020 -0.248 -0.248
## 795 AEG05 ~~ WAMI03 0.302 0.020 0.020 0.040 0.040
## 410 AEG =~ UWES05Vi 0.301 -0.011 -0.011 -0.011 -0.011
## 893 AEG08 ~~ UWES07De 0.300 -0.020 -0.020 -0.086 -0.086
## 716 AEG02 ~~ UWES06Ab 0.299 -0.020 -0.020 -0.042 -0.042
## 840 AEG06 ~~ UWES09Ab 0.298 -0.020 -0.020 -0.032 -0.032
## 1007 AEO03 ~~ UWES01Vi 0.295 0.020 0.020 0.059 0.059
## 729 AEG03 ~~ AEO03 0.293 0.020 0.020 0.053 0.053
## 588 AEC02 ~~ AEG06 0.291 0.020 0.020 0.112 0.112
## 545 AEC01 ~~ AEC02 0.289 0.024 0.024 0.202 0.202
## 1145 WAMI05 ~~ WAMI09 0.285 -0.020 -0.020 -0.078 -0.078
## 1036 AEO04 ~~ UWES09Ab 0.281 0.019 0.019 0.033 0.033
## 863 AEG07 ~~ UWES04.De 0.281 0.019 0.019 0.091 0.091
## 488 Engaj =~ AEG08 0.281 -0.009 -0.009 -0.009 -0.009
## 623 AEC03 ~~ AEG06 0.279 0.019 0.019 0.038 0.038
## 697 AEG02 ~~ AEO03 0.275 -0.019 -0.019 -0.038 -0.038
## 709 AEG02 ~~ WAMI09 0.273 -0.019 -0.019 -0.039 -0.039
## 927 AEG10 ~~ AEO06 0.264 -0.019 -0.019 -0.041 -0.041
## 531 AEC04 ~~ WAMI06 0.264 -0.019 -0.019 -0.121 -0.121
## 1129 WAMI04 ~~ WAMI07 0.262 0.019 0.019 0.079 0.079
## 864 AEG07 ~~ UWES05Vi 0.262 0.019 0.019 0.057 0.057
## 642 AEC03 ~~ WAMI09 0.257 -0.018 -0.018 -0.047 -0.047
## 799 AEG05 ~~ WAMI07 0.249 0.018 0.018 0.047 0.047
## 981 AEO02 ~~ WAMI07 0.249 0.018 0.018 0.052 0.052
## 987 AEO02 ~~ UWES03De 0.249 -0.018 -0.018 -0.087 -0.087
## 1031 AEO04 ~~ UWES04.De 0.246 0.018 0.018 0.081 0.081
## 884 AEG08 ~~ WAMI08 0.245 -0.018 -0.018 -0.095 -0.095
## 1178 WAMI07 ~~ UWES07De 0.244 -0.018 -0.018 -0.079 -0.079
## 805 AEG05 ~~ UWES03De 0.244 0.018 0.018 0.077 0.077
## 1125 WAMI03 ~~ UWES08Ab 0.238 0.018 0.018 0.064 0.064
## 1077 WAMI01 ~~ WAMI03 0.236 0.018 0.018 0.068 0.068
## 386 AEG =~ AEC04 0.231 0.017 0.017 0.017 0.017
## 1013 AEO03 ~~ UWES07De 0.230 0.018 0.018 0.072 0.072
## 704 AEG02 ~~ WAMI04 0.230 -0.017 -0.017 -0.052 -0.052
## 1163 WAMI06 ~~ UWES04.De 0.230 -0.018 -0.018 -0.099 -0.099
## 966 AEO01 ~~ UWES05Vi 0.227 0.017 0.017 0.057 0.057
## 375 AEC =~ WAMI09 0.225 0.009 0.009 0.009 0.009
## 535 AEC04 ~~ WAMI10 0.221 0.017 0.017 0.118 0.118
## 617 AEC02 ~~ UWES09Ab 0.221 0.017 0.017 0.091 0.091
## 1219 UWES02Vi ~~ UWES04.De 0.217 -0.018 -0.018 -0.124 -0.124
## 1014 AEO03 ~~ UWES08Ab 0.212 0.017 0.017 0.074 0.074
## 832 AEG06 ~~ UWES01Vi 0.209 -0.017 -0.017 -0.041 -0.041
## 1121 WAMI03 ~~ UWES04.De 0.206 -0.017 -0.017 -0.071 -0.071
## 779 AEG04 ~~ UWES07De 0.202 -0.016 -0.016 -0.057 -0.057
## 837 AEG06 ~~ UWES06Ab 0.199 0.016 0.016 0.037 0.037
## 1000 AEO03 ~~ WAMI04 0.198 -0.016 -0.016 -0.063 -0.063
## 544 AEC04 ~~ UWES09Ab 0.198 -0.016 -0.016 -0.078 -0.078
## 664 AEG01 ~~ AEO03 0.196 -0.017 -0.017 -0.045 -0.045
## 952 AEO01 ~~ WAMI01 0.192 0.016 0.016 0.070 0.070
## 657 AEG01 ~~ AEG06 0.190 0.016 0.016 0.037 0.037
## 880 AEG08 ~~ WAMI04 0.189 -0.016 -0.016 -0.064 -0.064
## 749 AEG03 ~~ UWES07De 0.187 -0.016 -0.016 -0.067 -0.067
## 746 AEG03 ~~ UWES04.De 0.187 -0.016 -0.016 -0.086 -0.086
## 878 AEG08 ~~ WAMI02 0.187 -0.016 -0.016 -0.052 -0.052
## 1103 WAMI02 ~~ UWES02Vi 0.186 -0.016 -0.016 -0.067 -0.067
## 956 AEO01 ~~ WAMI05 0.184 0.016 0.016 0.054 0.054
## 844 AEG07 ~~ AEO01 0.183 0.016 0.016 0.034 0.034
## 1064 AEO06 ~~ WAMI08 0.180 -0.015 -0.015 -0.069 -0.069
## 1167 WAMI06 ~~ UWES08Ab 0.177 -0.016 -0.016 -0.073 -0.073
## 750 AEG03 ~~ UWES08Ab 0.177 -0.015 -0.015 -0.070 -0.070
## 1011 AEO03 ~~ UWES05Vi 0.176 -0.015 -0.015 -0.052 -0.052
## 536 AEC04 ~~ UWES01Vi 0.175 -0.015 -0.015 -0.110 -0.110
## 628 AEC03 ~~ AEO01 0.174 -0.015 -0.015 -0.035 -0.035
## 906 AEG09 ~~ WAMI04 0.173 0.015 0.015 0.051 0.051
## 466 WAMI =~ AEO05 0.170 0.009 0.009 0.009 0.009
## 568 AEC01 ~~ WAMI06 0.170 0.015 0.015 0.050 0.050
## 995 AEO03 ~~ AEO05 0.169 -0.016 -0.016 -0.033 -0.033
## 979 AEO02 ~~ WAMI05 0.167 -0.015 -0.015 -0.059 -0.059
## 635 AEC03 ~~ WAMI02 0.164 -0.015 -0.015 -0.044 -0.044
## 651 AEC03 ~~ UWES08Ab 0.161 -0.015 -0.015 -0.061 -0.061
## 1201 WAMI09 ~~ UWES09Ab 0.159 -0.015 -0.015 -0.031 -0.031
## 820 AEG06 ~~ AEO05 0.158 0.015 0.015 0.026 0.026
## 392 AEG =~ AEO03 0.157 0.025 0.025 0.025 0.025
## 1212 UWES01Vi ~~ UWES04.De 0.157 -0.015 -0.015 -0.094 -0.094
## 1100 WAMI02 ~~ WAMI09 0.157 0.015 0.015 0.050 0.050
## 698 AEG02 ~~ AEO04 0.153 -0.014 -0.014 -0.024 -0.024
## 1030 AEO04 ~~ UWES03De 0.152 -0.014 -0.014 -0.053 -0.053
## 360 AEC =~ AEG10 0.152 0.013 0.013 0.013 0.013
## 932 AEG10 ~~ WAMI05 0.148 -0.014 -0.014 -0.049 -0.049
## 1155 WAMI05 ~~ UWES09Ab 0.145 -0.014 -0.014 -0.040 -0.040
## 564 AEC01 ~~ WAMI02 0.143 0.014 0.014 0.054 0.054
## 395 AEG =~ AEO06 0.141 0.023 0.023 0.023 0.023
## 710 AEG02 ~~ WAMI10 0.141 0.014 0.014 0.030 0.030
## 1002 AEO03 ~~ WAMI06 0.139 0.014 0.014 0.036 0.036
## 1009 AEO03 ~~ UWES03De 0.139 -0.014 -0.014 -0.060 -0.060
## 637 AEC03 ~~ WAMI04 0.138 0.013 0.013 0.050 0.050
## 717 AEG02 ~~ UWES07De 0.138 -0.013 -0.013 -0.043 -0.043
## 991 AEO02 ~~ UWES07De 0.135 -0.014 -0.014 -0.060 -0.060
## 404 AEG =~ WAMI09 0.133 0.007 0.007 0.007 0.007
## 980 AEO02 ~~ WAMI06 0.133 -0.013 -0.013 -0.039 -0.039
## 821 AEG06 ~~ AEO06 0.132 0.013 0.013 0.025 0.025
## 1224 UWES02Vi ~~ UWES09Ab 0.131 -0.013 -0.013 -0.036 -0.036
## 649 AEC03 ~~ UWES06Ab 0.130 -0.013 -0.013 -0.034 -0.034
## 967 AEO01 ~~ UWES06Ab 0.129 -0.013 -0.013 -0.035 -0.035
## 1148 WAMI05 ~~ UWES02Vi 0.129 -0.013 -0.013 -0.064 -0.064
## 1179 WAMI07 ~~ UWES08Ab 0.124 -0.013 -0.013 -0.060 -0.060
## 1052 AEO05 ~~ UWES05Vi 0.123 -0.013 -0.013 -0.037 -0.037
## 1115 WAMI03 ~~ WAMI08 0.122 -0.013 -0.013 -0.054 -0.054
## 862 AEG07 ~~ UWES03De 0.119 0.013 0.013 0.050 0.050
## 644 AEC03 ~~ UWES01Vi 0.116 0.012 0.012 0.035 0.035
## 744 AEG03 ~~ UWES02Vi 0.115 -0.012 -0.012 -0.042 -0.042
## 572 AEC01 ~~ WAMI10 0.112 0.012 0.012 0.043 0.043
## 354 AEC =~ AEG04 0.109 0.011 0.011 0.011 0.011
## 813 AEG06 ~~ AEG08 0.108 0.012 0.012 0.027 0.027
## 1181 WAMI08 ~~ WAMI09 0.107 0.012 0.012 0.067 0.067
## 739 AEG03 ~~ WAMI07 0.101 0.011 0.011 0.031 0.031
## 604 AEC02 ~~ WAMI06 0.100 0.011 0.011 0.083 0.083
## 507 AEC04 ~~ AEC01 0.098 0.014 0.014 0.106 0.106
## 569 AEC01 ~~ WAMI07 0.097 0.011 0.011 0.037 0.037
## 429 AEO =~ WAMI01 0.097 0.007 0.007 0.007 0.007
## 437 AEO =~ WAMI09 0.096 -0.007 -0.007 -0.007 -0.007
## 921 AEG09 ~~ UWES09Ab 0.096 0.011 0.011 0.019 0.019
## 801 AEG05 ~~ WAMI09 0.094 0.011 0.011 0.029 0.029
## 552 AEC01 ~~ AEG06 0.093 -0.011 -0.011 -0.029 -0.029
## 1172 WAMI07 ~~ UWES01Vi 0.092 -0.011 -0.011 -0.035 -0.035
## 824 AEG06 ~~ WAMI03 0.090 0.011 0.011 0.018 0.018
## 983 AEO02 ~~ WAMI09 0.089 -0.011 -0.011 -0.031 -0.031
## 581 AEC01 ~~ UWES09Ab 0.088 -0.011 -0.011 -0.027 -0.027
## 737 AEG03 ~~ WAMI05 0.088 -0.011 -0.011 -0.041 -0.041
## 361 AEC =~ AEO01 0.083 -0.008 -0.008 -0.008 -0.008
## 1063 AEO06 ~~ WAMI07 0.080 -0.010 -0.010 -0.024 -0.024
## 551 AEC01 ~~ AEG05 0.080 0.010 0.010 0.033 0.033
## 876 AEG08 ~~ AEO06 0.080 0.010 0.010 0.025 0.025
## 520 AEC04 ~~ AEO01 0.078 -0.010 -0.010 -0.061 -0.061
## 513 AEC04 ~~ AEG04 0.076 0.010 0.010 0.054 0.054
## 577 AEC01 ~~ UWES05Vi 0.072 -0.010 -0.010 -0.042 -0.042
## 774 AEG04 ~~ UWES02Vi 0.071 0.010 0.010 0.028 0.028
## 1102 WAMI02 ~~ UWES01Vi 0.071 0.010 0.010 0.037 0.037
## 889 AEG08 ~~ UWES03De 0.070 0.010 0.010 0.044 0.044
## 1221 UWES02Vi ~~ UWES06Ab 0.069 0.010 0.010 0.037 0.037
## 887 AEG08 ~~ UWES01Vi 0.069 0.010 0.010 0.030 0.030
## 599 AEC02 ~~ WAMI01 0.068 -0.010 -0.010 -0.118 -0.118
## 802 AEG05 ~~ WAMI10 0.067 0.009 0.009 0.026 0.026
## 570 AEC01 ~~ WAMI08 0.067 -0.009 -0.009 -0.060 -0.060
## 554 AEC01 ~~ AEG08 0.067 0.010 0.010 0.032 0.032
## 356 AEC =~ AEG06 0.066 0.008 0.008 0.008 0.008
## 592 AEC02 ~~ AEG10 0.064 0.009 0.009 0.062 0.062
## 964 AEO01 ~~ UWES03De 0.064 -0.009 -0.009 -0.039 -0.039
## 767 AEG04 ~~ WAMI05 0.061 -0.009 -0.009 -0.028 -0.028
## 626 AEC03 ~~ AEG09 0.061 0.009 0.009 0.019 0.019
## 903 AEG09 ~~ WAMI01 0.060 0.009 0.009 0.036 0.036
## 1149 WAMI05 ~~ UWES03De 0.060 -0.009 -0.009 -0.058 -0.058
## 806 AEG05 ~~ UWES04.De 0.058 0.009 0.009 0.045 0.045
## 523 AEC04 ~~ AEO04 0.058 -0.009 -0.009 -0.046 -0.046
## 1147 WAMI05 ~~ UWES01Vi 0.058 -0.009 -0.009 -0.038 -0.038
## 1074 AEO06 ~~ UWES08Ab 0.055 -0.009 -0.009 -0.033 -0.033
## 803 AEG05 ~~ UWES01Vi 0.055 0.008 0.008 0.025 0.025
## 686 AEG01 ~~ UWES09Ab 0.054 0.008 0.008 0.018 0.018
## 1184 WAMI08 ~~ UWES02Vi 0.054 0.009 0.009 0.058 0.058
## 522 AEC04 ~~ AEO03 0.053 -0.009 -0.009 -0.052 -0.052
## 527 AEC04 ~~ WAMI02 0.051 0.008 0.008 0.063 0.063
## 567 AEC01 ~~ WAMI05 0.049 -0.008 -0.008 -0.037 -0.037
## 955 AEO01 ~~ WAMI04 0.049 0.008 0.008 0.030 0.030
## 1028 AEO04 ~~ UWES01Vi 0.047 0.008 0.008 0.020 0.020
## 584 AEC02 ~~ AEG02 0.046 0.008 0.008 0.042 0.042
## 1131 WAMI04 ~~ WAMI09 0.045 -0.008 -0.008 -0.033 -0.033
## 758 AEG04 ~~ AEO02 0.044 0.008 0.008 0.018 0.018
## 663 AEG01 ~~ AEO02 0.044 0.008 0.008 0.023 0.023
## 846 AEG07 ~~ AEO03 0.042 -0.008 -0.008 -0.017 -0.017
## 738 AEG03 ~~ WAMI06 0.042 0.007 0.007 0.021 0.021
## 1227 UWES03De ~~ UWES06Ab 0.042 -0.008 -0.008 -0.038 -0.038
## 747 AEG03 ~~ UWES05Vi 0.041 0.007 0.007 0.026 0.026
## 556 AEC01 ~~ AEG10 0.041 -0.008 -0.008 -0.023 -0.023
## 692 AEG02 ~~ AEG08 0.040 -0.007 -0.007 -0.015 -0.015
## 718 AEG02 ~~ UWES08Ab 0.039 0.007 0.007 0.025 0.025
## 633 AEC03 ~~ AEO06 0.037 0.007 0.007 0.015 0.015
## 1138 WAMI04 ~~ UWES06Ab 0.037 0.007 0.007 0.030 0.030
## 1111 WAMI03 ~~ WAMI04 0.036 0.007 0.007 0.022 0.022
## 934 AEG10 ~~ WAMI07 0.035 -0.007 -0.007 -0.017 -0.017
## 353 AEC =~ AEG03 0.033 0.006 0.006 0.006 0.006
## 830 AEG06 ~~ WAMI09 0.032 0.006 0.006 0.014 0.014
## 741 AEG03 ~~ WAMI09 0.031 -0.006 -0.006 -0.018 -0.018
## 872 AEG08 ~~ AEO02 0.031 0.007 0.007 0.019 0.019
## 753 AEG04 ~~ AEG07 0.031 0.007 0.007 0.013 0.013
## 894 AEG08 ~~ UWES08Ab 0.031 0.006 0.006 0.030 0.030
## 909 AEG09 ~~ WAMI07 0.030 -0.006 -0.006 -0.014 -0.014
## 1128 WAMI04 ~~ WAMI06 0.030 0.007 0.007 0.027 0.027
## 942 AEG10 ~~ UWES05Vi 0.029 0.006 0.006 0.021 0.021
## 997 AEO03 ~~ WAMI01 0.029 0.006 0.006 0.029 0.029
## 606 AEC02 ~~ WAMI08 0.029 0.006 0.006 0.085 0.085
## 640 AEC03 ~~ WAMI07 0.028 0.006 0.006 0.015 0.015
## 643 AEC03 ~~ WAMI10 0.028 0.006 0.006 0.016 0.016
## 828 AEG06 ~~ WAMI07 0.027 0.006 0.006 0.013 0.013
## 732 AEG03 ~~ AEO06 0.027 0.006 0.006 0.014 0.014
## 728 AEG03 ~~ AEO02 0.026 -0.006 -0.006 -0.017 -0.017
## 1239 UWES05Vi ~~ UWES09Ab 0.026 0.006 0.006 0.016 0.016
## 1183 WAMI08 ~~ UWES01Vi 0.025 0.006 0.006 0.035 0.035
## 478 Engaj =~ AEC01 0.024 0.002 0.002 0.002 0.002
## 796 AEG05 ~~ WAMI04 0.023 -0.006 -0.006 -0.021 -0.021
## 1235 UWES04.De ~~ UWES09Ab 0.023 -0.006 -0.006 -0.024 -0.024
## 736 AEG03 ~~ WAMI04 0.023 -0.005 -0.005 -0.022 -0.022
## 586 AEC02 ~~ AEG04 0.022 0.005 0.005 0.032 0.032
## 993 AEO02 ~~ UWES09Ab 0.020 -0.005 -0.005 -0.011 -0.011
## 449 WAMI =~ AEC01 0.020 0.002 0.002 0.002 0.002
## 905 AEG09 ~~ WAMI03 0.019 0.005 0.005 0.009 0.009
## 1012 AEO03 ~~ UWES06Ab 0.018 0.005 0.005 0.014 0.014
## 877 AEG08 ~~ WAMI01 0.018 0.005 0.005 0.024 0.024
## 405 AEG =~ WAMI10 0.017 -0.002 -0.002 -0.002 -0.002
## 571 AEC01 ~~ WAMI09 0.016 -0.005 -0.005 -0.015 -0.015
## 1196 WAMI09 ~~ UWES04.De 0.016 0.005 0.005 0.026 0.026
## 1146 WAMI05 ~~ WAMI10 0.016 -0.005 -0.005 -0.020 -0.020
## 810 AEG05 ~~ UWES08Ab 0.016 -0.005 -0.005 -0.020 -0.020
## 1208 WAMI10 ~~ UWES07De 0.016 0.005 0.005 0.022 0.022
## 1050 AEO05 ~~ UWES03De 0.015 0.005 0.005 0.017 0.017
## 793 AEG05 ~~ WAMI01 0.015 0.004 0.004 0.020 0.020
## 1150 WAMI05 ~~ UWES04.De 0.014 0.004 0.004 0.034 0.034
## 596 AEC02 ~~ AEO04 0.013 -0.004 -0.004 -0.024 -0.024
## 1166 WAMI06 ~~ UWES07De 0.013 -0.004 -0.004 -0.018 -0.018
## 529 AEC04 ~~ WAMI04 0.013 0.004 0.004 0.039 0.039
## 1134 WAMI04 ~~ UWES02Vi 0.012 0.004 0.004 0.021 0.021
## 1054 AEO05 ~~ UWES07De 0.012 0.004 0.004 0.014 0.014
## 614 AEC02 ~~ UWES06Ab 0.011 -0.004 -0.004 -0.029 -0.029
## 911 AEG09 ~~ WAMI09 0.011 0.004 0.004 0.009 0.009
## 585 AEC02 ~~ AEG03 0.011 -0.004 -0.004 -0.028 -0.028
## 530 AEC04 ~~ WAMI05 0.010 -0.004 -0.004 -0.033 -0.033
## 860 AEG07 ~~ UWES01Vi 0.009 0.004 0.004 0.009 0.009
## 382 AEC =~ UWES06Ab 0.009 0.002 0.002 0.002 0.002
## 762 AEG04 ~~ AEO06 0.009 -0.003 -0.003 -0.007 -0.007
## 1135 WAMI04 ~~ UWES03De 0.008 -0.003 -0.003 -0.023 -0.023
## 1073 AEO06 ~~ UWES07De 0.008 0.003 0.003 0.012 0.012
## 1188 WAMI08 ~~ UWES06Ab 0.008 0.003 0.003 0.018 0.018
## 1072 AEO06 ~~ UWES06Ab 0.008 0.003 0.003 0.008 0.008
## 1137 WAMI04 ~~ UWES05Vi 0.007 0.003 0.003 0.017 0.017
## 1157 WAMI06 ~~ WAMI08 0.007 -0.003 -0.003 -0.017 -0.017
## 1153 WAMI05 ~~ UWES07De 0.006 0.003 0.003 0.017 0.017
## 1038 AEO05 ~~ WAMI01 0.006 0.003 0.003 0.011 0.011
## 748 AEG03 ~~ UWES06Ab 0.006 -0.003 -0.003 -0.008 -0.008
## 613 AEC02 ~~ UWES05Vi 0.005 0.003 0.003 0.024 0.024
## 772 AEG04 ~~ WAMI10 0.005 -0.003 -0.003 -0.006 -0.006
## 1191 WAMI08 ~~ UWES09Ab 0.005 -0.003 -0.003 -0.011 -0.011
## 543 AEC04 ~~ UWES08Ab 0.005 -0.003 -0.003 -0.028 -0.028
## 768 AEG04 ~~ WAMI06 0.005 0.003 0.003 0.006 0.006
## 1133 WAMI04 ~~ UWES01Vi 0.005 0.003 0.003 0.012 0.012
## 773 AEG04 ~~ UWES01Vi 0.005 -0.003 -0.003 -0.006 -0.006
## 1209 WAMI10 ~~ UWES08Ab 0.004 -0.002 -0.002 -0.012 -0.012
## 780 AEG04 ~~ UWES08Ab 0.004 -0.002 -0.002 -0.009 -0.009
## 954 AEO01 ~~ WAMI03 0.004 0.002 0.002 0.004 0.004
## 1182 WAMI08 ~~ WAMI10 0.004 0.002 0.002 0.014 0.014
## 726 AEG03 ~~ AEG10 0.004 0.002 0.002 0.006 0.006
## 662 AEG01 ~~ AEO01 0.004 0.002 0.002 0.006 0.006
## 1217 UWES01Vi ~~ UWES09Ab 0.003 0.002 0.002 0.005 0.005
## 601 AEC02 ~~ WAMI03 0.003 0.002 0.002 0.012 0.012
## 969 AEO01 ~~ UWES08Ab 0.003 -0.002 -0.002 -0.009 -0.009
## 939 AEG10 ~~ UWES02Vi 0.003 0.002 0.002 0.006 0.006
## 1039 AEO05 ~~ WAMI02 0.003 -0.002 -0.002 -0.005 -0.005
## 532 AEC04 ~~ WAMI07 0.002 0.002 0.002 0.011 0.011
## 715 AEG02 ~~ UWES05Vi 0.002 -0.002 -0.002 -0.004 -0.004
## 549 AEC01 ~~ AEG03 0.002 -0.002 -0.002 -0.005 -0.005
## 771 AEG04 ~~ WAMI09 0.002 -0.002 -0.002 -0.004 -0.004
## 845 AEG07 ~~ AEO02 0.002 -0.002 -0.002 -0.004 -0.004
## 1032 AEO04 ~~ UWES05Vi 0.001 0.001 0.001 0.004 0.004
## 931 AEG10 ~~ WAMI04 0.001 -0.001 -0.001 -0.004 -0.004
## 625 AEC03 ~~ AEG08 0.001 0.001 0.001 0.003 0.003
## 415 AEO =~ AEC04 0.001 0.001 0.001 0.001 0.001
## 557 AEC01 ~~ AEO01 0.001 0.001 0.001 0.003 0.003
## 1106 WAMI02 ~~ UWES05Vi 0.001 -0.001 -0.001 -0.004 -0.004
## 1231 UWES04.De ~~ UWES05Vi 0.001 -0.001 -0.001 -0.007 -0.007
## 833 AEG06 ~~ UWES02Vi 0.001 -0.001 -0.001 -0.002 -0.002
## 888 AEG08 ~~ UWES02Vi 0.000 -0.001 -0.001 -0.003 -0.003
## 1230 UWES03De ~~ UWES09Ab 0.000 0.001 0.001 0.003 0.003
## 515 AEC04 ~~ AEG06 0.000 0.001 0.001 0.003 0.003
## 910 AEG09 ~~ WAMI08 0.000 0.001 0.001 0.003 0.003
## 560 AEC01 ~~ AEO04 0.000 -0.001 -0.001 -0.002 -0.002
## 519 AEC04 ~~ AEG10 0.000 0.001 0.001 0.003 0.003
## 742 AEG03 ~~ WAMI10 0.000 0.000 0.000 -0.001 -0.001
## 534 AEC04 ~~ WAMI09 0.000 0.000 0.000 -0.003 -0.003
## 1057 AEO06 ~~ WAMI01 0.000 0.000 0.000 -0.002 -0.002
## 961 AEO01 ~~ WAMI10 0.000 0.000 0.000 0.000 0.000
## 459 WAMI =~ AEG08 0.000 0.000 0.000 0.000 0.0008.5.0.5 Alpha Ordinal and Omege
#Reliability
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.## AEC AEG AEO WAMI Engaj
## alpha 0.9242 NA NA NA NA
## alpha.ord 0.9371 0.9204 0.8714 0.9028 0.9651
## omega 0.9209 0.8743 0.8317 0.9297 0.9491
## omega2 0.9209 0.8743 0.8317 0.9297 0.9491
## omega3 0.9192 0.8749 0.8317 0.9450 0.9455
## avevar 0.7967 0.5324 0.5333 0.7190 0.75678.5.0.6 Correlations and Discriminant Validaity
discriminantValidity(fit, merge=T)## lhs op rhs est ci.lower ci.upper Df AIC BIC Chisq Chisq diff Df diff
## 1 AEC ~~ AEG 0.5863 0.5178 0.6548 694 NA NA 2334 93.19 4
## 2 AEC ~~ AEO 0.4473 0.3895 0.5052 694 NA NA 2789 193.85 4
## 3 AEC ~~ WAMI 0.2639 0.1974 0.3303 694 NA NA 5937 514.90 4
## 4 AEC ~~ Engaj 0.2569 0.1904 0.3233 694 NA NA 5699 470.52 4
## 5 AEG ~~ AEO 0.8536 0.8123 0.8950 694 NA NA 1713 73.40 4
## 6 AEG ~~ WAMI 0.4329 0.3600 0.5058 694 NA NA 8839 523.08 4
## 7 AEG ~~ Engaj 0.4644 0.3963 0.5324 694 NA NA 8170 515.84 4
## 8 AEO ~~ WAMI 0.5327 0.4733 0.5920 694 NA NA 5461 479.73 4
## 9 AEO ~~ Engaj 0.5941 0.5407 0.6474 694 NA NA 4905 469.13 4
## 10 WAMI ~~ Engaj 0.7937 0.7656 0.8218 694 NA NA 2007 95.28 4
## Pr(>Chisq)
## 1 2.770e-19
## 2 7.900e-41
## 3 4.015e-110
## 4 1.592e-100
## 5 4.348e-15
## 6 6.818e-112
## 7 2.506e-110
## 8 1.620e-102
## 9 3.175e-100
## 10 9.941e-208.5.0.7 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)
8.5.1 Predicting Latent as Factor Scores
data_predict <- predict(fit)
data <- cbind(data,data_predict)
write.csv(data,"data.csv")
#names(data)8.5.1.0.1 Correlation Matrix
CorMat <- cor(data[,c(281:285)],method = "pearson")
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))
9 Item Reponse Theory
9.1 Subsetting Data
data<-TDados[,c(234:237)]9.2 Descriptives
data<-as.matrix(data)
dsc<-descript(data)9.3 Alpha - per excluded item
dsc$alpha## value
## All Items 0.9242
## Excluding AEC01 0.8978
## Excluding AEC02 0.8918
## Excluding AEC03 0.9326
## Excluding AEC04 0.88159.4 Correlation Itens
rcor.test(data, method = "kendall")##
## AEC01 AEC02 AEC03 AEC04
## AEC01 ***** 0.730 0.556 0.721
## AEC02 <0.001 ***** 0.563 0.780
## AEC03 <0.001 <0.001 ***** 0.629
## AEC04 <0.001 <0.001 <0.001 *****
##
## upper diagonal part contains correlation coefficient estimates
## lower diagonal part contains corresponding p-values9.5 Empirical Plots - Total Raw Score and Responses
empirical_plot(data, c(1,2,3,4), smooth = TRUE)
9.6 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 Extrmt5 Extrmt6 Dscrmn
## AEC01 -1.985 -1.308 -0.568 0.465 1.388 1.847 3.782
## AEC02 -2.180 -1.437 -0.782 0.333 1.203 1.733 3.782
## AEC03 -2.016 -1.273 -0.428 0.460 1.376 1.864 3.782
## AEC04 -2.121 -1.414 -0.553 0.432 1.352 1.834 3.782
##
## Log.Lik: -3819margins(fit1)##
## Call:
## ltm::grm(data = data, constrained = T, IRT.param = T, Hessian = T)
##
## Fit on the Two-Way Margins
##
## AEC01 AEC02 AEC03 AEC04
## AEC01 - 140.93 3307.38 105.33
## AEC02 - 2412.13 187.60
## AEC03 *** *** - 186.12
## AEC04 *** *** -
##
## '***' 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 92867.3 ***
## 2 1 2 4 973.5
## 3 1 3 4 14885.4 ***
## 4 2 3 4 11192.0 ***
##
## '***' denotes triplets of items with lack-of-fit9.7 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 Extrmt5 Extrmt6 Dscrmn
## AEC01 -2.460 -1.513 -0.691 0.461 1.464 1.961 3.745
## AEC02 -2.107 -1.485 -0.816 0.388 1.318 1.958 3.572
## AEC03 -2.371 -1.669 -0.643 0.512 1.671 2.210 2.089
## AEC04 -2.211 -1.521 -0.634 0.480 1.579 2.031 3.152
##
## Log.Lik: -3828margins(fit1)##
## Call:
## ltm::grm(data = data, constrained = T, IRT.param = T, Hessian = T)
##
## Fit on the Two-Way Margins
##
## AEC01 AEC02 AEC03 AEC04
## AEC01 - 140.93 3307.38 105.33
## AEC02 - 2412.13 187.60
## AEC03 *** *** - 186.12
## AEC04 *** *** -
##
## '***' 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 92867.3 ***
## 2 1 2 4 973.5
## 3 1 3 4 14885.4 ***
## 4 2 3 4 11192.0 ***
##
## '***' denotes triplets of items with lack-of-fit9.8 Comparisons Constrained and Uconstrained
anova(fit1,fit2)##
## Likelihood Ratio Table
## AIC BIC log.Lik LRT df p.value
## fit1 7688 7805 -3819
## fit2 7711 7842 -3828 -16.69 3 19.9 Unconstrained Model
9.9.1 Coeficients
coef(fit2, simplify = TRUE,standardized=T,prob=T,order=T)## Extrmt1 Extrmt2 Extrmt3 Extrmt4 Extrmt5 Extrmt6 Dscrmn
## AEC01 -2.460 -1.513 -0.691 0.461 1.464 1.961 3.745
## AEC02 -2.107 -1.485 -0.816 0.388 1.318 1.958 3.572
## AEC03 -2.371 -1.669 -0.643 0.512 1.671 2.210 2.089
## AEC04 -2.211 -1.521 -0.634 0.480 1.579 2.031 3.1529.9.2 Information
information(fit2, c(-4, 4), items = c(1:4))##
## Call:
## grm(data = data, constrained = F, IRT.param = T, Hessian = T)
##
## Total Information = 57.36
## Information in (-4, 4) = 57.2 (99.73%)
## Based on items 1, 2, 3, 49.10 Item Response Category Characteristic Curves
op <- par(mfrow = c(2,2))
plot(fit2, lwd = 2, legend = TRUE, ncol = 2)
9.10.1 Item Information Curve
plot(fit2, type = "IIC")
9.10.2 Item Information Curve
plot(fit2, type = "IIC",item=0,zrange = c(-4, 4))
9.10.3 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")
9.10.4 Operational Characteristic Curve itens (upper)
op <- par(mfrow = c(2,2))
plot(fit2, type = "OCCu")
9.10.5 Operational Characteristic Curve itens (lower)
op <- par(mfrow = c(2,2))
plot(fit2,type='OCCl')
9.10.6 Person Parameters Factor Score
f.scores<-ltm::factor.scores(fit2)
plot(f.scores, main = "KDE for Person Parameters")