Abilities, Practice, and Visual Discrimination Tasks
Setup
library(pacman); p_load(psych, lavaan, EGAnet, sna, ggplot2, egg)
ZREG <- function(B1, B2, SEB1, SEB2) {
Z = (B1-B2)/sqrt((SEB1)^2 + (SEB2)^2)
return(Z)}
#Automatic Kaiser-Guttman Test
KGA <- function(x){
SL = x$e.values
which.min(SL >= 1) - 1}
#Automatic Warne & Larsen (2014) Kaiser-Guttman revision
MAPA <- function(x, a = 0.05, s = 2, d = 3){
LE = x$e.values[x$factors]; LECIL = LE - abs((qnorm(a/s) * sqrt((2*LE^2)/(x$n.obs)))); LECIU = LE + abs((qnorm(a/s) * sqrt((2*LE^2)/(x$n.obs))))
DEC <- ifelse(LECIL < 1, "dropped.", "retained.")
S1 <- cat(paste("The smallest factor had an eigenvalue of", round((LE), d), "with a confidence interval of", round((LECIL), d), "to", round((LECIU), d), "so the factor should be", DEC))}
#Automatic Percent of the Total Variance
PTV <- function(x){
TV = x$e.values/length(x$e.values)
return(TV)}
estimate.ED <- function (x, sample.size = NULL, rel.values = NULL, cov.mat = FALSE, small.sample.c = FALSE, round.digits = 2, print.summary = TRUE) {
indefinite.matrix = FALSE
if (is.data.frame(x) == TRUE) {
sample.size = nrow(x)
if (cov.mat == FALSE) {
matrix = cor(x, use="pairwise.complete.obs")}
else matrix = cov(x, use="pairwise.complete.obs")}
else {
matrix = x
if ( ((sum(diag(matrix)) != nrow(matrix) ) | (var(diag(matrix)) != 0)) & (cov.mat == FALSE) ) {
matrix = cov2cor(matrix)}}
if ( (cov.mat == FALSE) & (is.null(rel.values) == FALSE) ) {
rel.matrix = sqrt(crossprod(t(rel.values), t(rel.values)))
diag(rel.matrix) = 1
matrix = matrix/rel.matrix}
output = list()
if (sum(eigen(matrix)$values < 0) > 0) {
indefinite.matrix = TRUE
matrix = nearPD(matrix, corr=!cov.mat)$mat}
eigen_val = sort(eigen(matrix)$values)
eigen_val.c = NULL
if (small.sample.c == TRUE) {
if (is.data.frame(x) == TRUE) {
if(cov.mat == FALSE) {
if(is.null(rel.values) == TRUE) {
suppress = file()
sink(file = suppress)
tmp = tau_estimate(as.matrix(scale(x)))
sink()
close(suppress)
eigen_val.c = tmp } else {
sink("NUL")
tmp = nlshrink_cov(as.matrix(scale(x)))
sink()
matrix.c = tmp/rel.matrix
if (sum(eigen(matrix.c)$values < 0) > 0) {
indefinite.matrix = TRUE
matrix.c = nearPD(matrix.c, corr=TRUE)$mat }
eigen_val.c = sort(eigen(matrix.c)$values)}} else {
suppress = file()
sink(file = suppress)
tmp = tau_estimate(as.matrix(x))
sink()
close(suppress)
eigen_val.c = tmp }}
else if (is.null(sample.size) == FALSE) {
eigen_val.rounded = round(eigen_val, 6)
eigen_val.c = eigen_val
function.body = paste(eigen_val.rounded[1],"/(",eigen_val.rounded[1],"-x)")
for(index in 2:length(eigen_val.rounded)) {
function.body = paste(function.body, "+",eigen_val.rounded[index],"/(",eigen_val.rounded[index],"-x)")}
function.body = paste(function.body,"-",sample.size)
eval(parse(text = paste("f = function(x) {", function.body,"}")))
unique.eigen = sum(!duplicated(eigen_val.rounded[eigen_val.rounded != 0]) )
mu_val = uniroot.all(f, interval=c(0, max(eigen_val.rounded)), n=10000000)
mu_val = mu_val[which( abs(f(mu_val)) %in% sort(abs(f(mu_val)))[1:unique.eigen] ) ]
mu.index = 1
for (index in 1:length(eigen_val.rounded)) {
if (eigen_val.rounded[index] != 0) {
if (duplicated(eigen_val.rounded)[index] == FALSE) {
eigen_val.c[index] = sample.size * (eigen_val.rounded[index] - mu_val[mu.index])
mu.index = mu.index + 1
} else {
eigen_val.c[index] = eigen_val.c[index-1]}}}}}
K = length(eigen_val)
eigen_sum = sum(eigen_val)
norm_eigen_val = eigen_val/eigen_sum
eigen_var = var(eigen_val)*((K-1)/K)
output$n1 = prod(norm_eigen_val^(-norm_eigen_val))
output$n2 = (eigen_sum^2)/sum(eigen_val^2)
output$nInf = eigen_sum/max(eigen_val)
output$nC = K - ((K^2)/(eigen_sum^2))*eigen_var
if ( (small.sample.c == TRUE) & (is.null(eigen_val.c) == FALSE) ) {
eigen_sum.c = sum(eigen_val.c)
norm_eigen_val.c = eigen_val.c/eigen_sum.c
eigen_var.c = var(eigen_val.c)*((K-1)/K)
output$n1.c = max(prod(norm_eigen_val.c^(-norm_eigen_val.c)), output$n1)
output$n2.c = max((eigen_sum.c^2)/sum(eigen_val.c^2), output$n2)
output$nInf.c = max(eigen_sum.c/max(eigen_val.c), output$nInf)
output$nC.c = max(K - ((K^2)/(eigen_sum.c^2))*eigen_var.c, output$nC) }
if (print.summary == TRUE) {
description = "ED estimated from the"
if (cov.mat == TRUE) {description = paste(description, "covariance matrix;")}
else {description = paste(description, "correlation matrix;")}
if (is.null(rel.values) == FALSE) {description = paste(description, "disattenuated;")}
else {description = paste(description, "no disattenuation;")}
if ( (small.sample.c == TRUE) & (is.null(eigen_val.c) == FALSE) ) {
if (is.data.frame(x) == TRUE) {description = paste(description, "corrected for small-sample bias (Ledoit & Wolf 2015).")}
else {description = paste(description, "corrected for small-sample bias (Mestre 2008).")}}
else {description = paste(description, "no small-sample correction.")}
if (indefinite.matrix == TRUE) {description = paste(description, "Warning: an indefinite matrix was detected and replaced with the nearest positive definite matrix.")}
print(description, quote = FALSE)
cat("\n")}
return(lapply(output,round,round.digits))}
FITM <- c("chisq", "df", "nPar", "cfi", "rmsea", "rmsea.ci.lower", "rmsea.ci.upper", "aic", "bic", "srmr")
#Fleishman & Hempel (1954)
lowerFH54 <- '
1
0.75 1
0.73 0.85 1
0.66 0.85 0.85 1
0.64 0.84 0.83 0.9 1
0.57 0.79 0.79 0.88 0.9 1
0.63 0.77 0.81 0.86 0.87 0.85 1
0.59 0.79 0.79 0.85 0.86 0.86 0.9 1
0.28 0.3 0.3 0.26 0.22 0.23 0.23 0.24 1
0.51 0.46 0.45 0.4 0.37 0.34 0.36 0.34 0.63 1
0.49 0.4 0.39 0.36 0.36 0.29 0.33 0.3 0.32 0.54 1
0.38 0.31 0.29 0.27 0.25 0.2 0.25 0.24 0.23 0.43 0.52 1
0.5 0.45 0.46 0.41 0.37 0.31 0.32 0.35 0.44 0.61 0.46 0.29 1
0.55 0.41 0.44 0.38 0.37 0.27 0.33 0.29 0.34 0.59 0.52 0.3 0.57 1
0.43 0.47 0.45 0.42 0.39 0.34 0.36 0.38 0.23 0.4 0.34 0.17 0.44 0.43 1
0.5 0.38 0.39 0.34 0.32 0.24 0.29 0.29 0.45 0.61 0.43 0.32 0.58 0.6 0.33 1
0.44 0.38 0.42 0.35 0.31 0.27 0.28 0.3 0.42 0.51 0.3 0.3 0.4 0.44 0.35 0.53 1
0.47 0.39 0.46 0.4 0.38 0.31 0.39 0.35 0.31 0.54 0.44 0.32 0.58 0.49 0.46 0.59 0.46 1
0.46 0.41 0.44 0.4 0.36 0.33 0.39 0.34 0.37 0.49 0.33 0.17 0.55 0.45 0.32 0.41 0.34 0.49 1
0.33 0.32 0.35 0.34 0.33 0.28 0.31 0.28 0.4 0.5 0.26 0.23 0.48 0.39 0.32 0.32 0.22 0.37 0.55 1
0.51 0.51 0.59 0.51 0.5 0.47 0.5 0.49 0.22 0.38 0.27 0.26 0.31 0.32 0.29 0.24 0.28 0.4 0.26 0.27 1
0.4 0.45 0.44 0.44 0.42 0.39 0.39 0.36 0.08 0.22 0.22 0.29 0.23 0.31 0.2 0.19 0.29 0.21 0.18 0.19 0.35 1
0.5 0.44 0.48 0.42 0.38 0.33 0.35 0.33 0.39 0.54 0.37 0.3 0.52 0.56 0.38 0.55 0.47 0.41 0.43 0.33 0.34 0.36 1
0.36 0.3 0.31 0.32 0.28 0.25 0.24 0.26 0.13 0.28 0.27 0.3 0.31 0.3 0.24 0.22 0.31 0.26 0.2 0.18 0.28 0.2 0.22 1
0.08 0.22 0.27 0.3 0.3 0.27 0.33 0.27 0.09 0.05 -0.05 0.02 0.15 0.03 0.1 0.08 0.11 0.06 0.14 0.23 0.26 0.2 0.23 0.015 1
0.25 0.32 0.31 0.28 0.34 0.37 0.3 0.32 0.12 0.24 0.12 0.04 0.22 0.26 0.16 0.18 0.24 0.15 0.28 0.26 0.28 0.2 0.23 0.14 0.3 1'
#Fleishman & Hempel (1955)
lowerFH55 <- '
1
0.74 1
0.71 0.82 1
0.69 0.78 0.83 1
0.62 0.74 0.79 0.8 1
0.59 0.68 0.72 0.74 0.77 1
0.57 0.66 0.72 0.72 0.73 0.74 1
0.56 0.64 0.71 0.74 0.77 0.8 0.79 1
0.33 0.36 0.38 0.35 0.3 0.3 0.31 0.28 1
0.34 0.4 0.4 0.38 0.36 0.33 0.37 0.3 0.71 1
0.37 0.39 0.37 0.37 0.35 0.34 0.39 0.38 0.5 0.5 1
0.3 0.27 0.29 0.22 0.24 0.23 0.24 0.26 0.53 0.48 0.6 1
0.24 0.25 0.24 0.18 0.2 0.17 0.19 0.18 0.33 0.34 0.58 0.71 1
0.38 0.44 0.44 0.39 0.37 0.39 0.43 0.4 0.42 0.48 0.41 0.27 0.28 1
0.41 0.44 0.46 0.36 0.37 0.34 0.4 0.34 0.5 0.55 0.54 0.41 0.42 0.52 1
0.45 0.42 0.47 0.44 0.42 0.4 0.38 0.43 0.44 0.45 0.58 0.47 0.42 0.45 0.51 1
0.21 0.23 0.24 0.21 0.2 0.16 0.17 0.22 0.17 0.16 0.33 0.23 0.27 0.32 0.31 0.32 1
0.23 0.28 0.32 0.31 0.34 0.3 0.34 0.32 0.24 0.24 0.25 0.19 0.21 0.46 0.36 0.33 0.27 1
0.34 0.47 0.41 0.38 0.36 0.32 0.42 0.36 0.26 0.25 0.2 0.19 0.15 0.38 0.27 0.29 0.2 0.4 1
0.18 0.24 0.2 0.28 0.3 0.23 0.23 0.25 0.19 0.18 0.2 0.16 0.14 0.16 0.19 0.2 0.17 0.16 0.24 1
0 0.11 0.16 0.14 0.19 0.19 0.15 0.23 0.05 0.03 0.07 0.06 -0.01 0.25 0.07 0.13 0.23 0.27 0.31 0.32 1
0.12 0.14 0.17 0.24 0.26 0.21 0.2 0.25 -0.04 -0.02 -0.09 -0.1 -0.11 0.08 -0.06 0.04 0.03 0.04 0.14 0.1 0.21 1
0.04 0.09 0.12 0.13 0.14 0.14 0.14 0.2 0.02 0.02 -0.01 0 0 0.06 -0.04 0.05 -0.03 0.05 0.08 0.06 0.17 0.57 1
0.19 0.26 0.24 0.32 0.35 0.3 0.31 0.37 0.11 0.14 0.09 0.04 -0.03 0.23 0.08 0.19 0.19 0.26 0.3 0.24 0.34 0.61 0.44 1
0.09 0.24 0.22 0.29 0.3 0.28 0.27 0.33 0.09 0.1 0.07 -0.04 -0.07 0.25 0.08 0.14 0.15 0.21 0.3 0.2 0.3 0.49 0.49 0.73 1
0.44 0.48 0.45 0.44 0.41 0.37 0.43 0.38 0.23 0.24 0.46 0.29 0.33 0.39 0.4 0.47 0.38 0.34 0.38 0.2 0.24 0.16 0 0.28 0.19 1
0.29 0.28 0.3 0.31 0.31 0.25 0.27 0.24 0.15 0.06 0.25 0.21 0.23 0.27 0.23 0.24 0.32 0.22 0.35 0.2 0.24 0.15 0.1 0.23 0.2 0.4 1'
nFH54 <- 197
nFH55 <- 264
FH54.cor = getCov(lowerFH54, names = c("P1CC", "P2CC", "P3CC", "P4CC", "P5CC", "P6CC", "P7CC", "P8CC", "NumOpII", "DTR", "MP", "GenMec", "SpId", "PatCom", "VisPur", "Deco", "InsCom", "SpaOri", "SpeMar", "LogAcc", "RotPur", "PlaCon", "DisReac", "NutBolt", "ReaTim", "ROM"))
FH55.cor = getCov(lowerFH55, names = c("T1DRT", "T3DRT", "T5DRT", "T7DRT", "T9DRT", "T11DRT", "T13DRT", "T15DRT", "Wknow", "Caff", "MechPri", "GenMec", "TooFun", "SpId", "PatCom", "InsCom", "VisPur", "PurPegA", "SADEx", "ROMov", "RotAi", "VisRea", "AudRea", "JuViRea", "JuAuRea", "CoCo", "RoPu"))Analyses
Fleishman & Hempel (1955)
Exploratory
fa.parallel(FH55.cor, n.obs = nFH55)
## Parallel analysis suggests that the number of factors = 5 and the number of components = 4FAFH <- fa(FH55.cor, n.obs = nFH55, nfactors = 5)## Loading required namespace: GPArotationnfactors(FH55.cor, n.obs = nFH55); KGA(FAFH); MAPA(FAFH); PTV(FAFH); estimate.ED(FH55.cor); EGA(FH55.cor, plot.ega = T, n = nFH55)
##
## Number of factors
## Call: vss(x = x, n = n, rotate = rotate, diagonal = diagonal, fm = fm,
## n.obs = n.obs, plot = FALSE, title = title, use = use, cor = cor)
## VSS complexity 1 achieves a maximimum of 0.8 with 1 factors
## VSS complexity 2 achieves a maximimum of 0.88 with 2 factors
## The Velicer MAP achieves a minimum of 0.02 with 3 factors
## Empirical BIC achieves a minimum of -1114.05 with 4 factors
## Sample Size adjusted BIC achieves a minimum of -185.79 with 7 factors
##
## Statistics by number of factors
## vss1 vss2 map dof chisq prob sqresid fit RMSEA BIC SABIC complex
## 1 0.80 0.00 0.040 324 1859.1 2.5e-213 23.6 0.80 0.1339 53 1079.75 1.0
## 2 0.54 0.88 0.032 298 1274.9 8.5e-121 13.8 0.88 0.1114 -387 558.06 1.5
## 3 0.61 0.86 0.017 273 736.3 3.2e-44 9.5 0.92 0.0801 -786 79.63 1.6
## 4 0.56 0.81 0.018 249 597.9 1.0e-30 7.6 0.93 0.0728 -791 -1.08 1.6
## 5 0.52 0.74 0.018 226 440.7 5.4e-16 6.3 0.95 0.0599 -819 -102.88 1.8
## 6 0.52 0.72 0.020 204 314.5 1.0e-06 5.7 0.95 0.0451 -823 -176.18 1.9
## 7 0.50 0.68 0.023 183 254.4 3.8e-04 5.2 0.96 0.0383 -766 -185.79 2.0
## 8 0.49 0.65 0.025 163 216.3 3.3e-03 4.7 0.96 0.0350 -693 -175.83 2.1
## 9 0.49 0.71 0.031 144 167.3 9.0e-02 4.3 0.96 0.0244 -636 -179.11 2.1
## 10 0.48 0.67 0.037 126 132.1 3.4e-01 4.0 0.97 0.0130 -570 -171.01 2.1
## 11 0.48 0.70 0.043 109 114.9 3.3e-01 3.8 0.97 0.0138 -493 -147.32 2.1
## 12 0.48 0.70 0.050 93 95.6 4.1e-01 3.3 0.97 0.0095 -423 -128.16 2.1
## 13 0.48 0.67 0.056 78 74.6 5.9e-01 3.1 0.97 0.0000 -360 -113.06 2.2
## 14 0.49 0.69 0.067 64 60.1 6.1e-01 2.8 0.98 0.0000 -297 -93.82 2.2
## 15 0.49 0.69 0.078 51 45.3 7.0e-01 2.3 0.98 0.0000 -239 -77.33 2.2
## 16 0.49 0.66 0.085 39 28.8 8.8e-01 2.5 0.98 0.0000 -189 -65.03 2.3
## 17 0.49 0.69 0.088 28 20.8 8.3e-01 2.4 0.98 0.0000 -135 -46.58 2.3
## 18 0.49 0.68 0.102 18 9.2 9.5e-01 2.2 0.98 0.0000 -91 -34.07 2.2
## 19 0.48 0.67 0.118 9 4.9 8.5e-01 2.1 0.98 0.0000 -45 -16.78 2.3
## 20 0.47 0.64 0.141 1 1.6 2.1e-01 1.9 0.98 0.0458 -4 -0.85 2.3
## eChisq SRMR eCRMS eBIC
## 1 2790.36 0.12270 0.128 983.7
## 2 1140.61 0.07845 0.085 -521.0
## 3 463.60 0.05002 0.057 -1058.6
## 4 274.36 0.03848 0.046 -1114.0
## 5 154.73 0.02889 0.036 -1105.4
## 6 105.01 0.02380 0.031 -1032.5
## 7 73.19 0.01987 0.028 -947.2
## 8 52.45 0.01682 0.025 -856.4
## 9 37.38 0.01420 0.022 -765.6
## 10 28.57 0.01242 0.021 -674.0
## 11 23.09 0.01116 0.020 -584.7
## 12 16.94 0.00956 0.019 -501.6
## 13 11.36 0.00783 0.017 -423.6
## 14 8.38 0.00672 0.016 -348.5
## 15 5.50 0.00545 0.014 -278.9
## 16 3.89 0.00458 0.014 -213.6
## 17 2.81 0.00390 0.014 -153.3
## 18 1.14 0.00248 0.011 -99.2
## 19 0.56 0.00173 0.011 -49.6
## 20 0.16 0.00094 0.018 -5.4## [1] 5## The smallest factor had an eigenvalue of 1.159 with a confidence interval of 0.961 to 1.356 so the factor should be dropped.## [1] 0.357216410 0.117773799 0.077767620 0.053951925 0.042911576 0.036659075
## [7] 0.030002944 0.029192929 0.023995615 0.022658151 0.022102412 0.021036276
## [13] 0.018900390 0.018111880 0.016314323 0.015800280 0.014816278 0.012395111
## [19] 0.011294804 0.010202092 0.008869764 0.007739236 0.007237241 0.006538120
## [25] 0.006405234 0.005364654 0.004741861## [1] ED estimated from the correlation matrix; no disattenuation; no small-sample correction.## $n1
## [1] 12.3
##
## $n2
## [1] 6.27
##
## $nInf
## [1] 2.8
##
## $nC
## [1] 23.69## Warning in EGA(FH55.cor, plot.ega = T, n = nFH55): Previous versions of EGAnet
## (<= 0.9.8) checked unidimensionality using [4;muni.method = "expand"[0m as the
## default## [1;m[4;m
## Exploratory Graph Analysis
## [0m[0m## • model = glasso
## • algorithm = walktrap
## • correlation = cor_auto
## • unidimensional check = leading eigenvalue## Network estimated with:
## • gamma = 0.5
## • lambda.min.ratio = 0.1## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2
## EGA Results:
##
## Number of Dimensions:
## [1] 4
##
## Items per Dimension:
## items dimension
## Wknow Wknow 1
## Caff Caff 1
## MechPri MechPri 1
## GenMec GenMec 1
## TooFun TooFun 1
## PatCom PatCom 1
## InsCom InsCom 1
## SpId SpId 2
## VisPur VisPur 2
## PurPegA PurPegA 2
## SADEx SADEx 2
## ROMov ROMov 2
## RotAi RotAi 2
## CoCo CoCo 2
## RoPu RoPu 2
## VisRea VisRea 3
## AudRea AudRea 3
## JuViRea JuViRea 3
## JuAuRea JuAuRea 3
## T1DRT T1DRT 4
## T3DRT T3DRT 4
## T5DRT T5DRT 4
## T7DRT T7DRT 4
## T9DRT T9DRT 4
## T11DRT T11DRT 4
## T13DRT T13DRT 4
## T15DRT T15DRT 4NUM <- seq(1, 27, 1); EVS <- FAFH$e.values; TVP <- PTV(FAFH); bpdf <- data.frame("NUM" = NUM, "EVS" = EVS, "TVP" = TVP)
EVP <- ggplot(bpdf, aes(x = NUM, y = EVS, fill = as.factor(NUM))) + geom_bar(stat = "identity", show.legend = F) + xlab("Number") + ylab("Eigenvalue") + theme_bw() + scale_fill_hue(c = 30) + theme(text = element_text(size = 12, family = "serif"), plot.title = element_text(hjust = 0.5)) + geom_hline(yintercept = 1, color = "darkgray", linetype = "dashed", size = 1)
VPT <- ggplot(bpdf, aes(x = factor(1), y = TVP, fill = as.factor(NUM))) + geom_bar(stat = "identity", show.legend = F) + ylab("Percentage of Total Variance") + theme_bw() + scale_fill_hue(c = 50) + theme(text = element_text(size = 12, family = "serif"), plot.title = element_text(hjust = 0.5), axis.title.y = element_blank(), axis.text.y = element_blank(), axis.ticks.y = element_blank()) + coord_polar("y")ggarrange(EVP, VPT, ncol = 2)
Confirmatory
Separate Models
#T1
RegBFModel <- '
REA =~ VisRea + AudRea + JuViRea + JuAuRea
SPA =~ Wknow + Caff + MechPri + GenMec + TooFun + InsCom
ROT =~ SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
g =~ VisRea + AudRea + JuViRea + JuAuRea + Wknow + Caff + MechPri + GenMec + TooFun + PatCom + InsCom + SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
T1DRT ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH55.cor, sample.nobs = nFH55, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 34 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 58
##
## Number of observations 264
##
## Model Test User Model:
##
## Test statistic 393.004
## Degrees of freedom 152
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 2266.902
## Degrees of freedom 190
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.884
## Tucker-Lewis Index (TLI) 0.855
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -6545.028
## Loglikelihood unrestricted model (H1) -6348.526
##
## Akaike (AIC) 13206.056
## Bayesian (BIC) 13413.461
## Sample-size adjusted Bayesian (BIC) 13229.571
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.077
## 90 Percent confidence interval - lower 0.068
## 90 Percent confidence interval - upper 0.087
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.077
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA =~
## VisRea 0.711 0.057 12.466 0.000 0.711 0.712
## AudRea 0.600 0.060 10.042 0.000 0.600 0.601
## JuViRea 0.842 0.052 16.091 0.000 0.842 0.844
## JuAuRea 0.783 0.054 14.458 0.000 0.783 0.785
## SPA =~
## Wknow 0.242 0.057 4.224 0.000 0.242 0.243
## Caff 0.165 0.055 3.000 0.003 0.165 0.165
## MechPri 0.302 0.057 5.312 0.000 0.302 0.302
## GenMec 0.848 0.075 11.337 0.000 0.848 0.850
## TooFun 0.556 0.072 7.764 0.000 0.556 0.557
## InsCom 0.143 0.054 2.656 0.008 0.143 0.144
## ROT =~
## SpId 0.235 0.062 3.784 0.000 0.235 0.235
## VisPur 0.296 0.072 4.099 0.000 0.296 0.297
## PurPegA 0.359 0.070 5.126 0.000 0.359 0.359
## SADEx 0.461 0.071 6.518 0.000 0.461 0.462
## ROMov 0.307 0.075 4.065 0.000 0.307 0.307
## RotAi 0.613 0.079 7.768 0.000 0.613 0.614
## CoCo 0.334 0.066 5.050 0.000 0.334 0.335
## RoPu 0.417 0.073 5.683 0.000 0.417 0.418
## g =~
## VisRea 0.007 0.066 0.106 0.916 0.007 0.007
## AudRea 0.005 0.066 0.080 0.936 0.005 0.005
## JuViRea 0.229 0.065 3.515 0.000 0.229 0.230
## JuAuRea 0.190 0.066 2.901 0.004 0.190 0.190
## Wknow 0.644 0.059 10.902 0.000 0.644 0.645
## Caff 0.681 0.058 11.773 0.000 0.681 0.682
## MechPri 0.696 0.058 12.028 0.000 0.696 0.697
## GenMec 0.496 0.065 7.648 0.000 0.496 0.497
## TooFun 0.474 0.065 7.303 0.000 0.474 0.475
## PatCom 0.759 0.055 13.682 0.000 0.759 0.760
## InsCom 0.699 0.057 12.195 0.000 0.699 0.700
## SpId 0.660 0.058 11.333 0.000 0.660 0.662
## VisPur 0.390 0.064 6.116 0.000 0.390 0.391
## PurPegA 0.444 0.063 7.037 0.000 0.444 0.444
## SADEx 0.399 0.064 6.241 0.000 0.399 0.400
## ROMov 0.249 0.066 3.804 0.000 0.249 0.250
## RotAi 0.108 0.067 1.617 0.106 0.108 0.109
## CoCo 0.552 0.061 9.054 0.000 0.552 0.553
## RoPu 0.309 0.065 4.753 0.000 0.309 0.310
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## T1DRT ~
## g 0.568 0.060 9.429 0.000 0.568 0.569
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA ~~
## SPA 0.000 0.000 0.000
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## SPA ~~
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## ROT ~~
## g 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .VisRea 0.491 0.052 9.431 0.000 0.491 0.492
## .AudRea 0.637 0.061 10.400 0.000 0.637 0.639
## .JuViRea 0.234 0.042 5.553 0.000 0.234 0.235
## .JuAuRea 0.346 0.045 7.778 0.000 0.346 0.348
## .Wknow 0.523 0.050 10.516 0.000 0.523 0.525
## .Caff 0.505 0.050 10.170 0.000 0.505 0.507
## .MechPri 0.421 0.042 10.067 0.000 0.421 0.423
## .GenMec 0.031 0.106 0.292 0.770 0.031 0.031
## .TooFun 0.462 0.058 7.964 0.000 0.462 0.464
## .InsCom 0.487 0.049 9.974 0.000 0.487 0.489
## .SpId 0.505 0.050 10.009 0.000 0.505 0.507
## .VisPur 0.756 0.070 10.745 0.000 0.756 0.759
## .PurPegA 0.671 0.065 10.276 0.000 0.671 0.673
## .SADEx 0.624 0.067 9.381 0.000 0.624 0.627
## .ROMov 0.840 0.078 10.810 0.000 0.840 0.843
## .RotAi 0.609 0.086 7.098 0.000 0.609 0.611
## .CoCo 0.580 0.057 10.098 0.000 0.580 0.583
## .RoPu 0.726 0.073 10.010 0.000 0.726 0.729
## .PatCom 0.421 0.047 8.880 0.000 0.421 0.422
## .T1DRT 0.674 0.064 10.603 0.000 0.674 0.676
## REA 1.000 1.000 1.000
## SPA 1.000 1.000 1.000
## ROT 1.000 1.000 1.000
## g 1.000 1.000 1.000#T3
RegBFModel <- '
REA =~ VisRea + AudRea + JuViRea + JuAuRea
SPA =~ Wknow + Caff + MechPri + GenMec + TooFun + InsCom
ROT =~ SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
g =~ VisRea + AudRea + JuViRea + JuAuRea + Wknow + Caff + MechPri + GenMec + TooFun + PatCom + InsCom + SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
T3DRT ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH55.cor, sample.nobs = nFH55, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 34 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 58
##
## Number of observations 264
##
## Model Test User Model:
##
## Test statistic 397.239
## Degrees of freedom 152
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 2291.615
## Degrees of freedom 190
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.883
## Tucker-Lewis Index (TLI) 0.854
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -6534.789
## Loglikelihood unrestricted model (H1) -6336.169
##
## Akaike (AIC) 13185.577
## Bayesian (BIC) 13392.982
## Sample-size adjusted Bayesian (BIC) 13209.093
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.078
## 90 Percent confidence interval - lower 0.069
## 90 Percent confidence interval - upper 0.088
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.078
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA =~
## VisRea 0.713 0.057 12.500 0.000 0.713 0.715
## AudRea 0.602 0.060 10.078 0.000 0.602 0.603
## JuViRea 0.835 0.052 15.967 0.000 0.835 0.836
## JuAuRea 0.776 0.054 14.362 0.000 0.776 0.777
## SPA =~
## Wknow 0.259 0.057 4.588 0.000 0.259 0.260
## Caff 0.182 0.054 3.338 0.001 0.182 0.182
## MechPri 0.328 0.056 5.899 0.000 0.328 0.329
## GenMec 0.851 0.069 12.386 0.000 0.851 0.853
## TooFun 0.574 0.068 8.475 0.000 0.574 0.576
## InsCom 0.171 0.054 3.151 0.002 0.171 0.171
## ROT =~
## SpId 0.208 0.063 3.311 0.001 0.208 0.208
## VisPur 0.294 0.074 4.001 0.000 0.294 0.295
## PurPegA 0.340 0.071 4.789 0.000 0.340 0.341
## SADEx 0.434 0.071 6.067 0.000 0.434 0.434
## ROMov 0.300 0.077 3.914 0.000 0.300 0.301
## RotAi 0.603 0.081 7.435 0.000 0.603 0.604
## CoCo 0.321 0.067 4.786 0.000 0.321 0.322
## RoPu 0.421 0.075 5.613 0.000 0.421 0.422
## g =~
## VisRea 0.020 0.066 0.295 0.768 0.020 0.020
## AudRea 0.017 0.066 0.251 0.802 0.017 0.017
## JuViRea 0.249 0.065 3.832 0.000 0.249 0.250
## JuAuRea 0.222 0.065 3.402 0.001 0.222 0.222
## Wknow 0.638 0.059 10.789 0.000 0.638 0.639
## Caff 0.680 0.058 11.772 0.000 0.680 0.682
## MechPri 0.682 0.058 11.730 0.000 0.682 0.683
## GenMec 0.474 0.065 7.308 0.000 0.474 0.475
## TooFun 0.458 0.065 7.058 0.000 0.458 0.459
## PatCom 0.753 0.056 13.564 0.000 0.753 0.755
## InsCom 0.683 0.058 11.828 0.000 0.683 0.684
## SpId 0.672 0.058 11.604 0.000 0.672 0.674
## VisPur 0.390 0.064 6.111 0.000 0.390 0.391
## PurPegA 0.455 0.063 7.233 0.000 0.455 0.455
## SADEx 0.429 0.063 6.767 0.000 0.429 0.430
## ROMov 0.261 0.065 3.981 0.000 0.261 0.261
## RotAi 0.131 0.067 1.963 0.050 0.131 0.132
## CoCo 0.559 0.061 9.193 0.000 0.559 0.560
## RoPu 0.310 0.065 4.768 0.000 0.310 0.311
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## T3DRT ~
## g 0.625 0.059 10.609 0.000 0.625 0.626
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA ~~
## SPA 0.000 0.000 0.000
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## SPA ~~
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## ROT ~~
## g 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .VisRea 0.487 0.052 9.365 0.000 0.487 0.489
## .AudRea 0.633 0.061 10.365 0.000 0.633 0.636
## .JuViRea 0.237 0.042 5.652 0.000 0.237 0.238
## .JuAuRea 0.345 0.044 7.804 0.000 0.345 0.346
## .Wknow 0.522 0.050 10.542 0.000 0.522 0.524
## .Caff 0.500 0.049 10.193 0.000 0.500 0.502
## .MechPri 0.423 0.042 10.128 0.000 0.423 0.425
## .GenMec 0.047 0.092 0.506 0.613 0.047 0.047
## .TooFun 0.457 0.056 8.196 0.000 0.457 0.458
## .InsCom 0.501 0.049 10.160 0.000 0.501 0.503
## .SpId 0.501 0.050 10.008 0.000 0.501 0.503
## .VisPur 0.757 0.071 10.716 0.000 0.757 0.760
## .PurPegA 0.674 0.065 10.317 0.000 0.674 0.676
## .SADEx 0.624 0.066 9.499 0.000 0.624 0.626
## .ROMov 0.838 0.078 10.793 0.000 0.838 0.841
## .RotAi 0.615 0.088 7.017 0.000 0.615 0.618
## .CoCo 0.581 0.057 10.107 0.000 0.581 0.583
## .RoPu 0.723 0.073 9.857 0.000 0.723 0.726
## .PatCom 0.429 0.048 8.994 0.000 0.429 0.430
## .T3DRT 0.606 0.059 10.298 0.000 0.606 0.608
## REA 1.000 1.000 1.000
## SPA 1.000 1.000 1.000
## ROT 1.000 1.000 1.000
## g 1.000 1.000 1.000#T5
RegBFModel <- '
REA =~ VisRea + AudRea + JuViRea + JuAuRea
SPA =~ Wknow + Caff + MechPri + GenMec + TooFun + InsCom
ROT =~ SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
g =~ VisRea + AudRea + JuViRea + JuAuRea + Wknow + Caff + MechPri + GenMec + TooFun + PatCom + InsCom + SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
T5DRT ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH55.cor, sample.nobs = nFH55, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 33 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 58
##
## Number of observations 264
##
## Model Test User Model:
##
## Test statistic 384.566
## Degrees of freedom 152
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 2280.231
## Degrees of freedom 190
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.889
## Tucker-Lewis Index (TLI) 0.861
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -6534.144
## Loglikelihood unrestricted model (H1) -6341.861
##
## Akaike (AIC) 13184.289
## Bayesian (BIC) 13391.694
## Sample-size adjusted Bayesian (BIC) 13207.804
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.076
## 90 Percent confidence interval - lower 0.067
## 90 Percent confidence interval - upper 0.086
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.077
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA =~
## VisRea 0.711 0.057 12.454 0.000 0.711 0.713
## AudRea 0.600 0.060 10.036 0.000 0.600 0.601
## JuViRea 0.836 0.052 15.970 0.000 0.836 0.838
## JuAuRea 0.777 0.054 14.373 0.000 0.777 0.779
## SPA =~
## Wknow 0.252 0.057 4.452 0.000 0.252 0.253
## Caff 0.177 0.055 3.225 0.001 0.177 0.177
## MechPri 0.334 0.056 5.956 0.000 0.334 0.334
## GenMec 0.837 0.068 12.224 0.000 0.837 0.839
## TooFun 0.582 0.068 8.556 0.000 0.582 0.583
## InsCom 0.163 0.054 2.987 0.003 0.163 0.163
## ROT =~
## SpId 0.208 0.063 3.298 0.001 0.208 0.208
## VisPur 0.295 0.074 4.003 0.000 0.295 0.295
## PurPegA 0.337 0.071 4.739 0.000 0.337 0.337
## SADEx 0.447 0.072 6.217 0.000 0.447 0.448
## ROMov 0.303 0.077 3.930 0.000 0.303 0.303
## RotAi 0.582 0.080 7.237 0.000 0.582 0.583
## CoCo 0.331 0.068 4.910 0.000 0.331 0.332
## RoPu 0.427 0.075 5.682 0.000 0.427 0.427
## g =~
## VisRea 0.024 0.066 0.367 0.714 0.024 0.024
## AudRea 0.023 0.066 0.340 0.734 0.023 0.023
## JuViRea 0.245 0.065 3.770 0.000 0.245 0.246
## JuAuRea 0.217 0.065 3.331 0.001 0.217 0.218
## Wknow 0.643 0.059 10.920 0.000 0.643 0.645
## Caff 0.683 0.058 11.824 0.000 0.683 0.684
## MechPri 0.677 0.058 11.623 0.000 0.677 0.679
## GenMec 0.481 0.065 7.430 0.000 0.481 0.482
## TooFun 0.455 0.065 7.012 0.000 0.455 0.456
## PatCom 0.758 0.055 13.692 0.000 0.758 0.760
## InsCom 0.692 0.057 12.056 0.000 0.692 0.694
## SpId 0.672 0.058 11.599 0.000 0.672 0.673
## VisPur 0.390 0.064 6.113 0.000 0.390 0.391
## PurPegA 0.460 0.063 7.339 0.000 0.460 0.461
## SADEx 0.417 0.064 6.558 0.000 0.417 0.418
## ROMov 0.254 0.065 3.875 0.000 0.254 0.254
## RotAi 0.142 0.067 2.118 0.034 0.142 0.142
## CoCo 0.550 0.061 9.034 0.000 0.550 0.551
## RoPu 0.311 0.065 4.774 0.000 0.311 0.311
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## T5DRT ~
## g 0.626 0.059 10.644 0.000 0.626 0.628
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA ~~
## SPA 0.000 0.000 0.000
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## SPA ~~
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## ROT ~~
## g 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .VisRea 0.490 0.052 9.394 0.000 0.490 0.491
## .AudRea 0.636 0.061 10.381 0.000 0.636 0.638
## .JuViRea 0.237 0.042 5.633 0.000 0.237 0.238
## .JuAuRea 0.345 0.044 7.782 0.000 0.345 0.346
## .Wknow 0.519 0.049 10.512 0.000 0.519 0.521
## .Caff 0.499 0.049 10.183 0.000 0.499 0.501
## .MechPri 0.426 0.042 10.146 0.000 0.426 0.428
## .GenMec 0.064 0.089 0.721 0.471 0.064 0.064
## .TooFun 0.451 0.056 7.993 0.000 0.451 0.452
## .InsCom 0.490 0.049 10.078 0.000 0.490 0.492
## .SpId 0.502 0.050 10.020 0.000 0.502 0.503
## .VisPur 0.757 0.071 10.706 0.000 0.757 0.760
## .PurPegA 0.671 0.065 10.323 0.000 0.671 0.674
## .SADEx 0.622 0.067 9.347 0.000 0.622 0.625
## .ROMov 0.840 0.078 10.774 0.000 0.840 0.843
## .RotAi 0.638 0.086 7.442 0.000 0.638 0.640
## .CoCo 0.583 0.058 10.064 0.000 0.583 0.586
## .RoPu 0.718 0.073 9.780 0.000 0.718 0.720
## .PatCom 0.421 0.047 8.925 0.000 0.421 0.423
## .T5DRT 0.604 0.059 10.293 0.000 0.604 0.606
## REA 1.000 1.000 1.000
## SPA 1.000 1.000 1.000
## ROT 1.000 1.000 1.000
## g 1.000 1.000 1.000#T7
RegBFModel <- '
REA =~ VisRea + AudRea + JuViRea + JuAuRea
SPA =~ Wknow + Caff + MechPri + GenMec + TooFun + InsCom
ROT =~ SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
g =~ VisRea + AudRea + JuViRea + JuAuRea + Wknow + Caff + MechPri + GenMec + TooFun + PatCom + InsCom + SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
T7DRT ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH55.cor, sample.nobs = nFH55, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 33 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 58
##
## Number of observations 264
##
## Model Test User Model:
##
## Test statistic 401.716
## Degrees of freedom 152
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 2278.863
## Degrees of freedom 190
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.880
## Tucker-Lewis Index (TLI) 0.851
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -6543.403
## Loglikelihood unrestricted model (H1) -6342.545
##
## Akaike (AIC) 13202.806
## Bayesian (BIC) 13410.211
## Sample-size adjusted Bayesian (BIC) 13226.321
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.079
## 90 Percent confidence interval - lower 0.070
## 90 Percent confidence interval - upper 0.088
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.080
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA =~
## VisRea 0.712 0.057 12.462 0.000 0.712 0.713
## AudRea 0.602 0.060 10.070 0.000 0.602 0.603
## JuViRea 0.832 0.052 15.925 0.000 0.832 0.834
## JuAuRea 0.774 0.054 14.328 0.000 0.774 0.776
## SPA =~
## Wknow 0.256 0.057 4.526 0.000 0.256 0.257
## Caff 0.179 0.054 3.295 0.001 0.179 0.179
## MechPri 0.321 0.056 5.713 0.000 0.321 0.322
## GenMec 0.863 0.071 12.184 0.000 0.863 0.864
## TooFun 0.572 0.069 8.247 0.000 0.572 0.573
## InsCom 0.164 0.054 3.044 0.002 0.164 0.164
## ROT =~
## SpId 0.214 0.063 3.388 0.001 0.214 0.215
## VisPur 0.296 0.074 4.017 0.000 0.296 0.297
## PurPegA 0.340 0.071 4.788 0.000 0.340 0.341
## SADEx 0.454 0.072 6.290 0.000 0.454 0.454
## ROMov 0.289 0.077 3.765 0.000 0.289 0.289
## RotAi 0.584 0.080 7.262 0.000 0.584 0.585
## CoCo 0.332 0.068 4.915 0.000 0.332 0.332
## RoPu 0.426 0.075 5.671 0.000 0.426 0.426
## g =~
## VisRea 0.030 0.066 0.459 0.646 0.030 0.030
## AudRea 0.022 0.066 0.331 0.741 0.022 0.022
## JuViRea 0.257 0.065 3.948 0.000 0.257 0.257
## JuAuRea 0.228 0.065 3.484 0.000 0.228 0.228
## Wknow 0.644 0.059 10.904 0.000 0.644 0.646
## Caff 0.685 0.058 11.860 0.000 0.685 0.687
## MechPri 0.688 0.058 11.818 0.000 0.688 0.689
## GenMec 0.471 0.065 7.194 0.000 0.471 0.472
## TooFun 0.452 0.065 6.909 0.000 0.452 0.453
## PatCom 0.744 0.056 13.296 0.000 0.744 0.745
## InsCom 0.694 0.058 12.060 0.000 0.694 0.695
## SpId 0.667 0.058 11.455 0.000 0.667 0.668
## VisPur 0.389 0.064 6.077 0.000 0.389 0.390
## PurPegA 0.459 0.063 7.298 0.000 0.459 0.460
## SADEx 0.411 0.064 6.427 0.000 0.411 0.411
## ROMov 0.268 0.065 4.086 0.000 0.268 0.268
## RotAi 0.137 0.067 2.047 0.041 0.137 0.137
## CoCo 0.551 0.061 9.028 0.000 0.551 0.552
## RoPu 0.311 0.065 4.768 0.000 0.311 0.311
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## T7DRT ~
## g 0.580 0.060 9.659 0.000 0.580 0.581
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA ~~
## SPA 0.000 0.000 0.000
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## SPA ~~
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## ROT ~~
## g 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .VisRea 0.488 0.052 9.373 0.000 0.488 0.490
## .AudRea 0.633 0.061 10.358 0.000 0.633 0.636
## .JuViRea 0.237 0.042 5.657 0.000 0.237 0.238
## .JuAuRea 0.345 0.044 7.803 0.000 0.345 0.347
## .Wknow 0.515 0.049 10.482 0.000 0.515 0.517
## .Caff 0.494 0.049 10.114 0.000 0.494 0.496
## .MechPri 0.420 0.042 10.077 0.000 0.420 0.422
## .GenMec 0.030 0.099 0.302 0.762 0.030 0.030
## .TooFun 0.464 0.057 8.159 0.000 0.464 0.466
## .InsCom 0.488 0.049 10.017 0.000 0.488 0.490
## .SpId 0.506 0.050 10.014 0.000 0.506 0.507
## .VisPur 0.757 0.071 10.707 0.000 0.757 0.760
## .PurPegA 0.670 0.065 10.307 0.000 0.670 0.672
## .SADEx 0.622 0.067 9.298 0.000 0.622 0.624
## .ROMov 0.841 0.078 10.846 0.000 0.841 0.844
## .RotAi 0.636 0.086 7.402 0.000 0.636 0.638
## .CoCo 0.582 0.058 10.060 0.000 0.582 0.585
## .RoPu 0.718 0.073 9.806 0.000 0.718 0.721
## .PatCom 0.443 0.049 9.080 0.000 0.443 0.445
## .T7DRT 0.660 0.063 10.530 0.000 0.660 0.662
## REA 1.000 1.000 1.000
## SPA 1.000 1.000 1.000
## ROT 1.000 1.000 1.000
## g 1.000 1.000 1.000#T9
RegBFModel <- '
REA =~ VisRea + AudRea + JuViRea + JuAuRea
SPA =~ Wknow + Caff + MechPri + GenMec + TooFun + InsCom
ROT =~ SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
g =~ VisRea + AudRea + JuViRea + JuAuRea + Wknow + Caff + MechPri + GenMec + TooFun + PatCom + InsCom + SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
T9DRT ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH55.cor, sample.nobs = nFH55, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 33 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 58
##
## Number of observations 264
##
## Model Test User Model:
##
## Test statistic 402.447
## Degrees of freedom 152
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 2270.231
## Degrees of freedom 190
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.880
## Tucker-Lewis Index (TLI) 0.850
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -6548.084
## Loglikelihood unrestricted model (H1) -6346.861
##
## Akaike (AIC) 13212.169
## Bayesian (BIC) 13419.574
## Sample-size adjusted Bayesian (BIC) 13235.685
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.079
## 90 Percent confidence interval - lower 0.070
## 90 Percent confidence interval - upper 0.088
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.081
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA =~
## VisRea 0.713 0.057 12.473 0.000 0.713 0.714
## AudRea 0.602 0.060 10.070 0.000 0.602 0.603
## JuViRea 0.832 0.052 15.933 0.000 0.832 0.834
## JuAuRea 0.774 0.054 14.327 0.000 0.774 0.776
## SPA =~
## Wknow 0.254 0.057 4.440 0.000 0.254 0.254
## Caff 0.174 0.055 3.171 0.002 0.174 0.174
## MechPri 0.318 0.057 5.627 0.000 0.318 0.319
## GenMec 0.854 0.071 11.939 0.000 0.854 0.855
## TooFun 0.569 0.070 8.148 0.000 0.569 0.571
## InsCom 0.159 0.054 2.934 0.003 0.159 0.160
## ROT =~
## SpId 0.213 0.064 3.347 0.001 0.213 0.213
## VisPur 0.296 0.074 4.002 0.000 0.296 0.296
## PurPegA 0.335 0.071 4.712 0.000 0.335 0.336
## SADEx 0.459 0.073 6.333 0.000 0.459 0.460
## ROMov 0.284 0.077 3.690 0.000 0.284 0.285
## RotAi 0.571 0.080 7.101 0.000 0.571 0.572
## CoCo 0.337 0.068 4.969 0.000 0.337 0.338
## RoPu 0.431 0.075 5.724 0.000 0.431 0.432
## g =~
## VisRea 0.029 0.066 0.434 0.665 0.029 0.029
## AudRea 0.021 0.066 0.322 0.748 0.021 0.021
## JuViRea 0.258 0.065 3.969 0.000 0.258 0.259
## JuAuRea 0.226 0.065 3.461 0.001 0.226 0.227
## Wknow 0.641 0.059 10.816 0.000 0.641 0.642
## Caff 0.686 0.058 11.863 0.000 0.686 0.687
## MechPri 0.688 0.058 11.825 0.000 0.688 0.690
## GenMec 0.480 0.065 7.339 0.000 0.480 0.481
## TooFun 0.460 0.065 7.029 0.000 0.460 0.461
## PatCom 0.752 0.056 13.490 0.000 0.752 0.754
## InsCom 0.693 0.058 12.033 0.000 0.693 0.694
## SpId 0.666 0.058 11.438 0.000 0.666 0.668
## VisPur 0.389 0.064 6.084 0.000 0.389 0.390
## PurPegA 0.464 0.063 7.392 0.000 0.464 0.465
## SADEx 0.406 0.064 6.350 0.000 0.406 0.407
## ROMov 0.270 0.065 4.126 0.000 0.270 0.271
## RotAi 0.145 0.067 2.165 0.030 0.145 0.145
## CoCo 0.546 0.061 8.932 0.000 0.546 0.548
## RoPu 0.309 0.065 4.738 0.000 0.309 0.310
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## T9DRT ~
## g 0.552 0.061 9.092 0.000 0.552 0.553
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA ~~
## SPA 0.000 0.000 0.000
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## SPA ~~
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## ROT ~~
## g 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .VisRea 0.488 0.052 9.367 0.000 0.488 0.490
## .AudRea 0.633 0.061 10.359 0.000 0.633 0.636
## .JuViRea 0.237 0.042 5.648 0.000 0.237 0.237
## .JuAuRea 0.346 0.044 7.812 0.000 0.346 0.347
## .Wknow 0.521 0.050 10.505 0.000 0.521 0.523
## .Caff 0.496 0.049 10.101 0.000 0.496 0.498
## .MechPri 0.421 0.042 10.072 0.000 0.421 0.423
## .GenMec 0.038 0.099 0.380 0.704 0.038 0.038
## .TooFun 0.461 0.057 8.070 0.000 0.461 0.462
## .InsCom 0.491 0.049 10.014 0.000 0.491 0.492
## .SpId 0.507 0.051 10.018 0.000 0.507 0.509
## .VisPur 0.757 0.071 10.700 0.000 0.757 0.760
## .PurPegA 0.668 0.065 10.319 0.000 0.668 0.671
## .SADEx 0.620 0.067 9.210 0.000 0.620 0.623
## .ROMov 0.842 0.078 10.861 0.000 0.842 0.846
## .RotAi 0.649 0.085 7.634 0.000 0.649 0.652
## .CoCo 0.584 0.058 10.029 0.000 0.584 0.586
## .RoPu 0.715 0.073 9.725 0.000 0.715 0.717
## .PatCom 0.431 0.048 8.932 0.000 0.431 0.432
## .T9DRT 0.692 0.065 10.658 0.000 0.692 0.695
## REA 1.000 1.000 1.000
## SPA 1.000 1.000 1.000
## ROT 1.000 1.000 1.000
## g 1.000 1.000 1.000#T11
RegBFModel <- '
REA =~ VisRea + AudRea + JuViRea + JuAuRea
SPA =~ Wknow + Caff + MechPri + GenMec + TooFun + InsCom
ROT =~ SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
g =~ VisRea + AudRea + JuViRea + JuAuRea + Wknow + Caff + MechPri + GenMec + TooFun + PatCom + InsCom + SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
T11DRT ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH55.cor, sample.nobs = nFH55, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 33 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 58
##
## Number of observations 264
##
## Model Test User Model:
##
## Test statistic 383.050
## Degrees of freedom 152
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 2240.754
## Degrees of freedom 190
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.887
## Tucker-Lewis Index (TLI) 0.859
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -6553.124
## Loglikelihood unrestricted model (H1) -6361.600
##
## Akaike (AIC) 13222.249
## Bayesian (BIC) 13429.654
## Sample-size adjusted Bayesian (BIC) 13245.765
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.076
## 90 Percent confidence interval - lower 0.066
## 90 Percent confidence interval - upper 0.085
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.080
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA =~
## VisRea 0.714 0.057 12.504 0.000 0.714 0.715
## AudRea 0.601 0.060 10.058 0.000 0.601 0.602
## JuViRea 0.835 0.052 15.970 0.000 0.835 0.837
## JuAuRea 0.776 0.054 14.363 0.000 0.776 0.778
## SPA =~
## Wknow 0.248 0.057 4.332 0.000 0.248 0.248
## Caff 0.169 0.055 3.087 0.002 0.169 0.170
## MechPri 0.315 0.057 5.537 0.000 0.315 0.316
## GenMec 0.852 0.073 11.748 0.000 0.852 0.854
## TooFun 0.570 0.071 8.043 0.000 0.570 0.571
## InsCom 0.159 0.055 2.898 0.004 0.159 0.159
## ROT =~
## SpId 0.216 0.063 3.439 0.001 0.216 0.217
## VisPur 0.304 0.074 4.138 0.000 0.304 0.305
## PurPegA 0.343 0.071 4.844 0.000 0.343 0.344
## SADEx 0.468 0.072 6.490 0.000 0.468 0.469
## ROMov 0.291 0.077 3.789 0.000 0.291 0.291
## RotAi 0.562 0.079 7.097 0.000 0.562 0.563
## CoCo 0.351 0.068 5.185 0.000 0.351 0.352
## RoPu 0.445 0.075 5.938 0.000 0.445 0.446
## g =~
## VisRea 0.017 0.066 0.263 0.792 0.017 0.018
## AudRea 0.019 0.066 0.290 0.772 0.019 0.019
## JuViRea 0.248 0.065 3.797 0.000 0.248 0.248
## JuAuRea 0.220 0.065 3.364 0.001 0.220 0.221
## Wknow 0.648 0.059 10.958 0.000 0.648 0.649
## Caff 0.690 0.058 11.937 0.000 0.690 0.691
## MechPri 0.691 0.058 11.860 0.000 0.691 0.692
## GenMec 0.482 0.066 7.357 0.000 0.482 0.483
## TooFun 0.459 0.066 6.983 0.000 0.459 0.459
## PatCom 0.753 0.056 13.491 0.000 0.753 0.754
## InsCom 0.691 0.058 11.985 0.000 0.691 0.693
## SpId 0.672 0.058 11.546 0.000 0.672 0.673
## VisPur 0.383 0.064 5.975 0.000 0.383 0.384
## PurPegA 0.458 0.063 7.272 0.000 0.458 0.459
## SADEx 0.398 0.064 6.203 0.000 0.398 0.399
## ROMov 0.259 0.066 3.949 0.000 0.259 0.260
## RotAi 0.142 0.067 2.125 0.034 0.142 0.143
## CoCo 0.537 0.061 8.749 0.000 0.537 0.538
## RoPu 0.297 0.065 4.532 0.000 0.297 0.297
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## T11DRT ~
## g 0.517 0.061 8.424 0.000 0.517 0.518
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA ~~
## SPA 0.000 0.000 0.000
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## SPA ~~
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## ROT ~~
## g 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .VisRea 0.487 0.052 9.361 0.000 0.487 0.488
## .AudRea 0.634 0.061 10.373 0.000 0.634 0.637
## .JuViRea 0.237 0.042 5.643 0.000 0.237 0.238
## .JuAuRea 0.345 0.044 7.803 0.000 0.345 0.347
## .Wknow 0.515 0.049 10.451 0.000 0.515 0.517
## .Caff 0.492 0.049 10.049 0.000 0.492 0.494
## .MechPri 0.420 0.042 10.047 0.000 0.420 0.422
## .GenMec 0.037 0.101 0.368 0.713 0.037 0.037
## .TooFun 0.461 0.058 7.974 0.000 0.461 0.463
## .InsCom 0.493 0.049 10.013 0.000 0.493 0.495
## .SpId 0.498 0.050 9.959 0.000 0.498 0.500
## .VisPur 0.757 0.071 10.681 0.000 0.757 0.760
## .PurPegA 0.669 0.065 10.305 0.000 0.669 0.671
## .SADEx 0.619 0.067 9.187 0.000 0.619 0.621
## .ROMov 0.845 0.078 10.851 0.000 0.845 0.848
## .RotAi 0.661 0.083 7.925 0.000 0.661 0.663
## .CoCo 0.584 0.059 9.984 0.000 0.584 0.587
## .RoPu 0.710 0.074 9.639 0.000 0.710 0.713
## .PatCom 0.430 0.048 8.890 0.000 0.430 0.431
## .T11DRT 0.729 0.068 10.790 0.000 0.729 0.731
## REA 1.000 1.000 1.000
## SPA 1.000 1.000 1.000
## ROT 1.000 1.000 1.000
## g 1.000 1.000 1.000#T13
RegBFModel <- '
REA =~ VisRea + AudRea + JuViRea + JuAuRea
SPA =~ Wknow + Caff + MechPri + GenMec + TooFun + InsCom
ROT =~ SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
g =~ VisRea + AudRea + JuViRea + JuAuRea + Wknow + Caff + MechPri + GenMec + TooFun + PatCom + InsCom + SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
T13DRT ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH55.cor, sample.nobs = nFH55, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 33 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 58
##
## Number of observations 264
##
## Model Test User Model:
##
## Test statistic 396.962
## Degrees of freedom 152
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 2273.928
## Degrees of freedom 190
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.882
## Tucker-Lewis Index (TLI) 0.853
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -6543.493
## Loglikelihood unrestricted model (H1) -6345.012
##
## Akaike (AIC) 13202.986
## Bayesian (BIC) 13410.391
## Sample-size adjusted Bayesian (BIC) 13226.502
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.078
## 90 Percent confidence interval - lower 0.069
## 90 Percent confidence interval - upper 0.088
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.079
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA =~
## VisRea 0.713 0.057 12.492 0.000 0.713 0.715
## AudRea 0.602 0.060 10.062 0.000 0.602 0.603
## JuViRea 0.833 0.052 15.939 0.000 0.833 0.835
## JuAuRea 0.774 0.054 14.331 0.000 0.774 0.776
## SPA =~
## Wknow 0.261 0.057 4.587 0.000 0.261 0.262
## Caff 0.182 0.055 3.320 0.001 0.182 0.183
## MechPri 0.332 0.056 5.940 0.000 0.332 0.332
## GenMec 0.846 0.068 12.394 0.000 0.846 0.847
## TooFun 0.584 0.068 8.587 0.000 0.584 0.585
## InsCom 0.176 0.055 3.195 0.001 0.176 0.176
## ROT =~
## SpId 0.203 0.063 3.225 0.001 0.203 0.204
## VisPur 0.303 0.074 4.096 0.000 0.303 0.304
## PurPegA 0.330 0.071 4.643 0.000 0.330 0.330
## SADEx 0.445 0.072 6.173 0.000 0.445 0.446
## ROMov 0.297 0.077 3.857 0.000 0.297 0.298
## RotAi 0.581 0.081 7.206 0.000 0.581 0.582
## CoCo 0.335 0.068 4.939 0.000 0.335 0.335
## RoPu 0.434 0.075 5.762 0.000 0.434 0.435
## g =~
## VisRea 0.025 0.066 0.376 0.707 0.025 0.025
## AudRea 0.023 0.066 0.342 0.733 0.023 0.023
## JuViRea 0.256 0.065 3.935 0.000 0.256 0.257
## JuAuRea 0.226 0.065 3.464 0.001 0.226 0.227
## Wknow 0.637 0.059 10.739 0.000 0.637 0.638
## Caff 0.683 0.058 11.799 0.000 0.683 0.684
## MechPri 0.686 0.058 11.781 0.000 0.686 0.687
## GenMec 0.472 0.065 7.236 0.000 0.472 0.473
## TooFun 0.449 0.065 6.876 0.000 0.449 0.450
## PatCom 0.753 0.056 13.525 0.000 0.753 0.755
## InsCom 0.680 0.058 11.734 0.000 0.680 0.681
## SpId 0.677 0.058 11.675 0.000 0.677 0.678
## VisPur 0.382 0.064 5.964 0.000 0.382 0.383
## PurPegA 0.467 0.063 7.444 0.000 0.467 0.468
## SADEx 0.419 0.064 6.566 0.000 0.419 0.420
## ROMov 0.259 0.066 3.952 0.000 0.259 0.260
## RotAi 0.141 0.067 2.100 0.036 0.141 0.141
## CoCo 0.548 0.061 8.970 0.000 0.548 0.550
## RoPu 0.305 0.065 4.664 0.000 0.305 0.305
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## T13DRT ~
## g 0.580 0.060 9.653 0.000 0.580 0.581
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA ~~
## SPA 0.000 0.000 0.000
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## SPA ~~
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## ROT ~~
## g 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .VisRea 0.487 0.052 9.357 0.000 0.487 0.489
## .AudRea 0.634 0.061 10.365 0.000 0.634 0.636
## .JuViRea 0.237 0.042 5.652 0.000 0.237 0.238
## .JuAuRea 0.346 0.044 7.813 0.000 0.346 0.347
## .Wknow 0.522 0.050 10.521 0.000 0.522 0.524
## .Caff 0.497 0.049 10.137 0.000 0.497 0.498
## .MechPri 0.416 0.041 10.057 0.000 0.416 0.417
## .GenMec 0.058 0.090 0.653 0.514 0.058 0.059
## .TooFun 0.453 0.056 8.067 0.000 0.453 0.455
## .InsCom 0.503 0.050 10.153 0.000 0.503 0.505
## .SpId 0.497 0.050 9.959 0.000 0.497 0.499
## .VisPur 0.758 0.071 10.672 0.000 0.758 0.761
## .PurPegA 0.669 0.065 10.351 0.000 0.669 0.672
## .SADEx 0.623 0.066 9.376 0.000 0.623 0.625
## .ROMov 0.841 0.078 10.801 0.000 0.841 0.844
## .RotAi 0.639 0.086 7.446 0.000 0.639 0.642
## .CoCo 0.583 0.058 10.041 0.000 0.583 0.586
## .RoPu 0.715 0.074 9.701 0.000 0.715 0.717
## .PatCom 0.429 0.048 8.922 0.000 0.429 0.430
## .T13DRT 0.660 0.063 10.526 0.000 0.660 0.663
## REA 1.000 1.000 1.000
## SPA 1.000 1.000 1.000
## ROT 1.000 1.000 1.000
## g 1.000 1.000 1.000#T15
RegBFModel <- '
REA =~ VisRea + AudRea + JuViRea + JuAuRea
SPA =~ Wknow + Caff + MechPri + GenMec + TooFun + InsCom
ROT =~ SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
g =~ VisRea + AudRea + JuViRea + JuAuRea + Wknow + Caff + MechPri + GenMec + TooFun + PatCom + InsCom + SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
T15DRT ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH55.cor, sample.nobs = nFH55, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 33 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 58
##
## Number of observations 264
##
## Model Test User Model:
##
## Test statistic 401.208
## Degrees of freedom 152
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 2262.678
## Degrees of freedom 190
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.880
## Tucker-Lewis Index (TLI) 0.850
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -6551.241
## Loglikelihood unrestricted model (H1) -6350.637
##
## Akaike (AIC) 13218.483
## Bayesian (BIC) 13425.888
## Sample-size adjusted Bayesian (BIC) 13241.998
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.079
## 90 Percent confidence interval - lower 0.069
## 90 Percent confidence interval - upper 0.088
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.082
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA =~
## VisRea 0.714 0.057 12.503 0.000 0.714 0.715
## AudRea 0.601 0.060 10.047 0.000 0.601 0.602
## JuViRea 0.832 0.052 15.920 0.000 0.832 0.833
## JuAuRea 0.773 0.054 14.306 0.000 0.773 0.774
## SPA =~
## Wknow 0.253 0.058 4.380 0.000 0.253 0.253
## Caff 0.176 0.056 3.162 0.002 0.176 0.176
## MechPri 0.316 0.057 5.588 0.000 0.316 0.317
## GenMec 0.842 0.071 11.795 0.000 0.842 0.844
## TooFun 0.575 0.070 8.178 0.000 0.575 0.576
## InsCom 0.155 0.055 2.821 0.005 0.155 0.155
## ROT =~
## SpId 0.205 0.064 3.233 0.001 0.205 0.206
## VisPur 0.292 0.074 3.950 0.000 0.292 0.293
## PurPegA 0.334 0.071 4.675 0.000 0.334 0.334
## SADEx 0.461 0.073 6.340 0.000 0.461 0.462
## ROMov 0.288 0.077 3.723 0.000 0.288 0.288
## RotAi 0.557 0.080 6.943 0.000 0.557 0.558
## CoCo 0.341 0.068 5.011 0.000 0.341 0.342
## RoPu 0.444 0.076 5.860 0.000 0.444 0.445
## g =~
## VisRea 0.026 0.066 0.396 0.692 0.026 0.026
## AudRea 0.028 0.066 0.425 0.670 0.028 0.028
## JuViRea 0.261 0.065 4.011 0.000 0.261 0.262
## JuAuRea 0.231 0.065 3.526 0.000 0.231 0.231
## Wknow 0.638 0.059 10.756 0.000 0.638 0.640
## Caff 0.678 0.058 11.671 0.000 0.678 0.679
## MechPri 0.695 0.058 11.969 0.000 0.695 0.696
## GenMec 0.485 0.065 7.421 0.000 0.485 0.486
## TooFun 0.458 0.066 6.994 0.000 0.458 0.459
## PatCom 0.749 0.056 13.399 0.000 0.749 0.750
## InsCom 0.698 0.058 12.129 0.000 0.698 0.699
## SpId 0.673 0.058 11.582 0.000 0.673 0.675
## VisPur 0.394 0.064 6.165 0.000 0.394 0.395
## PurPegA 0.464 0.063 7.376 0.000 0.464 0.465
## SADEx 0.406 0.064 6.345 0.000 0.406 0.407
## ROMov 0.264 0.066 4.021 0.000 0.264 0.264
## RotAi 0.153 0.067 2.289 0.022 0.153 0.154
## CoCo 0.544 0.061 8.879 0.000 0.544 0.545
## RoPu 0.301 0.065 4.591 0.000 0.301 0.301
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## T15DRT ~
## g 0.533 0.061 8.732 0.000 0.533 0.534
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA ~~
## SPA 0.000 0.000 0.000
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## SPA ~~
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## ROT ~~
## g 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .VisRea 0.486 0.052 9.339 0.000 0.486 0.487
## .AudRea 0.634 0.061 10.367 0.000 0.634 0.637
## .JuViRea 0.237 0.042 5.656 0.000 0.237 0.237
## .JuAuRea 0.346 0.044 7.825 0.000 0.346 0.347
## .Wknow 0.525 0.050 10.512 0.000 0.525 0.527
## .Caff 0.506 0.050 10.165 0.000 0.506 0.508
## .MechPri 0.413 0.041 10.005 0.000 0.413 0.415
## .GenMec 0.052 0.096 0.537 0.591 0.052 0.052
## .TooFun 0.456 0.058 7.907 0.000 0.456 0.457
## .InsCom 0.486 0.049 9.954 0.000 0.486 0.487
## .SpId 0.501 0.050 9.975 0.000 0.501 0.503
## .VisPur 0.755 0.071 10.706 0.000 0.755 0.758
## .PurPegA 0.670 0.065 10.323 0.000 0.670 0.672
## .SADEx 0.619 0.067 9.172 0.000 0.619 0.621
## .ROMov 0.844 0.078 10.839 0.000 0.844 0.847
## .RotAi 0.663 0.084 7.882 0.000 0.663 0.665
## .CoCo 0.583 0.058 9.997 0.000 0.583 0.586
## .RoPu 0.709 0.074 9.573 0.000 0.709 0.711
## .PatCom 0.435 0.049 8.960 0.000 0.435 0.437
## .T15DRT 0.712 0.066 10.727 0.000 0.712 0.714
## REA 1.000 1.000 1.000
## SPA 1.000 1.000 1.000
## ROT 1.000 1.000 1.000
## g 1.000 1.000 1.000Cumulative Model
RegBFModel <- '
REA =~ VisRea + AudRea + JuViRea + JuAuRea
SPA =~ Wknow + Caff + MechPri + GenMec + TooFun + InsCom
ROT =~ SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
g =~ VisRea + AudRea + JuViRea + JuAuRea + Wknow + Caff + MechPri + GenMec + TooFun + PatCom + InsCom + SpId + VisPur + PurPegA + SADEx + ROMov + RotAi + CoCo + RoPu
T1DRT + T3DRT + T5DRT + T7DRT + T9DRT + T11DRT + T13DRT + T15DRT ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH55.cor, sample.nobs = nFH55, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 96 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 100
##
## Number of observations 264
##
## Model Test User Model:
##
## Test statistic 585.154
## Degrees of freedom 278
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 4601.392
## Degrees of freedom 351
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.928
## Tucker-Lewis Index (TLI) 0.909
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -8092.549
## Loglikelihood unrestricted model (H1) -7799.972
##
## Akaike (AIC) 16385.098
## Bayesian (BIC) 16742.693
## Sample-size adjusted Bayesian (BIC) 16425.642
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.065
## 90 Percent confidence interval - lower 0.057
## 90 Percent confidence interval - upper 0.072
## P-value RMSEA <= 0.05 0.001
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.080
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA =~
## VisRea 0.711 0.057 12.435 0.000 0.711 0.712
## AudRea 0.601 0.060 10.055 0.000 0.601 0.603
## JuViRea 0.831 0.052 15.913 0.000 0.831 0.833
## JuAuRea 0.773 0.054 14.312 0.000 0.773 0.775
## SPA =~
## Wknow 0.267 0.057 4.722 0.000 0.267 0.268
## Caff 0.192 0.055 3.501 0.000 0.192 0.193
## MechPri 0.345 0.055 6.284 0.000 0.345 0.345
## GenMec 0.831 0.065 12.725 0.000 0.831 0.833
## TooFun 0.593 0.066 9.013 0.000 0.593 0.594
## InsCom 0.173 0.054 3.192 0.001 0.173 0.173
## ROT =~
## SpId 0.194 0.063 3.076 0.002 0.194 0.194
## VisPur 0.288 0.074 3.895 0.000 0.288 0.289
## PurPegA 0.325 0.071 4.564 0.000 0.325 0.326
## SADEx 0.419 0.072 5.835 0.000 0.419 0.420
## ROMov 0.305 0.077 3.950 0.000 0.305 0.305
## RotAi 0.614 0.083 7.401 0.000 0.614 0.615
## CoCo 0.302 0.067 4.499 0.000 0.302 0.303
## RoPu 0.403 0.075 5.353 0.000 0.403 0.404
## g =~
## VisRea 0.038 0.066 0.575 0.565 0.038 0.038
## AudRea 0.027 0.066 0.407 0.684 0.027 0.027
## JuViRea 0.263 0.065 4.059 0.000 0.263 0.263
## JuAuRea 0.229 0.065 3.521 0.000 0.229 0.230
## Wknow 0.628 0.059 10.616 0.000 0.628 0.629
## Caff 0.669 0.058 11.548 0.000 0.669 0.670
## MechPri 0.677 0.058 11.657 0.000 0.677 0.678
## GenMec 0.473 0.064 7.359 0.000 0.473 0.474
## TooFun 0.448 0.065 6.947 0.000 0.448 0.449
## PatCom 0.749 0.055 13.499 0.000 0.749 0.751
## InsCom 0.689 0.057 11.994 0.000 0.689 0.690
## SpId 0.677 0.058 11.732 0.000 0.677 0.678
## VisPur 0.392 0.064 6.147 0.000 0.392 0.392
## PurPegA 0.465 0.063 7.445 0.000 0.465 0.466
## SADEx 0.441 0.063 6.988 0.000 0.441 0.442
## ROMov 0.262 0.065 4.014 0.000 0.262 0.263
## RotAi 0.139 0.067 2.086 0.037 0.139 0.140
## CoCo 0.571 0.060 9.459 0.000 0.571 0.572
## RoPu 0.325 0.065 5.024 0.000 0.325 0.326
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## T1DRT ~
## g 0.575 0.060 9.543 0.000 0.575 0.576
## T3DRT ~
## g 0.630 0.059 10.715 0.000 0.630 0.631
## T5DRT ~
## g 0.632 0.059 10.762 0.000 0.632 0.633
## T7DRT ~
## g 0.585 0.060 9.762 0.000 0.585 0.586
## T9DRT ~
## g 0.558 0.061 9.217 0.000 0.558 0.559
## T11DRT ~
## g 0.525 0.061 8.567 0.000 0.525 0.526
## T13DRT ~
## g 0.586 0.060 9.768 0.000 0.586 0.587
## T15DRT ~
## g 0.538 0.061 8.815 0.000 0.538 0.539
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REA ~~
## SPA 0.000 0.000 0.000
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## SPA ~~
## ROT 0.000 0.000 0.000
## g 0.000 0.000 0.000
## ROT ~~
## g 0.000 0.000 0.000
## .T1DRT ~~
## .T3DRT 0.375 0.051 7.382 0.000 0.375 0.594
## .T5DRT 0.344 0.050 6.912 0.000 0.344 0.546
## .T7DRT 0.351 0.051 6.870 0.000 0.351 0.532
## .T9DRT 0.297 0.050 5.918 0.000 0.297 0.440
## .T11DRT 0.286 0.051 5.654 0.000 0.286 0.413
## .T13DRT 0.231 0.048 4.833 0.000 0.231 0.351
## .T15DRT 0.249 0.049 5.035 0.000 0.249 0.363
## .T3DRT ~~
## .T5DRT 0.419 0.051 8.183 0.000 0.419 0.700
## .T7DRT 0.408 0.052 7.892 0.000 0.408 0.652
## .T9DRT 0.385 0.051 7.487 0.000 0.385 0.602
## .T11DRT 0.346 0.051 6.815 0.000 0.346 0.527
## .T13DRT 0.289 0.048 6.016 0.000 0.289 0.461
## .T15DRT 0.299 0.049 6.066 0.000 0.299 0.459
## .T5DRT ~~
## .T7DRT 0.457 0.053 8.551 0.000 0.457 0.732
## .T9DRT 0.434 0.053 8.176 0.000 0.434 0.679
## .T11DRT 0.385 0.052 7.408 0.000 0.385 0.588
## .T13DRT 0.347 0.050 6.990 0.000 0.347 0.556
## .T15DRT 0.367 0.051 7.171 0.000 0.367 0.565
## .T7DRT ~~
## .T9DRT 0.470 0.055 8.486 0.000 0.470 0.703
## .T11DRT 0.430 0.055 7.872 0.000 0.430 0.626
## .T13DRT 0.375 0.052 7.259 0.000 0.375 0.573
## .T15DRT 0.422 0.054 7.804 0.000 0.422 0.621
## .T9DRT ~~
## .T11DRT 0.474 0.057 8.359 0.000 0.474 0.675
## .T13DRT 0.400 0.053 7.554 0.000 0.400 0.599
## .T15DRT 0.467 0.056 8.304 0.000 0.467 0.671
## .T11DRT ~~
## .T13DRT 0.430 0.055 7.871 0.000 0.430 0.626
## .T15DRT 0.514 0.059 8.789 0.000 0.514 0.721
## .T13DRT ~~
## .T15DRT 0.472 0.056 8.453 0.000 0.472 0.695
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .VisRea 0.490 0.052 9.385 0.000 0.490 0.491
## .AudRea 0.634 0.061 10.361 0.000 0.634 0.636
## .JuViRea 0.237 0.042 5.649 0.000 0.237 0.238
## .JuAuRea 0.346 0.044 7.807 0.000 0.346 0.347
## .Wknow 0.531 0.050 10.609 0.000 0.531 0.533
## .Caff 0.511 0.049 10.332 0.000 0.511 0.513
## .MechPri 0.419 0.041 10.138 0.000 0.419 0.421
## .GenMec 0.081 0.081 1.000 0.317 0.081 0.081
## .TooFun 0.444 0.055 8.076 0.000 0.444 0.446
## .InsCom 0.492 0.048 10.162 0.000 0.492 0.494
## .SpId 0.501 0.050 10.040 0.000 0.501 0.503
## .VisPur 0.760 0.071 10.725 0.000 0.760 0.763
## .PurPegA 0.674 0.065 10.366 0.000 0.674 0.676
## .SADEx 0.626 0.065 9.566 0.000 0.626 0.629
## .ROMov 0.835 0.078 10.744 0.000 0.835 0.838
## .RotAi 0.600 0.091 6.623 0.000 0.600 0.602
## .CoCo 0.579 0.057 10.164 0.000 0.579 0.581
## .RoPu 0.728 0.073 9.958 0.000 0.728 0.731
## .PatCom 0.435 0.048 9.146 0.000 0.435 0.437
## .T1DRT 0.666 0.063 10.545 0.000 0.666 0.669
## .T3DRT 0.599 0.058 10.255 0.000 0.599 0.601
## .T5DRT 0.596 0.058 10.243 0.000 0.596 0.599
## .T7DRT 0.654 0.062 10.495 0.000 0.654 0.656
## .T9DRT 0.684 0.064 10.616 0.000 0.684 0.687
## .T11DRT 0.720 0.067 10.747 0.000 0.720 0.723
## .T13DRT 0.653 0.062 10.493 0.000 0.653 0.656
## .T15DRT 0.707 0.066 10.699 0.000 0.707 0.709
## REA 1.000 1.000 1.000
## SPA 1.000 1.000 1.000
## ROT 1.000 1.000 1.000
## g 1.000 1.000 1.000Differential Prediction?
From the separate models.
#T1 vs T3-T15
ZREG(.568, .625, .060, .059)## [1] -0.6773725ZREG(.568, .626, .060, .059)## [1] -0.6892562ZREG(.568, .580, .060, .060)## [1] -0.1414214ZREG(.568, .552, .060, .061)## [1] 0.1869971ZREG(.568, .517, .060, .061)## [1] 0.5960531ZREG(.568, .580, .060, .060)## [1] -0.1414214ZREG(.568, .533, .060, .061)## [1] 0.4090561#T3 vs T5-T15
ZREG(.625, .626, .059, .059)## [1] -0.01198486ZREG(.625, .580, .059, .060)## [1] 0.5347678ZREG(.625, .552, .059, .061)## [1] 0.8601938ZREG(.625, .517, .059, .061)## [1] 1.272615ZREG(.625, .580, .059, .060)## [1] 0.5347678ZREG(.625, .533, .059, .061)## [1] 1.08408#T5 vs T7-T15
ZREG(.626, .580, .059, .060)## [1] 0.5466515ZREG(.626, .552, .059, .061)## [1] 0.8719773ZREG(.626, .517, .059, .061)## [1] 1.284399ZREG(.626, .580, .059, .060)## [1] 0.5466515ZREG(.626, .533, .059, .061)## [1] 1.095863#T7 vs T9-T15
ZREG(.580, .552, .060, .061)## [1] 0.3272449ZREG(.580, .517, .060, .061)## [1] 0.7363009ZREG(.580, .580, .060, .060)## [1] 0ZREG(.580, .533, .060, .061)## [1] 0.5493039#T9 vs T11-T15
ZREG(.552, .517, .061, .061)## [1] 0.405717ZREG(.552, .580, .061, .060)## [1] -0.3272449ZREG(.552, .533, .061, .061)## [1] 0.2202464#T11 vs T13-T15
ZREG(.517, .580, .061, .060)## [1] -0.7363009ZREG(.517, .533, .061, .061)## [1] -0.1854706#T13 vs T15
ZREG(.580, .533, .060, .061)## [1] 0.5493039From the combined model.
#T1 vs T3-T15
ZREG(.575, .630, .060, .059)## [1] -0.653605ZREG(.575, .632, .060, .059)## [1] -0.6773725ZREG(.575, .585, .060, .060)## [1] -0.1178511ZREG(.575, .558, .060, .061)## [1] 0.1986844ZREG(.575, .525, .060, .061)## [1] 0.5843658ZREG(.575, .586, .060, .060)## [1] -0.1296362ZREG(.575, .538, .060, .061)## [1] 0.4324307#T3 vs T5-T15
ZREG(.630, .632, .059, .059)## [1] -0.02396972ZREG(.630, .585, .059, .060)## [1] 0.5347678ZREG(.630, .558, .059, .061)## [1] 0.8484103ZREG(.630, .525, .059, .061)## [1] 1.237265ZREG(.630, .586, .059, .060)## [1] 0.522884ZREG(.630, .538, .059, .061)## [1] 1.08408#T5 vs T7-T15
ZREG(.632, .585, .059, .060)## [1] 0.5585352ZREG(.632, .558, .059, .061)## [1] 0.8719773ZREG(.632, .525, .059, .061)## [1] 1.260832ZREG(.632, .586, .059, .060)## [1] 0.5466515ZREG(.632, .538, .059, .061)## [1] 1.107647#T7 vs T9-T15
ZREG(.585, .558, .060, .061)## [1] 0.3155575ZREG(.585, .525, .060, .061)## [1] 0.701239ZREG(.585, .586, .060, .060)## [1] -0.01178511ZREG(.585, .538, .060, .061)## [1] 0.5493039#T9 vs T11-T15
ZREG(.558, .525, .061, .061)## [1] 0.3825332ZREG(.558, .586, .061, .060)## [1] -0.3272449ZREG(.558, .538, .061, .061)## [1] 0.2318383#T11 vs T13-T15
ZREG(.525, .586, .061, .060)## [1] -0.7129263ZREG(.525, .538, .061, .061)## [1] -0.1506949#T13 vs T15
ZREG(.586, .538, .060, .061)## [1] 0.5609912Separate vs combined.
ZREG(.568, .575, .060, .060) #T1## [1] -0.08249579ZREG(.625, .630, .059, .059) #T3## [1] -0.0599243ZREG(.626, .632, .059, .059) #T5## [1] -0.07190916ZREG(.580, .585, .060, .060) #T7## [1] -0.05892557ZREG(.552, .558, .061, .061) #T9## [1] -0.06955149ZREG(.517, .525, .061, .061) #T11## [1] -0.09273532ZREG(.580, .586, .060, .060) #T13## [1] -0.07071068ZREG(.533, .538, .061, .061) #T15## [1] -0.05795957Extraction of estimates from models separate or together did not make a difference. The average correlation between the three factors used here was r = .469, although in the original manuscript, for the large number of extracted factors, it was .277, which is a crude lower-bound estimate of the outcome correlations. The [1:9] correlations averaged .580. The difference in g correlations between practice sessions was not significant, so this is merely a curiosity and unnecessary for correlated Bonferroni correction.
Discussion and Conclusions
Fleishman & Hempel (1955) extracted a large number of factors from a battery of several tests. They wanted to assess what effect practice had on the intercorrelations of those factors with a discrimination reaction task people were able to do a total of 15 times. This battery apparently had a general factor, or at least substantial general variance, excepting highly specific measures, because they are too easy. They observe that, over trials, the amount of variance specific to the practiced discrimination reaction task increased, suggesting that, as practice continued, a measure should become less g-loaded, perhaps.
Using their correlation matrix, I found that this was not the case. The g computed from the various tests was equally related to the discrimination reaction time task regardless of how many times it was practiced, up to 15 times. It appears that, Fleishman & Hempel extracted many more factors than were indicated with exploratory methods designed to determine the number of factors, and the conclusion of increasing specific variance may not have meant less g variance.
This finding can and should be expanded somewhat. It is presently not very similar to Lievens, Reeve & Heggestad’s (2007), Matton, Vautier & Raufaste’s (2011), te Nijenhuis, Voskuijl & Schijve’s (2001), Zhou & Cao’s (2020), Arendasy et al.’s (2016), Coyle’ (2006), te Nijenhuis, van Vianen & van der Flier’s (2007), Reeve & Lam’s (2005, 2007), or Sommer, Ardensay & Schuetzhoffer’s (2017). But, maybe to Arendasy & Sommer’s (2017), and some of the citations therein.
References
Fleishman, E. A., & Hempel, W. E. (1954). Changes in factor structure of a complex psychomotor test as a function of practice. Psychometrika, 19(3), 239–252. https://doi.org/10.1007/BF02289188
Fleishman, E. A., & Hempel, W. E. (1955). The relation between abilities and improvement with practice in a visual discrimination reaction task. Journal of Experimental Psychology, 49(5), 301–312. https://doi.org/10.1037/h0044697
Lievens, F., Reeve, C. L., & Heggestad, E. D. (2007). An examination of psychometric bias due to retesting on cognitive ability tests in selection settings. Journal of Applied Psychology, 92(6), 1672–1682. https://doi.org/10.1037/0021-9010.92.6.1672
te Nijenhuis, J., Voskuijl, O. F., & Schijve, N. B. (2001). Practice and coaching on IQ tests: Quite a lot of g. International Journal of Selection and Assessment, 9(4), 302–308. https://doi.org/10.1111/1468-2389.00182
Matton, N., Vautier, S., & Raufaste, E. (2011). Test-Specificity of the Advantage of Retaking Cognitive Ability Tests. International Journal of Selection and Assessment, 19(1), 11–17. https://doi.org/10.1111/j.1468-2389.2011.00530.x
Zhou, J., & Cao, Y. (2020). Does Retest Effect Impact Test Performance of Repeaters in Different Subgroups? ETS Research Report Series, 2020(1), 1–15. https://doi.org/10.1002/ets2.12300
Arendasy, M. E., Sommer, M., Gutierrez-Lobos, K., & Punter, J. F. (2016). Do individual differences in test preparation compromise the measurement fairness of admission tests? Intelligence, 55, 44–56. https://doi.org/10.1016/j.intell.2016.01.004
Coyle, T. R. (2006). Test-retest changes on scholastic aptitude tests are not related to g. Intelligence, 34(1), 15–27. https://doi.org/10.1016/j.intell.2005.04.001
te Nijenhuis, J., van Vianen, A. E. M., & van der Flier, H. (2007). Score gains on g-loaded tests: No g. Intelligence, 35(3), 283–300. https://doi.org/10.1016/j.intell.2006.07.006
Reeve, C. L., & Lam, H. (2005). The psychometric paradox of practice effects due to retesting: Measurement invariance and stable ability estimates in the face of observed score changes. Intelligence, 33(5), 535–549. https://doi.org/10.1016/j.intell.2005.05.003
Reeve, C. L., & Lam, H. (2007). The relation between practice effects, test-taker characteristics and degree of g-saturation. International Journal of Testing, 7(2), 225–242. https://doi.org/10.1080/15305050701193595
Sommer, M., Arendasy, M. E., & Schuetzhofer, B. (2017). Psychometric costs of retaking driving-related cognitive ability tests. Transportation Research Part F: Traffic Psychology and Behaviour, 44, 105–119. https://doi.org/10.1016/j.trf.2016.10.014\
Arendasy, M. E., & Sommer, M. (2017). Reducing the effect size of the retest effect: Examining different approaches. Intelligence, 62, 89–98. https://doi.org/10.1016/j.intell.2017.03.003
Woodrow, H. (1939). Factors in improvement with practice. The Journal of Psychology: Interdisciplinary and Applied, 7, 55–70. https://doi.org/10.1080/00223980.1939.9917620
sessionInfo()## R version 4.1.2 (2021-11-01)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 19044)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=English_United States.1252
## [2] LC_CTYPE=English_United States.1252
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C
## [5] LC_TIME=English_United States.1252
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] egg_0.4.5 gridExtra_2.3 ggplot2_3.3.5
## [4] sna_2.6 network_1.17.1 statnet.common_4.6.0
## [7] EGAnet_1.0.0 lavaan_0.6-9 psych_2.1.9
## [10] pacman_0.5.1
##
## loaded via a namespace (and not attached):
## [1] nlme_3.1-153 RColorBrewer_1.1-2 tools_4.1.2
## [4] backports_1.3.0 bslib_0.3.1 utf8_1.2.2
## [7] R6_2.5.1 rpart_4.1-15 Hmisc_4.7-0
## [10] DBI_1.1.2 colorspace_2.0-2 nnet_7.3-16
## [13] withr_2.4.2 GGally_2.1.2 tidyselect_1.1.1
## [16] mnormt_2.0.2 compiler_4.1.2 fdrtool_1.2.17
## [19] qgraph_1.9.2 htmlTable_2.4.0 NetworkToolbox_1.4.2
## [22] labeling_0.4.2 sass_0.4.0 scales_1.1.1
## [25] checkmate_2.0.0 pbapply_1.5-0 stringr_1.4.0
## [28] digest_0.6.28 pbivnorm_0.6.0 foreign_0.8-81
## [31] rmarkdown_2.11 base64enc_0.1-3 jpeg_0.1-9
## [34] pkgconfig_2.0.3 htmltools_0.5.2 highr_0.9
## [37] fastmap_1.1.0 htmlwidgets_1.5.4 rlang_0.4.12
## [40] rstudioapi_0.13 farver_2.1.0 jquerylib_0.1.4
## [43] generics_0.1.1 jsonlite_1.7.2 gtools_3.9.2
## [46] dplyr_1.0.7 magrittr_2.0.1 Formula_1.2-4
## [49] Matrix_1.3-4 Rcpp_1.0.7 munsell_0.5.0
## [52] fansi_0.5.0 abind_1.4-5 lifecycle_1.0.1
## [55] stringi_1.7.5 yaml_2.2.1 MASS_7.3-54
## [58] plyr_1.8.6 grid_4.1.2 parallel_4.1.2
## [61] crayon_1.4.2 lattice_0.20-45 splines_4.1.2
## [64] tmvnsim_1.0-2 knitr_1.36 pillar_1.6.4
## [67] igraph_1.2.7 corpcor_1.6.10 reshape2_1.4.4
## [70] codetools_0.2-18 stats4_4.1.2 GPArotation_2022.4-1
## [73] glue_1.4.2 evaluate_0.14 latticeExtra_0.6-29
## [76] data.table_1.14.2 png_0.1-7 vctrs_0.3.8
## [79] foreach_1.5.1 gtable_0.3.0 purrr_0.3.4
## [82] reshape_0.8.9 assertthat_0.2.1 xfun_0.27
## [85] coda_0.19-4 survival_3.2-13 glasso_1.11
## [88] tibble_3.1.5 iterators_1.0.13 cluster_2.1.2
## [91] ellipsis_0.3.2Postscript: Fleishman & Hempel (1954)
This data was far less usable than Fleishman & Hempel (1955) for two major reasons. Firstly and most importantly, content and resulting psychometric sampling error, and secondly, reliability. The latter issue is less important, as it only affects one set of items: reaction and movement time. These were highly correlated with one another, but movement time is generally not correlated with intelligence, and it acts as an age- and sex-related confounder to reaction time correlations. The both of them fail to correlate strongly with the rest of the other items for unknown reasons in the case of reaction time, and likely reasons in the case of movement time. There are all-positive g loadings, but RT and MT almost necessitate a factor all their own if we have group factors, which precludes baseline model identification. The EFAs and EGAs of just unpracticed tests even produce nonsense results and there are clearly cross-loadings that need to be modeled but obfuscate group factor identities even more if they are. The second issue is much more important. Woodrow (1939) had a much more diverse set of tests and found that practice effects were generally directionally consistent for specific factors, with positive correlations between practice and numerical, perceptual, and spatial ability, and negative correlations between practice and verbal, attention, and speed ability. The correlations with general intelligence were null, as others have both contradicted (te Nijenhuis, Voskuijl & Schijve, 2001) and supported (te Nijenhuis, van Vianen & van der Flier, 2007). In Fleishman & Hempel (1954), their battery was loaded with content of a psychomotor nature and little else, which should mostly be expected to yield negative correlations. The phenomenon where a given group factor “contaminates” a general factor occurs when a certain type of content is overrepresented when a factor is extracted, inflating loadings for items with that content, and making the extracted factor more like a mixture of a factor based on that content and what it should have been were it extracted without psychometric sampling error. A common solution is to use higher-order models, as this reduces psychometric sampling error in the face of sufficiently diverse group factors and insufficiently diverse indicators. With Fleishman & Hempel’s 1954 data, this was not possible, and a bifactor model was also inadmissible because it would still suffer severely from the psychometric sampling error a unified model would.
Nevertheless, the less interpretable results of the same analyses applied to that data are provided below, without significance tests.
Exploratory
fa.parallel(FH54.cor, n.obs = nFH54)
## Parallel analysis suggests that the number of factors = 3 and the number of components = 2FAFH <- fa(FH54.cor, n.obs = nFH54, nfactors = 3)
nfactors(FH54.cor, n.obs = nFH54); KGA(FAFH); MAPA(FAFH); PTV(FAFH); estimate.ED(FH54.cor); EGA(FH54.cor, plot.ega = T, n = nFH54)
##
## Number of factors
## Call: vss(x = x, n = n, rotate = rotate, diagonal = diagonal, fm = fm,
## n.obs = n.obs, plot = FALSE, title = title, use = use, cor = cor)
## VSS complexity 1 achieves a maximimum of 0.87 with 1 factors
## VSS complexity 2 achieves a maximimum of 0.93 with 2 factors
## The Velicer MAP achieves a minimum of 0.01 with 2 factors
## Empirical BIC achieves a minimum of -1167.12 with 2 factors
## Sample Size adjusted BIC achieves a minimum of -118.44 with 7 factors
##
## Statistics by number of factors
## vss1 vss2 map dof chisq prob sqresid fit RMSEA BIC SABIC
## 1 0.87 0.00 0.058 299 1431.03 5.9e-147 18.1 0.87 0.139 -148.6 798.6
## 2 0.66 0.93 0.014 274 504.05 8.2e-16 9.3 0.93 0.065 -943.5 -75.5
## 3 0.64 0.91 0.016 250 425.56 2.8e-11 7.8 0.94 0.059 -895.2 -103.3
## 4 0.57 0.81 0.017 227 369.37 7.0e-09 6.8 0.95 0.056 -829.9 -110.8
## 5 0.52 0.79 0.019 205 315.99 1.0e-06 6.1 0.96 0.052 -767.1 -117.6
## 6 0.57 0.84 0.021 184 272.87 2.3e-05 5.3 0.96 0.049 -699.2 -116.3
## 7 0.52 0.81 0.025 164 228.46 6.6e-04 4.9 0.96 0.044 -638.0 -118.4
## 8 0.52 0.78 0.031 145 192.09 5.4e-03 4.5 0.97 0.040 -574.0 -114.6
## 9 0.52 0.78 0.037 127 162.30 1.9e-02 3.9 0.97 0.037 -508.7 -106.3
## 10 0.51 0.81 0.045 110 145.73 1.3e-02 3.6 0.97 0.040 -435.4 -86.9
## 11 0.49 0.74 0.051 94 124.58 1.9e-02 3.3 0.98 0.040 -372.0 -74.2
## 12 0.47 0.72 0.056 79 96.55 8.7e-02 3.0 0.98 0.033 -320.8 -70.6
## 13 0.50 0.74 0.065 65 54.64 8.2e-01 2.6 0.98 0.000 -288.8 -82.8
## 14 0.47 0.77 0.078 52 44.88 7.5e-01 2.4 0.98 0.000 -229.8 -65.1
## 15 0.43 0.62 0.095 40 30.19 8.7e-01 2.1 0.98 0.000 -181.1 -54.4
## 16 0.42 0.59 0.118 29 21.14 8.5e-01 1.9 0.99 0.000 -132.1 -40.2
## 17 0.42 0.66 0.143 19 10.19 9.5e-01 1.7 0.99 0.000 -90.2 -30.0
## 18 0.44 0.73 0.167 10 5.73 8.4e-01 1.5 0.99 0.000 -47.1 -15.4
## 19 0.40 0.69 0.224 2 1.77 4.1e-01 1.7 0.99 0.000 -8.8 -2.5
## 20 0.37 0.55 0.203 -5 0.52 NA 1.5 0.99 NA NA NA
## complex eChisq SRMR eCRMS eBIC
## 1 1.0 1.5e+03 0.10953 0.1142 -44
## 2 1.3 2.8e+02 0.04680 0.0510 -1167
## 3 1.6 1.8e+02 0.03723 0.0425 -1143
## 4 1.9 1.3e+02 0.03213 0.0384 -1067
## 5 2.0 1.0e+02 0.02789 0.0351 -983
## 6 2.0 6.7e+01 0.02280 0.0303 -906
## 7 2.1 5.0e+01 0.01966 0.0277 -817
## 8 2.2 3.8e+01 0.01718 0.0257 -728
## 9 2.2 2.9e+01 0.01497 0.0239 -642
## 10 2.2 2.0e+01 0.01257 0.0216 -561
## 11 2.4 1.4e+01 0.01057 0.0196 -482
## 12 2.4 1.0e+01 0.00896 0.0182 -407
## 13 2.3 7.1e+00 0.00746 0.0167 -336
## 14 2.1 4.6e+00 0.00597 0.0149 -270
## 15 2.6 2.2e+00 0.00418 0.0119 -209
## 16 2.6 1.3e+00 0.00318 0.0106 -152
## 17 2.5 5.2e-01 0.00201 0.0083 -100
## 18 2.2 2.6e-01 0.00141 0.0081 -53
## 19 2.3 7.2e-02 0.00075 0.0096 -10
## 20 2.7 1.6e-02 0.00035 NA NA## [1] 4## The smallest factor had an eigenvalue of 1.405 with a confidence interval of 1.128 to 1.683 so the factor should be retained.## [1] 0.422641388 0.114365602 0.054056244 0.041773123 0.035797736 0.034762953
## [7] 0.031538949 0.029626917 0.026888054 0.025176932 0.024578513 0.022496450
## [13] 0.018283928 0.016775805 0.015510938 0.014790540 0.012057180 0.011510330
## [19] 0.009797753 0.009249920 0.007897302 0.005913997 0.004987006 0.003587609
## [25] 0.003274763 0.002660069## [1] ED estimated from the correlation matrix; no disattenuation; no small-sample correction.## $n1
## [1] 10.27
##
## $n2
## [1] 4.88
##
## $nInf
## [1] 2.37
##
## $nC
## [1] 21.67## Warning in EGA(FH54.cor, plot.ega = T, n = nFH54): Previous versions of EGAnet
## (<= 0.9.8) checked unidimensionality using [4;muni.method = "expand"[0m as the
## default## [1;m[4;m
## Exploratory Graph Analysis
## [0m[0m## • model = glasso
## • algorithm = walktrap
## • correlation = cor_auto
## • unidimensional check = leading eigenvalue## Network estimated with:
## • gamma = 0.5
## • lambda.min.ratio = 0.1
## EGA Results:
##
## Number of Dimensions:
## [1] 3
##
## Items per Dimension:
## items dimension
## P1CC P1CC 1
## P2CC P2CC 1
## P3CC P3CC 1
## RotPur RotPur 1
## PlaCon PlaCon 1
## ReaTim ReaTim 1
## ROM ROM 1
## NumOpII NumOpII 2
## DTR DTR 2
## MP MP 2
## GenMec GenMec 2
## SpId SpId 2
## PatCom PatCom 2
## VisPur VisPur 2
## Deco Deco 2
## InsCom InsCom 2
## SpaOri SpaOri 2
## SpeMar SpeMar 2
## LogAcc LogAcc 2
## DisReac DisReac 2
## NutBolt NutBolt 2
## P4CC P4CC 3
## P5CC P5CC 3
## P6CC P6CC 3
## P7CC P7CC 3
## P8CC P8CC 3NUM <- seq(1, 26, 1); EVS <- FAFH$e.values; TVP <- PTV(FAFH); bpdf <- data.frame("NUM" = NUM, "EVS" = EVS, "TVP" = TVP)
EVP <- ggplot(bpdf, aes(x = NUM, y = EVS, fill = as.factor(NUM))) + geom_bar(stat = "identity", show.legend = F) + xlab("Number") + ylab("Eigenvalue") + theme_bw() + scale_fill_hue(c = 30) + theme(text = element_text(size = 12, family = "serif"), plot.title = element_text(hjust = 0.5)) + geom_hline(yintercept = 1, color = "darkgray", linetype = "dashed", size = 1)
VPT <- ggplot(bpdf, aes(x = factor(1), y = TVP, fill = as.factor(NUM))) + geom_bar(stat = "identity", show.legend = F) + ylab("Percentage of Total Variance") + theme_bw() + scale_fill_hue(c = 50) + theme(text = element_text(size = 12, family = "serif"), plot.title = element_text(hjust = 0.5), axis.title.y = element_blank(), axis.text.y = element_blank(), axis.ticks.y = element_blank()) + coord_polar("y")ggarrange(EVP, VPT, ncol = 2)
Confirmatory
Separate Models
#T1
RegBFModel <- '
Num =~ NumOpII + DTR + SpId + PatCom + VisPur + Deco + InsCom + SpaOri + SpeMar + LogAcc + RotPur + DisReac
Spa =~ MP + GenMec + PlaCon + NutBolt
g =~ Num + Spa
P1CC ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH54.cor, sample.nobs = nFH54, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 41 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 36
##
## Number of observations 197
##
## Model Test User Model:
##
## Test statistic 260.724
## Degrees of freedom 117
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 1533.676
## Degrees of freedom 136
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.897
## Tucker-Lewis Index (TLI) 0.880
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4107.027
## Loglikelihood unrestricted model (H1) -3976.665
##
## Akaike (AIC) 8286.055
## Bayesian (BIC) 8404.250
## Sample-size adjusted Bayesian (BIC) 8290.204
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.079
## 90 Percent confidence interval - lower 0.066
## 90 Percent confidence interval - upper 0.092
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.058
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Num =~
## NumOpII 0.278 0.049 5.639 0.000 0.574 0.575
## DTR 0.392 0.060 6.562 0.000 0.811 0.813
## SpId 0.370 0.058 6.428 0.000 0.766 0.768
## PatCom 0.359 0.057 6.352 0.000 0.743 0.745
## VisPur 0.261 0.048 5.459 0.000 0.541 0.542
## Deco 0.361 0.057 6.362 0.000 0.746 0.748
## InsCom 0.297 0.051 5.841 0.000 0.615 0.616
## SpaOri 0.341 0.055 6.216 0.000 0.704 0.706
## SpeMar 0.306 0.052 5.918 0.000 0.632 0.633
## LogAcc 0.268 0.048 5.532 0.000 0.554 0.555
## RotPur 0.226 0.045 5.007 0.000 0.467 0.469
## DisReac 0.332 0.054 6.149 0.000 0.687 0.689
## Spa =~
## MP 0.336 0.081 4.148 0.000 0.732 0.734
## GenMec 0.285 0.069 4.113 0.000 0.622 0.624
## PlaCon 0.194 0.054 3.609 0.000 0.423 0.424
## NutBolt 0.205 0.055 3.697 0.000 0.447 0.448
## g =~
## Num 1.810 0.346 5.226 0.000 0.875 0.875
## Spa 1.939 0.520 3.726 0.000 0.889 0.889
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## P1CC ~
## g 0.777 0.066 11.708 0.000 0.777 0.779
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .NumOpII 0.666 0.070 9.515 0.000 0.666 0.669
## .DTR 0.337 0.041 8.300 0.000 0.337 0.339
## .SpId 0.408 0.047 8.728 0.000 0.408 0.410
## .PatCom 0.443 0.050 8.889 0.000 0.443 0.445
## .VisPur 0.703 0.073 9.580 0.000 0.703 0.706
## .Deco 0.439 0.049 8.871 0.000 0.439 0.441
## .InsCom 0.617 0.066 9.416 0.000 0.617 0.620
## .SpaOri 0.499 0.055 9.098 0.000 0.499 0.501
## .SpeMar 0.596 0.064 9.369 0.000 0.596 0.599
## .LogAcc 0.688 0.072 9.555 0.000 0.688 0.692
## .RotPur 0.776 0.080 9.692 0.000 0.776 0.780
## .DisReac 0.523 0.057 9.176 0.000 0.523 0.526
## .MP 0.458 0.069 6.647 0.000 0.458 0.461
## .GenMec 0.608 0.074 8.240 0.000 0.608 0.611
## .PlaCon 0.816 0.087 9.367 0.000 0.816 0.820
## .NutBolt 0.795 0.086 9.283 0.000 0.795 0.799
## .P1CC 0.391 0.061 6.430 0.000 0.391 0.393
## .Num 1.000 0.234 0.234
## .Spa 1.000 0.210 0.210
## g 1.000 1.000 1.000#T2
RegBFModel <- '
Num =~ NumOpII + DTR + SpId + PatCom + VisPur + Deco + InsCom + SpaOri + SpeMar + LogAcc + RotPur + DisReac
Spa =~ MP + GenMec + PlaCon + NutBolt
g =~ Num + Spa
P2CC ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH54.cor, sample.nobs = nFH54, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 42 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 36
##
## Number of observations 197
##
## Model Test User Model:
##
## Test statistic 276.906
## Degrees of freedom 117
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 1510.930
## Degrees of freedom 136
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.884
## Tucker-Lewis Index (TLI) 0.865
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4126.492
## Loglikelihood unrestricted model (H1) -3988.039
##
## Akaike (AIC) 8324.983
## Bayesian (BIC) 8443.179
## Sample-size adjusted Bayesian (BIC) 8329.132
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.083
## 90 Percent confidence interval - lower 0.071
## 90 Percent confidence interval - upper 0.096
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.061
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Num =~
## NumOpII 0.274 0.058 4.746 0.000 0.583 0.584
## DTR 0.383 0.073 5.229 0.000 0.816 0.818
## SpId 0.361 0.070 5.157 0.000 0.768 0.770
## PatCom 0.346 0.068 5.102 0.000 0.735 0.737
## VisPur 0.256 0.055 4.626 0.000 0.545 0.546
## Deco 0.348 0.068 5.111 0.000 0.741 0.742
## InsCom 0.288 0.060 4.833 0.000 0.614 0.615
## SpaOri 0.330 0.066 5.040 0.000 0.703 0.705
## SpeMar 0.297 0.061 4.878 0.000 0.631 0.633
## LogAcc 0.262 0.056 4.671 0.000 0.558 0.560
## RotPur 0.219 0.051 4.325 0.000 0.466 0.467
## DisReac 0.322 0.064 5.004 0.000 0.685 0.687
## Spa =~
## MP 0.346 0.087 4.002 0.000 0.731 0.733
## GenMec 0.296 0.074 3.974 0.000 0.625 0.627
## PlaCon 0.204 0.058 3.529 0.000 0.430 0.431
## NutBolt 0.208 0.058 3.563 0.000 0.440 0.441
## g =~
## Num 1.878 0.451 4.166 0.000 0.883 0.883
## Spa 1.859 0.533 3.486 0.000 0.881 0.881
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## P2CC ~
## g 0.674 0.070 9.577 0.000 0.674 0.676
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .NumOpII 0.655 0.069 9.488 0.000 0.655 0.659
## .DTR 0.330 0.040 8.214 0.000 0.330 0.331
## .SpId 0.405 0.047 8.695 0.000 0.405 0.408
## .PatCom 0.454 0.051 8.919 0.000 0.454 0.457
## .VisPur 0.698 0.073 9.567 0.000 0.698 0.702
## .Deco 0.446 0.050 8.886 0.000 0.446 0.449
## .InsCom 0.618 0.066 9.412 0.000 0.618 0.622
## .SpaOri 0.501 0.055 9.092 0.000 0.501 0.503
## .SpeMar 0.597 0.064 9.362 0.000 0.597 0.600
## .LogAcc 0.683 0.072 9.540 0.000 0.683 0.687
## .RotPur 0.778 0.080 9.690 0.000 0.778 0.782
## .DisReac 0.525 0.057 9.170 0.000 0.525 0.528
## .MP 0.460 0.070 6.543 0.000 0.460 0.462
## .GenMec 0.604 0.074 8.127 0.000 0.604 0.607
## .PlaCon 0.810 0.087 9.312 0.000 0.810 0.814
## .NutBolt 0.802 0.086 9.276 0.000 0.802 0.806
## .P2CC 0.540 0.070 7.722 0.000 0.540 0.543
## .Num 1.000 0.221 0.221
## .Spa 1.000 0.224 0.224
## g 1.000 1.000 1.000#T3
RegBFModel <- '
Num =~ NumOpII + DTR + SpId + PatCom + VisPur + Deco + InsCom + SpaOri + SpeMar + LogAcc + RotPur + DisReac
Spa =~ MP + GenMec + PlaCon + NutBolt
g =~ Num + Spa
P3CC ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH54.cor, sample.nobs = nFH54, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 43 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 36
##
## Number of observations 197
##
## Model Test User Model:
##
## Test statistic 289.017
## Degrees of freedom 117
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 1530.080
## Degrees of freedom 136
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.877
## Tucker-Lewis Index (TLI) 0.857
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4122.972
## Loglikelihood unrestricted model (H1) -3978.463
##
## Akaike (AIC) 8317.944
## Bayesian (BIC) 8436.140
## Sample-size adjusted Bayesian (BIC) 8322.093
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.086
## 90 Percent confidence interval - lower 0.074
## 90 Percent confidence interval - upper 0.099
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.063
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Num =~
## NumOpII 0.226 0.067 3.368 0.001 0.579 0.581
## DTR 0.316 0.089 3.530 0.000 0.811 0.813
## SpId 0.298 0.085 3.509 0.000 0.766 0.768
## PatCom 0.286 0.082 3.492 0.000 0.736 0.737
## VisPur 0.212 0.064 3.327 0.001 0.544 0.546
## Deco 0.287 0.082 3.494 0.000 0.738 0.740
## InsCom 0.240 0.070 3.404 0.001 0.615 0.617
## SpaOri 0.275 0.079 3.475 0.001 0.707 0.709
## SpeMar 0.246 0.072 3.419 0.001 0.632 0.634
## LogAcc 0.218 0.065 3.345 0.001 0.559 0.560
## RotPur 0.185 0.057 3.226 0.001 0.475 0.476
## DisReac 0.268 0.077 3.462 0.001 0.687 0.689
## Spa =~
## MP 0.397 0.078 5.098 0.000 0.736 0.738
## GenMec 0.338 0.068 4.998 0.000 0.628 0.629
## PlaCon 0.226 0.055 4.108 0.000 0.419 0.421
## NutBolt 0.237 0.056 4.226 0.000 0.440 0.441
## g =~
## Num 2.365 0.783 3.022 0.003 0.921 0.921
## Spa 1.562 0.364 4.285 0.000 0.842 0.842
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## P3CC ~
## g 0.682 0.070 9.714 0.000 0.682 0.684
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .NumOpII 0.659 0.069 9.500 0.000 0.659 0.663
## .DTR 0.337 0.041 8.286 0.000 0.337 0.339
## .SpId 0.408 0.047 8.716 0.000 0.408 0.410
## .PatCom 0.454 0.051 8.926 0.000 0.454 0.456
## .VisPur 0.699 0.073 9.571 0.000 0.699 0.702
## .Deco 0.450 0.050 8.910 0.000 0.450 0.452
## .InsCom 0.616 0.065 9.411 0.000 0.616 0.619
## .SpaOri 0.495 0.054 9.078 0.000 0.495 0.497
## .SpeMar 0.595 0.064 9.363 0.000 0.595 0.598
## .LogAcc 0.683 0.072 9.543 0.000 0.683 0.686
## .RotPur 0.769 0.079 9.680 0.000 0.769 0.773
## .DisReac 0.522 0.057 9.168 0.000 0.522 0.525
## .MP 0.453 0.071 6.386 0.000 0.453 0.455
## .GenMec 0.601 0.075 8.063 0.000 0.601 0.604
## .PlaCon 0.819 0.088 9.335 0.000 0.819 0.823
## .NutBolt 0.802 0.087 9.261 0.000 0.802 0.806
## .P3CC 0.530 0.069 7.640 0.000 0.530 0.533
## .Num 1.000 0.152 0.152
## .Spa 1.000 0.291 0.291
## g 1.000 1.000 1.000#T4
RegBFModel <- '
Num =~ NumOpII + DTR + SpId + PatCom + VisPur + Deco + InsCom + SpaOri + SpeMar + LogAcc + RotPur + DisReac
Spa =~ MP + GenMec + PlaCon + NutBolt
g =~ Num + Spa
P4CC ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH54.cor, sample.nobs = nFH54, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 45 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 36
##
## Number of observations 197
##
## Model Test User Model:
##
## Test statistic 274.396
## Degrees of freedom 117
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 1493.905
## Degrees of freedom 136
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.884
## Tucker-Lewis Index (TLI) 0.865
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4133.749
## Loglikelihood unrestricted model (H1) -3996.551
##
## Akaike (AIC) 8339.497
## Bayesian (BIC) 8457.693
## Sample-size adjusted Bayesian (BIC) 8343.646
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.083
## 90 Percent confidence interval - lower 0.070
## 90 Percent confidence interval - upper 0.095
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.062
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Num =~
## NumOpII 0.272 0.062 4.353 0.000 0.582 0.583
## DTR 0.380 0.081 4.719 0.000 0.814 0.816
## SpId 0.358 0.077 4.667 0.000 0.767 0.769
## PatCom 0.344 0.074 4.627 0.000 0.736 0.738
## VisPur 0.253 0.059 4.255 0.000 0.542 0.543
## Deco 0.346 0.075 4.633 0.000 0.741 0.743
## InsCom 0.286 0.065 4.422 0.000 0.613 0.615
## SpaOri 0.330 0.072 4.585 0.000 0.706 0.708
## SpeMar 0.295 0.066 4.459 0.000 0.632 0.633
## LogAcc 0.262 0.061 4.304 0.000 0.561 0.562
## RotPur 0.217 0.054 4.021 0.000 0.465 0.467
## DisReac 0.320 0.070 4.553 0.000 0.685 0.687
## Spa =~
## MP 0.349 0.091 3.842 0.000 0.731 0.733
## GenMec 0.297 0.078 3.818 0.000 0.624 0.625
## PlaCon 0.203 0.060 3.404 0.001 0.425 0.426
## NutBolt 0.212 0.061 3.466 0.001 0.445 0.446
## g =~
## Num 1.894 0.504 3.759 0.000 0.884 0.884
## Spa 1.845 0.559 3.303 0.001 0.879 0.879
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## P4CC ~
## g 0.626 0.072 8.688 0.000 0.626 0.628
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .NumOpII 0.657 0.069 9.488 0.000 0.657 0.660
## .DTR 0.332 0.040 8.225 0.000 0.332 0.334
## .SpId 0.406 0.047 8.689 0.000 0.406 0.408
## .PatCom 0.454 0.051 8.909 0.000 0.454 0.456
## .VisPur 0.701 0.073 9.570 0.000 0.701 0.705
## .Deco 0.446 0.050 8.879 0.000 0.446 0.449
## .InsCom 0.619 0.066 9.409 0.000 0.619 0.622
## .SpaOri 0.497 0.055 9.071 0.000 0.497 0.499
## .SpeMar 0.596 0.064 9.356 0.000 0.596 0.599
## .LogAcc 0.680 0.071 9.533 0.000 0.680 0.684
## .RotPur 0.778 0.080 9.689 0.000 0.778 0.782
## .DisReac 0.525 0.057 9.165 0.000 0.525 0.528
## .MP 0.460 0.071 6.504 0.000 0.460 0.462
## .GenMec 0.606 0.075 8.114 0.000 0.606 0.609
## .PlaCon 0.814 0.087 9.319 0.000 0.814 0.818
## .NutBolt 0.797 0.086 9.245 0.000 0.797 0.801
## .P4CC 0.603 0.074 8.153 0.000 0.603 0.606
## .Num 1.000 0.218 0.218
## .Spa 1.000 0.227 0.227
## g 1.000 1.000 1.000#T5
RegBFModel <- '
Num =~ NumOpII + DTR + SpId + PatCom + VisPur + Deco + InsCom + SpaOri + SpeMar + LogAcc + RotPur + DisReac
Spa =~ MP + GenMec + PlaCon + NutBolt
g =~ Num + Spa
P5CC ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH54.cor, sample.nobs = nFH54, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 42 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 36
##
## Number of observations 197
##
## Model Test User Model:
##
## Test statistic 268.992
## Degrees of freedom 117
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 1478.103
## Degrees of freedom 136
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.887
## Tucker-Lewis Index (TLI) 0.868
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4138.948
## Loglikelihood unrestricted model (H1) -4004.452
##
## Akaike (AIC) 8349.896
## Bayesian (BIC) 8468.092
## Sample-size adjusted Bayesian (BIC) 8354.045
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.081
## 90 Percent confidence interval - lower 0.068
## 90 Percent confidence interval - upper 0.094
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.062
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Num =~
## NumOpII 0.285 0.063 4.507 0.000 0.582 0.583
## DTR 0.400 0.081 4.918 0.000 0.815 0.817
## SpId 0.376 0.077 4.857 0.000 0.767 0.769
## PatCom 0.362 0.075 4.815 0.000 0.737 0.739
## VisPur 0.265 0.060 4.393 0.000 0.540 0.541
## Deco 0.364 0.075 4.822 0.000 0.742 0.744
## InsCom 0.300 0.066 4.580 0.000 0.612 0.614
## SpaOri 0.346 0.073 4.765 0.000 0.706 0.708
## SpeMar 0.309 0.067 4.621 0.000 0.630 0.632
## LogAcc 0.275 0.062 4.452 0.000 0.561 0.562
## RotPur 0.227 0.055 4.132 0.000 0.463 0.464
## DisReac 0.335 0.071 4.727 0.000 0.684 0.686
## Spa =~
## MP 0.336 0.100 3.367 0.001 0.739 0.741
## GenMec 0.284 0.084 3.361 0.001 0.624 0.625
## PlaCon 0.191 0.063 3.058 0.002 0.420 0.422
## NutBolt 0.200 0.064 3.101 0.002 0.439 0.440
## g =~
## Num 1.778 0.466 3.815 0.000 0.872 0.872
## Spa 1.956 0.674 2.904 0.004 0.890 0.890
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## P5CC ~
## g 0.588 0.073 8.044 0.000 0.588 0.590
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .NumOpII 0.657 0.069 9.486 0.000 0.657 0.660
## .DTR 0.331 0.040 8.203 0.000 0.331 0.332
## .SpId 0.407 0.047 8.686 0.000 0.407 0.409
## .PatCom 0.451 0.051 8.894 0.000 0.451 0.453
## .VisPur 0.703 0.073 9.571 0.000 0.703 0.707
## .Deco 0.444 0.050 8.864 0.000 0.444 0.446
## .InsCom 0.620 0.066 9.410 0.000 0.620 0.623
## .SpaOri 0.496 0.055 9.066 0.000 0.496 0.499
## .SpeMar 0.598 0.064 9.358 0.000 0.598 0.601
## .LogAcc 0.680 0.071 9.531 0.000 0.680 0.684
## .RotPur 0.780 0.081 9.691 0.000 0.780 0.784
## .DisReac 0.527 0.057 9.166 0.000 0.527 0.529
## .MP 0.449 0.071 6.366 0.000 0.449 0.451
## .GenMec 0.606 0.075 8.129 0.000 0.606 0.609
## .PlaCon 0.818 0.088 9.340 0.000 0.818 0.822
## .NutBolt 0.802 0.087 9.274 0.000 0.802 0.807
## .P5CC 0.649 0.077 8.439 0.000 0.649 0.652
## .Num 1.000 0.240 0.240
## .Spa 1.000 0.207 0.207
## g 1.000 1.000 1.000#T6
RegBFModel <- '
Num =~ NumOpII + DTR + SpId + PatCom + VisPur + Deco + InsCom + SpaOri + SpeMar + LogAcc + RotPur + DisReac
Spa =~ MP + GenMec + PlaCon + NutBolt
g =~ Num + Spa
P6CC ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH54.cor, sample.nobs = nFH54, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 44 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 36
##
## Number of observations 197
##
## Model Test User Model:
##
## Test statistic 268.029
## Degrees of freedom 117
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 1457.649
## Degrees of freedom 136
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.886
## Tucker-Lewis Index (TLI) 0.867
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4148.693
## Loglikelihood unrestricted model (H1) -4014.679
##
## Akaike (AIC) 8369.387
## Bayesian (BIC) 8487.582
## Sample-size adjusted Bayesian (BIC) 8373.536
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.081
## 90 Percent confidence interval - lower 0.068
## 90 Percent confidence interval - upper 0.094
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.062
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Num =~
## NumOpII 0.275 0.078 3.509 0.000 0.585 0.587
## DTR 0.385 0.104 3.689 0.000 0.818 0.820
## SpId 0.360 0.098 3.662 0.000 0.767 0.769
## PatCom 0.346 0.095 3.643 0.000 0.735 0.737
## VisPur 0.253 0.073 3.447 0.001 0.538 0.539
## Deco 0.349 0.096 3.647 0.000 0.742 0.744
## InsCom 0.288 0.081 3.539 0.000 0.612 0.614
## SpaOri 0.331 0.092 3.621 0.000 0.705 0.707
## SpeMar 0.296 0.083 3.558 0.000 0.630 0.632
## LogAcc 0.263 0.076 3.478 0.001 0.560 0.562
## RotPur 0.217 0.065 3.314 0.001 0.461 0.462
## DisReac 0.321 0.089 3.605 0.000 0.684 0.685
## Spa =~
## MP 0.358 0.108 3.318 0.001 0.743 0.745
## GenMec 0.303 0.092 3.310 0.001 0.629 0.631
## PlaCon 0.198 0.066 2.988 0.003 0.410 0.411
## NutBolt 0.210 0.069 3.049 0.002 0.436 0.438
## g =~
## Num 1.878 0.646 2.905 0.004 0.883 0.883
## Spa 1.819 0.663 2.746 0.006 0.876 0.876
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## P6CC ~
## g 0.496 0.076 6.551 0.000 0.496 0.497
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .NumOpII 0.652 0.069 9.475 0.000 0.652 0.655
## .DTR 0.325 0.040 8.154 0.000 0.325 0.327
## .SpId 0.407 0.047 8.682 0.000 0.407 0.409
## .PatCom 0.454 0.051 8.903 0.000 0.454 0.457
## .VisPur 0.705 0.074 9.574 0.000 0.705 0.709
## .Deco 0.445 0.050 8.863 0.000 0.445 0.447
## .InsCom 0.620 0.066 9.407 0.000 0.620 0.623
## .SpaOri 0.498 0.055 9.068 0.000 0.498 0.500
## .SpeMar 0.598 0.064 9.356 0.000 0.598 0.601
## .LogAcc 0.681 0.071 9.530 0.000 0.681 0.685
## .RotPur 0.783 0.081 9.693 0.000 0.783 0.787
## .DisReac 0.528 0.058 9.165 0.000 0.528 0.530
## .MP 0.443 0.071 6.235 0.000 0.443 0.445
## .GenMec 0.599 0.074 8.040 0.000 0.599 0.602
## .PlaCon 0.827 0.088 9.364 0.000 0.827 0.831
## .NutBolt 0.804 0.087 9.271 0.000 0.804 0.809
## .P6CC 0.749 0.084 8.966 0.000 0.749 0.753
## .Num 1.000 0.221 0.221
## .Spa 1.000 0.232 0.232
## g 1.000 1.000 1.000#T7
RegBFModel <- '
Num =~ NumOpII + DTR + SpId + PatCom + VisPur + Deco + InsCom + SpaOri + SpeMar + LogAcc + RotPur + DisReac
Spa =~ MP + GenMec + PlaCon + NutBolt
g =~ Num + Spa
P7CC ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH54.cor, sample.nobs = nFH54, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 43 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 36
##
## Number of observations 197
##
## Model Test User Model:
##
## Test statistic 270.662
## Degrees of freedom 117
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 1471.671
## Degrees of freedom 136
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.885
## Tucker-Lewis Index (TLI) 0.866
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4142.999
## Loglikelihood unrestricted model (H1) -4007.668
##
## Akaike (AIC) 8357.998
## Bayesian (BIC) 8476.193
## Sample-size adjusted Bayesian (BIC) 8362.147
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.082
## 90 Percent confidence interval - lower 0.069
## 90 Percent confidence interval - upper 0.094
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.062
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Num =~
## NumOpII 0.275 0.070 3.903 0.000 0.583 0.585
## DTR 0.384 0.092 4.158 0.000 0.816 0.819
## SpId 0.360 0.087 4.119 0.000 0.765 0.767
## PatCom 0.347 0.085 4.093 0.000 0.736 0.738
## VisPur 0.254 0.066 3.823 0.000 0.539 0.540
## Deco 0.349 0.085 4.098 0.000 0.742 0.744
## InsCom 0.288 0.073 3.946 0.000 0.612 0.613
## SpaOri 0.333 0.082 4.065 0.000 0.708 0.709
## SpeMar 0.298 0.075 3.976 0.000 0.632 0.634
## LogAcc 0.264 0.068 3.864 0.000 0.561 0.562
## RotPur 0.218 0.060 3.649 0.000 0.463 0.464
## DisReac 0.322 0.080 4.039 0.000 0.683 0.685
## Spa =~
## MP 0.358 0.099 3.598 0.000 0.743 0.744
## GenMec 0.304 0.085 3.587 0.000 0.631 0.633
## PlaCon 0.199 0.062 3.192 0.001 0.412 0.413
## NutBolt 0.209 0.064 3.253 0.001 0.434 0.435
## g =~
## Num 1.874 0.571 3.282 0.001 0.882 0.882
## Spa 1.819 0.603 3.018 0.003 0.876 0.876
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## P7CC ~
## g 0.551 0.074 7.420 0.000 0.551 0.553
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .NumOpII 0.655 0.069 9.481 0.000 0.655 0.658
## .DTR 0.328 0.040 8.182 0.000 0.328 0.330
## .SpId 0.409 0.047 8.697 0.000 0.409 0.411
## .PatCom 0.453 0.051 8.900 0.000 0.453 0.455
## .VisPur 0.705 0.074 9.573 0.000 0.705 0.708
## .Deco 0.445 0.050 8.865 0.000 0.445 0.447
## .InsCom 0.621 0.066 9.411 0.000 0.621 0.624
## .SpaOri 0.494 0.055 9.057 0.000 0.494 0.497
## .SpeMar 0.595 0.064 9.351 0.000 0.595 0.598
## .LogAcc 0.681 0.071 9.531 0.000 0.681 0.684
## .RotPur 0.781 0.081 9.691 0.000 0.781 0.785
## .DisReac 0.528 0.058 9.169 0.000 0.528 0.531
## .MP 0.444 0.071 6.272 0.000 0.444 0.446
## .GenMec 0.597 0.074 8.035 0.000 0.597 0.600
## .PlaCon 0.825 0.088 9.363 0.000 0.825 0.829
## .NutBolt 0.807 0.087 9.287 0.000 0.807 0.811
## .P7CC 0.691 0.080 8.670 0.000 0.691 0.695
## .Num 1.000 0.222 0.222
## .Spa 1.000 0.232 0.232
## g 1.000 1.000 1.000#T8
RegBFModel <- '
Num =~ NumOpII + DTR + SpId + PatCom + VisPur + Deco + InsCom + SpaOri + SpeMar + LogAcc + RotPur + DisReac
Spa =~ MP + GenMec + PlaCon + NutBolt
g =~ Num + Spa
P8CC ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH54.cor, sample.nobs = nFH54, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 41 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 36
##
## Number of observations 197
##
## Model Test User Model:
##
## Test statistic 266.775
## Degrees of freedom 117
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 1462.830
## Degrees of freedom 136
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.887
## Tucker-Lewis Index (TLI) 0.869
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4145.476
## Loglikelihood unrestricted model (H1) -4012.089
##
## Akaike (AIC) 8362.952
## Bayesian (BIC) 8481.148
## Sample-size adjusted Bayesian (BIC) 8367.101
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.081
## 90 Percent confidence interval - lower 0.068
## 90 Percent confidence interval - upper 0.093
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.062
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Num =~
## NumOpII 0.263 0.078 3.380 0.001 0.584 0.586
## DTR 0.367 0.104 3.540 0.000 0.816 0.818
## SpId 0.345 0.098 3.517 0.000 0.768 0.770
## PatCom 0.331 0.094 3.499 0.000 0.735 0.737
## VisPur 0.243 0.073 3.328 0.001 0.540 0.541
## Deco 0.334 0.095 3.504 0.000 0.743 0.745
## InsCom 0.276 0.081 3.408 0.001 0.613 0.615
## SpaOri 0.318 0.091 3.481 0.000 0.706 0.708
## SpeMar 0.284 0.083 3.424 0.001 0.630 0.632
## LogAcc 0.252 0.075 3.352 0.001 0.560 0.561
## RotPur 0.208 0.065 3.209 0.001 0.462 0.464
## DisReac 0.307 0.089 3.465 0.001 0.683 0.684
## Spa =~
## MP 0.373 0.099 3.775 0.000 0.742 0.744
## GenMec 0.318 0.085 3.756 0.000 0.634 0.635
## PlaCon 0.204 0.062 3.287 0.001 0.407 0.408
## NutBolt 0.219 0.065 3.382 0.001 0.437 0.438
## g =~
## Num 1.985 0.696 2.851 0.004 0.893 0.893
## Spa 1.723 0.556 3.099 0.002 0.865 0.865
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## P8CC ~
## g 0.526 0.075 7.005 0.000 0.526 0.527
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .NumOpII 0.653 0.069 9.478 0.000 0.653 0.657
## .DTR 0.329 0.040 8.183 0.000 0.329 0.330
## .SpId 0.405 0.047 8.678 0.000 0.405 0.407
## .PatCom 0.455 0.051 8.908 0.000 0.455 0.457
## .VisPur 0.703 0.073 9.571 0.000 0.703 0.707
## .Deco 0.443 0.050 8.859 0.000 0.443 0.446
## .InsCom 0.619 0.066 9.406 0.000 0.619 0.622
## .SpaOri 0.496 0.055 9.064 0.000 0.496 0.499
## .SpeMar 0.598 0.064 9.357 0.000 0.598 0.601
## .LogAcc 0.682 0.072 9.533 0.000 0.682 0.685
## .RotPur 0.781 0.081 9.691 0.000 0.781 0.785
## .DisReac 0.529 0.058 9.171 0.000 0.529 0.531
## .MP 0.444 0.071 6.257 0.000 0.444 0.446
## .GenMec 0.594 0.074 7.993 0.000 0.594 0.597
## .PlaCon 0.830 0.088 9.376 0.000 0.830 0.834
## .NutBolt 0.804 0.087 9.269 0.000 0.804 0.808
## .P8CC 0.719 0.082 8.807 0.000 0.719 0.722
## .Num 1.000 0.202 0.202
## .Spa 1.000 0.252 0.252
## g 1.000 1.000 1.000Cumulative Model
RegBFModel <- '
Num =~ NumOpII + DTR + SpId + PatCom + VisPur + Deco + InsCom + SpaOri + SpeMar + LogAcc + RotPur + DisReac
Spa =~ MP + GenMec + PlaCon + NutBolt
g =~ Num + Spa
P1CC + P2CC + P3CC + P4CC + P5CC + P6CC + P7CC + P8CC ~ g'
RegBFFit <- cfa(RegBFModel, sample.cov = FH54.cor, sample.nobs = nFH54, std.lv = T, orthogonal = T)
summary(RegBFFit, stand = T, fit = T)## lavaan 0.6-9 ended normally after 128 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 78
##
## Number of observations 197
##
## Model Test User Model:
##
## Test statistic 374.901
## Degrees of freedom 222
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 3812.986
## Degrees of freedom 276
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.957
## Tucker-Lewis Index (TLI) 0.946
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4977.668
## Loglikelihood unrestricted model (H1) -4790.218
##
## Akaike (AIC) 10111.337
## Bayesian (BIC) 10367.427
## Sample-size adjusted Bayesian (BIC) 10120.326
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.059
## 90 Percent confidence interval - lower 0.049
## 90 Percent confidence interval - upper 0.069
## P-value RMSEA <= 0.05 0.075
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.070
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Num =~
## NumOpII 0.263 0.048 5.457 0.000 0.571 0.572
## DTR 0.371 0.059 6.289 0.000 0.807 0.809
## SpId 0.353 0.057 6.183 0.000 0.767 0.769
## PatCom 0.342 0.056 6.111 0.000 0.742 0.744
## VisPur 0.251 0.047 5.331 0.000 0.545 0.547
## Deco 0.342 0.056 6.114 0.000 0.743 0.745
## InsCom 0.284 0.050 5.661 0.000 0.616 0.618
## SpaOri 0.325 0.054 5.995 0.000 0.705 0.707
## SpeMar 0.291 0.051 5.728 0.000 0.633 0.634
## LogAcc 0.255 0.047 5.376 0.000 0.554 0.556
## RotPur 0.219 0.044 4.936 0.000 0.475 0.476
## DisReac 0.317 0.053 5.940 0.000 0.689 0.691
## Spa =~
## MP 0.343 0.076 4.489 0.000 0.723 0.725
## GenMec 0.293 0.066 4.422 0.000 0.617 0.618
## PlaCon 0.208 0.054 3.881 0.000 0.437 0.439
## NutBolt 0.215 0.054 3.943 0.000 0.452 0.453
## g =~
## Num 1.928 0.375 5.135 0.000 0.888 0.888
## Spa 1.854 0.459 4.043 0.000 0.880 0.880
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## P1CC ~
## g 0.775 0.066 11.681 0.000 0.775 0.777
## P2CC ~
## g 0.675 0.070 9.655 0.000 0.675 0.676
## P3CC ~
## g 0.694 0.069 10.027 0.000 0.694 0.696
## P4CC ~
## g 0.627 0.071 8.797 0.000 0.627 0.629
## P5CC ~
## g 0.588 0.072 8.111 0.000 0.588 0.589
## P6CC ~
## g 0.499 0.075 6.682 0.000 0.499 0.500
## P7CC ~
## g 0.553 0.073 7.543 0.000 0.553 0.555
## P8CC ~
## g 0.531 0.074 7.181 0.000 0.531 0.532
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .P1CC ~~
## .P2CC 0.224 0.054 4.122 0.000 0.224 0.484
## .P3CC 0.189 0.053 3.562 0.000 0.189 0.419
## .P4CC 0.171 0.053 3.222 0.001 0.171 0.350
## .P5CC 0.182 0.054 3.389 0.001 0.182 0.358
## .P6CC 0.181 0.054 3.341 0.001 0.181 0.333
## .P7CC 0.198 0.054 3.652 0.000 0.198 0.380
## .P8CC 0.176 0.054 3.271 0.001 0.176 0.331
## .P2CC ~~
## .P3CC 0.377 0.061 6.148 0.000 0.377 0.717
## .P4CC 0.422 0.064 6.597 0.000 0.422 0.741
## .P5CC 0.439 0.065 6.748 0.000 0.439 0.742
## .P6CC 0.449 0.066 6.793 0.000 0.449 0.708
## .P7CC 0.393 0.063 6.187 0.000 0.393 0.644
## .P8CC 0.428 0.065 6.576 0.000 0.428 0.690
## .P3CC ~~
## .P4CC 0.410 0.063 6.488 0.000 0.410 0.738
## .P5CC 0.418 0.064 6.543 0.000 0.418 0.724
## .P6CC 0.440 0.065 6.730 0.000 0.440 0.711
## .P7CC 0.422 0.064 6.563 0.000 0.422 0.710
## .P8CC 0.418 0.064 6.500 0.000 0.418 0.690
## .P4CC ~~
## .P5CC 0.527 0.070 7.561 0.000 0.527 0.843
## .P6CC 0.563 0.072 7.813 0.000 0.563 0.840
## .P7CC 0.508 0.069 7.352 0.000 0.508 0.790
## .P8CC 0.513 0.070 7.373 0.000 0.513 0.783
## .P5CC ~~
## .P6CC 0.602 0.074 8.089 0.000 0.602 0.865
## .P7CC 0.540 0.071 7.596 0.000 0.540 0.808
## .P8CC 0.544 0.072 7.603 0.000 0.544 0.799
## .P6CC ~~
## .P7CC 0.570 0.073 7.754 0.000 0.570 0.795
## .P8CC 0.591 0.075 7.908 0.000 0.591 0.810
## .P7CC ~~
## .P8CC 0.602 0.075 8.066 0.000 0.602 0.859
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .NumOpII 0.669 0.070 9.525 0.000 0.669 0.672
## .DTR 0.344 0.041 8.369 0.000 0.344 0.346
## .SpId 0.407 0.047 8.737 0.000 0.407 0.409
## .PatCom 0.444 0.050 8.907 0.000 0.444 0.447
## .VisPur 0.697 0.073 9.575 0.000 0.697 0.701
## .Deco 0.443 0.050 8.901 0.000 0.443 0.445
## .InsCom 0.615 0.065 9.418 0.000 0.615 0.618
## .SpaOri 0.497 0.055 9.103 0.000 0.497 0.500
## .SpeMar 0.595 0.063 9.373 0.000 0.595 0.598
## .LogAcc 0.688 0.072 9.558 0.000 0.688 0.691
## .RotPur 0.769 0.079 9.685 0.000 0.769 0.773
## .DisReac 0.520 0.057 9.175 0.000 0.520 0.523
## .MP 0.473 0.069 6.810 0.000 0.473 0.475
## .GenMec 0.614 0.074 8.277 0.000 0.614 0.618
## .PlaCon 0.804 0.086 9.315 0.000 0.804 0.808
## .NutBolt 0.791 0.085 9.261 0.000 0.791 0.795
## .P1CC 0.395 0.061 6.519 0.000 0.395 0.397
## .P2CC 0.540 0.069 7.828 0.000 0.540 0.543
## .P3CC 0.513 0.067 7.621 0.000 0.513 0.516
## .P4CC 0.601 0.073 8.256 0.000 0.601 0.604
## .P5CC 0.650 0.076 8.551 0.000 0.650 0.653
## .P6CC 0.746 0.082 9.048 0.000 0.746 0.750
## .P7CC 0.689 0.079 8.767 0.000 0.689 0.692
## .P8CC 0.713 0.080 8.891 0.000 0.713 0.717
## .Num 1.000 0.212 0.212
## .Spa 1.000 0.225 0.225
## g 1.000 1.000 1.000