Reanalysis of ‘Ability and Prior Job Knowledge in Complex Training Performance’
Jay Lasker
April 20, 2020
Startup
Packages
library(pacman)
p_load(psych, lavaan, semPlot, cowplot, gridExtra, ggplot2, knitr, dplyr)Functions
#Congruence coefficient formula because Psych's fa.congruence function is broken
CONGO <- function(F1, F2) {
PHI = sum(F1*F2) / sqrt(sum(F1^2)*sum(F2^2))
return(PHI)}
#ALTCONGO <- function(F1, F2) {
# FA = mean(F1); FB = mean(F2)
# PHI = sum((F1-FA)*(F2-FB)) / sqrt(sum((F1-FA)^2) * sum((F2-FB)^2))
# return(PHI)}Rationale
Reanalysis of Ree, Carretta & Teachout (1995). Their model showed no relationship between prior job knowledge and job knowledge acquired on the job, a theoretically interesting finding because it reinforces the idea that prior job knowledge is not the relevant thing for employers to care about if they’re aiming for long-term employment. I tested the fit of these models, pruned insignificant paths, and also assessed (1) the relationship between a “general factor” of workplace performance and the AFOQT g and (2) the relationship between the vector of AFOQT subtest g loadings and the vectors of criterion correlations.
Analysis
Data Input
#Corrected full correlation matrix
lower = '
1
0.58 1
0.73 0.58 1
0.53 0.67 0.55 1
0.68 0.46 0.77 0.46 1
0.55 0.71 0.51 0.6 0.4 1
0.48 0.66 0.45 0.62 0.37 0.6 1
0.34 0.41 0.33 0.43 0.28 0.39 0.49 1
0.3 0.31 0.34 0.34 0.32 0.25 0.33 0.56 1
0.24 0.26 0.24 0.25 0.18 0.28 0.23 0.19 0.2 1
0.25 0.22 0.23 0.19 0.2 0.23 0.18 0.15 0.16 0.23 1
0.19 0.23 0.19 0.19 0.16 0.22 0.18 0.14 0.14 0.22 0.18 1
0.23 0.25 0.24 0.23 0.17 0.27 0.21 0.19 0.19 0.27 0.24 0.21 1
0.2 0.23 0.18 0.19 0.11 0.16 0.22 0.12 0.1 0.24 0.22 0.23 0.16 1
0.14 0.19 0.14 0.17 0.1 0.13 0.17 0.1 0.11 0.2 0.2 0.21 0.22 0.23 1
0.17 0.23 0.17 0.23 0.12 0.15 0.19 0.12 0.15 0.17 0.2 0.19 0.22 0.24 0.2 1
0.18 0.2 0.18 0.19 0.14 0.12 0.2 0.11 0.12 0.16 0.2 0.17 0.16 0.27 0.21 0.22 1
0.22 0.22 0.22 0.2 0.17 0.17 0.19 0.12 0.13 0.23 0.19 0.22 0.23 0.26 0.25 0.26 0.24 1
0.2 0.27 0.21 0.21 0.15 0.2 0.22 0.12 0.1 0.23 0.18 0.17 0.2 0.21 0.2 0.17 0.19 0.24 1
0.19 0.23 0.18 0.23 0.12 0.18 0.23 0.14 0.12 0.18 0.2 0.16 0.16 0.2 0.2 0.22 0.2 0.23 0.24 1
0.03 0.1 0.02 0.11 0 0.08 0.14 0.13 0.1 0.09 0.06 0.08 0.11 0.16 0.14 0.12 0.11 0.11 0.14 0.14 1
0.09 0.13 0.07 0.14 0.04 0.11 0.16 0.13 0.09 0.11 0.09 0.08 0.1 0.13 0.15 0.12 0.13 0.13 0.15 0.13 0.26 1
0.12 0.15 0.11 0.16 0.06 0.1 0.19 0.13 0.09 0.15 0.1 0.16 0.13 0.18 0.14 0.12 0.13 0.13 0.14 0.15 0.26 0.29 1
0.05 0.11 0.05 0.13 0 0.12 0.15 0.14 0.08 0.09 0.08 0.07 0.12 0.09 0.12 0.11 0.09 0.12 0.15 0.11 0.22 0.2 0.2 1
0.06 0.07 0.03 0.09 0.01 0.07 0.1 0.12 0.05 0.06 0.06 0.06 0.06 0.11 0.09 0.1 0.07 0.06 0.09 0.07 0.22 0.2 0.2 0.19 1
0.11 0.15 0.11 0.16 0.06 0.09 0.18 0.13 0.06 0.11 0.11 0.09 0.1 0.15 0.14 0.12 0.09 0.12 0.16 0.14 0.19 0.18 0.21 0.18 0.16 1'
#Corrected AFOQT correlation matrix
lowerAFOQT = '
1
0.58 1
0.73 0.58 1
0.53 0.67 0.55 1
0.68 0.46 0.77 0.46 1
0.55 0.71 0.51 0.6 0.4 1
0.48 0.66 0.45 0.62 0.37 0.6 1'
#Corrected work knowledeg correlation matrix
lowerWK = '
1
0.56 1
0.19 0.2 1
0.15 0.16 0.23 1
0.14 0.14 0.22 0.18 1
0.19 0.19 0.27 0.24 0.21 1
0.12 0.1 0.24 0.22 0.23 0.16 1
0.1 0.11 0.2 0.2 0.21 0.22 0.23 1
0.12 0.15 0.17 0.2 0.19 0.22 0.24 0.2 1
0.11 0.12 0.16 0.2 0.17 0.16 0.27 0.21 0.22 1
0.12 0.13 0.23 0.19 0.22 0.23 0.26 0.25 0.26 0.24 1
0.12 0.1 0.23 0.18 0.17 0.2 0.21 0.2 0.17 0.19 0.24 1
0.14 0.12 0.18 0.2 0.16 0.16 0.2 0.2 0.22 0.2 0.23 0.24 1
0.13 0.1 0.09 0.06 0.08 0.11 0.16 0.14 0.12 0.11 0.11 0.14 0.14 1
0.13 0.09 0.11 0.09 0.08 0.1 0.13 0.15 0.12 0.13 0.13 0.15 0.13 0.26 1
0.13 0.09 0.15 0.1 0.16 0.13 0.18 0.14 0.12 0.13 0.13 0.14 0.15 0.26 0.29 1
0.14 0.08 0.09 0.08 0.07 0.12 0.09 0.12 0.11 0.09 0.12 0.15 0.11 0.22 0.2 0.2 1
0.12 0.05 0.06 0.06 0.06 0.06 0.11 0.09 0.1 0.07 0.06 0.09 0.07 0.22 0.2 0.2 0.19 1
0.13 0.06 0.11 0.11 0.09 0.1 0.15 0.14 0.12 0.09 0.12 0.16 0.14 0.19 0.18 0.21 0.18 0.16 1'
#Variable names
Names = list("VA", "AR", "RC", "DI", "WK", "MK", "SR", "IC", "AI", "A1", "A2", "A3", "A4", "A5", "A6", "A7", "A8", "A9", "A10", "A11", "CF1", "CF2", "CF3", "CF4", "CF5", "CF6")
NamesAFOQT = list("VA", "AR", "RC", "DI", "WK", "MK", "SR")
NamesWK = list("IC", "AI", "A1", "A2", "A3", "A4", "A5", "A6", "A7", "A8", "A9", "A10", "A11", "CF1", "CF2", "CF3", "CF4", "CF5", "CF6")
#Convert to variance-covariance matrices
dat.cor = getCov(lower, names = Names)
SDs <- c(4.23, 4.4, 5.93, 3.93, 5.83, 6.04, 6.73, 4.76, 4.08, 3.19, 3.38, 3.41, 3.36, 4.89, 5.37, 5.43, 4.6, 3.38, 3.7, 3.76, 7.6, 5.77, 4.93, 5.74, 4.69, 4.78)
dat.cov = lavaan::cor2cov(R = dat.cor, sds = SDs)
datAFOQT.cor = getCov(lowerAFOQT, names = NamesAFOQT)
SDsAFOQT <- c(4.23, 4.4, 5.93, 3.93, 5.83, 6.04, 6.73)
datAFOQT.cov = lavaan::cor2cov(R = datAFOQT.cor, sds = SDsAFOQT)
datWK.cor = getCov(lowerWK, names = NamesWK)
SDsWK <- c(4.76, 4.08, 3.19, 3.38, 3.41, 3.36, 4.89, 5.37, 5.43, 4.6, 3.38, 3.7, 3.76, 7.6, 5.77, 4.93, 5.74, 4.69, 4.78)
datWK.cov = lavaan::cor2cov(R = datWK.cor, sds = SDsWK)
#g vectors and validities
gvals <- read.csv("gvals.csv")
#MCVs <- read.csv("MCVs.csv")
#Fit measures
FITS <- c("chisq", "df", "nPar", "cfi", "rmsea", "rmsea.ci.lower", "rmsea.ci.upper", "bic2")
#Variaable groups
AFLATS <- list(
VER = c("VA", "RC", "WK"),
QUA = c("AR", "DI", "MK", "SR"),
JKP = c("IC", "AI"),
JKTI =c("A1", "A2", "A3", "A4"),
JKTII = c("A5", "A6", "A7", "A8"),
JKTIII = c("A9", "A10", "A11"),
WSI = c("CF1", "CF2", "CF3"),
WSII = c("CF4", "CF5", "CF6"))g Loadings
EFA g loadings to compare to the CFA g loadings. First, the AFOQT g loadings are assessed alongside all of the variables and then on their own. The PCA loadings are abundantly similar.
fa.parallel(dat.cov, n.obs = 3428)
## Parallel analysis suggests that the number of factors = 6 and the number of components = NAfa.parallel(datAFOQT.cov, n.obs = 3428)
## Parallel analysis suggests that the number of factors = 2 and the number of components = NAfa.parallel(datWK.cov, n.obs = 3428)
## Parallel analysis suggests that the number of factors = 5 and the number of components = NAEFAALL <- fa(dat.cov, nfactors = 1, n.obs = 3428)
EFAAFOQT <- fa(datAFOQT.cov, nfactors = 1, n.obs = 3428)
EFAWK <- fa(datWK.cov, nfactors = 1, n.obs = 3428)
print(EFAALL, digits = 3)## Factor Analysis using method = minres
## Call: fa(r = dat.cov, nfactors = 1, n.obs = 3428)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## VA 0.711 0.5059 0.494 1
## AR 0.779 0.6067 0.393 1
## RC 0.713 0.5079 0.492 1
## DI 0.734 0.5385 0.461 1
## WK 0.594 0.3528 0.647 1
## MK 0.692 0.4789 0.521 1
## SR 0.706 0.4983 0.502 1
## IC 0.527 0.2776 0.722 1
## AI 0.453 0.2050 0.795 1
## A1 0.412 0.1696 0.830 1
## A2 0.369 0.1362 0.864 1
## A3 0.346 0.1199 0.880 1
## A4 0.397 0.1573 0.843 1
## A5 0.363 0.1318 0.868 1
## A6 0.320 0.1022 0.898 1
## A7 0.347 0.1203 0.880 1
## A8 0.329 0.1082 0.892 1
## A9 0.377 0.1422 0.858 1
## A10 0.371 0.1374 0.863 1
## A11 0.355 0.1260 0.874 1
## CF1 0.207 0.0430 0.957 1
## CF2 0.241 0.0582 0.942 1
## CF3 0.274 0.0752 0.925 1
## CF4 0.210 0.0440 0.956 1
## CF5 0.162 0.0261 0.974 1
## CF6 0.246 0.0607 0.939 1
##
## MR1
## SS loadings 5.73
## Proportion Var 0.22
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 325 and the objective function was 7.595 with Chi Square of 25955.76
## The degrees of freedom for the model are 299 and the objective function was 2.54
##
## The root mean square of the residuals (RMSR) is 0.077
## The df corrected root mean square of the residuals is 0.08
##
## The harmonic number of observations is 3428 with the empirical chi square 13283.77 with prob < 0
## The total number of observations was 3428 with Likelihood Chi Square = 8677.591 with prob < 0
##
## Tucker Lewis Index of factoring reliability = 0.6446
## RMSEA index = 0.0904 and the 90 % confidence intervals are 0.0888 0.0921
## BIC = 6243.811
## Fit based upon off diagonal values = 0.888
## Measures of factor score adequacy
## MR1
## Correlation of (regression) scores with factors 0.951
## Multiple R square of scores with factors 0.905
## Minimum correlation of possible factor scores 0.809print(EFAAFOQT, digits = 3)## Factor Analysis using method = minres
## Call: fa(r = datAFOQT.cov, nfactors = 1, n.obs = 3428)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## VA 0.788 0.621 0.379 1
## AR 0.818 0.669 0.331 1
## RC 0.797 0.636 0.364 1
## DI 0.756 0.572 0.428 1
## WK 0.687 0.473 0.527 1
## MK 0.743 0.552 0.448 1
## SR 0.694 0.482 0.518 1
##
## MR1
## SS loadings 4.005
## Proportion Var 0.572
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 21 and the objective function was 4.434 with Chi Square of 15181.2
## The degrees of freedom for the model are 14 and the objective function was 0.785
##
## The root mean square of the residuals (RMSR) is 0.096
## The df corrected root mean square of the residuals is 0.118
##
## The harmonic number of observations is 3428 with the empirical chi square 1340.158 with prob < 1.23e-277
## The total number of observations was 3428 with Likelihood Chi Square = 2686.405 with prob < 0
##
## Tucker Lewis Index of factoring reliability = 0.7355
## RMSEA index = 0.236 and the 90 % confidence intervals are 0.2285 0.2436
## BIC = 2572.449
## Fit based upon off diagonal values = 0.972
## Measures of factor score adequacy
## MR1
## Correlation of (regression) scores with factors 0.953
## Multiple R square of scores with factors 0.909
## Minimum correlation of possible factor scores 0.817print(EFAWK, digits = 3)## Factor Analysis using method = minres
## Call: fa(r = datWK.cov, nfactors = 1, n.obs = 3428)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## IC 0.384 0.1471 0.853 1
## AI 0.355 0.1259 0.874 1
## A1 0.451 0.2032 0.797 1
## A2 0.410 0.1680 0.832 1
## A3 0.400 0.1603 0.840 1
## A4 0.440 0.1932 0.807 1
## A5 0.474 0.2247 0.775 1
## A6 0.445 0.1977 0.802 1
## A7 0.436 0.1900 0.810 1
## A8 0.413 0.1702 0.830 1
## A9 0.475 0.2252 0.775 1
## A10 0.438 0.1917 0.808 1
## A11 0.426 0.1816 0.818 1
## CF1 0.349 0.1216 0.878 1
## CF2 0.355 0.1260 0.874 1
## CF3 0.389 0.1517 0.848 1
## CF4 0.312 0.0972 0.903 1
## CF5 0.257 0.0659 0.934 1
## CF6 0.328 0.1075 0.892 1
##
## MR1
## SS loadings 3.049
## Proportion Var 0.160
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 171 and the objective function was 2.461 with Chi Square of 8415.737
## The degrees of freedom for the model are 152 and the objective function was 0.658
##
## The root mean square of the residuals (RMSR) is 0.056
## The df corrected root mean square of the residuals is 0.06
##
## The harmonic number of observations is 3428 with the empirical chi square 3720.531 with prob < 0
## The total number of observations was 3428 with Likelihood Chi Square = 2249.024 with prob < 0
##
## Tucker Lewis Index of factoring reliability = 0.7138
## RMSEA index = 0.0634 and the 90 % confidence intervals are 0.0611 0.0658
## BIC = 1011.784
## Fit based upon off diagonal values = 0.89
## Measures of factor score adequacy
## MR1
## Correlation of (regression) scores with factors 0.887
## Multiple R square of scores with factors 0.787
## Minimum correlation of possible factor scores 0.573FACS <- data.frame("ALL" = c(0.711, 0.779, 0.713, 0.734, 0.594, 0.692, 0.706), "SOLO" = c(0.788, 0.818, 0.797, 0.756, 0.687, 0.743, 0.694))
cor(FACS$ALL, FACS$SOLO)## [1] 0.7562782cor(FACS$ALL, FACS$SOLO, method = "spearman")## [1] 0.8571429CONGO(FACS$ALL, FACS$SOLO)## [1] 0.9988212The g loadings are practically identical despite very different variables being included alongside the AFOQT subtests. Presumably this should also be the case for loadings from a CFA. The initial unified factor model did not fit well (which is typical of single-factor models with more than a handful of variables), so I added the three largest residual covariances in the modification indices. Factorial identity was probably maintained regardless of this choice though.
#Unified g model
UNG.model <- '
g =~ VA + AR + RC + DI + WK + MK + SR
WK ~~ RC + VA
VA ~~ RC'
UNG.fit <- cfa(UNG.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T)
fitmeasures(UNG.fit, FITS)## chisq df npar cfi rmsea
## 139.579 11.000 17.000 0.992 0.058
## rmsea.ci.lower rmsea.ci.upper bic2
## 0.050 0.067 132236.399parameterEstimates(UNG.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| g | VA | 2.822 | 0.067 | 42.310 | 0 | 0.667 |
| g | AR | 3.853 | 0.062 | 62.457 | 0 | 0.876 |
| g | RC | 3.881 | 0.094 | 41.248 | 0 | 0.655 |
| g | DI | 3.059 | 0.058 | 52.316 | 0 | 0.778 |
| g | WK | 3.070 | 0.097 | 31.541 | 0 | 0.527 |
| g | MK | 4.822 | 0.089 | 54.287 | 0 | 0.798 |
| g | SR | 5.081 | 0.101 | 50.092 | 0 | 0.755 |
#CFA g loadings with (MI) and without changes from the modification indices
CFAC <- data.frame(CFA = c(0.786, 0.812, 0.792, 0.755, 0.697, 0.747, 0.698)); FACS <- cbind(FACS, CFAC)
CFACMI <- data.frame(CFAMI = c(0.667, 0.876, 0.655, 0.778, 0.527, 0.798, 0.755)); FACS <- cbind(FACS, CFACMI)
cor(FACS$ALL, FACS$CFA)## [1] 0.7349784cor(FACS$SOLO, FACS$CFA)## [1] 0.9990583cor(FACS$ALL, FACS$CFA, method = "spearman")## [1] 0.8571429cor(FACS$SOLO, FACS$CFA, method = "spearman")## [1] 1CONGO(FACS$ALL, FACS$CFA)## [1] 0.9987532CONGO(FACS$SOLO, FACS$CFA)## [1] 0.9999753cor(FACS$ALL, FACS$CFAMI)## [1] 0.848595cor(FACS$SOLO, FACS$CFAMI)## [1] 0.4439311cor(FACS$ALL, FACS$CFAMI, method = "spearman")## [1] 0.5cor(FACS$SOLO, FACS$CFAMI, method = "spearman")## [1] 0.3928571CONGO(FACS$ALL, FACS$CFAMI)## [1] 0.9957417CONGO(FACS$SOLO, FACS$CFAMI)## [1] 0.9914298cor(FACS$CFA, FACS$CFAMI)## [1] 0.430421cor(FACS$CFA, FACS$CFAMI, method = "spearman")## [1] 0.3928571CONGO(FACS$CFA, FACS$CFAMI)## [1] 0.9912775Confirmatory Factor Models
#AFOQT model from the paper
AFOQT.model <- '
Verbal =~ VA + RC + WK
Quant =~ AR + DI + MK + SR
g =~ VA + AR + RC + DI + WK + MK + SR'
AFOQT.fit <- cfa(AFOQT.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T, control=list(rel.tol=1e-4))
fitmeasures(AFOQT.fit, FITS)## chisq df npar cfi rmsea
## 104.156 7.000 21.000 0.994 0.064
## rmsea.ci.lower rmsea.ci.upper bic2
## 0.053 0.075 132220.824parameterEstimates(AFOQT.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| Verbal | VA | 1.168 | 2.774 | 0.421 | 0.674 | 0.276 |
| Verbal | RC | 2.481 | 4.146 | 0.598 | 0.550 | 0.419 |
| Verbal | WK | 3.921 | 1.386 | 2.830 | 0.005 | 0.673 |
| Quant | AR | 2.018 | 2.034 | 0.992 | 0.321 | 0.459 |
| Quant | DI | 1.483 | 1.783 | 0.832 | 0.406 | 0.377 |
| Quant | MK | 2.502 | 2.573 | 0.972 | 0.331 | 0.414 |
| Quant | SR | 3.329 | 1.573 | 2.116 | 0.034 | 0.495 |
| g | VA | 3.334 | 1.270 | 2.625 | 0.009 | 0.789 |
| g | AR | 3.265 | 1.245 | 2.622 | 0.009 | 0.742 |
| g | RC | 4.619 | 1.760 | 2.625 | 0.009 | 0.779 |
| g | DI | 2.672 | 1.015 | 2.632 | 0.008 | 0.680 |
| g | WK | 3.652 | 1.393 | 2.621 | 0.009 | 0.627 |
| g | MK | 4.107 | 1.567 | 2.622 | 0.009 | 0.680 |
| g | SR | 4.008 | 1.532 | 2.617 | 0.009 | 0.596 |
#Higher-order AFOQT model
AFOQTHOF.model <- '
Verbal =~ VA + RC + WK
Quant =~ AR + DI + MK + SR
g =~ Verbal + Quant'
AFOQTHOF.fit <- cfa(AFOQTHOF.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T)## Warning in lav_model_vcov(lavmodel = lavmodel2, lavsamplestats = lavsamplestats, : lavaan WARNING:
## Could not compute standard errors! The information matrix could
## not be inverted. This may be a symptom that the model is not
## identified.fitmeasures(AFOQTHOF.fit, FITS)## chisq df npar cfi rmsea
## 368.582 12.000 16.000 0.977 0.093
## rmsea.ci.lower rmsea.ci.upper bic2
## 0.085 0.101 132460.439parameterEstimates(AFOQTHOF.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| Verbal | VA | 1.821 | NA | NA | NA | 0.821 |
| Verbal | RC | 2.827 | NA | NA | NA | 0.909 |
| Verbal | WK | 2.534 | NA | NA | NA | 0.829 |
| Quant | AR | 2.052 | NA | NA | NA | 0.876 |
| Quant | DI | 1.635 | NA | NA | NA | 0.781 |
| Quant | MK | 2.556 | NA | NA | NA | 0.795 |
| Quant | SR | 2.708 | NA | NA | NA | 0.756 |
| g | Verbal | 1.624 | NA | NA | NA | 0.851 |
| g | Quant | 1.590 | NA | NA | NA | 0.846 |
This HOF model will be unidentified without more variables, but the fit is probably fine to compare.
#AFOQT model with two factors rather than g
AFOQTII.model <- '
Verbal =~ VA + RC + WK
Quant =~ AR + DI + MK + SR'
AFOQTII.fit <- cfa(AFOQTII.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = F)
fitmeasures(AFOQTII.fit, FITS)## chisq df npar cfi rmsea
## 368.582 13.000 15.000 0.977 0.089
## rmsea.ci.lower rmsea.ci.upper bic2
## 0.082 0.097 132455.477parameterEstimates(AFOQTII.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| Verbal | VA | 3.473 | 0.061 | 56.733 | 0 | 0.821 |
| Verbal | RC | 5.392 | 0.081 | 66.243 | 0 | 0.909 |
| Verbal | WK | 4.832 | 0.084 | 57.522 | 0 | 0.829 |
| Quant | AR | 3.853 | 0.062 | 62.364 | 0 | 0.876 |
| Quant | DI | 3.070 | 0.058 | 52.537 | 0 | 0.781 |
| Quant | MK | 4.801 | 0.089 | 53.881 | 0 | 0.795 |
| Quant | SR | 5.086 | 0.102 | 50.102 | 0 | 0.756 |
#Work knowledge model
WORK.model <- '
JKP =~ IC + AI
JKTI =~ A1 + A2 + A3 + A4
JKTII =~ A5 + A6 + A7 + A8
JKTIII =~ A9 + A10 + A11
WSI =~ CF1 + CF2 + CF3
WSII =~ CF4 + CF5 + CF6'
WORK.fit <- cfa(WORK.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = F)
fitmeasures(WORK.fit, FITS)## chisq df npar cfi rmsea
## 323.090 137.000 53.000 0.977 0.020
## rmsea.ci.lower rmsea.ci.upper bic2
## 0.017 0.023 371356.231parameterEstimates(WORK.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| JKP | IC | 3.750 | 0.119 | 31.406 | 0 | 0.788 |
| JKP | AI | 2.900 | 0.097 | 29.863 | 0 | 0.711 |
| JKTI | A1 | 1.618 | 0.062 | 26.161 | 0 | 0.507 |
| JKTI | A2 | 1.563 | 0.066 | 23.769 | 0 | 0.463 |
| JKTI | A3 | 1.504 | 0.067 | 22.609 | 0 | 0.441 |
| JKTI | A4 | 1.655 | 0.065 | 25.390 | 0 | 0.493 |
| JKTII | A5 | 2.521 | 0.093 | 27.036 | 0 | 0.516 |
| JKTII | A6 | 2.555 | 0.103 | 24.859 | 0 | 0.476 |
| JKTII | A7 | 2.534 | 0.104 | 24.362 | 0 | 0.467 |
| JKTII | A8 | 2.088 | 0.088 | 23.667 | 0 | 0.454 |
| JKTIII | A9 | 1.790 | 0.067 | 26.643 | 0 | 0.530 |
| JKTIII | A10 | 1.737 | 0.073 | 23.797 | 0 | 0.469 |
| JKTIII | A11 | 1.717 | 0.074 | 23.160 | 0 | 0.457 |
| WSI | CF1 | 3.877 | 0.156 | 24.789 | 0 | 0.510 |
| WSI | CF2 | 2.964 | 0.119 | 24.953 | 0 | 0.514 |
| WSI | CF3 | 2.639 | 0.102 | 25.954 | 0 | 0.535 |
| WSII | CF4 | 2.514 | 0.127 | 19.854 | 0 | 0.438 |
| WSII | CF5 | 1.895 | 0.102 | 18.520 | 0 | 0.404 |
| WSII | CF6 | 2.005 | 0.105 | 19.143 | 0 | 0.420 |
#Work HOF-g Model
WORKG.model <- '
JKP =~ IC + AI
JKTI =~ A1 + A2 + A3 + A4
JKTII =~ A5 + A6 + A7 + A8
JKTIII =~ A9 + A10 + A11
WSI =~ CF1 + CF2 + CF3
WSII =~ CF4 + CF5 + CF6
WG =~ JKP + JKTI + JKTII + JKTIII + WSI + WSII
WSI ~~ WSII'
WORKG.fit <- cfa(WORKG.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T)
fitmeasures(WORKG.fit, FITS)## chisq df npar cfi rmsea
## 413.589 145.000 45.000 0.968 0.023
## rmsea.ci.lower rmsea.ci.upper bic2
## 0.021 0.026 371407.033parameterEstimates(WORKG.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| JKP | IC | 3.315 | 0.120 | 27.655 | 0 | 0.765 |
| JKP | AI | 2.722 | 0.098 | 27.860 | 0 | 0.732 |
| JKTI | A1 | 0.707 | 0.071 | 9.894 | 0 | 0.505 |
| JKTI | A2 | 0.685 | 0.070 | 9.794 | 0 | 0.462 |
| JKTI | A3 | 0.664 | 0.068 | 9.734 | 0 | 0.444 |
| JKTI | A4 | 0.724 | 0.073 | 9.868 | 0 | 0.492 |
| JKTII | A5 | 0.715 | 0.163 | 4.375 | 0 | 0.514 |
| JKTII | A6 | 0.723 | 0.165 | 4.373 | 0 | 0.473 |
| JKTII | A7 | 0.726 | 0.166 | 4.372 | 0 | 0.470 |
| JKTII | A8 | 0.596 | 0.136 | 4.370 | 0 | 0.455 |
| JKTIII | A9 | 0.526 | 0.133 | 3.965 | 0 | 0.529 |
| JKTIII | A10 | 0.510 | 0.128 | 3.973 | 0 | 0.468 |
| JKTIII | A11 | 0.507 | 0.128 | 3.973 | 0 | 0.458 |
| WSI | CF1 | 3.226 | 0.146 | 22.080 | 0 | 0.507 |
| WSI | CF2 | 2.476 | 0.111 | 22.258 | 0 | 0.513 |
| WSI | CF3 | 2.228 | 0.097 | 23.044 | 0 | 0.540 |
| WSII | CF4 | 2.095 | 0.124 | 16.947 | 0 | 0.437 |
| WSII | CF5 | 1.586 | 0.098 | 16.185 | 0 | 0.404 |
| WSII | CF6 | 1.682 | 0.101 | 16.593 | 0 | 0.421 |
| WG | JKP | 0.452 | 0.028 | 16.397 | 0 | 0.412 |
| WG | JKTI | 2.050 | 0.223 | 9.194 | 0 | 0.899 |
| WG | JKTII | 3.368 | 0.802 | 4.202 | 0 | 0.959 |
| WG | JKTIII | 3.247 | 0.846 | 3.836 | 0 | 0.956 |
| WG | WSI | 0.653 | 0.040 | 16.178 | 0 | 0.547 |
| WG | WSII | 0.655 | 0.050 | 13.016 | 0 | 0.548 |
This model is far less parsimonious and fits worse. Fitting a few residual covariances, it becomes more parsimonious and just as well-fitting, but that’s not particularly interesting.
#Work BF-g Model
WORKGBF.model <- '
JKP =~ IC + AI
JKTI =~ A1 + A2 + A3 + A4
JKTII =~ A5 + A6 + A7 + A8
JKTIII =~ A9 + A10 + A11
WSI =~ CF1 + CF2 + CF3
WSII =~ CF4 + CF5 + CF6
WG =~ IC + AI + A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8 + A9 + A10 + A11 + CF1 + CF2 + CF3 + CF4 + CF5 + CF6'
WORKGBF.fit <- cfa(WORKGBF.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T)## Warning in lav_model_vcov(lavmodel = lavmodel2, lavsamplestats = lavsamplestats, : lavaan WARNING:
## Could not compute standard errors! The information matrix could
## not be inverted. This may be a symptom that the model is not
## identified.fitmeasures(WORKGBF.fit, FITS)## chisq df npar cfi rmsea
## 719.876 133.000 57.000 0.929 0.036
## rmsea.ci.lower rmsea.ci.upper bic2
## 0.033 0.038 371772.867parameterEstimates(WORKGBF.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| JKP | IC | 3.283 | NA | NA | NA | 0.690 |
| JKP | AI | 2.744 | NA | NA | NA | 0.673 |
| JKTI | A1 | 0.851 | NA | NA | NA | 0.267 |
| JKTI | A2 | 0.661 | NA | NA | NA | 0.196 |
| JKTI | A3 | 0.421 | NA | NA | NA | 0.124 |
| JKTI | A4 | 1.083 | NA | NA | NA | 0.322 |
| JKTII | A5 | 1.016 | NA | NA | NA | 0.208 |
| JKTII | A6 | 0.229 | NA | NA | NA | 0.043 |
| JKTII | A7 | 0.567 | NA | NA | NA | 0.104 |
| JKTII | A8 | 1.573 | NA | NA | NA | 0.342 |
| JKTIII | A9 | 0.234 | NA | NA | NA | 0.069 |
| JKTIII | A10 | 0.951 | NA | NA | NA | 0.257 |
| JKTIII | A11 | 0.699 | NA | NA | NA | 0.186 |
| WSI | CF1 | 2.854 | NA | NA | NA | 0.376 |
| WSI | CF2 | 2.561 | NA | NA | NA | 0.444 |
| WSI | CF3 | 2.036 | NA | NA | NA | 0.413 |
| WSII | CF4 | 2.074 | NA | NA | NA | 0.361 |
| WSII | CF5 | 1.669 | NA | NA | NA | 0.356 |
| WSII | CF6 | 1.244 | NA | NA | NA | 0.260 |
| WG | IC | 1.530 | NA | NA | NA | 0.321 |
| WG | AI | 1.217 | NA | NA | NA | 0.298 |
| WG | A1 | 1.402 | NA | NA | NA | 0.440 |
| WG | A2 | 1.377 | NA | NA | NA | 0.408 |
| WG | A3 | 1.384 | NA | NA | NA | 0.406 |
| WG | A4 | 1.423 | NA | NA | NA | 0.424 |
| WG | A5 | 2.358 | NA | NA | NA | 0.482 |
| WG | A6 | 2.483 | NA | NA | NA | 0.462 |
| WG | A7 | 2.425 | NA | NA | NA | 0.447 |
| WG | A8 | 1.902 | NA | NA | NA | 0.414 |
| WG | A9 | 1.693 | NA | NA | NA | 0.501 |
| WG | A10 | 1.641 | NA | NA | NA | 0.443 |
| WG | A11 | 1.629 | NA | NA | NA | 0.433 |
| WG | CF1 | 2.301 | NA | NA | NA | 0.303 |
| WG | CF2 | 1.777 | NA | NA | NA | 0.308 |
| WG | CF3 | 1.707 | NA | NA | NA | 0.346 |
| WG | CF4 | 1.606 | NA | NA | NA | 0.280 |
| WG | CF5 | 1.028 | NA | NA | NA | 0.219 |
| WG | CF6 | 1.468 | NA | NA | NA | 0.307 |
Clearly the model can’t be identified with the JKP factor.
WORKGBFII.model <- '
IC ~~ AI
JKTI =~ A1 + A2 + A3 + A4
JKTII =~ A5 + A6 + A7 + A8
JKTIII =~ A9 + A10 + A11
WSI =~ CF1 + CF2 + CF3
WSII =~ CF4 + CF5 + CF6
WG =~ IC + AI + A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8 + A9 + A10 + A11 + CF1 + CF2 + CF3 + CF4 + CF5 + CF6'
WORKGBFII.fit <- cfa(WORKGBFII.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T)
fitmeasures(WORKGBFII.fit, FITS)## chisq df npar cfi rmsea
## 719.876 134.000 56.000 0.929 0.036
## rmsea.ci.lower rmsea.ci.upper bic2
## 0.033 0.038 371767.904parameterEstimates(WORKGBFII.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| JKTI | A1 | 0.851 | 0.154 | 5.536 | 0.000 | 0.267 |
| JKTI | A2 | 0.661 | 0.136 | 4.858 | 0.000 | 0.196 |
| JKTI | A3 | 0.421 | 0.130 | 3.243 | 0.001 | 0.124 |
| JKTI | A4 | 1.083 | 0.187 | 5.778 | 0.000 | 0.322 |
| JKTII | A5 | 1.016 | 0.390 | 2.603 | 0.009 | 0.208 |
| JKTII | A6 | 0.229 | 0.225 | 1.017 | 0.309 | 0.043 |
| JKTII | A7 | 0.567 | 0.250 | 2.270 | 0.023 | 0.104 |
| JKTII | A8 | 1.573 | 0.581 | 2.708 | 0.007 | 0.342 |
| JKTIII | A9 | 0.234 | 0.180 | 1.300 | 0.193 | 0.069 |
| JKTIII | A10 | 0.951 | 0.645 | 1.475 | 0.140 | 0.257 |
| JKTIII | A11 | 0.699 | 0.483 | 1.446 | 0.148 | 0.186 |
| WSI | CF1 | 2.854 | 0.227 | 12.584 | 0.000 | 0.376 |
| WSI | CF2 | 2.561 | 0.193 | 13.274 | 0.000 | 0.444 |
| WSI | CF3 | 2.036 | 0.156 | 13.063 | 0.000 | 0.413 |
| WSII | CF4 | 2.074 | 0.268 | 7.729 | 0.000 | 0.361 |
| WSII | CF5 | 1.669 | 0.218 | 7.670 | 0.000 | 0.356 |
| WSII | CF6 | 1.244 | 0.171 | 7.285 | 0.000 | 0.260 |
| WG | IC | 1.530 | 0.092 | 16.714 | 0.000 | 0.321 |
| WG | AI | 1.217 | 0.079 | 15.440 | 0.000 | 0.298 |
| WG | A1 | 1.402 | 0.062 | 22.755 | 0.000 | 0.440 |
| WG | A2 | 1.377 | 0.066 | 20.956 | 0.000 | 0.408 |
| WG | A3 | 1.384 | 0.066 | 20.829 | 0.000 | 0.406 |
| WG | A4 | 1.423 | 0.065 | 21.826 | 0.000 | 0.424 |
| WG | A5 | 2.358 | 0.094 | 24.961 | 0.000 | 0.482 |
| WG | A6 | 2.483 | 0.104 | 23.940 | 0.000 | 0.462 |
| WG | A7 | 2.425 | 0.105 | 23.065 | 0.000 | 0.447 |
| WG | A8 | 1.902 | 0.091 | 20.919 | 0.000 | 0.414 |
| WG | A9 | 1.693 | 0.064 | 26.308 | 0.000 | 0.501 |
| WG | A10 | 1.641 | 0.072 | 22.889 | 0.000 | 0.443 |
| WG | A11 | 1.629 | 0.073 | 22.306 | 0.000 | 0.433 |
| WG | CF1 | 2.301 | 0.147 | 15.608 | 0.000 | 0.303 |
| WG | CF2 | 1.777 | 0.112 | 15.889 | 0.000 | 0.308 |
| WG | CF3 | 1.707 | 0.095 | 18.002 | 0.000 | 0.346 |
| WG | CF4 | 1.606 | 0.112 | 14.397 | 0.000 | 0.280 |
| WG | CF5 | 1.028 | 0.092 | 11.182 | 0.000 | 0.219 |
| WG | CF6 | 1.468 | 0.092 | 15.884 | 0.000 | 0.307 |
And many of the indicators no longer load on their respective factors, but it may be inappropriate to remove them, so one of the models below retains insignificant indicators.
WORKGBFIIINS.model <- '
IC ~~ AI
JKTI =~ A1 + A2 + A3 + A4
JKTII =~ A5 + A6 + A7 + A8
JKTIII =~ A9 + A10 + A11
WSI =~ CF1 + CF2 + CF3
WSII =~ CF4 + CF5 + CF6
WG =~ IC + AI + A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8 + A9 + A10 + A11 + CF1 + CF2 + CF3 + CF4 + CF5 + CF6
WSI ~~ WSII'
WORKGBFIII.model <- '
IC ~~ AI
JKTI =~ A1 + A2 + A3 + A4
JKTII =~ A5 + A7 + A8
WSI =~ CF1 + CF2 + CF3
WSII =~ CF4 + CF5 + CF6
WG =~ IC + AI + A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8 + A9 + A10 + A11 + CF1 + CF2 + CF3 + CF4 + CF5 + CF6
WSI ~~ WSII'
WORKGBFIIINS.fit <- cfa(WORKGBFIIINS.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T)
WORKGBFIII.fit <- cfa(WORKGBFIII.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T)
fitmeasures(WORKGBFIIINS.fit, FITS)## chisq df npar cfi rmsea
## 360.186 133.000 57.000 0.973 0.022
## rmsea.ci.lower rmsea.ci.upper bic2
## 0.020 0.025 371413.177fitmeasures(WORKGBFIII.fit, FITS)## chisq df npar cfi rmsea
## 370.262 137.000 53.000 0.972 0.022
## rmsea.ci.lower rmsea.ci.upper bic2
## 0.020 0.025 371403.404parameterEstimates(WORKGBFIIINS.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| JKTI | A1 | 0.773 | 0.170 | 4.546 | 0.000 | 0.243 |
| JKTI | A2 | 0.582 | 0.145 | 4.017 | 0.000 | 0.172 |
| JKTI | A3 | 0.329 | 0.138 | 2.389 | 0.017 | 0.096 |
| JKTI | A4 | 1.074 | 0.224 | 4.789 | 0.000 | 0.320 |
| JKTII | A5 | 0.956 | 0.466 | 2.052 | 0.040 | 0.196 |
| JKTII | A6 | 0.142 | 0.235 | 0.605 | 0.545 | 0.027 |
| JKTII | A7 | 0.479 | 0.265 | 1.808 | 0.071 | 0.088 |
| JKTII | A8 | 1.534 | 0.721 | 2.127 | 0.033 | 0.333 |
| JKTIII | A9 | 0.145 | 0.196 | 0.736 | 0.462 | 0.043 |
| JKTIII | A10 | 1.132 | 1.351 | 0.838 | 0.402 | 0.306 |
| JKTIII | A11 | 0.580 | 0.707 | 0.820 | 0.412 | 0.154 |
| WSI | CF1 | 3.384 | 0.186 | 18.166 | 0.000 | 0.445 |
| WSI | CF2 | 2.520 | 0.141 | 17.934 | 0.000 | 0.437 |
| WSI | CF3 | 2.100 | 0.118 | 17.743 | 0.000 | 0.426 |
| WSII | CF4 | 2.090 | 0.148 | 14.135 | 0.000 | 0.364 |
| WSII | CF5 | 1.889 | 0.126 | 14.965 | 0.000 | 0.403 |
| WSII | CF6 | 1.421 | 0.119 | 11.954 | 0.000 | 0.297 |
| WG | IC | 1.492 | 0.092 | 16.224 | 0.000 | 0.313 |
| WG | AI | 1.227 | 0.079 | 15.535 | 0.000 | 0.301 |
| WG | A1 | 1.436 | 0.062 | 23.157 | 0.000 | 0.450 |
| WG | A2 | 1.418 | 0.066 | 21.476 | 0.000 | 0.420 |
| WG | A3 | 1.422 | 0.067 | 21.275 | 0.000 | 0.417 |
| WG | A4 | 1.451 | 0.066 | 22.094 | 0.000 | 0.432 |
| WG | A5 | 2.379 | 0.095 | 25.032 | 0.000 | 0.487 |
| WG | A6 | 2.504 | 0.104 | 24.028 | 0.000 | 0.466 |
| WG | A7 | 2.459 | 0.106 | 23.288 | 0.000 | 0.453 |
| WG | A8 | 1.939 | 0.092 | 21.167 | 0.000 | 0.422 |
| WG | A9 | 1.733 | 0.065 | 26.815 | 0.000 | 0.513 |
| WG | A10 | 1.637 | 0.072 | 22.665 | 0.000 | 0.442 |
| WG | A11 | 1.638 | 0.074 | 22.274 | 0.000 | 0.436 |
| WG | CF1 | 1.998 | 0.149 | 13.426 | 0.000 | 0.263 |
| WG | CF2 | 1.578 | 0.113 | 13.989 | 0.000 | 0.273 |
| WG | CF3 | 1.538 | 0.096 | 16.064 | 0.000 | 0.312 |
| WG | CF4 | 1.376 | 0.113 | 12.203 | 0.000 | 0.240 |
| WG | CF5 | 0.817 | 0.093 | 8.791 | 0.000 | 0.174 |
| WG | CF6 | 1.308 | 0.093 | 13.998 | 0.000 | 0.274 |
parameterEstimates(WORKGBFIII.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| JKTI | A1 | 0.794 | 0.164 | 4.830 | 0.000 | 0.249 |
| JKTI | A2 | 0.600 | 0.141 | 4.249 | 0.000 | 0.178 |
| JKTI | A3 | 0.358 | 0.134 | 2.666 | 0.008 | 0.105 |
| JKTI | A4 | 1.083 | 0.213 | 5.075 | 0.000 | 0.322 |
| JKTII | A5 | 1.063 | 0.446 | 2.384 | 0.017 | 0.218 |
| JKTII | A7 | 0.533 | 0.251 | 2.121 | 0.034 | 0.098 |
| JKTII | A8 | 1.370 | 0.565 | 2.425 | 0.015 | 0.298 |
| WSI | CF1 | 3.382 | 0.186 | 18.177 | 0.000 | 0.445 |
| WSI | CF2 | 2.519 | 0.140 | 17.947 | 0.000 | 0.437 |
| WSI | CF3 | 2.103 | 0.118 | 17.778 | 0.000 | 0.427 |
| WSII | CF4 | 2.088 | 0.148 | 14.138 | 0.000 | 0.364 |
| WSII | CF5 | 1.891 | 0.126 | 14.985 | 0.000 | 0.403 |
| WSII | CF6 | 1.420 | 0.119 | 11.957 | 0.000 | 0.297 |
| WG | IC | 1.481 | 0.092 | 16.154 | 0.000 | 0.311 |
| WG | AI | 1.216 | 0.079 | 15.436 | 0.000 | 0.298 |
| WG | A1 | 1.427 | 0.062 | 23.196 | 0.000 | 0.447 |
| WG | A2 | 1.410 | 0.066 | 21.500 | 0.000 | 0.417 |
| WG | A3 | 1.410 | 0.066 | 21.244 | 0.000 | 0.413 |
| WG | A4 | 1.441 | 0.065 | 22.099 | 0.000 | 0.429 |
| WG | A5 | 2.371 | 0.093 | 25.487 | 0.000 | 0.485 |
| WG | A6 | 2.513 | 0.100 | 25.080 | 0.000 | 0.468 |
| WG | A7 | 2.448 | 0.104 | 23.447 | 0.000 | 0.451 |
| WG | A8 | 1.946 | 0.089 | 21.839 | 0.000 | 0.423 |
| WG | A9 | 1.743 | 0.062 | 27.963 | 0.000 | 0.516 |
| WG | A10 | 1.684 | 0.069 | 24.324 | 0.000 | 0.455 |
| WG | A11 | 1.680 | 0.070 | 23.836 | 0.000 | 0.447 |
| WG | CF1 | 2.001 | 0.148 | 13.491 | 0.000 | 0.263 |
| WG | CF2 | 1.580 | 0.112 | 14.055 | 0.000 | 0.274 |
| WG | CF3 | 1.533 | 0.095 | 16.070 | 0.000 | 0.311 |
| WG | CF4 | 1.379 | 0.112 | 12.270 | 0.000 | 0.240 |
| WG | CF5 | 0.814 | 0.093 | 8.794 | 0.000 | 0.174 |
| WG | CF6 | 1.310 | 0.093 | 14.070 | 0.000 | 0.274 |
It’ll be interesting to see to what degree these measures share a general dimension. I’ll check for a two-level higher-order, a three-level higher-order, and a bifactor model. There’s no conceptually clear mixed g/group factors model, but if someone suggests one, I’ll fit it.
#Fit the models
HOF.fit <- cfa(HOF.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T)
HOFREG.fit <- cfa(HOFREG.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T)
HOFRREG.fit <- cfa(HOFRREG.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T) #reversed regression
CHCHOF.fit <- cfa(CHCHOF.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T)## Warning in lav_model_vcov(lavmodel = lavmodel2, lavsamplestats = lavsamplestats, : lavaan WARNING:
## Could not compute standard errors! The information matrix could
## not be inverted. This may be a symptom that the model is not
## identified.BF.fit <- cfa(BF.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T)
BFREG.fit <- cfa(BFREG.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T)
BFRREG.fit <- cfa(BFRREG.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T) #reversed regression
CHCBF.fit <- cfa(CHCBF.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T)## Warning in lav_model_vcov(lavmodel = lavmodel2, lavsamplestats = lavsamplestats, : lavaan WARNING:
## Could not compute standard errors! The information matrix could
## not be inverted. This may be a symptom that the model is not
## identified.parameterEstimates(HOF.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| Verbal | VA | 2.298 | 0.060 | 38.513 | 0 | 0.822 |
| Verbal | RC | 3.568 | 0.088 | 40.571 | 0 | 0.910 |
| Verbal | WK | 3.191 | 0.082 | 38.702 | 0 | 0.828 |
| Quant | AR | 1.058 | 0.183 | 5.795 | 0 | 0.874 |
| Quant | DI | 0.848 | 0.146 | 5.792 | 0 | 0.784 |
| Quant | MK | 1.313 | 0.227 | 5.793 | 0 | 0.790 |
| Quant | SR | 1.410 | 0.243 | 5.789 | 0 | 0.761 |
| g | Verbal | 1.134 | 0.046 | 24.498 | 0 | 0.750 |
| g | Quant | 3.493 | 0.651 | 5.366 | 0 | 0.961 |
| JKP | IC | 3.235 | 0.104 | 31.228 | 0 | 0.801 |
| JKP | AI | 2.418 | 0.075 | 32.211 | 0 | 0.699 |
| JKTI | A1 | 0.686 | 0.070 | 9.776 | 0 | 0.512 |
| JKTI | A2 | 0.649 | 0.067 | 9.656 | 0 | 0.457 |
| JKTI | A3 | 0.627 | 0.065 | 9.595 | 0 | 0.438 |
| JKTI | A4 | 0.702 | 0.072 | 9.751 | 0 | 0.497 |
| JKTII | A5 | 1.193 | 0.100 | 11.937 | 0 | 0.517 |
| JKTII | A6 | 1.173 | 0.100 | 11.715 | 0 | 0.463 |
| JKTII | A7 | 1.212 | 0.103 | 11.768 | 0 | 0.473 |
| JKTII | A8 | 0.997 | 0.085 | 11.696 | 0 | 0.460 |
| JKTIII | A9 | 0.681 | 0.093 | 7.358 | 0 | 0.509 |
| JKTIII | A10 | 0.708 | 0.096 | 7.353 | 0 | 0.484 |
| JKTIII | A11 | 0.692 | 0.094 | 7.343 | 0 | 0.465 |
| WSI | CF1 | 2.964 | 0.149 | 19.824 | 0 | 0.480 |
| WSI | CF2 | 2.444 | 0.117 | 20.912 | 0 | 0.521 |
| WSI | CF3 | 2.234 | 0.103 | 21.594 | 0 | 0.558 |
| WSII | CF4 | 1.975 | 0.134 | 14.738 | 0 | 0.439 |
| WSII | CF5 | 1.336 | 0.101 | 13.276 | 0 | 0.363 |
| WSII | CF6 | 1.701 | 0.114 | 14.905 | 0 | 0.454 |
| WG | JKP | 0.624 | 0.031 | 20.275 | 0 | 0.530 |
| WG | JKTI | 2.159 | 0.233 | 9.249 | 0 | 0.907 |
| WG | JKTII | 1.870 | 0.167 | 11.198 | 0 | 0.882 |
| WG | JKTIII | 2.320 | 0.330 | 7.037 | 0 | 0.918 |
| WG | WSI | 0.718 | 0.042 | 17.162 | 0 | 0.583 |
| WG | WSII | 0.790 | 0.058 | 13.577 | 0 | 0.620 |
parameterEstimates(HOFREG.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| Verbal | VA | 2.298 | 0.060 | 38.513 | 0 | 0.822 |
| Verbal | RC | 3.568 | 0.088 | 40.571 | 0 | 0.910 |
| Verbal | WK | 3.191 | 0.082 | 38.702 | 0 | 0.828 |
| Quant | AR | 1.058 | 0.183 | 5.795 | 0 | 0.874 |
| Quant | DI | 0.848 | 0.146 | 5.792 | 0 | 0.784 |
| Quant | MK | 1.313 | 0.227 | 5.793 | 0 | 0.790 |
| Quant | SR | 1.410 | 0.243 | 5.789 | 0 | 0.761 |
| g | Verbal | 1.134 | 0.046 | 24.498 | 0 | 0.750 |
| g | Quant | 3.493 | 0.651 | 5.366 | 0 | 0.961 |
| JKP | IC | 3.235 | 0.104 | 31.228 | 0 | 0.801 |
| JKP | AI | 2.418 | 0.075 | 32.211 | 0 | 0.699 |
| JKTI | A1 | 0.686 | 0.070 | 9.776 | 0 | 0.512 |
| JKTI | A2 | 0.649 | 0.067 | 9.656 | 0 | 0.457 |
| JKTI | A3 | 0.627 | 0.065 | 9.595 | 0 | 0.438 |
| JKTI | A4 | 0.702 | 0.072 | 9.751 | 0 | 0.497 |
| JKTII | A5 | 1.193 | 0.100 | 11.937 | 0 | 0.517 |
| JKTII | A6 | 1.173 | 0.100 | 11.716 | 0 | 0.463 |
| JKTII | A7 | 1.212 | 0.103 | 11.768 | 0 | 0.473 |
| JKTII | A8 | 0.997 | 0.085 | 11.696 | 0 | 0.460 |
| JKTIII | A9 | 0.681 | 0.093 | 7.358 | 0 | 0.509 |
| JKTIII | A10 | 0.708 | 0.096 | 7.353 | 0 | 0.484 |
| JKTIII | A11 | 0.692 | 0.094 | 7.342 | 0 | 0.465 |
| WSI | CF1 | 2.964 | 0.149 | 19.824 | 0 | 0.480 |
| WSI | CF2 | 2.444 | 0.117 | 20.912 | 0 | 0.521 |
| WSI | CF3 | 2.234 | 0.103 | 21.594 | 0 | 0.558 |
| WSII | CF4 | 1.975 | 0.134 | 14.738 | 0 | 0.439 |
| WSII | CF5 | 1.336 | 0.101 | 13.276 | 0 | 0.363 |
| WSII | CF6 | 1.701 | 0.114 | 14.905 | 0 | 0.454 |
| WG | JKP | 0.464 | 0.024 | 19.277 | 0 | 0.530 |
| WG | JKTI | 1.606 | 0.177 | 9.072 | 0 | 0.907 |
| WG | JKTII | 1.391 | 0.127 | 10.928 | 0 | 0.882 |
| WG | JKTIII | 1.725 | 0.248 | 6.958 | 0 | 0.918 |
| WG | WSI | 0.534 | 0.032 | 16.539 | 0 | 0.583 |
| WG | WSII | 0.588 | 0.044 | 13.260 | 0 | 0.620 |
parameterEstimates(HOFRREG.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| Verbal | VA | 2.298 | 0.060 | 38.514 | 0 | 0.822 |
| Verbal | RC | 3.568 | 0.088 | 40.572 | 0 | 0.910 |
| Verbal | WK | 3.191 | 0.082 | 38.702 | 0 | 0.828 |
| Quant | AR | 1.058 | 0.183 | 5.795 | 0 | 0.874 |
| Quant | DI | 0.848 | 0.146 | 5.792 | 0 | 0.784 |
| Quant | MK | 1.313 | 0.227 | 5.792 | 0 | 0.790 |
| Quant | SR | 1.410 | 0.243 | 5.789 | 0 | 0.761 |
| g | Verbal | 0.843 | 0.033 | 25.517 | 0 | 0.750 |
| g | Quant | 2.598 | 0.504 | 5.154 | 0 | 0.961 |
| JKP | IC | 3.235 | 0.104 | 31.228 | 0 | 0.801 |
| JKP | AI | 2.418 | 0.075 | 32.211 | 0 | 0.699 |
| JKTI | A1 | 0.686 | 0.070 | 9.776 | 0 | 0.512 |
| JKTI | A2 | 0.649 | 0.067 | 9.656 | 0 | 0.457 |
| JKTI | A3 | 0.627 | 0.065 | 9.595 | 0 | 0.438 |
| JKTI | A4 | 0.702 | 0.072 | 9.751 | 0 | 0.497 |
| JKTII | A5 | 1.193 | 0.100 | 11.937 | 0 | 0.517 |
| JKTII | A6 | 1.173 | 0.100 | 11.715 | 0 | 0.463 |
| JKTII | A7 | 1.212 | 0.103 | 11.768 | 0 | 0.473 |
| JKTII | A8 | 0.997 | 0.085 | 11.696 | 0 | 0.460 |
| JKTIII | A9 | 0.681 | 0.093 | 7.358 | 0 | 0.509 |
| JKTIII | A10 | 0.708 | 0.096 | 7.353 | 0 | 0.484 |
| JKTIII | A11 | 0.692 | 0.094 | 7.342 | 0 | 0.465 |
| WSI | CF1 | 2.964 | 0.149 | 19.824 | 0 | 0.480 |
| WSI | CF2 | 2.444 | 0.117 | 20.912 | 0 | 0.521 |
| WSI | CF3 | 2.234 | 0.103 | 21.594 | 0 | 0.558 |
| WSII | CF4 | 1.975 | 0.134 | 14.738 | 0 | 0.439 |
| WSII | CF5 | 1.336 | 0.101 | 13.276 | 0 | 0.363 |
| WSII | CF6 | 1.701 | 0.114 | 14.905 | 0 | 0.454 |
| WG | JKP | 0.624 | 0.031 | 20.275 | 0 | 0.530 |
| WG | JKTI | 2.159 | 0.233 | 9.249 | 0 | 0.907 |
| WG | JKTII | 1.870 | 0.167 | 11.198 | 0 | 0.882 |
| WG | JKTIII | 2.320 | 0.330 | 7.037 | 0 | 0.918 |
| WG | WSI | 0.718 | 0.042 | 17.162 | 0 | 0.583 |
| WG | WSII | 0.790 | 0.058 | 13.577 | 0 | 0.620 |
parameterEstimates(CHCHOF.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| Verbal | VA | 2.298 | NA | NA | NA | 0.822 |
| Verbal | RC | 3.568 | NA | NA | NA | 0.910 |
| Verbal | WK | 3.191 | NA | NA | NA | 0.828 |
| Quant | AR | 1.058 | NA | NA | NA | 0.874 |
| Quant | DI | 0.848 | NA | NA | NA | 0.784 |
| Quant | MK | 1.313 | NA | NA | NA | 0.790 |
| Quant | SR | 1.410 | NA | NA | NA | 0.761 |
| g | Verbal | 0.643 | NA | NA | NA | 0.750 |
| g | Quant | 1.982 | NA | NA | NA | 0.961 |
| JKP | IC | 3.235 | NA | NA | NA | 0.801 |
| JKP | AI | 2.418 | NA | NA | NA | 0.699 |
| JKTI | A1 | 0.686 | NA | NA | NA | 0.512 |
| JKTI | A2 | 0.649 | NA | NA | NA | 0.457 |
| JKTI | A3 | 0.627 | NA | NA | NA | 0.438 |
| JKTI | A4 | 0.702 | NA | NA | NA | 0.497 |
| JKTII | A5 | 1.193 | NA | NA | NA | 0.517 |
| JKTII | A6 | 1.173 | NA | NA | NA | 0.463 |
| JKTII | A7 | 1.212 | NA | NA | NA | 0.473 |
| JKTII | A8 | 0.997 | NA | NA | NA | 0.460 |
| JKTIII | A9 | 0.681 | NA | NA | NA | 0.509 |
| JKTIII | A10 | 0.708 | NA | NA | NA | 0.484 |
| JKTIII | A11 | 0.692 | NA | NA | NA | 0.465 |
| WSI | CF1 | 2.964 | NA | NA | NA | 0.480 |
| WSI | CF2 | 2.444 | NA | NA | NA | 0.521 |
| WSI | CF3 | 2.234 | NA | NA | NA | 0.558 |
| WSII | CF4 | 1.975 | NA | NA | NA | 0.439 |
| WSII | CF5 | 1.336 | NA | NA | NA | 0.363 |
| WSII | CF6 | 1.701 | NA | NA | NA | 0.454 |
| WG | JKP | 0.365 | NA | NA | NA | 0.530 |
| WG | JKTI | 1.261 | NA | NA | NA | 0.907 |
| WG | JKTII | 1.092 | NA | NA | NA | 0.882 |
| WG | JKTIII | 1.355 | NA | NA | NA | 0.918 |
| WG | WSI | 0.419 | NA | NA | NA | 0.583 |
| WG | WSII | 0.462 | NA | NA | NA | 0.620 |
| GHI | g | 1.452 | NA | NA | NA | 0.824 |
| GHI | WG | 1.390 | NA | NA | NA | 0.812 |
parameterEstimates(BF.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| Verbal | VA | 2.014 | 0.059 | 34.030 | 0.000 | 0.476 |
| Verbal | RC | 3.638 | 0.082 | 44.248 | 0.000 | 0.614 |
| Verbal | WK | 4.010 | 0.087 | 45.879 | 0.000 | 0.688 |
| Quant | AR | 0.703 | 0.196 | 3.593 | 0.000 | 0.160 |
| Quant | DI | -1.000 | 0.430 | -2.327 | 0.020 | -0.254 |
| Quant | MK | 0.964 | 0.256 | 3.760 | 0.000 | 0.160 |
| Quant | SR | 0.005 | 0.190 | 0.027 | 0.978 | 0.001 |
| g | VA | 2.816 | 0.067 | 41.819 | 0.000 | 0.666 |
| g | RC | 3.898 | 0.095 | 41.149 | 0.000 | 0.657 |
| g | WK | 3.084 | 0.097 | 31.680 | 0.000 | 0.529 |
| g | AR | 3.834 | 0.068 | 56.611 | 0.000 | 0.871 |
| g | DI | 3.205 | 0.065 | 49.593 | 0.000 | 0.816 |
| g | MK | 4.744 | 0.099 | 47.968 | 0.000 | 0.785 |
| g | SR | 5.090 | 0.103 | 49.291 | 0.000 | 0.756 |
| JKTI | A1 | 0.726 | 0.163 | 4.460 | 0.000 | 0.227 |
| JKTI | A2 | 0.610 | 0.150 | 4.057 | 0.000 | 0.180 |
| JKTI | A3 | 0.357 | 0.140 | 2.556 | 0.011 | 0.105 |
| JKTI | A4 | 1.004 | 0.213 | 4.706 | 0.000 | 0.299 |
| JKTII | A5 | 1.397 | 0.253 | 5.532 | 0.000 | 0.286 |
| JKTII | A6 | 0.718 | 0.197 | 3.638 | 0.000 | 0.134 |
| JKTII | A7 | 0.866 | 0.203 | 4.276 | 0.000 | 0.159 |
| JKTII | A8 | 1.509 | 0.269 | 5.617 | 0.000 | 0.328 |
| JKTIII | A9 | 0.451 | 0.170 | 2.658 | 0.008 | 0.134 |
| JKTIII | A10 | 0.892 | 0.313 | 2.849 | 0.004 | 0.241 |
| JKTIII | A11 | 0.809 | 0.287 | 2.813 | 0.005 | 0.215 |
| WSI | CF1 | 2.981 | 0.223 | 13.354 | 0.000 | 0.392 |
| WSI | CF2 | 2.600 | 0.186 | 13.993 | 0.000 | 0.451 |
| WSI | CF3 | 2.084 | 0.151 | 13.793 | 0.000 | 0.423 |
| WSII | CF4 | 2.104 | 0.260 | 8.091 | 0.000 | 0.367 |
| WSII | CF5 | 1.712 | 0.213 | 8.042 | 0.000 | 0.365 |
| WSII | CF6 | 1.279 | 0.167 | 7.636 | 0.000 | 0.268 |
| WG | IC | 2.012 | 0.088 | 22.846 | 0.000 | 0.423 |
| WG | AI | 1.493 | 0.077 | 19.496 | 0.000 | 0.366 |
| WG | A1 | 1.469 | 0.060 | 24.613 | 0.000 | 0.461 |
| WG | A2 | 1.396 | 0.064 | 21.804 | 0.000 | 0.413 |
| WG | A3 | 1.392 | 0.065 | 21.495 | 0.000 | 0.408 |
| WG | A4 | 1.485 | 0.063 | 23.480 | 0.000 | 0.442 |
| WG | A5 | 2.211 | 0.092 | 24.147 | 0.000 | 0.452 |
| WG | A6 | 2.272 | 0.101 | 22.445 | 0.000 | 0.423 |
| WG | A7 | 2.325 | 0.102 | 22.763 | 0.000 | 0.428 |
| WG | A8 | 1.797 | 0.088 | 20.514 | 0.000 | 0.391 |
| WG | A9 | 1.593 | 0.063 | 25.381 | 0.000 | 0.471 |
| WG | A10 | 1.630 | 0.069 | 23.508 | 0.000 | 0.441 |
| WG | A11 | 1.605 | 0.071 | 22.684 | 0.000 | 0.427 |
| WG | CF1 | 2.133 | 0.145 | 14.724 | 0.000 | 0.281 |
| WG | CF2 | 1.710 | 0.110 | 15.594 | 0.000 | 0.296 |
| WG | CF3 | 1.654 | 0.093 | 17.784 | 0.000 | 0.336 |
| WG | CF4 | 1.559 | 0.109 | 14.247 | 0.000 | 0.272 |
| WG | CF5 | 0.970 | 0.090 | 10.745 | 0.000 | 0.207 |
| WG | CF6 | 1.441 | 0.091 | 15.896 | 0.000 | 0.302 |
parameterEstimates(BFREG.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| Verbal | VA | 2.014 | 0.059 | 34.031 | 0.000 | 0.476 |
| Verbal | RC | 3.638 | 0.082 | 44.248 | 0.000 | 0.614 |
| Verbal | WK | 4.010 | 0.087 | 45.879 | 0.000 | 0.688 |
| Quant | AR | 0.703 | 0.196 | 3.592 | 0.000 | 0.160 |
| Quant | DI | -1.000 | 0.430 | -2.327 | 0.020 | -0.255 |
| Quant | MK | 0.964 | 0.256 | 3.760 | 0.000 | 0.160 |
| Quant | SR | 0.005 | 0.190 | 0.027 | 0.978 | 0.001 |
| g | VA | 2.816 | 0.067 | 41.819 | 0.000 | 0.666 |
| g | RC | 3.898 | 0.095 | 41.149 | 0.000 | 0.657 |
| g | WK | 3.084 | 0.097 | 31.680 | 0.000 | 0.529 |
| g | AR | 3.834 | 0.068 | 56.612 | 0.000 | 0.871 |
| g | DI | 3.205 | 0.065 | 49.593 | 0.000 | 0.816 |
| g | MK | 4.744 | 0.099 | 47.969 | 0.000 | 0.786 |
| g | SR | 5.090 | 0.103 | 49.291 | 0.000 | 0.756 |
| JKTI | A1 | 0.726 | 0.163 | 4.459 | 0.000 | 0.227 |
| JKTI | A2 | 0.610 | 0.150 | 4.057 | 0.000 | 0.180 |
| JKTI | A3 | 0.357 | 0.140 | 2.556 | 0.011 | 0.105 |
| JKTI | A4 | 1.004 | 0.213 | 4.706 | 0.000 | 0.299 |
| JKTII | A5 | 1.397 | 0.253 | 5.532 | 0.000 | 0.286 |
| JKTII | A6 | 0.718 | 0.197 | 3.638 | 0.000 | 0.134 |
| JKTII | A7 | 0.866 | 0.203 | 4.276 | 0.000 | 0.159 |
| JKTII | A8 | 1.509 | 0.269 | 5.618 | 0.000 | 0.328 |
| JKTIII | A9 | 0.451 | 0.170 | 2.658 | 0.008 | 0.134 |
| JKTIII | A10 | 0.892 | 0.313 | 2.849 | 0.004 | 0.241 |
| JKTIII | A11 | 0.808 | 0.287 | 2.813 | 0.005 | 0.215 |
| WSI | CF1 | 2.981 | 0.223 | 13.354 | 0.000 | 0.392 |
| WSI | CF2 | 2.600 | 0.186 | 13.993 | 0.000 | 0.451 |
| WSI | CF3 | 2.084 | 0.151 | 13.793 | 0.000 | 0.423 |
| WSII | CF4 | 2.104 | 0.260 | 8.090 | 0.000 | 0.367 |
| WSII | CF5 | 1.712 | 0.213 | 8.042 | 0.000 | 0.365 |
| WSII | CF6 | 1.279 | 0.167 | 7.636 | 0.000 | 0.268 |
| WG | IC | 1.538 | 0.070 | 22.015 | 0.000 | 0.423 |
| WG | AI | 1.141 | 0.060 | 18.972 | 0.000 | 0.366 |
| WG | A1 | 1.123 | 0.048 | 23.495 | 0.000 | 0.461 |
| WG | A2 | 1.068 | 0.051 | 21.016 | 0.000 | 0.413 |
| WG | A3 | 1.064 | 0.051 | 20.740 | 0.000 | 0.408 |
| WG | A4 | 1.136 | 0.050 | 22.503 | 0.000 | 0.442 |
| WG | A5 | 1.691 | 0.073 | 23.099 | 0.000 | 0.452 |
| WG | A6 | 1.737 | 0.080 | 21.600 | 0.000 | 0.423 |
| WG | A7 | 1.778 | 0.081 | 21.883 | 0.000 | 0.428 |
| WG | A8 | 1.374 | 0.069 | 19.859 | 0.000 | 0.391 |
| WG | A9 | 1.218 | 0.050 | 24.188 | 0.000 | 0.471 |
| WG | A10 | 1.246 | 0.055 | 22.551 | 0.000 | 0.441 |
| WG | A11 | 1.227 | 0.056 | 21.820 | 0.000 | 0.427 |
| WG | CF1 | 1.631 | 0.113 | 14.495 | 0.000 | 0.281 |
| WG | CF2 | 1.308 | 0.085 | 15.323 | 0.000 | 0.296 |
| WG | CF3 | 1.265 | 0.073 | 17.384 | 0.000 | 0.336 |
| WG | CF4 | 1.192 | 0.085 | 14.040 | 0.000 | 0.272 |
| WG | CF5 | 0.741 | 0.070 | 10.655 | 0.000 | 0.207 |
| WG | CF6 | 1.102 | 0.071 | 15.610 | 0.000 | 0.302 |
parameterEstimates(BFRREG.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| Verbal | VA | 2.014 | 0.059 | 34.030 | 0.000 | 0.476 |
| Verbal | RC | 3.638 | 0.082 | 44.248 | 0.000 | 0.614 |
| Verbal | WK | 4.010 | 0.087 | 45.879 | 0.000 | 0.688 |
| Quant | AR | 0.703 | 0.196 | 3.593 | 0.000 | 0.160 |
| Quant | DI | -1.000 | 0.430 | -2.327 | 0.020 | -0.254 |
| Quant | MK | 0.964 | 0.256 | 3.760 | 0.000 | 0.160 |
| Quant | SR | 0.005 | 0.190 | 0.027 | 0.978 | 0.001 |
| g | VA | 2.153 | 0.056 | 38.516 | 0.000 | 0.666 |
| g | RC | 2.980 | 0.078 | 37.991 | 0.000 | 0.657 |
| g | WK | 2.358 | 0.078 | 30.169 | 0.000 | 0.529 |
| g | AR | 2.931 | 0.064 | 45.887 | 0.000 | 0.871 |
| g | DI | 2.450 | 0.058 | 42.032 | 0.000 | 0.816 |
| g | MK | 3.627 | 0.089 | 40.902 | 0.000 | 0.785 |
| g | SR | 3.892 | 0.088 | 44.157 | 0.000 | 0.756 |
| JKTI | A1 | 0.726 | 0.163 | 4.460 | 0.000 | 0.228 |
| JKTI | A2 | 0.610 | 0.150 | 4.057 | 0.000 | 0.180 |
| JKTI | A3 | 0.357 | 0.140 | 2.556 | 0.011 | 0.105 |
| JKTI | A4 | 1.004 | 0.213 | 4.706 | 0.000 | 0.299 |
| JKTII | A5 | 1.397 | 0.253 | 5.532 | 0.000 | 0.286 |
| JKTII | A6 | 0.718 | 0.197 | 3.638 | 0.000 | 0.134 |
| JKTII | A7 | 0.866 | 0.203 | 4.275 | 0.000 | 0.159 |
| JKTII | A8 | 1.509 | 0.269 | 5.617 | 0.000 | 0.328 |
| JKTIII | A9 | 0.451 | 0.170 | 2.658 | 0.008 | 0.134 |
| JKTIII | A10 | 0.892 | 0.313 | 2.849 | 0.004 | 0.241 |
| JKTIII | A11 | 0.809 | 0.287 | 2.813 | 0.005 | 0.215 |
| WSI | CF1 | 2.981 | 0.223 | 13.354 | 0.000 | 0.392 |
| WSI | CF2 | 2.600 | 0.186 | 13.993 | 0.000 | 0.451 |
| WSI | CF3 | 2.084 | 0.151 | 13.793 | 0.000 | 0.423 |
| WSII | CF4 | 2.104 | 0.260 | 8.091 | 0.000 | 0.367 |
| WSII | CF5 | 1.712 | 0.213 | 8.043 | 0.000 | 0.365 |
| WSII | CF6 | 1.279 | 0.167 | 7.636 | 0.000 | 0.268 |
| WG | IC | 2.012 | 0.088 | 22.846 | 0.000 | 0.423 |
| WG | AI | 1.493 | 0.077 | 19.496 | 0.000 | 0.366 |
| WG | A1 | 1.469 | 0.060 | 24.613 | 0.000 | 0.461 |
| WG | A2 | 1.396 | 0.064 | 21.804 | 0.000 | 0.413 |
| WG | A3 | 1.392 | 0.065 | 21.495 | 0.000 | 0.408 |
| WG | A4 | 1.485 | 0.063 | 23.480 | 0.000 | 0.442 |
| WG | A5 | 2.211 | 0.092 | 24.147 | 0.000 | 0.452 |
| WG | A6 | 2.272 | 0.101 | 22.445 | 0.000 | 0.423 |
| WG | A7 | 2.325 | 0.102 | 22.763 | 0.000 | 0.428 |
| WG | A8 | 1.797 | 0.088 | 20.514 | 0.000 | 0.391 |
| WG | A9 | 1.593 | 0.063 | 25.381 | 0.000 | 0.471 |
| WG | A10 | 1.630 | 0.069 | 23.508 | 0.000 | 0.441 |
| WG | A11 | 1.605 | 0.071 | 22.684 | 0.000 | 0.427 |
| WG | CF1 | 2.133 | 0.145 | 14.724 | 0.000 | 0.281 |
| WG | CF2 | 1.710 | 0.110 | 15.594 | 0.000 | 0.296 |
| WG | CF3 | 1.654 | 0.093 | 17.783 | 0.000 | 0.336 |
| WG | CF4 | 1.559 | 0.109 | 14.247 | 0.000 | 0.272 |
| WG | CF5 | 0.970 | 0.090 | 10.745 | 0.000 | 0.207 |
| WG | CF6 | 1.441 | 0.091 | 15.896 | 0.000 | 0.302 |
parameterEstimates(CHCBF.fit, stand = T) %>%
filter(op == "=~") %>% select('Latent Factor' = lhs, Indicator = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Factor Loadings")| Latent Factor | Indicator | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| Verbal | VA | 2.014 | NA | NA | NA | 0.476 |
| Verbal | RC | 3.638 | NA | NA | NA | 0.614 |
| Verbal | WK | 4.010 | NA | NA | NA | 0.688 |
| Quant | AR | 0.703 | NA | NA | NA | 0.160 |
| Quant | DI | -1.000 | NA | NA | NA | -0.254 |
| Quant | MK | 0.964 | NA | NA | NA | 0.160 |
| Quant | SR | 0.005 | NA | NA | NA | 0.001 |
| g | VA | 1.056 | NA | NA | NA | 0.666 |
| g | RC | 1.461 | NA | NA | NA | 0.657 |
| g | WK | 1.156 | NA | NA | NA | 0.529 |
| g | AR | 1.437 | NA | NA | NA | 0.871 |
| g | DI | 1.201 | NA | NA | NA | 0.816 |
| g | MK | 1.778 | NA | NA | NA | 0.785 |
| g | SR | 1.908 | NA | NA | NA | 0.756 |
| JKTI | A1 | 0.726 | NA | NA | NA | 0.228 |
| JKTI | A2 | 0.610 | NA | NA | NA | 0.180 |
| JKTI | A3 | 0.357 | NA | NA | NA | 0.105 |
| JKTI | A4 | 1.004 | NA | NA | NA | 0.299 |
| JKTII | A5 | 1.397 | NA | NA | NA | 0.286 |
| JKTII | A6 | 0.718 | NA | NA | NA | 0.134 |
| JKTII | A7 | 0.866 | NA | NA | NA | 0.159 |
| JKTII | A8 | 1.510 | NA | NA | NA | 0.328 |
| JKTIII | A9 | 0.451 | NA | NA | NA | 0.134 |
| JKTIII | A10 | 0.892 | NA | NA | NA | 0.241 |
| JKTIII | A11 | 0.809 | NA | NA | NA | 0.215 |
| WSI | CF1 | 2.981 | NA | NA | NA | 0.392 |
| WSI | CF2 | 2.600 | NA | NA | NA | 0.451 |
| WSI | CF3 | 2.084 | NA | NA | NA | 0.423 |
| WSII | CF4 | 2.104 | NA | NA | NA | 0.367 |
| WSII | CF5 | 1.712 | NA | NA | NA | 0.365 |
| WSII | CF6 | 1.279 | NA | NA | NA | 0.268 |
| WG | IC | 1.446 | NA | NA | NA | 0.423 |
| WG | AI | 1.073 | NA | NA | NA | 0.366 |
| WG | A1 | 1.056 | NA | NA | NA | 0.461 |
| WG | A2 | 1.004 | NA | NA | NA | 0.413 |
| WG | A3 | 1.001 | NA | NA | NA | 0.408 |
| WG | A4 | 1.068 | NA | NA | NA | 0.442 |
| WG | A5 | 1.589 | NA | NA | NA | 0.452 |
| WG | A6 | 1.633 | NA | NA | NA | 0.423 |
| WG | A7 | 1.671 | NA | NA | NA | 0.428 |
| WG | A8 | 1.292 | NA | NA | NA | 0.391 |
| WG | A9 | 1.145 | NA | NA | NA | 0.471 |
| WG | A10 | 1.172 | NA | NA | NA | 0.441 |
| WG | A11 | 1.153 | NA | NA | NA | 0.427 |
| WG | CF1 | 1.533 | NA | NA | NA | 0.281 |
| WG | CF2 | 1.229 | NA | NA | NA | 0.296 |
| WG | CF3 | 1.189 | NA | NA | NA | 0.336 |
| WG | CF4 | 1.120 | NA | NA | NA | 0.272 |
| WG | CF5 | 0.697 | NA | NA | NA | 0.207 |
| WG | CF6 | 1.036 | NA | NA | NA | 0.302 |
| GHI | g | 2.473 | NA | NA | NA | 0.927 |
| GHI | WG | 0.967 | NA | NA | NA | 0.695 |
round(cbind(HOF = fitMeasures(HOF.fit, FITS),
HOFREG = fitMeasures(HOFREG.fit, FITS),
HOFRREG = fitMeasures(HOFRREG.fit, FITS),
CHCHOF = fitMeasures(CHCHOF.fit, FITS),
BF = fitMeasures(BF.fit, FITS),
BFREG = fitMeasures(BFREG.fit, FITS),
BFRREG = fitMeasures(BFRREG.fit, FITS),
CHCBF = fitMeasures(CHCBF.fit, FITS)),3)## HOF HOFREG HOFRREG CHCHOF BF
## chisq 2452.119 2452.119 2452.119 2452.119 2132.810
## df 290.000 290.000 290.000 289.000 273.000
## npar 61.000 61.000 61.000 62.000 78.000
## cfi 0.916 0.916 0.916 0.916 0.928
## rmsea 0.047 0.047 0.047 0.047 0.045
## rmsea.ci.lower 0.045 0.045 0.045 0.045 0.043
## rmsea.ci.upper 0.048 0.048 0.048 0.048 0.046
## bic2 503137.423 503137.423 503137.423 503142.386 502902.473
## BFREG BFRREG CHCBF
## chisq 2132.810 2132.810 2132.810
## df 273.000 273.000 272.000
## npar 78.000 78.000 79.000
## cfi 0.928 0.928 0.928
## rmsea 0.045 0.045 0.045
## rmsea.ci.lower 0.043 0.043 0.043
## rmsea.ci.upper 0.046 0.046 0.046
## bic2 502902.473 502902.473 502907.435#Plots
semPaths(HOF.fit, "model", "std", title = F, residuals = F, groups = "AFLATS", pastel = T, mar = c(2, 1, 3, 1), layout = "tree2", exoVar = F, exoCov = T)
semPaths(HOFREG.fit, "model", "std", title = F, residuals = F, groups = "AFLATS", pastel = T, mar = c(2, 1, 3, 1), layout = "tree3", exoVar = F, exoCov = F)
semPaths(HOFRREG.fit, "model", "std", title = F, residuals = F, groups = "AFLATS", pastel = T, mar = c(2, 1, 3, 1), layout = "tree", exoVar = F, exoCov = F)
semPaths(CHCHOF.fit, "model", "std", title = F, residuals = F, groups = "AFLATS", pastel = T, mar = c(2, 1, 3, 1), layout = "tree2", exoVar = F, exoCov = F)
#semPaths(BF.fit, "model", "std", title = F, residuals = F, groups = "AFLATS", pastel = T, mar = c(2, 1, 3, 1), layout = "tree3", exoVar = F, exoCov = F, bifactor = c("g", "WG")) #r between g's = 0.64, ~identical parameters as other BF models
suppressWarnings(semPaths(BFREG.fit, "model", "std", title = F, residuals = F, groups = "AFLATS", pastel = T, mar = c(2, 1, 3, 1), layout = "tree2", exoVar = F, exoCov = F, bifactor = c("g", "WG")))
suppressWarnings(semPaths(BFRREG.fit, "model", "std", title = F, residuals = F, groups = "AFLATS", pastel = T, mar = c(2, 1, 3, 1), layout = "circle2", exoVar = F, exoCov = F, bifactor = c("g", "WG")))
suppressWarnings(semPaths(CHCBF.fit, "model", "std", title = F, residuals = F, groups = "AFLATS", pastel = T, mar = c(2, 1, 3, 1), layout = "tree3", exoVar = F, exoCov = F, bifactor = c("g", "WG", "GHI")))
suppressWarnings(semPaths(CHCBF.fit, "model", "std", title = F, residuals = F, groups = "AFLATS", pastel = T, mar = c(2, 1, 3, 1), layout = "circle3", exoVar = F, exoCov = F, bifactor = c("g", "WG", "GHI")))
Mediation Models
#Mediation models
MEDMI.model <- '
Verbal =~ VA + RC + WK
Quant =~ AR + DI + MK + SR
g =~ Verbal + Quant
JKP =~ IC + AI
JKTI =~ A1 + A2 + A3 + A4
JKTII =~ A5 + A6 + A7 + A8
JKTIII =~ A9 + A10 + A11
WSI =~ CF1 + CF2 + CF3
WSII =~ CF4 + CF5 + CF6
JKP ~ g
JKTI ~ g + JKP
JKTII ~ g + JKTI
JKTIII ~ g+ JKTII
WSI ~ g + JKP + JKTII
WSII ~ g + WSI + JKTIII'
MEDMI.fit <- sem(MEDMI.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T, check.gradient = F, control=list(rel.tol=1e-4))
MEDMII.model <- '
Verbal =~ VA + RC + WK
Quant =~ AR + DI + MK + SR
g =~ Verbal + Quant
JKP =~ IC + AI
JKTI =~ A1 + A2 + A3 + A4
JKTII =~ A5 + A6 + A7 + A8
JKTIII =~ A9 + A10 + A11
WSI =~ CF1 + CF2 + CF3
WSII =~ CF4 + CF5 + CF6
JKP ~ g
JKTI ~ g + JKP
JKTII ~ g + JKTI
JKTIII ~ g + JKTII
WSI ~ JKP + JKTII
WSII ~ JKTIII + WSI'
MEDMII.fit <- sem(MEDMII.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T, check.gradient = F, control=list(rel.tol=1e-4))
MEDMIII.model <- '
Verbal =~ VA + RC + WK
Quant =~ AR + DI + MK + SR
g =~ Verbal + Quant
JKP =~ IC + AI
JKTI =~ A1 + A2 + A3 + A4
JKTII =~ A5 + A6 + A7 + A8
JKTIII =~ A9 + A10 + A11
WSI =~ CF1 + CF2 + CF3
WSII =~ CF4 + CF5 + CF6
JKP ~ g
JKTI ~ g
JKTII ~ g + JKTI
JKTIII ~ g + JKTII
WSI ~ JKP + JKTII
WSII ~ WSI'
MEDMIII.fit <- sem(MEDMIII.model, sample.cov = dat.cov, sample.nobs = 3428, std.lv = T, orthogonal = T, check.gradient = F, control=list(rel.tol=1e-4))parameterEstimates(MEDMI.fit, stand = T) %>%
filter(op == "~") %>% select('Dependent' = lhs, "Independent" = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Model Paths")| Dependent | Independent | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| JKP | g | 0.824 | 0.036 | 23.066 | 0.000 | 0.636 |
| JKTI | g | 0.837 | 0.056 | 15.021 | 0.000 | 0.640 |
| JKTI | JKP | 0.007 | 0.031 | 0.220 | 0.826 | 0.007 |
| JKTII | g | -0.196 | 0.101 | -1.929 | 0.054 | -0.095 |
| JKTII | JKTI | 1.459 | 0.162 | 9.010 | 0.000 | 0.931 |
| JKTIII | g | 0.463 | 0.148 | 3.136 | 0.002 | 0.133 |
| JKTIII | JKTII | 1.506 | 0.439 | 3.429 | 0.001 | 0.884 |
| WSI | g | -0.131 | 0.051 | -2.576 | 0.010 | -0.108 |
| WSI | JKP | 0.192 | 0.033 | 5.843 | 0.000 | 0.205 |
| WSI | JKTII | 0.312 | 0.034 | 9.281 | 0.000 | 0.528 |
| WSII | g | 0.092 | 0.096 | 0.954 | 0.340 | 0.038 |
| WSII | WSI | 1.723 | 0.362 | 4.758 | 0.000 | 0.873 |
| WSII | JKTIII | 0.030 | 0.037 | 0.789 | 0.430 | 0.043 |
parameterEstimates(MEDMI.fit, stand = T) %>%
filter(op == "~") %>% select('Dependent' = lhs, "Independent" = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Model Paths")| Dependent | Independent | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| JKP | g | 0.824 | 0.036 | 23.066 | 0.000 | 0.636 |
| JKTI | g | 0.837 | 0.056 | 15.021 | 0.000 | 0.640 |
| JKTI | JKP | 0.007 | 0.031 | 0.220 | 0.826 | 0.007 |
| JKTII | g | -0.196 | 0.101 | -1.929 | 0.054 | -0.095 |
| JKTII | JKTI | 1.459 | 0.162 | 9.010 | 0.000 | 0.931 |
| JKTIII | g | 0.463 | 0.148 | 3.136 | 0.002 | 0.133 |
| JKTIII | JKTII | 1.506 | 0.439 | 3.429 | 0.001 | 0.884 |
| WSI | g | -0.131 | 0.051 | -2.576 | 0.010 | -0.108 |
| WSI | JKP | 0.192 | 0.033 | 5.843 | 0.000 | 0.205 |
| WSI | JKTII | 0.312 | 0.034 | 9.281 | 0.000 | 0.528 |
| WSII | g | 0.092 | 0.096 | 0.954 | 0.340 | 0.038 |
| WSII | WSI | 1.723 | 0.362 | 4.758 | 0.000 | 0.873 |
| WSII | JKTIII | 0.030 | 0.037 | 0.789 | 0.430 | 0.043 |
parameterEstimates(MEDMII.fit, stand = T) %>%
filter(op == "~") %>% select('Dependent' = lhs, "Independent" = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Model Paths")| Dependent | Independent | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| JKP | g | 0.821 | 0.036 | 23.088 | 0.000 | 0.635 |
| JKTI | g | 0.843 | 0.056 | 15.095 | 0.000 | 0.642 |
| JKTI | JKP | 0.011 | 0.031 | 0.365 | 0.715 | 0.011 |
| JKTII | g | -0.271 | 0.112 | -2.414 | 0.016 | -0.128 |
| JKTII | JKTI | 1.551 | 0.184 | 8.412 | 0.000 | 0.960 |
| JKTIII | g | 0.479 | 0.156 | 3.065 | 0.002 | 0.133 |
| JKTIII | JKTII | 1.503 | 0.468 | 3.209 | 0.001 | 0.888 |
| WSI | JKP | 0.137 | 0.024 | 5.733 | 0.000 | 0.149 |
| WSI | JKTII | 0.268 | 0.030 | 9.044 | 0.000 | 0.478 |
| WSII | JKTIII | 0.050 | 0.030 | 1.673 | 0.094 | 0.078 |
| WSII | WSI | 1.640 | 0.316 | 5.196 | 0.000 | 0.857 |
parameterEstimates(MEDMIII.fit, stand = T) %>%
filter(op == "~") %>% select('Dependent' = lhs, "Independent" = rhs, B = est, SE = se, Z = z, 'p-value' = pvalue, Beta = std.all) %>%
kable(digits = 3, format = "pandoc", caption = "Model Paths")| Dependent | Independent | B | SE | Z | p-value | Beta |
|---|---|---|---|---|---|---|
| JKP | g | 0.822 | 0.035 | 23.481 | 0.000 | 0.635 |
| JKTI | g | 0.852 | 0.045 | 18.824 | 0.000 | 0.649 |
| JKTII | g | -0.275 | 0.113 | -2.433 | 0.015 | -0.129 |
| JKTII | JKTI | 1.560 | 0.186 | 8.368 | 0.000 | 0.961 |
| JKTIII | g | 0.479 | 0.161 | 2.978 | 0.003 | 0.130 |
| JKTIII | JKTII | 1.532 | 0.491 | 3.121 | 0.002 | 0.891 |
| WSI | JKP | 0.140 | 0.024 | 5.866 | 0.000 | 0.150 |
| WSI | JKTII | 0.281 | 0.030 | 9.433 | 0.000 | 0.496 |
| WSII | WSI | 1.795 | 0.341 | 5.258 | 0.000 | 0.908 |
round(cbind(MEDMI = fitMeasures(MEDMI.fit, FITS),
MEDMII = fitMeasures(MEDMII.fit, FITS),
MEDMIII = fitMeasures(MEDMIII.fit, FITS)),3)## MEDMI MEDMII MEDMIII
## chisq 1500.957 1509.660 1512.256
## df 284.000 286.000 288.000
## npar 67.000 65.000 63.000
## cfi 0.953 0.952 0.952
## rmsea 0.035 0.035 0.035
## rmsea.ci.lower 0.034 0.034 0.033
## rmsea.ci.upper 0.037 0.037 0.037
## bic2 502216.034 502214.813 502207.485semPaths(MEDMI.fit, "model", title = F, residuals = F, groups = "AFLATS", pastel = T, mar = c(2, 1, 3, 1), layout = "tree3", exoVar = F, exoCov = F)
semPaths(MEDMII.fit, "model", title = F, residuals = F, groups = "AFLATS", pastel = T, mar = c(2, 1, 3, 1), layout = "tree3", exoVar = F, exoCov = F)
semPaths(MEDMIII.fit, "model", title = F, residuals = F, groups = "AFLATS", pastel = T, mar = c(2, 1, 3, 1), layout = "tree3", exoVar = F, exoCov = F)
It does seem accurate to say that prior job knowledge has a limited role in skill acquisition and a minor one in performance dependent on skills acquired on the job. For clarity: prior knowledge has an obvious role when performance is required immediately.
Vector Correlations
describe(gvals)## vars n mean sd median trimmed mad min max range skew kurtosis
## ï..Test* 1 7 4.00 2.16 4.00 4.00 2.97 1.00 7.00 6.00 0.00 -1.71
## CFAgL 2 7 0.76 0.05 0.76 0.76 0.06 0.70 0.81 0.11 -0.20 -1.80
## EFAgL 3 7 0.75 0.05 0.76 0.75 0.06 0.69 0.82 0.13 -0.19 -1.79
## Note* 4 7 1.14 0.38 1.00 1.14 0.00 1.00 2.00 1.00 1.62 0.80
## ICR 5 7 0.38 0.07 0.39 0.38 0.07 0.28 0.49 0.21 0.07 -1.48
## AIR 6 7 0.31 0.03 0.32 0.31 0.03 0.25 0.34 0.09 -0.94 -0.55
## A1R 7 7 0.24 0.03 0.24 0.24 0.01 0.18 0.28 0.10 -0.68 -0.60
## A2R 8 7 0.21 0.03 0.22 0.21 0.03 0.18 0.25 0.07 -0.04 -1.73
## A3R 9 7 0.19 0.02 0.19 0.19 0.01 0.16 0.23 0.07 0.20 -1.42
## A4R 10 7 0.23 0.03 0.23 0.23 0.03 0.17 0.27 0.10 -0.55 -0.91
## A5R 11 7 0.18 0.04 0.19 0.18 0.04 0.11 0.23 0.12 -0.61 -1.01
## A6R 12 7 0.15 0.03 0.14 0.15 0.04 0.10 0.19 0.09 -0.16 -1.45
## A7R 13 7 0.18 0.04 0.17 0.18 0.03 0.12 0.23 0.11 0.01 -1.59
## A8R 14 7 0.17 0.03 0.18 0.17 0.03 0.12 0.20 0.08 -0.66 -1.42
## A9R 15 7 0.20 0.02 0.20 0.20 0.03 0.17 0.22 0.05 -0.22 -1.94
## A10R 16 7 0.21 0.04 0.21 0.21 0.01 0.15 0.27 0.12 0.10 -0.61
## A11R 17 7 0.19 0.04 0.19 0.19 0.06 0.12 0.23 0.11 -0.61 -1.09
## CF1R 18 7 0.07 0.05 0.08 0.07 0.07 0.00 0.14 0.14 -0.03 -1.87
## CF2R 19 7 0.11 0.04 0.11 0.11 0.04 0.04 0.16 0.12 -0.23 -1.58
## CF3R 20 7 0.13 0.04 0.12 0.13 0.04 0.06 0.19 0.13 -0.06 -1.43
## CF4R 21 7 0.09 0.05 0.11 0.09 0.06 0.00 0.15 0.15 -0.35 -1.66
## CF5R 22 7 0.06 0.03 0.07 0.06 0.03 0.01 0.10 0.09 -0.38 -1.49
## CF6R 23 7 0.12 0.04 0.11 0.12 0.06 0.06 0.18 0.12 -0.06 -1.67
## se
## ï..Test* 0.82
## CFAgL 0.02
## EFAgL 0.02
## Note* 0.14
## ICR 0.03
## AIR 0.01
## A1R 0.01
## A2R 0.01
## A3R 0.01
## A4R 0.01
## A5R 0.02
## A6R 0.01
## A7R 0.02
## A8R 0.01
## A9R 0.01
## A10R 0.01
## A11R 0.02
## CF1R 0.02
## CF2R 0.02
## CF3R 0.02
## CF4R 0.02
## CF5R 0.01
## CF6R 0.02describe(MCVs)## vars n mean sd median trimmed mad min max range skew
## Criteria* 1 19 10.00 5.63 10.00 10.00 7.41 1.00 19.00 18.00 0.00
## gCFA 2 19 0.32 0.32 0.33 0.31 0.48 -0.11 0.82 0.93 0.01
## gEFA 3 19 0.34 0.30 0.38 0.34 0.43 -0.07 0.84 0.91 -0.04
## gAVG 4 19 0.33 0.31 0.35 0.33 0.47 -0.09 0.83 0.92 -0.02
## gCFASp 5 19 0.32 0.28 0.28 0.31 0.30 -0.07 0.88 0.95 0.16
## gEFASp 6 19 0.35 0.29 0.36 0.34 0.30 -0.09 0.90 0.99 0.03
## gAVGSp 7 19 0.33 0.28 0.32 0.32 0.30 -0.02 0.89 0.91 0.18
## gCFAFc 8 19 0.96 0.05 0.98 0.97 0.02 0.81 1.00 0.19 -1.69
## gEFAFc 9 19 0.96 0.05 0.98 0.97 0.01 0.81 1.00 0.19 -1.71
## gAVGFc 10 19 0.96 0.05 0.98 0.97 0.02 0.81 1.00 0.19 -1.70
## kurtosis se
## Criteria* -1.39 1.29
## gCFA -1.65 0.07
## gEFA -1.63 0.07
## gAVG -1.64 0.07
## gCFASp -1.12 0.06
## gEFASp -1.30 0.07
## gAVGSp -1.28 0.06
## gCFAFc 1.81 0.01
## gEFAFc 1.87 0.01
## gAVGFc 1.84 0.01mean(MCVs$gAVG)## [1] 0.3298947mean(MCVs$gAVGSp)## [1] 0.3347632mean(MCVs$gAVGFc)## [1] 0.9630789print(PEAR <- ggplot(MCVs, aes(x = Criteria, y = gAVG, fill = Criteria)) + geom_bar(stat = "identity", show.legend = F) + coord_flip() + scale_fill_hue(c = 40) + theme_bw() + ylab("Pearson MCV Correlation") + xlab("Criteria"))
print(SPEAR <- ggplot(MCVs, aes(x = Criteria, y = gAVGSp, fill = Criteria)) + geom_bar(stat = "identity", show.legend = F) + coord_flip() + scale_fill_hue(c = 40) + theme_bw() + ylab("Spearman MCV Correlation") + xlab("Criteria"))
print(TUCK <- ggplot(MCVs, aes(x = Criteria, y = gAVGFc-1, fill = Criteria)) + geom_bar(stat = "identity", show.legend = F) + coord_flip() + scale_fill_hue(c = 40) + theme_bw() + ylab("Tucker's Congruence Coefficient - 1") + xlab("Criteria") + geom_hline(yintercept = -0.01, linetype = "longdash", color = "darkred", size = 1) + geom_hline(yintercept = -0.05, linetype = "dashed", color = "darkred", size = 1) + geom_hline(yintercept = -0.10, color = "darkred", linetype = "dotted", size = 1))
#grid.arrange(PEAR, SPEAR, TUCK, nrow = 3)The correlations between the work knowledge, but not the flight check, variables, were greater for more g loaded subtests. The g loadings and the subtest correlations were, in some cases, clearly, and in other cases, arguably or clearly not, congruent.
References
Ree, M. J., Carretta, T. R., & Teachout, M. S. (1995). Role of ability and prior knowledge in complex training performance. Journal of Applied Psychology, 80(6), 721-730. https://doi.org/10.1037/0021-9010.80.6.721