Wong et al. (1995) - Reanalysis
library(pacman); p_load(lavaan, psych)
NP <- function(N, S = 2) {
NP = 1-pnorm(qnorm(1-(N^(-6/5))/S))
return(NP)}
CONGO <- function(F1, F2) {
PHI = sum(F1*F2) / sqrt(sum(F1^2)*sum(F2^2))
return(PHI)}
CRITR <- function(n, alpha = .05) {
df <- n - 2; CRITT <- qt(alpha/2, df, lower.tail = F)
CRITR <- sqrt((CRITT^2)/((CRITT^2) + df ))
return(CRITR)}
FITM <- c("chisq", "df", "nPar", "cfi", "rmsea", "rmsea.ci.lower", "rmsea.ci.upper", "aic", "bic")
NP(c(134, 227))## [1] 0.0014010197 0.0007442845CRITR(c(134, 227)); CRITR(c(134, 227), c(0.0014, 0.00074))## [1] 0.1696749 0.1302517## [1] 0.2732637 0.2223778lowerWEA951 <- '
1
0.24 1
0.26 0.05 1
0.23 0.09 0.25 1
0.23 0.01 0.04 -0.01 1
0.25 0.05 0.22 0.21 0.06 1
0.14 0.03 0.5 0.13 0.07 0.28 1
-0.07 -0.01 0.07 0.4 -0.17 0.12 0.1 1
0.1 -0.07 0.14 0.12 -0.17 0.12 0.21 0.09 1
0.21 0.15 0.19 0.09 -0.06 0.19 0.21 0.12 0.49 1
0.13 0.09 0.24 0.04 0.05 0.28 0.32 0.12 0.33 0.56 1
0.02 0.04 0 0.23 -0.16 -0.01 0.17 0.24 0.25 0.46 0.44 1'
lowerWEA952 <- '
1
0.31 1
0.2 0.06 1
0.17 0.21 0.35 1
0.13 0.16 0.19 0.16 1
0.12 0.15 0.02 0.05 0.28 1
0.11 0.02 0.37 0.15 0.15 0.11 1
0.08 0.14 0.21 0.33 0.12 0.11 0.26 1
0.23 0.11 0.05 0.16 0.2 0.04 -0.01 0.13 1
0.25 0.34 0.05 0.07 0.3 0.25 0.15 0.13 0.12 1
0.08 0 0.44 0.21 0.09 0.01 0.55 0.28 0.1 0.1 1
0.03 0.18 0.07 0.51 0.06 0.07 0.16 0.56 0.16 0.06 0.27 1
0.06 -0.03 0.01 0.06 0.09 -0.04 0.11 0.12 0.18 0.07 0.06 0.05 1
0.17 0.11 0.09 0.08 0.1 0.2 0.03 0.06 0.07 0.16 0.09 0.04 0.24 1
-0.03 0.08 0.22 0.13 0.13 0.09 0.28 0.1 0.11 0.05 0.35 0.18 0.13 0.14 1
0.04 0.15 0.05 0.49 0.11 -0.02 0.1 0.24 0.16 0.02 0.14 0.5 0.12 0.07 0.37 1'
nWEA951 <- 134
nWEA952 <- 227
WEA951.cor = getCov(lowerWEA951, names = c("IQV", "IQNV", "IQSR", "IQOR", "SPV", "SPNV", "SPSR", "SPOR", "HIV", "HINV", "HISR", "HIOR"))
WEA952.cor = getCov(lowerWEA952, names = c("IQV", "IQNV", "IQSR", "IQOR", "SPV", "SPNV", "SPSR", "SPOR", "SIV", "SINV", "SISR", "SIOR", "SKV", "SKNV", "SKSR", "SKOR"))Analysis
Exploratory
fa.parallel(WEA951.cor, n.obs = nWEA951)
## Parallel analysis suggests that the number of factors = 4 and the number of components = 3fa.parallel(WEA952.cor, n.obs = nWEA952)
## Parallel analysis suggests that the number of factors = 4 and the number of components = 3FA1 <- fa(WEA951.cor, n.obs = nWEA951, nfactors = 4)## Loading required namespace: GPArotationFA2 <- fa(WEA952.cor, n.obs = nWEA952, nfactors = 4)
print(FA1$loadings, cutoff = 0.2)##
## Loadings:
## MR1 MR4 MR3 MR2
## IQV 0.729
## IQNV 0.274
## IQSR 0.594
## IQOR 0.892
## SPV 0.345
## SPNV 0.284
## SPSR 0.784
## SPOR 0.481 -0.267
## HIV 0.480
## HINV 0.862
## HISR 0.618 0.225
## HIOR 0.602 0.201
##
## MR1 MR4 MR3 MR2
## SS loadings 1.787 1.133 1.126 0.909
## Proportion Var 0.149 0.094 0.094 0.076
## Cumulative Var 0.149 0.243 0.337 0.413print(FA2$loadings, cutoff = 0.2)##
## Loadings:
## MR3 MR1 MR2 MR4
## IQV 0.469
## IQNV 0.488
## IQSR 0.536
## IQOR 0.512
## SPV 0.440
## SPNV 0.397
## SPSR 0.682
## SPOR 0.208 0.555
## SIV 0.260
## SINV 0.604
## SISR 0.778
## SIOR 0.839
## SKV 0.259
## SKNV 0.309 0.205
## SKSR 0.320 0.541
## SKOR 0.342 0.630
##
## MR3 MR1 MR2 MR4
## SS loadings 1.549 1.493 1.394 0.885
## Proportion Var 0.097 0.093 0.087 0.055
## Cumulative Var 0.097 0.190 0.277 0.333Their Models, Exactly
#Experiment 1
WEA951.model <- '
AI =~ IQV + IQNV + IQSR + IQOR
SP =~ SPV + SPNV + SPSR + SPOR
HI =~ HIV + HINV + HISR + HIOR
AI ~~ SP + HI
SP ~~ HI
VERBAL =~ IQV + SPV + HIV
NONVERBAL =~ IQNV + SPNV + HINV
SELFREP =~ IQSR + SPSR + HISR
OTHER =~ IQOR + SPOR + HIOR'
WEA951.fit <- cfa(WEA951.model, sample.cov = WEA951.cor, sample.nobs = nWEA951, std.lv = T, orthogonal = T); "\n"## Warning in lav_object_post_check(object): lavaan WARNING: some estimated ov
## variances are negative## [1] "\n"summary(WEA951.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 59 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 39
##
## Number of observations 134
##
## Model Test User Model:
##
## Test statistic 48.782
## Degrees of freedom 39
## P-value (Chi-square) 0.136
##
## Model Test Baseline Model:
##
## Test statistic 331.949
## Degrees of freedom 66
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.963
## Tucker-Lewis Index (TLI) 0.938
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2134.047
## Loglikelihood unrestricted model (H1) -2109.656
##
## Akaike (AIC) 4346.094
## Bayesian (BIC) 4459.110
## Sample-size adjusted Bayesian (BIC) 4335.743
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.043
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.078
## P-value RMSEA <= 0.05 0.588
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.057
##
## 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
## AI =~
## IQV 0.579 0.111 5.215 0.000 0.579 0.582
## IQNV 0.248 0.113 2.204 0.028 0.248 0.250
## IQSR 0.494 0.106 4.660 0.000 0.494 0.493
## IQOR 0.522 0.107 4.882 0.000 0.522 0.512
## SP =~
## SPV -0.039 0.112 -0.350 0.727 -0.039 -0.039
## SPNV -0.613 0.138 -4.439 0.000 -0.613 -0.615
## SPSR -0.424 0.109 -3.896 0.000 -0.424 -0.428
## SPOR -0.217 0.109 -1.986 0.047 -0.217 -0.216
## HI =~
## HIV 0.529 0.088 6.028 0.000 0.529 0.534
## HINV 0.848 0.085 9.932 0.000 0.848 0.853
## HISR 0.670 0.085 7.868 0.000 0.670 0.677
## HIOR 0.538 0.087 6.190 0.000 0.538 0.537
## VERBAL =~
## IQV 0.169 0.274 0.618 0.537 0.169 0.170
## SPV 1.183 1.840 0.643 0.520 1.183 1.188
## HIV -0.126 0.209 -0.599 0.549 -0.126 -0.127
## NONVERBAL =~
## IQNV 0.263 0.250 1.050 0.294 0.263 0.264
## SPNV -0.201 0.225 -0.893 0.372 -0.201 -0.202
## HINV 0.294 0.293 1.006 0.315 0.294 0.296
## SELFREP =~
## IQSR 0.568 0.175 3.241 0.001 0.568 0.568
## SPSR 0.635 0.194 3.265 0.001 0.635 0.640
## HISR 0.199 0.091 2.185 0.029 0.199 0.201
## OTHER =~
## IQOR 0.656 0.147 4.464 0.000 0.656 0.644
## SPOR 0.551 0.135 4.092 0.000 0.551 0.550
## HIOR 0.338 0.100 3.376 0.001 0.338 0.337
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AI ~~
## SP -0.665 0.137 -4.844 0.000 -0.665 -0.665
## HI 0.316 0.119 2.658 0.008 0.316 0.316
## SP ~~
## HI -0.517 0.133 -3.885 0.000 -0.517 -0.517
## AI ~~
## VERBAL 0.000 0.000 0.000
## NONVERBAL 0.000 0.000 0.000
## SELFREP 0.000 0.000 0.000
## OTHER 0.000 0.000 0.000
## SP ~~
## VERBAL 0.000 0.000 0.000
## NONVERBAL 0.000 0.000 0.000
## SELFREP 0.000 0.000 0.000
## OTHER 0.000 0.000 0.000
## HI ~~
## VERBAL 0.000 0.000 0.000
## NONVERBAL 0.000 0.000 0.000
## SELFREP 0.000 0.000 0.000
## OTHER 0.000 0.000 0.000
## VERBAL ~~
## NONVERBAL 0.000 0.000 0.000
## SELFREP 0.000 0.000 0.000
## OTHER 0.000 0.000 0.000
## NONVERBAL ~~
## SELFREP 0.000 0.000 0.000
## OTHER 0.000 0.000 0.000
## SELFREP ~~
## OTHER 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .IQV 0.624 0.151 4.120 0.000 0.624 0.632
## .IQNV 0.859 0.172 4.996 0.000 0.859 0.868
## .IQSR 0.435 0.193 2.254 0.024 0.435 0.434
## .IQOR 0.335 0.181 1.847 0.065 0.335 0.323
## .SPV -0.410 4.355 -0.094 0.925 -0.410 -0.413
## .SPNV 0.577 0.194 2.970 0.003 0.577 0.581
## .SPSR 0.401 0.232 1.725 0.085 0.401 0.407
## .SPOR 0.654 0.143 4.569 0.000 0.654 0.651
## .HIV 0.687 0.107 6.390 0.000 0.687 0.699
## .HINV 0.183 0.198 0.923 0.356 0.183 0.185
## .HISR 0.492 0.082 6.000 0.000 0.492 0.502
## .HIOR 0.600 0.094 6.397 0.000 0.600 0.598
## AI 1.000 1.000 1.000
## SP 1.000 1.000 1.000
## HI 1.000 1.000 1.000
## VERBAL 1.000 1.000 1.000
## NONVERBAL 1.000 1.000 1.000
## SELFREP 1.000 1.000 1.000
## OTHER 1.000 1.000 1.000resid(WEA951.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQV IQNV IQSR IQOR SPV SPNV SPSR SPOR HIV HINV
## IQV 0.000
## IQNV 0.095 0.000
## IQSR -0.027 -0.073 0.000
## IQOR -0.068 -0.038 -0.003 0.000
## SPV 0.013 0.003 0.027 -0.023 0.000
## SPNV 0.012 0.001 0.018 0.001 0.036 0.000
## SPSR -0.026 -0.041 -0.004 -0.016 0.053 0.017 0.000
## SPOR -0.154 -0.046 -0.001 -0.028 -0.179 -0.013 0.008 0.000
## HIV 0.023 -0.112 0.057 0.034 -0.030 -0.050 0.092 0.030 0.000
## HINV 0.053 0.005 0.057 -0.048 -0.077 -0.022 0.021 0.025 0.035 0.000
## HISR 0.006 0.037 0.021 -0.069 0.036 0.065 0.042 0.044 -0.031 -0.017
## HIOR -0.079 -0.002 -0.084 -0.074 -0.171 -0.181 0.051 -0.005 -0.037 0.002
## HISR HIOR
## IQV
## IQNV
## IQSR
## IQOR
## SPV
## SPNV
## SPSR
## SPOR
## HIV
## HINV
## HISR 0.000
## HIOR 0.077 0.000WEA951M.model <- '
AI =~ IQV + IQNV + IQSR + IQOR
SP =~ SPV + SPNV + SPSR + SPOR
HI =~ HIV + HINV + HISR + HIOR
AI ~~ SP + HI
SP ~~ HI
VERBAL =~ IQV + SPV + HIV
NONVERBAL =~ IQNV + SPNV + HINV
SELFREP =~ IQSR + SPSR + HISR
OTHER =~ IQOR + SPOR + HIOR
SPV ~~ 0*SPV
IQOR ~~ 0*IQOR'
WEA951M.fit <- cfa(WEA951M.model, sample.cov = WEA951.cor, sample.nobs = nWEA951, std.lv = T); "\n"## Warning in lav_object_post_check(object): lavaan WARNING: covariance matrix of latent variables
## is not positive definite;
## use lavInspect(fit, "cov.lv") to investigate.## [1] "\n"summary(WEA951M.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 329 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 55
##
## Number of observations 134
##
## Model Test User Model:
##
## Test statistic 28.427
## Degrees of freedom 23
## P-value (Chi-square) 0.200
##
## Model Test Baseline Model:
##
## Test statistic 331.949
## Degrees of freedom 66
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.980
## Tucker-Lewis Index (TLI) 0.941
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2123.869
## Loglikelihood unrestricted model (H1) -2109.656
##
## Akaike (AIC) 4357.739
## Bayesian (BIC) 4517.120
## Sample-size adjusted Bayesian (BIC) 4343.142
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.042
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.087
## P-value RMSEA <= 0.05 0.569
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.035
##
## 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
## AI =~
## IQV 0.611 0.244 2.507 0.012 0.611 0.613
## IQNV 0.332 0.338 0.983 0.326 0.332 0.334
## IQSR 1.350 1.938 0.697 0.486 1.350 1.355
## IQOR 1.861 1.473 1.263 0.206 1.861 1.868
## SP =~
## SPV -0.109 1.121 -0.097 0.923 -0.109 -0.109
## SPNV -0.839 0.763 -1.100 0.271 -0.839 -0.842
## SPSR -0.945 1.120 -0.844 0.399 -0.945 -0.949
## SPOR -0.750 0.739 -1.015 0.310 -0.750 -0.753
## HI =~
## HIV 0.508 0.315 1.612 0.107 0.508 0.510
## HINV 0.976 0.415 2.354 0.019 0.976 0.980
## HISR 0.824 0.324 2.546 0.011 0.824 0.827
## HIOR 0.828 0.380 2.178 0.029 0.828 0.831
## VERBAL =~
## IQV -0.161 0.267 -0.602 0.547 -0.161 -0.161
## SPV 0.931 0.644 1.445 0.148 0.931 0.934
## HIV -0.346 0.240 -1.441 0.150 -0.346 -0.347
## NONVERBAL =~
## IQNV 0.113 0.373 0.302 0.763 0.113 0.113
## SPNV 0.304 0.971 0.314 0.754 0.304 0.306
## HINV 0.244 0.761 0.320 0.749 0.244 0.245
## SELFREP =~
## IQSR 1.163 1.571 0.740 0.459 1.163 1.168
## SPSR 0.773 0.881 0.877 0.380 0.773 0.776
## HISR 0.317 0.413 0.769 0.442 0.317 0.319
## OTHER =~
## IQOR 1.744 1.301 1.341 0.180 1.744 1.751
## SPOR 0.889 0.637 1.395 0.163 0.889 0.892
## HIOR 0.675 0.462 1.460 0.144 0.675 0.677
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AI ~~
## SP -0.914 0.172 -5.306 0.000 -0.914 -0.914
## HI 0.592 0.441 1.342 0.180 0.592 0.592
## SP ~~
## HI -0.721 0.269 -2.677 0.007 -0.721 -0.721
## AI ~~
## VERBAL 0.575 0.702 0.819 0.413 0.575 0.575
## NONVERBAL -1.071 1.117 -0.958 0.338 -1.071 -1.071
## SELFREP -0.799 0.570 -1.400 0.161 -0.799 -0.799
## OTHER -0.849 0.238 -3.566 0.000 -0.849 -0.849
## SP ~~
## VERBAL -0.564 0.821 -0.687 0.492 -0.564 -0.564
## NONVERBAL 1.068 1.062 1.006 0.314 1.068 1.068
## SELFREP 0.675 0.797 0.847 0.397 0.675 0.675
## OTHER 0.787 0.351 2.244 0.025 0.787 0.787
## HI ~~
## VERBAL 0.284 0.897 0.317 0.751 0.284 0.284
## NONVERBAL -0.785 0.869 -0.903 0.367 -0.785 -0.785
## SELFREP -0.452 0.743 -0.609 0.543 -0.452 -0.452
## OTHER -0.547 0.473 -1.158 0.247 -0.547 -0.547
## VERBAL ~~
## NONVERBAL -1.591 3.385 -0.470 0.638 -1.591 -1.591
## SELFREP -0.673 0.467 -1.443 0.149 -0.673 -0.673
## OTHER -0.642 0.540 -1.189 0.235 -0.642 -0.642
## NONVERBAL ~~
## SELFREP 0.873 0.651 1.341 0.180 0.873 0.873
## OTHER 1.012 0.988 1.024 0.306 1.012 1.012
## SELFREP ~~
## OTHER 0.720 0.583 1.235 0.217 0.720 0.720
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SPV 0.000 0.000 0.000
## .IQOR 0.000 0.000 0.000
## .IQV 0.706 0.121 5.819 0.000 0.706 0.711
## .IQNV 0.950 0.119 7.978 0.000 0.950 0.957
## .IQSR 0.325 0.268 1.214 0.225 0.325 0.328
## .SPNV 0.742 0.133 5.557 0.000 0.742 0.747
## .SPSR 0.488 0.156 3.119 0.002 0.488 0.492
## .SPOR 0.689 0.110 6.259 0.000 0.689 0.694
## .HIV 0.715 0.098 7.305 0.000 0.715 0.720
## .HINV 0.354 0.098 3.598 0.000 0.354 0.356
## .HISR 0.449 0.081 5.545 0.000 0.449 0.452
## .HIOR 0.463 0.101 4.604 0.000 0.463 0.467
## AI 1.000 1.000 1.000
## SP 1.000 1.000 1.000
## HI 1.000 1.000 1.000
## VERBAL 1.000 1.000 1.000
## NONVERBAL 1.000 1.000 1.000
## SELFREP 1.000 1.000 1.000
## OTHER 1.000 1.000 1.000resid(WEA951M.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQV IQNV IQSR IQOR SPV SPNV SPSR SPOR HIV HINV
## IQV 0.000
## IQNV 0.112 0.000
## IQSR 0.000 -0.042 0.000
## IQOR -0.012 -0.011 0.003 0.000
## SPV -0.001 -0.021 -0.003 0.000 0.000
## SPNV -0.023 -0.030 -0.028 0.001 0.014 0.000
## SPSR -0.010 -0.015 0.006 -0.004 0.012 0.025 0.000
## SPOR -0.051 0.002 0.007 0.005 -0.037 0.047 -0.052 0.000
## HIV 0.005 -0.121 -0.002 0.028 0.000 -0.071 0.044 0.011 0.000
## HINV -0.003 0.103 0.027 0.001 -0.005 -0.025 -0.034 0.042 0.050 0.000
## HISR -0.011 0.053 -0.014 -0.008 -0.011 0.072 0.001 0.032 -0.011 -0.019
## HIOR 0.039 0.064 -0.018 -0.004 0.019 -0.076 0.020 -0.008 -0.054 0.001
## HISR HIOR
## IQV
## IQNV
## IQSR
## IQOR
## SPV
## SPNV
## SPSR
## SPOR
## HIV
## HINV
## HISR 0.000
## HIOR 0.023 0.000There were no violations of local independence.
#Experiment 2
WEA952.model <- '
AI =~ IQV + IQNV + IQSR + IQOR
SP =~ SPV + SPNV + SPSR + SPOR + SIV + SINV + SISR + SIOR
SK =~ SKV + SKNV + SKSR + SKOR
AI ~~ SP + SK
SP ~~ SK
VERBAL =~ IQV + SPV + SKV + SIV
NONVERBAL =~ IQNV + SPNV + SKNV + SINV
SELFREP =~ IQSR + SPSR + SKSR + SISR
OTHER =~ IQOR + SPOR + SKOR + SIOR'
WEA952.fit <- cfa(WEA952.model, sample.cov = WEA952.cor, sample.nobs = nWEA952, std.lv = T, orthogonal = T); "\n"## Warning in lav_object_post_check(object): lavaan WARNING: some estimated ov
## variances are negative## [1] "\n"summary(WEA952.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 63 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 51
##
## Number of observations 227
##
## Model Test User Model:
##
## Test statistic 147.121
## Degrees of freedom 85
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 772.511
## Degrees of freedom 120
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.905
## Tucker-Lewis Index (TLI) 0.866
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4832.872
## Loglikelihood unrestricted model (H1) -4759.312
##
## Akaike (AIC) 9767.745
## Bayesian (BIC) 9942.417
## Sample-size adjusted Bayesian (BIC) 9780.784
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.057
## 90 Percent confidence interval - lower 0.041
## 90 Percent confidence interval - upper 0.072
## P-value RMSEA <= 0.05 0.227
##
## 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
## AI =~
## IQV 0.393 0.085 4.646 0.000 0.393 0.395
## IQNV 0.314 0.084 3.764 0.000 0.314 0.315
## IQSR 0.550 0.085 6.485 0.000 0.550 0.549
## IQOR 0.583 0.085 6.878 0.000 0.583 0.578
## SP =~
## SPV 0.518 0.095 5.474 0.000 0.518 0.520
## SPNV 0.344 0.093 3.709 0.000 0.344 0.346
## SPSR 0.391 0.088 4.433 0.000 0.391 0.391
## SPOR 0.414 0.088 4.724 0.000 0.414 0.412
## SIV 0.210 0.097 2.171 0.030 0.210 0.211
## SINV 0.417 0.089 4.667 0.000 0.417 0.421
## SISR 0.330 0.087 3.785 0.000 0.330 0.329
## SIOR 0.310 0.084 3.704 0.000 0.310 0.308
## SK =~
## SKV 0.241 0.089 2.714 0.007 0.241 0.242
## SKNV 0.257 0.089 2.893 0.004 0.257 0.258
## SKSR 0.573 0.103 5.556 0.000 0.573 0.573
## SKOR 0.535 0.097 5.523 0.000 0.535 0.538
## VERBAL =~
## IQV 0.127 0.240 0.531 0.596 0.127 0.128
## SPV 0.068 0.137 0.493 0.622 0.068 0.068
## SKV 0.104 0.199 0.521 0.602 0.104 0.104
## SIV 1.277 2.301 0.555 0.579 1.277 1.283
## NONVERBAL =~
## IQNV 0.439 0.145 3.023 0.003 0.439 0.440
## SPNV 0.206 0.104 1.974 0.048 0.206 0.207
## SKNV 0.187 0.101 1.843 0.065 0.187 0.187
## SINV 0.543 0.169 3.219 0.001 0.543 0.548
## SELFREP =~
## IQSR 0.449 0.074 6.107 0.000 0.449 0.448
## SPSR 0.554 0.079 7.004 0.000 0.554 0.554
## SKSR 0.360 0.075 4.815 0.000 0.360 0.360
## SISR 0.764 0.084 9.102 0.000 0.764 0.764
## OTHER =~
## IQOR 0.539 0.068 7.974 0.000 0.539 0.534
## SPOR 0.492 0.073 6.777 0.000 0.492 0.489
## SKOR 0.529 0.068 7.764 0.000 0.529 0.532
## SIOR 0.843 0.072 11.750 0.000 0.843 0.836
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AI ~~
## SP 0.569 0.095 6.019 0.000 0.569 0.569
## SK 0.359 0.111 3.225 0.001 0.359 0.359
## SP ~~
## SK 0.400 0.114 3.516 0.000 0.400 0.400
## AI ~~
## VERBAL 0.000 0.000 0.000
## NONVERBAL 0.000 0.000 0.000
## SELFREP 0.000 0.000 0.000
## OTHER 0.000 0.000 0.000
## SP ~~
## VERBAL 0.000 0.000 0.000
## NONVERBAL 0.000 0.000 0.000
## SELFREP 0.000 0.000 0.000
## OTHER 0.000 0.000 0.000
## SK ~~
## VERBAL 0.000 0.000 0.000
## NONVERBAL 0.000 0.000 0.000
## SELFREP 0.000 0.000 0.000
## OTHER 0.000 0.000 0.000
## VERBAL ~~
## NONVERBAL 0.000 0.000 0.000
## SELFREP 0.000 0.000 0.000
## OTHER 0.000 0.000 0.000
## NONVERBAL ~~
## SELFREP 0.000 0.000 0.000
## OTHER 0.000 0.000 0.000
## SELFREP ~~
## OTHER 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .IQV 0.821 0.101 8.085 0.000 0.821 0.828
## .IQNV 0.703 0.132 5.325 0.000 0.703 0.707
## .IQSR 0.498 0.078 6.368 0.000 0.498 0.497
## .IQOR 0.388 0.076 5.134 0.000 0.388 0.380
## .SPV 0.722 0.099 7.288 0.000 0.722 0.725
## .SPNV 0.830 0.088 9.404 0.000 0.830 0.838
## .SPSR 0.540 0.071 7.606 0.000 0.540 0.540
## .SPOR 0.598 0.068 8.805 0.000 0.598 0.591
## .SIV -0.685 5.878 -0.117 0.907 -0.685 -0.692
## .SINV 0.513 0.171 3.004 0.003 0.513 0.523
## .SISR 0.308 0.094 3.285 0.001 0.308 0.308
## .SIOR 0.209 0.078 2.680 0.007 0.209 0.206
## .SKV 0.922 0.097 9.467 0.000 0.922 0.931
## .SKNV 0.895 0.092 9.702 0.000 0.895 0.899
## .SKSR 0.542 0.105 5.160 0.000 0.542 0.542
## .SKOR 0.424 0.089 4.786 0.000 0.424 0.428
## AI 1.000 1.000 1.000
## SP 1.000 1.000 1.000
## SK 1.000 1.000 1.000
## VERBAL 1.000 1.000 1.000
## NONVERBAL 1.000 1.000 1.000
## SELFREP 1.000 1.000 1.000
## OTHER 1.000 1.000 1.000resid(WEA952.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQV IQNV IQSR IQOR SPV SPNV SPSR SPOR SIV SINV
## IQV 0.000
## IQNV 0.185 0.000
## IQSR -0.017 -0.113 0.000
## IQOR -0.058 0.028 0.033 0.000
## SPV 0.004 0.067 0.028 -0.011 0.000
## SPNV 0.042 -0.003 -0.088 -0.064 0.100 0.000
## SPSR 0.022 -0.050 -0.001 0.021 -0.053 -0.025 0.000
## SPOR -0.013 0.066 0.081 -0.067 -0.094 -0.032 0.099 0.000
## SIV 0.019 0.072 -0.016 0.091 0.003 -0.033 -0.092 0.043 0.000
## SINV 0.155 0.023 -0.082 -0.068 0.081 -0.009 -0.014 -0.043 0.031 0.000
## SISR 0.006 -0.059 -0.006 0.102 -0.081 -0.104 -0.002 0.144 0.031 -0.039
## SIOR -0.039 0.125 -0.026 -0.038 -0.100 -0.037 0.040 0.024 0.095 -0.070
## SKV 0.012 -0.057 -0.038 0.010 0.033 -0.073 0.072 0.080 0.026 0.029
## SKNV 0.133 -0.001 0.039 0.027 0.046 0.126 -0.010 0.018 0.048 0.014
## SKSR -0.111 0.015 -0.054 0.011 0.011 0.011 -0.009 0.006 0.062 -0.046
## SKOR -0.036 0.089 -0.056 0.095 -0.002 -0.094 0.016 -0.108 0.115 -0.070
## SISR SIOR SKV SKNV SKSR SKOR
## IQV
## IQNV
## IQSR
## IQOR
## SPV
## SPNV
## SPSR
## SPOR
## SIV
## SINV
## SISR 0.000
## SIOR 0.169 0.000
## SKV 0.028 0.020 0.000
## SKNV 0.056 0.008 0.178 0.000
## SKSR 0.000 0.109 -0.009 -0.008 0.000
## SKOR 0.069 -0.011 -0.010 -0.069 0.062 0.000WEA952M.model <- '
AI =~ IQV + IQNV + IQSR + IQOR
SP =~ SPV + SPNV + SPSR + SPOR + SIV + SINV + SISR + SIOR
SK =~ SKV + SKNV + SKSR + SKOR
AI ~~ SP + SK
SP ~~ SK
VERBAL =~ IQV + SPV + SKV + SIV
NONVERBAL =~ IQNV + SPNV + SKNV + SINV
SELFREP =~ IQSR + SPSR + SKSR + SISR
OTHER =~ IQOR + SPOR + SKOR + SIOR
SIV ~~ 0*SIV'
WEA952M.fit <- cfa(WEA952M.model, sample.cov = WEA952.cor, sample.nobs = nWEA952, std.lv = T, orthogonal = T)
summary(WEA952M.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 35 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 50
##
## Number of observations 227
##
## Model Test User Model:
##
## Test statistic 147.155
## Degrees of freedom 86
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 772.511
## Degrees of freedom 120
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.906
## Tucker-Lewis Index (TLI) 0.869
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4832.889
## Loglikelihood unrestricted model (H1) -4759.312
##
## Akaike (AIC) 9765.778
## Bayesian (BIC) 9937.025
## Sample-size adjusted Bayesian (BIC) 9778.561
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.056
## 90 Percent confidence interval - lower 0.040
## 90 Percent confidence interval - upper 0.071
## P-value RMSEA <= 0.05 0.251
##
## 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
## AI =~
## IQV 0.390 0.084 4.642 0.000 0.390 0.392
## IQNV 0.314 0.084 3.753 0.000 0.314 0.314
## IQSR 0.551 0.085 6.478 0.000 0.551 0.550
## IQOR 0.585 0.085 6.880 0.000 0.585 0.580
## SP =~
## SPV 0.516 0.095 5.455 0.000 0.516 0.518
## SPNV 0.343 0.093 3.694 0.000 0.343 0.345
## SPSR 0.390 0.088 4.414 0.000 0.390 0.390
## SPOR 0.415 0.088 4.721 0.000 0.415 0.413
## SIV 0.214 0.096 2.215 0.027 0.214 0.215
## SINV 0.415 0.089 4.639 0.000 0.415 0.419
## SISR 0.331 0.087 3.791 0.000 0.331 0.331
## SIOR 0.312 0.084 3.713 0.000 0.312 0.309
## SK =~
## SKV 0.238 0.088 2.703 0.007 0.238 0.240
## SKNV 0.255 0.089 2.876 0.004 0.255 0.256
## SKSR 0.575 0.104 5.551 0.000 0.575 0.575
## SKOR 0.536 0.097 5.515 0.000 0.536 0.539
## VERBAL =~
## IQV 0.167 0.064 2.606 0.009 0.167 0.168
## SPV 0.085 0.071 1.200 0.230 0.085 0.085
## SKV 0.139 0.066 2.120 0.034 0.139 0.140
## SIV 0.972 0.048 20.106 0.000 0.972 0.977
## NONVERBAL =~
## IQNV 0.439 0.144 3.043 0.002 0.439 0.440
## SPNV 0.208 0.104 1.993 0.046 0.208 0.209
## SKNV 0.188 0.101 1.861 0.063 0.188 0.189
## SINV 0.544 0.168 3.245 0.001 0.544 0.549
## SELFREP =~
## IQSR 0.449 0.074 6.095 0.000 0.449 0.448
## SPSR 0.554 0.079 6.993 0.000 0.554 0.554
## SKSR 0.359 0.075 4.797 0.000 0.359 0.359
## SISR 0.763 0.084 9.080 0.000 0.763 0.763
## OTHER =~
## IQOR 0.538 0.068 7.947 0.000 0.538 0.533
## SPOR 0.491 0.073 6.748 0.000 0.491 0.488
## SKOR 0.528 0.068 7.741 0.000 0.528 0.531
## SIOR 0.842 0.072 11.714 0.000 0.842 0.836
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AI ~~
## SP 0.569 0.095 6.017 0.000 0.569 0.569
## SK 0.358 0.111 3.228 0.001 0.358 0.358
## SP ~~
## SK 0.401 0.114 3.526 0.000 0.401 0.401
## AI ~~
## VERBAL 0.000 0.000 0.000
## NONVERBAL 0.000 0.000 0.000
## SELFREP 0.000 0.000 0.000
## OTHER 0.000 0.000 0.000
## SP ~~
## VERBAL 0.000 0.000 0.000
## NONVERBAL 0.000 0.000 0.000
## SELFREP 0.000 0.000 0.000
## OTHER 0.000 0.000 0.000
## SK ~~
## VERBAL 0.000 0.000 0.000
## NONVERBAL 0.000 0.000 0.000
## SELFREP 0.000 0.000 0.000
## OTHER 0.000 0.000 0.000
## VERBAL ~~
## NONVERBAL 0.000 0.000 0.000
## SELFREP 0.000 0.000 0.000
## OTHER 0.000 0.000 0.000
## NONVERBAL ~~
## SELFREP 0.000 0.000 0.000
## OTHER 0.000 0.000 0.000
## SELFREP ~~
## OTHER 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SIV 0.000 0.000 0.000
## .IQV 0.811 0.087 9.367 0.000 0.811 0.818
## .IQNV 0.704 0.131 5.367 0.000 0.704 0.708
## .IQSR 0.498 0.078 6.355 0.000 0.498 0.497
## .IQOR 0.386 0.076 5.098 0.000 0.386 0.379
## .SPV 0.721 0.098 7.363 0.000 0.721 0.725
## .SPNV 0.830 0.088 9.402 0.000 0.830 0.838
## .SPSR 0.540 0.071 7.604 0.000 0.540 0.541
## .SPOR 0.598 0.068 8.802 0.000 0.598 0.591
## .SINV 0.513 0.170 3.012 0.003 0.513 0.523
## .SISR 0.309 0.094 3.288 0.001 0.309 0.308
## .SIOR 0.209 0.078 2.674 0.007 0.209 0.206
## .SKV 0.915 0.090 10.147 0.000 0.915 0.923
## .SKNV 0.895 0.092 9.705 0.000 0.895 0.899
## .SKSR 0.541 0.106 5.121 0.000 0.541 0.541
## .SKOR 0.424 0.089 4.768 0.000 0.424 0.428
## AI 1.000 1.000 1.000
## SP 1.000 1.000 1.000
## SK 1.000 1.000 1.000
## VERBAL 1.000 1.000 1.000
## NONVERBAL 1.000 1.000 1.000
## SELFREP 1.000 1.000 1.000
## OTHER 1.000 1.000 1.000resid(WEA952M.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQV IQNV IQSR IQOR SPV SPNV SPSR SPOR SIV SINV
## IQV 0.000
## IQNV 0.187 0.000
## IQSR -0.016 -0.113 0.000
## IQOR -0.057 0.028 0.031 0.000
## SPV 0.000 0.067 0.028 -0.011 0.000
## SPNV 0.043 -0.003 -0.088 -0.064 0.102 0.000
## SPSR 0.023 -0.050 0.000 0.021 -0.052 -0.024 0.000
## SPOR -0.012 0.066 0.081 -0.066 -0.094 -0.032 0.099 0.000
## SIV 0.018 0.072 -0.017 0.089 0.005 -0.034 -0.094 0.041 0.000
## SINV 0.157 0.024 -0.081 -0.068 0.083 -0.009 -0.013 -0.043 0.030 0.000
## SISR 0.006 -0.059 -0.005 0.101 -0.081 -0.104 -0.002 0.144 0.029 -0.038
## SIOR -0.039 0.125 -0.027 -0.038 -0.100 -0.037 0.039 0.024 0.094 -0.070
## SKV 0.003 -0.057 -0.037 0.010 0.028 -0.073 0.073 0.080 0.023 0.030
## SKNV 0.134 -0.002 0.040 0.027 0.047 0.125 -0.010 0.018 0.048 0.013
## SKSR -0.111 0.015 -0.054 0.011 0.011 0.011 -0.009 0.005 0.061 -0.046
## SKOR -0.036 0.089 -0.056 0.095 -0.002 -0.094 0.016 -0.108 0.114 -0.070
## SISR SIOR SKV SKNV SKSR SKOR
## IQV
## IQNV
## IQSR
## IQOR
## SPV
## SPNV
## SPSR
## SPOR
## SIV
## SINV
## SISR 0.000
## SIOR 0.168 0.000
## SKV 0.028 0.020 0.000
## SKNV 0.056 0.008 0.179 0.000
## SKSR 0.000 0.109 -0.008 -0.007 0.000
## SKOR 0.069 -0.010 -0.009 -0.068 0.060 0.000There were six violations of local independence.
Their Models, Without Method Factors
#Experiment 1
WEA951.model <- '
AI =~ IQV + IQNV + IQSR + IQOR
SP =~ SPV + SPNV + SPSR + SPOR
HI =~ HIV + HINV + HISR + HIOR'
WEA951.fit <- cfa(WEA951.model, sample.cov = WEA951.cor, sample.nobs = nWEA951, std.lv = T)
summary(WEA951.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 23 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 27
##
## Number of observations 134
##
## Model Test User Model:
##
## Test statistic 114.891
## Degrees of freedom 51
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 331.949
## Degrees of freedom 66
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.760
## Tucker-Lewis Index (TLI) 0.689
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2167.101
## Loglikelihood unrestricted model (H1) -2109.656
##
## Akaike (AIC) 4388.203
## Bayesian (BIC) 4466.445
## Sample-size adjusted Bayesian (BIC) 4381.037
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.097
## 90 Percent confidence interval - lower 0.073
## 90 Percent confidence interval - upper 0.120
## P-value RMSEA <= 0.05 0.001
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.085
##
## 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
## AI =~
## IQV 0.386 0.101 3.808 0.000 0.386 0.388
## IQNV 0.135 0.104 1.305 0.192 0.135 0.136
## IQSR 0.699 0.110 6.343 0.000 0.699 0.702
## IQOR 0.387 0.101 3.819 0.000 0.387 0.389
## SP =~
## SPV -0.059 0.102 -0.576 0.564 -0.059 -0.059
## SPNV -0.429 0.100 -4.284 0.000 -0.429 -0.431
## SPSR -0.631 0.111 -5.694 0.000 -0.631 -0.633
## SPOR -0.212 0.101 -2.095 0.036 -0.212 -0.213
## HI =~
## HIV 0.541 0.089 6.065 0.000 0.541 0.543
## HINV 0.809 0.084 9.609 0.000 0.809 0.812
## HISR 0.707 0.086 8.255 0.000 0.707 0.710
## HIOR 0.558 0.089 6.285 0.000 0.558 0.560
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AI ~~
## SP -0.946 0.152 -6.237 0.000 -0.946 -0.946
## HI 0.374 0.120 3.112 0.002 0.374 0.374
## SP ~~
## HI -0.543 0.127 -4.289 0.000 -0.543 -0.543
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .IQV 0.843 0.113 7.494 0.000 0.843 0.850
## .IQNV 0.974 0.120 8.114 0.000 0.974 0.982
## .IQSR 0.504 0.129 3.905 0.000 0.504 0.507
## .IQOR 0.843 0.113 7.489 0.000 0.843 0.849
## .SPV 0.989 0.121 8.174 0.000 0.989 0.997
## .SPNV 0.808 0.110 7.320 0.000 0.808 0.814
## .SPSR 0.595 0.124 4.797 0.000 0.595 0.599
## .SPOR 0.948 0.118 8.026 0.000 0.948 0.955
## .HIV 0.700 0.096 7.289 0.000 0.700 0.705
## .HINV 0.338 0.085 3.965 0.000 0.338 0.341
## .HISR 0.492 0.085 5.797 0.000 0.492 0.496
## .HIOR 0.682 0.095 7.201 0.000 0.682 0.687
## AI 1.000 1.000 1.000
## SP 1.000 1.000 1.000
## HI 1.000 1.000 1.000resid(WEA951.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQV IQNV IQSR IQOR SPV SPNV SPSR SPOR HIV HINV
## IQV 0.000
## IQNV 0.187 0.000
## IQSR -0.012 -0.045 0.000
## IQOR 0.079 0.037 -0.023 0.000
## SPV 0.208 0.002 0.001 -0.032 0.000
## SPNV 0.092 -0.005 -0.066 0.052 0.035 0.000
## SPSR -0.092 -0.051 0.080 -0.103 0.033 0.007 0.000
## SPOR -0.148 -0.037 -0.071 0.322 -0.183 0.028 -0.035 0.000
## HIV 0.021 -0.098 -0.002 0.041 -0.187 -0.007 0.024 0.027 0.000
## HINV 0.092 0.109 -0.023 -0.028 -0.086 0.000 -0.069 0.026 0.049 0.000
## HISR 0.027 0.054 0.054 -0.063 0.027 0.114 0.076 0.038 -0.055 -0.016
## HIOR -0.061 0.012 -0.147 0.149 -0.178 -0.141 -0.022 0.175 -0.054 0.005
## HISR HIOR
## IQV
## IQNV
## IQSR
## IQOR
## SPV
## SPNV
## SPSR
## SPOR
## HIV
## HINV
## HISR 0.000
## HIOR 0.043 0.000There were five violations of local independence.
#Experiment 2
WEA952.model <- '
AI =~ IQV + IQNV + IQSR + IQOR
SP =~ SPV + SPNV + SPSR + SPOR + SIV + SINV + SISR + SIOR
SK =~ SKV + SKNV + SKSR + SKOR'
WEA952.fit <- cfa(WEA952.model, sample.cov = WEA952.cor, sample.nobs = nWEA952, std.lv = T)
summary(WEA952.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 25 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 35
##
## Number of observations 227
##
## Model Test User Model:
##
## Test statistic 394.271
## Degrees of freedom 101
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 772.511
## Degrees of freedom 120
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.551
## Tucker-Lewis Index (TLI) 0.466
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4956.447
## Loglikelihood unrestricted model (H1) -4759.312
##
## Akaike (AIC) 9982.894
## Bayesian (BIC) 10102.767
## Sample-size adjusted Bayesian (BIC) 9991.842
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.113
## 90 Percent confidence interval - lower 0.101
## 90 Percent confidence interval - upper 0.125
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.103
##
## 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
## AI =~
## IQV 0.223 0.074 3.019 0.003 0.223 0.223
## IQNV 0.271 0.074 3.678 0.000 0.271 0.271
## IQSR 0.394 0.073 5.382 0.000 0.394 0.394
## IQOR 0.858 0.085 10.146 0.000 0.858 0.860
## SP =~
## SPV 0.210 0.074 2.833 0.005 0.210 0.210
## SPNV 0.137 0.075 1.840 0.066 0.137 0.138
## SPSR 0.356 0.073 4.905 0.000 0.356 0.357
## SPOR 0.657 0.067 9.737 0.000 0.657 0.658
## SIV 0.234 0.074 3.170 0.002 0.234 0.235
## SINV 0.177 0.074 2.381 0.017 0.177 0.177
## SISR 0.434 0.071 6.081 0.000 0.434 0.435
## SIOR 0.770 0.066 11.645 0.000 0.770 0.771
## SK =~
## SKV 0.169 0.076 2.230 0.026 0.169 0.170
## SKNV 0.135 0.076 1.774 0.076 0.135 0.135
## SKSR 0.438 0.076 5.763 0.000 0.438 0.439
## SKOR 0.828 0.093 8.891 0.000 0.828 0.830
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AI ~~
## SP 0.690 0.075 9.242 0.000 0.690 0.690
## SK 0.622 0.090 6.936 0.000 0.622 0.622
## SP ~~
## SK 0.625 0.082 7.597 0.000 0.625 0.625
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .IQV 0.946 0.090 10.501 0.000 0.946 0.950
## .IQNV 0.922 0.089 10.415 0.000 0.922 0.926
## .IQSR 0.841 0.084 10.024 0.000 0.841 0.844
## .IQOR 0.259 0.116 2.225 0.026 0.259 0.260
## .SPV 0.952 0.090 10.515 0.000 0.952 0.956
## .SPNV 0.977 0.092 10.596 0.000 0.977 0.981
## .SPSR 0.869 0.085 10.213 0.000 0.869 0.873
## .SPOR 0.564 0.069 8.205 0.000 0.564 0.567
## .SIV 0.941 0.090 10.478 0.000 0.941 0.945
## .SINV 0.964 0.091 10.556 0.000 0.964 0.969
## .SISR 0.807 0.081 9.942 0.000 0.807 0.811
## .SIOR 0.403 0.067 6.028 0.000 0.403 0.405
## .SKV 0.967 0.092 10.548 0.000 0.967 0.971
## .SKNV 0.977 0.092 10.589 0.000 0.977 0.982
## .SKSR 0.804 0.084 9.557 0.000 0.804 0.808
## .SKOR 0.310 0.129 2.394 0.017 0.310 0.311
## AI 1.000 1.000 1.000
## SP 1.000 1.000 1.000
## SK 1.000 1.000 1.000resid(WEA952.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQV IQNV IQSR IQOR SPV SPNV SPSR SPOR SIV SINV
## IQV 0.000
## IQNV 0.249 0.000
## IQSR 0.112 -0.047 0.000
## IQOR -0.022 -0.023 0.011 0.000
## SPV 0.098 0.121 0.133 0.035 0.000
## SPNV 0.099 0.124 -0.017 -0.032 0.251 0.000
## SPSR 0.055 -0.047 0.273 -0.062 0.075 0.061 0.000
## SPOR -0.021 0.017 0.031 -0.061 -0.019 0.019 0.025 0.000
## SIV 0.194 0.066 -0.014 0.021 0.151 0.008 -0.094 -0.025 0.000
## SINV 0.223 0.307 0.002 -0.035 0.263 0.226 0.087 0.013 0.078 0.000
## SISR 0.013 -0.081 0.322 -0.048 -0.002 -0.050 0.395 -0.006 -0.002 0.023
## SIOR -0.089 0.036 -0.140 0.052 -0.102 -0.036 -0.115 0.052 -0.021 -0.077
## SKV 0.036 -0.059 -0.032 -0.031 0.068 -0.055 0.072 0.050 0.155 0.051
## SKNV 0.151 0.087 0.057 0.008 0.082 0.188 0.000 0.004 0.050 0.145
## SKSR -0.091 0.006 0.112 -0.105 0.072 0.052 0.182 -0.081 0.046 0.001
## SKOR -0.075 0.010 -0.154 0.046 0.001 -0.091 -0.085 -0.102 0.038 -0.072
## SISR SIOR SKV SKNV SKSR SKOR
## IQV
## IQNV
## IQSR
## IQOR
## SPV
## SPNV
## SPSR
## SPOR
## SIV
## SINV
## SISR 0.000
## SIOR -0.066 0.000
## SKV 0.014 -0.032 0.000
## SKNV 0.053 -0.025 0.217 0.000
## SKSR 0.231 -0.032 0.056 0.081 0.000
## SKOR -0.086 0.100 -0.021 -0.042 0.006 0.000There were nineteen violations of local independence.
Assessing Objective and Subjective Relationships
#Experiment 1 - Objective
WEA951O.model <- '
AI =~ IQV + IQNV
SP =~ SPV + SPNV
HI =~ HIV + HINV'
WEA951O.fit <- cfa(WEA951O.model, sample.cov = WEA951.cor, sample.nobs = nWEA951, std.lv = T); "\n"## Warning in lav_object_post_check(object): lavaan WARNING: some estimated ov
## variances are negative## Warning in lav_object_post_check(object): lavaan WARNING: covariance matrix of latent variables
## is not positive definite;
## use lavInspect(fit, "cov.lv") to investigate.## [1] "\n"summary(WEA951O.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 64 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 15
##
## Number of observations 134
##
## Model Test User Model:
##
## Test statistic 14.259
## Degrees of freedom 6
## P-value (Chi-square) 0.027
##
## Model Test Baseline Model:
##
## Test statistic 81.341
## Degrees of freedom 15
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.876
## Tucker-Lewis Index (TLI) 0.689
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1104.274
## Loglikelihood unrestricted model (H1) -1097.145
##
## Akaike (AIC) 2238.549
## Bayesian (BIC) 2282.017
## Sample-size adjusted Bayesian (BIC) 2234.568
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.101
## 90 Percent confidence interval - lower 0.032
## 90 Percent confidence interval - upper 0.170
## P-value RMSEA <= 0.05 0.094
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.067
##
## 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
## AI =~
## IQV 0.852 0.286 2.982 0.003 0.852 0.855
## IQNV 0.280 0.124 2.253 0.024 0.280 0.281
## SP =~
## SPV 0.216 0.170 1.274 0.203 0.216 0.217
## SPNV 0.275 0.205 1.342 0.179 0.275 0.276
## HI =~
## HIV 0.416 0.212 1.960 0.050 0.416 0.417
## HINV 1.169 0.552 2.118 0.034 1.169 1.174
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AI ~~
## SP 1.105 0.825 1.340 0.180 1.105 1.105
## HI 0.214 0.154 1.394 0.163 0.214 0.214
## SP ~~
## HI 0.299 0.324 0.922 0.356 0.299 0.299
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .IQV 0.266 0.474 0.562 0.574 0.266 0.268
## .IQNV 0.914 0.123 7.449 0.000 0.914 0.921
## .SPV 0.946 0.132 7.174 0.000 0.946 0.953
## .SPNV 0.917 0.152 6.024 0.000 0.917 0.924
## .HIV 0.820 0.191 4.290 0.000 0.820 0.826
## .HINV -0.375 1.287 -0.291 0.771 -0.375 -0.378
## AI 1.000 1.000 1.000
## SP 1.000 1.000 1.000
## HI 1.000 1.000 1.000resid(WEA951O.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQV IQNV SPV SPNV HIV HINV
## IQV 0.000
## IQNV 0.000 0.000
## SPV 0.025 -0.057 0.000
## SPNV -0.011 -0.036 0.000 0.000
## HIV 0.023 -0.095 -0.197 0.086 0.000
## HINV -0.005 0.079 -0.136 0.093 0.000 0.000WEA951OM.model <- '
AI =~ IQV + IQNV
SP =~ SPV + SPNV
HI =~ HIV + HINV
HINV ~~ 0*HINV
AI ~~ 1*SP'
WEA951OM.fit <- cfa(WEA951OM.model, sample.cov = WEA951.cor, sample.nobs = nWEA951, std.lv = T); "\n"## Warning in lav_object_post_check(object): lavaan WARNING: covariance matrix of latent variables
## is not positive definite;
## use lavInspect(fit, "cov.lv") to investigate.## [1] "\n"summary(WEA951OM.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 27 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 13
##
## Number of observations 134
##
## Model Test User Model:
##
## Test statistic 14.393
## Degrees of freedom 8
## P-value (Chi-square) 0.072
##
## Model Test Baseline Model:
##
## Test statistic 81.341
## Degrees of freedom 15
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.904
## Tucker-Lewis Index (TLI) 0.819
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1104.342
## Loglikelihood unrestricted model (H1) -1097.145
##
## Akaike (AIC) 2234.683
## Bayesian (BIC) 2272.355
## Sample-size adjusted Bayesian (BIC) 2231.233
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.077
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.140
## P-value RMSEA <= 0.05 0.211
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.068
##
## 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
## AI =~
## IQV 0.913 0.298 3.060 0.002 0.913 0.917
## IQNV 0.261 0.120 2.176 0.030 0.261 0.262
## SP =~
## SPV 0.228 0.115 1.989 0.047 0.228 0.229
## SPNV 0.285 0.126 2.266 0.023 0.285 0.286
## HI =~
## HIV 0.488 0.081 6.047 0.000 0.488 0.490
## HINV 0.996 0.061 16.371 0.000 0.996 1.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AI ~~
## SP 1.000 1.000 1.000
## HI 0.234 0.115 2.032 0.042 0.234 0.234
## SP ~~
## HI 0.310 0.254 1.224 0.221 0.310 0.310
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .HINV 0.000 0.000 0.000
## .IQV 0.159 0.532 0.298 0.765 0.159 0.160
## .IQNV 0.924 0.121 7.616 0.000 0.924 0.931
## .SPV 0.941 0.120 7.830 0.000 0.941 0.948
## .SPNV 0.911 0.123 7.385 0.000 0.911 0.918
## .HIV 0.754 0.092 8.185 0.000 0.754 0.760
## AI 1.000 1.000 1.000
## SP 1.000 1.000 1.000
## HI 1.000 1.000 1.000resid(WEA951OM.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQV IQNV SPV SPNV HIV HINV
## IQV 0.000
## IQNV 0.000 0.000
## SPV 0.020 -0.050 0.000
## SPNV -0.012 -0.025 -0.005 0.000
## HIV -0.005 -0.100 -0.205 0.076 0.000
## HINV -0.004 0.089 -0.131 0.101 0.000 0.000There was one violation of local independence.
#Experiment 1 - Subjective
WEA951O.model <- '
AI =~ IQSR + IQOR
SP =~ SPSR + SPOR
HI =~ HISR + HIOR'
WEA951O.fit <- cfa(WEA951O.model, sample.cov = WEA951.cor, sample.nobs = nWEA951, std.lv = T); "\n"## Warning in lav_object_post_check(object): lavaan WARNING: covariance matrix of latent variables
## is not positive definite;
## use lavInspect(fit, "cov.lv") to investigate.## [1] "\n"summary(WEA951O.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 35 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 15
##
## Number of observations 134
##
## Model Test User Model:
##
## Test statistic 39.368
## Degrees of freedom 6
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 133.801
## Degrees of freedom 15
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.719
## Tucker-Lewis Index (TLI) 0.298
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1090.599
## Loglikelihood unrestricted model (H1) -1070.915
##
## Akaike (AIC) 2211.198
## Bayesian (BIC) 2254.665
## Sample-size adjusted Bayesian (BIC) 2207.217
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.204
## 90 Percent confidence interval - lower 0.146
## 90 Percent confidence interval - upper 0.266
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.098
##
## 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
## AI =~
## IQSR 0.744 0.154 4.848 0.000 0.744 0.747
## IQOR 0.333 0.103 3.230 0.001 0.333 0.335
## SP =~
## SPSR 0.533 0.207 2.579 0.010 0.533 0.535
## SPOR 0.186 0.108 1.721 0.085 0.186 0.187
## HI =~
## HISR 0.848 0.168 5.040 0.000 0.848 0.852
## HIOR 0.515 0.123 4.188 0.000 0.515 0.517
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AI ~~
## SP 1.190 0.471 2.523 0.012 1.190 1.190
## HI 0.327 0.140 2.335 0.020 0.327 0.327
## SP ~~
## HI 0.715 0.304 2.349 0.019 0.715 0.715
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .IQSR 0.438 0.208 2.106 0.035 0.438 0.442
## .IQOR 0.881 0.115 7.666 0.000 0.881 0.888
## .SPSR 0.709 0.221 3.210 0.001 0.709 0.714
## .SPOR 0.958 0.120 8.007 0.000 0.958 0.965
## .HISR 0.273 0.263 1.038 0.299 0.273 0.275
## .HIOR 0.728 0.131 5.562 0.000 0.728 0.733
## AI 1.000 1.000 1.000
## SP 1.000 1.000 1.000
## HI 1.000 1.000 1.000resid(WEA951O.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQSR IQOR SPSR SPOR HISR HIOR
## IQSR 0.000
## IQOR 0.000 0.000
## SPSR 0.025 -0.083 0.000
## SPOR -0.096 0.326 0.000 0.000
## HISR 0.032 -0.053 -0.005 0.006 0.000
## HIOR -0.126 0.173 -0.027 0.171 0.000 0.000WEA951OM.model <- '
AI =~ IQSR + IQOR
SP =~ SPSR + SPOR
HI =~ HISR + HIOR
AI ~~ 1*SP'
WEA951OM.fit <- cfa(WEA951OM.model, sample.cov = WEA951.cor, sample.nobs = nWEA951, std.lv = T); "\n"## Warning in lav_object_post_check(object): lavaan WARNING: covariance matrix of latent variables
## is not positive definite;
## use lavInspect(fit, "cov.lv") to investigate.## [1] "\n"summary(WEA951OM.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 23 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 14
##
## Number of observations 134
##
## Model Test User Model:
##
## Test statistic 39.464
## Degrees of freedom 7
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 133.801
## Degrees of freedom 15
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.727
## Tucker-Lewis Index (TLI) 0.414
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1090.647
## Loglikelihood unrestricted model (H1) -1070.915
##
## Akaike (AIC) 2209.294
## Bayesian (BIC) 2249.864
## Sample-size adjusted Bayesian (BIC) 2205.578
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.186
## 90 Percent confidence interval - lower 0.132
## 90 Percent confidence interval - upper 0.245
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.101
##
## 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
## AI =~
## IQSR 0.798 0.155 5.154 0.000 0.798 0.801
## IQOR 0.314 0.103 3.044 0.002 0.314 0.315
## SP =~
## SPSR 0.602 0.129 4.675 0.000 0.602 0.604
## SPOR 0.183 0.097 1.890 0.059 0.183 0.183
## HI =~
## HISR 0.880 0.182 4.833 0.000 0.880 0.883
## HIOR 0.497 0.125 3.976 0.000 0.497 0.499
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AI ~~
## SP 1.000 1.000 1.000
## HI 0.306 0.130 2.350 0.019 0.306 0.306
## SP ~~
## HI 0.616 0.196 3.143 0.002 0.616 0.616
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .IQSR 0.355 0.224 1.586 0.113 0.355 0.358
## .IQOR 0.894 0.116 7.738 0.000 0.894 0.901
## .SPSR 0.630 0.146 4.331 0.000 0.630 0.635
## .SPOR 0.959 0.118 8.104 0.000 0.959 0.966
## .HISR 0.219 0.299 0.734 0.463 0.219 0.221
## .HIOR 0.746 0.132 5.670 0.000 0.746 0.751
## AI 1.000 1.000 1.000
## SP 1.000 1.000 1.000
## HI 1.000 1.000 1.000resid(WEA951OM.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQSR IQOR SPSR SPOR HISR HIOR
## IQSR 0.000
## IQOR -0.002 0.000
## SPSR 0.016 -0.060 0.000
## SPOR -0.077 0.342 -0.011 0.000
## HISR 0.023 -0.045 -0.009 0.020 0.000
## HIOR -0.122 0.182 -0.016 0.184 0.000 0.000There were three violations of local independence.
#Experiment 2 - Objective
WEA952O.model <- '
AI =~ IQV + IQNV
SP =~ SPV + SPNV + SIV + SINV
SK =~ SKV + SKNV'
WEA952O.fit <- cfa(WEA952O.model, sample.cov = WEA952.cor, sample.nobs = nWEA952, std.lv = T)
summary(WEA952O.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 34 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 19
##
## Number of observations 227
##
## Model Test User Model:
##
## Test statistic 31.343
## Degrees of freedom 17
## P-value (Chi-square) 0.018
##
## Model Test Baseline Model:
##
## Test statistic 168.074
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.898
## Tucker-Lewis Index (TLI) 0.831
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2504.418
## Loglikelihood unrestricted model (H1) -2488.747
##
## Akaike (AIC) 5046.836
## Bayesian (BIC) 5111.910
## Sample-size adjusted Bayesian (BIC) 5051.693
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.061
## 90 Percent confidence interval - lower 0.025
## 90 Percent confidence interval - upper 0.094
## P-value RMSEA <= 0.05 0.267
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.052
##
## 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
## AI =~
## IQV 0.524 0.090 5.814 0.000 0.524 0.525
## IQNV 0.589 0.095 6.171 0.000 0.589 0.590
## SP =~
## SPV 0.481 0.082 5.858 0.000 0.481 0.482
## SPNV 0.418 0.082 5.106 0.000 0.418 0.419
## SIV 0.269 0.083 3.253 0.001 0.269 0.269
## SINV 0.631 0.085 7.391 0.000 0.631 0.633
## SK =~
## SKV 0.285 0.132 2.155 0.031 0.285 0.286
## SKNV 0.838 0.343 2.443 0.015 0.838 0.840
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AI ~~
## SP 0.742 0.114 6.514 0.000 0.742 0.742
## SK 0.282 0.153 1.841 0.066 0.282 0.282
## SP ~~
## SK 0.338 0.161 2.096 0.036 0.338 0.338
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .IQV 0.721 0.097 7.454 0.000 0.721 0.724
## .IQNV 0.649 0.106 6.098 0.000 0.649 0.652
## .SPV 0.765 0.088 8.664 0.000 0.765 0.768
## .SPNV 0.821 0.089 9.271 0.000 0.821 0.824
## .SIV 0.923 0.091 10.157 0.000 0.923 0.927
## .SINV 0.597 0.096 6.229 0.000 0.597 0.600
## .SKV 0.914 0.108 8.456 0.000 0.914 0.918
## .SKNV 0.294 0.568 0.516 0.606 0.294 0.295
## AI 1.000 1.000 1.000
## SP 1.000 1.000 1.000
## SK 1.000 1.000 1.000resid(WEA952O.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQV IQNV SPV SPNV SIV SINV SKV SKNV
## IQV 0.000
## IQNV 0.000 0.000
## SPV -0.058 -0.051 0.000
## SPNV -0.043 -0.034 0.078 0.000
## SIV 0.125 -0.008 0.070 -0.073 0.000
## SINV 0.003 0.063 -0.005 -0.015 -0.050 0.000
## SKV 0.018 -0.078 0.043 -0.081 0.154 0.009 0.000
## SKNV 0.046 -0.030 -0.037 0.081 -0.006 -0.020 0.000 0.000There was one violation of local independence.
#Experiment 2 - Subjective
WEA952O.model <- '
AI =~ IQSR + IQOR
SP =~ SPSR + SPOR + SISR + SIOR
SK =~ SKSR + SKOR'
WEA952O.fit <- cfa(WEA952O.model, sample.cov = WEA952.cor, sample.nobs = nWEA952, std.lv = T); "\n"## Warning in lav_object_post_check(object): lavaan WARNING: some estimated ov
## variances are negative## [1] "\n"summary(WEA952O.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 50 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 19
##
## Number of observations 227
##
## Model Test User Model:
##
## Test statistic 182.052
## Degrees of freedom 17
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 521.714
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.666
## Tucker-Lewis Index (TLI) 0.449
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2402.952
## Loglikelihood unrestricted model (H1) -2311.926
##
## Akaike (AIC) 4843.905
## Bayesian (BIC) 4908.979
## Sample-size adjusted Bayesian (BIC) 4848.763
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.207
## 90 Percent confidence interval - lower 0.180
## 90 Percent confidence interval - upper 0.234
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.147
##
## 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
## AI =~
## IQSR 0.235 0.096 2.464 0.014 0.235 0.236
## IQOR 1.481 0.438 3.380 0.001 1.481 1.484
## SP =~
## SPSR 0.220 0.070 3.119 0.002 0.220 0.220
## SPOR 0.608 0.068 8.979 0.000 0.608 0.609
## SISR 0.318 0.070 4.560 0.000 0.318 0.319
## SIOR 0.916 0.068 13.425 0.000 0.916 0.918
## SK =~
## SKSR 0.323 0.082 3.924 0.000 0.323 0.324
## SKOR 1.139 0.185 6.161 0.000 1.139 1.142
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AI ~~
## SP 0.368 0.124 2.978 0.003 0.368 0.368
## SK 0.296 0.111 2.660 0.008 0.296 0.296
## SP ~~
## SK 0.456 0.092 4.933 0.000 0.456 0.456
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .IQSR 0.940 0.094 9.986 0.000 0.940 0.944
## .IQOR -1.197 1.304 -0.918 0.359 -1.197 -1.202
## .SPSR 0.947 0.090 10.567 0.000 0.947 0.952
## .SPOR 0.626 0.070 8.903 0.000 0.626 0.629
## .SISR 0.894 0.086 10.443 0.000 0.894 0.898
## .SIOR 0.157 0.085 1.842 0.065 0.157 0.158
## .SKSR 0.891 0.090 9.904 0.000 0.891 0.895
## .SKOR -0.303 0.413 -0.733 0.463 -0.303 -0.304
## AI 1.000 1.000 1.000
## SP 1.000 1.000 1.000
## SK 1.000 1.000 1.000resid(WEA952O.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQSR IQOR SPSR SPOR SISR SIOR SKSR SKOR
## IQSR 0.000
## IQOR 0.000 0.000
## SPSR 0.351 0.030 0.000
## SPOR 0.157 -0.003 0.126 0.000
## SISR 0.412 0.036 0.480 0.086 0.000
## SIOR -0.010 0.008 -0.042 0.001 -0.023 0.000
## SKSR 0.197 -0.012 0.247 0.010 0.303 0.044 0.000
## SKOR -0.030 -0.011 -0.015 -0.077 -0.026 0.022 0.000 0.000WEA952OM.model <- '
AI =~ IQSR + IQOR
SP =~ SPSR + SPOR + SISR + SIOR
SK =~ SKSR + SKOR
IQOR ~~ 0*IQOR
SKOR ~~ 0*SKOR'
WEA952OM.fit <- cfa(WEA952OM.model, sample.cov = WEA952.cor, sample.nobs = nWEA952, std.lv = T)
summary(WEA952OM.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 24 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 17
##
## Number of observations 227
##
## Model Test User Model:
##
## Test statistic 185.405
## Degrees of freedom 19
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 521.714
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.663
## Tucker-Lewis Index (TLI) 0.503
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2404.629
## Loglikelihood unrestricted model (H1) -2311.926
##
## Akaike (AIC) 4843.258
## Bayesian (BIC) 4901.482
## Sample-size adjusted Bayesian (BIC) 4847.604
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.196
## 90 Percent confidence interval - lower 0.171
## 90 Percent confidence interval - upper 0.223
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.136
##
## 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
## AI =~
## IQSR 0.349 0.064 5.443 0.000 0.349 0.350
## IQOR 0.998 0.047 21.307 0.000 0.998 1.000
## SP =~
## SPSR 0.269 0.072 3.740 0.000 0.269 0.269
## SPOR 0.634 0.067 9.397 0.000 0.634 0.635
## SISR 0.362 0.071 5.108 0.000 0.362 0.363
## SIOR 0.865 0.067 12.954 0.000 0.865 0.867
## SK =~
## SKSR 0.369 0.064 5.776 0.000 0.369 0.370
## SKOR 0.998 0.047 21.307 0.000 0.998 1.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AI ~~
## SP 0.575 0.055 10.425 0.000 0.575 0.575
## SK 0.490 0.050 9.715 0.000 0.490 0.490
## SP ~~
## SK 0.531 0.058 9.171 0.000 0.531 0.531
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .IQOR 0.000 0.000 0.000
## .SKOR 0.000 0.000 0.000
## .IQSR 0.874 0.082 10.654 0.000 0.874 0.878
## .SPSR 0.923 0.088 10.468 0.000 0.923 0.928
## .SPOR 0.594 0.069 8.584 0.000 0.594 0.597
## .SISR 0.865 0.084 10.281 0.000 0.865 0.868
## .SIOR 0.247 0.075 3.277 0.001 0.247 0.248
## .SKSR 0.859 0.081 10.654 0.000 0.859 0.863
## AI 1.000 1.000 1.000
## SP 1.000 1.000 1.000
## SK 1.000 1.000 1.000resid(WEA952OM.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQSR IQOR SPSR SPOR SISR SIOR SKSR SKOR
## IQSR 0.000
## IQOR 0.000 0.000
## SPSR 0.316 -0.005 0.000
## SPOR 0.082 -0.035 0.089 0.000
## SISR 0.367 0.001 0.452 0.050 0.000
## SIOR -0.105 0.011 -0.073 0.009 -0.045 0.000
## SKSR 0.157 -0.051 0.227 -0.025 0.279 0.010 0.000
## SKOR -0.121 0.000 -0.043 -0.097 -0.053 0.040 0.000 0.000There were six violations of local independence.
Objective versus Subjective
#Experiment 1
WEA951.model <- '
AIO =~ IQV + IQNV
AIS =~ IQSR + IQOR
SPO =~ SPV + SPNV
SPS =~ SPSR + SPOR
HIO =~ HIV + HINV
HIS =~ HISR + HIOR'
WEA951.fit <- cfa(WEA951.model, sample.cov = WEA951.cor, sample.nobs = nWEA951, std.lv = T); "\n"## Warning in lav_object_post_check(object): lavaan WARNING: covariance matrix of latent variables
## is not positive definite;
## use lavInspect(fit, "cov.lv") to investigate.## [1] "\n"summary(WEA951.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 71 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 39
##
## Number of observations 134
##
## Model Test User Model:
##
## Test statistic 87.580
## Degrees of freedom 39
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 331.949
## Degrees of freedom 66
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.817
## Tucker-Lewis Index (TLI) 0.691
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2153.446
## Loglikelihood unrestricted model (H1) -2109.656
##
## Akaike (AIC) 4384.892
## Bayesian (BIC) 4497.908
## Sample-size adjusted Bayesian (BIC) 4374.542
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.096
## 90 Percent confidence interval - lower 0.069
## 90 Percent confidence interval - upper 0.123
## P-value RMSEA <= 0.05 0.004
##
## 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
## AIO =~
## IQV 0.923 0.302 3.058 0.002 0.923 0.926
## IQNV 0.258 0.118 2.185 0.029 0.258 0.259
## AIS =~
## IQSR 0.618 0.118 5.236 0.000 0.618 0.620
## IQOR 0.401 0.101 3.982 0.000 0.401 0.403
## SPO =~
## SPV 0.151 0.131 1.150 0.250 0.151 0.151
## SPNV 0.395 0.273 1.448 0.148 0.395 0.397
## SPS =~
## SPSR 0.441 0.178 2.473 0.013 0.441 0.443
## SPOR 0.225 0.117 1.917 0.055 0.225 0.226
## HIO =~
## HIV 0.529 0.091 5.814 0.000 0.529 0.531
## HINV 0.920 0.100 9.199 0.000 0.920 0.924
## HIS =~
## HISR 0.753 0.092 8.214 0.000 0.753 0.756
## HIOR 0.580 0.089 6.486 0.000 0.580 0.582
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AIO ~~
## AIS 0.491 0.203 2.418 0.016 0.491 0.491
## SPO 0.784 0.588 1.333 0.182 0.784 0.784
## SPS 0.219 0.217 1.009 0.313 0.219 0.219
## HIO 0.247 0.124 1.992 0.046 0.247 0.247
## HIS 0.148 0.123 1.198 0.231 0.148 0.148
## AIS ~~
## SPO 0.915 0.652 1.402 0.161 0.915 0.915
## SPS 1.536 0.601 2.557 0.011 1.536 1.536
## HIO 0.320 0.138 2.318 0.020 0.320 0.320
## HIS 0.369 0.157 2.352 0.019 0.369 0.369
## SPO ~~
## SPS 1.371 1.067 1.285 0.199 1.371 1.371
## HIO 0.404 0.336 1.202 0.229 0.404 0.404
## HIS 0.568 0.435 1.304 0.192 0.568 0.568
## SPS ~~
## HIO 0.546 0.262 2.085 0.037 0.546 0.546
## HIS 0.899 0.364 2.467 0.014 0.899 0.899
## HIO ~~
## HIS 0.817 0.095 8.612 0.000 0.817 0.817
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .IQV 0.141 0.544 0.260 0.795 0.141 0.142
## .IQNV 0.926 0.121 7.661 0.000 0.926 0.933
## .IQSR 0.610 0.133 4.585 0.000 0.610 0.615
## .IQOR 0.831 0.112 7.443 0.000 0.831 0.838
## .SPV 0.970 0.122 7.936 0.000 0.970 0.977
## .SPNV 0.836 0.229 3.645 0.000 0.836 0.843
## .SPSR 0.798 0.171 4.675 0.000 0.798 0.804
## .SPOR 0.942 0.121 7.805 0.000 0.942 0.949
## .HIV 0.713 0.099 7.236 0.000 0.713 0.719
## .HINV 0.146 0.141 1.035 0.301 0.146 0.147
## .HISR 0.426 0.099 4.309 0.000 0.426 0.429
## .HIOR 0.656 0.094 6.951 0.000 0.656 0.661
## AIO 1.000 1.000 1.000
## AIS 1.000 1.000 1.000
## SPO 1.000 1.000 1.000
## SPS 1.000 1.000 1.000
## HIO 1.000 1.000 1.000
## HIS 1.000 1.000 1.000resid(WEA951.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQV IQNV IQSR IQOR SPV SPNV SPSR SPOR HIV HINV
## IQV 0.000
## IQNV 0.000 0.000
## IQSR -0.022 -0.029 0.000
## IQOR 0.047 0.039 0.000 0.000
## SPV 0.120 -0.021 -0.046 -0.066 0.000
## SPNV -0.038 -0.031 -0.005 0.064 0.000 0.000
## SPSR 0.050 0.005 0.078 -0.144 -0.022 0.039 0.000
## SPOR -0.116 -0.023 -0.145 0.260 -0.217 -0.003 0.000 0.000
## HIV -0.021 -0.104 0.035 0.052 -0.202 0.035 0.082 0.025 0.000
## HINV -0.001 0.091 0.007 -0.029 -0.116 0.042 -0.013 0.006 0.000 0.000
## HISR 0.027 0.061 0.067 -0.072 -0.015 0.110 0.019 -0.033 0.002 -0.010
## HIOR -0.060 0.018 -0.133 0.143 -0.210 -0.141 -0.062 0.122 -0.002 0.021
## HISR HIOR
## IQV
## IQNV
## IQSR
## IQOR
## SPV
## SPNV
## SPSR
## SPOR
## HIV
## HINV
## HISR 0.000
## HIOR 0.000 0.000WEA951OM.model <- '
AIO =~ IQV + IQNV
AIS =~ IQSR + IQOR
SPO =~ SPV + SPNV
SPS =~ SPSR + SPOR
HIO =~ HIV + HINV
HIS =~ HISR + HIOR
SPS ~~ 1*AIS + 1*SPO'
WEA951OM.fit <- cfa(WEA951OM.model, sample.cov = WEA951.cor, sample.nobs = nWEA951, std.lv = T); "\n"## Warning in lav_object_post_check(object): lavaan WARNING: covariance matrix of latent variables
## is not positive definite;
## use lavInspect(fit, "cov.lv") to investigate.## [1] "\n"summary(WEA951OM.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 54 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 37
##
## Number of observations 134
##
## Model Test User Model:
##
## Test statistic 89.181
## Degrees of freedom 41
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 331.949
## Degrees of freedom 66
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.819
## Tucker-Lewis Index (TLI) 0.708
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2154.247
## Loglikelihood unrestricted model (H1) -2109.656
##
## Akaike (AIC) 4382.493
## Bayesian (BIC) 4489.713
## Sample-size adjusted Bayesian (BIC) 4372.673
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.094
## 90 Percent confidence interval - lower 0.067
## 90 Percent confidence interval - upper 0.120
## P-value RMSEA <= 0.05 0.005
##
## 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
## AIO =~
## IQV 0.946 0.326 2.905 0.004 0.946 0.948
## IQNV 0.252 0.120 2.101 0.036 0.252 0.253
## AIS =~
## IQSR 0.716 0.120 5.991 0.000 0.716 0.719
## IQOR 0.375 0.100 3.749 0.000 0.375 0.376
## SPO =~
## SPV 0.175 0.098 1.779 0.075 0.175 0.175
## SPNV 0.399 0.126 3.156 0.002 0.399 0.400
## SPS =~
## SPSR 0.621 0.113 5.513 0.000 0.621 0.623
## SPOR 0.245 0.097 2.530 0.011 0.245 0.246
## HIO =~
## HIV 0.529 0.091 5.822 0.000 0.529 0.531
## HINV 0.919 0.100 9.198 0.000 0.919 0.923
## HIS =~
## HISR 0.761 0.092 8.274 0.000 0.761 0.763
## HIOR 0.576 0.089 6.432 0.000 0.576 0.577
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AIS ~~
## SPS 1.000 1.000 1.000
## SPO ~~
## SPS 1.000 1.000 1.000
## AIO ~~
## AIS 0.421 0.183 2.298 0.022 0.421 0.421
## SPO 0.762 0.373 2.042 0.041 0.762 0.762
## SPS 0.176 0.150 1.177 0.239 0.176 0.176
## HIO 0.239 0.124 1.930 0.054 0.239 0.239
## HIS 0.141 0.121 1.172 0.241 0.141 0.141
## AIS ~~
## SPO 0.757 0.293 2.586 0.010 0.757 0.757
## HIO 0.288 0.124 2.323 0.020 0.288 0.288
## HIS 0.323 0.139 2.315 0.021 0.323 0.323
## SPO ~~
## HIO 0.378 0.221 1.708 0.088 0.378 0.378
## HIS 0.549 0.249 2.208 0.027 0.549 0.549
## SPS ~~
## HIO 0.401 0.145 2.766 0.006 0.401 0.401
## HIS 0.660 0.166 3.980 0.000 0.660 0.660
## HIO ~~
## HIS 0.814 0.095 8.588 0.000 0.814 0.814
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .IQV 0.100 0.604 0.166 0.868 0.100 0.101
## .IQNV 0.929 0.121 7.654 0.000 0.929 0.936
## .IQSR 0.480 0.146 3.276 0.001 0.480 0.483
## .IQOR 0.852 0.112 7.594 0.000 0.852 0.858
## .SPV 0.962 0.119 8.103 0.000 0.962 0.969
## .SPNV 0.834 0.127 6.558 0.000 0.834 0.840
## .SPSR 0.607 0.126 4.824 0.000 0.607 0.612
## .SPOR 0.933 0.116 8.024 0.000 0.933 0.940
## .HIV 0.713 0.099 7.233 0.000 0.713 0.718
## .HINV 0.148 0.140 1.051 0.293 0.148 0.149
## .HISR 0.415 0.100 4.154 0.000 0.415 0.418
## .HIOR 0.662 0.095 6.991 0.000 0.662 0.666
## AIO 1.000 1.000 1.000
## AIS 1.000 1.000 1.000
## SPO 1.000 1.000 1.000
## SPS 1.000 1.000 1.000
## HIO 1.000 1.000 1.000
## HIS 1.000 1.000 1.000resid(WEA951OM.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQV IQNV IQSR IQOR SPV SPNV SPSR SPOR HIV HINV
## IQV 0.000
## IQNV 0.000 0.000
## IQSR -0.027 -0.027 0.000
## IQOR 0.080 0.050 -0.020 0.000
## SPV 0.103 -0.024 -0.055 -0.060 0.000
## SPNV -0.039 -0.027 0.002 0.096 -0.010 0.000
## SPSR 0.036 0.002 0.052 -0.104 -0.039 0.031 0.000
## SPOR -0.111 -0.021 -0.107 0.307 -0.213 0.022 -0.053 0.000
## HIV -0.020 -0.102 0.030 0.062 -0.205 0.040 0.077 0.038 0.000
## HINV 0.001 0.094 -0.001 -0.010 -0.121 0.050 -0.021 0.029 0.000 0.000
## HISR 0.028 0.063 0.063 -0.053 -0.023 0.112 0.006 -0.004 0.000 -0.013
## HIOR -0.057 0.019 -0.134 0.160 -0.216 -0.137 -0.067 0.146 0.000 0.026
## HISR HIOR
## IQV
## IQNV
## IQSR
## IQOR
## SPV
## SPNV
## SPSR
## SPOR
## HIV
## HINV
## HISR 0.000
## HIOR -0.001 0.000There were three violations of local independence but none with scaling.
#Experiment 2
WEA952.model <- '
AIO =~ IQV + IQNV
AIS =~ IQSR + IQOR
SPO =~ SPV + SPNV + SIV + SINV
SPS =~ SPSR + SPOR + SISR + SIOR
SKO =~ SKV + SKNV
SKS =~ SKSR + SKOR'
WEA952.fit <- cfa(WEA952.model, sample.cov = WEA952.cor, sample.nobs = nWEA952, std.lv = T); "\n"## Warning in lav_object_post_check(object): lavaan WARNING: some estimated ov
## variances are negative## [1] "\n"summary(WEA952.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 53 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 47
##
## Number of observations 227
##
## Model Test User Model:
##
## Test statistic 281.169
## Degrees of freedom 89
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 772.511
## Degrees of freedom 120
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.705
## Tucker-Lewis Index (TLI) 0.603
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4899.896
## Loglikelihood unrestricted model (H1) -4759.312
##
## Akaike (AIC) 9893.792
## Bayesian (BIC) 10054.765
## Sample-size adjusted Bayesian (BIC) 9905.809
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.098
## 90 Percent confidence interval - lower 0.085
## 90 Percent confidence interval - upper 0.110
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.090
##
## 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
## AIO =~
## IQV 0.509 0.086 5.940 0.000 0.509 0.510
## IQNV 0.606 0.093 6.541 0.000 0.606 0.607
## AIS =~
## IQSR 0.290 0.082 3.524 0.000 0.290 0.291
## IQOR 1.200 0.213 5.632 0.000 1.200 1.203
## SPO =~
## SPV 0.481 0.082 5.894 0.000 0.481 0.482
## SPNV 0.420 0.082 5.145 0.000 0.420 0.421
## SIV 0.281 0.082 3.420 0.001 0.281 0.282
## SINV 0.623 0.084 7.389 0.000 0.623 0.624
## SPS =~
## SPSR 0.259 0.072 3.612 0.000 0.259 0.259
## SPOR 0.632 0.067 9.374 0.000 0.632 0.633
## SISR 0.350 0.071 4.943 0.000 0.350 0.350
## SIOR 0.874 0.067 13.082 0.000 0.874 0.876
## SKO =~
## SKV 0.334 0.120 2.780 0.005 0.334 0.335
## SKNV 0.715 0.225 3.183 0.001 0.715 0.717
## SKS =~
## SKSR 0.346 0.080 4.321 0.000 0.346 0.347
## SKOR 1.063 0.154 6.918 0.000 1.063 1.066
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AIO ~~
## AIS 0.271 0.091 2.966 0.003 0.271 0.271
## SPO 0.740 0.114 6.490 0.000 0.740 0.740
## SPS 0.250 0.104 2.404 0.016 0.250 0.250
## SKO 0.301 0.146 2.065 0.039 0.301 0.301
## SKS 0.172 0.092 1.879 0.060 0.172 0.172
## AIS ~~
## SPO 0.154 0.078 1.978 0.048 0.154 0.154
## SPS 0.472 0.100 4.706 0.000 0.472 0.472
## SKO 0.090 0.079 1.141 0.254 0.090 0.090
## SKS 0.391 0.101 3.878 0.000 0.391 0.391
## SPO ~~
## SPS 0.226 0.097 2.339 0.019 0.226 0.226
## SKO 0.393 0.148 2.650 0.008 0.393 0.393
## SKS 0.090 0.084 1.073 0.283 0.090 0.090
## SPS ~~
## SKO 0.105 0.103 1.022 0.307 0.105 0.105
## SKS 0.495 0.090 5.509 0.000 0.495 0.495
## SKO ~~
## SKS 0.109 0.089 1.226 0.220 0.109 0.109
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .IQV 0.736 0.092 8.012 0.000 0.736 0.739
## .IQNV 0.628 0.104 6.037 0.000 0.628 0.631
## .IQSR 0.911 0.090 10.070 0.000 0.911 0.915
## .IQOR -0.445 0.506 -0.879 0.380 -0.445 -0.447
## .SPV 0.764 0.088 8.701 0.000 0.764 0.768
## .SPNV 0.819 0.088 9.285 0.000 0.819 0.823
## .SIV 0.916 0.091 10.114 0.000 0.916 0.920
## .SINV 0.607 0.094 6.472 0.000 0.607 0.610
## .SPSR 0.929 0.089 10.490 0.000 0.929 0.933
## .SPOR 0.597 0.069 8.629 0.000 0.597 0.599
## .SISR 0.873 0.085 10.325 0.000 0.873 0.877
## .SIOR 0.232 0.076 3.029 0.002 0.232 0.233
## .SKV 0.884 0.107 8.246 0.000 0.884 0.888
## .SKNV 0.484 0.314 1.543 0.123 0.484 0.487
## .SKSR 0.876 0.089 9.875 0.000 0.876 0.879
## .SKOR -0.135 0.314 -0.431 0.666 -0.135 -0.136
## AIO 1.000 1.000 1.000
## AIS 1.000 1.000 1.000
## SPO 1.000 1.000 1.000
## SPS 1.000 1.000 1.000
## SKO 1.000 1.000 1.000
## SKS 1.000 1.000 1.000resid(WEA952.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQV IQNV IQSR IQOR SPV SPNV SIV SINV SPSR SPOR
## IQV 0.000
## IQNV 0.000 0.000
## IQSR 0.160 0.012 0.000
## IQOR 0.004 0.012 0.000 0.000
## SPV -0.052 -0.057 0.168 0.071 0.000
## SPNV -0.039 -0.039 0.001 -0.028 0.077 0.000
## SIV 0.123 -0.017 0.037 0.108 0.064 -0.079 0.000
## SINV 0.014 0.059 0.022 -0.046 -0.001 -0.013 -0.056 0.000
## SPSR 0.077 -0.019 0.334 0.003 0.122 0.085 -0.027 0.113 0.000
## SPOR -0.001 0.044 0.123 -0.029 0.051 0.050 0.090 0.041 0.096 0.000
## SISR 0.035 -0.053 0.392 0.011 0.052 -0.023 0.078 0.050 0.459 0.058
## SIOR -0.082 0.047 -0.050 0.013 -0.036 -0.013 0.104 -0.064 -0.067 0.006
## SKV 0.009 -0.091 0.001 0.024 0.027 -0.095 0.143 -0.012 0.101 0.098
## SKNV 0.060 -0.021 0.071 0.002 -0.036 0.082 -0.009 -0.016 0.010 0.012
## SKSR -0.061 0.044 0.181 -0.033 0.115 0.077 0.101 0.030 0.235 -0.009
## SKOR -0.054 0.039 -0.071 -0.011 0.064 -0.060 0.133 -0.040 -0.037 -0.094
## SISR SIOR SKV SKNV SKSR SKOR
## IQV
## IQNV
## IQSR
## IQOR
## SPV
## SPNV
## SIV
## SINV
## SPSR
## SPOR
## SISR 0.000
## SIOR -0.037 0.000
## SKV 0.048 0.019 0.000
## SKNV 0.064 -0.026 0.000 0.000
## SKSR 0.290 0.029 0.117 0.113 0.000
## SKOR -0.045 0.038 0.081 -0.014 0.000 0.000WEA952OM.model <- '
AIO =~ IQV + IQNV
AIS =~ IQSR + IQOR
SPO =~ SPV + SPNV + SIV + SINV
SPS =~ SPSR + SPOR + SISR + SIOR
SKO =~ SKV + SKNV
SKS =~ SKSR + SKOR
IQOR ~~ 0*IQOR
SKOR ~~ 0*SKOR'
WEA952OM.fit <- cfa(WEA952OM.model, sample.cov = WEA952.cor, sample.nobs = nWEA952, std.lv = T)
summary(WEA952OM.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 44 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 45
##
## Number of observations 227
##
## Model Test User Model:
##
## Test statistic 282.248
## Degrees of freedom 91
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 772.511
## Degrees of freedom 120
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.707
## Tucker-Lewis Index (TLI) 0.613
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4900.436
## Loglikelihood unrestricted model (H1) -4759.312
##
## Akaike (AIC) 9890.871
## Bayesian (BIC) 10044.994
## Sample-size adjusted Bayesian (BIC) 9902.376
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.096
## 90 Percent confidence interval - lower 0.084
## 90 Percent confidence interval - upper 0.109
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.087
##
## 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
## AIO =~
## IQV 0.517 0.086 6.019 0.000 0.517 0.518
## IQNV 0.597 0.092 6.521 0.000 0.597 0.598
## AIS =~
## IQSR 0.349 0.064 5.443 0.000 0.349 0.350
## IQOR 0.998 0.047 21.307 0.000 0.998 1.000
## SPO =~
## SPV 0.482 0.082 5.914 0.000 0.482 0.483
## SPNV 0.419 0.082 5.134 0.000 0.419 0.420
## SIV 0.285 0.082 3.460 0.001 0.285 0.285
## SINV 0.621 0.084 7.377 0.000 0.621 0.622
## SPS =~
## SPSR 0.287 0.072 3.984 0.000 0.287 0.288
## SPOR 0.644 0.067 9.567 0.000 0.644 0.646
## SISR 0.375 0.071 5.277 0.000 0.375 0.376
## SIOR 0.847 0.066 12.744 0.000 0.847 0.849
## SKO =~
## SKV 0.339 0.119 2.854 0.004 0.339 0.340
## SKNV 0.704 0.215 3.271 0.001 0.704 0.706
## SKS =~
## SKSR 0.369 0.064 5.776 0.000 0.369 0.370
## SKOR 0.998 0.047 21.307 0.000 0.998 1.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AIO ~~
## AIS 0.342 0.091 3.750 0.000 0.342 0.342
## SPO 0.743 0.114 6.512 0.000 0.743 0.743
## SPS 0.255 0.106 2.405 0.016 0.255 0.255
## SKO 0.307 0.146 2.100 0.036 0.307 0.307
## SKS 0.182 0.094 1.925 0.054 0.182 0.182
## AIS ~~
## SPO 0.199 0.087 2.292 0.022 0.199 0.199
## SPS 0.579 0.055 10.468 0.000 0.579 0.579
## SKO 0.121 0.095 1.277 0.202 0.121 0.121
## SKS 0.490 0.050 9.715 0.000 0.490 0.490
## SPO ~~
## SPS 0.245 0.098 2.496 0.013 0.245 0.245
## SKO 0.398 0.147 2.706 0.007 0.398 0.398
## SKS 0.104 0.089 1.176 0.239 0.104 0.104
## SPS ~~
## SKO 0.117 0.106 1.103 0.270 0.117 0.117
## SKS 0.529 0.058 9.052 0.000 0.529 0.529
## SKO ~~
## SKS 0.129 0.095 1.355 0.175 0.129 0.129
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .IQOR 0.000 0.000 0.000
## .SKOR 0.000 0.000 0.000
## .IQV 0.728 0.092 7.894 0.000 0.728 0.731
## .IQNV 0.639 0.102 6.269 0.000 0.639 0.642
## .IQSR 0.874 0.082 10.654 0.000 0.874 0.877
## .SPV 0.763 0.088 8.689 0.000 0.763 0.766
## .SPNV 0.820 0.088 9.295 0.000 0.820 0.824
## .SIV 0.915 0.091 10.101 0.000 0.915 0.919
## .SINV 0.610 0.094 6.523 0.000 0.610 0.613
## .SPSR 0.913 0.088 10.422 0.000 0.913 0.917
## .SPOR 0.581 0.069 8.443 0.000 0.581 0.583
## .SISR 0.855 0.084 10.223 0.000 0.855 0.859
## .SIOR 0.279 0.073 3.830 0.000 0.279 0.280
## .SKV 0.881 0.107 8.236 0.000 0.881 0.884
## .SKNV 0.499 0.296 1.687 0.092 0.499 0.502
## .SKSR 0.859 0.081 10.654 0.000 0.859 0.863
## AIO 1.000 1.000 1.000
## AIS 1.000 1.000 1.000
## SPO 1.000 1.000 1.000
## SPS 1.000 1.000 1.000
## SKO 1.000 1.000 1.000
## SKS 1.000 1.000 1.000resid(WEA952OM.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQV IQNV IQSR IQOR SPV SPNV SIV SINV SPSR SPOR
## IQV 0.000
## IQNV 0.000 0.000
## IQSR 0.138 -0.012 0.000
## IQOR -0.007 0.005 0.000 0.000
## SPV -0.056 -0.055 0.156 0.064 0.000
## SPNV -0.042 -0.036 -0.009 -0.034 0.077 0.000
## SIV 0.120 -0.017 0.030 0.103 0.062 -0.080 0.000
## SINV 0.011 0.064 0.007 -0.054 -0.001 -0.011 -0.057 0.000
## SPSR 0.072 -0.024 0.312 -0.017 0.116 0.080 -0.030 0.106 0.000
## SPOR -0.005 0.042 0.079 -0.044 0.044 0.044 0.085 0.032 0.074 0.000
## SISR 0.030 -0.057 0.364 -0.008 0.046 -0.029 0.074 0.043 0.442 0.037
## SIOR -0.082 0.051 -0.102 0.019 -0.040 -0.017 0.101 -0.069 -0.084 0.012
## SKV 0.006 -0.092 -0.004 0.019 0.025 -0.097 0.141 -0.014 0.099 0.094
## SKNV 0.058 -0.020 0.060 -0.005 -0.036 0.082 -0.010 -0.015 0.006 0.007
## SKSR -0.065 0.040 0.157 -0.051 0.111 0.074 0.099 0.026 0.224 -0.026
## SKOR -0.054 0.041 -0.122 0.000 0.060 -0.064 0.130 -0.045 -0.052 -0.102
## SISR SIOR SKV SKNV SKSR SKOR
## IQV
## IQNV
## IQSR
## IQOR
## SPV
## SPNV
## SIV
## SINV
## SPSR
## SPOR
## SISR 0.000
## SIOR -0.049 0.000
## SKV 0.045 0.016 0.000
## SKNV 0.059 -0.030 0.000 0.000
## SKSR 0.276 0.014 0.114 0.106 0.000
## SKOR -0.059 0.051 0.076 -0.021 0.000 0.000There were eight violations of local independence but scaling reduced them to three.
Just One g for Objective Measurements?
#Experiment 2 - Objective
WEA952O.model <- '
AI =~ IQV + IQNV
SP =~ SPV + SPNV + SIV + SINV
SK =~ SKV + SKNV
AI ~~ 1*SP'
WEA952O.fit <- cfa(WEA952O.model, sample.cov = WEA952.cor, sample.nobs = nWEA952, std.lv = T); "\n"## Warning in lav_object_post_check(object): lavaan WARNING: covariance matrix of latent variables
## is not positive definite;
## use lavInspect(fit, "cov.lv") to investigate.## [1] "\n"summary(WEA952O.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 32 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 18
##
## Number of observations 227
##
## Model Test User Model:
##
## Test statistic 35.730
## Degrees of freedom 18
## P-value (Chi-square) 0.008
##
## Model Test Baseline Model:
##
## Test statistic 168.074
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.873
## Tucker-Lewis Index (TLI) 0.803
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2506.611
## Loglikelihood unrestricted model (H1) -2488.747
##
## Akaike (AIC) 5049.223
## Bayesian (BIC) 5110.872
## Sample-size adjusted Bayesian (BIC) 5053.825
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.066
## 90 Percent confidence interval - lower 0.033
## 90 Percent confidence interval - upper 0.097
## P-value RMSEA <= 0.05 0.187
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.055
##
## 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
## AI =~
## IQV 0.454 0.081 5.621 0.000 0.454 0.455
## IQNV 0.500 0.081 6.182 0.000 0.500 0.501
## SP =~
## SPV 0.447 0.080 5.579 0.000 0.447 0.448
## SPNV 0.395 0.081 4.903 0.000 0.395 0.396
## SIV 0.278 0.081 3.422 0.001 0.278 0.279
## SINV 0.612 0.081 7.535 0.000 0.612 0.614
## SK =~
## SKV 0.290 0.131 2.221 0.026 0.290 0.291
## SKNV 0.824 0.327 2.523 0.012 0.824 0.826
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AI ~~
## SP 1.000 1.000 1.000
## SK 0.338 0.174 1.940 0.052 0.338 0.338
## SP ~~
## SK 0.357 0.165 2.170 0.030 0.357 0.357
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .IQV 0.789 0.087 9.037 0.000 0.789 0.793
## .IQNV 0.745 0.087 8.548 0.000 0.745 0.749
## .SPV 0.795 0.087 9.143 0.000 0.795 0.799
## .SPNV 0.840 0.088 9.549 0.000 0.840 0.843
## .SIV 0.918 0.090 10.157 0.000 0.918 0.922
## .SINV 0.621 0.089 6.954 0.000 0.621 0.623
## .SKV 0.912 0.108 8.449 0.000 0.912 0.916
## .SKNV 0.316 0.532 0.595 0.552 0.316 0.318
## AI 1.000 1.000 1.000
## SP 1.000 1.000 1.000
## SK 1.000 1.000 1.000resid(WEA952O.fit, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## IQV IQNV SPV SPNV SIV SINV SKV SKNV
## IQV 0.000
## IQNV 0.082 0.000
## SPV -0.074 -0.065 0.000
## SPNV -0.060 -0.048 0.103 0.000
## SIV 0.103 -0.030 0.075 -0.070 0.000
## SINV -0.029 0.032 0.025 0.007 -0.051 0.000
## SKV 0.015 -0.079 0.043 -0.081 0.151 0.006 0.000
## SKNV 0.043 -0.030 -0.032 0.083 -0.012 -0.021 0.000 0.000pchisq(c(35.730-31.343), 1, lower.tail = F)## [1] 0.03621398A model with AI and SP modeled as identical constructs does not fit meaningfully worse (AIC/BIC) than one in which they are freely related; with a scaled p-value, the model does not fit meaningfully worse in terms of \(\chi^2\) exact fit either.
Conclusion
Though measurement was obviously poor and fit was frequently dubious, it appears that objective academic and social perception measures were strongly related (r = 0.762, 0.743 in experiments 1 and 2 respectively, at baseline, with both consistent with 1 in these data).
References
Wong, C.-M. T., Day, J. D., Maxwell, S. E., & Meara, N. M. (1995). A multitrait-multimethod study of academic and social intelligence in college students. Journal of Educational Psychology, 87(1), 117–133. https://doi.org/10.1037/0022-0663.87.1.117