Goldberg Factor Analysis
Setup
library(pacman); p_load(VIM, psych, lavaan)
CONGO <- function(F1, F2) {
PHI = sum(F1*F2) / sqrt(sum(F1^2)*sum(F2^2))
return(PHI)}
FITM <- c("chisq", "df", "nPar", "cfi", "rmsea", "rmsea.ci.lower", "rmsea.ci.upper", "aic", "bic")
dataw <- subset(data, white == 1)I do not own this data. To obtain it, contact Zach Goldberg.
describe(data); describe(dataw)TargetVars <- c("revrr_favors", "revrr_tryharder", "rr_slavery", "rr_deserve", "racineq_discrim", "disc_blacks", "nodisc_equalincomes", "wpa_advantages", "wpa_opensdoors", "wpa_easier")
aggr(data[, TargetVars], col=c('gold', 'darkred'), numbers = T, sortVars = T, labels = names(data[, TargetVars]), cex.axis = .7, gap = 3, ylab = c("Proportion Missing", "Pattern"))## Warning in plot.aggr(res, ...): not enough horizontal space to display
## frequencies
##
## Variables sorted by number of missings:
## Variable Count
## racineq_discrim 0.04593301
## disc_blacks 0.04593301
## nodisc_equalincomes 0.04593301
## revrr_favors 0.04401914
## revrr_tryharder 0.04401914
## rr_slavery 0.04401914
## rr_deserve 0.04401914
## wpa_advantages 0.04210526
## wpa_opensdoors 0.04210526
## wpa_easier 0.04210526Analysis
ZGModOne <- '
g =~ revrr_favors + revrr_tryharder + rr_slavery + rr_deserve + racineq_discrim + disc_blacks + nodisc_equalincomes + wpa_advantages + wpa_opensdoors + wpa_easier'
ZGModHOF <- '
RR =~ revrr_favors + revrr_tryharder
DISC =~ rr_slavery + rr_deserve + racineq_discrim + disc_blacks + nodisc_equalincomes
WP =~ wpa_advantages + wpa_opensdoors + wpa_easier
g =~ RR + DISC + WP'
ZGModCGF <- '
RR =~ revrr_favors + revrr_tryharder
DISC =~ rr_slavery + rr_deserve + racineq_discrim + disc_blacks + nodisc_equalincomes
WP =~ wpa_advantages + wpa_opensdoors + wpa_easier'
ZGRunOne <- sem(ZGModOne, data = data, std.lv = T, check.gradient = F, control= list(rel.tol = 1e-4), ordered = c("revrr_favors", "revrr_tryharder", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "wpa_advantages", "wpa_opensdoors", "wpa_easier"))
ZGRunHOF <- sem(ZGModHOF, data = data, std.lv = T, check.gradient = F, control= list(rel.tol = 1e-4), ordered = c("revrr_favors", "revrr_tryharder", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "wpa_advantages", "wpa_opensdoors", "wpa_easier"))
ZGRunCGF <- sem(ZGModCGF, data = data, std.lv = T, check.gradient = F, control= list(rel.tol = 1e-4), ordered = c("revrr_favors", "revrr_tryharder", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "wpa_advantages", "wpa_opensdoors", "wpa_easier"))
summary(ZGRunOne, stand = T, fit = T); summary(ZGRunHOF, stand = T, fit = T); summary(ZGRunCGF, stand = T, fit = T)## lavaan 0.6-7 ended normally after 22 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 56
##
## Used Total
## Number of observations 994 1045
##
## Model Test User Model:
## Standard Robust
## Test Statistic 804.331 1488.429
## Degrees of freedom 35 35
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.547
## Shift parameter 17.229
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 124493.294 36788.489
## Degrees of freedom 45 45
## P-value 0.000 0.000
## Scaling correction factor 3.387
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.994 0.960
## Tucker-Lewis Index (TLI) 0.992 0.949
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.149 0.204
## 90 Percent confidence interval - lower 0.140 0.196
## 90 Percent confidence interval - upper 0.158 0.213
## P-value RMSEA <= 0.05 0.000 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.064 0.064
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## g =~
## revrr_favors 0.866 0.009 91.371 0.000 0.866 0.866
## revrr_tryhardr 0.847 0.010 81.889 0.000 0.847 0.847
## rr_slavery 0.840 0.011 76.627 0.000 0.840 0.840
## rr_deserve 0.837 0.011 79.332 0.000 0.837 0.837
## racineq_discrm 21.612 0.988 21.884 0.000 21.612 0.776
## disc_blacks 0.809 0.012 66.308 0.000 0.809 0.809
## nodisc_eqlncms 0.647 0.018 35.766 0.000 0.647 0.647
## wpa_advantages 0.958 0.004 234.486 0.000 0.958 0.958
## wpa_opensdoors 0.930 0.005 185.186 0.000 0.930 0.930
## wpa_easier 0.934 0.005 196.256 0.000 0.934 0.934
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.000 0.000 0.000
## .revrr_tryhardr 0.000 0.000 0.000
## .rr_slavery 0.000 0.000 0.000
## .rr_deserve 0.000 0.000 0.000
## .racineq_discrm 65.165 1.074 60.662 0.000 65.165 2.341
## .disc_blacks 0.000 0.000 0.000
## .nodisc_eqlncms 0.000 0.000 0.000
## .wpa_advantages 0.000 0.000 0.000
## .wpa_opensdoors 0.000 0.000 0.000
## .wpa_easier 0.000 0.000 0.000
## g 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favrs|t1 -1.123 0.050 -22.290 0.000 -1.123 -1.123
## revrr_favrs|t2 -0.563 0.042 -13.357 0.000 -0.563 -0.563
## revrr_favrs|t3 -0.167 0.040 -4.183 0.000 -0.167 -0.167
## revrr_favrs|t4 0.446 0.041 10.803 0.000 0.446 0.446
## rvrr_tryhrdr|1 -1.429 0.059 -24.348 0.000 -1.429 -1.429
## rvrr_tryhrdr|2 -0.830 0.045 -18.376 0.000 -0.830 -0.830
## rvrr_tryhrdr|3 -0.434 0.041 -10.553 0.000 -0.434 -0.434
## rvrr_tryhrdr|4 0.177 0.040 4.436 0.000 0.177 0.177
## rr_slavery|t1 -1.307 0.055 -23.786 0.000 -1.307 -1.307
## rr_slavery|t2 -0.877 0.046 -19.128 0.000 -0.877 -0.877
## rr_slavery|t3 -0.569 0.042 -13.480 0.000 -0.569 -0.569
## rr_slavery|t4 0.121 0.040 3.043 0.002 0.121 0.121
## rr_deserve|t1 -1.388 0.057 -24.198 0.000 -1.388 -1.388
## rr_deserve|t2 -0.881 0.046 -19.185 0.000 -0.881 -0.881
## rr_deserve|t3 -0.350 0.041 -8.605 0.000 -0.350 -0.350
## rr_deserve|t4 0.350 0.041 8.605 0.000 0.350 0.350
## disc_blacks|t1 -2.031 0.090 -22.573 0.000 -2.031 -2.031
## disc_blacks|t2 -1.356 0.056 -24.052 0.000 -1.356 -1.356
## disc_blacks|t3 -0.548 0.042 -13.047 0.000 -0.548 -0.548
## disc_blacks|t4 0.206 0.040 5.132 0.000 0.206 0.206
## ndsc_qlncms|t1 -1.822 0.076 -23.956 0.000 -1.822 -1.822
## ndsc_qlncms|t2 -1.337 0.056 -23.957 0.000 -1.337 -1.337
## ndsc_qlncms|t3 -0.919 0.047 -19.753 0.000 -0.919 -0.919
## ndsc_qlncms|t4 -0.407 0.041 -9.925 0.000 -0.407 -0.407
## ndsc_qlncms|t5 0.170 0.040 4.246 0.000 0.170 0.170
## ndsc_qlncms|t6 0.962 0.047 20.365 0.000 0.962 0.962
## wpa_advntgs|t1 -1.714 0.070 -24.378 0.000 -1.714 -1.714
## wpa_advntgs|t2 -1.250 0.053 -23.406 0.000 -1.250 -1.250
## wpa_advntgs|t3 -1.041 0.049 -21.384 0.000 -1.041 -1.041
## wpa_advntgs|t4 -0.799 0.045 -17.848 0.000 -0.799 -0.799
## wpa_advntgs|t5 -0.318 0.041 -7.849 0.000 -0.318 -0.318
## wpa_advntgs|t6 0.358 0.041 8.794 0.000 0.358 0.358
## wpa_opnsdrs|t1 -1.642 0.067 -24.532 0.000 -1.642 -1.642
## wpa_opnsdrs|t2 -1.171 0.051 -22.760 0.000 -1.171 -1.171
## wpa_opnsdrs|t3 -0.915 0.046 -19.697 0.000 -0.915 -0.915
## wpa_opnsdrs|t4 -0.629 0.043 -14.712 0.000 -0.629 -0.629
## wpa_opnsdrs|t5 -0.142 0.040 -3.550 0.000 -0.142 -0.142
## wpa_opnsdrs|t6 0.551 0.042 13.109 0.000 0.551 0.551
## wpa_easier|t1 -1.632 0.067 -24.545 0.000 -1.632 -1.632
## wpa_easier|t2 -1.147 0.051 -22.528 0.000 -1.147 -1.147
## wpa_easier|t3 -0.962 0.047 -20.365 0.000 -0.962 -0.962
## wpa_easier|t4 -0.689 0.043 -15.871 0.000 -0.689 -0.689
## wpa_easier|t5 -0.234 0.040 -5.828 0.000 -0.234 -0.234
## wpa_easier|t6 0.432 0.041 10.490 0.000 0.432 0.432
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.250 0.250 0.250
## .revrr_tryhardr 0.282 0.282 0.282
## .rr_slavery 0.295 0.295 0.295
## .rr_deserve 0.300 0.300 0.300
## .racineq_discrm 307.714 11.833 26.005 0.000 307.714 0.397
## .disc_blacks 0.345 0.345 0.345
## .nodisc_eqlncms 0.582 0.582 0.582
## .wpa_advantages 0.082 0.082 0.082
## .wpa_opensdoors 0.135 0.135 0.135
## .wpa_easier 0.127 0.127 0.127
## g 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favors 1.000 1.000 1.000
## revrr_tryhardr 1.000 1.000 1.000
## rr_slavery 1.000 1.000 1.000
## rr_deserve 1.000 1.000 1.000
## disc_blacks 1.000 1.000 1.000
## nodisc_eqlncms 1.000 1.000 1.000
## wpa_advantages 1.000 1.000 1.000
## wpa_opensdoors 1.000 1.000 1.000
## wpa_easier 1.000 1.000 1.000## lavaan 0.6-7 ended normally after 193 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 59
##
## Used Total
## Number of observations 994 1045
##
## Model Test User Model:
## Standard Robust
## Test Statistic 90.600 339.638
## Degrees of freedom 32 32
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.275
## Shift parameter 10.332
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 124493.294 36788.489
## Degrees of freedom 45 45
## P-value 0.000 0.000
## Scaling correction factor 3.387
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 0.992
## Tucker-Lewis Index (TLI) 0.999 0.988
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.043 0.098
## 90 Percent confidence interval - lower 0.033 0.089
## 90 Percent confidence interval - upper 0.053 0.108
## P-value RMSEA <= 0.05 0.859 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.025 0.025
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RR =~
## revrr_favors 0.416 0.019 21.622 0.000 0.941 0.941
## revrr_tryhardr 0.401 0.018 22.827 0.000 0.907 0.907
## DISC =~
## rr_slavery 0.039 0.136 0.290 0.772 0.883 0.883
## rr_deserve 0.039 0.135 0.290 0.772 0.874 0.874
## racineq_discrm 1.002 3.464 0.289 0.772 22.437 0.808
## disc_blacks 0.038 0.132 0.290 0.772 0.855 0.855
## nodisc_eqlncms 0.030 0.104 0.290 0.772 0.675 0.675
## WP =~
## wpa_advantages 0.490 0.018 27.426 0.000 0.973 0.973
## wpa_opensdoors 0.475 0.017 28.064 0.000 0.943 0.943
## wpa_easier 0.479 0.017 27.989 0.000 0.951 0.951
## g =~
## RR 2.026 0.114 17.778 0.000 0.897 0.897
## DISC 22.359 77.314 0.289 0.772 0.999 0.999
## WP 1.714 0.085 20.214 0.000 0.864 0.864
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.000 0.000 0.000
## .revrr_tryhardr 0.000 0.000 0.000
## .rr_slavery 0.000 0.000 0.000
## .rr_deserve 0.000 0.000 0.000
## .racineq_discrm 65.165 1.074 60.662 0.000 65.165 2.347
## .disc_blacks 0.000 0.000 0.000
## .nodisc_eqlncms 0.000 0.000 0.000
## .wpa_advantages 0.000 0.000 0.000
## .wpa_opensdoors 0.000 0.000 0.000
## .wpa_easier 0.000 0.000 0.000
## .RR 0.000 0.000 0.000
## .DISC 0.000 0.000 0.000
## .WP 0.000 0.000 0.000
## g 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favrs|t1 -1.123 0.050 -22.290 0.000 -1.123 -1.123
## revrr_favrs|t2 -0.563 0.042 -13.357 0.000 -0.563 -0.563
## revrr_favrs|t3 -0.167 0.040 -4.183 0.000 -0.167 -0.167
## revrr_favrs|t4 0.446 0.041 10.803 0.000 0.446 0.446
## rvrr_tryhrdr|1 -1.429 0.059 -24.348 0.000 -1.429 -1.429
## rvrr_tryhrdr|2 -0.830 0.045 -18.376 0.000 -0.830 -0.830
## rvrr_tryhrdr|3 -0.434 0.041 -10.553 0.000 -0.434 -0.434
## rvrr_tryhrdr|4 0.177 0.040 4.436 0.000 0.177 0.177
## rr_slavery|t1 -1.307 0.055 -23.786 0.000 -1.307 -1.307
## rr_slavery|t2 -0.877 0.046 -19.128 0.000 -0.877 -0.877
## rr_slavery|t3 -0.569 0.042 -13.480 0.000 -0.569 -0.569
## rr_slavery|t4 0.121 0.040 3.043 0.002 0.121 0.121
## rr_deserve|t1 -1.388 0.057 -24.198 0.000 -1.388 -1.388
## rr_deserve|t2 -0.881 0.046 -19.185 0.000 -0.881 -0.881
## rr_deserve|t3 -0.350 0.041 -8.605 0.000 -0.350 -0.350
## rr_deserve|t4 0.350 0.041 8.605 0.000 0.350 0.350
## disc_blacks|t1 -2.031 0.090 -22.573 0.000 -2.031 -2.031
## disc_blacks|t2 -1.356 0.056 -24.052 0.000 -1.356 -1.356
## disc_blacks|t3 -0.548 0.042 -13.047 0.000 -0.548 -0.548
## disc_blacks|t4 0.206 0.040 5.132 0.000 0.206 0.206
## ndsc_qlncms|t1 -1.822 0.076 -23.956 0.000 -1.822 -1.822
## ndsc_qlncms|t2 -1.337 0.056 -23.957 0.000 -1.337 -1.337
## ndsc_qlncms|t3 -0.919 0.047 -19.753 0.000 -0.919 -0.919
## ndsc_qlncms|t4 -0.407 0.041 -9.925 0.000 -0.407 -0.407
## ndsc_qlncms|t5 0.170 0.040 4.246 0.000 0.170 0.170
## ndsc_qlncms|t6 0.962 0.047 20.365 0.000 0.962 0.962
## wpa_advntgs|t1 -1.714 0.070 -24.378 0.000 -1.714 -1.714
## wpa_advntgs|t2 -1.250 0.053 -23.406 0.000 -1.250 -1.250
## wpa_advntgs|t3 -1.041 0.049 -21.384 0.000 -1.041 -1.041
## wpa_advntgs|t4 -0.799 0.045 -17.848 0.000 -0.799 -0.799
## wpa_advntgs|t5 -0.318 0.041 -7.849 0.000 -0.318 -0.318
## wpa_advntgs|t6 0.358 0.041 8.794 0.000 0.358 0.358
## wpa_opnsdrs|t1 -1.642 0.067 -24.532 0.000 -1.642 -1.642
## wpa_opnsdrs|t2 -1.171 0.051 -22.760 0.000 -1.171 -1.171
## wpa_opnsdrs|t3 -0.915 0.046 -19.697 0.000 -0.915 -0.915
## wpa_opnsdrs|t4 -0.629 0.043 -14.712 0.000 -0.629 -0.629
## wpa_opnsdrs|t5 -0.142 0.040 -3.550 0.000 -0.142 -0.142
## wpa_opnsdrs|t6 0.551 0.042 13.109 0.000 0.551 0.551
## wpa_easier|t1 -1.632 0.067 -24.545 0.000 -1.632 -1.632
## wpa_easier|t2 -1.147 0.051 -22.528 0.000 -1.147 -1.147
## wpa_easier|t3 -0.962 0.047 -20.365 0.000 -0.962 -0.962
## wpa_easier|t4 -0.689 0.043 -15.871 0.000 -0.689 -0.689
## wpa_easier|t5 -0.234 0.040 -5.828 0.000 -0.234 -0.234
## wpa_easier|t6 0.432 0.041 10.490 0.000 0.432 0.432
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.115 0.115 0.115
## .revrr_tryhardr 0.178 0.178 0.178
## .rr_slavery 0.220 0.220 0.220
## .rr_deserve 0.235 0.235 0.235
## .racineq_discrm 267.574 11.258 23.768 0.000 267.574 0.347
## .disc_blacks 0.269 0.269 0.269
## .nodisc_eqlncms 0.544 0.544 0.544
## .wpa_advantages 0.054 0.054 0.054
## .wpa_opensdoors 0.111 0.111 0.111
## .wpa_easier 0.095 0.095 0.095
## .RR 1.000 0.196 0.196
## .DISC 1.000 0.002 0.002
## .WP 1.000 0.254 0.254
## g 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favors 1.000 1.000 1.000
## revrr_tryhardr 1.000 1.000 1.000
## rr_slavery 1.000 1.000 1.000
## rr_deserve 1.000 1.000 1.000
## disc_blacks 1.000 1.000 1.000
## nodisc_eqlncms 1.000 1.000 1.000
## wpa_advantages 1.000 1.000 1.000
## wpa_opensdoors 1.000 1.000 1.000
## wpa_easier 1.000 1.000 1.000## lavaan 0.6-7 ended normally after 31 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 59
##
## Used Total
## Number of observations 994 1045
##
## Model Test User Model:
## Standard Robust
## Test Statistic 78.185 294.508
## Degrees of freedom 32 32
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.275
## Shift parameter 10.325
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 124493.294 36788.489
## Degrees of freedom 45 45
## P-value 0.000 0.000
## Scaling correction factor 3.387
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 0.993
## Tucker-Lewis Index (TLI) 0.999 0.990
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.038 0.091
## 90 Percent confidence interval - lower 0.027 0.082
## 90 Percent confidence interval - upper 0.049 0.101
## P-value RMSEA <= 0.05 0.965 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.024 0.024
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RR =~
## revrr_favors 0.941 0.008 111.516 0.000 0.941 0.941
## revrr_tryhardr 0.907 0.009 101.259 0.000 0.907 0.907
## DISC =~
## rr_slavery 0.874 0.010 83.883 0.000 0.874 0.874
## rr_deserve 0.867 0.010 86.769 0.000 0.867 0.867
## racineq_discrm 22.278 0.996 22.369 0.000 22.278 0.802
## disc_blacks 0.848 0.012 72.300 0.000 0.848 0.848
## nodisc_eqlncms 0.670 0.018 37.247 0.000 0.670 0.670
## WP =~
## wpa_advantages 0.973 0.004 251.870 0.000 0.973 0.973
## wpa_opensdoors 0.943 0.005 198.434 0.000 0.943 0.943
## wpa_easier 0.951 0.004 219.065 0.000 0.951 0.951
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RR ~~
## DISC 0.917 0.009 104.094 0.000 0.917 0.917
## WP 0.757 0.015 48.982 0.000 0.757 0.757
## DISC ~~
## WP 0.879 0.010 92.449 0.000 0.879 0.879
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.000 0.000 0.000
## .revrr_tryhardr 0.000 0.000 0.000
## .rr_slavery 0.000 0.000 0.000
## .rr_deserve 0.000 0.000 0.000
## .racineq_discrm 65.165 1.074 60.662 0.000 65.165 2.347
## .disc_blacks 0.000 0.000 0.000
## .nodisc_eqlncms 0.000 0.000 0.000
## .wpa_advantages 0.000 0.000 0.000
## .wpa_opensdoors 0.000 0.000 0.000
## .wpa_easier 0.000 0.000 0.000
## RR 0.000 0.000 0.000
## DISC 0.000 0.000 0.000
## WP 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favrs|t1 -1.123 0.050 -22.290 0.000 -1.123 -1.123
## revrr_favrs|t2 -0.563 0.042 -13.357 0.000 -0.563 -0.563
## revrr_favrs|t3 -0.167 0.040 -4.183 0.000 -0.167 -0.167
## revrr_favrs|t4 0.446 0.041 10.803 0.000 0.446 0.446
## rvrr_tryhrdr|1 -1.429 0.059 -24.348 0.000 -1.429 -1.429
## rvrr_tryhrdr|2 -0.830 0.045 -18.376 0.000 -0.830 -0.830
## rvrr_tryhrdr|3 -0.434 0.041 -10.553 0.000 -0.434 -0.434
## rvrr_tryhrdr|4 0.177 0.040 4.436 0.000 0.177 0.177
## rr_slavery|t1 -1.307 0.055 -23.786 0.000 -1.307 -1.307
## rr_slavery|t2 -0.877 0.046 -19.128 0.000 -0.877 -0.877
## rr_slavery|t3 -0.569 0.042 -13.480 0.000 -0.569 -0.569
## rr_slavery|t4 0.121 0.040 3.043 0.002 0.121 0.121
## rr_deserve|t1 -1.388 0.057 -24.198 0.000 -1.388 -1.388
## rr_deserve|t2 -0.881 0.046 -19.185 0.000 -0.881 -0.881
## rr_deserve|t3 -0.350 0.041 -8.605 0.000 -0.350 -0.350
## rr_deserve|t4 0.350 0.041 8.605 0.000 0.350 0.350
## disc_blacks|t1 -2.031 0.090 -22.573 0.000 -2.031 -2.031
## disc_blacks|t2 -1.356 0.056 -24.052 0.000 -1.356 -1.356
## disc_blacks|t3 -0.548 0.042 -13.047 0.000 -0.548 -0.548
## disc_blacks|t4 0.206 0.040 5.132 0.000 0.206 0.206
## ndsc_qlncms|t1 -1.822 0.076 -23.956 0.000 -1.822 -1.822
## ndsc_qlncms|t2 -1.337 0.056 -23.957 0.000 -1.337 -1.337
## ndsc_qlncms|t3 -0.919 0.047 -19.753 0.000 -0.919 -0.919
## ndsc_qlncms|t4 -0.407 0.041 -9.925 0.000 -0.407 -0.407
## ndsc_qlncms|t5 0.170 0.040 4.246 0.000 0.170 0.170
## ndsc_qlncms|t6 0.962 0.047 20.365 0.000 0.962 0.962
## wpa_advntgs|t1 -1.714 0.070 -24.378 0.000 -1.714 -1.714
## wpa_advntgs|t2 -1.250 0.053 -23.406 0.000 -1.250 -1.250
## wpa_advntgs|t3 -1.041 0.049 -21.384 0.000 -1.041 -1.041
## wpa_advntgs|t4 -0.799 0.045 -17.848 0.000 -0.799 -0.799
## wpa_advntgs|t5 -0.318 0.041 -7.849 0.000 -0.318 -0.318
## wpa_advntgs|t6 0.358 0.041 8.794 0.000 0.358 0.358
## wpa_opnsdrs|t1 -1.642 0.067 -24.532 0.000 -1.642 -1.642
## wpa_opnsdrs|t2 -1.171 0.051 -22.760 0.000 -1.171 -1.171
## wpa_opnsdrs|t3 -0.915 0.046 -19.697 0.000 -0.915 -0.915
## wpa_opnsdrs|t4 -0.629 0.043 -14.712 0.000 -0.629 -0.629
## wpa_opnsdrs|t5 -0.142 0.040 -3.550 0.000 -0.142 -0.142
## wpa_opnsdrs|t6 0.551 0.042 13.109 0.000 0.551 0.551
## wpa_easier|t1 -1.632 0.067 -24.545 0.000 -1.632 -1.632
## wpa_easier|t2 -1.147 0.051 -22.528 0.000 -1.147 -1.147
## wpa_easier|t3 -0.962 0.047 -20.365 0.000 -0.962 -0.962
## wpa_easier|t4 -0.689 0.043 -15.871 0.000 -0.689 -0.689
## wpa_easier|t5 -0.234 0.040 -5.828 0.000 -0.234 -0.234
## wpa_easier|t6 0.432 0.041 10.490 0.000 0.432 0.432
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.115 0.115 0.115
## .revrr_tryhardr 0.178 0.178 0.178
## .rr_slavery 0.236 0.236 0.236
## .rr_deserve 0.249 0.249 0.249
## .racineq_discrm 274.677 11.323 24.258 0.000 274.677 0.356
## .disc_blacks 0.282 0.282 0.282
## .nodisc_eqlncms 0.551 0.551 0.551
## .wpa_advantages 0.053 0.053 0.053
## .wpa_opensdoors 0.111 0.111 0.111
## .wpa_easier 0.095 0.095 0.095
## RR 1.000 1.000 1.000
## DISC 1.000 1.000 1.000
## WP 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favors 1.000 1.000 1.000
## revrr_tryhardr 1.000 1.000 1.000
## rr_slavery 1.000 1.000 1.000
## rr_deserve 1.000 1.000 1.000
## disc_blacks 1.000 1.000 1.000
## nodisc_eqlncms 1.000 1.000 1.000
## wpa_advantages 1.000 1.000 1.000
## wpa_opensdoors 1.000 1.000 1.000
## wpa_easier 1.000 1.000 1.000SING <- c(0.866, 0.847, 0.840, 0.837, 0.776, 0.809, 0.647, 0.958, 0.930, 0.934)
HOFG <- c(0.844, 0.814, 0.882, 0.873, 0.807, 0.854, 0.674, 0.841, 0.815, 0.822)
cor(SING, HOFG); cor(SING, HOFG, method = "spearman"); CONGO(SING, HOFG)## [1] 0.6448956## [1] 0.2## [1] 0.9970064These data are staggeringly general. 68% of the total variance is general with a uniqueness of 29.6%; 96.6% of the common variance is general whilst only 0.7% and 1.8% of the total relies in the DISC and WP factors alongside 0.9% and 2.5% of the common variance. \(\omega\) is 0.958, \(\omega_h\) is 0.949 and relative \(\omega\) is 0.991. A unit-weighted summary score of the variables in this dataset would correlate at r = 0.974 with its general factor. The H is 0.958, PUC is 0.689 and FDI is 0.979. For DISC, RR and WP respectively, \(\omega\) values are 0.837, 0.911 and 0.896, \(\omega_hs\) values, however, are 0.038, <0.001 and 0.071, with pitifully low values for the relative \(\omega\) and unit-weighted score correlations (r’s of 0.195, 0.002 and 0.266). The values for H are 0.063, <0.001 and 0.158, with FDIs of 0.251, 0.004 and 0.397. Factor scores for non-general factors would be basically useless after being residualized of the variance all the variables have in common and summary scores for each of the three group factors all better represent what the factors have in common rather than anything unique to any of them.
It is not possible to check the above models for measurement invariance because some categories of some of the variables are empty in the non-white group. However, were we to use a non-robust model, we would arrive at the following results:
ZGRunOneC.fit <- cfa(ZGModOne, data = data, group = "white", std.lv = T, orthogonal = F)## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'white' contains missing valuesZGRunOneM.fit <- cfa(ZGModOne, data = data, group = "white", std.lv = F, orthogonal = F, group.equal = "loadings")## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'white' contains missing valuesZGRunOneS.fit <- cfa(ZGModOne, data = data, group = "white", std.lv = F, orthogonal = F, group.equal = c("loadings", "intercepts"))## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'white' contains missing valuesZGRunOneF.fit <- cfa(ZGModOne, data = data, group = "white", std.lv = F, orthogonal = F, group.equal = c("loadings", "intercepts", "residuals"))## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'white' contains missing valuesZGRunOneLA.fit <- cfa(ZGModOne, data = data, group = "white", std.lv = T, orthogonal = F, group.equal = c("loadings", "intercepts", "residuals", "means"))## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'white' contains missing valuesZGRunHOFC.fit <- cfa(ZGModHOF, data = data, group = "white", std.lv = T, orthogonal = F)## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'white' contains missing values## Warning in lav_model_estimate(lavmodel = lavmodel, lavpartable = lavpartable, : lavaan WARNING: the optimizer (NLMINB) claimed the model converged,
## but not all elements of the gradient are (near) zero;
## the optimizer may not have found a local solution
## use check.gradient = FALSE to skip this check.## Warning in lav_model_vcov(lavmodel = lavmodel, 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.ZGRunHOFM.fit <- cfa(ZGModHOF, data = data, group = "white", std.lv = F, orthogonal = F, group.equal = "loadings")## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'white' contains missing values## Warning in lav_object_post_check(object): lavaan WARNING: some estimated lv
## variances are negativeZGRunHOFS.fit <- cfa(ZGModHOF, data = data, group = "white", std.lv = F, orthogonal = F, group.equal = c("loadings", "intercepts"))## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'white' contains missing values## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## The variance-covariance matrix of the estimated parameters (vcov)
## does not appear to be positive definite! The smallest eigenvalue
## (= 3.692044e-13) is close to zero. This may be a symptom that the
## model is not identified.## Warning in lav_object_post_check(object): lavaan WARNING: some estimated lv
## variances are negativeZGRunHOFF.fit <- cfa(ZGModHOF, data = data, group = "white", std.lv = F, orthogonal = F, group.equal = c("loadings", "intercepts", "residuals"))## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'white' contains missing values
## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: some estimated lv variances are negativeZGRunHOFLA.fit <- cfa(ZGModHOF, data = data, group = "white", std.lv = T, orthogonal = F, group.equal = c("loadings", "intercepts", "residuals", "means"))## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'white' contains missing valuesZGRunCGFC.fit <- cfa(ZGModCGF, data = data, group = "white", std.lv = T, orthogonal = F)## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'white' contains missing valuesZGRunCGFM.fit <- cfa(ZGModCGF, data = data, group = "white", std.lv = F, orthogonal = F, group.equal = "loadings")## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'white' contains missing valuesZGRunCGFS.fit <- cfa(ZGModCGF, data = data, group = "white", std.lv = F, orthogonal = F, group.equal = c("loadings", "intercepts"))## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'white' contains missing valuesZGRunCGFF.fit <- cfa(ZGModCGF, data = data, group = "white", std.lv = F, orthogonal = F, group.equal = c("loadings", "intercepts", "residuals"))## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'white' contains missing valuesZGRunCGFLA.fit <- cfa(ZGModCGF, data = data, group = "white", std.lv = T, orthogonal = F, group.equal = c("loadings", "intercepts", "residuals", "means"))## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'white' contains missing valuesround(cbind(CONFIGURAL = fitMeasures(ZGRunOneC.fit, FITM),
METRIC = fitMeasures(ZGRunOneM.fit, FITM),
SCALAR = fitMeasures(ZGRunOneS.fit, FITM),
STRICT = fitMeasures(ZGRunOneF.fit, FITM),
MEANS = fitMeasures(ZGRunOneLA.fit, FITM)), 3)## CONFIGURAL METRIC SCALAR STRICT MEANS
## chisq 1233.218 1278.822 1289.586 1313.736 1314.755
## df 70.000 79.000 88.000 98.000 99.000
## npar 60.000 51.000 42.000 32.000 31.000
## cfi 0.867 0.862 0.862 0.861 0.861
## rmsea 0.183 0.175 0.166 0.158 0.157
## rmsea.ci.lower 0.174 0.166 0.158 0.150 0.150
## rmsea.ci.upper 0.192 0.183 0.174 0.166 0.165
## aic 33989.915 34017.520 34010.284 34014.433 34013.453
## bic 34284.020 34267.509 34216.157 34171.289 34165.407round(cbind(CONFIGURAL = fitMeasures(ZGRunHOFC.fit, FITM),
METRIC = fitMeasures(ZGRunHOFM.fit, FITM),
SCALAR = fitMeasures(ZGRunHOFS.fit, FITM),
STRICT = fitMeasures(ZGRunHOFF.fit, FITM),
MEANS = fitMeasures(ZGRunHOFLA.fit, FITM)), 3)## CONFIGURAL METRIC SCALAR STRICT MEANS
## chisq 232.661 243.063 256.198 283.642 296.831
## df 64.000 73.000 79.000 89.000 93.000
## npar 66.000 57.000 51.000 41.000 37.000
## cfi 0.981 0.980 0.980 0.978 0.977
## rmsea 0.073 0.068 0.067 0.066 0.066
## rmsea.ci.lower 0.063 0.059 0.058 0.058 0.058
## rmsea.ci.upper 0.083 0.078 0.076 0.075 0.075
## aic 33001.359 32993.761 32994.896 33002.339 33007.528
## bic 33324.874 33273.160 33244.885 33203.311 33188.892round(cbind(CONFIGURAL = fitMeasures(ZGRunCGFC.fit, FITM),
METRIC = fitMeasures(ZGRunCGFM.fit, FITM),
SCALAR = fitMeasures(ZGRunCGFS.fit, FITM),
STRICT = fitMeasures(ZGRunCGFF.fit, FITM),
MEANS = fitMeasures(ZGRunCGFLA.fit, FITM)), 3)## CONFIGURAL METRIC SCALAR STRICT MEANS
## chisq 221.989 239.822 252.534 281.217 282.675
## df 64.000 71.000 78.000 88.000 91.000
## npar 66.000 59.000 52.000 42.000 39.000
## cfi 0.982 0.981 0.980 0.978 0.978
## rmsea 0.070 0.069 0.067 0.066 0.065
## rmsea.ci.lower 0.060 0.060 0.058 0.058 0.057
## rmsea.ci.upper 0.081 0.079 0.076 0.075 0.074
## aic 32990.687 32994.520 32993.231 33001.914 32997.373
## bic 33314.202 33283.722 33248.122 33207.787 33188.540summary(ZGRunHOFC.fit, stand = T, fit = T)## lavaan 0.6-7 ended normally after 281 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 66
##
## Number of observations per group: Used Total
## 1 938 952
## 0 56 59
##
## Model Test User Model:
##
## Test statistic 232.661
## Degrees of freedom 64
## P-value (Chi-square) 0.000
## Test statistic for each group:
## 1 166.031
## 0 66.631
##
## Model Test Baseline Model:
##
## Test statistic 8807.297
## Degrees of freedom 90
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.981
## Tucker-Lewis Index (TLI) 0.973
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -16434.679
## Loglikelihood unrestricted model (H1) -16318.349
##
## Akaike (AIC) 33001.359
## Bayesian (BIC) 33324.874
## Sample-size adjusted Bayesian (BIC) 33115.255
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.073
## 90 Percent confidence interval - lower 0.063
## 90 Percent confidence interval - upper 0.083
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.026
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RR =~
## revrr_favors 0.646 NA 1.297 0.913
## revrr_tryhardr 0.562 NA 1.128 0.859
## DISC =~
## rr_slavery 0.007 NA 1.081 0.809
## rr_deserve 0.007 NA 1.067 0.833
## racineq_discrm 0.145 NA 23.345 0.838
## disc_blacks 0.005 NA 0.832 0.793
## nodisc_eqlncms 0.007 NA 1.052 0.667
## WP =~
## wpa_advantages 0.806 NA 1.635 0.942
## wpa_opensdoors 0.809 NA 1.642 0.923
## wpa_easier 0.817 NA 1.658 0.923
## g =~
## RR 1.741 NA 0.867 0.867
## DISC 160.795 NA 1.000 1.000
## WP 1.765 NA 0.870 0.870
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 3.473 NA 3.473 2.444
## .revrr_tryhardr 3.812 NA 3.812 2.904
## .rr_slavery 3.875 NA 3.875 2.901
## .rr_deserve 3.725 NA 3.725 2.910
## .racineq_discrm 65.000 NA 65.000 2.334
## .disc_blacks 3.997 NA 3.997 3.812
## .nodisc_eqlncms 4.965 NA 4.965 3.149
## .wpa_advantages 5.465 NA 5.465 3.150
## .wpa_opensdoors 5.223 NA 5.223 2.936
## .wpa_easier 5.324 NA 5.324 2.964
## .RR 0.000 0.000 0.000
## .DISC 0.000 0.000 0.000
## .WP 0.000 0.000 0.000
## g 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.336 NA 0.336 0.166
## .revrr_tryhardr 0.450 NA 0.450 0.261
## .rr_slavery 0.617 NA 0.617 0.346
## .rr_deserve 0.501 NA 0.501 0.306
## .racineq_discrm 230.361 NA 230.361 0.297
## .disc_blacks 0.408 NA 0.408 0.371
## .nodisc_eqlncms 1.380 NA 1.380 0.555
## .wpa_advantages 0.337 NA 0.337 0.112
## .wpa_opensdoors 0.470 NA 0.470 0.149
## .wpa_easier 0.480 NA 0.480 0.149
## .RR 1.000 0.248 0.248
## .DISC 1.000 0.000 0.000
## .WP 1.000 0.243 0.243
## g 1.000 1.000 1.000
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RR =~
## revrr_favors 0.492 NA 1.125 0.860
## revrr_tryhardr 0.456 NA 1.042 0.811
## DISC =~
## rr_slavery 0.028 NA 1.099 0.892
## rr_deserve 0.026 NA 1.035 0.838
## racineq_discrm 0.453 NA 18.028 0.682
## disc_blacks 0.012 NA 0.459 0.597
## nodisc_eqlncms 0.023 NA 0.915 0.546
## WP =~
## wpa_advantages 1.257 NA 1.458 0.969
## wpa_opensdoors 1.292 NA 1.498 0.924
## wpa_easier 1.451 NA 1.682 0.971
## g =~
## RR 2.055 NA 0.899 0.899
## DISC 39.747 NA 1.000 1.000
## WP 0.587 NA 0.506 0.506
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 3.536 NA 3.536 2.701
## .revrr_tryhardr 3.911 NA 3.911 3.042
## .rr_slavery 3.982 NA 3.982 3.233
## .rr_deserve 3.786 NA 3.786 3.065
## .racineq_discrm 67.929 NA 67.929 2.571
## .disc_blacks 4.375 NA 4.375 5.688
## .nodisc_eqlncms 4.786 NA 4.786 2.854
## .wpa_advantages 5.643 NA 5.643 3.749
## .wpa_opensdoors 5.375 NA 5.375 3.316
## .wpa_easier 5.518 NA 5.518 3.186
## .RR 0.000 0.000 0.000
## .DISC 0.000 0.000 0.000
## .WP 0.000 0.000 0.000
## g 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.447 NA 0.447 0.261
## .revrr_tryhardr 0.566 NA 0.566 0.343
## .rr_slavery 0.310 NA 0.310 0.204
## .rr_deserve 0.455 NA 0.455 0.298
## .racineq_discrm 373.217 NA 373.217 0.535
## .disc_blacks 0.381 NA 0.381 0.643
## .nodisc_eqlncms 1.975 NA 1.975 0.702
## .wpa_advantages 0.138 NA 0.138 0.061
## .wpa_opensdoors 0.382 NA 0.382 0.145
## .wpa_easier 0.170 NA 0.170 0.057
## .RR 1.000 0.191 0.191
## .DISC 1.000 0.001 0.001
## .WP 1.000 0.743 0.743
## g 1.000 1.000 1.000ZGRunOne <- sem(ZGModOne, data = dataw, std.lv = T, check.gradient = F, control= list(rel.tol = 1e-4), ordered = c("revrr_favors", "revrr_tryharder", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "wpa_advantages", "wpa_opensdoors", "wpa_easier"))
ZGRunHOF <- sem(ZGModHOF, data = dataw, std.lv = T, check.gradient = F, control= list(rel.tol = 1e-4), ordered = c("revrr_favors", "revrr_tryharder", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "wpa_advantages", "wpa_opensdoors", "wpa_easier"))
ZGRunCGF <- sem(ZGModCGF, data = dataw, std.lv = T, check.gradient = F, control= list(rel.tol = 1e-4), ordered = c("revrr_favors", "revrr_tryharder", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "wpa_advantages", "wpa_opensdoors", "wpa_easier"))
summary(ZGRunOne, stand = T, fit = T); summary(ZGRunHOF, stand = T, fit = T); summary(ZGRunCGF, stand = T, fit = T)## lavaan 0.6-7 ended normally after 21 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 56
##
## Used Total
## Number of observations 938 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 678.393 1363.274
## Degrees of freedom 35 35
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.504
## Shift parameter 16.462
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 120256.467 35381.257
## Degrees of freedom 45 45
## P-value 0.000 0.000
## Scaling correction factor 3.402
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.995 0.962
## Tucker-Lewis Index (TLI) 0.993 0.952
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.140 0.201
## 90 Percent confidence interval - lower 0.131 0.192
## 90 Percent confidence interval - upper 0.149 0.210
## P-value RMSEA <= 0.05 0.000 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.060 0.060
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## g =~
## revrr_favors 0.870 0.010 91.198 0.000 0.870 0.870
## revrr_tryhardr 0.852 0.010 81.397 0.000 0.852 0.852
## rr_slavery 0.842 0.011 73.922 0.000 0.842 0.842
## rr_deserve 0.842 0.011 77.599 0.000 0.842 0.842
## racineq_discrm 21.807 1.021 21.351 0.000 21.807 0.782
## disc_blacks 0.818 0.012 67.048 0.000 0.818 0.818
## nodisc_eqlncms 0.652 0.018 35.291 0.000 0.652 0.652
## wpa_advantages 0.957 0.004 237.166 0.000 0.957 0.957
## wpa_opensdoors 0.932 0.005 183.160 0.000 0.932 0.932
## wpa_easier 0.931 0.005 179.320 0.000 0.931 0.931
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.000 0.000 0.000
## .revrr_tryhardr 0.000 0.000 0.000
## .rr_slavery 0.000 0.000 0.000
## .rr_deserve 0.000 0.000 0.000
## .racineq_discrm 65.000 1.101 59.046 0.000 65.000 2.331
## .disc_blacks 0.000 0.000 0.000
## .nodisc_eqlncms 0.000 0.000 0.000
## .wpa_advantages 0.000 0.000 0.000
## .wpa_opensdoors 0.000 0.000 0.000
## .wpa_easier 0.000 0.000 0.000
## g 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favrs|t1 -1.116 0.052 -21.586 0.000 -1.116 -1.116
## revrr_favrs|t2 -0.550 0.043 -12.716 0.000 -0.550 -0.550
## revrr_favrs|t3 -0.169 0.041 -4.110 0.000 -0.169 -0.169
## revrr_favrs|t4 0.442 0.042 10.406 0.000 0.442 0.442
## rvrr_tryhrdr|1 -1.427 0.060 -23.645 0.000 -1.427 -1.427
## rvrr_tryhrdr|2 -0.825 0.046 -17.767 0.000 -0.825 -0.825
## rvrr_tryhrdr|3 -0.430 0.042 -10.148 0.000 -0.430 -0.430
## rvrr_tryhrdr|4 0.183 0.041 4.436 0.000 0.183 0.183
## rr_slavery|t1 -1.305 0.057 -23.092 0.000 -1.305 -1.305
## rr_slavery|t2 -0.867 0.047 -18.424 0.000 -0.867 -0.867
## rr_slavery|t3 -0.557 0.043 -12.844 0.000 -0.557 -0.557
## rr_slavery|t4 0.118 0.041 2.871 0.004 0.118 0.118
## rr_deserve|t1 -1.391 0.059 -23.516 0.000 -1.391 -1.391
## rr_deserve|t2 -0.871 0.047 -18.483 0.000 -0.871 -0.871
## rr_deserve|t3 -0.346 0.042 -8.272 0.000 -0.346 -0.346
## rr_deserve|t4 0.349 0.042 8.337 0.000 0.349 0.349
## disc_blacks|t1 -2.007 0.091 -22.117 0.000 -2.007 -2.007
## disc_blacks|t2 -1.330 0.057 -23.235 0.000 -1.330 -1.330
## disc_blacks|t3 -0.523 0.043 -12.141 0.000 -0.523 -0.523
## disc_blacks|t4 0.224 0.041 5.413 0.000 0.224 0.224
## ndsc_qlncms|t1 -1.838 0.079 -23.195 0.000 -1.838 -1.838
## ndsc_qlncms|t2 -1.350 0.058 -23.335 0.000 -1.350 -1.350
## ndsc_qlncms|t3 -0.923 0.048 -19.244 0.000 -0.923 -0.923
## ndsc_qlncms|t4 -0.415 0.042 -9.825 0.000 -0.415 -0.415
## ndsc_qlncms|t5 0.164 0.041 3.980 0.000 0.164 0.164
## ndsc_qlncms|t6 0.960 0.049 19.759 0.000 0.960 0.960
## wpa_advntgs|t1 -1.709 0.072 -23.694 0.000 -1.709 -1.709
## wpa_advntgs|t2 -1.239 0.055 -22.656 0.000 -1.239 -1.239
## wpa_advntgs|t3 -1.021 0.050 -20.537 0.000 -1.021 -1.021
## wpa_advntgs|t4 -0.792 0.046 -17.222 0.000 -0.792 -0.792
## wpa_advntgs|t5 -0.312 0.042 -7.494 0.000 -0.312 -0.312
## wpa_advntgs|t6 0.355 0.042 8.467 0.000 0.355 0.355
## wpa_opnsdrs|t1 -1.644 0.069 -23.828 0.000 -1.644 -1.644
## wpa_opnsdrs|t2 -1.157 0.053 -21.978 0.000 -1.157 -1.157
## wpa_opnsdrs|t3 -0.903 0.048 -18.954 0.000 -0.903 -0.903
## wpa_opnsdrs|t4 -0.620 0.044 -14.114 0.000 -0.620 -0.620
## wpa_opnsdrs|t5 -0.145 0.041 -3.523 0.000 -0.145 -0.145
## wpa_opnsdrs|t6 0.553 0.043 12.780 0.000 0.553 0.553
## wpa_easier|t1 -1.634 0.069 -23.841 0.000 -1.634 -1.634
## wpa_easier|t2 -1.141 0.052 -21.833 0.000 -1.141 -1.141
## wpa_easier|t3 -0.952 0.048 -19.646 0.000 -0.952 -0.952
## wpa_easier|t4 -0.680 0.045 -15.246 0.000 -0.680 -0.680
## wpa_easier|t5 -0.232 0.041 -5.608 0.000 -0.232 -0.232
## wpa_easier|t6 0.442 0.042 10.406 0.000 0.442 0.442
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.243 0.243 0.243
## .revrr_tryhardr 0.274 0.274 0.274
## .rr_slavery 0.291 0.291 0.291
## .rr_deserve 0.292 0.292 0.292
## .racineq_discrm 302.119 11.911 25.364 0.000 302.119 0.389
## .disc_blacks 0.331 0.331 0.331
## .nodisc_eqlncms 0.574 0.574 0.574
## .wpa_advantages 0.085 0.085 0.085
## .wpa_opensdoors 0.132 0.132 0.132
## .wpa_easier 0.133 0.133 0.133
## g 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favors 1.000 1.000 1.000
## revrr_tryhardr 1.000 1.000 1.000
## rr_slavery 1.000 1.000 1.000
## rr_deserve 1.000 1.000 1.000
## disc_blacks 1.000 1.000 1.000
## nodisc_eqlncms 1.000 1.000 1.000
## wpa_advantages 1.000 1.000 1.000
## wpa_opensdoors 1.000 1.000 1.000
## wpa_easier 1.000 1.000 1.000## lavaan 0.6-7 ended normally after 182 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 59
##
## Used Total
## Number of observations 938 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 77.124 307.166
## Degrees of freedom 32 32
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.259
## Shift parameter 9.561
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 120256.467 35381.257
## Degrees of freedom 45 45
## P-value 0.000 0.000
## Scaling correction factor 3.402
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 0.992
## Tucker-Lewis Index (TLI) 0.999 0.989
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.039 0.096
## 90 Percent confidence interval - lower 0.028 0.086
## 90 Percent confidence interval - upper 0.050 0.106
## P-value RMSEA <= 0.05 0.951 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.024 0.024
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RR =~
## revrr_favors 0.416 0.020 21.108 0.000 0.942 0.942
## revrr_tryhardr 0.402 0.018 22.106 0.000 0.910 0.910
## DISC =~
## rr_slavery 0.046 0.117 0.390 0.697 0.882 0.882
## rr_deserve 0.045 0.116 0.390 0.697 0.877 0.877
## racineq_discrm 1.165 2.992 0.389 0.697 22.577 0.811
## disc_blacks 0.044 0.114 0.390 0.697 0.860 0.860
## nodisc_eqlncms 0.035 0.090 0.390 0.697 0.679 0.679
## WP =~
## wpa_advantages 0.466 0.018 25.881 0.000 0.970 0.970
## wpa_opensdoors 0.454 0.017 26.223 0.000 0.945 0.945
## wpa_easier 0.455 0.017 26.343 0.000 0.947 0.947
## g =~
## RR 2.030 0.117 17.280 0.000 0.897 0.897
## DISC 19.347 49.729 0.389 0.697 0.999 0.999
## WP 1.826 0.093 19.532 0.000 0.877 0.877
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.000 0.000 0.000
## .revrr_tryhardr 0.000 0.000 0.000
## .rr_slavery 0.000 0.000 0.000
## .rr_deserve 0.000 0.000 0.000
## .racineq_discrm 65.000 1.101 59.046 0.000 65.000 2.335
## .disc_blacks 0.000 0.000 0.000
## .nodisc_eqlncms 0.000 0.000 0.000
## .wpa_advantages 0.000 0.000 0.000
## .wpa_opensdoors 0.000 0.000 0.000
## .wpa_easier 0.000 0.000 0.000
## .RR 0.000 0.000 0.000
## .DISC 0.000 0.000 0.000
## .WP 0.000 0.000 0.000
## g 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favrs|t1 -1.116 0.052 -21.586 0.000 -1.116 -1.116
## revrr_favrs|t2 -0.550 0.043 -12.716 0.000 -0.550 -0.550
## revrr_favrs|t3 -0.169 0.041 -4.110 0.000 -0.169 -0.169
## revrr_favrs|t4 0.442 0.042 10.406 0.000 0.442 0.442
## rvrr_tryhrdr|1 -1.427 0.060 -23.645 0.000 -1.427 -1.427
## rvrr_tryhrdr|2 -0.825 0.046 -17.767 0.000 -0.825 -0.825
## rvrr_tryhrdr|3 -0.430 0.042 -10.148 0.000 -0.430 -0.430
## rvrr_tryhrdr|4 0.183 0.041 4.436 0.000 0.183 0.183
## rr_slavery|t1 -1.305 0.057 -23.092 0.000 -1.305 -1.305
## rr_slavery|t2 -0.867 0.047 -18.424 0.000 -0.867 -0.867
## rr_slavery|t3 -0.557 0.043 -12.844 0.000 -0.557 -0.557
## rr_slavery|t4 0.118 0.041 2.871 0.004 0.118 0.118
## rr_deserve|t1 -1.391 0.059 -23.516 0.000 -1.391 -1.391
## rr_deserve|t2 -0.871 0.047 -18.483 0.000 -0.871 -0.871
## rr_deserve|t3 -0.346 0.042 -8.272 0.000 -0.346 -0.346
## rr_deserve|t4 0.349 0.042 8.337 0.000 0.349 0.349
## disc_blacks|t1 -2.007 0.091 -22.117 0.000 -2.007 -2.007
## disc_blacks|t2 -1.330 0.057 -23.235 0.000 -1.330 -1.330
## disc_blacks|t3 -0.523 0.043 -12.141 0.000 -0.523 -0.523
## disc_blacks|t4 0.224 0.041 5.413 0.000 0.224 0.224
## ndsc_qlncms|t1 -1.838 0.079 -23.195 0.000 -1.838 -1.838
## ndsc_qlncms|t2 -1.350 0.058 -23.335 0.000 -1.350 -1.350
## ndsc_qlncms|t3 -0.923 0.048 -19.244 0.000 -0.923 -0.923
## ndsc_qlncms|t4 -0.415 0.042 -9.825 0.000 -0.415 -0.415
## ndsc_qlncms|t5 0.164 0.041 3.980 0.000 0.164 0.164
## ndsc_qlncms|t6 0.960 0.049 19.759 0.000 0.960 0.960
## wpa_advntgs|t1 -1.709 0.072 -23.694 0.000 -1.709 -1.709
## wpa_advntgs|t2 -1.239 0.055 -22.656 0.000 -1.239 -1.239
## wpa_advntgs|t3 -1.021 0.050 -20.537 0.000 -1.021 -1.021
## wpa_advntgs|t4 -0.792 0.046 -17.222 0.000 -0.792 -0.792
## wpa_advntgs|t5 -0.312 0.042 -7.494 0.000 -0.312 -0.312
## wpa_advntgs|t6 0.355 0.042 8.467 0.000 0.355 0.355
## wpa_opnsdrs|t1 -1.644 0.069 -23.828 0.000 -1.644 -1.644
## wpa_opnsdrs|t2 -1.157 0.053 -21.978 0.000 -1.157 -1.157
## wpa_opnsdrs|t3 -0.903 0.048 -18.954 0.000 -0.903 -0.903
## wpa_opnsdrs|t4 -0.620 0.044 -14.114 0.000 -0.620 -0.620
## wpa_opnsdrs|t5 -0.145 0.041 -3.523 0.000 -0.145 -0.145
## wpa_opnsdrs|t6 0.553 0.043 12.780 0.000 0.553 0.553
## wpa_easier|t1 -1.634 0.069 -23.841 0.000 -1.634 -1.634
## wpa_easier|t2 -1.141 0.052 -21.833 0.000 -1.141 -1.141
## wpa_easier|t3 -0.952 0.048 -19.646 0.000 -0.952 -0.952
## wpa_easier|t4 -0.680 0.045 -15.246 0.000 -0.680 -0.680
## wpa_easier|t5 -0.232 0.041 -5.608 0.000 -0.232 -0.232
## wpa_easier|t6 0.442 0.042 10.406 0.000 0.442 0.442
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.113 0.113 0.113
## .revrr_tryhardr 0.172 0.172 0.172
## .rr_slavery 0.222 0.222 0.222
## .rr_deserve 0.230 0.230 0.230
## .racineq_discrm 265.299 11.399 23.273 0.000 265.299 0.342
## .disc_blacks 0.260 0.260 0.260
## .nodisc_eqlncms 0.539 0.539 0.539
## .wpa_advantages 0.059 0.059 0.059
## .wpa_opensdoors 0.108 0.108 0.108
## .wpa_easier 0.103 0.103 0.103
## .RR 1.000 0.195 0.195
## .DISC 1.000 0.003 0.003
## .WP 1.000 0.231 0.231
## g 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favors 1.000 1.000 1.000
## revrr_tryhardr 1.000 1.000 1.000
## rr_slavery 1.000 1.000 1.000
## rr_deserve 1.000 1.000 1.000
## disc_blacks 1.000 1.000 1.000
## nodisc_eqlncms 1.000 1.000 1.000
## wpa_advantages 1.000 1.000 1.000
## wpa_opensdoors 1.000 1.000 1.000
## wpa_easier 1.000 1.000 1.000## lavaan 0.6-7 ended normally after 29 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 59
##
## Used Total
## Number of observations 938 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 65.713 263.112
## Degrees of freedom 32 32
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.259
## Shift parameter 9.555
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 120256.467 35381.257
## Degrees of freedom 45 45
## P-value 0.000 0.000
## Scaling correction factor 3.402
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 0.993
## Tucker-Lewis Index (TLI) 1.000 0.991
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.034 0.088
## 90 Percent confidence interval - lower 0.022 0.078
## 90 Percent confidence interval - upper 0.045 0.098
## P-value RMSEA <= 0.05 0.992 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.023 0.023
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RR =~
## revrr_favors 0.942 0.008 112.591 0.000 0.942 0.942
## revrr_tryhardr 0.910 0.009 99.987 0.000 0.910 0.910
## DISC =~
## rr_slavery 0.874 0.011 80.169 0.000 0.874 0.874
## rr_deserve 0.870 0.010 84.302 0.000 0.870 0.870
## racineq_discrm 22.428 1.029 21.794 0.000 22.428 0.806
## disc_blacks 0.852 0.012 72.671 0.000 0.852 0.852
## nodisc_eqlncms 0.674 0.018 36.698 0.000 0.674 0.674
## WP =~
## wpa_advantages 0.970 0.004 259.523 0.000 0.970 0.970
## wpa_opensdoors 0.945 0.005 197.038 0.000 0.945 0.945
## wpa_easier 0.947 0.005 198.726 0.000 0.947 0.947
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RR ~~
## DISC 0.916 0.009 101.345 0.000 0.916 0.916
## WP 0.770 0.015 49.924 0.000 0.770 0.770
## DISC ~~
## WP 0.891 0.009 98.108 0.000 0.891 0.891
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.000 0.000 0.000
## .revrr_tryhardr 0.000 0.000 0.000
## .rr_slavery 0.000 0.000 0.000
## .rr_deserve 0.000 0.000 0.000
## .racineq_discrm 65.000 1.101 59.046 0.000 65.000 2.335
## .disc_blacks 0.000 0.000 0.000
## .nodisc_eqlncms 0.000 0.000 0.000
## .wpa_advantages 0.000 0.000 0.000
## .wpa_opensdoors 0.000 0.000 0.000
## .wpa_easier 0.000 0.000 0.000
## RR 0.000 0.000 0.000
## DISC 0.000 0.000 0.000
## WP 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favrs|t1 -1.116 0.052 -21.586 0.000 -1.116 -1.116
## revrr_favrs|t2 -0.550 0.043 -12.716 0.000 -0.550 -0.550
## revrr_favrs|t3 -0.169 0.041 -4.110 0.000 -0.169 -0.169
## revrr_favrs|t4 0.442 0.042 10.406 0.000 0.442 0.442
## rvrr_tryhrdr|1 -1.427 0.060 -23.645 0.000 -1.427 -1.427
## rvrr_tryhrdr|2 -0.825 0.046 -17.767 0.000 -0.825 -0.825
## rvrr_tryhrdr|3 -0.430 0.042 -10.148 0.000 -0.430 -0.430
## rvrr_tryhrdr|4 0.183 0.041 4.436 0.000 0.183 0.183
## rr_slavery|t1 -1.305 0.057 -23.092 0.000 -1.305 -1.305
## rr_slavery|t2 -0.867 0.047 -18.424 0.000 -0.867 -0.867
## rr_slavery|t3 -0.557 0.043 -12.844 0.000 -0.557 -0.557
## rr_slavery|t4 0.118 0.041 2.871 0.004 0.118 0.118
## rr_deserve|t1 -1.391 0.059 -23.516 0.000 -1.391 -1.391
## rr_deserve|t2 -0.871 0.047 -18.483 0.000 -0.871 -0.871
## rr_deserve|t3 -0.346 0.042 -8.272 0.000 -0.346 -0.346
## rr_deserve|t4 0.349 0.042 8.337 0.000 0.349 0.349
## disc_blacks|t1 -2.007 0.091 -22.117 0.000 -2.007 -2.007
## disc_blacks|t2 -1.330 0.057 -23.235 0.000 -1.330 -1.330
## disc_blacks|t3 -0.523 0.043 -12.141 0.000 -0.523 -0.523
## disc_blacks|t4 0.224 0.041 5.413 0.000 0.224 0.224
## ndsc_qlncms|t1 -1.838 0.079 -23.195 0.000 -1.838 -1.838
## ndsc_qlncms|t2 -1.350 0.058 -23.335 0.000 -1.350 -1.350
## ndsc_qlncms|t3 -0.923 0.048 -19.244 0.000 -0.923 -0.923
## ndsc_qlncms|t4 -0.415 0.042 -9.825 0.000 -0.415 -0.415
## ndsc_qlncms|t5 0.164 0.041 3.980 0.000 0.164 0.164
## ndsc_qlncms|t6 0.960 0.049 19.759 0.000 0.960 0.960
## wpa_advntgs|t1 -1.709 0.072 -23.694 0.000 -1.709 -1.709
## wpa_advntgs|t2 -1.239 0.055 -22.656 0.000 -1.239 -1.239
## wpa_advntgs|t3 -1.021 0.050 -20.537 0.000 -1.021 -1.021
## wpa_advntgs|t4 -0.792 0.046 -17.222 0.000 -0.792 -0.792
## wpa_advntgs|t5 -0.312 0.042 -7.494 0.000 -0.312 -0.312
## wpa_advntgs|t6 0.355 0.042 8.467 0.000 0.355 0.355
## wpa_opnsdrs|t1 -1.644 0.069 -23.828 0.000 -1.644 -1.644
## wpa_opnsdrs|t2 -1.157 0.053 -21.978 0.000 -1.157 -1.157
## wpa_opnsdrs|t3 -0.903 0.048 -18.954 0.000 -0.903 -0.903
## wpa_opnsdrs|t4 -0.620 0.044 -14.114 0.000 -0.620 -0.620
## wpa_opnsdrs|t5 -0.145 0.041 -3.523 0.000 -0.145 -0.145
## wpa_opnsdrs|t6 0.553 0.043 12.780 0.000 0.553 0.553
## wpa_easier|t1 -1.634 0.069 -23.841 0.000 -1.634 -1.634
## wpa_easier|t2 -1.141 0.052 -21.833 0.000 -1.141 -1.141
## wpa_easier|t3 -0.952 0.048 -19.646 0.000 -0.952 -0.952
## wpa_easier|t4 -0.680 0.045 -15.246 0.000 -0.680 -0.680
## wpa_easier|t5 -0.232 0.041 -5.608 0.000 -0.232 -0.232
## wpa_easier|t6 0.442 0.042 10.406 0.000 0.442 0.442
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.112 0.112 0.112
## .revrr_tryhardr 0.172 0.172 0.172
## .rr_slavery 0.237 0.237 0.237
## .rr_deserve 0.244 0.244 0.244
## .racineq_discrm 271.862 11.462 23.719 0.000 271.862 0.351
## .disc_blacks 0.274 0.274 0.274
## .nodisc_eqlncms 0.546 0.546 0.546
## .wpa_advantages 0.059 0.059 0.059
## .wpa_opensdoors 0.108 0.108 0.108
## .wpa_easier 0.103 0.103 0.103
## RR 1.000 1.000 1.000
## DISC 1.000 1.000 1.000
## WP 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favors 1.000 1.000 1.000
## revrr_tryhardr 1.000 1.000 1.000
## rr_slavery 1.000 1.000 1.000
## rr_deserve 1.000 1.000 1.000
## disc_blacks 1.000 1.000 1.000
## nodisc_eqlncms 1.000 1.000 1.000
## wpa_advantages 1.000 1.000 1.000
## wpa_opensdoors 1.000 1.000 1.000
## wpa_easier 1.000 1.000 1.000SING <- c(0.870, 0.852, 0.842, 0.842, 0.782, 0.818, 0.652, 0.957, 0.932, 0.931)
HOFG <- c(0.845, 0.816, 0.881, 0.876, 0.810, 0.859, 0.678, 0.851, 0.829, 0.831)
cor(SING, HOFG); cor(SING, HOFG, method = "spearman"); CONGO(SING, HOFG)## [1] 0.704234## [1] 0.218846## [1] 0.9975578In the white subsample, these data are still staggeringly general. 68.8% of the total variance is general with a uniqueness of 29.1%; 97% of the common variance is general whilst only 0.7% and 1.5% of the total relies in the DISC and WP factors alongside 0.9% and 2.1% of the common variance. \(\omega\) is 0.960, \(\omega_h\) is 0.952 and relative \(\omega\) is 0.992. A unit-weighted summary score of the variables in this dataset would correlate at r = 0.976 with its general factor. The H is 0.960, PUC is 0.689 and FDI is 0.980. For DISC, RR and WP respectively, \(\omega\) values are 0.829, 0.913 and 0.900, \(\omega_hs\) values, however, are 0.038, <0.001 and 0.058, with pitifully low values for the relative \(\omega\) and unit-weighted score correlations (r’s of 0.195, 0.002 and 0.241). The values for H are 0.062, <0.001 and 0.133, with FDIs of 0.252, 0.004 and 0.364.
ZGModHOFBR <- '
RR =~ rr_slavery + rr_deserve + revrr_favors + revrr_tryharder
DISC =~ racineq_discrim + disc_blacks + nodisc_equalincomes
WP =~ wpa_advantages + wpa_opensdoors + wpa_easier
g =~ RR + DISC + WP'
ZGModCGFBR <- '
RR =~ rr_slavery + rr_deserve + revrr_favors + revrr_tryharder
DISC =~ racineq_discrim + disc_blacks + nodisc_equalincomes
WP =~ wpa_advantages + wpa_opensdoors + wpa_easier'
ZGRunHOFBR <- sem(ZGModHOFBR, data = data, std.lv = T, check.gradient = F, control= list(rel.tol = 1e-4), ordered = c("revrr_favors", "revrr_tryharder", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "wpa_advantages", "wpa_opensdoors", "wpa_easier"))
ZGRunCGFBR <- sem(ZGModCGFBR, data = data, std.lv = T, check.gradient = F, control= list(rel.tol = 1e-4), ordered = c("revrr_favors", "revrr_tryharder", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "wpa_advantages", "wpa_opensdoors", "wpa_easier"))
ZGRunHOFBRW <- sem(ZGModHOFBR, data = dataw, std.lv = T, check.gradient = F, control= list(rel.tol = 1e-4), ordered = c("revrr_favors", "revrr_tryharder", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "wpa_advantages", "wpa_opensdoors", "wpa_easier"))
ZGRunCGFBRW <- sem(ZGModCGFBR, data = dataw, std.lv = T, check.gradient = F, control= list(rel.tol = 1e-4), ordered = c("revrr_favors", "revrr_tryharder", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "wpa_advantages", "wpa_opensdoors", "wpa_easier"))
summary(ZGRunHOFBR, stand = T, fit = T); summary(ZGRunCGFBR, stand = T, fit = T); summary(ZGRunHOFBRW, stand = T, fit = T); summary(ZGRunCGFBRW, stand = T, fit = T)## lavaan 0.6-7 ended normally after 128 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 59
##
## Used Total
## Number of observations 994 1045
##
## Model Test User Model:
## Standard Robust
## Test Statistic 112.675 422.625
## Degrees of freedom 32 32
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.273
## Shift parameter 9.686
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 124493.294 36788.489
## Degrees of freedom 45 45
## P-value 0.000 0.000
## Scaling correction factor 3.387
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.999 0.989
## Tucker-Lewis Index (TLI) 0.999 0.985
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.050 0.111
## 90 Percent confidence interval - lower 0.040 0.102
## 90 Percent confidence interval - upper 0.061 0.120
## P-value RMSEA <= 0.05 0.456 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.024 0.024
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RR =~
## rr_slavery 0.359 0.018 19.697 0.000 0.890 0.890
## rr_deserve 0.356 0.019 19.199 0.000 0.884 0.884
## revrr_favors 0.363 0.018 19.795 0.000 0.902 0.902
## revrr_tryhardr 0.353 0.018 20.127 0.000 0.876 0.876
## DISC =~
## racineq_discrm 2.423 1.768 1.370 0.171 22.726 0.818
## disc_blacks 0.092 0.068 1.367 0.172 0.867 0.867
## nodisc_eqlncms 0.073 0.053 1.373 0.170 0.684 0.684
## WP =~
## wpa_advantages 0.439 0.018 24.229 0.000 0.973 0.973
## wpa_opensdoors 0.425 0.017 24.708 0.000 0.942 0.942
## wpa_easier 0.429 0.017 24.702 0.000 0.951 0.951
## g =~
## RR 2.273 0.140 16.288 0.000 0.915 0.915
## DISC 9.327 6.825 1.367 0.172 0.994 0.994
## WP 1.978 0.103 19.135 0.000 0.892 0.892
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .rr_slavery 0.000 0.000 0.000
## .rr_deserve 0.000 0.000 0.000
## .revrr_favors 0.000 0.000 0.000
## .revrr_tryhardr 0.000 0.000 0.000
## .racineq_discrm 65.165 1.074 60.662 0.000 65.165 2.345
## .disc_blacks 0.000 0.000 0.000
## .nodisc_eqlncms 0.000 0.000 0.000
## .wpa_advantages 0.000 0.000 0.000
## .wpa_opensdoors 0.000 0.000 0.000
## .wpa_easier 0.000 0.000 0.000
## .RR 0.000 0.000 0.000
## .DISC 0.000 0.000 0.000
## .WP 0.000 0.000 0.000
## g 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## rr_slavery|t1 -1.307 0.055 -23.786 0.000 -1.307 -1.307
## rr_slavery|t2 -0.877 0.046 -19.128 0.000 -0.877 -0.877
## rr_slavery|t3 -0.569 0.042 -13.480 0.000 -0.569 -0.569
## rr_slavery|t4 0.121 0.040 3.043 0.002 0.121 0.121
## rr_deserve|t1 -1.388 0.057 -24.198 0.000 -1.388 -1.388
## rr_deserve|t2 -0.881 0.046 -19.185 0.000 -0.881 -0.881
## rr_deserve|t3 -0.350 0.041 -8.605 0.000 -0.350 -0.350
## rr_deserve|t4 0.350 0.041 8.605 0.000 0.350 0.350
## revrr_favrs|t1 -1.123 0.050 -22.290 0.000 -1.123 -1.123
## revrr_favrs|t2 -0.563 0.042 -13.357 0.000 -0.563 -0.563
## revrr_favrs|t3 -0.167 0.040 -4.183 0.000 -0.167 -0.167
## revrr_favrs|t4 0.446 0.041 10.803 0.000 0.446 0.446
## rvrr_tryhrdr|1 -1.429 0.059 -24.348 0.000 -1.429 -1.429
## rvrr_tryhrdr|2 -0.830 0.045 -18.376 0.000 -0.830 -0.830
## rvrr_tryhrdr|3 -0.434 0.041 -10.553 0.000 -0.434 -0.434
## rvrr_tryhrdr|4 0.177 0.040 4.436 0.000 0.177 0.177
## disc_blacks|t1 -2.031 0.090 -22.573 0.000 -2.031 -2.031
## disc_blacks|t2 -1.356 0.056 -24.052 0.000 -1.356 -1.356
## disc_blacks|t3 -0.548 0.042 -13.047 0.000 -0.548 -0.548
## disc_blacks|t4 0.206 0.040 5.132 0.000 0.206 0.206
## ndsc_qlncms|t1 -1.822 0.076 -23.956 0.000 -1.822 -1.822
## ndsc_qlncms|t2 -1.337 0.056 -23.957 0.000 -1.337 -1.337
## ndsc_qlncms|t3 -0.919 0.047 -19.753 0.000 -0.919 -0.919
## ndsc_qlncms|t4 -0.407 0.041 -9.925 0.000 -0.407 -0.407
## ndsc_qlncms|t5 0.170 0.040 4.246 0.000 0.170 0.170
## ndsc_qlncms|t6 0.962 0.047 20.365 0.000 0.962 0.962
## wpa_advntgs|t1 -1.714 0.070 -24.378 0.000 -1.714 -1.714
## wpa_advntgs|t2 -1.250 0.053 -23.406 0.000 -1.250 -1.250
## wpa_advntgs|t3 -1.041 0.049 -21.384 0.000 -1.041 -1.041
## wpa_advntgs|t4 -0.799 0.045 -17.848 0.000 -0.799 -0.799
## wpa_advntgs|t5 -0.318 0.041 -7.849 0.000 -0.318 -0.318
## wpa_advntgs|t6 0.358 0.041 8.794 0.000 0.358 0.358
## wpa_opnsdrs|t1 -1.642 0.067 -24.532 0.000 -1.642 -1.642
## wpa_opnsdrs|t2 -1.171 0.051 -22.760 0.000 -1.171 -1.171
## wpa_opnsdrs|t3 -0.915 0.046 -19.697 0.000 -0.915 -0.915
## wpa_opnsdrs|t4 -0.629 0.043 -14.712 0.000 -0.629 -0.629
## wpa_opnsdrs|t5 -0.142 0.040 -3.550 0.000 -0.142 -0.142
## wpa_opnsdrs|t6 0.551 0.042 13.109 0.000 0.551 0.551
## wpa_easier|t1 -1.632 0.067 -24.545 0.000 -1.632 -1.632
## wpa_easier|t2 -1.147 0.051 -22.528 0.000 -1.147 -1.147
## wpa_easier|t3 -0.962 0.047 -20.365 0.000 -0.962 -0.962
## wpa_easier|t4 -0.689 0.043 -15.871 0.000 -0.689 -0.689
## wpa_easier|t5 -0.234 0.040 -5.828 0.000 -0.234 -0.234
## wpa_easier|t6 0.432 0.041 10.490 0.000 0.432 0.432
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .rr_slavery 0.207 0.207 0.207
## .rr_deserve 0.219 0.219 0.219
## .revrr_favors 0.187 0.187 0.187
## .revrr_tryhardr 0.232 0.232 0.232
## .racineq_discrm 255.454 11.885 21.494 0.000 255.454 0.331
## .disc_blacks 0.248 0.248 0.248
## .nodisc_eqlncms 0.532 0.532 0.532
## .wpa_advantages 0.053 0.053 0.053
## .wpa_opensdoors 0.112 0.112 0.112
## .wpa_easier 0.095 0.095 0.095
## .RR 1.000 0.162 0.162
## .DISC 1.000 0.011 0.011
## .WP 1.000 0.204 0.204
## g 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## rr_slavery 1.000 1.000 1.000
## rr_deserve 1.000 1.000 1.000
## revrr_favors 1.000 1.000 1.000
## revrr_tryhardr 1.000 1.000 1.000
## disc_blacks 1.000 1.000 1.000
## nodisc_eqlncms 1.000 1.000 1.000
## wpa_advantages 1.000 1.000 1.000
## wpa_opensdoors 1.000 1.000 1.000
## wpa_easier 1.000 1.000 1.000## lavaan 0.6-7 ended normally after 33 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 59
##
## Used Total
## Number of observations 994 1045
##
## Model Test User Model:
## Standard Robust
## Test Statistic 111.579 418.451
## Degrees of freedom 32 32
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.273
## Shift parameter 9.686
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 124493.294 36788.489
## Degrees of freedom 45 45
## P-value 0.000 0.000
## Scaling correction factor 3.387
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.999 0.989
## Tucker-Lewis Index (TLI) 0.999 0.985
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.050 0.110
## 90 Percent confidence interval - lower 0.040 0.101
## 90 Percent confidence interval - upper 0.060 0.120
## P-value RMSEA <= 0.05 0.478 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.024 0.024
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RR =~
## rr_slavery 0.891 0.010 89.199 0.000 0.891 0.891
## rr_deserve 0.884 0.010 89.118 0.000 0.884 0.884
## revrr_favors 0.902 0.009 102.803 0.000 0.902 0.902
## revrr_tryhardr 0.876 0.010 90.381 0.000 0.876 0.876
## DISC =~
## racineq_discrm 22.503 1.009 22.299 0.000 22.503 0.810
## disc_blacks 0.855 0.014 62.546 0.000 0.855 0.855
## nodisc_eqlncms 0.677 0.018 36.945 0.000 0.677 0.677
## WP =~
## wpa_advantages 0.973 0.004 251.605 0.000 0.973 0.973
## wpa_opensdoors 0.942 0.005 198.117 0.000 0.942 0.942
## wpa_easier 0.951 0.004 219.080 0.000 0.951 0.951
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RR ~~
## DISC 0.925 0.011 82.813 0.000 0.925 0.925
## WP 0.815 0.012 67.549 0.000 0.815 0.815
## DISC ~~
## WP 0.902 0.011 78.554 0.000 0.902 0.902
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .rr_slavery 0.000 0.000 0.000
## .rr_deserve 0.000 0.000 0.000
## .revrr_favors 0.000 0.000 0.000
## .revrr_tryhardr 0.000 0.000 0.000
## .racineq_discrm 65.165 1.074 60.662 0.000 65.165 2.346
## .disc_blacks 0.000 0.000 0.000
## .nodisc_eqlncms 0.000 0.000 0.000
## .wpa_advantages 0.000 0.000 0.000
## .wpa_opensdoors 0.000 0.000 0.000
## .wpa_easier 0.000 0.000 0.000
## RR 0.000 0.000 0.000
## DISC 0.000 0.000 0.000
## WP 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## rr_slavery|t1 -1.307 0.055 -23.786 0.000 -1.307 -1.307
## rr_slavery|t2 -0.877 0.046 -19.128 0.000 -0.877 -0.877
## rr_slavery|t3 -0.569 0.042 -13.480 0.000 -0.569 -0.569
## rr_slavery|t4 0.121 0.040 3.043 0.002 0.121 0.121
## rr_deserve|t1 -1.388 0.057 -24.198 0.000 -1.388 -1.388
## rr_deserve|t2 -0.881 0.046 -19.185 0.000 -0.881 -0.881
## rr_deserve|t3 -0.350 0.041 -8.605 0.000 -0.350 -0.350
## rr_deserve|t4 0.350 0.041 8.605 0.000 0.350 0.350
## revrr_favrs|t1 -1.123 0.050 -22.290 0.000 -1.123 -1.123
## revrr_favrs|t2 -0.563 0.042 -13.357 0.000 -0.563 -0.563
## revrr_favrs|t3 -0.167 0.040 -4.183 0.000 -0.167 -0.167
## revrr_favrs|t4 0.446 0.041 10.803 0.000 0.446 0.446
## rvrr_tryhrdr|1 -1.429 0.059 -24.348 0.000 -1.429 -1.429
## rvrr_tryhrdr|2 -0.830 0.045 -18.376 0.000 -0.830 -0.830
## rvrr_tryhrdr|3 -0.434 0.041 -10.553 0.000 -0.434 -0.434
## rvrr_tryhrdr|4 0.177 0.040 4.436 0.000 0.177 0.177
## disc_blacks|t1 -2.031 0.090 -22.573 0.000 -2.031 -2.031
## disc_blacks|t2 -1.356 0.056 -24.052 0.000 -1.356 -1.356
## disc_blacks|t3 -0.548 0.042 -13.047 0.000 -0.548 -0.548
## disc_blacks|t4 0.206 0.040 5.132 0.000 0.206 0.206
## ndsc_qlncms|t1 -1.822 0.076 -23.956 0.000 -1.822 -1.822
## ndsc_qlncms|t2 -1.337 0.056 -23.957 0.000 -1.337 -1.337
## ndsc_qlncms|t3 -0.919 0.047 -19.753 0.000 -0.919 -0.919
## ndsc_qlncms|t4 -0.407 0.041 -9.925 0.000 -0.407 -0.407
## ndsc_qlncms|t5 0.170 0.040 4.246 0.000 0.170 0.170
## ndsc_qlncms|t6 0.962 0.047 20.365 0.000 0.962 0.962
## wpa_advntgs|t1 -1.714 0.070 -24.378 0.000 -1.714 -1.714
## wpa_advntgs|t2 -1.250 0.053 -23.406 0.000 -1.250 -1.250
## wpa_advntgs|t3 -1.041 0.049 -21.384 0.000 -1.041 -1.041
## wpa_advntgs|t4 -0.799 0.045 -17.848 0.000 -0.799 -0.799
## wpa_advntgs|t5 -0.318 0.041 -7.849 0.000 -0.318 -0.318
## wpa_advntgs|t6 0.358 0.041 8.794 0.000 0.358 0.358
## wpa_opnsdrs|t1 -1.642 0.067 -24.532 0.000 -1.642 -1.642
## wpa_opnsdrs|t2 -1.171 0.051 -22.760 0.000 -1.171 -1.171
## wpa_opnsdrs|t3 -0.915 0.046 -19.697 0.000 -0.915 -0.915
## wpa_opnsdrs|t4 -0.629 0.043 -14.712 0.000 -0.629 -0.629
## wpa_opnsdrs|t5 -0.142 0.040 -3.550 0.000 -0.142 -0.142
## wpa_opnsdrs|t6 0.551 0.042 13.109 0.000 0.551 0.551
## wpa_easier|t1 -1.632 0.067 -24.545 0.000 -1.632 -1.632
## wpa_easier|t2 -1.147 0.051 -22.528 0.000 -1.147 -1.147
## wpa_easier|t3 -0.962 0.047 -20.365 0.000 -0.962 -0.962
## wpa_easier|t4 -0.689 0.043 -15.871 0.000 -0.689 -0.689
## wpa_easier|t5 -0.234 0.040 -5.828 0.000 -0.234 -0.234
## wpa_easier|t6 0.432 0.041 10.490 0.000 0.432 0.432
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .rr_slavery 0.207 0.207 0.207
## .rr_deserve 0.219 0.219 0.219
## .revrr_favors 0.187 0.187 0.187
## .revrr_tryhardr 0.232 0.232 0.232
## .racineq_discrm 265.123 11.932 22.219 0.000 265.123 0.344
## .disc_blacks 0.268 0.268 0.268
## .nodisc_eqlncms 0.542 0.542 0.542
## .wpa_advantages 0.053 0.053 0.053
## .wpa_opensdoors 0.112 0.112 0.112
## .wpa_easier 0.095 0.095 0.095
## RR 1.000 1.000 1.000
## DISC 1.000 1.000 1.000
## WP 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## rr_slavery 1.000 1.000 1.000
## rr_deserve 1.000 1.000 1.000
## revrr_favors 1.000 1.000 1.000
## revrr_tryhardr 1.000 1.000 1.000
## disc_blacks 1.000 1.000 1.000
## nodisc_eqlncms 1.000 1.000 1.000
## wpa_advantages 1.000 1.000 1.000
## wpa_opensdoors 1.000 1.000 1.000
## wpa_easier 1.000 1.000 1.000## lavaan 0.6-7 ended normally after 85 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 59
##
## Used Total
## Number of observations 938 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 118.708 435.737
## Degrees of freedom 32 32
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.279
## Shift parameter 9.916
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 120256.467 35381.257
## Degrees of freedom 45 45
## P-value 0.000 0.000
## Scaling correction factor 3.402
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.999 0.989
## Tucker-Lewis Index (TLI) 0.999 0.984
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.054 0.116
## 90 Percent confidence interval - lower 0.044 0.106
## 90 Percent confidence interval - upper 0.064 0.126
## P-value RMSEA <= 0.05 0.259 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.026 0.026
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RR =~
## rr_slavery 0.345 0.018 19.617 0.000 0.889 0.889
## rr_deserve 0.344 0.018 19.098 0.000 0.886 0.886
## revrr_favors 0.351 0.018 19.694 0.000 0.903 0.903
## revrr_tryhardr 0.341 0.017 20.002 0.000 0.879 0.879
## DISC =~
## racineq_discrm 4.616 0.954 4.841 0.000 23.028 0.826
## disc_blacks 0.177 0.037 4.832 0.000 0.881 0.881
## nodisc_eqlncms 0.139 0.028 4.892 0.000 0.694 0.694
## WP =~
## wpa_advantages 0.415 0.019 22.246 0.000 0.970 0.970
## wpa_opensdoors 0.404 0.018 22.442 0.000 0.944 0.944
## wpa_easier 0.405 0.018 22.598 0.000 0.947 0.947
## g =~
## RR 2.373 0.146 16.274 0.000 0.922 0.922
## DISC 4.887 1.016 4.809 0.000 0.980 0.980
## WP 2.115 0.118 17.922 0.000 0.904 0.904
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .rr_slavery 0.000 0.000 0.000
## .rr_deserve 0.000 0.000 0.000
## .revrr_favors 0.000 0.000 0.000
## .revrr_tryhardr 0.000 0.000 0.000
## .racineq_discrm 65.000 1.101 59.046 0.000 65.000 2.333
## .disc_blacks 0.000 0.000 0.000
## .nodisc_eqlncms 0.000 0.000 0.000
## .wpa_advantages 0.000 0.000 0.000
## .wpa_opensdoors 0.000 0.000 0.000
## .wpa_easier 0.000 0.000 0.000
## .RR 0.000 0.000 0.000
## .DISC 0.000 0.000 0.000
## .WP 0.000 0.000 0.000
## g 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## rr_slavery|t1 -1.305 0.057 -23.092 0.000 -1.305 -1.305
## rr_slavery|t2 -0.867 0.047 -18.424 0.000 -0.867 -0.867
## rr_slavery|t3 -0.557 0.043 -12.844 0.000 -0.557 -0.557
## rr_slavery|t4 0.118 0.041 2.871 0.004 0.118 0.118
## rr_deserve|t1 -1.391 0.059 -23.516 0.000 -1.391 -1.391
## rr_deserve|t2 -0.871 0.047 -18.483 0.000 -0.871 -0.871
## rr_deserve|t3 -0.346 0.042 -8.272 0.000 -0.346 -0.346
## rr_deserve|t4 0.349 0.042 8.337 0.000 0.349 0.349
## revrr_favrs|t1 -1.116 0.052 -21.586 0.000 -1.116 -1.116
## revrr_favrs|t2 -0.550 0.043 -12.716 0.000 -0.550 -0.550
## revrr_favrs|t3 -0.169 0.041 -4.110 0.000 -0.169 -0.169
## revrr_favrs|t4 0.442 0.042 10.406 0.000 0.442 0.442
## rvrr_tryhrdr|1 -1.427 0.060 -23.645 0.000 -1.427 -1.427
## rvrr_tryhrdr|2 -0.825 0.046 -17.767 0.000 -0.825 -0.825
## rvrr_tryhrdr|3 -0.430 0.042 -10.148 0.000 -0.430 -0.430
## rvrr_tryhrdr|4 0.183 0.041 4.436 0.000 0.183 0.183
## disc_blacks|t1 -2.007 0.091 -22.117 0.000 -2.007 -2.007
## disc_blacks|t2 -1.330 0.057 -23.235 0.000 -1.330 -1.330
## disc_blacks|t3 -0.523 0.043 -12.141 0.000 -0.523 -0.523
## disc_blacks|t4 0.224 0.041 5.413 0.000 0.224 0.224
## ndsc_qlncms|t1 -1.838 0.079 -23.195 0.000 -1.838 -1.838
## ndsc_qlncms|t2 -1.350 0.058 -23.335 0.000 -1.350 -1.350
## ndsc_qlncms|t3 -0.923 0.048 -19.244 0.000 -0.923 -0.923
## ndsc_qlncms|t4 -0.415 0.042 -9.825 0.000 -0.415 -0.415
## ndsc_qlncms|t5 0.164 0.041 3.980 0.000 0.164 0.164
## ndsc_qlncms|t6 0.960 0.049 19.759 0.000 0.960 0.960
## wpa_advntgs|t1 -1.709 0.072 -23.694 0.000 -1.709 -1.709
## wpa_advntgs|t2 -1.239 0.055 -22.656 0.000 -1.239 -1.239
## wpa_advntgs|t3 -1.021 0.050 -20.537 0.000 -1.021 -1.021
## wpa_advntgs|t4 -0.792 0.046 -17.222 0.000 -0.792 -0.792
## wpa_advntgs|t5 -0.312 0.042 -7.494 0.000 -0.312 -0.312
## wpa_advntgs|t6 0.355 0.042 8.467 0.000 0.355 0.355
## wpa_opnsdrs|t1 -1.644 0.069 -23.828 0.000 -1.644 -1.644
## wpa_opnsdrs|t2 -1.157 0.053 -21.978 0.000 -1.157 -1.157
## wpa_opnsdrs|t3 -0.903 0.048 -18.954 0.000 -0.903 -0.903
## wpa_opnsdrs|t4 -0.620 0.044 -14.114 0.000 -0.620 -0.620
## wpa_opnsdrs|t5 -0.145 0.041 -3.523 0.000 -0.145 -0.145
## wpa_opnsdrs|t6 0.553 0.043 12.780 0.000 0.553 0.553
## wpa_easier|t1 -1.634 0.069 -23.841 0.000 -1.634 -1.634
## wpa_easier|t2 -1.141 0.052 -21.833 0.000 -1.141 -1.141
## wpa_easier|t3 -0.952 0.048 -19.646 0.000 -0.952 -0.952
## wpa_easier|t4 -0.680 0.045 -15.246 0.000 -0.680 -0.680
## wpa_easier|t5 -0.232 0.041 -5.608 0.000 -0.232 -0.232
## wpa_easier|t6 0.442 0.042 10.406 0.000 0.442 0.442
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .rr_slavery 0.210 0.210 0.210
## .rr_deserve 0.216 0.216 0.216
## .revrr_favors 0.185 0.185 0.185
## .revrr_tryhardr 0.227 0.227 0.227
## .racineq_discrm 246.010 12.118 20.300 0.000 246.010 0.317
## .disc_blacks 0.224 0.224 0.224
## .nodisc_eqlncms 0.518 0.518 0.518
## .wpa_advantages 0.059 0.059 0.059
## .wpa_opensdoors 0.108 0.108 0.108
## .wpa_easier 0.103 0.103 0.103
## .RR 1.000 0.151 0.151
## .DISC 1.000 0.040 0.040
## .WP 1.000 0.183 0.183
## g 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## rr_slavery 1.000 1.000 1.000
## rr_deserve 1.000 1.000 1.000
## revrr_favors 1.000 1.000 1.000
## revrr_tryhardr 1.000 1.000 1.000
## disc_blacks 1.000 1.000 1.000
## nodisc_eqlncms 1.000 1.000 1.000
## wpa_advantages 1.000 1.000 1.000
## wpa_opensdoors 1.000 1.000 1.000
## wpa_easier 1.000 1.000 1.000## lavaan 0.6-7 ended normally after 33 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 59
##
## Used Total
## Number of observations 938 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 116.178 426.489
## Degrees of freedom 32 32
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.279
## Shift parameter 9.917
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 120256.467 35381.257
## Degrees of freedom 45 45
## P-value 0.000 0.000
## Scaling correction factor 3.402
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.999 0.989
## Tucker-Lewis Index (TLI) 0.999 0.984
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.053 0.115
## 90 Percent confidence interval - lower 0.043 0.105
## 90 Percent confidence interval - upper 0.064 0.125
## P-value RMSEA <= 0.05 0.301 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.025 0.025
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RR =~
## rr_slavery 0.889 0.010 85.511 0.000 0.889 0.889
## rr_deserve 0.885 0.010 87.151 0.000 0.885 0.885
## revrr_favors 0.903 0.009 102.526 0.000 0.903 0.903
## revrr_tryhardr 0.879 0.010 89.495 0.000 0.879 0.879
## DISC =~
## racineq_discrm 22.679 1.041 21.789 0.000 22.679 0.814
## disc_blacks 0.862 0.013 64.233 0.000 0.862 0.862
## nodisc_eqlncms 0.682 0.019 36.383 0.000 0.682 0.682
## WP =~
## wpa_advantages 0.970 0.004 259.341 0.000 0.970 0.970
## wpa_opensdoors 0.944 0.005 196.643 0.000 0.944 0.944
## wpa_easier 0.947 0.005 198.654 0.000 0.947 0.947
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RR ~~
## DISC 0.927 0.011 86.312 0.000 0.927 0.927
## WP 0.831 0.011 72.749 0.000 0.831 0.831
## DISC ~~
## WP 0.907 0.012 78.638 0.000 0.907 0.907
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .rr_slavery 0.000 0.000 0.000
## .rr_deserve 0.000 0.000 0.000
## .revrr_favors 0.000 0.000 0.000
## .revrr_tryhardr 0.000 0.000 0.000
## .racineq_discrm 65.000 1.101 59.046 0.000 65.000 2.334
## .disc_blacks 0.000 0.000 0.000
## .nodisc_eqlncms 0.000 0.000 0.000
## .wpa_advantages 0.000 0.000 0.000
## .wpa_opensdoors 0.000 0.000 0.000
## .wpa_easier 0.000 0.000 0.000
## RR 0.000 0.000 0.000
## DISC 0.000 0.000 0.000
## WP 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## rr_slavery|t1 -1.305 0.057 -23.092 0.000 -1.305 -1.305
## rr_slavery|t2 -0.867 0.047 -18.424 0.000 -0.867 -0.867
## rr_slavery|t3 -0.557 0.043 -12.844 0.000 -0.557 -0.557
## rr_slavery|t4 0.118 0.041 2.871 0.004 0.118 0.118
## rr_deserve|t1 -1.391 0.059 -23.516 0.000 -1.391 -1.391
## rr_deserve|t2 -0.871 0.047 -18.483 0.000 -0.871 -0.871
## rr_deserve|t3 -0.346 0.042 -8.272 0.000 -0.346 -0.346
## rr_deserve|t4 0.349 0.042 8.337 0.000 0.349 0.349
## revrr_favrs|t1 -1.116 0.052 -21.586 0.000 -1.116 -1.116
## revrr_favrs|t2 -0.550 0.043 -12.716 0.000 -0.550 -0.550
## revrr_favrs|t3 -0.169 0.041 -4.110 0.000 -0.169 -0.169
## revrr_favrs|t4 0.442 0.042 10.406 0.000 0.442 0.442
## rvrr_tryhrdr|1 -1.427 0.060 -23.645 0.000 -1.427 -1.427
## rvrr_tryhrdr|2 -0.825 0.046 -17.767 0.000 -0.825 -0.825
## rvrr_tryhrdr|3 -0.430 0.042 -10.148 0.000 -0.430 -0.430
## rvrr_tryhrdr|4 0.183 0.041 4.436 0.000 0.183 0.183
## disc_blacks|t1 -2.007 0.091 -22.117 0.000 -2.007 -2.007
## disc_blacks|t2 -1.330 0.057 -23.235 0.000 -1.330 -1.330
## disc_blacks|t3 -0.523 0.043 -12.141 0.000 -0.523 -0.523
## disc_blacks|t4 0.224 0.041 5.413 0.000 0.224 0.224
## ndsc_qlncms|t1 -1.838 0.079 -23.195 0.000 -1.838 -1.838
## ndsc_qlncms|t2 -1.350 0.058 -23.335 0.000 -1.350 -1.350
## ndsc_qlncms|t3 -0.923 0.048 -19.244 0.000 -0.923 -0.923
## ndsc_qlncms|t4 -0.415 0.042 -9.825 0.000 -0.415 -0.415
## ndsc_qlncms|t5 0.164 0.041 3.980 0.000 0.164 0.164
## ndsc_qlncms|t6 0.960 0.049 19.759 0.000 0.960 0.960
## wpa_advntgs|t1 -1.709 0.072 -23.694 0.000 -1.709 -1.709
## wpa_advntgs|t2 -1.239 0.055 -22.656 0.000 -1.239 -1.239
## wpa_advntgs|t3 -1.021 0.050 -20.537 0.000 -1.021 -1.021
## wpa_advntgs|t4 -0.792 0.046 -17.222 0.000 -0.792 -0.792
## wpa_advntgs|t5 -0.312 0.042 -7.494 0.000 -0.312 -0.312
## wpa_advntgs|t6 0.355 0.042 8.467 0.000 0.355 0.355
## wpa_opnsdrs|t1 -1.644 0.069 -23.828 0.000 -1.644 -1.644
## wpa_opnsdrs|t2 -1.157 0.053 -21.978 0.000 -1.157 -1.157
## wpa_opnsdrs|t3 -0.903 0.048 -18.954 0.000 -0.903 -0.903
## wpa_opnsdrs|t4 -0.620 0.044 -14.114 0.000 -0.620 -0.620
## wpa_opnsdrs|t5 -0.145 0.041 -3.523 0.000 -0.145 -0.145
## wpa_opnsdrs|t6 0.553 0.043 12.780 0.000 0.553 0.553
## wpa_easier|t1 -1.634 0.069 -23.841 0.000 -1.634 -1.634
## wpa_easier|t2 -1.141 0.052 -21.833 0.000 -1.141 -1.141
## wpa_easier|t3 -0.952 0.048 -19.646 0.000 -0.952 -0.952
## wpa_easier|t4 -0.680 0.045 -15.246 0.000 -0.680 -0.680
## wpa_easier|t5 -0.232 0.041 -5.608 0.000 -0.232 -0.232
## wpa_easier|t6 0.442 0.042 10.406 0.000 0.442 0.442
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .rr_slavery 0.210 0.210 0.210
## .rr_deserve 0.216 0.216 0.216
## .revrr_favors 0.185 0.185 0.185
## .revrr_tryhardr 0.227 0.227 0.227
## .racineq_discrm 261.133 12.169 21.458 0.000 261.133 0.337
## .disc_blacks 0.256 0.256 0.256
## .nodisc_eqlncms 0.535 0.535 0.535
## .wpa_advantages 0.059 0.059 0.059
## .wpa_opensdoors 0.109 0.109 0.109
## .wpa_easier 0.103 0.103 0.103
## RR 1.000 1.000 1.000
## DISC 1.000 1.000 1.000
## WP 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## rr_slavery 1.000 1.000 1.000
## rr_deserve 1.000 1.000 1.000
## revrr_favors 1.000 1.000 1.000
## revrr_tryhardr 1.000 1.000 1.000
## disc_blacks 1.000 1.000 1.000
## nodisc_eqlncms 1.000 1.000 1.000
## wpa_advantages 1.000 1.000 1.000
## wpa_opensdoors 1.000 1.000 1.000
## wpa_easier 1.000 1.000 1.000