Additional Analyses for Goldberg
Setup
library(pacman); p_load(psych, VIM, lavaan, semPlot)
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.scaled", "rmsea", "rmsea.ci.lower", "rmsea.ci.upper", "srmr")These analyses utilize the white subset of the full dataset.
Analysis
One
ZGModOne <- '
General =~ racineq_discrim + wpa_advantages + wpa_opensdoors + wpa_easier + shame_racistmean + shame_means2bewhite + shame_racistendencies + guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior + image_shame_disgraced + image_shame_howseen + image_shame_humiliated + rr_slavery + rr_deserve + disc_blacks + nodisc_equalincomes + revshame_notashamed + revrr_favors + revrr_tryharder'
ZGRunOne <- cfa(ZGModOne, data = data, std.lv = T, ordered = c("wpa_advantages", "wpa_opensdoors", "wpa_easier", "shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))
summary(ZGRunOne, stand = T, fit = T)## lavaan 0.6-7 ended normally after 72 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 133
##
## Used Total
## Number of observations 936 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 7331.085 6645.229
## Degrees of freedom 189 189
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.125
## Shift parameter 127.272
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 388166.805 71255.951
## Degrees of freedom 210 210
## P-value 0.000 0.000
## Scaling correction factor 5.461
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.982 0.909
## Tucker-Lewis Index (TLI) 0.980 0.899
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.201 0.191
## 90 Percent confidence interval - lower 0.197 0.187
## 90 Percent confidence interval - upper 0.205 0.195
## 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 0.115 0.115
##
## 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
## General =~
## racineq_discrm 20.035 1.011 19.820 0.000 20.035 0.720
## wpa_advantages 0.927 0.006 165.225 0.000 0.927 0.927
## wpa_opensdoors 0.900 0.007 136.944 0.000 0.900 0.900
## wpa_easier 0.902 0.007 134.843 0.000 0.902 0.902
## shame_racistmn 0.852 0.009 94.622 0.000 0.852 0.852
## shame_mns2bwht 0.896 0.007 135.718 0.000 0.896 0.896
## sham_rcstndncs 0.855 0.009 95.159 0.000 0.855 0.855
## guilt_racism 0.889 0.007 136.024 0.000 0.889 0.889
## guilt_inequlty 0.897 0.006 147.931 0.000 0.897 0.897
## guilt_treatmnt 0.916 0.005 171.410 0.000 0.916 0.916
## guilt_behavior 0.909 0.006 163.142 0.000 0.909 0.909
## img_shm_dsgrcd 0.752 0.013 58.892 0.000 0.752 0.752
## image_shm_hwsn 0.821 0.010 80.208 0.000 0.821 0.821
## imag_shm_hmltd 0.691 0.015 45.583 0.000 0.691 0.691
## rr_slavery 0.797 0.014 58.066 0.000 0.797 0.797
## rr_deserve 0.808 0.013 64.221 0.000 0.808 0.808
## disc_blacks 0.796 0.013 59.254 0.000 0.796 0.796
## nodisc_eqlncms 0.613 0.019 31.930 0.000 0.613 0.613
## revsham_ntshmd 0.668 0.017 39.984 0.000 0.668 0.668
## revrr_favors 0.811 0.012 68.353 0.000 0.811 0.811
## revrr_tryhardr 0.792 0.013 60.820 0.000 0.792 0.792
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .racineq_discrm 65.034 1.101 59.079 0.000 65.034 2.338
## .wpa_advantages 0.000 0.000 0.000
## .wpa_opensdoors 0.000 0.000 0.000
## .wpa_easier 0.000 0.000 0.000
## .shame_racistmn 0.000 0.000 0.000
## .shame_mns2bwht 0.000 0.000 0.000
## .sham_rcstndncs 0.000 0.000 0.000
## .guilt_racism 0.000 0.000 0.000
## .guilt_inequlty 0.000 0.000 0.000
## .guilt_treatmnt 0.000 0.000 0.000
## .guilt_behavior 0.000 0.000 0.000
## .img_shm_dsgrcd 0.000 0.000 0.000
## .image_shm_hwsn 0.000 0.000 0.000
## .imag_shm_hmltd 0.000 0.000 0.000
## .rr_slavery 0.000 0.000 0.000
## .rr_deserve 0.000 0.000 0.000
## .disc_blacks 0.000 0.000 0.000
## .nodisc_eqlncms 0.000 0.000 0.000
## .revsham_ntshmd 0.000 0.000 0.000
## .revrr_favors 0.000 0.000 0.000
## .revrr_tryhardr 0.000 0.000 0.000
## General 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## wpa_advntgs|t1 -1.708 0.072 -23.671 0.000 -1.708 -1.708
## wpa_advntgs|t2 -1.244 0.055 -22.665 0.000 -1.244 -1.244
## wpa_advntgs|t3 -1.025 0.050 -20.553 0.000 -1.025 -1.025
## wpa_advntgs|t4 -0.794 0.046 -17.239 0.000 -0.794 -0.794
## wpa_advntgs|t5 -0.313 0.042 -7.502 0.000 -0.313 -0.313
## wpa_advntgs|t6 0.355 0.042 8.476 0.000 0.355 0.355
## wpa_opnsdrs|t1 -1.643 0.069 -23.804 0.000 -1.643 -1.643
## wpa_opnsdrs|t2 -1.161 0.053 -21.990 0.000 -1.161 -1.161
## wpa_opnsdrs|t3 -0.905 0.048 -18.970 0.000 -0.905 -0.905
## wpa_opnsdrs|t4 -0.622 0.044 -14.128 0.000 -0.622 -0.622
## wpa_opnsdrs|t5 -0.145 0.041 -3.527 0.000 -0.145 -0.145
## wpa_opnsdrs|t6 0.555 0.043 12.793 0.000 0.555 0.555
## wpa_easier|t1 -1.633 0.069 -23.817 0.000 -1.633 -1.633
## wpa_easier|t2 -1.145 0.052 -21.846 0.000 -1.145 -1.145
## wpa_easier|t3 -0.955 0.049 -19.662 0.000 -0.955 -0.955
## wpa_easier|t4 -0.681 0.045 -15.261 0.000 -0.681 -0.681
## wpa_easier|t5 -0.232 0.041 -5.614 0.000 -0.232 -0.232
## wpa_easier|t6 0.443 0.042 10.417 0.000 0.443 0.443
## sham_rcstmn|t1 -1.390 0.059 -23.486 0.000 -1.390 -1.390
## sham_rcstmn|t2 -0.930 0.048 -19.318 0.000 -0.930 -0.930
## sham_rcstmn|t3 -0.695 0.045 -15.511 0.000 -0.695 -0.695
## sham_rcstmn|t4 -0.425 0.042 -10.030 0.000 -0.425 -0.425
## sham_rcstmn|t5 0.080 0.041 1.960 0.050 0.080 0.080
## sham_rcstmn|t6 0.674 0.045 15.136 0.000 0.674 0.674
## shm_mns2bwht|1 -1.145 0.052 -21.846 0.000 -1.145 -1.145
## shm_mns2bwht|2 -0.722 0.045 -16.009 0.000 -0.722 -0.722
## shm_mns2bwht|3 -0.555 0.043 -12.793 0.000 -0.555 -0.555
## shm_mns2bwht|4 -0.257 0.041 -6.200 0.000 -0.257 -0.257
## shm_mns2bwht|5 0.224 0.041 5.419 0.000 0.224 0.224
## shm_mns2bwht|6 0.740 0.045 16.319 0.000 0.740 0.740
## shm_rcstndnc|1 -1.397 0.059 -23.514 0.000 -1.397 -1.397
## shm_rcstndnc|2 -1.047 0.050 -20.823 0.000 -1.047 -1.047
## shm_rcstndnc|3 -0.842 0.047 -18.024 0.000 -0.842 -0.842
## shm_rcstndnc|4 -0.542 0.043 -12.537 0.000 -0.542 -0.542
## shm_rcstndnc|5 -0.038 0.041 -0.915 0.360 -0.038 -0.038
## shm_rcstndnc|6 0.561 0.043 12.921 0.000 0.561 0.561
## guilt_racsm|t1 -0.913 0.048 -19.087 0.000 -0.913 -0.913
## guilt_racsm|t2 -0.376 0.042 -8.929 0.000 -0.376 -0.376
## guilt_racsm|t3 -0.170 0.041 -4.114 0.000 -0.170 -0.170
## guilt_racsm|t4 0.107 0.041 2.613 0.009 0.107 0.107
## guilt_racsm|t5 0.688 0.045 15.386 0.000 0.688 0.688
## guilt_racsm|t6 1.310 0.057 23.097 0.000 1.310 1.310
## guilt_nqlty|t1 -1.193 0.054 -22.270 0.000 -1.193 -1.193
## guilt_nqlty|t2 -0.747 0.045 -16.442 0.000 -0.747 -0.747
## guilt_nqlty|t3 -0.487 0.043 -11.383 0.000 -0.487 -0.487
## guilt_nqlty|t4 -0.224 0.041 -5.419 0.000 -0.224 -0.224
## guilt_nqlty|t5 0.313 0.042 7.502 0.000 0.313 0.313
## guilt_nqlty|t6 0.985 0.049 20.057 0.000 0.985 0.985
## gult_trtmnt|t1 -1.177 0.053 -22.132 0.000 -1.177 -1.177
## gult_trtmnt|t2 -0.750 0.045 -16.504 0.000 -0.750 -0.750
## gult_trtmnt|t3 -0.545 0.043 -12.601 0.000 -0.545 -0.545
## gult_trtmnt|t4 -0.271 0.042 -6.526 0.000 -0.271 -0.271
## gult_trtmnt|t5 0.260 0.041 6.266 0.000 0.260 0.260
## gult_trtmnt|t6 0.850 0.047 18.144 0.000 0.850 0.850
## guilt_behvr|t1 -1.057 0.050 -20.929 0.000 -1.057 -1.057
## guilt_behvr|t2 -0.654 0.044 -14.759 0.000 -0.654 -0.654
## guilt_behvr|t3 -0.437 0.042 -10.288 0.000 -0.437 -0.437
## guilt_behvr|t4 -0.208 0.041 -5.028 0.000 -0.208 -0.208
## guilt_behvr|t5 0.319 0.042 7.632 0.000 0.319 0.319
## guilt_behvr|t6 0.985 0.049 20.057 0.000 0.985 0.985
## img_shm_dsgr|1 -1.255 0.055 -22.748 0.000 -1.255 -1.255
## img_shm_dsgr|2 -0.743 0.045 -16.380 0.000 -0.743 -0.743
## img_shm_dsgr|3 -0.524 0.043 -12.153 0.000 -0.524 -0.524
## img_shm_dsgr|4 -0.110 0.041 -2.678 0.007 -0.110 -0.110
## img_shm_dsgr|5 0.475 0.043 11.126 0.000 0.475 0.475
## img_shm_dsgr|6 1.156 0.053 21.943 0.000 1.156 1.156
## img_shm_hwsn|1 -1.209 0.054 -22.405 0.000 -1.209 -1.209
## img_shm_hwsn|2 -0.719 0.045 -15.947 0.000 -0.719 -0.719
## img_shm_hwsn|3 -0.490 0.043 -11.447 0.000 -0.490 -0.490
## img_shm_hwsn|4 -0.097 0.041 -2.352 0.019 -0.097 -0.097
## img_shm_hwsn|5 0.545 0.043 12.601 0.000 0.545 0.545
## img_shm_hwsn|6 1.232 0.055 22.580 0.000 1.232 1.232
## img_shm_hmlt|1 -1.071 0.051 -21.087 0.000 -1.071 -1.071
## img_shm_hmlt|2 -0.505 0.043 -11.769 0.000 -0.505 -0.505
## img_shm_hmlt|3 -0.213 0.041 -5.158 0.000 -0.213 -0.213
## img_shm_hmlt|4 0.219 0.041 5.288 0.000 0.219 0.219
## img_shm_hmlt|5 0.790 0.046 17.178 0.000 0.790 0.790
## img_shm_hmlt|6 1.419 0.060 23.592 0.000 1.419 1.419
## rr_slavery|t1 -1.310 0.057 -23.097 0.000 -1.310 -1.310
## rr_slavery|t2 -0.869 0.047 -18.441 0.000 -0.869 -0.869
## rr_slavery|t3 -0.558 0.043 -12.857 0.000 -0.558 -0.558
## rr_slavery|t4 0.118 0.041 2.874 0.004 0.118 0.118
## rr_deserve|t1 -1.397 0.059 -23.514 0.000 -1.397 -1.397
## rr_deserve|t2 -0.873 0.047 -18.500 0.000 -0.873 -0.873
## rr_deserve|t3 -0.347 0.042 -8.281 0.000 -0.347 -0.347
## rr_deserve|t4 0.350 0.042 8.346 0.000 0.350 0.350
## disc_blacks|t1 -2.006 0.091 -22.100 0.000 -2.006 -2.006
## disc_blacks|t2 -1.336 0.057 -23.238 0.000 -1.336 -1.336
## disc_blacks|t3 -0.524 0.043 -12.153 0.000 -0.524 -0.524
## disc_blacks|t4 0.224 0.041 5.419 0.000 0.224 0.224
## ndsc_qlncms|t1 -1.837 0.079 -23.176 0.000 -1.837 -1.837
## ndsc_qlncms|t2 -1.356 0.058 -23.336 0.000 -1.356 -1.356
## ndsc_qlncms|t3 -0.926 0.048 -19.261 0.000 -0.926 -0.926
## ndsc_qlncms|t4 -0.416 0.042 -9.836 0.000 -0.416 -0.416
## ndsc_qlncms|t5 0.164 0.041 3.984 0.000 0.164 0.164
## ndsc_qlncms|t6 0.963 0.049 19.776 0.000 0.963 0.963
## rvshm_ntshmd|1 -1.419 0.060 -23.592 0.000 -1.419 -1.419
## rvshm_ntshmd|2 -0.850 0.047 -18.144 0.000 -0.850 -0.850
## rvshm_ntshmd|3 -0.539 0.043 -12.473 0.000 -0.539 -0.539
## rvshm_ntshmd|4 0.132 0.041 3.201 0.001 0.132 0.132
## rvshm_ntshmd|5 0.428 0.042 10.094 0.000 0.428 0.428
## rvshm_ntshmd|6 0.942 0.048 19.491 0.000 0.942 0.942
## revrr_favrs|t1 -1.120 0.052 -21.600 0.000 -1.120 -1.120
## revrr_favrs|t2 -0.552 0.043 -12.729 0.000 -0.552 -0.552
## revrr_favrs|t3 -0.170 0.041 -4.114 0.000 -0.170 -0.170
## revrr_favrs|t4 0.443 0.042 10.417 0.000 0.443 0.443
## rvrr_tryhrdr|1 -1.426 0.060 -23.616 0.000 -1.426 -1.426
## rvrr_tryhrdr|2 -0.823 0.046 -17.724 0.000 -0.823 -0.823
## rvrr_tryhrdr|3 -0.428 0.042 -10.094 0.000 -0.428 -0.428
## rvrr_tryhrdr|4 0.183 0.041 4.441 0.000 0.183 0.183
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .racineq_discrm 372.604 16.277 22.892 0.000 372.604 0.481
## .wpa_advantages 0.140 0.140 0.140
## .wpa_opensdoors 0.189 0.189 0.189
## .wpa_easier 0.186 0.186 0.186
## .shame_racistmn 0.275 0.275 0.275
## .shame_mns2bwht 0.197 0.197 0.197
## .sham_rcstndncs 0.269 0.269 0.269
## .guilt_racism 0.210 0.210 0.210
## .guilt_inequlty 0.195 0.195 0.195
## .guilt_treatmnt 0.161 0.161 0.161
## .guilt_behavior 0.174 0.174 0.174
## .img_shm_dsgrcd 0.434 0.434 0.434
## .image_shm_hwsn 0.326 0.326 0.326
## .imag_shm_hmltd 0.523 0.523 0.523
## .rr_slavery 0.364 0.364 0.364
## .rr_deserve 0.347 0.347 0.347
## .disc_blacks 0.366 0.366 0.366
## .nodisc_eqlncms 0.625 0.625 0.625
## .revsham_ntshmd 0.554 0.554 0.554
## .revrr_favors 0.343 0.343 0.343
## .revrr_tryhardr 0.373 0.373 0.373
## General 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## wpa_advantages 1.000 1.000 1.000
## wpa_opensdoors 1.000 1.000 1.000
## wpa_easier 1.000 1.000 1.000
## shame_racistmn 1.000 1.000 1.000
## shame_mns2bwht 1.000 1.000 1.000
## sham_rcstndncs 1.000 1.000 1.000
## guilt_racism 1.000 1.000 1.000
## guilt_inequlty 1.000 1.000 1.000
## guilt_treatmnt 1.000 1.000 1.000
## guilt_behavior 1.000 1.000 1.000
## img_shm_dsgrcd 1.000 1.000 1.000
## image_shm_hwsn 1.000 1.000 1.000
## imag_shm_hmltd 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
## revsham_ntshmd 1.000 1.000 1.000
## revrr_favors 1.000 1.000 1.000
## revrr_tryhardr 1.000 1.000 1.000resid(ZGRunOne, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## rcnq_d wp_dvn wp_pns wpa_sr shm_rcstm shm_m2 shm_rcstn
## racineq_discrim 0.000
## wpa_advantages 0.036 0.000
## wpa_opensdoors 0.037 0.083 0.000
## wpa_easier 0.044 0.078 0.083 0.000
## shame_racistmean 0.065 -0.048 -0.025 -0.004 0.000
## shame_means2bewhite -0.018 -0.126 -0.105 -0.099 0.079 0.000
## shame_racistendencies -0.010 -0.145 -0.122 -0.115 0.056 0.070 0.000
## guilt_racism -0.087 -0.235 -0.203 -0.192 -0.030 0.050 0.017
## guilt_inequality -0.038 -0.187 -0.168 -0.148 -0.034 -0.009 0.019
## guilt_treatment -0.096 -0.237 -0.222 -0.203 -0.063 -0.034 0.014
## guilt_behavior -0.087 -0.215 -0.207 -0.188 -0.052 0.002 0.015
## image_shame_disgraced -0.119 -0.273 -0.235 -0.229 -0.072 -0.035 0.016
## image_shame_howseen -0.125 -0.279 -0.240 -0.239 -0.060 -0.007 0.018
## image_shame_humiliated -0.154 -0.322 -0.274 -0.289 -0.126 -0.034 -0.040
## rr_slavery 0.103 0.015 -0.004 0.011 0.009 -0.061 -0.048
## rr_deserve 0.117 -0.026 -0.041 -0.008 0.020 -0.036 -0.024
## disc_blacks 0.110 0.010 0.035 0.039 0.063 -0.028 -0.013
## nodisc_equalincomes 0.178 0.006 0.012 0.032 0.042 -0.022 -0.019
## revshame_notashamed -0.038 -0.097 -0.077 -0.094 0.046 0.108 0.060
## revrr_favors 0.094 -0.032 -0.051 -0.049 -0.024 -0.093 -0.062
## revrr_tryharder 0.051 -0.042 -0.071 -0.065 -0.029 -0.090 -0.067
## glt_rc glt_nq glt_tr glt_bh img_shm_d img_shm_hw
## racineq_discrim
## wpa_advantages
## wpa_opensdoors
## wpa_easier
## shame_racistmean
## shame_means2bewhite
## shame_racistendencies
## guilt_racism 0.000
## guilt_inequality 0.051 0.000
## guilt_treatment 0.040 0.071 0.000
## guilt_behavior 0.064 0.042 0.060 0.000
## image_shame_disgraced -0.015 -0.019 -0.036 -0.013 0.000
## image_shame_howseen 0.007 -0.021 -0.013 0.000 0.191 0.000
## image_shame_humiliated 0.049 -0.015 -0.010 0.011 0.221 0.225
## rr_slavery -0.147 -0.116 -0.151 -0.158 -0.157 -0.221
## rr_deserve -0.110 -0.083 -0.129 -0.113 -0.136 -0.167
## disc_blacks -0.115 -0.089 -0.119 -0.103 -0.095 -0.120
## nodisc_equalincomes -0.097 -0.055 -0.099 -0.087 -0.037 -0.079
## revshame_notashamed 0.036 -0.037 -0.027 0.009 -0.062 -0.027
## revrr_favors -0.180 -0.145 -0.156 -0.167 -0.203 -0.238
## revrr_tryharder -0.182 -0.145 -0.163 -0.181 -0.208 -0.240
## img_shm_hm rr_slv rr_dsr dsc_bl ndsc_q rvshm_ rvrr_f
## racineq_discrim
## wpa_advantages
## wpa_opensdoors
## wpa_easier
## shame_racistmean
## shame_means2bewhite
## shame_racistendencies
## guilt_racism
## guilt_inequality
## guilt_treatment
## guilt_behavior
## image_shame_disgraced
## image_shame_howseen
## image_shame_humiliated 0.000
## rr_slavery -0.239 0.000
## rr_deserve -0.218 0.137 0.000
## disc_blacks -0.170 0.043 0.097 0.000
## nodisc_equalincomes -0.127 0.097 0.107 0.079 0.000
## revshame_notashamed -0.052 -0.035 -0.027 0.007 -0.047 0.000
## revrr_favors -0.320 0.116 0.115 0.050 0.037 0.030 0.000
## revrr_tryharder -0.298 0.127 0.097 0.056 0.060 0.030 0.216
## rvrr_t
## racineq_discrim
## wpa_advantages
## wpa_opensdoors
## wpa_easier
## shame_racistmean
## shame_means2bewhite
## shame_racistendencies
## guilt_racism
## guilt_inequality
## guilt_treatment
## guilt_behavior
## image_shame_disgraced
## image_shame_howseen
## image_shame_humiliated
## rr_slavery
## rr_deserve
## disc_blacks
## nodisc_equalincomes
## revshame_notashamed
## revrr_favors
## revrr_tryharder 0.000
##
## $mean
## racineq_discrim wpa_advantages wpa_opensdoors
## 0 0 0
## wpa_easier shame_racistmean shame_means2bewhite
## 0 0 0
## shame_racistendencies guilt_racism guilt_inequality
## 0 0 0
## guilt_treatment guilt_behavior image_shame_disgraced
## 0 0 0
## image_shame_howseen image_shame_humiliated rr_slavery
## 0 0 0
## rr_deserve disc_blacks nodisc_equalincomes
## 0 0 0
## revshame_notashamed revrr_favors revrr_tryharder
## 0 0 0
##
## $th
## wpa_advantages|t1 wpa_advantages|t2 wpa_advantages|t3
## 0 0 0
## wpa_advantages|t4 wpa_advantages|t5 wpa_advantages|t6
## 0 0 0
## wpa_opensdoors|t1 wpa_opensdoors|t2 wpa_opensdoors|t3
## 0 0 0
## wpa_opensdoors|t4 wpa_opensdoors|t5 wpa_opensdoors|t6
## 0 0 0
## wpa_easier|t1 wpa_easier|t2 wpa_easier|t3
## 0 0 0
## wpa_easier|t4 wpa_easier|t5 wpa_easier|t6
## 0 0 0
## shame_racistmean|t1 shame_racistmean|t2 shame_racistmean|t3
## 0 0 0
## shame_racistmean|t4 shame_racistmean|t5 shame_racistmean|t6
## 0 0 0
## shame_means2bewhite|t1 shame_means2bewhite|t2 shame_means2bewhite|t3
## 0 0 0
## shame_means2bewhite|t4 shame_means2bewhite|t5 shame_means2bewhite|t6
## 0 0 0
## shame_racistendencies|t1 shame_racistendencies|t2 shame_racistendencies|t3
## 0 0 0
## shame_racistendencies|t4 shame_racistendencies|t5 shame_racistendencies|t6
## 0 0 0
## guilt_racism|t1 guilt_racism|t2 guilt_racism|t3
## 0 0 0
## guilt_racism|t4 guilt_racism|t5 guilt_racism|t6
## 0 0 0
## guilt_inequality|t1 guilt_inequality|t2 guilt_inequality|t3
## 0 0 0
## guilt_inequality|t4 guilt_inequality|t5 guilt_inequality|t6
## 0 0 0
## guilt_treatment|t1 guilt_treatment|t2 guilt_treatment|t3
## 0 0 0
## guilt_treatment|t4 guilt_treatment|t5 guilt_treatment|t6
## 0 0 0
## guilt_behavior|t1 guilt_behavior|t2 guilt_behavior|t3
## 0 0 0
## guilt_behavior|t4 guilt_behavior|t5 guilt_behavior|t6
## 0 0 0
## image_shame_disgraced|t1 image_shame_disgraced|t2 image_shame_disgraced|t3
## 0 0 0
## image_shame_disgraced|t4 image_shame_disgraced|t5 image_shame_disgraced|t6
## 0 0 0
## image_shame_howseen|t1 image_shame_howseen|t2 image_shame_howseen|t3
## 0 0 0
## image_shame_howseen|t4 image_shame_howseen|t5 image_shame_howseen|t6
## 0 0 0
## image_shame_humiliated|t1 image_shame_humiliated|t2 image_shame_humiliated|t3
## 0 0 0
## image_shame_humiliated|t4 image_shame_humiliated|t5 image_shame_humiliated|t6
## 0 0 0
## rr_slavery|t1 rr_slavery|t2 rr_slavery|t3
## 0 0 0
## rr_slavery|t4 rr_deserve|t1 rr_deserve|t2
## 0 0 0
## rr_deserve|t3 rr_deserve|t4 disc_blacks|t1
## 0 0 0
## disc_blacks|t2 disc_blacks|t3 disc_blacks|t4
## 0 0 0
## nodisc_equalincomes|t1 nodisc_equalincomes|t2 nodisc_equalincomes|t3
## 0 0 0
## nodisc_equalincomes|t4 nodisc_equalincomes|t5 nodisc_equalincomes|t6
## 0 0 0
## revshame_notashamed|t1 revshame_notashamed|t2 revshame_notashamed|t3
## 0 0 0
## revshame_notashamed|t4 revshame_notashamed|t5 revshame_notashamed|t6
## 0 0 0
## revrr_favors|t1 revrr_favors|t2 revrr_favors|t3
## 0 0 0
## revrr_favors|t4 revrr_tryharder|t1 revrr_tryharder|t2
## 0 0 0
## revrr_tryharder|t3 revrr_tryharder|t4
## 0 0Local independence is violated (critical r = \(\pm0.064\) at p = 0.05 and r = \(\pm0.163\) at the sample-sized adjusted p-value of 5.707e-07).
ZGModCGF <- '
RR =~ revrr_favors + revrr_tryharder
DISC =~ rr_slavery + rr_deserve + racineq_discrim + disc_blacks + nodisc_equalincomes
WP =~ wpa_advantages + wpa_opensdoors + wpa_easier
MORAL =~ revshame_notashamed + shame_racistmean + shame_means2bewhite + shame_racistendencies
GUILT =~ guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior
IMAGE =~ image_shame_disgraced + image_shame_howseen + image_shame_humiliated'
ZGRunCGF <- cfa(ZGModCGF, data = data, std.lv = T, ordered = c("wpa_advantages", "wpa_opensdoors", "wpa_easier", "shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))
summary(ZGRunCGF, stand = T, fit = T)## lavaan 0.6-7 ended normally after 86 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 148
##
## Used Total
## Number of observations 936 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 520.462 1327.081
## Degrees of freedom 174 174
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.416
## Shift parameter 76.779
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 388166.805 71255.951
## Degrees of freedom 210 210
## P-value 0.000 0.000
## Scaling correction factor 5.461
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.999 0.984
## Tucker-Lewis Index (TLI) 0.999 0.980
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.046 0.084
## 90 Percent confidence interval - lower 0.042 0.080
## 90 Percent confidence interval - upper 0.051 0.088
## P-value RMSEA <= 0.05 0.916 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.031 0.031
##
## 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 0.009 106.097 0.000 0.941 0.941
## revrr_tryhardr 0.912 0.010 95.864 0.000 0.912 0.912
## DISC =~
## rr_slavery 0.856 0.013 67.595 0.000 0.856 0.856
## rr_deserve 0.870 0.011 77.404 0.000 0.870 0.870
## racineq_discrm 22.334 1.059 21.082 0.000 22.334 0.803
## disc_blacks 0.866 0.013 68.835 0.000 0.866 0.866
## nodisc_eqlncms 0.674 0.019 35.455 0.000 0.674 0.674
## WP =~
## wpa_advantages 0.964 0.005 211.700 0.000 0.964 0.964
## wpa_opensdoors 0.945 0.005 180.772 0.000 0.945 0.945
## wpa_easier 0.952 0.005 181.181 0.000 0.952 0.952
## MORAL =~
## revsham_ntshmd 0.703 0.017 42.229 0.000 0.703 0.703
## shame_racistmn 0.897 0.008 109.316 0.000 0.897 0.897
## shame_mns2bwht 0.937 0.006 167.233 0.000 0.937 0.937
## sham_rcstndncs 0.896 0.008 108.358 0.000 0.896 0.896
## GUILT =~
## guilt_racism 0.926 0.006 165.211 0.000 0.926 0.926
## guilt_inequlty 0.932 0.005 181.765 0.000 0.932 0.932
## guilt_treatmnt 0.941 0.005 203.586 0.000 0.941 0.941
## guilt_behavior 0.939 0.005 201.761 0.000 0.939 0.939
## IMAGE =~
## img_shm_dsgrcd 0.871 0.010 85.441 0.000 0.871 0.871
## image_shm_hwsn 0.966 0.007 131.250 0.000 0.966 0.966
## imag_shm_hmltd 0.805 0.013 63.080 0.000 0.805 0.805
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RR ~~
## DISC 0.918 0.009 101.192 0.000 0.918 0.918
## WP 0.769 0.015 49.653 0.000 0.769 0.769
## MORAL 0.770 0.016 47.217 0.000 0.770 0.770
## GUILT 0.646 0.021 31.033 0.000 0.646 0.646
## IMAGE 0.443 0.028 15.615 0.000 0.443 0.443
## DISC ~~
## WP 0.891 0.009 97.750 0.000 0.891 0.891
## MORAL 0.868 0.011 82.480 0.000 0.868 0.868
## GUILT 0.750 0.015 49.033 0.000 0.750 0.750
## IMAGE 0.594 0.023 25.503 0.000 0.594 0.594
## WP ~~
## MORAL 0.813 0.013 63.291 0.000 0.813 0.813
## GUILT 0.699 0.017 39.962 0.000 0.699 0.699
## IMAGE 0.511 0.026 19.849 0.000 0.511 0.511
## MORAL ~~
## GUILT 0.920 0.007 140.271 0.000 0.920 0.920
## IMAGE 0.779 0.014 55.407 0.000 0.779 0.779
## GUILT ~~
## IMAGE 0.819 0.012 71.012 0.000 0.819 0.819
##
## 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 65.034 1.101 59.079 0.000 65.034 2.338
## .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
## .revsham_ntshmd 0.000 0.000 0.000
## .shame_racistmn 0.000 0.000 0.000
## .shame_mns2bwht 0.000 0.000 0.000
## .sham_rcstndncs 0.000 0.000 0.000
## .guilt_racism 0.000 0.000 0.000
## .guilt_inequlty 0.000 0.000 0.000
## .guilt_treatmnt 0.000 0.000 0.000
## .guilt_behavior 0.000 0.000 0.000
## .img_shm_dsgrcd 0.000 0.000 0.000
## .image_shm_hwsn 0.000 0.000 0.000
## .imag_shm_hmltd 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
## MORAL 0.000 0.000 0.000
## GUILT 0.000 0.000 0.000
## IMAGE 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favrs|t1 -1.120 0.052 -21.600 0.000 -1.120 -1.120
## revrr_favrs|t2 -0.552 0.043 -12.729 0.000 -0.552 -0.552
## revrr_favrs|t3 -0.170 0.041 -4.114 0.000 -0.170 -0.170
## revrr_favrs|t4 0.443 0.042 10.417 0.000 0.443 0.443
## rvrr_tryhrdr|1 -1.426 0.060 -23.616 0.000 -1.426 -1.426
## rvrr_tryhrdr|2 -0.823 0.046 -17.724 0.000 -0.823 -0.823
## rvrr_tryhrdr|3 -0.428 0.042 -10.094 0.000 -0.428 -0.428
## rvrr_tryhrdr|4 0.183 0.041 4.441 0.000 0.183 0.183
## rr_slavery|t1 -1.310 0.057 -23.097 0.000 -1.310 -1.310
## rr_slavery|t2 -0.869 0.047 -18.441 0.000 -0.869 -0.869
## rr_slavery|t3 -0.558 0.043 -12.857 0.000 -0.558 -0.558
## rr_slavery|t4 0.118 0.041 2.874 0.004 0.118 0.118
## rr_deserve|t1 -1.397 0.059 -23.514 0.000 -1.397 -1.397
## rr_deserve|t2 -0.873 0.047 -18.500 0.000 -0.873 -0.873
## rr_deserve|t3 -0.347 0.042 -8.281 0.000 -0.347 -0.347
## rr_deserve|t4 0.350 0.042 8.346 0.000 0.350 0.350
## disc_blacks|t1 -2.006 0.091 -22.100 0.000 -2.006 -2.006
## disc_blacks|t2 -1.336 0.057 -23.238 0.000 -1.336 -1.336
## disc_blacks|t3 -0.524 0.043 -12.153 0.000 -0.524 -0.524
## disc_blacks|t4 0.224 0.041 5.419 0.000 0.224 0.224
## ndsc_qlncms|t1 -1.837 0.079 -23.176 0.000 -1.837 -1.837
## ndsc_qlncms|t2 -1.356 0.058 -23.336 0.000 -1.356 -1.356
## ndsc_qlncms|t3 -0.926 0.048 -19.261 0.000 -0.926 -0.926
## ndsc_qlncms|t4 -0.416 0.042 -9.836 0.000 -0.416 -0.416
## ndsc_qlncms|t5 0.164 0.041 3.984 0.000 0.164 0.164
## ndsc_qlncms|t6 0.963 0.049 19.776 0.000 0.963 0.963
## wpa_advntgs|t1 -1.708 0.072 -23.671 0.000 -1.708 -1.708
## wpa_advntgs|t2 -1.244 0.055 -22.665 0.000 -1.244 -1.244
## wpa_advntgs|t3 -1.025 0.050 -20.553 0.000 -1.025 -1.025
## wpa_advntgs|t4 -0.794 0.046 -17.239 0.000 -0.794 -0.794
## wpa_advntgs|t5 -0.313 0.042 -7.502 0.000 -0.313 -0.313
## wpa_advntgs|t6 0.355 0.042 8.476 0.000 0.355 0.355
## wpa_opnsdrs|t1 -1.643 0.069 -23.804 0.000 -1.643 -1.643
## wpa_opnsdrs|t2 -1.161 0.053 -21.990 0.000 -1.161 -1.161
## wpa_opnsdrs|t3 -0.905 0.048 -18.970 0.000 -0.905 -0.905
## wpa_opnsdrs|t4 -0.622 0.044 -14.128 0.000 -0.622 -0.622
## wpa_opnsdrs|t5 -0.145 0.041 -3.527 0.000 -0.145 -0.145
## wpa_opnsdrs|t6 0.555 0.043 12.793 0.000 0.555 0.555
## wpa_easier|t1 -1.633 0.069 -23.817 0.000 -1.633 -1.633
## wpa_easier|t2 -1.145 0.052 -21.846 0.000 -1.145 -1.145
## wpa_easier|t3 -0.955 0.049 -19.662 0.000 -0.955 -0.955
## wpa_easier|t4 -0.681 0.045 -15.261 0.000 -0.681 -0.681
## wpa_easier|t5 -0.232 0.041 -5.614 0.000 -0.232 -0.232
## wpa_easier|t6 0.443 0.042 10.417 0.000 0.443 0.443
## rvshm_ntshmd|1 -1.419 0.060 -23.592 0.000 -1.419 -1.419
## rvshm_ntshmd|2 -0.850 0.047 -18.144 0.000 -0.850 -0.850
## rvshm_ntshmd|3 -0.539 0.043 -12.473 0.000 -0.539 -0.539
## rvshm_ntshmd|4 0.132 0.041 3.201 0.001 0.132 0.132
## rvshm_ntshmd|5 0.428 0.042 10.094 0.000 0.428 0.428
## rvshm_ntshmd|6 0.942 0.048 19.491 0.000 0.942 0.942
## sham_rcstmn|t1 -1.390 0.059 -23.486 0.000 -1.390 -1.390
## sham_rcstmn|t2 -0.930 0.048 -19.318 0.000 -0.930 -0.930
## sham_rcstmn|t3 -0.695 0.045 -15.511 0.000 -0.695 -0.695
## sham_rcstmn|t4 -0.425 0.042 -10.030 0.000 -0.425 -0.425
## sham_rcstmn|t5 0.080 0.041 1.960 0.050 0.080 0.080
## sham_rcstmn|t6 0.674 0.045 15.136 0.000 0.674 0.674
## shm_mns2bwht|1 -1.145 0.052 -21.846 0.000 -1.145 -1.145
## shm_mns2bwht|2 -0.722 0.045 -16.009 0.000 -0.722 -0.722
## shm_mns2bwht|3 -0.555 0.043 -12.793 0.000 -0.555 -0.555
## shm_mns2bwht|4 -0.257 0.041 -6.200 0.000 -0.257 -0.257
## shm_mns2bwht|5 0.224 0.041 5.419 0.000 0.224 0.224
## shm_mns2bwht|6 0.740 0.045 16.319 0.000 0.740 0.740
## shm_rcstndnc|1 -1.397 0.059 -23.514 0.000 -1.397 -1.397
## shm_rcstndnc|2 -1.047 0.050 -20.823 0.000 -1.047 -1.047
## shm_rcstndnc|3 -0.842 0.047 -18.024 0.000 -0.842 -0.842
## shm_rcstndnc|4 -0.542 0.043 -12.537 0.000 -0.542 -0.542
## shm_rcstndnc|5 -0.038 0.041 -0.915 0.360 -0.038 -0.038
## shm_rcstndnc|6 0.561 0.043 12.921 0.000 0.561 0.561
## guilt_racsm|t1 -0.913 0.048 -19.087 0.000 -0.913 -0.913
## guilt_racsm|t2 -0.376 0.042 -8.929 0.000 -0.376 -0.376
## guilt_racsm|t3 -0.170 0.041 -4.114 0.000 -0.170 -0.170
## guilt_racsm|t4 0.107 0.041 2.613 0.009 0.107 0.107
## guilt_racsm|t5 0.688 0.045 15.386 0.000 0.688 0.688
## guilt_racsm|t6 1.310 0.057 23.097 0.000 1.310 1.310
## guilt_nqlty|t1 -1.193 0.054 -22.270 0.000 -1.193 -1.193
## guilt_nqlty|t2 -0.747 0.045 -16.442 0.000 -0.747 -0.747
## guilt_nqlty|t3 -0.487 0.043 -11.383 0.000 -0.487 -0.487
## guilt_nqlty|t4 -0.224 0.041 -5.419 0.000 -0.224 -0.224
## guilt_nqlty|t5 0.313 0.042 7.502 0.000 0.313 0.313
## guilt_nqlty|t6 0.985 0.049 20.057 0.000 0.985 0.985
## gult_trtmnt|t1 -1.177 0.053 -22.132 0.000 -1.177 -1.177
## gult_trtmnt|t2 -0.750 0.045 -16.504 0.000 -0.750 -0.750
## gult_trtmnt|t3 -0.545 0.043 -12.601 0.000 -0.545 -0.545
## gult_trtmnt|t4 -0.271 0.042 -6.526 0.000 -0.271 -0.271
## gult_trtmnt|t5 0.260 0.041 6.266 0.000 0.260 0.260
## gult_trtmnt|t6 0.850 0.047 18.144 0.000 0.850 0.850
## guilt_behvr|t1 -1.057 0.050 -20.929 0.000 -1.057 -1.057
## guilt_behvr|t2 -0.654 0.044 -14.759 0.000 -0.654 -0.654
## guilt_behvr|t3 -0.437 0.042 -10.288 0.000 -0.437 -0.437
## guilt_behvr|t4 -0.208 0.041 -5.028 0.000 -0.208 -0.208
## guilt_behvr|t5 0.319 0.042 7.632 0.000 0.319 0.319
## guilt_behvr|t6 0.985 0.049 20.057 0.000 0.985 0.985
## img_shm_dsgr|1 -1.255 0.055 -22.748 0.000 -1.255 -1.255
## img_shm_dsgr|2 -0.743 0.045 -16.380 0.000 -0.743 -0.743
## img_shm_dsgr|3 -0.524 0.043 -12.153 0.000 -0.524 -0.524
## img_shm_dsgr|4 -0.110 0.041 -2.678 0.007 -0.110 -0.110
## img_shm_dsgr|5 0.475 0.043 11.126 0.000 0.475 0.475
## img_shm_dsgr|6 1.156 0.053 21.943 0.000 1.156 1.156
## img_shm_hwsn|1 -1.209 0.054 -22.405 0.000 -1.209 -1.209
## img_shm_hwsn|2 -0.719 0.045 -15.947 0.000 -0.719 -0.719
## img_shm_hwsn|3 -0.490 0.043 -11.447 0.000 -0.490 -0.490
## img_shm_hwsn|4 -0.097 0.041 -2.352 0.019 -0.097 -0.097
## img_shm_hwsn|5 0.545 0.043 12.601 0.000 0.545 0.545
## img_shm_hwsn|6 1.232 0.055 22.580 0.000 1.232 1.232
## img_shm_hmlt|1 -1.071 0.051 -21.087 0.000 -1.071 -1.071
## img_shm_hmlt|2 -0.505 0.043 -11.769 0.000 -0.505 -0.505
## img_shm_hmlt|3 -0.213 0.041 -5.158 0.000 -0.213 -0.213
## img_shm_hmlt|4 0.219 0.041 5.288 0.000 0.219 0.219
## img_shm_hmlt|5 0.790 0.046 17.178 0.000 0.790 0.790
## img_shm_hmlt|6 1.419 0.060 23.592 0.000 1.419 1.419
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.114 0.114 0.114
## .revrr_tryhardr 0.169 0.169 0.169
## .rr_slavery 0.268 0.268 0.268
## .rr_deserve 0.243 0.243 0.243
## .racineq_discrm 275.189 13.902 19.794 0.000 275.189 0.356
## .disc_blacks 0.249 0.249 0.249
## .nodisc_eqlncms 0.545 0.545 0.545
## .wpa_advantages 0.070 0.070 0.070
## .wpa_opensdoors 0.106 0.106 0.106
## .wpa_easier 0.093 0.093 0.093
## .revsham_ntshmd 0.505 0.505 0.505
## .shame_racistmn 0.195 0.195 0.195
## .shame_mns2bwht 0.122 0.122 0.122
## .sham_rcstndncs 0.197 0.197 0.197
## .guilt_racism 0.142 0.142 0.142
## .guilt_inequlty 0.131 0.131 0.131
## .guilt_treatmnt 0.115 0.115 0.115
## .guilt_behavior 0.118 0.118 0.118
## .img_shm_dsgrcd 0.241 0.241 0.241
## .image_shm_hwsn 0.068 0.068 0.068
## .imag_shm_hmltd 0.352 0.352 0.352
## RR 1.000 1.000 1.000
## DISC 1.000 1.000 1.000
## WP 1.000 1.000 1.000
## MORAL 1.000 1.000 1.000
## GUILT 1.000 1.000 1.000
## IMAGE 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
## revsham_ntshmd 1.000 1.000 1.000
## shame_racistmn 1.000 1.000 1.000
## shame_mns2bwht 1.000 1.000 1.000
## sham_rcstndncs 1.000 1.000 1.000
## guilt_racism 1.000 1.000 1.000
## guilt_inequlty 1.000 1.000 1.000
## guilt_treatmnt 1.000 1.000 1.000
## guilt_behavior 1.000 1.000 1.000
## img_shm_dsgrcd 1.000 1.000 1.000
## image_shm_hwsn 1.000 1.000 1.000
## imag_shm_hmltd 1.000 1.000 1.000resid(ZGRunCGF, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## rvrr_f rvrr_t rr_slv rr_dsr rcnq_d dsc_bl ndsc_q wp_dvn
## revrr_favors 0.000
## revrr_tryharder 0.000 0.000
## rr_slavery 0.023 0.043 0.000
## rr_deserve 0.018 0.009 0.036 0.000
## racineq_discrim -0.016 -0.051 -0.010 0.000 0.000
## disc_blacks -0.053 -0.039 -0.064 -0.014 -0.013 0.000
## nodisc_equalincomes -0.049 -0.019 0.008 0.015 0.078 -0.017 0.000
## wpa_advantages 0.022 0.017 0.020 -0.024 0.015 0.004 -0.005 0.000
## wpa_opensdoors -0.005 -0.020 -0.006 -0.046 0.009 0.023 -0.004 0.007
## wpa_easier -0.007 -0.017 0.005 -0.017 0.013 0.023 0.013 -0.004
## revshame_notashamed 0.062 0.066 -0.025 -0.019 -0.047 0.010 -0.050 -0.029
## shame_racistmean 0.016 0.016 0.021 0.031 0.053 0.067 0.039 0.039
## shame_means2bewhite -0.045 -0.037 -0.043 -0.020 -0.026 -0.019 -0.021 -0.029
## shame_racistendencies -0.019 -0.019 -0.032 -0.010 -0.019 -0.006 -0.020 -0.054
## guilt_racism -0.023 -0.024 -0.034 0.003 -0.005 -0.009 -0.021 -0.035
## guilt_inequality 0.015 0.016 0.001 0.033 0.047 0.019 0.023 0.017
## guilt_treatment 0.014 0.009 -0.025 -0.003 -0.003 -0.002 -0.014 -0.021
## guilt_behavior -0.001 -0.014 -0.036 0.008 0.001 0.010 -0.005 -0.005
## image_shame_disgraced 0.044 0.036 0.000 0.022 0.007 0.055 0.076 -0.004
## image_shame_howseen 0.025 0.020 -0.057 -0.003 0.006 0.037 0.038 0.007
## image_shame_humiliated -0.096 -0.076 -0.098 -0.075 -0.041 -0.034 -0.026 -0.078
## wp_pns wpa_sr rvshm_ shm_rcstm shm_m2 shm_rcstn glt_rc
## revrr_favors
## revrr_tryharder
## rr_slavery
## rr_deserve
## racineq_discrim
## disc_blacks
## nodisc_equalincomes
## wpa_advantages
## wpa_opensdoors 0.000
## wpa_easier -0.005 0.000
## revshame_notashamed -0.016 -0.035 0.000
## shame_racistmean 0.052 0.070 -0.016 0.000
## shame_means2bewhite -0.018 -0.016 0.047 0.001 0.000
## shame_racistendencies -0.041 -0.037 0.001 -0.020 -0.004 0.000
## guilt_racism -0.015 -0.007 0.031 -0.037 0.049 0.014 0.000
## guilt_inequality 0.024 0.040 -0.040 -0.039 -0.009 0.018 -0.015
## guilt_treatment -0.019 -0.003 -0.024 -0.059 -0.023 0.022 -0.017
## guilt_behavior -0.009 0.007 0.009 -0.053 0.008 0.018 0.002
## image_shame_disgraced 0.022 0.026 -0.037 -0.040 0.003 0.051 -0.007
## image_shame_howseen 0.033 0.032 -0.008 -0.036 0.024 0.046 0.004
## image_shame_humiliated -0.041 -0.057 -0.032 -0.100 -0.003 -0.011 0.052
## glt_nq glt_tr glt_bh img_shm_d img_shm_hw img_shm_hm
## revrr_favors
## revrr_tryharder
## rr_slavery
## rr_deserve
## racineq_discrim
## disc_blacks
## nodisc_equalincomes
## wpa_advantages
## wpa_opensdoors
## wpa_easier
## revshame_notashamed
## shame_racistmean
## shame_means2bewhite
## shame_racistendencies
## guilt_racism
## guilt_inequality 0.000
## guilt_treatment 0.016 0.000
## guilt_behavior -0.018 0.010 0.000
## image_shame_disgraced -0.009 -0.018 0.001 0.000
## image_shame_howseen -0.022 -0.005 0.004 -0.032 0.000
## image_shame_humiliated -0.010 0.003 0.020 0.039 0.015 0.000
##
## $mean
## revrr_favors revrr_tryharder rr_slavery
## 0 0 0
## rr_deserve racineq_discrim disc_blacks
## 0 0 0
## nodisc_equalincomes wpa_advantages wpa_opensdoors
## 0 0 0
## wpa_easier revshame_notashamed shame_racistmean
## 0 0 0
## shame_means2bewhite shame_racistendencies guilt_racism
## 0 0 0
## guilt_inequality guilt_treatment guilt_behavior
## 0 0 0
## image_shame_disgraced image_shame_howseen image_shame_humiliated
## 0 0 0
##
## $th
## revrr_favors|t1 revrr_favors|t2 revrr_favors|t3
## 0 0 0
## revrr_favors|t4 revrr_tryharder|t1 revrr_tryharder|t2
## 0 0 0
## revrr_tryharder|t3 revrr_tryharder|t4 rr_slavery|t1
## 0 0 0
## rr_slavery|t2 rr_slavery|t3 rr_slavery|t4
## 0 0 0
## rr_deserve|t1 rr_deserve|t2 rr_deserve|t3
## 0 0 0
## rr_deserve|t4 disc_blacks|t1 disc_blacks|t2
## 0 0 0
## disc_blacks|t3 disc_blacks|t4 nodisc_equalincomes|t1
## 0 0 0
## nodisc_equalincomes|t2 nodisc_equalincomes|t3 nodisc_equalincomes|t4
## 0 0 0
## nodisc_equalincomes|t5 nodisc_equalincomes|t6 wpa_advantages|t1
## 0 0 0
## wpa_advantages|t2 wpa_advantages|t3 wpa_advantages|t4
## 0 0 0
## wpa_advantages|t5 wpa_advantages|t6 wpa_opensdoors|t1
## 0 0 0
## wpa_opensdoors|t2 wpa_opensdoors|t3 wpa_opensdoors|t4
## 0 0 0
## wpa_opensdoors|t5 wpa_opensdoors|t6 wpa_easier|t1
## 0 0 0
## wpa_easier|t2 wpa_easier|t3 wpa_easier|t4
## 0 0 0
## wpa_easier|t5 wpa_easier|t6 revshame_notashamed|t1
## 0 0 0
## revshame_notashamed|t2 revshame_notashamed|t3 revshame_notashamed|t4
## 0 0 0
## revshame_notashamed|t5 revshame_notashamed|t6 shame_racistmean|t1
## 0 0 0
## shame_racistmean|t2 shame_racistmean|t3 shame_racistmean|t4
## 0 0 0
## shame_racistmean|t5 shame_racistmean|t6 shame_means2bewhite|t1
## 0 0 0
## shame_means2bewhite|t2 shame_means2bewhite|t3 shame_means2bewhite|t4
## 0 0 0
## shame_means2bewhite|t5 shame_means2bewhite|t6 shame_racistendencies|t1
## 0 0 0
## shame_racistendencies|t2 shame_racistendencies|t3 shame_racistendencies|t4
## 0 0 0
## shame_racistendencies|t5 shame_racistendencies|t6 guilt_racism|t1
## 0 0 0
## guilt_racism|t2 guilt_racism|t3 guilt_racism|t4
## 0 0 0
## guilt_racism|t5 guilt_racism|t6 guilt_inequality|t1
## 0 0 0
## guilt_inequality|t2 guilt_inequality|t3 guilt_inequality|t4
## 0 0 0
## guilt_inequality|t5 guilt_inequality|t6 guilt_treatment|t1
## 0 0 0
## guilt_treatment|t2 guilt_treatment|t3 guilt_treatment|t4
## 0 0 0
## guilt_treatment|t5 guilt_treatment|t6 guilt_behavior|t1
## 0 0 0
## guilt_behavior|t2 guilt_behavior|t3 guilt_behavior|t4
## 0 0 0
## guilt_behavior|t5 guilt_behavior|t6 image_shame_disgraced|t1
## 0 0 0
## image_shame_disgraced|t2 image_shame_disgraced|t3 image_shame_disgraced|t4
## 0 0 0
## image_shame_disgraced|t5 image_shame_disgraced|t6 image_shame_howseen|t1
## 0 0 0
## image_shame_howseen|t2 image_shame_howseen|t3 image_shame_howseen|t4
## 0 0 0
## image_shame_howseen|t5 image_shame_howseen|t6 image_shame_humiliated|t1
## 0 0 0
## image_shame_humiliated|t2 image_shame_humiliated|t3 image_shame_humiliated|t4
## 0 0 0
## image_shame_humiliated|t5 image_shame_humiliated|t6
## 0 0lavInspect(ZGRunCGF, "cor.lv")## RR DISC WP MORAL GUILT IMAGE
## RR 1.000
## DISC 0.918 1.000
## WP 0.769 0.891 1.000
## MORAL 0.770 0.868 0.813 1.000
## GUILT 0.646 0.750 0.699 0.920 1.000
## IMAGE 0.443 0.594 0.511 0.779 0.819 1.000Local independence was less violated in the multiple-factor model.
ZGModHOF <- '
RR =~ revrr_favors + revrr_tryharder
DISC =~ rr_slavery + rr_deserve + racineq_discrim + disc_blacks + nodisc_equalincomes
WP =~ wpa_advantages + wpa_opensdoors + wpa_easier
MORAL =~ revshame_notashamed + shame_racistmean + shame_means2bewhite + shame_racistendencies
GUILT =~ guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior
IMAGE =~ image_shame_disgraced + image_shame_howseen + image_shame_humiliated
General =~ RR + DISC + WP + MORAL + GUILT + IMAGE'
ZGRunHOF <- cfa(ZGModHOF, data = data, std.lv = T, ordered = c("wpa_advantages", "wpa_opensdoors", "wpa_easier", "shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))
summary(ZGRunHOF, stand = T, fit = T)## lavaan 0.6-7 ended normally after 165 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 139
##
## Used Total
## Number of observations 936 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 2696.693 3815.334
## Degrees of freedom 183 183
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.728
## Shift parameter 108.641
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 388166.805 71255.951
## Degrees of freedom 210 210
## P-value 0.000 0.000
## Scaling correction factor 5.461
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.994 0.949
## Tucker-Lewis Index (TLI) 0.993 0.941
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.121 0.146
## 90 Percent confidence interval - lower 0.117 0.142
## 90 Percent confidence interval - upper 0.125 0.150
## 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 0.075 0.075
##
## 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 0.512 0.019 27.256 0.000 0.942 0.942
## revrr_tryhardr 0.495 0.017 29.300 0.000 0.911 0.911
## DISC =~
## rr_slavery 0.301 0.016 19.207 0.000 0.865 0.865
## rr_deserve 0.304 0.015 19.716 0.000 0.873 0.873
## racineq_discrm 7.569 0.486 15.563 0.000 21.758 0.782
## disc_blacks 0.301 0.016 18.781 0.000 0.865 0.865
## nodisc_eqlncms 0.231 0.012 19.001 0.000 0.665 0.665
## WP =~
## wpa_advantages 0.509 0.017 30.089 0.000 0.966 0.966
## wpa_opensdoors 0.497 0.016 30.686 0.000 0.944 0.944
## wpa_easier 0.501 0.017 30.246 0.000 0.952 0.952
## MORAL =~
## revsham_ntshmd 0.149 0.012 12.593 0.000 0.702 0.702
## shame_racistmn 0.190 0.015 12.444 0.000 0.892 0.892
## shame_mns2bwht 0.200 0.016 12.412 0.000 0.940 0.940
## sham_rcstndncs 0.191 0.015 12.455 0.000 0.898 0.898
## GUILT =~
## guilt_racism 0.391 0.013 29.261 0.000 0.927 0.927
## guilt_inequlty 0.392 0.013 29.766 0.000 0.930 0.930
## guilt_treatmnt 0.397 0.013 29.633 0.000 0.941 0.941
## guilt_behavior 0.396 0.013 29.594 0.000 0.940 0.940
## IMAGE =~
## img_shm_dsgrcd 0.539 0.014 38.761 0.000 0.866 0.866
## image_shm_hwsn 0.608 0.018 34.003 0.000 0.977 0.977
## imag_shm_hmltd 0.496 0.012 40.150 0.000 0.796 0.796
## General =~
## RR 1.546 0.078 19.900 0.000 0.840 0.840
## DISC 2.695 0.158 17.031 0.000 0.938 0.938
## WP 1.614 0.076 21.274 0.000 0.850 0.850
## MORAL 4.587 0.388 11.821 0.000 0.977 0.977
## GUILT 2.150 0.093 23.233 0.000 0.907 0.907
## IMAGE 1.257 0.055 22.759 0.000 0.782 0.782
##
## 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 65.034 1.101 59.079 0.000 65.034 2.338
## .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
## .revsham_ntshmd 0.000 0.000 0.000
## .shame_racistmn 0.000 0.000 0.000
## .shame_mns2bwht 0.000 0.000 0.000
## .sham_rcstndncs 0.000 0.000 0.000
## .guilt_racism 0.000 0.000 0.000
## .guilt_inequlty 0.000 0.000 0.000
## .guilt_treatmnt 0.000 0.000 0.000
## .guilt_behavior 0.000 0.000 0.000
## .img_shm_dsgrcd 0.000 0.000 0.000
## .image_shm_hwsn 0.000 0.000 0.000
## .imag_shm_hmltd 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
## .MORAL 0.000 0.000 0.000
## .GUILT 0.000 0.000 0.000
## .IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favrs|t1 -1.120 0.052 -21.600 0.000 -1.120 -1.120
## revrr_favrs|t2 -0.552 0.043 -12.729 0.000 -0.552 -0.552
## revrr_favrs|t3 -0.170 0.041 -4.114 0.000 -0.170 -0.170
## revrr_favrs|t4 0.443 0.042 10.417 0.000 0.443 0.443
## rvrr_tryhrdr|1 -1.426 0.060 -23.616 0.000 -1.426 -1.426
## rvrr_tryhrdr|2 -0.823 0.046 -17.724 0.000 -0.823 -0.823
## rvrr_tryhrdr|3 -0.428 0.042 -10.094 0.000 -0.428 -0.428
## rvrr_tryhrdr|4 0.183 0.041 4.441 0.000 0.183 0.183
## rr_slavery|t1 -1.310 0.057 -23.097 0.000 -1.310 -1.310
## rr_slavery|t2 -0.869 0.047 -18.441 0.000 -0.869 -0.869
## rr_slavery|t3 -0.558 0.043 -12.857 0.000 -0.558 -0.558
## rr_slavery|t4 0.118 0.041 2.874 0.004 0.118 0.118
## rr_deserve|t1 -1.397 0.059 -23.514 0.000 -1.397 -1.397
## rr_deserve|t2 -0.873 0.047 -18.500 0.000 -0.873 -0.873
## rr_deserve|t3 -0.347 0.042 -8.281 0.000 -0.347 -0.347
## rr_deserve|t4 0.350 0.042 8.346 0.000 0.350 0.350
## disc_blacks|t1 -2.006 0.091 -22.100 0.000 -2.006 -2.006
## disc_blacks|t2 -1.336 0.057 -23.238 0.000 -1.336 -1.336
## disc_blacks|t3 -0.524 0.043 -12.153 0.000 -0.524 -0.524
## disc_blacks|t4 0.224 0.041 5.419 0.000 0.224 0.224
## ndsc_qlncms|t1 -1.837 0.079 -23.176 0.000 -1.837 -1.837
## ndsc_qlncms|t2 -1.356 0.058 -23.336 0.000 -1.356 -1.356
## ndsc_qlncms|t3 -0.926 0.048 -19.261 0.000 -0.926 -0.926
## ndsc_qlncms|t4 -0.416 0.042 -9.836 0.000 -0.416 -0.416
## ndsc_qlncms|t5 0.164 0.041 3.984 0.000 0.164 0.164
## ndsc_qlncms|t6 0.963 0.049 19.776 0.000 0.963 0.963
## wpa_advntgs|t1 -1.708 0.072 -23.671 0.000 -1.708 -1.708
## wpa_advntgs|t2 -1.244 0.055 -22.665 0.000 -1.244 -1.244
## wpa_advntgs|t3 -1.025 0.050 -20.553 0.000 -1.025 -1.025
## wpa_advntgs|t4 -0.794 0.046 -17.239 0.000 -0.794 -0.794
## wpa_advntgs|t5 -0.313 0.042 -7.502 0.000 -0.313 -0.313
## wpa_advntgs|t6 0.355 0.042 8.476 0.000 0.355 0.355
## wpa_opnsdrs|t1 -1.643 0.069 -23.804 0.000 -1.643 -1.643
## wpa_opnsdrs|t2 -1.161 0.053 -21.990 0.000 -1.161 -1.161
## wpa_opnsdrs|t3 -0.905 0.048 -18.970 0.000 -0.905 -0.905
## wpa_opnsdrs|t4 -0.622 0.044 -14.128 0.000 -0.622 -0.622
## wpa_opnsdrs|t5 -0.145 0.041 -3.527 0.000 -0.145 -0.145
## wpa_opnsdrs|t6 0.555 0.043 12.793 0.000 0.555 0.555
## wpa_easier|t1 -1.633 0.069 -23.817 0.000 -1.633 -1.633
## wpa_easier|t2 -1.145 0.052 -21.846 0.000 -1.145 -1.145
## wpa_easier|t3 -0.955 0.049 -19.662 0.000 -0.955 -0.955
## wpa_easier|t4 -0.681 0.045 -15.261 0.000 -0.681 -0.681
## wpa_easier|t5 -0.232 0.041 -5.614 0.000 -0.232 -0.232
## wpa_easier|t6 0.443 0.042 10.417 0.000 0.443 0.443
## rvshm_ntshmd|1 -1.419 0.060 -23.592 0.000 -1.419 -1.419
## rvshm_ntshmd|2 -0.850 0.047 -18.144 0.000 -0.850 -0.850
## rvshm_ntshmd|3 -0.539 0.043 -12.473 0.000 -0.539 -0.539
## rvshm_ntshmd|4 0.132 0.041 3.201 0.001 0.132 0.132
## rvshm_ntshmd|5 0.428 0.042 10.094 0.000 0.428 0.428
## rvshm_ntshmd|6 0.942 0.048 19.491 0.000 0.942 0.942
## sham_rcstmn|t1 -1.390 0.059 -23.486 0.000 -1.390 -1.390
## sham_rcstmn|t2 -0.930 0.048 -19.318 0.000 -0.930 -0.930
## sham_rcstmn|t3 -0.695 0.045 -15.511 0.000 -0.695 -0.695
## sham_rcstmn|t4 -0.425 0.042 -10.030 0.000 -0.425 -0.425
## sham_rcstmn|t5 0.080 0.041 1.960 0.050 0.080 0.080
## sham_rcstmn|t6 0.674 0.045 15.136 0.000 0.674 0.674
## shm_mns2bwht|1 -1.145 0.052 -21.846 0.000 -1.145 -1.145
## shm_mns2bwht|2 -0.722 0.045 -16.009 0.000 -0.722 -0.722
## shm_mns2bwht|3 -0.555 0.043 -12.793 0.000 -0.555 -0.555
## shm_mns2bwht|4 -0.257 0.041 -6.200 0.000 -0.257 -0.257
## shm_mns2bwht|5 0.224 0.041 5.419 0.000 0.224 0.224
## shm_mns2bwht|6 0.740 0.045 16.319 0.000 0.740 0.740
## shm_rcstndnc|1 -1.397 0.059 -23.514 0.000 -1.397 -1.397
## shm_rcstndnc|2 -1.047 0.050 -20.823 0.000 -1.047 -1.047
## shm_rcstndnc|3 -0.842 0.047 -18.024 0.000 -0.842 -0.842
## shm_rcstndnc|4 -0.542 0.043 -12.537 0.000 -0.542 -0.542
## shm_rcstndnc|5 -0.038 0.041 -0.915 0.360 -0.038 -0.038
## shm_rcstndnc|6 0.561 0.043 12.921 0.000 0.561 0.561
## guilt_racsm|t1 -0.913 0.048 -19.087 0.000 -0.913 -0.913
## guilt_racsm|t2 -0.376 0.042 -8.929 0.000 -0.376 -0.376
## guilt_racsm|t3 -0.170 0.041 -4.114 0.000 -0.170 -0.170
## guilt_racsm|t4 0.107 0.041 2.613 0.009 0.107 0.107
## guilt_racsm|t5 0.688 0.045 15.386 0.000 0.688 0.688
## guilt_racsm|t6 1.310 0.057 23.097 0.000 1.310 1.310
## guilt_nqlty|t1 -1.193 0.054 -22.270 0.000 -1.193 -1.193
## guilt_nqlty|t2 -0.747 0.045 -16.442 0.000 -0.747 -0.747
## guilt_nqlty|t3 -0.487 0.043 -11.383 0.000 -0.487 -0.487
## guilt_nqlty|t4 -0.224 0.041 -5.419 0.000 -0.224 -0.224
## guilt_nqlty|t5 0.313 0.042 7.502 0.000 0.313 0.313
## guilt_nqlty|t6 0.985 0.049 20.057 0.000 0.985 0.985
## gult_trtmnt|t1 -1.177 0.053 -22.132 0.000 -1.177 -1.177
## gult_trtmnt|t2 -0.750 0.045 -16.504 0.000 -0.750 -0.750
## gult_trtmnt|t3 -0.545 0.043 -12.601 0.000 -0.545 -0.545
## gult_trtmnt|t4 -0.271 0.042 -6.526 0.000 -0.271 -0.271
## gult_trtmnt|t5 0.260 0.041 6.266 0.000 0.260 0.260
## gult_trtmnt|t6 0.850 0.047 18.144 0.000 0.850 0.850
## guilt_behvr|t1 -1.057 0.050 -20.929 0.000 -1.057 -1.057
## guilt_behvr|t2 -0.654 0.044 -14.759 0.000 -0.654 -0.654
## guilt_behvr|t3 -0.437 0.042 -10.288 0.000 -0.437 -0.437
## guilt_behvr|t4 -0.208 0.041 -5.028 0.000 -0.208 -0.208
## guilt_behvr|t5 0.319 0.042 7.632 0.000 0.319 0.319
## guilt_behvr|t6 0.985 0.049 20.057 0.000 0.985 0.985
## img_shm_dsgr|1 -1.255 0.055 -22.748 0.000 -1.255 -1.255
## img_shm_dsgr|2 -0.743 0.045 -16.380 0.000 -0.743 -0.743
## img_shm_dsgr|3 -0.524 0.043 -12.153 0.000 -0.524 -0.524
## img_shm_dsgr|4 -0.110 0.041 -2.678 0.007 -0.110 -0.110
## img_shm_dsgr|5 0.475 0.043 11.126 0.000 0.475 0.475
## img_shm_dsgr|6 1.156 0.053 21.943 0.000 1.156 1.156
## img_shm_hwsn|1 -1.209 0.054 -22.405 0.000 -1.209 -1.209
## img_shm_hwsn|2 -0.719 0.045 -15.947 0.000 -0.719 -0.719
## img_shm_hwsn|3 -0.490 0.043 -11.447 0.000 -0.490 -0.490
## img_shm_hwsn|4 -0.097 0.041 -2.352 0.019 -0.097 -0.097
## img_shm_hwsn|5 0.545 0.043 12.601 0.000 0.545 0.545
## img_shm_hwsn|6 1.232 0.055 22.580 0.000 1.232 1.232
## img_shm_hmlt|1 -1.071 0.051 -21.087 0.000 -1.071 -1.071
## img_shm_hmlt|2 -0.505 0.043 -11.769 0.000 -0.505 -0.505
## img_shm_hmlt|3 -0.213 0.041 -5.158 0.000 -0.213 -0.213
## img_shm_hmlt|4 0.219 0.041 5.288 0.000 0.219 0.219
## img_shm_hmlt|5 0.790 0.046 17.178 0.000 0.790 0.790
## img_shm_hmlt|6 1.419 0.060 23.592 0.000 1.419 1.419
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.112 0.112 0.112
## .revrr_tryhardr 0.170 0.170 0.170
## .rr_slavery 0.252 0.252 0.252
## .rr_deserve 0.237 0.237 0.237
## .racineq_discrm 300.568 14.444 20.809 0.000 300.568 0.388
## .disc_blacks 0.252 0.252 0.252
## .nodisc_eqlncms 0.558 0.558 0.558
## .wpa_advantages 0.068 0.068 0.068
## .wpa_opensdoors 0.108 0.108 0.108
## .wpa_easier 0.094 0.094 0.094
## .revsham_ntshmd 0.508 0.508 0.508
## .shame_racistmn 0.204 0.204 0.204
## .shame_mns2bwht 0.116 0.116 0.116
## .sham_rcstndncs 0.194 0.194 0.194
## .guilt_racism 0.140 0.140 0.140
## .guilt_inequlty 0.135 0.135 0.135
## .guilt_treatmnt 0.114 0.114 0.114
## .guilt_behavior 0.116 0.116 0.116
## .img_shm_dsgrcd 0.250 0.250 0.250
## .image_shm_hwsn 0.046 0.046 0.046
## .imag_shm_hmltd 0.367 0.367 0.367
## .RR 1.000 0.295 0.295
## .DISC 1.000 0.121 0.121
## .WP 1.000 0.277 0.277
## .MORAL 1.000 0.045 0.045
## .GUILT 1.000 0.178 0.178
## .IMAGE 1.000 0.388 0.388
## General 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
## revsham_ntshmd 1.000 1.000 1.000
## shame_racistmn 1.000 1.000 1.000
## shame_mns2bwht 1.000 1.000 1.000
## sham_rcstndncs 1.000 1.000 1.000
## guilt_racism 1.000 1.000 1.000
## guilt_inequlty 1.000 1.000 1.000
## guilt_treatmnt 1.000 1.000 1.000
## guilt_behavior 1.000 1.000 1.000
## img_shm_dsgrcd 1.000 1.000 1.000
## image_shm_hwsn 1.000 1.000 1.000
## imag_shm_hmltd 1.000 1.000 1.000resid(ZGRunHOF, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## rvrr_f rvrr_t rr_slv rr_dsr rcnq_d dsc_bl ndsc_q wp_dvn
## revrr_favors 0.000
## revrr_tryharder 0.000 0.000
## rr_slavery 0.121 0.139 0.000
## rr_deserve 0.122 0.111 0.026 0.000
## racineq_discrim 0.098 0.060 0.000 0.016 0.000
## disc_blacks 0.054 0.066 -0.070 -0.015 0.007 0.000
## nodisc_equalincomes 0.041 0.068 0.010 0.022 0.100 -0.008 0.000
## wpa_advantages 0.070 0.065 0.089 0.051 0.102 0.082 0.063 0.000
## wpa_opensdoors 0.044 0.028 0.063 0.030 0.097 0.101 0.064 0.006
## wpa_easier 0.042 0.031 0.075 0.059 0.100 0.102 0.081 -0.005
## revshame_notashamed 0.029 0.035 -0.058 -0.049 -0.059 -0.017 -0.065 -0.040
## shame_racistmean -0.024 -0.022 -0.019 -0.005 0.039 0.035 0.021 0.026
## shame_means2bewhite -0.093 -0.083 -0.092 -0.064 -0.047 -0.059 -0.045 -0.049
## shame_racistendencies -0.063 -0.061 -0.077 -0.051 -0.037 -0.043 -0.042 -0.072
## guilt_racism -0.125 -0.121 -0.121 -0.081 -0.064 -0.089 -0.077 -0.100
## guilt_inequality -0.085 -0.079 -0.084 -0.049 -0.010 -0.058 -0.031 -0.047
## guilt_treatment -0.089 -0.090 -0.112 -0.087 -0.062 -0.082 -0.070 -0.088
## guilt_behavior -0.104 -0.113 -0.124 -0.076 -0.058 -0.071 -0.061 -0.071
## image_shame_disgraced -0.129 -0.130 -0.107 -0.083 -0.075 -0.046 0.002 -0.132
## image_shame_howseen -0.177 -0.175 -0.186 -0.130 -0.094 -0.086 -0.052 -0.145
## image_shame_humiliated -0.253 -0.227 -0.193 -0.169 -0.114 -0.125 -0.092 -0.192
## wp_pns wpa_sr rvshm_ shm_rcstm shm_m2 shm_rcstn glt_rc
## revrr_favors
## revrr_tryharder
## rr_slavery
## rr_deserve
## racineq_discrim
## disc_blacks
## nodisc_equalincomes
## wpa_advantages
## wpa_opensdoors 0.000
## wpa_easier -0.003 0.000
## revshame_notashamed -0.026 -0.045 0.000
## shame_racistmean 0.042 0.059 -0.011 0.000
## shame_means2bewhite -0.035 -0.034 0.047 0.003 0.000
## shame_racistendencies -0.056 -0.053 0.001 -0.017 -0.008 0.000
## guilt_racism -0.077 -0.071 0.053 -0.006 0.074 0.040 0.000
## guilt_inequality -0.037 -0.021 -0.015 -0.005 0.020 0.047 -0.014
## guilt_treatment -0.082 -0.067 0.000 -0.027 0.003 0.049 -0.018
## guilt_behavior -0.072 -0.057 0.032 -0.021 0.033 0.045 0.000
## image_shame_disgraced -0.101 -0.098 -0.024 -0.022 0.016 0.065 0.083
## image_shame_howseen -0.114 -0.117 -0.003 -0.027 0.027 0.050 0.094
## image_shame_humiliated -0.152 -0.169 -0.017 -0.080 0.013 0.005 0.139
## glt_nq glt_tr glt_bh img_shm_d img_shm_hw img_shm_hm
## revrr_favors
## revrr_tryharder
## rr_slavery
## rr_deserve
## racineq_discrim
## disc_blacks
## nodisc_equalincomes
## wpa_advantages
## wpa_opensdoors
## wpa_easier
## revshame_notashamed
## shame_racistmean
## shame_means2bewhite
## shame_racistendencies
## guilt_racism
## guilt_inequality 0.000
## guilt_treatment 0.018 0.000
## guilt_behavior -0.016 0.008 0.000
## image_shame_disgraced 0.084 0.075 0.093 0.000
## image_shame_howseen 0.071 0.087 0.095 -0.037 0.000
## image_shame_humiliated 0.079 0.092 0.108 0.051 0.015 0.000
##
## $mean
## revrr_favors revrr_tryharder rr_slavery
## 0 0 0
## rr_deserve racineq_discrim disc_blacks
## 0 0 0
## nodisc_equalincomes wpa_advantages wpa_opensdoors
## 0 0 0
## wpa_easier revshame_notashamed shame_racistmean
## 0 0 0
## shame_means2bewhite shame_racistendencies guilt_racism
## 0 0 0
## guilt_inequality guilt_treatment guilt_behavior
## 0 0 0
## image_shame_disgraced image_shame_howseen image_shame_humiliated
## 0 0 0
##
## $th
## revrr_favors|t1 revrr_favors|t2 revrr_favors|t3
## 0 0 0
## revrr_favors|t4 revrr_tryharder|t1 revrr_tryharder|t2
## 0 0 0
## revrr_tryharder|t3 revrr_tryharder|t4 rr_slavery|t1
## 0 0 0
## rr_slavery|t2 rr_slavery|t3 rr_slavery|t4
## 0 0 0
## rr_deserve|t1 rr_deserve|t2 rr_deserve|t3
## 0 0 0
## rr_deserve|t4 disc_blacks|t1 disc_blacks|t2
## 0 0 0
## disc_blacks|t3 disc_blacks|t4 nodisc_equalincomes|t1
## 0 0 0
## nodisc_equalincomes|t2 nodisc_equalincomes|t3 nodisc_equalincomes|t4
## 0 0 0
## nodisc_equalincomes|t5 nodisc_equalincomes|t6 wpa_advantages|t1
## 0 0 0
## wpa_advantages|t2 wpa_advantages|t3 wpa_advantages|t4
## 0 0 0
## wpa_advantages|t5 wpa_advantages|t6 wpa_opensdoors|t1
## 0 0 0
## wpa_opensdoors|t2 wpa_opensdoors|t3 wpa_opensdoors|t4
## 0 0 0
## wpa_opensdoors|t5 wpa_opensdoors|t6 wpa_easier|t1
## 0 0 0
## wpa_easier|t2 wpa_easier|t3 wpa_easier|t4
## 0 0 0
## wpa_easier|t5 wpa_easier|t6 revshame_notashamed|t1
## 0 0 0
## revshame_notashamed|t2 revshame_notashamed|t3 revshame_notashamed|t4
## 0 0 0
## revshame_notashamed|t5 revshame_notashamed|t6 shame_racistmean|t1
## 0 0 0
## shame_racistmean|t2 shame_racistmean|t3 shame_racistmean|t4
## 0 0 0
## shame_racistmean|t5 shame_racistmean|t6 shame_means2bewhite|t1
## 0 0 0
## shame_means2bewhite|t2 shame_means2bewhite|t3 shame_means2bewhite|t4
## 0 0 0
## shame_means2bewhite|t5 shame_means2bewhite|t6 shame_racistendencies|t1
## 0 0 0
## shame_racistendencies|t2 shame_racistendencies|t3 shame_racistendencies|t4
## 0 0 0
## shame_racistendencies|t5 shame_racistendencies|t6 guilt_racism|t1
## 0 0 0
## guilt_racism|t2 guilt_racism|t3 guilt_racism|t4
## 0 0 0
## guilt_racism|t5 guilt_racism|t6 guilt_inequality|t1
## 0 0 0
## guilt_inequality|t2 guilt_inequality|t3 guilt_inequality|t4
## 0 0 0
## guilt_inequality|t5 guilt_inequality|t6 guilt_treatment|t1
## 0 0 0
## guilt_treatment|t2 guilt_treatment|t3 guilt_treatment|t4
## 0 0 0
## guilt_treatment|t5 guilt_treatment|t6 guilt_behavior|t1
## 0 0 0
## guilt_behavior|t2 guilt_behavior|t3 guilt_behavior|t4
## 0 0 0
## guilt_behavior|t5 guilt_behavior|t6 image_shame_disgraced|t1
## 0 0 0
## image_shame_disgraced|t2 image_shame_disgraced|t3 image_shame_disgraced|t4
## 0 0 0
## image_shame_disgraced|t5 image_shame_disgraced|t6 image_shame_howseen|t1
## 0 0 0
## image_shame_howseen|t2 image_shame_howseen|t3 image_shame_howseen|t4
## 0 0 0
## image_shame_howseen|t5 image_shame_howseen|t6 image_shame_humiliated|t1
## 0 0 0
## image_shame_humiliated|t2 image_shame_humiliated|t3 image_shame_humiliated|t4
## 0 0 0
## image_shame_humiliated|t5 image_shame_humiliated|t6
## 0 0ZGModBF <- '
DISC =~ rr_slavery + rr_deserve + racineq_discrim + disc_blacks + nodisc_equalincomes
WP =~ wpa_advantages + wpa_opensdoors + wpa_easier
MORAL =~ revshame_notashamed + shame_racistmean + shame_means2bewhite + shame_racistendencies
GUILT =~ guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior
IMAGE =~ image_shame_disgraced + image_shame_howseen + image_shame_humiliated
General =~ racineq_discrim + wpa_advantages + wpa_opensdoors + wpa_easier + shame_racistmean + shame_means2bewhite + shame_racistendencies + guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior + image_shame_disgraced + image_shame_howseen + image_shame_humiliated + rr_slavery + rr_deserve + disc_blacks + nodisc_equalincomes + revshame_notashamed + revrr_favors + revrr_tryharder'
ZGRunBF <- cfa(ZGModBF, data = data, std.lv = T, orthogonal = T, check.gradient = F, control = list(rel.tol = 1e-4), ordered = c("wpa_advantages", "wpa_opensdoors", "wpa_easier", "shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))
summary(ZGRunBF, stand = T, fit = T)## lavaan 0.6-7 ended normally after 56 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 152
##
## Used Total
## Number of observations 936 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 2998.168 3969.608
## Degrees of freedom 170 170
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.776
## Shift parameter 105.726
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 388166.805 71255.951
## Degrees of freedom 210 210
## P-value 0.000 0.000
## Scaling correction factor 5.461
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.993 0.947
## Tucker-Lewis Index (TLI) 0.991 0.934
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.133 0.155
## 90 Percent confidence interval - lower 0.129 0.150
## 90 Percent confidence interval - upper 0.138 0.159
## 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 0.078 0.078
##
## 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
## DISC =~
## rr_slavery 0.300 0.024 12.393 0.000 0.300 0.300
## rr_deserve 0.393 0.025 15.491 0.000 0.393 0.393
## racineq_discrm 9.719 0.713 13.632 0.000 9.719 0.343
## disc_blacks 0.182 0.023 7.965 0.000 0.182 0.182
## nodisc_eqlncms 0.315 0.033 9.427 0.000 0.315 0.315
## WP =~
## wpa_advantages 0.523 0.019 27.953 0.000 0.523 0.523
## wpa_opensdoors 0.517 0.018 28.276 0.000 0.517 0.517
## wpa_easier 0.483 0.018 26.812 0.000 0.483 0.483
## MORAL =~
## revsham_ntshmd 0.291 0.040 7.347 0.000 0.291 0.291
## shame_racistmn 0.134 0.023 5.890 0.000 0.134 0.134
## shame_mns2bwht 0.305 0.035 8.819 0.000 0.305 0.305
## sham_rcstndncs 0.109 0.022 4.943 0.000 0.109 0.109
## GUILT =~
## guilt_racism 0.338 0.017 20.036 0.000 0.338 0.338
## guilt_inequlty 0.398 0.017 23.700 0.000 0.398 0.398
## guilt_treatmnt 0.461 0.016 28.143 0.000 0.461 0.461
## guilt_behavior 0.388 0.016 23.898 0.000 0.388 0.388
## IMAGE =~
## img_shm_dsgrcd 0.532 0.018 28.833 0.000 0.532 0.532
## image_shm_hwsn 0.531 0.017 31.408 0.000 0.531 0.531
## imag_shm_hmltd 0.624 0.019 32.880 0.000 0.624 0.624
## General =~
## racineq_discrm 20.131 1.028 19.580 0.000 20.131 0.710
## wpa_advantages 0.815 0.013 62.743 0.000 0.815 0.815
## wpa_opensdoors 0.795 0.014 58.615 0.000 0.795 0.795
## wpa_easier 0.812 0.013 63.119 0.000 0.812 0.812
## shame_racistmn 0.872 0.009 94.972 0.000 0.872 0.872
## shame_mns2bwht 0.914 0.007 130.782 0.000 0.914 0.914
## sham_rcstndncs 0.880 0.009 95.063 0.000 0.880 0.880
## guilt_racism 0.852 0.009 90.014 0.000 0.852 0.852
## guilt_inequlty 0.839 0.010 82.574 0.000 0.839 0.839
## guilt_treatmnt 0.838 0.010 80.921 0.000 0.838 0.838
## guilt_behavior 0.853 0.010 88.188 0.000 0.853 0.853
## img_shm_dsgrcd 0.682 0.017 40.690 0.000 0.682 0.682
## image_shm_hwsn 0.771 0.013 57.637 0.000 0.771 0.771
## imag_shm_hmltd 0.598 0.020 30.002 0.000 0.598 0.598
## rr_slavery 0.804 0.014 55.700 0.000 0.804 0.804
## rr_deserve 0.810 0.014 60.005 0.000 0.810 0.810
## disc_blacks 0.815 0.014 59.784 0.000 0.815 0.815
## nodisc_eqlncms 0.614 0.020 30.273 0.000 0.614 0.614
## revsham_ntshmd 0.674 0.018 37.666 0.000 0.674 0.674
## revrr_favors 0.838 0.011 73.424 0.000 0.838 0.838
## revrr_tryhardr 0.818 0.013 64.679 0.000 0.818 0.818
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DISC ~~
## WP 0.000 0.000 0.000
## MORAL 0.000 0.000 0.000
## GUILT 0.000 0.000 0.000
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
## WP ~~
## MORAL 0.000 0.000 0.000
## GUILT 0.000 0.000 0.000
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
## MORAL ~~
## GUILT 0.000 0.000 0.000
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
## GUILT ~~
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
## IMAGE ~~
## General 0.000 0.000 0.000
##
## 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
## .racineq_discrm 65.034 1.101 59.079 0.000 65.034 2.293
## .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
## .revsham_ntshmd 0.000 0.000 0.000
## .shame_racistmn 0.000 0.000 0.000
## .shame_mns2bwht 0.000 0.000 0.000
## .sham_rcstndncs 0.000 0.000 0.000
## .guilt_racism 0.000 0.000 0.000
## .guilt_inequlty 0.000 0.000 0.000
## .guilt_treatmnt 0.000 0.000 0.000
## .guilt_behavior 0.000 0.000 0.000
## .img_shm_dsgrcd 0.000 0.000 0.000
## .image_shm_hwsn 0.000 0.000 0.000
## .imag_shm_hmltd 0.000 0.000 0.000
## .revrr_favors 0.000 0.000 0.000
## .revrr_tryhardr 0.000 0.000 0.000
## DISC 0.000 0.000 0.000
## WP 0.000 0.000 0.000
## MORAL 0.000 0.000 0.000
## GUILT 0.000 0.000 0.000
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## rr_slavery|t1 -1.310 0.057 -23.097 0.000 -1.310 -1.310
## rr_slavery|t2 -0.869 0.047 -18.441 0.000 -0.869 -0.869
## rr_slavery|t3 -0.558 0.043 -12.857 0.000 -0.558 -0.558
## rr_slavery|t4 0.118 0.041 2.874 0.004 0.118 0.118
## rr_deserve|t1 -1.397 0.059 -23.514 0.000 -1.397 -1.397
## rr_deserve|t2 -0.873 0.047 -18.500 0.000 -0.873 -0.873
## rr_deserve|t3 -0.347 0.042 -8.281 0.000 -0.347 -0.347
## rr_deserve|t4 0.350 0.042 8.346 0.000 0.350 0.350
## disc_blacks|t1 -2.006 0.091 -22.100 0.000 -2.006 -2.006
## disc_blacks|t2 -1.336 0.057 -23.238 0.000 -1.336 -1.336
## disc_blacks|t3 -0.524 0.043 -12.153 0.000 -0.524 -0.524
## disc_blacks|t4 0.224 0.041 5.419 0.000 0.224 0.224
## ndsc_qlncms|t1 -1.837 0.079 -23.176 0.000 -1.837 -1.837
## ndsc_qlncms|t2 -1.356 0.058 -23.336 0.000 -1.356 -1.356
## ndsc_qlncms|t3 -0.926 0.048 -19.261 0.000 -0.926 -0.926
## ndsc_qlncms|t4 -0.416 0.042 -9.836 0.000 -0.416 -0.416
## ndsc_qlncms|t5 0.164 0.041 3.984 0.000 0.164 0.164
## ndsc_qlncms|t6 0.963 0.049 19.776 0.000 0.963 0.963
## wpa_advntgs|t1 -1.708 0.072 -23.671 0.000 -1.708 -1.708
## wpa_advntgs|t2 -1.244 0.055 -22.665 0.000 -1.244 -1.244
## wpa_advntgs|t3 -1.025 0.050 -20.553 0.000 -1.025 -1.025
## wpa_advntgs|t4 -0.794 0.046 -17.239 0.000 -0.794 -0.794
## wpa_advntgs|t5 -0.313 0.042 -7.502 0.000 -0.313 -0.313
## wpa_advntgs|t6 0.355 0.042 8.476 0.000 0.355 0.355
## wpa_opnsdrs|t1 -1.643 0.069 -23.804 0.000 -1.643 -1.643
## wpa_opnsdrs|t2 -1.161 0.053 -21.990 0.000 -1.161 -1.161
## wpa_opnsdrs|t3 -0.905 0.048 -18.970 0.000 -0.905 -0.905
## wpa_opnsdrs|t4 -0.622 0.044 -14.128 0.000 -0.622 -0.622
## wpa_opnsdrs|t5 -0.145 0.041 -3.527 0.000 -0.145 -0.145
## wpa_opnsdrs|t6 0.555 0.043 12.793 0.000 0.555 0.555
## wpa_easier|t1 -1.633 0.069 -23.817 0.000 -1.633 -1.633
## wpa_easier|t2 -1.145 0.052 -21.846 0.000 -1.145 -1.145
## wpa_easier|t3 -0.955 0.049 -19.662 0.000 -0.955 -0.955
## wpa_easier|t4 -0.681 0.045 -15.261 0.000 -0.681 -0.681
## wpa_easier|t5 -0.232 0.041 -5.614 0.000 -0.232 -0.232
## wpa_easier|t6 0.443 0.042 10.417 0.000 0.443 0.443
## rvshm_ntshmd|1 -1.419 0.060 -23.592 0.000 -1.419 -1.419
## rvshm_ntshmd|2 -0.850 0.047 -18.144 0.000 -0.850 -0.850
## rvshm_ntshmd|3 -0.539 0.043 -12.473 0.000 -0.539 -0.539
## rvshm_ntshmd|4 0.132 0.041 3.201 0.001 0.132 0.132
## rvshm_ntshmd|5 0.428 0.042 10.094 0.000 0.428 0.428
## rvshm_ntshmd|6 0.942 0.048 19.491 0.000 0.942 0.942
## sham_rcstmn|t1 -1.390 0.059 -23.486 0.000 -1.390 -1.390
## sham_rcstmn|t2 -0.930 0.048 -19.318 0.000 -0.930 -0.930
## sham_rcstmn|t3 -0.695 0.045 -15.511 0.000 -0.695 -0.695
## sham_rcstmn|t4 -0.425 0.042 -10.030 0.000 -0.425 -0.425
## sham_rcstmn|t5 0.080 0.041 1.960 0.050 0.080 0.080
## sham_rcstmn|t6 0.674 0.045 15.136 0.000 0.674 0.674
## shm_mns2bwht|1 -1.145 0.052 -21.846 0.000 -1.145 -1.145
## shm_mns2bwht|2 -0.722 0.045 -16.009 0.000 -0.722 -0.722
## shm_mns2bwht|3 -0.555 0.043 -12.793 0.000 -0.555 -0.555
## shm_mns2bwht|4 -0.257 0.041 -6.200 0.000 -0.257 -0.257
## shm_mns2bwht|5 0.224 0.041 5.419 0.000 0.224 0.224
## shm_mns2bwht|6 0.740 0.045 16.319 0.000 0.740 0.740
## shm_rcstndnc|1 -1.397 0.059 -23.514 0.000 -1.397 -1.397
## shm_rcstndnc|2 -1.047 0.050 -20.823 0.000 -1.047 -1.047
## shm_rcstndnc|3 -0.842 0.047 -18.024 0.000 -0.842 -0.842
## shm_rcstndnc|4 -0.542 0.043 -12.537 0.000 -0.542 -0.542
## shm_rcstndnc|5 -0.038 0.041 -0.915 0.360 -0.038 -0.038
## shm_rcstndnc|6 0.561 0.043 12.921 0.000 0.561 0.561
## guilt_racsm|t1 -0.913 0.048 -19.087 0.000 -0.913 -0.913
## guilt_racsm|t2 -0.376 0.042 -8.929 0.000 -0.376 -0.376
## guilt_racsm|t3 -0.170 0.041 -4.114 0.000 -0.170 -0.170
## guilt_racsm|t4 0.107 0.041 2.613 0.009 0.107 0.107
## guilt_racsm|t5 0.688 0.045 15.386 0.000 0.688 0.688
## guilt_racsm|t6 1.310 0.057 23.097 0.000 1.310 1.310
## guilt_nqlty|t1 -1.193 0.054 -22.270 0.000 -1.193 -1.193
## guilt_nqlty|t2 -0.747 0.045 -16.442 0.000 -0.747 -0.747
## guilt_nqlty|t3 -0.487 0.043 -11.383 0.000 -0.487 -0.487
## guilt_nqlty|t4 -0.224 0.041 -5.419 0.000 -0.224 -0.224
## guilt_nqlty|t5 0.313 0.042 7.502 0.000 0.313 0.313
## guilt_nqlty|t6 0.985 0.049 20.057 0.000 0.985 0.985
## gult_trtmnt|t1 -1.177 0.053 -22.132 0.000 -1.177 -1.177
## gult_trtmnt|t2 -0.750 0.045 -16.504 0.000 -0.750 -0.750
## gult_trtmnt|t3 -0.545 0.043 -12.601 0.000 -0.545 -0.545
## gult_trtmnt|t4 -0.271 0.042 -6.526 0.000 -0.271 -0.271
## gult_trtmnt|t5 0.260 0.041 6.266 0.000 0.260 0.260
## gult_trtmnt|t6 0.850 0.047 18.144 0.000 0.850 0.850
## guilt_behvr|t1 -1.057 0.050 -20.929 0.000 -1.057 -1.057
## guilt_behvr|t2 -0.654 0.044 -14.759 0.000 -0.654 -0.654
## guilt_behvr|t3 -0.437 0.042 -10.288 0.000 -0.437 -0.437
## guilt_behvr|t4 -0.208 0.041 -5.028 0.000 -0.208 -0.208
## guilt_behvr|t5 0.319 0.042 7.632 0.000 0.319 0.319
## guilt_behvr|t6 0.985 0.049 20.057 0.000 0.985 0.985
## img_shm_dsgr|1 -1.255 0.055 -22.748 0.000 -1.255 -1.255
## img_shm_dsgr|2 -0.743 0.045 -16.380 0.000 -0.743 -0.743
## img_shm_dsgr|3 -0.524 0.043 -12.153 0.000 -0.524 -0.524
## img_shm_dsgr|4 -0.110 0.041 -2.678 0.007 -0.110 -0.110
## img_shm_dsgr|5 0.475 0.043 11.126 0.000 0.475 0.475
## img_shm_dsgr|6 1.156 0.053 21.943 0.000 1.156 1.156
## img_shm_hwsn|1 -1.209 0.054 -22.405 0.000 -1.209 -1.209
## img_shm_hwsn|2 -0.719 0.045 -15.947 0.000 -0.719 -0.719
## img_shm_hwsn|3 -0.490 0.043 -11.447 0.000 -0.490 -0.490
## img_shm_hwsn|4 -0.097 0.041 -2.352 0.019 -0.097 -0.097
## img_shm_hwsn|5 0.545 0.043 12.601 0.000 0.545 0.545
## img_shm_hwsn|6 1.232 0.055 22.580 0.000 1.232 1.232
## img_shm_hmlt|1 -1.071 0.051 -21.087 0.000 -1.071 -1.071
## img_shm_hmlt|2 -0.505 0.043 -11.769 0.000 -0.505 -0.505
## img_shm_hmlt|3 -0.213 0.041 -5.158 0.000 -0.213 -0.213
## img_shm_hmlt|4 0.219 0.041 5.288 0.000 0.219 0.219
## img_shm_hmlt|5 0.790 0.046 17.178 0.000 0.790 0.790
## img_shm_hmlt|6 1.419 0.060 23.592 0.000 1.419 1.419
## revrr_favrs|t1 -1.120 0.052 -21.600 0.000 -1.120 -1.120
## revrr_favrs|t2 -0.552 0.043 -12.729 0.000 -0.552 -0.552
## revrr_favrs|t3 -0.170 0.041 -4.114 0.000 -0.170 -0.170
## revrr_favrs|t4 0.443 0.042 10.417 0.000 0.443 0.443
## rvrr_tryhrdr|1 -1.426 0.060 -23.616 0.000 -1.426 -1.426
## rvrr_tryhrdr|2 -0.823 0.046 -17.724 0.000 -0.823 -0.823
## rvrr_tryhrdr|3 -0.428 0.042 -10.094 0.000 -0.428 -0.428
## rvrr_tryhrdr|4 0.183 0.041 4.441 0.000 0.183 0.183
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .rr_slavery 0.263 0.263 0.263
## .rr_deserve 0.189 0.189 0.189
## .racineq_discrm 304.419 11.360 26.797 0.000 304.419 0.379
## .disc_blacks 0.303 0.303 0.303
## .nodisc_eqlncms 0.523 0.523 0.523
## .wpa_advantages 0.063 0.063 0.063
## .wpa_opensdoors 0.100 0.100 0.100
## .wpa_easier 0.107 0.107 0.107
## .revsham_ntshmd 0.461 0.461 0.461
## .shame_racistmn 0.222 0.222 0.222
## .shame_mns2bwht 0.071 0.071 0.071
## .sham_rcstndncs 0.214 0.214 0.214
## .guilt_racism 0.160 0.160 0.160
## .guilt_inequlty 0.137 0.137 0.137
## .guilt_treatmnt 0.085 0.085 0.085
## .guilt_behavior 0.122 0.122 0.122
## .img_shm_dsgrcd 0.251 0.251 0.251
## .image_shm_hwsn 0.124 0.124 0.124
## .imag_shm_hmltd 0.253 0.253 0.253
## .revrr_favors 0.297 0.297 0.297
## .revrr_tryhardr 0.331 0.331 0.331
## DISC 1.000 1.000 1.000
## WP 1.000 1.000 1.000
## MORAL 1.000 1.000 1.000
## GUILT 1.000 1.000 1.000
## IMAGE 1.000 1.000 1.000
## General 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
## 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
## revsham_ntshmd 1.000 1.000 1.000
## shame_racistmn 1.000 1.000 1.000
## shame_mns2bwht 1.000 1.000 1.000
## sham_rcstndncs 1.000 1.000 1.000
## guilt_racism 1.000 1.000 1.000
## guilt_inequlty 1.000 1.000 1.000
## guilt_treatmnt 1.000 1.000 1.000
## guilt_behavior 1.000 1.000 1.000
## img_shm_dsgrcd 1.000 1.000 1.000
## image_shm_hwsn 1.000 1.000 1.000
## imag_shm_hmltd 1.000 1.000 1.000
## revrr_favors 1.000 1.000 1.000
## revrr_tryhardr 1.000 1.000 1.000resid(ZGRunBF, "cor")## $type
## [1] "cor.bollen"
##
## $cov
## rr_slv rr_dsr rcnq_d dsc_bl ndsc_q wp_dvn wp_pns wpa_sr
## rr_slavery 0.000
## rr_deserve 0.011 0.000
## racineq_discrim 0.003 -0.011 0.000
## disc_blacks -0.032 0.009 0.042 0.000
## nodisc_equalincomes -0.004 -0.020 0.075 0.009 0.000
## wpa_advantages 0.099 0.063 0.125 0.084 0.073 0.000
## wpa_opensdoors 0.075 0.043 0.121 0.104 0.075 0.000 0.000
## wpa_easier 0.077 0.063 0.117 0.096 0.086 0.000 0.000 0.000
## revshame_notashamed -0.045 -0.034 -0.035 -0.010 -0.052 -0.027 -0.011 -0.038
## shame_racistmean -0.014 0.002 0.060 0.031 0.029 0.031 0.048 0.056
## shame_means2bewhite -0.082 -0.053 -0.022 -0.059 -0.034 -0.040 -0.025 -0.033
## shame_racistendencies -0.074 -0.046 -0.019 -0.049 -0.036 -0.069 -0.052 -0.058
## guilt_racism -0.124 -0.083 -0.052 -0.101 -0.076 -0.105 -0.080 -0.082
## guilt_inequality -0.076 -0.038 0.013 -0.058 -0.021 -0.038 -0.027 -0.020
## guilt_treatment -0.094 -0.068 -0.031 -0.073 -0.053 -0.070 -0.063 -0.057
## guilt_behavior -0.119 -0.069 -0.038 -0.074 -0.054 -0.067 -0.066 -0.060
## image_shame_disgraced -0.106 -0.081 -0.062 -0.052 0.005 -0.131 -0.100 -0.104
## image_shame_howseen -0.187 -0.129 -0.081 -0.094 -0.049 -0.146 -0.113 -0.124
## image_shame_humiliated -0.170 -0.144 -0.081 -0.107 -0.072 -0.168 -0.127 -0.151
## revrr_favors 0.088 0.091 0.082 0.013 0.019 0.036 0.012 0.001
## revrr_tryharder 0.101 0.074 0.041 0.020 0.042 0.026 -0.008 -0.014
## rvshm_ shm_rcstm shm_m2 shm_rcstn glt_rc glt_nq glt_tr
## rr_slavery
## rr_deserve
## racineq_discrim
## disc_blacks
## nodisc_equalincomes
## wpa_advantages
## wpa_opensdoors
## wpa_easier
## revshame_notashamed 0.000
## shame_racistmean -0.012 0.000
## shame_means2bewhite 0.001 0.004 0.000
## shame_racistendencies 0.007 0.002 -0.002 0.000
## guilt_racism 0.055 -0.016 0.067 0.027 0.000
## guilt_inequality -0.003 -0.001 0.027 0.048 -0.001 0.000
## guilt_treatment 0.020 -0.013 0.021 0.060 -0.015 0.007 0.000
## guilt_behavior 0.042 -0.021 0.037 0.042 0.014 -0.012 0.000
## image_shame_disgraced -0.020 -0.026 0.015 0.059 0.072 0.083 0.081
## image_shame_howseen 0.001 -0.033 0.024 0.042 0.080 0.069 0.093
## image_shame_humiliated 0.006 -0.059 0.038 0.025 0.153 0.103 0.122
## revrr_favors 0.006 -0.065 -0.132 -0.107 -0.174 -0.121 -0.116
## revrr_tryharder 0.008 -0.068 -0.127 -0.109 -0.175 -0.121 -0.122
## glt_bh img_shm_d img_shm_hw img_shm_hm rvrr_f rvrr_t
## rr_slavery
## rr_deserve
## racineq_discrim
## disc_blacks
## nodisc_equalincomes
## wpa_advantages
## wpa_opensdoors
## wpa_easier
## revshame_notashamed
## shame_racistmean
## shame_means2bewhite
## shame_racistendencies
## guilt_racism
## guilt_inequality
## guilt_treatment
## guilt_behavior 0.000
## image_shame_disgraced 0.089 0.000
## image_shame_howseen 0.089 0.000 0.000
## image_shame_humiliated 0.129 0.000 0.000 0.000
## revrr_favors -0.145 -0.165 -0.219 -0.261 0.000
## revrr_tryharder -0.158 -0.170 -0.221 -0.240 0.173 0.000
##
## $mean
## rr_slavery rr_deserve racineq_discrim
## 0 0 0
## disc_blacks nodisc_equalincomes wpa_advantages
## 0 0 0
## wpa_opensdoors wpa_easier revshame_notashamed
## 0 0 0
## shame_racistmean shame_means2bewhite shame_racistendencies
## 0 0 0
## guilt_racism guilt_inequality guilt_treatment
## 0 0 0
## guilt_behavior image_shame_disgraced image_shame_howseen
## 0 0 0
## image_shame_humiliated revrr_favors revrr_tryharder
## 0 0 0
##
## $th
## rr_slavery|t1 rr_slavery|t2 rr_slavery|t3
## 0 0 0
## rr_slavery|t4 rr_deserve|t1 rr_deserve|t2
## 0 0 0
## rr_deserve|t3 rr_deserve|t4 disc_blacks|t1
## 0 0 0
## disc_blacks|t2 disc_blacks|t3 disc_blacks|t4
## 0 0 0
## nodisc_equalincomes|t1 nodisc_equalincomes|t2 nodisc_equalincomes|t3
## 0 0 0
## nodisc_equalincomes|t4 nodisc_equalincomes|t5 nodisc_equalincomes|t6
## 0 0 0
## wpa_advantages|t1 wpa_advantages|t2 wpa_advantages|t3
## 0 0 0
## wpa_advantages|t4 wpa_advantages|t5 wpa_advantages|t6
## 0 0 0
## wpa_opensdoors|t1 wpa_opensdoors|t2 wpa_opensdoors|t3
## 0 0 0
## wpa_opensdoors|t4 wpa_opensdoors|t5 wpa_opensdoors|t6
## 0 0 0
## wpa_easier|t1 wpa_easier|t2 wpa_easier|t3
## 0 0 0
## wpa_easier|t4 wpa_easier|t5 wpa_easier|t6
## 0 0 0
## revshame_notashamed|t1 revshame_notashamed|t2 revshame_notashamed|t3
## 0 0 0
## revshame_notashamed|t4 revshame_notashamed|t5 revshame_notashamed|t6
## 0 0 0
## shame_racistmean|t1 shame_racistmean|t2 shame_racistmean|t3
## 0 0 0
## shame_racistmean|t4 shame_racistmean|t5 shame_racistmean|t6
## 0 0 0
## shame_means2bewhite|t1 shame_means2bewhite|t2 shame_means2bewhite|t3
## 0 0 0
## shame_means2bewhite|t4 shame_means2bewhite|t5 shame_means2bewhite|t6
## 0 0 0
## shame_racistendencies|t1 shame_racistendencies|t2 shame_racistendencies|t3
## 0 0 0
## shame_racistendencies|t4 shame_racistendencies|t5 shame_racistendencies|t6
## 0 0 0
## guilt_racism|t1 guilt_racism|t2 guilt_racism|t3
## 0 0 0
## guilt_racism|t4 guilt_racism|t5 guilt_racism|t6
## 0 0 0
## guilt_inequality|t1 guilt_inequality|t2 guilt_inequality|t3
## 0 0 0
## guilt_inequality|t4 guilt_inequality|t5 guilt_inequality|t6
## 0 0 0
## guilt_treatment|t1 guilt_treatment|t2 guilt_treatment|t3
## 0 0 0
## guilt_treatment|t4 guilt_treatment|t5 guilt_treatment|t6
## 0 0 0
## guilt_behavior|t1 guilt_behavior|t2 guilt_behavior|t3
## 0 0 0
## guilt_behavior|t4 guilt_behavior|t5 guilt_behavior|t6
## 0 0 0
## image_shame_disgraced|t1 image_shame_disgraced|t2 image_shame_disgraced|t3
## 0 0 0
## image_shame_disgraced|t4 image_shame_disgraced|t5 image_shame_disgraced|t6
## 0 0 0
## image_shame_howseen|t1 image_shame_howseen|t2 image_shame_howseen|t3
## 0 0 0
## image_shame_howseen|t4 image_shame_howseen|t5 image_shame_howseen|t6
## 0 0 0
## image_shame_humiliated|t1 image_shame_humiliated|t2 image_shame_humiliated|t3
## 0 0 0
## image_shame_humiliated|t4 image_shame_humiliated|t5 image_shame_humiliated|t6
## 0 0 0
## revrr_favors|t1 revrr_favors|t2 revrr_favors|t3
## 0 0 0
## revrr_favors|t4 revrr_tryharder|t1 revrr_tryharder|t2
## 0 0 0
## revrr_tryharder|t3 revrr_tryharder|t4
## 0 0round(cbind(Single = fitMeasures(ZGRunOne, FITM),
"Correlated Group" = fitMeasures(ZGRunCGF, FITM),
"Higher-Order" = fitMeasures(ZGRunHOF, FITM),
Bifactor = fitMeasures(ZGRunBF, FITM)), 3)## Single Correlated Group Higher-Order Bifactor
## chisq 7331.085 520.462 2696.693 2998.168
## df 189.000 174.000 183.000 170.000
## npar 133.000 148.000 139.000 152.000
## cfi.scaled 0.909 0.984 0.949 0.947
## rmsea 0.201 0.046 0.121 0.133
## rmsea.ci.lower 0.197 0.042 0.117 0.129
## rmsea.ci.upper 0.205 0.051 0.125 0.138
## srmr 0.115 0.031 0.075 0.078There are 14 significant residual correlations in a bifactor model and factor collapse occurred for RR. A correlated group factor model has the best fit in terms of (1) model fit measures/closeness of fit and (2) local independence. However, all models are strongly general.
lowerCFG = '
1.000
0.918 1.000
0.769 0.891 1.000
0.770 0.868 0.813 1.000
0.646 0.750 0.699 0.920 1.000
0.443 0.594 0.511 0.779 0.819 1.000'
Names = list("RR", "DISC", "WP", "MORAL", "GUILT", "IMAGE")
CFGH = getCov(lowerCFG, names = Names)
fa.parallel(CFGH, n.obs = 936)## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Parallel analysis suggests that the number of factors = 2 and the number of components = 1FA1 <- fa(CFGH, n.obs = 936, nfactors = 1); FA1; fa(CFGH, n.obs = 936, nfactors = 2); fa(CFGH, n.obs = 936, nfactors = 3)## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Factor Analysis using method = minres
## Call: fa(r = CFGH, nfactors = 1, n.obs = 936)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 h2 u2 com
## RR 0.82 0.67 0.330 1
## DISC 0.95 0.90 0.104 1
## WP 0.85 0.73 0.272 1
## MORAL 0.98 0.96 0.035 1
## GUILT 0.88 0.78 0.220 1
## IMAGE 0.71 0.50 0.502 1
##
## MR1
## SS loadings 4.54
## Proportion Var 0.76
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 15 and the objective function was 8.26 with Chi Square of 7698.35
## The degrees of freedom for the model are 9 and the objective function was 2.31
##
## The root mean square of the residuals (RMSR) is 0.09
## The df corrected root mean square of the residuals is 0.12
##
## The harmonic number of observations is 936 with the empirical chi square 252.1 with prob < 3.6e-49
## The total number of observations was 936 with Likelihood Chi Square = 2148.07 with prob < 0
##
## Tucker Lewis Index of factoring reliability = 0.536
## RMSEA index = 0.504 and the 90 % confidence intervals are 0.486 0.522
## BIC = 2086.5
## Fit based upon off diagonal values = 0.98## Loading required namespace: GPArotation## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Factor Analysis using method = minres
## Call: fa(r = CFGH, nfactors = 2, n.obs = 936)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR2 h2 u2 com
## RR 0.96 -0.08 0.83 0.1738 1.0
## DISC 0.96 0.05 1.00 -0.0028 1.0
## WP 0.80 0.11 0.77 0.2266 1.0
## MORAL 0.43 0.63 0.96 0.0396 1.8
## GUILT 0.14 0.86 0.92 0.0798 1.1
## IMAGE -0.13 0.96 0.76 0.2390 1.0
##
## MR1 MR2
## SS loadings 2.94 2.30
## Proportion Var 0.49 0.38
## Cumulative Var 0.49 0.87
## Proportion Explained 0.56 0.44
## Cumulative Proportion 0.56 1.00
##
## With factor correlations of
## MR1 MR2
## MR1 1.0 0.7
## MR2 0.7 1.0
##
## Mean item complexity = 1.1
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 15 and the objective function was 8.26 with Chi Square of 7698.35
## The degrees of freedom for the model are 4 and the objective function was 0.37
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic number of observations is 936 with the empirical chi square 5.14 with prob < 0.27
## The total number of observations was 936 with Likelihood Chi Square = 348.73 with prob < 3.3e-74
##
## Tucker Lewis Index of factoring reliability = 0.832
## RMSEA index = 0.303 and the 90 % confidence intervals are 0.277 0.331
## BIC = 321.37
## Fit based upon off diagonal values = 1## Factor Analysis using method = minres
## Call: fa(r = CFGH, nfactors = 3, n.obs = 936)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR2 MR1 MR3 h2 u2 com
## RR 0.00 1.02 -0.03 1.00 0.0028 1.0
## DISC 0.19 0.54 0.34 0.94 0.0597 2.0
## WP 0.01 -0.01 1.00 1.00 0.0037 1.0
## MORAL 0.68 0.20 0.19 0.95 0.0465 1.3
## GUILT 0.89 0.06 0.05 0.92 0.0822 1.0
## IMAGE 0.98 -0.09 -0.08 0.76 0.2361 1.0
##
## MR2 MR1 MR3
## SS loadings 2.48 1.66 1.43
## Proportion Var 0.41 0.28 0.24
## Cumulative Var 0.41 0.69 0.93
## Proportion Explained 0.45 0.30 0.26
## Cumulative Proportion 0.45 0.74 1.00
##
## With factor correlations of
## MR2 MR1 MR3
## MR2 1.00 0.62 0.68
## MR1 0.62 1.00 0.79
## MR3 0.68 0.79 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 15 and the objective function was 8.26 with Chi Square of 7698.35
## The degrees of freedom for the model are 0 and the objective function was 0.08
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is NA
##
## The harmonic number of observations is 936 with the empirical chi square 0.89 with prob < NA
## The total number of observations was 936 with Likelihood Chi Square = 76.12 with prob < NA
##
## Tucker Lewis Index of factoring reliability = -Inf
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR2 MR1 MR3
## Correlation of (regression) scores with factors 0.98 1 1.00
## Multiple R square of scores with factors 0.96 1 1.00
## Minimum correlation of possible factor scores 0.93 1 0.99FA1$loadings##
## Loadings:
## MR1
## RR 0.818
## DISC 0.947
## WP 0.853
## MORAL 0.982
## GUILT 0.883
## IMAGE 0.706
##
## MR1
## SS loadings 4.536
## Proportion Var 0.756Two factors does not work and neither does three; one shows extreme generality (75.6% of total factor covariance variance), as expected.
BFG <- c(0.838, 0.818, 0.804, 0.810, 0.710, 0.815, 0.614, 0.815, 0.795, 0.812, 0.674, 0.872, 0.914, 0.880, 0.852, 0.839, 0.838, 0.853, 0.682, 0.771, 0.598)
HOG <- c(0.791, 0.765, 0.811, 0.819, 0.734, 0.811, 0.624, 0.821, 0.802, 0.809, 0.686, 0.871, 0.918, 0.877, 0.841, 0.844, 0.853, 0.853, 0.677, 0.764, 0.622)
CFG <- c(0.770, 0.746, 0.811, 0.824, 0.760, 0.820, 0.638, 0.822, 0.806, 0.812, 0.690, 0.881, 0.920, 0.880, 0.818, 0.823, 0.831, 0.829, 0.615, 0.682, 0.568)
BFS <- c(0.000, 0.000, 0.300, 0.393, 0.343, 0.182, 0.315, 0.523, 0.517, 0.483, 0.291, 0.134, 0.305, 0.109, 0.338, 0.398, 0.461, 0.388, 0.532, 0.531, 0.624)
HOS <- c(0.277, 0.268, 0.104, 0.105, 0.094, 0.104, 0.080, 0.268, 0.262, 0.264, 0.032, 0.041, 0.043, 0.041, 0.164, 0.165, 0.167, 0.167, 0.336, 0.380, 0.309)
CFS <- c(0.311, 0.302, 0.088, 0.090, 0.083, 0.089, 0.070, 0.263, 0.257, 0.259, 0.025, 0.032, 0.033, 0.032, 0.204, 0.205, 0.207, 0.207, 0.437, 0.485, 0.404)
cor(BFG, HOG); cor(BFG, HOG, method = "spearman"); CONGO(BFG, HOG)## [1] 0.9762652## [1] 0.9141743## [1] 0.9997321cor(CFG, HOG); cor(CFG, HOG, method = "spearman"); CONGO(CFG, HOG)## [1] 0.9585811## [1] 0.9746591## [1] 0.9994223cor(BFG, CFG); cor(BFG, CFG, method = "spearman"); CONGO(BFG, CFG)## [1] 0.9198236## [1] 0.8596493## [1] 0.9989982cor(BFS, HOS); cor(BFS, HOS, method = "spearman"); CONGO(BFS, HOS)## [1] 0.4404844## [1] 0.5837401## [1] 0.8670351cor(CFS, HOS); cor(CFS, HOS, method = "spearman"); CONGO(CFS, HOS)## [1] 0.9813824## [1] 0.9993496## [1] 0.9919418cor(BFS, CFS); cor(BFS, CFS, method = "spearman"); CONGO(BFS, CFS)## [1] 0.4529971## [1] 0.5713357## [1] 0.8474028The general variance is estimated consistently between the higher-order, correlated group factor and bifactor models but the specific variance is not except in the higher-order and correlated group factor cases, which is unsurprising since they are practically the same things. All models are extremely general. The total variance explained by all factors in each model is 67.9% in the single-factor model, 67.2% in the higher-order model, 77.8% in the bifactor model and 79% in the correlated group factor model and 67% when the correlated group factor model is transformed into a higher-order one.
The PUC for the higher-order model is 0.862 and around 0.836 in the bifactor model although this is, properly-speaking, a slight underestimate. Each of the following statistics is listed in the following model order: higher-order, bifactor and finally transformed correlated group factor. \(\omega_t\) is 0.976, 0.984, 0.975; \(\omega_h\) is 0.966, 0.947, 0.962; relative \(\omega\) values are 0.990, 0.962, 0.987; factor correlations are 0.983, 0.973, 0.981; H values are 0.977, 0.977, 0.976; FDI values are 0.988, 0.989, 0.988; the total variances explained in general are 0.631, 0.632, 0.614; and general variance accounts for 93.8%, 81.2%, 91.6% of the common variance, with 32.8%, 22.2%, 33.0% of variance being unique. All-in-all, each model showed extreme unidimensionality.
The \(\omega_{hs}\), H, FDI, total variance and explained common variance for the RR, DISC, WP, MORAL, GUILT and IMAGE factors are 0.088/0.138/0.372/0.007/0.011, 0.014/0.046/0.215/0.002/0.003, 0.086/0.184/0.429/0.010/0.015, 0.002/0.006/0.079/<0.001/<0.001, 0.034/0.102/0.319/0.005/0.008 and 0.161/0.287/0.535/0.017/0.025 in the higher-order model and 0/0/0/0/0, 0.130/0.359/0.599/0.024/0.030, 0.274/0.511/0.715/0.037/0.047, 0.055/0.184/0.429/0.010/0.013, 0.174/0.433/0.658/0.030/0.039 and 0.371/0.588/0.767/0.045/0.058 in the bifactor model. Values were similar for the transformed correlated group factor and higher-order models.
\(\omega_{hs}\) values were all negligibly small in the higher-order model excepting the IMAGE factor, which was small, but not negligible. In the bifactor model, the WP and guilt factors were likewise small but not negligible and the IMAGE factor was large for a group factor, making it worthwhile to consider it independently.
Because of the unidimensionality of these data, most of the criterion validity is in the general variance but there is room for a potentially meaningful amount of reliable group factor variance. There can also be meaningful variance derived from differences in reliability, item specificities, and measurement and responses biases. Investigations using these constructs would benefit from path modeling with latent variables to overcome potential reliability problems.
Two
ZGOne <- '
General =~ revshame_notashamed + shame_racistmean + shame_means2bewhite + shame_racistendencies + guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior + image_shame_disgraced + image_shame_howseen + image_shame_humiliated'
ZGCGF <- '
MORAL =~ revshame_notashamed + shame_racistmean + shame_means2bewhite + shame_racistendencies
GUILT =~ guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior
IMAGE =~ image_shame_disgraced + image_shame_howseen + image_shame_humiliated'
ZGHOF <- '
MORAL =~ revshame_notashamed + shame_racistmean + shame_means2bewhite + shame_racistendencies
GUILT =~ guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior
IMAGE =~ image_shame_disgraced + image_shame_howseen + image_shame_humiliated
General =~ MORAL + GUILT + IMAGE'
ZGBF <- '
MORAL =~ revshame_notashamed + shame_racistmean + shame_means2bewhite + shame_racistendencies
GUILT =~ guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior
IMAGE =~ image_shame_disgraced + image_shame_howseen + image_shame_humiliated
General =~ revshame_notashamed + shame_racistmean + shame_means2bewhite + shame_racistendencies + guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior + image_shame_disgraced + image_shame_howseen + image_shame_humiliated'
ZGRunOne <- cfa(ZGOne, data = data, std.lv = T, ordered = c("shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))
ZGRunCGF <- cfa(ZGCGF, data = data, std.lv = T, ordered = c("shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))
ZGRunHOF <- cfa(ZGHOF, data = data, std.lv = T, ordered = c("shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))
ZGRunBF <- cfa(ZGBF, data = data, orthogonal = T, std.lv = T, ordered = c("shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))
summary(ZGRunOne, stand = T, fit = T); summary(ZGRunCGF, stand = T, fit = T); summary(ZGRunHOF, stand = T, fit = T); summary(ZGRunBF, stand = T, fit = T)## lavaan 0.6-7 ended normally after 21 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 77
##
## Used Total
## Number of observations 937 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 1136.174 2139.310
## Degrees of freedom 44 44
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.536
## Shift parameter 19.566
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 193784.680 53113.355
## Degrees of freedom 55 55
## P-value 0.000 0.000
## Scaling correction factor 3.651
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.994 0.961
## Tucker-Lewis Index (TLI) 0.993 0.951
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.163 0.226
## 90 Percent confidence interval - lower 0.155 0.217
## 90 Percent confidence interval - upper 0.171 0.234
## 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
## General =~
## revsham_ntshmd 0.675 0.016 40.952 0.000 0.675 0.675
## shame_racistmn 0.831 0.011 78.447 0.000 0.831 0.831
## shame_mns2bwht 0.912 0.006 147.231 0.000 0.912 0.912
## sham_rcstndncs 0.873 0.008 102.880 0.000 0.873 0.873
## guilt_racism 0.913 0.006 162.059 0.000 0.913 0.913
## guilt_inequlty 0.915 0.005 168.652 0.000 0.915 0.915
## guilt_treatmnt 0.934 0.005 205.100 0.000 0.934 0.934
## guilt_behavior 0.927 0.005 196.013 0.000 0.927 0.927
## img_shm_dsgrcd 0.799 0.011 70.756 0.000 0.799 0.799
## image_shm_hwsn 0.862 0.009 101.226 0.000 0.862 0.862
## imag_shm_hmltd 0.763 0.013 58.644 0.000 0.763 0.763
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revsham_ntshmd 0.000 0.000 0.000
## .shame_racistmn 0.000 0.000 0.000
## .shame_mns2bwht 0.000 0.000 0.000
## .sham_rcstndncs 0.000 0.000 0.000
## .guilt_racism 0.000 0.000 0.000
## .guilt_inequlty 0.000 0.000 0.000
## .guilt_treatmnt 0.000 0.000 0.000
## .guilt_behavior 0.000 0.000 0.000
## .img_shm_dsgrcd 0.000 0.000 0.000
## .image_shm_hwsn 0.000 0.000 0.000
## .imag_shm_hmltd 0.000 0.000 0.000
## General 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## rvshm_ntshmd|1 -1.419 0.060 -23.606 0.000 -1.419 -1.419
## rvshm_ntshmd|2 -0.851 0.047 -18.165 0.000 -0.851 -0.851
## rvshm_ntshmd|3 -0.540 0.043 -12.499 0.000 -0.540 -0.540
## rvshm_ntshmd|4 0.130 0.041 3.166 0.002 0.130 0.130
## rvshm_ntshmd|5 0.426 0.042 10.057 0.000 0.426 0.426
## rvshm_ntshmd|6 0.939 0.048 19.454 0.000 0.939 0.939
## sham_rcstmn|t1 -1.391 0.059 -23.501 0.000 -1.391 -1.391
## sham_rcstmn|t2 -0.930 0.048 -19.339 0.000 -0.930 -0.930
## sham_rcstmn|t3 -0.696 0.045 -15.535 0.000 -0.696 -0.696
## sham_rcstmn|t4 -0.426 0.042 -10.057 0.000 -0.426 -0.426
## sham_rcstmn|t5 0.079 0.041 1.926 0.054 0.079 0.079
## sham_rcstmn|t6 0.675 0.045 15.159 0.000 0.675 0.675
## shm_mns2bwht|1 -1.146 0.052 -21.864 0.000 -1.146 -1.146
## shm_mns2bwht|2 -0.723 0.045 -16.032 0.000 -0.723 -0.723
## shm_mns2bwht|3 -0.556 0.043 -12.818 0.000 -0.556 -0.556
## shm_mns2bwht|4 -0.258 0.041 -6.230 0.000 -0.258 -0.258
## shm_mns2bwht|5 0.223 0.041 5.383 0.000 0.223 0.223
## shm_mns2bwht|6 0.741 0.045 16.341 0.000 0.741 0.741
## shm_rcstndnc|1 -1.398 0.059 -23.529 0.000 -1.398 -1.398
## shm_rcstndnc|2 -1.048 0.050 -20.842 0.000 -1.048 -1.048
## shm_rcstndnc|3 -0.843 0.047 -18.046 0.000 -0.843 -0.843
## shm_rcstndnc|4 -0.543 0.043 -12.563 0.000 -0.543 -0.543
## shm_rcstndnc|5 -0.039 0.041 -0.947 0.344 -0.039 -0.039
## shm_rcstndnc|6 0.559 0.043 12.882 0.000 0.559 0.559
## guilt_racsm|t1 -0.914 0.048 -19.108 0.000 -0.914 -0.914
## guilt_racsm|t2 -0.377 0.042 -8.957 0.000 -0.377 -0.377
## guilt_racsm|t3 -0.171 0.041 -4.145 0.000 -0.171 -0.171
## guilt_racsm|t4 0.106 0.041 2.579 0.010 0.106 0.106
## guilt_racsm|t5 0.685 0.045 15.347 0.000 0.685 0.685
## guilt_racsm|t6 1.311 0.057 23.113 0.000 1.311 1.311
## guilt_nqlty|t1 -1.194 0.054 -22.288 0.000 -1.194 -1.194
## guilt_nqlty|t2 -0.748 0.045 -16.465 0.000 -0.748 -0.748
## guilt_nqlty|t3 -0.488 0.043 -11.409 0.000 -0.488 -0.488
## guilt_nqlty|t4 -0.225 0.041 -5.448 0.000 -0.225 -0.225
## guilt_nqlty|t5 0.311 0.042 7.465 0.000 0.311 0.311
## guilt_nqlty|t6 0.985 0.049 20.077 0.000 0.985 0.985
## gult_trtmnt|t1 -1.177 0.053 -22.149 0.000 -1.177 -1.177
## gult_trtmnt|t2 -0.751 0.045 -16.526 0.000 -0.751 -0.751
## gult_trtmnt|t3 -0.546 0.043 -12.627 0.000 -0.546 -0.546
## gult_trtmnt|t4 -0.272 0.042 -6.555 0.000 -0.272 -0.272
## gult_trtmnt|t5 0.258 0.041 6.230 0.000 0.258 0.258
## gult_trtmnt|t6 0.851 0.047 18.165 0.000 0.851 0.851
## guilt_behvr|t1 -1.057 0.050 -20.948 0.000 -1.057 -1.057
## guilt_behvr|t2 -0.655 0.044 -14.783 0.000 -0.655 -0.655
## guilt_behvr|t3 -0.438 0.042 -10.315 0.000 -0.438 -0.438
## guilt_behvr|t4 -0.209 0.041 -5.057 0.000 -0.209 -0.209
## guilt_behvr|t5 0.317 0.042 7.595 0.000 0.317 0.317
## guilt_behvr|t6 0.985 0.049 20.077 0.000 0.985 0.985
## img_shm_dsgr|1 -1.256 0.055 -22.765 0.000 -1.256 -1.256
## img_shm_dsgr|2 -0.744 0.045 -16.403 0.000 -0.744 -0.744
## img_shm_dsgr|3 -0.525 0.043 -12.179 0.000 -0.525 -0.525
## img_shm_dsgr|4 -0.111 0.041 -2.710 0.007 -0.111 -0.111
## img_shm_dsgr|5 0.473 0.043 11.088 0.000 0.473 0.473
## img_shm_dsgr|6 1.156 0.053 21.960 0.000 1.156 1.156
## img_shm_hwsn|1 -1.210 0.054 -22.422 0.000 -1.210 -1.210
## img_shm_hwsn|2 -0.720 0.045 -15.970 0.000 -0.720 -0.720
## img_shm_hwsn|3 -0.491 0.043 -11.474 0.000 -0.491 -0.491
## img_shm_hwsn|4 -0.098 0.041 -2.383 0.017 -0.098 -0.098
## img_shm_hwsn|5 0.543 0.043 12.563 0.000 0.543 0.543
## img_shm_hwsn|6 1.233 0.055 22.597 0.000 1.233 1.233
## img_shm_hmlt|1 -1.072 0.051 -21.106 0.000 -1.072 -1.072
## img_shm_hmlt|2 -0.506 0.043 -11.795 0.000 -0.506 -0.506
## img_shm_hmlt|3 -0.214 0.041 -5.188 0.000 -0.214 -0.214
## img_shm_hmlt|4 0.217 0.041 5.253 0.000 0.217 0.217
## img_shm_hmlt|5 0.787 0.046 17.139 0.000 0.787 0.787
## img_shm_hmlt|6 1.419 0.060 23.606 0.000 1.419 1.419
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revsham_ntshmd 0.544 0.544 0.544
## .shame_racistmn 0.310 0.310 0.310
## .shame_mns2bwht 0.168 0.168 0.168
## .sham_rcstndncs 0.239 0.239 0.239
## .guilt_racism 0.166 0.166 0.166
## .guilt_inequlty 0.164 0.164 0.164
## .guilt_treatmnt 0.128 0.128 0.128
## .guilt_behavior 0.140 0.140 0.140
## .img_shm_dsgrcd 0.362 0.362 0.362
## .image_shm_hwsn 0.256 0.256 0.256
## .imag_shm_hmltd 0.418 0.418 0.418
## General 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revsham_ntshmd 1.000 1.000 1.000
## shame_racistmn 1.000 1.000 1.000
## shame_mns2bwht 1.000 1.000 1.000
## sham_rcstndncs 1.000 1.000 1.000
## guilt_racism 1.000 1.000 1.000
## guilt_inequlty 1.000 1.000 1.000
## guilt_treatmnt 1.000 1.000 1.000
## guilt_behavior 1.000 1.000 1.000
## img_shm_dsgrcd 1.000 1.000 1.000
## image_shm_hwsn 1.000 1.000 1.000
## imag_shm_hmltd 1.000 1.000 1.000## lavaan 0.6-7 ended normally after 41 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 80
##
## Used Total
## Number of observations 937 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 128.185 466.827
## Degrees of freedom 41 41
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.280
## Shift parameter 9.182
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 193784.680 53113.355
## Degrees of freedom 55 55
## P-value 0.000 0.000
## Scaling correction factor 3.651
##
## 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 0.048 0.105
## 90 Percent confidence interval - lower 0.038 0.097
## 90 Percent confidence interval - upper 0.057 0.114
## P-value RMSEA <= 0.05 0.644 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.022 0.022
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## MORAL =~
## revsham_ntshmd 0.706 0.016 43.233 0.000 0.706 0.706
## shame_racistmn 0.858 0.010 86.690 0.000 0.858 0.858
## shame_mns2bwht 0.954 0.005 184.806 0.000 0.954 0.954
## sham_rcstndncs 0.912 0.008 118.188 0.000 0.912 0.912
## GUILT =~
## guilt_racism 0.930 0.005 178.120 0.000 0.930 0.930
## guilt_inequlty 0.926 0.005 180.643 0.000 0.926 0.926
## guilt_treatmnt 0.944 0.004 219.907 0.000 0.944 0.944
## guilt_behavior 0.940 0.004 215.743 0.000 0.940 0.940
## IMAGE =~
## img_shm_dsgrcd 0.863 0.010 88.602 0.000 0.863 0.863
## image_shm_hwsn 0.960 0.006 148.547 0.000 0.960 0.960
## imag_shm_hmltd 0.822 0.012 70.499 0.000 0.822 0.822
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## MORAL ~~
## GUILT 0.915 0.007 138.481 0.000 0.915 0.915
## IMAGE 0.779 0.014 55.702 0.000 0.779 0.779
## GUILT ~~
## IMAGE 0.820 0.011 71.319 0.000 0.820 0.820
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revsham_ntshmd 0.000 0.000 0.000
## .shame_racistmn 0.000 0.000 0.000
## .shame_mns2bwht 0.000 0.000 0.000
## .sham_rcstndncs 0.000 0.000 0.000
## .guilt_racism 0.000 0.000 0.000
## .guilt_inequlty 0.000 0.000 0.000
## .guilt_treatmnt 0.000 0.000 0.000
## .guilt_behavior 0.000 0.000 0.000
## .img_shm_dsgrcd 0.000 0.000 0.000
## .image_shm_hwsn 0.000 0.000 0.000
## .imag_shm_hmltd 0.000 0.000 0.000
## MORAL 0.000 0.000 0.000
## GUILT 0.000 0.000 0.000
## IMAGE 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## rvshm_ntshmd|1 -1.419 0.060 -23.606 0.000 -1.419 -1.419
## rvshm_ntshmd|2 -0.851 0.047 -18.165 0.000 -0.851 -0.851
## rvshm_ntshmd|3 -0.540 0.043 -12.499 0.000 -0.540 -0.540
## rvshm_ntshmd|4 0.130 0.041 3.166 0.002 0.130 0.130
## rvshm_ntshmd|5 0.426 0.042 10.057 0.000 0.426 0.426
## rvshm_ntshmd|6 0.939 0.048 19.454 0.000 0.939 0.939
## sham_rcstmn|t1 -1.391 0.059 -23.501 0.000 -1.391 -1.391
## sham_rcstmn|t2 -0.930 0.048 -19.339 0.000 -0.930 -0.930
## sham_rcstmn|t3 -0.696 0.045 -15.535 0.000 -0.696 -0.696
## sham_rcstmn|t4 -0.426 0.042 -10.057 0.000 -0.426 -0.426
## sham_rcstmn|t5 0.079 0.041 1.926 0.054 0.079 0.079
## sham_rcstmn|t6 0.675 0.045 15.159 0.000 0.675 0.675
## shm_mns2bwht|1 -1.146 0.052 -21.864 0.000 -1.146 -1.146
## shm_mns2bwht|2 -0.723 0.045 -16.032 0.000 -0.723 -0.723
## shm_mns2bwht|3 -0.556 0.043 -12.818 0.000 -0.556 -0.556
## shm_mns2bwht|4 -0.258 0.041 -6.230 0.000 -0.258 -0.258
## shm_mns2bwht|5 0.223 0.041 5.383 0.000 0.223 0.223
## shm_mns2bwht|6 0.741 0.045 16.341 0.000 0.741 0.741
## shm_rcstndnc|1 -1.398 0.059 -23.529 0.000 -1.398 -1.398
## shm_rcstndnc|2 -1.048 0.050 -20.842 0.000 -1.048 -1.048
## shm_rcstndnc|3 -0.843 0.047 -18.046 0.000 -0.843 -0.843
## shm_rcstndnc|4 -0.543 0.043 -12.563 0.000 -0.543 -0.543
## shm_rcstndnc|5 -0.039 0.041 -0.947 0.344 -0.039 -0.039
## shm_rcstndnc|6 0.559 0.043 12.882 0.000 0.559 0.559
## guilt_racsm|t1 -0.914 0.048 -19.108 0.000 -0.914 -0.914
## guilt_racsm|t2 -0.377 0.042 -8.957 0.000 -0.377 -0.377
## guilt_racsm|t3 -0.171 0.041 -4.145 0.000 -0.171 -0.171
## guilt_racsm|t4 0.106 0.041 2.579 0.010 0.106 0.106
## guilt_racsm|t5 0.685 0.045 15.347 0.000 0.685 0.685
## guilt_racsm|t6 1.311 0.057 23.113 0.000 1.311 1.311
## guilt_nqlty|t1 -1.194 0.054 -22.288 0.000 -1.194 -1.194
## guilt_nqlty|t2 -0.748 0.045 -16.465 0.000 -0.748 -0.748
## guilt_nqlty|t3 -0.488 0.043 -11.409 0.000 -0.488 -0.488
## guilt_nqlty|t4 -0.225 0.041 -5.448 0.000 -0.225 -0.225
## guilt_nqlty|t5 0.311 0.042 7.465 0.000 0.311 0.311
## guilt_nqlty|t6 0.985 0.049 20.077 0.000 0.985 0.985
## gult_trtmnt|t1 -1.177 0.053 -22.149 0.000 -1.177 -1.177
## gult_trtmnt|t2 -0.751 0.045 -16.526 0.000 -0.751 -0.751
## gult_trtmnt|t3 -0.546 0.043 -12.627 0.000 -0.546 -0.546
## gult_trtmnt|t4 -0.272 0.042 -6.555 0.000 -0.272 -0.272
## gult_trtmnt|t5 0.258 0.041 6.230 0.000 0.258 0.258
## gult_trtmnt|t6 0.851 0.047 18.165 0.000 0.851 0.851
## guilt_behvr|t1 -1.057 0.050 -20.948 0.000 -1.057 -1.057
## guilt_behvr|t2 -0.655 0.044 -14.783 0.000 -0.655 -0.655
## guilt_behvr|t3 -0.438 0.042 -10.315 0.000 -0.438 -0.438
## guilt_behvr|t4 -0.209 0.041 -5.057 0.000 -0.209 -0.209
## guilt_behvr|t5 0.317 0.042 7.595 0.000 0.317 0.317
## guilt_behvr|t6 0.985 0.049 20.077 0.000 0.985 0.985
## img_shm_dsgr|1 -1.256 0.055 -22.765 0.000 -1.256 -1.256
## img_shm_dsgr|2 -0.744 0.045 -16.403 0.000 -0.744 -0.744
## img_shm_dsgr|3 -0.525 0.043 -12.179 0.000 -0.525 -0.525
## img_shm_dsgr|4 -0.111 0.041 -2.710 0.007 -0.111 -0.111
## img_shm_dsgr|5 0.473 0.043 11.088 0.000 0.473 0.473
## img_shm_dsgr|6 1.156 0.053 21.960 0.000 1.156 1.156
## img_shm_hwsn|1 -1.210 0.054 -22.422 0.000 -1.210 -1.210
## img_shm_hwsn|2 -0.720 0.045 -15.970 0.000 -0.720 -0.720
## img_shm_hwsn|3 -0.491 0.043 -11.474 0.000 -0.491 -0.491
## img_shm_hwsn|4 -0.098 0.041 -2.383 0.017 -0.098 -0.098
## img_shm_hwsn|5 0.543 0.043 12.563 0.000 0.543 0.543
## img_shm_hwsn|6 1.233 0.055 22.597 0.000 1.233 1.233
## img_shm_hmlt|1 -1.072 0.051 -21.106 0.000 -1.072 -1.072
## img_shm_hmlt|2 -0.506 0.043 -11.795 0.000 -0.506 -0.506
## img_shm_hmlt|3 -0.214 0.041 -5.188 0.000 -0.214 -0.214
## img_shm_hmlt|4 0.217 0.041 5.253 0.000 0.217 0.217
## img_shm_hmlt|5 0.787 0.046 17.139 0.000 0.787 0.787
## img_shm_hmlt|6 1.419 0.060 23.606 0.000 1.419 1.419
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revsham_ntshmd 0.501 0.501 0.501
## .shame_racistmn 0.264 0.264 0.264
## .shame_mns2bwht 0.090 0.090 0.090
## .sham_rcstndncs 0.167 0.167 0.167
## .guilt_racism 0.135 0.135 0.135
## .guilt_inequlty 0.143 0.143 0.143
## .guilt_treatmnt 0.110 0.110 0.110
## .guilt_behavior 0.117 0.117 0.117
## .img_shm_dsgrcd 0.256 0.256 0.256
## .image_shm_hwsn 0.078 0.078 0.078
## .imag_shm_hmltd 0.324 0.324 0.324
## MORAL 1.000 1.000 1.000
## GUILT 1.000 1.000 1.000
## IMAGE 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revsham_ntshmd 1.000 1.000 1.000
## shame_racistmn 1.000 1.000 1.000
## shame_mns2bwht 1.000 1.000 1.000
## sham_rcstndncs 1.000 1.000 1.000
## guilt_racism 1.000 1.000 1.000
## guilt_inequlty 1.000 1.000 1.000
## guilt_treatmnt 1.000 1.000 1.000
## guilt_behavior 1.000 1.000 1.000
## img_shm_dsgrcd 1.000 1.000 1.000
## image_shm_hwsn 1.000 1.000 1.000
## imag_shm_hmltd 1.000 1.000 1.000## lavaan 0.6-7 ended normally after 124 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 80
##
## Used Total
## Number of observations 937 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 128.185 466.827
## Degrees of freedom 41 41
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.280
## Shift parameter 9.182
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 193784.680 53113.355
## Degrees of freedom 55 55
## P-value 0.000 0.000
## Scaling correction factor 3.651
##
## 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 0.048 0.105
## 90 Percent confidence interval - lower 0.038 0.097
## 90 Percent confidence interval - upper 0.057 0.114
## P-value RMSEA <= 0.05 0.644 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.022 0.022
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## MORAL =~
## revsham_ntshmd 0.255 0.014 18.542 0.000 0.706 0.706
## shame_racistmn 0.310 0.016 19.470 0.000 0.858 0.858
## shame_mns2bwht 0.344 0.019 18.419 0.000 0.954 0.954
## sham_rcstndncs 0.329 0.018 18.607 0.000 0.912 0.912
## GUILT =~
## guilt_racism 0.178 0.030 5.911 0.000 0.930 0.930
## guilt_inequlty 0.177 0.030 5.926 0.000 0.926 0.926
## guilt_treatmnt 0.181 0.031 5.914 0.000 0.944 0.944
## guilt_behavior 0.180 0.030 5.918 0.000 0.940 0.940
## IMAGE =~
## img_shm_dsgrcd 0.474 0.014 34.426 0.000 0.863 0.863
## image_shm_hwsn 0.528 0.017 31.015 0.000 0.960 0.960
## imag_shm_hmltd 0.452 0.013 35.343 0.000 0.822 0.822
## General =~
## MORAL 2.585 0.162 15.989 0.000 0.933 0.933
## GUILT 5.127 0.903 5.681 0.000 0.982 0.982
## IMAGE 1.519 0.068 22.411 0.000 0.835 0.835
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revsham_ntshmd 0.000 0.000 0.000
## .shame_racistmn 0.000 0.000 0.000
## .shame_mns2bwht 0.000 0.000 0.000
## .sham_rcstndncs 0.000 0.000 0.000
## .guilt_racism 0.000 0.000 0.000
## .guilt_inequlty 0.000 0.000 0.000
## .guilt_treatmnt 0.000 0.000 0.000
## .guilt_behavior 0.000 0.000 0.000
## .img_shm_dsgrcd 0.000 0.000 0.000
## .image_shm_hwsn 0.000 0.000 0.000
## .imag_shm_hmltd 0.000 0.000 0.000
## .MORAL 0.000 0.000 0.000
## .GUILT 0.000 0.000 0.000
## .IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## rvshm_ntshmd|1 -1.419 0.060 -23.606 0.000 -1.419 -1.419
## rvshm_ntshmd|2 -0.851 0.047 -18.165 0.000 -0.851 -0.851
## rvshm_ntshmd|3 -0.540 0.043 -12.499 0.000 -0.540 -0.540
## rvshm_ntshmd|4 0.130 0.041 3.166 0.002 0.130 0.130
## rvshm_ntshmd|5 0.426 0.042 10.057 0.000 0.426 0.426
## rvshm_ntshmd|6 0.939 0.048 19.454 0.000 0.939 0.939
## sham_rcstmn|t1 -1.391 0.059 -23.501 0.000 -1.391 -1.391
## sham_rcstmn|t2 -0.930 0.048 -19.339 0.000 -0.930 -0.930
## sham_rcstmn|t3 -0.696 0.045 -15.535 0.000 -0.696 -0.696
## sham_rcstmn|t4 -0.426 0.042 -10.057 0.000 -0.426 -0.426
## sham_rcstmn|t5 0.079 0.041 1.926 0.054 0.079 0.079
## sham_rcstmn|t6 0.675 0.045 15.159 0.000 0.675 0.675
## shm_mns2bwht|1 -1.146 0.052 -21.864 0.000 -1.146 -1.146
## shm_mns2bwht|2 -0.723 0.045 -16.032 0.000 -0.723 -0.723
## shm_mns2bwht|3 -0.556 0.043 -12.818 0.000 -0.556 -0.556
## shm_mns2bwht|4 -0.258 0.041 -6.230 0.000 -0.258 -0.258
## shm_mns2bwht|5 0.223 0.041 5.383 0.000 0.223 0.223
## shm_mns2bwht|6 0.741 0.045 16.341 0.000 0.741 0.741
## shm_rcstndnc|1 -1.398 0.059 -23.529 0.000 -1.398 -1.398
## shm_rcstndnc|2 -1.048 0.050 -20.842 0.000 -1.048 -1.048
## shm_rcstndnc|3 -0.843 0.047 -18.046 0.000 -0.843 -0.843
## shm_rcstndnc|4 -0.543 0.043 -12.563 0.000 -0.543 -0.543
## shm_rcstndnc|5 -0.039 0.041 -0.947 0.344 -0.039 -0.039
## shm_rcstndnc|6 0.559 0.043 12.882 0.000 0.559 0.559
## guilt_racsm|t1 -0.914 0.048 -19.108 0.000 -0.914 -0.914
## guilt_racsm|t2 -0.377 0.042 -8.957 0.000 -0.377 -0.377
## guilt_racsm|t3 -0.171 0.041 -4.145 0.000 -0.171 -0.171
## guilt_racsm|t4 0.106 0.041 2.579 0.010 0.106 0.106
## guilt_racsm|t5 0.685 0.045 15.347 0.000 0.685 0.685
## guilt_racsm|t6 1.311 0.057 23.113 0.000 1.311 1.311
## guilt_nqlty|t1 -1.194 0.054 -22.288 0.000 -1.194 -1.194
## guilt_nqlty|t2 -0.748 0.045 -16.465 0.000 -0.748 -0.748
## guilt_nqlty|t3 -0.488 0.043 -11.409 0.000 -0.488 -0.488
## guilt_nqlty|t4 -0.225 0.041 -5.448 0.000 -0.225 -0.225
## guilt_nqlty|t5 0.311 0.042 7.465 0.000 0.311 0.311
## guilt_nqlty|t6 0.985 0.049 20.077 0.000 0.985 0.985
## gult_trtmnt|t1 -1.177 0.053 -22.149 0.000 -1.177 -1.177
## gult_trtmnt|t2 -0.751 0.045 -16.526 0.000 -0.751 -0.751
## gult_trtmnt|t3 -0.546 0.043 -12.627 0.000 -0.546 -0.546
## gult_trtmnt|t4 -0.272 0.042 -6.555 0.000 -0.272 -0.272
## gult_trtmnt|t5 0.258 0.041 6.230 0.000 0.258 0.258
## gult_trtmnt|t6 0.851 0.047 18.165 0.000 0.851 0.851
## guilt_behvr|t1 -1.057 0.050 -20.948 0.000 -1.057 -1.057
## guilt_behvr|t2 -0.655 0.044 -14.783 0.000 -0.655 -0.655
## guilt_behvr|t3 -0.438 0.042 -10.315 0.000 -0.438 -0.438
## guilt_behvr|t4 -0.209 0.041 -5.057 0.000 -0.209 -0.209
## guilt_behvr|t5 0.317 0.042 7.595 0.000 0.317 0.317
## guilt_behvr|t6 0.985 0.049 20.077 0.000 0.985 0.985
## img_shm_dsgr|1 -1.256 0.055 -22.765 0.000 -1.256 -1.256
## img_shm_dsgr|2 -0.744 0.045 -16.403 0.000 -0.744 -0.744
## img_shm_dsgr|3 -0.525 0.043 -12.179 0.000 -0.525 -0.525
## img_shm_dsgr|4 -0.111 0.041 -2.710 0.007 -0.111 -0.111
## img_shm_dsgr|5 0.473 0.043 11.088 0.000 0.473 0.473
## img_shm_dsgr|6 1.156 0.053 21.960 0.000 1.156 1.156
## img_shm_hwsn|1 -1.210 0.054 -22.422 0.000 -1.210 -1.210
## img_shm_hwsn|2 -0.720 0.045 -15.970 0.000 -0.720 -0.720
## img_shm_hwsn|3 -0.491 0.043 -11.474 0.000 -0.491 -0.491
## img_shm_hwsn|4 -0.098 0.041 -2.383 0.017 -0.098 -0.098
## img_shm_hwsn|5 0.543 0.043 12.563 0.000 0.543 0.543
## img_shm_hwsn|6 1.233 0.055 22.597 0.000 1.233 1.233
## img_shm_hmlt|1 -1.072 0.051 -21.106 0.000 -1.072 -1.072
## img_shm_hmlt|2 -0.506 0.043 -11.795 0.000 -0.506 -0.506
## img_shm_hmlt|3 -0.214 0.041 -5.188 0.000 -0.214 -0.214
## img_shm_hmlt|4 0.217 0.041 5.253 0.000 0.217 0.217
## img_shm_hmlt|5 0.787 0.046 17.139 0.000 0.787 0.787
## img_shm_hmlt|6 1.419 0.060 23.606 0.000 1.419 1.419
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revsham_ntshmd 0.501 0.501 0.501
## .shame_racistmn 0.264 0.264 0.264
## .shame_mns2bwht 0.090 0.090 0.090
## .sham_rcstndncs 0.167 0.167 0.167
## .guilt_racism 0.135 0.135 0.135
## .guilt_inequlty 0.143 0.143 0.143
## .guilt_treatmnt 0.110 0.110 0.110
## .guilt_behavior 0.117 0.117 0.117
## .img_shm_dsgrcd 0.256 0.256 0.256
## .image_shm_hwsn 0.078 0.078 0.078
## .imag_shm_hmltd 0.324 0.324 0.324
## .MORAL 1.000 0.130 0.130
## .GUILT 1.000 0.037 0.037
## .IMAGE 1.000 0.302 0.302
## General 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revsham_ntshmd 1.000 1.000 1.000
## shame_racistmn 1.000 1.000 1.000
## shame_mns2bwht 1.000 1.000 1.000
## sham_rcstndncs 1.000 1.000 1.000
## guilt_racism 1.000 1.000 1.000
## guilt_inequlty 1.000 1.000 1.000
## guilt_treatmnt 1.000 1.000 1.000
## guilt_behavior 1.000 1.000 1.000
## img_shm_dsgrcd 1.000 1.000 1.000
## image_shm_hwsn 1.000 1.000 1.000
## imag_shm_hmltd 1.000 1.000 1.000## lavaan 0.6-7 ended normally after 52 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 88
##
## Used Total
## Number of observations 937 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 50.815 226.125
## Degrees of freedom 33 33
## P-value (Chi-square) 0.025 0.000
## Scaling correction factor 0.232
## Shift parameter 6.922
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 193784.680 53113.355
## Degrees of freedom 55 55
## P-value 0.000 0.000
## Scaling correction factor 3.651
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 0.996
## Tucker-Lewis Index (TLI) 1.000 0.994
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.024 0.079
## 90 Percent confidence interval - lower 0.009 0.069
## 90 Percent confidence interval - upper 0.037 0.089
## P-value RMSEA <= 0.05 1.000 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.016 0.016
##
## 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
## MORAL =~
## revsham_ntshmd 0.320 0.022 14.280 0.000 0.320 0.320
## shame_racistmn 0.399 0.026 15.539 0.000 0.399 0.399
## shame_mns2bwht 0.365 0.020 18.418 0.000 0.365 0.365
## sham_rcstndncs 0.225 0.021 10.513 0.000 0.225 0.225
## GUILT =~
## guilt_racism 0.011 0.025 0.424 0.671 0.011 0.011
## guilt_inequlty 0.175 0.032 5.548 0.000 0.175 0.175
## guilt_treatmnt 0.414 0.046 9.082 0.000 0.414 0.414
## guilt_behavior 0.122 0.027 4.549 0.000 0.122 0.122
## IMAGE =~
## img_shm_dsgrcd 0.480 0.019 24.720 0.000 0.480 0.480
## image_shm_hwsn 0.470 0.017 27.033 0.000 0.470 0.470
## imag_shm_hmltd 0.532 0.020 26.199 0.000 0.532 0.532
## General =~
## revsham_ntshmd 0.648 0.018 35.329 0.000 0.648 0.648
## shame_racistmn 0.786 0.014 54.985 0.000 0.786 0.786
## shame_mns2bwht 0.885 0.009 104.022 0.000 0.885 0.885
## sham_rcstndncs 0.864 0.010 84.596 0.000 0.864 0.864
## guilt_racism 0.937 0.006 154.928 0.000 0.937 0.937
## guilt_inequlty 0.903 0.008 116.985 0.000 0.903 0.903
## guilt_treatmnt 0.909 0.009 106.606 0.000 0.909 0.909
## guilt_behavior 0.927 0.006 145.498 0.000 0.927 0.927
## img_shm_dsgrcd 0.722 0.016 46.379 0.000 0.722 0.722
## image_shm_hwsn 0.808 0.012 68.936 0.000 0.808 0.808
## imag_shm_hmltd 0.672 0.018 37.713 0.000 0.672 0.672
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## MORAL ~~
## GUILT 0.000 0.000 0.000
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
## GUILT ~~
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
## IMAGE ~~
## General 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revsham_ntshmd 0.000 0.000 0.000
## .shame_racistmn 0.000 0.000 0.000
## .shame_mns2bwht 0.000 0.000 0.000
## .sham_rcstndncs 0.000 0.000 0.000
## .guilt_racism 0.000 0.000 0.000
## .guilt_inequlty 0.000 0.000 0.000
## .guilt_treatmnt 0.000 0.000 0.000
## .guilt_behavior 0.000 0.000 0.000
## .img_shm_dsgrcd 0.000 0.000 0.000
## .image_shm_hwsn 0.000 0.000 0.000
## .imag_shm_hmltd 0.000 0.000 0.000
## MORAL 0.000 0.000 0.000
## GUILT 0.000 0.000 0.000
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## rvshm_ntshmd|1 -1.419 0.060 -23.606 0.000 -1.419 -1.419
## rvshm_ntshmd|2 -0.851 0.047 -18.165 0.000 -0.851 -0.851
## rvshm_ntshmd|3 -0.540 0.043 -12.499 0.000 -0.540 -0.540
## rvshm_ntshmd|4 0.130 0.041 3.166 0.002 0.130 0.130
## rvshm_ntshmd|5 0.426 0.042 10.057 0.000 0.426 0.426
## rvshm_ntshmd|6 0.939 0.048 19.454 0.000 0.939 0.939
## sham_rcstmn|t1 -1.391 0.059 -23.501 0.000 -1.391 -1.391
## sham_rcstmn|t2 -0.930 0.048 -19.339 0.000 -0.930 -0.930
## sham_rcstmn|t3 -0.696 0.045 -15.535 0.000 -0.696 -0.696
## sham_rcstmn|t4 -0.426 0.042 -10.057 0.000 -0.426 -0.426
## sham_rcstmn|t5 0.079 0.041 1.926 0.054 0.079 0.079
## sham_rcstmn|t6 0.675 0.045 15.159 0.000 0.675 0.675
## shm_mns2bwht|1 -1.146 0.052 -21.864 0.000 -1.146 -1.146
## shm_mns2bwht|2 -0.723 0.045 -16.032 0.000 -0.723 -0.723
## shm_mns2bwht|3 -0.556 0.043 -12.818 0.000 -0.556 -0.556
## shm_mns2bwht|4 -0.258 0.041 -6.230 0.000 -0.258 -0.258
## shm_mns2bwht|5 0.223 0.041 5.383 0.000 0.223 0.223
## shm_mns2bwht|6 0.741 0.045 16.341 0.000 0.741 0.741
## shm_rcstndnc|1 -1.398 0.059 -23.529 0.000 -1.398 -1.398
## shm_rcstndnc|2 -1.048 0.050 -20.842 0.000 -1.048 -1.048
## shm_rcstndnc|3 -0.843 0.047 -18.046 0.000 -0.843 -0.843
## shm_rcstndnc|4 -0.543 0.043 -12.563 0.000 -0.543 -0.543
## shm_rcstndnc|5 -0.039 0.041 -0.947 0.344 -0.039 -0.039
## shm_rcstndnc|6 0.559 0.043 12.882 0.000 0.559 0.559
## guilt_racsm|t1 -0.914 0.048 -19.108 0.000 -0.914 -0.914
## guilt_racsm|t2 -0.377 0.042 -8.957 0.000 -0.377 -0.377
## guilt_racsm|t3 -0.171 0.041 -4.145 0.000 -0.171 -0.171
## guilt_racsm|t4 0.106 0.041 2.579 0.010 0.106 0.106
## guilt_racsm|t5 0.685 0.045 15.347 0.000 0.685 0.685
## guilt_racsm|t6 1.311 0.057 23.113 0.000 1.311 1.311
## guilt_nqlty|t1 -1.194 0.054 -22.288 0.000 -1.194 -1.194
## guilt_nqlty|t2 -0.748 0.045 -16.465 0.000 -0.748 -0.748
## guilt_nqlty|t3 -0.488 0.043 -11.409 0.000 -0.488 -0.488
## guilt_nqlty|t4 -0.225 0.041 -5.448 0.000 -0.225 -0.225
## guilt_nqlty|t5 0.311 0.042 7.465 0.000 0.311 0.311
## guilt_nqlty|t6 0.985 0.049 20.077 0.000 0.985 0.985
## gult_trtmnt|t1 -1.177 0.053 -22.149 0.000 -1.177 -1.177
## gult_trtmnt|t2 -0.751 0.045 -16.526 0.000 -0.751 -0.751
## gult_trtmnt|t3 -0.546 0.043 -12.627 0.000 -0.546 -0.546
## gult_trtmnt|t4 -0.272 0.042 -6.555 0.000 -0.272 -0.272
## gult_trtmnt|t5 0.258 0.041 6.230 0.000 0.258 0.258
## gult_trtmnt|t6 0.851 0.047 18.165 0.000 0.851 0.851
## guilt_behvr|t1 -1.057 0.050 -20.948 0.000 -1.057 -1.057
## guilt_behvr|t2 -0.655 0.044 -14.783 0.000 -0.655 -0.655
## guilt_behvr|t3 -0.438 0.042 -10.315 0.000 -0.438 -0.438
## guilt_behvr|t4 -0.209 0.041 -5.057 0.000 -0.209 -0.209
## guilt_behvr|t5 0.317 0.042 7.595 0.000 0.317 0.317
## guilt_behvr|t6 0.985 0.049 20.077 0.000 0.985 0.985
## img_shm_dsgr|1 -1.256 0.055 -22.765 0.000 -1.256 -1.256
## img_shm_dsgr|2 -0.744 0.045 -16.403 0.000 -0.744 -0.744
## img_shm_dsgr|3 -0.525 0.043 -12.179 0.000 -0.525 -0.525
## img_shm_dsgr|4 -0.111 0.041 -2.710 0.007 -0.111 -0.111
## img_shm_dsgr|5 0.473 0.043 11.088 0.000 0.473 0.473
## img_shm_dsgr|6 1.156 0.053 21.960 0.000 1.156 1.156
## img_shm_hwsn|1 -1.210 0.054 -22.422 0.000 -1.210 -1.210
## img_shm_hwsn|2 -0.720 0.045 -15.970 0.000 -0.720 -0.720
## img_shm_hwsn|3 -0.491 0.043 -11.474 0.000 -0.491 -0.491
## img_shm_hwsn|4 -0.098 0.041 -2.383 0.017 -0.098 -0.098
## img_shm_hwsn|5 0.543 0.043 12.563 0.000 0.543 0.543
## img_shm_hwsn|6 1.233 0.055 22.597 0.000 1.233 1.233
## img_shm_hmlt|1 -1.072 0.051 -21.106 0.000 -1.072 -1.072
## img_shm_hmlt|2 -0.506 0.043 -11.795 0.000 -0.506 -0.506
## img_shm_hmlt|3 -0.214 0.041 -5.188 0.000 -0.214 -0.214
## img_shm_hmlt|4 0.217 0.041 5.253 0.000 0.217 0.217
## img_shm_hmlt|5 0.787 0.046 17.139 0.000 0.787 0.787
## img_shm_hmlt|6 1.419 0.060 23.606 0.000 1.419 1.419
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revsham_ntshmd 0.477 0.477 0.477
## .shame_racistmn 0.222 0.222 0.222
## .shame_mns2bwht 0.083 0.083 0.083
## .sham_rcstndncs 0.203 0.203 0.203
## .guilt_racism 0.122 0.122 0.122
## .guilt_inequlty 0.154 0.154 0.154
## .guilt_treatmnt 0.002 0.002 0.002
## .guilt_behavior 0.126 0.126 0.126
## .img_shm_dsgrcd 0.248 0.248 0.248
## .image_shm_hwsn 0.127 0.127 0.127
## .imag_shm_hmltd 0.265 0.265 0.265
## MORAL 1.000 1.000 1.000
## GUILT 1.000 1.000 1.000
## IMAGE 1.000 1.000 1.000
## General 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revsham_ntshmd 1.000 1.000 1.000
## shame_racistmn 1.000 1.000 1.000
## shame_mns2bwht 1.000 1.000 1.000
## sham_rcstndncs 1.000 1.000 1.000
## guilt_racism 1.000 1.000 1.000
## guilt_inequlty 1.000 1.000 1.000
## guilt_treatmnt 1.000 1.000 1.000
## guilt_behavior 1.000 1.000 1.000
## img_shm_dsgrcd 1.000 1.000 1.000
## image_shm_hwsn 1.000 1.000 1.000
## imag_shm_hmltd 1.000 1.000 1.000In the bifactor model, \(\omega_t\) is 0.977, \(\omega_h\) is 0.927, relative \(\omega\) is 0.949, the factor correlation is 0.963, H is 0.972, PUC is 0.727, FDI is 0.986, 68.8% of the total varaince is general, 84.4% of the common variance is general and 18.5% of the total variance is unique. For the MORAL, GUILT and IMAGE factors, \(\omega_{hs}\), H, FDI, total variance explained and common variance explained are 0.134/0.338/0.581/0.040/0.050, 0.036/0.202/0.450/0.020/0.024, 0.286/0.494/0.703/0.067/0.082.
ZGBFPB <- '
MORAL =~ revshame_notashamed + shame_racistmean + shame_means2bewhite + shame_racistendencies
GUILT =~ guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior
IMAGE =~ image_shame_disgraced + image_shame_howseen + image_shame_humiliated
General =~ revshame_notashamed + shame_racistmean + shame_means2bewhite + shame_racistendencies + guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior + image_shame_disgraced + image_shame_howseen + image_shame_humiliated
problack_meanZ ~ MORAL + GUILT + IMAGE + General'
ZGRunBFPB <- sem(ZGBFPB, data = data, orthogonal = T, std.lv = T, ordered = c("shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))
summary(ZGRunBFPB, stand = T, fit = T, ci = T)## lavaan 0.6-7 ended normally after 61 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 94
##
## Used Total
## Number of observations 937 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 54.487 264.004
## Degrees of freedom 40 40
## P-value (Chi-square) 0.063 0.000
## Scaling correction factor 0.214
## Shift parameter 9.618
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 196506.234 51153.692
## Degrees of freedom 66 66
## P-value 0.000 0.000
## Scaling correction factor 3.845
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 0.996
## Tucker-Lewis Index (TLI) 1.000 0.993
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.020 0.077
## 90 Percent confidence interval - lower 0.000 0.069
## 90 Percent confidence interval - upper 0.032 0.086
## P-value RMSEA <= 0.05 1.000 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.017 0.017
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## MORAL =~
## revsham_ntshmd 0.316 0.022 14.115 0.000 0.273 0.360
## shame_racistmn 0.407 0.025 16.003 0.000 0.358 0.457
## shame_mns2bwht 0.359 0.020 18.250 0.000 0.321 0.398
## sham_rcstndncs 0.224 0.022 10.412 0.000 0.182 0.266
## GUILT =~
## guilt_racism 0.012 0.026 0.462 0.644 -0.038 0.062
## guilt_inequlty 0.177 0.032 5.605 0.000 0.115 0.238
## guilt_treatmnt 0.410 0.044 9.274 0.000 0.323 0.497
## guilt_behavior 0.124 0.027 4.603 0.000 0.071 0.177
## IMAGE =~
## img_shm_dsgrcd 0.478 0.019 24.669 0.000 0.440 0.516
## image_shm_hwsn 0.470 0.017 27.035 0.000 0.436 0.504
## imag_shm_hmltd 0.534 0.020 26.461 0.000 0.494 0.573
## General =~
## revsham_ntshmd 0.649 0.018 35.315 0.000 0.613 0.685
## shame_racistmn 0.787 0.014 54.930 0.000 0.759 0.815
## shame_mns2bwht 0.885 0.009 103.899 0.000 0.869 0.902
## sham_rcstndncs 0.864 0.010 84.491 0.000 0.844 0.884
## guilt_racism 0.936 0.006 153.891 0.000 0.925 0.948
## guilt_inequlty 0.903 0.008 116.627 0.000 0.888 0.918
## guilt_treatmnt 0.909 0.009 106.254 0.000 0.892 0.926
## guilt_behavior 0.927 0.006 144.779 0.000 0.914 0.939
## img_shm_dsgrcd 0.723 0.016 46.497 0.000 0.692 0.753
## image_shm_hwsn 0.808 0.012 68.796 0.000 0.785 0.831
## imag_shm_hmltd 0.671 0.018 37.655 0.000 0.636 0.706
## Std.lv Std.all
##
## 0.316 0.316
## 0.407 0.407
## 0.359 0.359
## 0.224 0.224
##
## 0.012 0.012
## 0.177 0.177
## 0.410 0.410
## 0.124 0.124
##
## 0.478 0.478
## 0.470 0.470
## 0.534 0.534
##
## 0.649 0.649
## 0.787 0.787
## 0.885 0.885
## 0.864 0.864
## 0.936 0.936
## 0.903 0.903
## 0.909 0.909
## 0.927 0.927
## 0.723 0.723
## 0.808 0.808
## 0.671 0.671
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## problack_meanZ ~
## MORAL 0.234 0.032 7.362 0.000 0.171 0.296
## GUILT 0.043 0.032 1.317 0.188 -0.021 0.106
## IMAGE -0.156 0.026 -6.092 0.000 -0.206 -0.106
## General 0.714 0.040 18.039 0.000 0.636 0.791
## Std.lv Std.all
##
## 0.234 0.233
## 0.043 0.043
## -0.156 -0.155
## 0.714 0.711
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## MORAL ~~
## GUILT 0.000 0.000 0.000
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
## GUILT ~~
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
## IMAGE ~~
## General 0.000 0.000 0.000
## Std.lv Std.all
##
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## 0.000 0.000
## 0.000 0.000
##
## 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .revsham_ntshmd 0.000 0.000 0.000
## .shame_racistmn 0.000 0.000 0.000
## .shame_mns2bwht 0.000 0.000 0.000
## .sham_rcstndncs 0.000 0.000 0.000
## .guilt_racism 0.000 0.000 0.000
## .guilt_inequlty 0.000 0.000 0.000
## .guilt_treatmnt 0.000 0.000 0.000
## .guilt_behavior 0.000 0.000 0.000
## .img_shm_dsgrcd 0.000 0.000 0.000
## .image_shm_hwsn 0.000 0.000 0.000
## .imag_shm_hmltd 0.000 0.000 0.000
## .problack_meanZ -0.014 0.033 -0.409 0.682 -0.079 0.052
## MORAL 0.000 0.000 0.000
## GUILT 0.000 0.000 0.000
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
## Std.lv Std.all
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## -0.014 -0.014
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## rvshm_ntshmd|1 -1.419 0.060 -23.606 0.000 -1.537 -1.301
## rvshm_ntshmd|2 -0.851 0.047 -18.165 0.000 -0.943 -0.759
## rvshm_ntshmd|3 -0.540 0.043 -12.499 0.000 -0.625 -0.455
## rvshm_ntshmd|4 0.130 0.041 3.166 0.002 0.050 0.211
## rvshm_ntshmd|5 0.426 0.042 10.057 0.000 0.343 0.509
## rvshm_ntshmd|6 0.939 0.048 19.454 0.000 0.844 1.033
## sham_rcstmn|t1 -1.391 0.059 -23.501 0.000 -1.507 -1.275
## sham_rcstmn|t2 -0.930 0.048 -19.339 0.000 -1.025 -0.836
## sham_rcstmn|t3 -0.696 0.045 -15.535 0.000 -0.783 -0.608
## sham_rcstmn|t4 -0.426 0.042 -10.057 0.000 -0.509 -0.343
## sham_rcstmn|t5 0.079 0.041 1.926 0.054 -0.001 0.159
## sham_rcstmn|t6 0.675 0.045 15.159 0.000 0.588 0.763
## shm_mns2bwht|1 -1.146 0.052 -21.864 0.000 -1.249 -1.043
## shm_mns2bwht|2 -0.723 0.045 -16.032 0.000 -0.812 -0.635
## shm_mns2bwht|3 -0.556 0.043 -12.818 0.000 -0.641 -0.471
## shm_mns2bwht|4 -0.258 0.041 -6.230 0.000 -0.340 -0.177
## shm_mns2bwht|5 0.223 0.041 5.383 0.000 0.142 0.304
## shm_mns2bwht|6 0.741 0.045 16.341 0.000 0.652 0.829
## shm_rcstndnc|1 -1.398 0.059 -23.529 0.000 -1.514 -1.281
## shm_rcstndnc|2 -1.048 0.050 -20.842 0.000 -1.147 -0.950
## shm_rcstndnc|3 -0.843 0.047 -18.046 0.000 -0.935 -0.752
## shm_rcstndnc|4 -0.543 0.043 -12.563 0.000 -0.628 -0.458
## shm_rcstndnc|5 -0.039 0.041 -0.947 0.344 -0.119 0.042
## shm_rcstndnc|6 0.559 0.043 12.882 0.000 0.474 0.644
## guilt_racsm|t1 -0.914 0.048 -19.108 0.000 -1.008 -0.820
## guilt_racsm|t2 -0.377 0.042 -8.957 0.000 -0.459 -0.294
## guilt_racsm|t3 -0.171 0.041 -4.145 0.000 -0.251 -0.090
## guilt_racsm|t4 0.106 0.041 2.579 0.010 0.025 0.186
## guilt_racsm|t5 0.685 0.045 15.347 0.000 0.598 0.773
## guilt_racsm|t6 1.311 0.057 23.113 0.000 1.200 1.422
## guilt_nqlty|t1 -1.194 0.054 -22.288 0.000 -1.299 -1.089
## guilt_nqlty|t2 -0.748 0.045 -16.465 0.000 -0.837 -0.659
## guilt_nqlty|t3 -0.488 0.043 -11.409 0.000 -0.572 -0.404
## guilt_nqlty|t4 -0.225 0.041 -5.448 0.000 -0.306 -0.144
## guilt_nqlty|t5 0.311 0.042 7.465 0.000 0.230 0.393
## guilt_nqlty|t6 0.985 0.049 20.077 0.000 0.889 1.082
## gult_trtmnt|t1 -1.177 0.053 -22.149 0.000 -1.282 -1.073
## gult_trtmnt|t2 -0.751 0.045 -16.526 0.000 -0.840 -0.662
## gult_trtmnt|t3 -0.546 0.043 -12.627 0.000 -0.631 -0.462
## gult_trtmnt|t4 -0.272 0.042 -6.555 0.000 -0.354 -0.191
## gult_trtmnt|t5 0.258 0.041 6.230 0.000 0.177 0.340
## gult_trtmnt|t6 0.851 0.047 18.165 0.000 0.759 0.943
## guilt_behvr|t1 -1.057 0.050 -20.948 0.000 -1.156 -0.959
## guilt_behvr|t2 -0.655 0.044 -14.783 0.000 -0.742 -0.568
## guilt_behvr|t3 -0.438 0.042 -10.315 0.000 -0.521 -0.354
## guilt_behvr|t4 -0.209 0.041 -5.057 0.000 -0.290 -0.128
## guilt_behvr|t5 0.317 0.042 7.595 0.000 0.235 0.399
## guilt_behvr|t6 0.985 0.049 20.077 0.000 0.889 1.082
## img_shm_dsgr|1 -1.256 0.055 -22.765 0.000 -1.364 -1.148
## img_shm_dsgr|2 -0.744 0.045 -16.403 0.000 -0.833 -0.655
## img_shm_dsgr|3 -0.525 0.043 -12.179 0.000 -0.609 -0.440
## img_shm_dsgr|4 -0.111 0.041 -2.710 0.007 -0.192 -0.031
## img_shm_dsgr|5 0.473 0.043 11.088 0.000 0.390 0.557
## img_shm_dsgr|6 1.156 0.053 21.960 0.000 1.053 1.259
## img_shm_hwsn|1 -1.210 0.054 -22.422 0.000 -1.316 -1.104
## img_shm_hwsn|2 -0.720 0.045 -15.970 0.000 -0.808 -0.631
## img_shm_hwsn|3 -0.491 0.043 -11.474 0.000 -0.575 -0.407
## img_shm_hwsn|4 -0.098 0.041 -2.383 0.017 -0.178 -0.017
## img_shm_hwsn|5 0.543 0.043 12.563 0.000 0.458 0.628
## img_shm_hwsn|6 1.233 0.055 22.597 0.000 1.126 1.340
## img_shm_hmlt|1 -1.072 0.051 -21.106 0.000 -1.171 -0.972
## img_shm_hmlt|2 -0.506 0.043 -11.795 0.000 -0.591 -0.422
## img_shm_hmlt|3 -0.214 0.041 -5.188 0.000 -0.295 -0.133
## img_shm_hmlt|4 0.217 0.041 5.253 0.000 0.136 0.298
## img_shm_hmlt|5 0.787 0.046 17.139 0.000 0.697 0.877
## img_shm_hmlt|6 1.419 0.060 23.606 0.000 1.301 1.537
## Std.lv Std.all
## -1.419 -1.419
## -0.851 -0.851
## -0.540 -0.540
## 0.130 0.130
## 0.426 0.426
## 0.939 0.939
## -1.391 -1.391
## -0.930 -0.930
## -0.696 -0.696
## -0.426 -0.426
## 0.079 0.079
## 0.675 0.675
## -1.146 -1.146
## -0.723 -0.723
## -0.556 -0.556
## -0.258 -0.258
## 0.223 0.223
## 0.741 0.741
## -1.398 -1.398
## -1.048 -1.048
## -0.843 -0.843
## -0.543 -0.543
## -0.039 -0.039
## 0.559 0.559
## -0.914 -0.914
## -0.377 -0.377
## -0.171 -0.171
## 0.106 0.106
## 0.685 0.685
## 1.311 1.311
## -1.194 -1.194
## -0.748 -0.748
## -0.488 -0.488
## -0.225 -0.225
## 0.311 0.311
## 0.985 0.985
## -1.177 -1.177
## -0.751 -0.751
## -0.546 -0.546
## -0.272 -0.272
## 0.258 0.258
## 0.851 0.851
## -1.057 -1.057
## -0.655 -0.655
## -0.438 -0.438
## -0.209 -0.209
## 0.317 0.317
## 0.985 0.985
## -1.256 -1.256
## -0.744 -0.744
## -0.525 -0.525
## -0.111 -0.111
## 0.473 0.473
## 1.156 1.156
## -1.210 -1.210
## -0.720 -0.720
## -0.491 -0.491
## -0.098 -0.098
## 0.543 0.543
## 1.233 1.233
## -1.072 -1.072
## -0.506 -0.506
## -0.214 -0.214
## 0.217 0.217
## 0.787 0.787
## 1.419 1.419
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .revsham_ntshmd 0.479 0.479 0.479
## .shame_racistmn 0.215 0.215 0.215
## .shame_mns2bwht 0.087 0.087 0.087
## .sham_rcstndncs 0.204 0.204 0.204
## .guilt_racism 0.123 0.123 0.123
## .guilt_inequlty 0.153 0.153 0.153
## .guilt_treatmnt 0.006 0.006 0.006
## .guilt_behavior 0.126 0.126 0.126
## .img_shm_dsgrcd 0.249 0.249 0.249
## .image_shm_hwsn 0.127 0.127 0.127
## .imag_shm_hmltd 0.264 0.264 0.264
## .problack_meanZ 0.418 0.022 18.753 0.000 0.374 0.461
## MORAL 1.000 1.000 1.000
## GUILT 1.000 1.000 1.000
## IMAGE 1.000 1.000 1.000
## General 1.000 1.000 1.000
## Std.lv Std.all
## 0.479 0.479
## 0.215 0.215
## 0.087 0.087
## 0.204 0.204
## 0.123 0.123
## 0.153 0.153
## 0.006 0.006
## 0.126 0.126
## 0.249 0.249
## 0.127 0.127
## 0.264 0.264
## 0.418 0.414
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## revsham_ntshmd 1.000 1.000 1.000
## shame_racistmn 1.000 1.000 1.000
## shame_mns2bwht 1.000 1.000 1.000
## sham_rcstndncs 1.000 1.000 1.000
## guilt_racism 1.000 1.000 1.000
## guilt_inequlty 1.000 1.000 1.000
## guilt_treatmnt 1.000 1.000 1.000
## guilt_behavior 1.000 1.000 1.000
## img_shm_dsgrcd 1.000 1.000 1.000
## image_shm_hwsn 1.000 1.000 1.000
## imag_shm_hmltd 1.000 1.000 1.000
## Std.lv Std.all
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000ZGBFPBO <- '
MORAL =~ revshame_notashamed + shame_racistmean + shame_means2bewhite + shame_racistendencies
GUILT =~ guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior
IMAGE =~ image_shame_disgraced + image_shame_howseen + image_shame_humiliated
General =~ revshame_notashamed + shame_racistmean + shame_means2bewhite + shame_racistendencies + guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior + image_shame_disgraced + image_shame_howseen + image_shame_humiliated
problack_meanZ ~ MORAL + GUILT + IMAGE
problack_meanZ ~~ 0*problack_meanZ'
ZGRunBFPBO <- sem(ZGBFPBO, data = data, orthogonal = T, std.lv = T, ordered = c("shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))
summary(ZGRunBFPBO, stand = T, fit = T, ci = T)## lavaan 0.6-7 ended normally after 47 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 92
##
## Used Total
## Number of observations 937 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 1075.071 1241.542
## Degrees of freedom 42 42
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.886
## Shift parameter 27.692
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 196506.234 51153.692
## Degrees of freedom 66 66
## P-value 0.000 0.000
## Scaling correction factor 3.845
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.995 0.977
## Tucker-Lewis Index (TLI) 0.992 0.963
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.162 0.175
## 90 Percent confidence interval - lower 0.154 0.166
## 90 Percent confidence interval - upper 0.171 0.183
## 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 0.155 0.155
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## MORAL =~
## revsham_ntshmd 0.383 0.018 21.555 0.000 0.348 0.418
## shame_racistmn 0.451 0.018 24.478 0.000 0.415 0.487
## shame_mns2bwht 0.360 0.017 21.324 0.000 0.327 0.393
## sham_rcstndncs 0.275 0.018 14.912 0.000 0.239 0.311
## GUILT =~
## guilt_racism 0.251 0.020 12.525 0.000 0.212 0.291
## guilt_inequlty 0.369 0.016 22.946 0.000 0.337 0.400
## guilt_treatmnt 0.390 0.015 25.271 0.000 0.359 0.420
## guilt_behavior 0.311 0.017 17.790 0.000 0.277 0.345
## IMAGE =~
## img_shm_dsgrcd 0.479 0.019 25.812 0.000 0.442 0.515
## image_shm_hwsn 0.462 0.017 26.541 0.000 0.428 0.497
## imag_shm_hmltd 0.516 0.019 26.544 0.000 0.478 0.554
## General =~
## revsham_ntshmd 0.644 0.018 35.934 0.000 0.609 0.679
## shame_racistmn 0.782 0.014 54.747 0.000 0.754 0.810
## shame_mns2bwht 0.896 0.009 98.998 0.000 0.878 0.914
## sham_rcstndncs 0.869 0.010 83.284 0.000 0.849 0.890
## guilt_racism 0.899 0.007 127.314 0.000 0.885 0.913
## guilt_inequlty 0.862 0.008 106.374 0.000 0.846 0.878
## guilt_treatmnt 0.875 0.008 110.697 0.000 0.859 0.890
## guilt_behavior 0.891 0.007 123.694 0.000 0.877 0.906
## img_shm_dsgrcd 0.732 0.016 46.085 0.000 0.701 0.763
## image_shm_hwsn 0.822 0.012 67.814 0.000 0.799 0.846
## imag_shm_hmltd 0.683 0.018 37.677 0.000 0.648 0.719
## Std.lv Std.all
##
## 0.383 0.383
## 0.451 0.451
## 0.360 0.360
## 0.275 0.275
##
## 0.251 0.251
## 0.369 0.369
## 0.390 0.390
## 0.311 0.311
##
## 0.479 0.479
## 0.462 0.462
## 0.516 0.516
##
## 0.644 0.644
## 0.782 0.782
## 0.896 0.896
## 0.869 0.869
## 0.899 0.899
## 0.862 0.862
## 0.875 0.875
## 0.891 0.891
## 0.732 0.732
## 0.822 0.822
## 0.683 0.683
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## problack_meanZ ~
## MORAL 0.872 0.048 18.107 0.000 0.778 0.966
## GUILT 0.900 0.043 21.138 0.000 0.816 0.983
## IMAGE 0.544 0.059 9.254 0.000 0.429 0.659
## Std.lv Std.all
##
## 0.872 0.638
## 0.900 0.659
## 0.544 0.398
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## MORAL ~~
## GUILT 0.000 0.000 0.000
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
## GUILT ~~
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
## IMAGE ~~
## General 0.000 0.000 0.000
## Std.lv Std.all
##
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## 0.000 0.000
## 0.000 0.000
##
## 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .revsham_ntshmd 0.000 0.000 0.000
## .shame_racistmn 0.000 0.000 0.000
## .shame_mns2bwht 0.000 0.000 0.000
## .sham_rcstndncs 0.000 0.000 0.000
## .guilt_racism 0.000 0.000 0.000
## .guilt_inequlty 0.000 0.000 0.000
## .guilt_treatmnt 0.000 0.000 0.000
## .guilt_behavior 0.000 0.000 0.000
## .img_shm_dsgrcd 0.000 0.000 0.000
## .image_shm_hwsn 0.000 0.000 0.000
## .imag_shm_hmltd 0.000 0.000 0.000
## .problack_meanZ -0.014 0.033 -0.409 0.682 -0.079 0.052
## MORAL 0.000 0.000 0.000
## GUILT 0.000 0.000 0.000
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
## Std.lv Std.all
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## -0.014 -0.010
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## rvshm_ntshmd|1 -1.419 0.060 -23.606 0.000 -1.537 -1.301
## rvshm_ntshmd|2 -0.851 0.047 -18.165 0.000 -0.943 -0.759
## rvshm_ntshmd|3 -0.540 0.043 -12.499 0.000 -0.625 -0.455
## rvshm_ntshmd|4 0.130 0.041 3.166 0.002 0.050 0.211
## rvshm_ntshmd|5 0.426 0.042 10.057 0.000 0.343 0.509
## rvshm_ntshmd|6 0.939 0.048 19.454 0.000 0.844 1.033
## sham_rcstmn|t1 -1.391 0.059 -23.501 0.000 -1.507 -1.275
## sham_rcstmn|t2 -0.930 0.048 -19.339 0.000 -1.025 -0.836
## sham_rcstmn|t3 -0.696 0.045 -15.535 0.000 -0.783 -0.608
## sham_rcstmn|t4 -0.426 0.042 -10.057 0.000 -0.509 -0.343
## sham_rcstmn|t5 0.079 0.041 1.926 0.054 -0.001 0.159
## sham_rcstmn|t6 0.675 0.045 15.159 0.000 0.588 0.763
## shm_mns2bwht|1 -1.146 0.052 -21.864 0.000 -1.249 -1.043
## shm_mns2bwht|2 -0.723 0.045 -16.032 0.000 -0.812 -0.635
## shm_mns2bwht|3 -0.556 0.043 -12.818 0.000 -0.641 -0.471
## shm_mns2bwht|4 -0.258 0.041 -6.230 0.000 -0.340 -0.177
## shm_mns2bwht|5 0.223 0.041 5.383 0.000 0.142 0.304
## shm_mns2bwht|6 0.741 0.045 16.341 0.000 0.652 0.829
## shm_rcstndnc|1 -1.398 0.059 -23.529 0.000 -1.514 -1.281
## shm_rcstndnc|2 -1.048 0.050 -20.842 0.000 -1.147 -0.950
## shm_rcstndnc|3 -0.843 0.047 -18.046 0.000 -0.935 -0.752
## shm_rcstndnc|4 -0.543 0.043 -12.563 0.000 -0.628 -0.458
## shm_rcstndnc|5 -0.039 0.041 -0.947 0.344 -0.119 0.042
## shm_rcstndnc|6 0.559 0.043 12.882 0.000 0.474 0.644
## guilt_racsm|t1 -0.914 0.048 -19.108 0.000 -1.008 -0.820
## guilt_racsm|t2 -0.377 0.042 -8.957 0.000 -0.459 -0.294
## guilt_racsm|t3 -0.171 0.041 -4.145 0.000 -0.251 -0.090
## guilt_racsm|t4 0.106 0.041 2.579 0.010 0.025 0.186
## guilt_racsm|t5 0.685 0.045 15.347 0.000 0.598 0.773
## guilt_racsm|t6 1.311 0.057 23.113 0.000 1.200 1.422
## guilt_nqlty|t1 -1.194 0.054 -22.288 0.000 -1.299 -1.089
## guilt_nqlty|t2 -0.748 0.045 -16.465 0.000 -0.837 -0.659
## guilt_nqlty|t3 -0.488 0.043 -11.409 0.000 -0.572 -0.404
## guilt_nqlty|t4 -0.225 0.041 -5.448 0.000 -0.306 -0.144
## guilt_nqlty|t5 0.311 0.042 7.465 0.000 0.230 0.393
## guilt_nqlty|t6 0.985 0.049 20.077 0.000 0.889 1.082
## gult_trtmnt|t1 -1.177 0.053 -22.149 0.000 -1.282 -1.073
## gult_trtmnt|t2 -0.751 0.045 -16.526 0.000 -0.840 -0.662
## gult_trtmnt|t3 -0.546 0.043 -12.627 0.000 -0.631 -0.462
## gult_trtmnt|t4 -0.272 0.042 -6.555 0.000 -0.354 -0.191
## gult_trtmnt|t5 0.258 0.041 6.230 0.000 0.177 0.340
## gult_trtmnt|t6 0.851 0.047 18.165 0.000 0.759 0.943
## guilt_behvr|t1 -1.057 0.050 -20.948 0.000 -1.156 -0.959
## guilt_behvr|t2 -0.655 0.044 -14.783 0.000 -0.742 -0.568
## guilt_behvr|t3 -0.438 0.042 -10.315 0.000 -0.521 -0.354
## guilt_behvr|t4 -0.209 0.041 -5.057 0.000 -0.290 -0.128
## guilt_behvr|t5 0.317 0.042 7.595 0.000 0.235 0.399
## guilt_behvr|t6 0.985 0.049 20.077 0.000 0.889 1.082
## img_shm_dsgr|1 -1.256 0.055 -22.765 0.000 -1.364 -1.148
## img_shm_dsgr|2 -0.744 0.045 -16.403 0.000 -0.833 -0.655
## img_shm_dsgr|3 -0.525 0.043 -12.179 0.000 -0.609 -0.440
## img_shm_dsgr|4 -0.111 0.041 -2.710 0.007 -0.192 -0.031
## img_shm_dsgr|5 0.473 0.043 11.088 0.000 0.390 0.557
## img_shm_dsgr|6 1.156 0.053 21.960 0.000 1.053 1.259
## img_shm_hwsn|1 -1.210 0.054 -22.422 0.000 -1.316 -1.104
## img_shm_hwsn|2 -0.720 0.045 -15.970 0.000 -0.808 -0.631
## img_shm_hwsn|3 -0.491 0.043 -11.474 0.000 -0.575 -0.407
## img_shm_hwsn|4 -0.098 0.041 -2.383 0.017 -0.178 -0.017
## img_shm_hwsn|5 0.543 0.043 12.563 0.000 0.458 0.628
## img_shm_hwsn|6 1.233 0.055 22.597 0.000 1.126 1.340
## img_shm_hmlt|1 -1.072 0.051 -21.106 0.000 -1.171 -0.972
## img_shm_hmlt|2 -0.506 0.043 -11.795 0.000 -0.591 -0.422
## img_shm_hmlt|3 -0.214 0.041 -5.188 0.000 -0.295 -0.133
## img_shm_hmlt|4 0.217 0.041 5.253 0.000 0.136 0.298
## img_shm_hmlt|5 0.787 0.046 17.139 0.000 0.697 0.877
## img_shm_hmlt|6 1.419 0.060 23.606 0.000 1.301 1.537
## Std.lv Std.all
## -1.419 -1.419
## -0.851 -0.851
## -0.540 -0.540
## 0.130 0.130
## 0.426 0.426
## 0.939 0.939
## -1.391 -1.391
## -0.930 -0.930
## -0.696 -0.696
## -0.426 -0.426
## 0.079 0.079
## 0.675 0.675
## -1.146 -1.146
## -0.723 -0.723
## -0.556 -0.556
## -0.258 -0.258
## 0.223 0.223
## 0.741 0.741
## -1.398 -1.398
## -1.048 -1.048
## -0.843 -0.843
## -0.543 -0.543
## -0.039 -0.039
## 0.559 0.559
## -0.914 -0.914
## -0.377 -0.377
## -0.171 -0.171
## 0.106 0.106
## 0.685 0.685
## 1.311 1.311
## -1.194 -1.194
## -0.748 -0.748
## -0.488 -0.488
## -0.225 -0.225
## 0.311 0.311
## 0.985 0.985
## -1.177 -1.177
## -0.751 -0.751
## -0.546 -0.546
## -0.272 -0.272
## 0.258 0.258
## 0.851 0.851
## -1.057 -1.057
## -0.655 -0.655
## -0.438 -0.438
## -0.209 -0.209
## 0.317 0.317
## 0.985 0.985
## -1.256 -1.256
## -0.744 -0.744
## -0.525 -0.525
## -0.111 -0.111
## 0.473 0.473
## 1.156 1.156
## -1.210 -1.210
## -0.720 -0.720
## -0.491 -0.491
## -0.098 -0.098
## 0.543 0.543
## 1.233 1.233
## -1.072 -1.072
## -0.506 -0.506
## -0.214 -0.214
## 0.217 0.217
## 0.787 0.787
## 1.419 1.419
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .problack_meanZ 0.000 0.000 0.000
## .revsham_ntshmd 0.439 0.439 0.439
## .shame_racistmn 0.185 0.185 0.185
## .shame_mns2bwht 0.068 0.068 0.068
## .sham_rcstndncs 0.169 0.169 0.169
## .guilt_racism 0.129 0.129 0.129
## .guilt_inequlty 0.121 0.121 0.121
## .guilt_treatmnt 0.083 0.083 0.083
## .guilt_behavior 0.109 0.109 0.109
## .img_shm_dsgrcd 0.235 0.235 0.235
## .image_shm_hwsn 0.110 0.110 0.110
## .imag_shm_hmltd 0.267 0.267 0.267
## MORAL 1.000 1.000 1.000
## GUILT 1.000 1.000 1.000
## IMAGE 1.000 1.000 1.000
## General 1.000 1.000 1.000
## Std.lv Std.all
## 0.000 0.000
## 0.439 0.439
## 0.185 0.185
## 0.068 0.068
## 0.169 0.169
## 0.129 0.129
## 0.121 0.121
## 0.083 0.083
## 0.109 0.109
## 0.235 0.235
## 0.110 0.110
## 0.267 0.267
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## revsham_ntshmd 1.000 1.000 1.000
## shame_racistmn 1.000 1.000 1.000
## shame_mns2bwht 1.000 1.000 1.000
## sham_rcstndncs 1.000 1.000 1.000
## guilt_racism 1.000 1.000 1.000
## guilt_inequlty 1.000 1.000 1.000
## guilt_treatmnt 1.000 1.000 1.000
## guilt_behavior 1.000 1.000 1.000
## img_shm_dsgrcd 1.000 1.000 1.000
## image_shm_hwsn 1.000 1.000 1.000
## imag_shm_hmltd 1.000 1.000 1.000
## Std.lv Std.all
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000ZGLAT <- list(
MORAL = c("revshame_notashamed", "shame_racistmean", "shame_means2bewhite", "shame_racistendencies"),
GUILT = c("guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior"),
IMAGE = c("image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated"))
semPaths(ZGRunBFPB, "model", "std", title = F, residuals = F, groups = "ZGLAT", pastel = T, mar = c(2, 1, 3, 1), bifactor = c("General"), layout = "tree2", exoCov = T)## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
semPaths(ZGRunBFPBO, "model", "std", title = F, residuals = F, groups = "ZGLAT", pastel = T, mar = c(2, 1, 3, 1), bifactor = c("General"), layout = "tree2", exoCov = T)## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
## Warning in if (w <= 0) w <- 1e-07: the condition has length > 1 and only the
## first element will be used
Paternoster et al. (1998) provided a formula to test whether two different regression coefficients were themselves significantly different:
\(Z = \frac{\beta_1 - \beta_2}{\sqrt{(SE \beta_1)^2 + (SE \beta_2)^2}}\)
It is an open question whether the MORAL and IMAGE factors show differential validity.
ZREG <- function(B1, B2, SEB1, SEB2) {
Z = (B1-B2)/sqrt((SEB1)^2 + (SEB2)^2)
return(Z)}
ZREG(0.234, -0.156, 0.032, 0.026); ZREG(0.872, 0.544, 0.048, 0.059)## [1] 9.458889## [1] 4.312431The general variance is more predictive but there is evidence for differential predictive validity for the MORAL and IMAGE factors. With p value scaling in this sample, the MORAL and IMAGE factors in a model without the general factor are not significantly different (Critical Z = 4.87 versus 4.31 observed). A model with general variance explicitly removed is preferable to one that allows it to confound the investigation of differential validity claims.
Three
ZGModSGIRO <- '
General =~ revrr_favors + revrr_tryharder + rr_deserve + rr_slavery + revshame_notashamed + shame_racistmean + shame_means2bewhite + shame_racistendencies + guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior + image_shame_disgraced + image_shame_howseen + image_shame_humiliated'
ZGModSGIRC <- '
RR =~ revrr_favors + revrr_tryharder + rr_deserve + rr_slavery
MORAL =~ revshame_notashamed + shame_racistmean + shame_means2bewhite + shame_racistendencies
GUILT =~ guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior
IMAGE =~ image_shame_disgraced + image_shame_howseen + image_shame_humiliated'
ZGModSGIRH <- '
RR =~ revrr_favors + revrr_tryharder + rr_deserve + rr_slavery
MORAL =~ revshame_notashamed + shame_racistmean + shame_means2bewhite + shame_racistendencies
GUILT =~ guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior
IMAGE =~ image_shame_disgraced + image_shame_howseen + image_shame_humiliated
General =~ RR + MORAL + GUILT + IMAGE'
ZGModSGIRB <- '
RR =~ revrr_favors + revrr_tryharder + rr_deserve + rr_slavery
MORAL =~ revshame_notashamed + shame_racistmean + shame_means2bewhite + shame_racistendencies
GUILT =~ guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior
IMAGE =~ image_shame_disgraced + image_shame_howseen + image_shame_humiliated
General =~ revrr_favors + revrr_tryharder + rr_deserve + rr_slavery + revshame_notashamed + shame_racistmean + shame_means2bewhite + shame_racistendencies + guilt_racism + guilt_inequality + guilt_treatment + guilt_behavior + image_shame_disgraced + image_shame_howseen + image_shame_humiliated'
ZGRunSGIRO <- cfa(ZGModSGIRO, data = data, std.lv = T, ordered = c("shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "rr_slavery", "rr_deserve", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))
ZGRunSGIRC <- cfa(ZGModSGIRC, data = data, std.lv = T, ordered = c("shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "rr_slavery", "rr_deserve", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))
ZGRunSGIRH <- cfa(ZGModSGIRH, data = data, std.lv = T, ordered = c("shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "rr_slavery", "rr_deserve", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))
ZGRunSGIRB <- cfa(ZGModSGIRB, data = data, std.lv = T, orthogonal = T, check.gradient = F, control = list(rel.tol = 1e-3), ordered = c("shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "rr_slavery", "rr_deserve", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))
summary(ZGRunSGIRO, stand = T, fit = T); summary(ZGRunSGIRC, stand = T, fit = T); summary(ZGRunSGIRH, stand = T, fit = T); summary(ZGRunSGIRB, stand = T, fit = T)## lavaan 0.6-7 ended normally after 24 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 97
##
## Used Total
## Number of observations 936 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 3714.446 4291.314
## Degrees of freedom 90 90
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.876
## Shift parameter 52.695
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 241677.114 57840.451
## Degrees of freedom 105 105
## P-value 0.000 0.000
## Scaling correction factor 4.184
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.985 0.927
## Tucker-Lewis Index (TLI) 0.982 0.915
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.208 0.223
## 90 Percent confidence interval - lower 0.202 0.218
## 90 Percent confidence interval - upper 0.213 0.229
## 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 0.112 0.112
##
## 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
## General =~
## revrr_favors 0.812 0.012 67.527 0.000 0.812 0.812
## revrr_tryhardr 0.795 0.013 60.688 0.000 0.795 0.795
## rr_deserve 0.790 0.014 57.972 0.000 0.790 0.790
## rr_slavery 0.775 0.015 51.435 0.000 0.775 0.775
## revsham_ntshmd 0.680 0.016 41.952 0.000 0.680 0.680
## shame_racistmn 0.842 0.010 85.991 0.000 0.842 0.842
## shame_mns2bwht 0.907 0.006 143.763 0.000 0.907 0.907
## sham_rcstndncs 0.869 0.008 102.675 0.000 0.869 0.869
## guilt_racism 0.904 0.006 151.725 0.000 0.904 0.904
## guilt_inequlty 0.908 0.006 160.927 0.000 0.908 0.908
## guilt_treatmnt 0.928 0.005 194.337 0.000 0.928 0.928
## guilt_behavior 0.921 0.005 182.079 0.000 0.921 0.921
## img_shm_dsgrcd 0.779 0.012 65.937 0.000 0.779 0.779
## image_shm_hwsn 0.845 0.009 91.071 0.000 0.845 0.845
## imag_shm_hmltd 0.730 0.014 52.375 0.000 0.730 0.730
##
## 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_deserve 0.000 0.000 0.000
## .rr_slavery 0.000 0.000 0.000
## .revsham_ntshmd 0.000 0.000 0.000
## .shame_racistmn 0.000 0.000 0.000
## .shame_mns2bwht 0.000 0.000 0.000
## .sham_rcstndncs 0.000 0.000 0.000
## .guilt_racism 0.000 0.000 0.000
## .guilt_inequlty 0.000 0.000 0.000
## .guilt_treatmnt 0.000 0.000 0.000
## .guilt_behavior 0.000 0.000 0.000
## .img_shm_dsgrcd 0.000 0.000 0.000
## .image_shm_hwsn 0.000 0.000 0.000
## .imag_shm_hmltd 0.000 0.000 0.000
## General 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favrs|t1 -1.120 0.052 -21.600 0.000 -1.120 -1.120
## revrr_favrs|t2 -0.552 0.043 -12.729 0.000 -0.552 -0.552
## revrr_favrs|t3 -0.170 0.041 -4.114 0.000 -0.170 -0.170
## revrr_favrs|t4 0.443 0.042 10.417 0.000 0.443 0.443
## rvrr_tryhrdr|1 -1.426 0.060 -23.616 0.000 -1.426 -1.426
## rvrr_tryhrdr|2 -0.823 0.046 -17.724 0.000 -0.823 -0.823
## rvrr_tryhrdr|3 -0.428 0.042 -10.094 0.000 -0.428 -0.428
## rvrr_tryhrdr|4 0.183 0.041 4.441 0.000 0.183 0.183
## rr_deserve|t1 -1.397 0.059 -23.514 0.000 -1.397 -1.397
## rr_deserve|t2 -0.873 0.047 -18.500 0.000 -0.873 -0.873
## rr_deserve|t3 -0.347 0.042 -8.281 0.000 -0.347 -0.347
## rr_deserve|t4 0.350 0.042 8.346 0.000 0.350 0.350
## rr_slavery|t1 -1.310 0.057 -23.097 0.000 -1.310 -1.310
## rr_slavery|t2 -0.869 0.047 -18.441 0.000 -0.869 -0.869
## rr_slavery|t3 -0.558 0.043 -12.857 0.000 -0.558 -0.558
## rr_slavery|t4 0.118 0.041 2.874 0.004 0.118 0.118
## rvshm_ntshmd|1 -1.419 0.060 -23.592 0.000 -1.419 -1.419
## rvshm_ntshmd|2 -0.850 0.047 -18.144 0.000 -0.850 -0.850
## rvshm_ntshmd|3 -0.539 0.043 -12.473 0.000 -0.539 -0.539
## rvshm_ntshmd|4 0.132 0.041 3.201 0.001 0.132 0.132
## rvshm_ntshmd|5 0.428 0.042 10.094 0.000 0.428 0.428
## rvshm_ntshmd|6 0.942 0.048 19.491 0.000 0.942 0.942
## sham_rcstmn|t1 -1.390 0.059 -23.486 0.000 -1.390 -1.390
## sham_rcstmn|t2 -0.930 0.048 -19.318 0.000 -0.930 -0.930
## sham_rcstmn|t3 -0.695 0.045 -15.511 0.000 -0.695 -0.695
## sham_rcstmn|t4 -0.425 0.042 -10.030 0.000 -0.425 -0.425
## sham_rcstmn|t5 0.080 0.041 1.960 0.050 0.080 0.080
## sham_rcstmn|t6 0.674 0.045 15.136 0.000 0.674 0.674
## shm_mns2bwht|1 -1.145 0.052 -21.846 0.000 -1.145 -1.145
## shm_mns2bwht|2 -0.722 0.045 -16.009 0.000 -0.722 -0.722
## shm_mns2bwht|3 -0.555 0.043 -12.793 0.000 -0.555 -0.555
## shm_mns2bwht|4 -0.257 0.041 -6.200 0.000 -0.257 -0.257
## shm_mns2bwht|5 0.224 0.041 5.419 0.000 0.224 0.224
## shm_mns2bwht|6 0.740 0.045 16.319 0.000 0.740 0.740
## shm_rcstndnc|1 -1.397 0.059 -23.514 0.000 -1.397 -1.397
## shm_rcstndnc|2 -1.047 0.050 -20.823 0.000 -1.047 -1.047
## shm_rcstndnc|3 -0.842 0.047 -18.024 0.000 -0.842 -0.842
## shm_rcstndnc|4 -0.542 0.043 -12.537 0.000 -0.542 -0.542
## shm_rcstndnc|5 -0.038 0.041 -0.915 0.360 -0.038 -0.038
## shm_rcstndnc|6 0.561 0.043 12.921 0.000 0.561 0.561
## guilt_racsm|t1 -0.913 0.048 -19.087 0.000 -0.913 -0.913
## guilt_racsm|t2 -0.376 0.042 -8.929 0.000 -0.376 -0.376
## guilt_racsm|t3 -0.170 0.041 -4.114 0.000 -0.170 -0.170
## guilt_racsm|t4 0.107 0.041 2.613 0.009 0.107 0.107
## guilt_racsm|t5 0.688 0.045 15.386 0.000 0.688 0.688
## guilt_racsm|t6 1.310 0.057 23.097 0.000 1.310 1.310
## guilt_nqlty|t1 -1.193 0.054 -22.270 0.000 -1.193 -1.193
## guilt_nqlty|t2 -0.747 0.045 -16.442 0.000 -0.747 -0.747
## guilt_nqlty|t3 -0.487 0.043 -11.383 0.000 -0.487 -0.487
## guilt_nqlty|t4 -0.224 0.041 -5.419 0.000 -0.224 -0.224
## guilt_nqlty|t5 0.313 0.042 7.502 0.000 0.313 0.313
## guilt_nqlty|t6 0.985 0.049 20.057 0.000 0.985 0.985
## gult_trtmnt|t1 -1.177 0.053 -22.132 0.000 -1.177 -1.177
## gult_trtmnt|t2 -0.750 0.045 -16.504 0.000 -0.750 -0.750
## gult_trtmnt|t3 -0.545 0.043 -12.601 0.000 -0.545 -0.545
## gult_trtmnt|t4 -0.271 0.042 -6.526 0.000 -0.271 -0.271
## gult_trtmnt|t5 0.260 0.041 6.266 0.000 0.260 0.260
## gult_trtmnt|t6 0.850 0.047 18.144 0.000 0.850 0.850
## guilt_behvr|t1 -1.057 0.050 -20.929 0.000 -1.057 -1.057
## guilt_behvr|t2 -0.654 0.044 -14.759 0.000 -0.654 -0.654
## guilt_behvr|t3 -0.437 0.042 -10.288 0.000 -0.437 -0.437
## guilt_behvr|t4 -0.208 0.041 -5.028 0.000 -0.208 -0.208
## guilt_behvr|t5 0.319 0.042 7.632 0.000 0.319 0.319
## guilt_behvr|t6 0.985 0.049 20.057 0.000 0.985 0.985
## img_shm_dsgr|1 -1.255 0.055 -22.748 0.000 -1.255 -1.255
## img_shm_dsgr|2 -0.743 0.045 -16.380 0.000 -0.743 -0.743
## img_shm_dsgr|3 -0.524 0.043 -12.153 0.000 -0.524 -0.524
## img_shm_dsgr|4 -0.110 0.041 -2.678 0.007 -0.110 -0.110
## img_shm_dsgr|5 0.475 0.043 11.126 0.000 0.475 0.475
## img_shm_dsgr|6 1.156 0.053 21.943 0.000 1.156 1.156
## img_shm_hwsn|1 -1.209 0.054 -22.405 0.000 -1.209 -1.209
## img_shm_hwsn|2 -0.719 0.045 -15.947 0.000 -0.719 -0.719
## img_shm_hwsn|3 -0.490 0.043 -11.447 0.000 -0.490 -0.490
## img_shm_hwsn|4 -0.097 0.041 -2.352 0.019 -0.097 -0.097
## img_shm_hwsn|5 0.545 0.043 12.601 0.000 0.545 0.545
## img_shm_hwsn|6 1.232 0.055 22.580 0.000 1.232 1.232
## img_shm_hmlt|1 -1.071 0.051 -21.087 0.000 -1.071 -1.071
## img_shm_hmlt|2 -0.505 0.043 -11.769 0.000 -0.505 -0.505
## img_shm_hmlt|3 -0.213 0.041 -5.158 0.000 -0.213 -0.213
## img_shm_hmlt|4 0.219 0.041 5.288 0.000 0.219 0.219
## img_shm_hmlt|5 0.790 0.046 17.178 0.000 0.790 0.790
## img_shm_hmlt|6 1.419 0.060 23.592 0.000 1.419 1.419
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.341 0.341 0.341
## .revrr_tryhardr 0.368 0.368 0.368
## .rr_deserve 0.376 0.376 0.376
## .rr_slavery 0.400 0.400 0.400
## .revsham_ntshmd 0.537 0.537 0.537
## .shame_racistmn 0.291 0.291 0.291
## .shame_mns2bwht 0.178 0.178 0.178
## .sham_rcstndncs 0.245 0.245 0.245
## .guilt_racism 0.183 0.183 0.183
## .guilt_inequlty 0.175 0.175 0.175
## .guilt_treatmnt 0.138 0.138 0.138
## .guilt_behavior 0.152 0.152 0.152
## .img_shm_dsgrcd 0.393 0.393 0.393
## .image_shm_hwsn 0.287 0.287 0.287
## .imag_shm_hmltd 0.467 0.467 0.467
## General 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_deserve 1.000 1.000 1.000
## rr_slavery 1.000 1.000 1.000
## revsham_ntshmd 1.000 1.000 1.000
## shame_racistmn 1.000 1.000 1.000
## shame_mns2bwht 1.000 1.000 1.000
## sham_rcstndncs 1.000 1.000 1.000
## guilt_racism 1.000 1.000 1.000
## guilt_inequlty 1.000 1.000 1.000
## guilt_treatmnt 1.000 1.000 1.000
## guilt_behavior 1.000 1.000 1.000
## img_shm_dsgrcd 1.000 1.000 1.000
## image_shm_hwsn 1.000 1.000 1.000
## imag_shm_hmltd 1.000 1.000 1.000## lavaan 0.6-7 ended normally after 45 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 103
##
## Used Total
## Number of observations 936 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 346.958 839.372
## Degrees of freedom 84 84
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.431
## Shift parameter 34.396
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 241677.114 57840.451
## Degrees of freedom 105 105
## P-value 0.000 0.000
## Scaling correction factor 4.184
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.999 0.987
## 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 0.058 0.098
## 90 Percent confidence interval - lower 0.052 0.092
## 90 Percent confidence interval - upper 0.064 0.104
## P-value RMSEA <= 0.05 0.020 0.000
##
## Robust RMSEA NA
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.033 0.033
##
## 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 0.902 0.010 93.110 0.000 0.902 0.902
## revrr_tryhardr 0.881 0.011 80.956 0.000 0.881 0.881
## rr_deserve 0.901 0.012 75.639 0.000 0.901 0.901
## rr_slavery 0.870 0.013 66.458 0.000 0.870 0.870
## MORAL =~
## revsham_ntshmd 0.711 0.016 44.065 0.000 0.711 0.711
## shame_racistmn 0.873 0.009 95.335 0.000 0.873 0.873
## shame_mns2bwht 0.945 0.005 177.028 0.000 0.945 0.945
## sham_rcstndncs 0.907 0.008 116.772 0.000 0.907 0.907
## GUILT =~
## guilt_racism 0.928 0.005 173.004 0.000 0.928 0.928
## guilt_inequlty 0.928 0.005 181.175 0.000 0.928 0.928
## guilt_treatmnt 0.943 0.004 215.974 0.000 0.943 0.943
## guilt_behavior 0.939 0.005 208.530 0.000 0.939 0.939
## IMAGE =~
## img_shm_dsgrcd 0.867 0.010 87.960 0.000 0.867 0.867
## image_shm_hwsn 0.962 0.007 140.397 0.000 0.962 0.962
## imag_shm_hmltd 0.814 0.012 67.109 0.000 0.814 0.814
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RR ~~
## MORAL 0.819 0.013 63.236 0.000 0.819 0.819
## GUILT 0.700 0.017 40.503 0.000 0.700 0.700
## IMAGE 0.501 0.026 19.412 0.000 0.501 0.501
## MORAL ~~
## GUILT 0.917 0.007 139.322 0.000 0.917 0.917
## IMAGE 0.779 0.014 55.508 0.000 0.779 0.779
## GUILT ~~
## IMAGE 0.819 0.012 71.139 0.000 0.819 0.819
##
## 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_deserve 0.000 0.000 0.000
## .rr_slavery 0.000 0.000 0.000
## .revsham_ntshmd 0.000 0.000 0.000
## .shame_racistmn 0.000 0.000 0.000
## .shame_mns2bwht 0.000 0.000 0.000
## .sham_rcstndncs 0.000 0.000 0.000
## .guilt_racism 0.000 0.000 0.000
## .guilt_inequlty 0.000 0.000 0.000
## .guilt_treatmnt 0.000 0.000 0.000
## .guilt_behavior 0.000 0.000 0.000
## .img_shm_dsgrcd 0.000 0.000 0.000
## .image_shm_hwsn 0.000 0.000 0.000
## .imag_shm_hmltd 0.000 0.000 0.000
## RR 0.000 0.000 0.000
## MORAL 0.000 0.000 0.000
## GUILT 0.000 0.000 0.000
## IMAGE 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favrs|t1 -1.120 0.052 -21.600 0.000 -1.120 -1.120
## revrr_favrs|t2 -0.552 0.043 -12.729 0.000 -0.552 -0.552
## revrr_favrs|t3 -0.170 0.041 -4.114 0.000 -0.170 -0.170
## revrr_favrs|t4 0.443 0.042 10.417 0.000 0.443 0.443
## rvrr_tryhrdr|1 -1.426 0.060 -23.616 0.000 -1.426 -1.426
## rvrr_tryhrdr|2 -0.823 0.046 -17.724 0.000 -0.823 -0.823
## rvrr_tryhrdr|3 -0.428 0.042 -10.094 0.000 -0.428 -0.428
## rvrr_tryhrdr|4 0.183 0.041 4.441 0.000 0.183 0.183
## rr_deserve|t1 -1.397 0.059 -23.514 0.000 -1.397 -1.397
## rr_deserve|t2 -0.873 0.047 -18.500 0.000 -0.873 -0.873
## rr_deserve|t3 -0.347 0.042 -8.281 0.000 -0.347 -0.347
## rr_deserve|t4 0.350 0.042 8.346 0.000 0.350 0.350
## rr_slavery|t1 -1.310 0.057 -23.097 0.000 -1.310 -1.310
## rr_slavery|t2 -0.869 0.047 -18.441 0.000 -0.869 -0.869
## rr_slavery|t3 -0.558 0.043 -12.857 0.000 -0.558 -0.558
## rr_slavery|t4 0.118 0.041 2.874 0.004 0.118 0.118
## rvshm_ntshmd|1 -1.419 0.060 -23.592 0.000 -1.419 -1.419
## rvshm_ntshmd|2 -0.850 0.047 -18.144 0.000 -0.850 -0.850
## rvshm_ntshmd|3 -0.539 0.043 -12.473 0.000 -0.539 -0.539
## rvshm_ntshmd|4 0.132 0.041 3.201 0.001 0.132 0.132
## rvshm_ntshmd|5 0.428 0.042 10.094 0.000 0.428 0.428
## rvshm_ntshmd|6 0.942 0.048 19.491 0.000 0.942 0.942
## sham_rcstmn|t1 -1.390 0.059 -23.486 0.000 -1.390 -1.390
## sham_rcstmn|t2 -0.930 0.048 -19.318 0.000 -0.930 -0.930
## sham_rcstmn|t3 -0.695 0.045 -15.511 0.000 -0.695 -0.695
## sham_rcstmn|t4 -0.425 0.042 -10.030 0.000 -0.425 -0.425
## sham_rcstmn|t5 0.080 0.041 1.960 0.050 0.080 0.080
## sham_rcstmn|t6 0.674 0.045 15.136 0.000 0.674 0.674
## shm_mns2bwht|1 -1.145 0.052 -21.846 0.000 -1.145 -1.145
## shm_mns2bwht|2 -0.722 0.045 -16.009 0.000 -0.722 -0.722
## shm_mns2bwht|3 -0.555 0.043 -12.793 0.000 -0.555 -0.555
## shm_mns2bwht|4 -0.257 0.041 -6.200 0.000 -0.257 -0.257
## shm_mns2bwht|5 0.224 0.041 5.419 0.000 0.224 0.224
## shm_mns2bwht|6 0.740 0.045 16.319 0.000 0.740 0.740
## shm_rcstndnc|1 -1.397 0.059 -23.514 0.000 -1.397 -1.397
## shm_rcstndnc|2 -1.047 0.050 -20.823 0.000 -1.047 -1.047
## shm_rcstndnc|3 -0.842 0.047 -18.024 0.000 -0.842 -0.842
## shm_rcstndnc|4 -0.542 0.043 -12.537 0.000 -0.542 -0.542
## shm_rcstndnc|5 -0.038 0.041 -0.915 0.360 -0.038 -0.038
## shm_rcstndnc|6 0.561 0.043 12.921 0.000 0.561 0.561
## guilt_racsm|t1 -0.913 0.048 -19.087 0.000 -0.913 -0.913
## guilt_racsm|t2 -0.376 0.042 -8.929 0.000 -0.376 -0.376
## guilt_racsm|t3 -0.170 0.041 -4.114 0.000 -0.170 -0.170
## guilt_racsm|t4 0.107 0.041 2.613 0.009 0.107 0.107
## guilt_racsm|t5 0.688 0.045 15.386 0.000 0.688 0.688
## guilt_racsm|t6 1.310 0.057 23.097 0.000 1.310 1.310
## guilt_nqlty|t1 -1.193 0.054 -22.270 0.000 -1.193 -1.193
## guilt_nqlty|t2 -0.747 0.045 -16.442 0.000 -0.747 -0.747
## guilt_nqlty|t3 -0.487 0.043 -11.383 0.000 -0.487 -0.487
## guilt_nqlty|t4 -0.224 0.041 -5.419 0.000 -0.224 -0.224
## guilt_nqlty|t5 0.313 0.042 7.502 0.000 0.313 0.313
## guilt_nqlty|t6 0.985 0.049 20.057 0.000 0.985 0.985
## gult_trtmnt|t1 -1.177 0.053 -22.132 0.000 -1.177 -1.177
## gult_trtmnt|t2 -0.750 0.045 -16.504 0.000 -0.750 -0.750
## gult_trtmnt|t3 -0.545 0.043 -12.601 0.000 -0.545 -0.545
## gult_trtmnt|t4 -0.271 0.042 -6.526 0.000 -0.271 -0.271
## gult_trtmnt|t5 0.260 0.041 6.266 0.000 0.260 0.260
## gult_trtmnt|t6 0.850 0.047 18.144 0.000 0.850 0.850
## guilt_behvr|t1 -1.057 0.050 -20.929 0.000 -1.057 -1.057
## guilt_behvr|t2 -0.654 0.044 -14.759 0.000 -0.654 -0.654
## guilt_behvr|t3 -0.437 0.042 -10.288 0.000 -0.437 -0.437
## guilt_behvr|t4 -0.208 0.041 -5.028 0.000 -0.208 -0.208
## guilt_behvr|t5 0.319 0.042 7.632 0.000 0.319 0.319
## guilt_behvr|t6 0.985 0.049 20.057 0.000 0.985 0.985
## img_shm_dsgr|1 -1.255 0.055 -22.748 0.000 -1.255 -1.255
## img_shm_dsgr|2 -0.743 0.045 -16.380 0.000 -0.743 -0.743
## img_shm_dsgr|3 -0.524 0.043 -12.153 0.000 -0.524 -0.524
## img_shm_dsgr|4 -0.110 0.041 -2.678 0.007 -0.110 -0.110
## img_shm_dsgr|5 0.475 0.043 11.126 0.000 0.475 0.475
## img_shm_dsgr|6 1.156 0.053 21.943 0.000 1.156 1.156
## img_shm_hwsn|1 -1.209 0.054 -22.405 0.000 -1.209 -1.209
## img_shm_hwsn|2 -0.719 0.045 -15.947 0.000 -0.719 -0.719
## img_shm_hwsn|3 -0.490 0.043 -11.447 0.000 -0.490 -0.490
## img_shm_hwsn|4 -0.097 0.041 -2.352 0.019 -0.097 -0.097
## img_shm_hwsn|5 0.545 0.043 12.601 0.000 0.545 0.545
## img_shm_hwsn|6 1.232 0.055 22.580 0.000 1.232 1.232
## img_shm_hmlt|1 -1.071 0.051 -21.087 0.000 -1.071 -1.071
## img_shm_hmlt|2 -0.505 0.043 -11.769 0.000 -0.505 -0.505
## img_shm_hmlt|3 -0.213 0.041 -5.158 0.000 -0.213 -0.213
## img_shm_hmlt|4 0.219 0.041 5.288 0.000 0.219 0.219
## img_shm_hmlt|5 0.790 0.046 17.178 0.000 0.790 0.790
## img_shm_hmlt|6 1.419 0.060 23.592 0.000 1.419 1.419
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.187 0.187 0.187
## .revrr_tryhardr 0.223 0.223 0.223
## .rr_deserve 0.187 0.187 0.187
## .rr_slavery 0.243 0.243 0.243
## .revsham_ntshmd 0.494 0.494 0.494
## .shame_racistmn 0.238 0.238 0.238
## .shame_mns2bwht 0.107 0.107 0.107
## .sham_rcstndncs 0.178 0.178 0.178
## .guilt_racism 0.138 0.138 0.138
## .guilt_inequlty 0.139 0.139 0.139
## .guilt_treatmnt 0.110 0.110 0.110
## .guilt_behavior 0.118 0.118 0.118
## .img_shm_dsgrcd 0.248 0.248 0.248
## .image_shm_hwsn 0.074 0.074 0.074
## .imag_shm_hmltd 0.338 0.338 0.338
## RR 1.000 1.000 1.000
## MORAL 1.000 1.000 1.000
## GUILT 1.000 1.000 1.000
## IMAGE 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_deserve 1.000 1.000 1.000
## rr_slavery 1.000 1.000 1.000
## revsham_ntshmd 1.000 1.000 1.000
## shame_racistmn 1.000 1.000 1.000
## shame_mns2bwht 1.000 1.000 1.000
## sham_rcstndncs 1.000 1.000 1.000
## guilt_racism 1.000 1.000 1.000
## guilt_inequlty 1.000 1.000 1.000
## guilt_treatmnt 1.000 1.000 1.000
## guilt_behavior 1.000 1.000 1.000
## img_shm_dsgrcd 1.000 1.000 1.000
## image_shm_hwsn 1.000 1.000 1.000
## imag_shm_hmltd 1.000 1.000 1.000## lavaan 0.6-7 ended normally after 143 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 101
##
## Used Total
## Number of observations 936 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 693.870 1395.055
## Degrees of freedom 86 86
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.511
## Shift parameter 38.483
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 241677.114 57840.451
## Degrees of freedom 105 105
## P-value 0.000 0.000
## Scaling correction factor 4.184
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.997 0.977
## Tucker-Lewis Index (TLI) 0.997 0.972
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.087 0.128
## 90 Percent confidence interval - lower 0.081 0.122
## 90 Percent confidence interval - upper 0.093 0.134
## 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 0.052 0.052
##
## 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 0.578 0.016 36.988 0.000 0.901 0.901
## revrr_tryhardr 0.564 0.015 37.094 0.000 0.880 0.880
## rr_deserve 0.580 0.017 33.396 0.000 0.904 0.904
## rr_slavery 0.558 0.016 35.288 0.000 0.870 0.870
## MORAL =~
## revsham_ntshmd 0.122 0.019 6.461 0.000 0.712 0.712
## shame_racistmn 0.150 0.023 6.469 0.000 0.876 0.876
## shame_mns2bwht 0.161 0.025 6.400 0.000 0.943 0.943
## sham_rcstndncs 0.155 0.024 6.405 0.000 0.906 0.906
## GUILT =~
## guilt_racism 0.303 0.016 19.567 0.000 0.928 0.928
## guilt_inequlty 0.303 0.015 19.800 0.000 0.928 0.928
## guilt_treatmnt 0.308 0.016 19.649 0.000 0.943 0.943
## guilt_behavior 0.307 0.016 19.675 0.000 0.939 0.939
## IMAGE =~
## img_shm_dsgrcd 0.499 0.014 35.757 0.000 0.865 0.865
## image_shm_hwsn 0.558 0.017 32.014 0.000 0.966 0.966
## imag_shm_hmltd 0.468 0.013 36.901 0.000 0.811 0.811
## General =~
## RR 1.196 0.057 21.010 0.000 0.767 0.767
## MORAL 5.771 0.931 6.200 0.000 0.985 0.985
## GUILT 2.891 0.169 17.099 0.000 0.945 0.945
## IMAGE 1.415 0.063 22.520 0.000 0.817 0.817
##
## 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_deserve 0.000 0.000 0.000
## .rr_slavery 0.000 0.000 0.000
## .revsham_ntshmd 0.000 0.000 0.000
## .shame_racistmn 0.000 0.000 0.000
## .shame_mns2bwht 0.000 0.000 0.000
## .sham_rcstndncs 0.000 0.000 0.000
## .guilt_racism 0.000 0.000 0.000
## .guilt_inequlty 0.000 0.000 0.000
## .guilt_treatmnt 0.000 0.000 0.000
## .guilt_behavior 0.000 0.000 0.000
## .img_shm_dsgrcd 0.000 0.000 0.000
## .image_shm_hwsn 0.000 0.000 0.000
## .imag_shm_hmltd 0.000 0.000 0.000
## .RR 0.000 0.000 0.000
## .MORAL 0.000 0.000 0.000
## .GUILT 0.000 0.000 0.000
## .IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favrs|t1 -1.120 0.052 -21.600 0.000 -1.120 -1.120
## revrr_favrs|t2 -0.552 0.043 -12.729 0.000 -0.552 -0.552
## revrr_favrs|t3 -0.170 0.041 -4.114 0.000 -0.170 -0.170
## revrr_favrs|t4 0.443 0.042 10.417 0.000 0.443 0.443
## rvrr_tryhrdr|1 -1.426 0.060 -23.616 0.000 -1.426 -1.426
## rvrr_tryhrdr|2 -0.823 0.046 -17.724 0.000 -0.823 -0.823
## rvrr_tryhrdr|3 -0.428 0.042 -10.094 0.000 -0.428 -0.428
## rvrr_tryhrdr|4 0.183 0.041 4.441 0.000 0.183 0.183
## rr_deserve|t1 -1.397 0.059 -23.514 0.000 -1.397 -1.397
## rr_deserve|t2 -0.873 0.047 -18.500 0.000 -0.873 -0.873
## rr_deserve|t3 -0.347 0.042 -8.281 0.000 -0.347 -0.347
## rr_deserve|t4 0.350 0.042 8.346 0.000 0.350 0.350
## rr_slavery|t1 -1.310 0.057 -23.097 0.000 -1.310 -1.310
## rr_slavery|t2 -0.869 0.047 -18.441 0.000 -0.869 -0.869
## rr_slavery|t3 -0.558 0.043 -12.857 0.000 -0.558 -0.558
## rr_slavery|t4 0.118 0.041 2.874 0.004 0.118 0.118
## rvshm_ntshmd|1 -1.419 0.060 -23.592 0.000 -1.419 -1.419
## rvshm_ntshmd|2 -0.850 0.047 -18.144 0.000 -0.850 -0.850
## rvshm_ntshmd|3 -0.539 0.043 -12.473 0.000 -0.539 -0.539
## rvshm_ntshmd|4 0.132 0.041 3.201 0.001 0.132 0.132
## rvshm_ntshmd|5 0.428 0.042 10.094 0.000 0.428 0.428
## rvshm_ntshmd|6 0.942 0.048 19.491 0.000 0.942 0.942
## sham_rcstmn|t1 -1.390 0.059 -23.486 0.000 -1.390 -1.390
## sham_rcstmn|t2 -0.930 0.048 -19.318 0.000 -0.930 -0.930
## sham_rcstmn|t3 -0.695 0.045 -15.511 0.000 -0.695 -0.695
## sham_rcstmn|t4 -0.425 0.042 -10.030 0.000 -0.425 -0.425
## sham_rcstmn|t5 0.080 0.041 1.960 0.050 0.080 0.080
## sham_rcstmn|t6 0.674 0.045 15.136 0.000 0.674 0.674
## shm_mns2bwht|1 -1.145 0.052 -21.846 0.000 -1.145 -1.145
## shm_mns2bwht|2 -0.722 0.045 -16.009 0.000 -0.722 -0.722
## shm_mns2bwht|3 -0.555 0.043 -12.793 0.000 -0.555 -0.555
## shm_mns2bwht|4 -0.257 0.041 -6.200 0.000 -0.257 -0.257
## shm_mns2bwht|5 0.224 0.041 5.419 0.000 0.224 0.224
## shm_mns2bwht|6 0.740 0.045 16.319 0.000 0.740 0.740
## shm_rcstndnc|1 -1.397 0.059 -23.514 0.000 -1.397 -1.397
## shm_rcstndnc|2 -1.047 0.050 -20.823 0.000 -1.047 -1.047
## shm_rcstndnc|3 -0.842 0.047 -18.024 0.000 -0.842 -0.842
## shm_rcstndnc|4 -0.542 0.043 -12.537 0.000 -0.542 -0.542
## shm_rcstndnc|5 -0.038 0.041 -0.915 0.360 -0.038 -0.038
## shm_rcstndnc|6 0.561 0.043 12.921 0.000 0.561 0.561
## guilt_racsm|t1 -0.913 0.048 -19.087 0.000 -0.913 -0.913
## guilt_racsm|t2 -0.376 0.042 -8.929 0.000 -0.376 -0.376
## guilt_racsm|t3 -0.170 0.041 -4.114 0.000 -0.170 -0.170
## guilt_racsm|t4 0.107 0.041 2.613 0.009 0.107 0.107
## guilt_racsm|t5 0.688 0.045 15.386 0.000 0.688 0.688
## guilt_racsm|t6 1.310 0.057 23.097 0.000 1.310 1.310
## guilt_nqlty|t1 -1.193 0.054 -22.270 0.000 -1.193 -1.193
## guilt_nqlty|t2 -0.747 0.045 -16.442 0.000 -0.747 -0.747
## guilt_nqlty|t3 -0.487 0.043 -11.383 0.000 -0.487 -0.487
## guilt_nqlty|t4 -0.224 0.041 -5.419 0.000 -0.224 -0.224
## guilt_nqlty|t5 0.313 0.042 7.502 0.000 0.313 0.313
## guilt_nqlty|t6 0.985 0.049 20.057 0.000 0.985 0.985
## gult_trtmnt|t1 -1.177 0.053 -22.132 0.000 -1.177 -1.177
## gult_trtmnt|t2 -0.750 0.045 -16.504 0.000 -0.750 -0.750
## gult_trtmnt|t3 -0.545 0.043 -12.601 0.000 -0.545 -0.545
## gult_trtmnt|t4 -0.271 0.042 -6.526 0.000 -0.271 -0.271
## gult_trtmnt|t5 0.260 0.041 6.266 0.000 0.260 0.260
## gult_trtmnt|t6 0.850 0.047 18.144 0.000 0.850 0.850
## guilt_behvr|t1 -1.057 0.050 -20.929 0.000 -1.057 -1.057
## guilt_behvr|t2 -0.654 0.044 -14.759 0.000 -0.654 -0.654
## guilt_behvr|t3 -0.437 0.042 -10.288 0.000 -0.437 -0.437
## guilt_behvr|t4 -0.208 0.041 -5.028 0.000 -0.208 -0.208
## guilt_behvr|t5 0.319 0.042 7.632 0.000 0.319 0.319
## guilt_behvr|t6 0.985 0.049 20.057 0.000 0.985 0.985
## img_shm_dsgr|1 -1.255 0.055 -22.748 0.000 -1.255 -1.255
## img_shm_dsgr|2 -0.743 0.045 -16.380 0.000 -0.743 -0.743
## img_shm_dsgr|3 -0.524 0.043 -12.153 0.000 -0.524 -0.524
## img_shm_dsgr|4 -0.110 0.041 -2.678 0.007 -0.110 -0.110
## img_shm_dsgr|5 0.475 0.043 11.126 0.000 0.475 0.475
## img_shm_dsgr|6 1.156 0.053 21.943 0.000 1.156 1.156
## img_shm_hwsn|1 -1.209 0.054 -22.405 0.000 -1.209 -1.209
## img_shm_hwsn|2 -0.719 0.045 -15.947 0.000 -0.719 -0.719
## img_shm_hwsn|3 -0.490 0.043 -11.447 0.000 -0.490 -0.490
## img_shm_hwsn|4 -0.097 0.041 -2.352 0.019 -0.097 -0.097
## img_shm_hwsn|5 0.545 0.043 12.601 0.000 0.545 0.545
## img_shm_hwsn|6 1.232 0.055 22.580 0.000 1.232 1.232
## img_shm_hmlt|1 -1.071 0.051 -21.087 0.000 -1.071 -1.071
## img_shm_hmlt|2 -0.505 0.043 -11.769 0.000 -0.505 -0.505
## img_shm_hmlt|3 -0.213 0.041 -5.158 0.000 -0.213 -0.213
## img_shm_hmlt|4 0.219 0.041 5.288 0.000 0.219 0.219
## img_shm_hmlt|5 0.790 0.046 17.178 0.000 0.790 0.790
## img_shm_hmlt|6 1.419 0.060 23.592 0.000 1.419 1.419
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.189 0.189 0.189
## .revrr_tryhardr 0.226 0.226 0.226
## .rr_deserve 0.182 0.182 0.182
## .rr_slavery 0.243 0.243 0.243
## .revsham_ntshmd 0.493 0.493 0.493
## .shame_racistmn 0.233 0.233 0.233
## .shame_mns2bwht 0.111 0.111 0.111
## .sham_rcstndncs 0.179 0.179 0.179
## .guilt_racism 0.138 0.138 0.138
## .guilt_inequlty 0.139 0.139 0.139
## .guilt_treatmnt 0.110 0.110 0.110
## .guilt_behavior 0.118 0.118 0.118
## .img_shm_dsgrcd 0.251 0.251 0.251
## .image_shm_hwsn 0.067 0.067 0.067
## .imag_shm_hmltd 0.343 0.343 0.343
## .RR 1.000 0.412 0.412
## .MORAL 1.000 0.029 0.029
## .GUILT 1.000 0.107 0.107
## .IMAGE 1.000 0.333 0.333
## General 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_deserve 1.000 1.000 1.000
## rr_slavery 1.000 1.000 1.000
## revsham_ntshmd 1.000 1.000 1.000
## shame_racistmn 1.000 1.000 1.000
## shame_mns2bwht 1.000 1.000 1.000
## sham_rcstndncs 1.000 1.000 1.000
## guilt_racism 1.000 1.000 1.000
## guilt_inequlty 1.000 1.000 1.000
## guilt_treatmnt 1.000 1.000 1.000
## guilt_behavior 1.000 1.000 1.000
## img_shm_dsgrcd 1.000 1.000 1.000
## image_shm_hwsn 1.000 1.000 1.000
## imag_shm_hmltd 1.000 1.000 1.000## lavaan 0.6-7 ended normally after 40 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of free parameters 112
##
## Used Total
## Number of observations 936 952
##
## Model Test User Model:
## Standard Robust
## Test Statistic 550.254 1326.823
## Degrees of freedom 75 75
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.425
## Shift parameter 33.124
## simple second-order correction
##
## Model Test Baseline Model:
##
## Test statistic 241677.114 57840.451
## Degrees of freedom 105 105
## P-value 0.000 0.000
## Scaling correction factor 4.184
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.998 0.978
## Tucker-Lewis Index (TLI) 0.997 0.970
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.082 0.134
## 90 Percent confidence interval - lower 0.076 0.127
## 90 Percent confidence interval - upper 0.089 0.140
## 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 0.049 0.049
##
## 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 0.643 0.019 33.495 0.000 0.643 0.643
## revrr_tryhardr 0.644 0.020 32.340 0.000 0.644 0.644
## rr_deserve 0.463 0.019 24.507 0.000 0.463 0.463
## rr_slavery 0.514 0.020 25.326 0.000 0.514 0.514
## MORAL =~
## revsham_ntshmd 0.217 0.044 4.927 0.000 0.217 0.217
## shame_racistmn 0.151 0.035 4.350 0.000 0.151 0.151
## shame_mns2bwht 0.284 0.049 5.856 0.000 0.284 0.284
## sham_rcstndncs 0.010 0.030 0.347 0.728 0.010 0.010
## GUILT =~
## guilt_racism 0.212 0.021 10.022 0.000 0.212 0.212
## guilt_inequlty 0.317 0.021 15.451 0.000 0.317 0.317
## guilt_treatmnt 0.397 0.019 21.365 0.000 0.397 0.397
## guilt_behavior 0.286 0.019 14.730 0.000 0.286 0.286
## IMAGE =~
## img_shm_dsgrcd 0.495 0.019 25.698 0.000 0.495 0.495
## image_shm_hwsn 0.490 0.017 28.066 0.000 0.490 0.490
## imag_shm_hmltd 0.572 0.020 28.229 0.000 0.572 0.572
## General =~
## revrr_favors 0.668 0.020 33.867 0.000 0.668 0.668
## revrr_tryhardr 0.645 0.021 30.602 0.000 0.645 0.645
## rr_deserve 0.726 0.018 41.476 0.000 0.726 0.726
## rr_slavery 0.684 0.020 33.649 0.000 0.684 0.684
## revsham_ntshmd 0.695 0.018 39.659 0.000 0.695 0.695
## shame_racistmn 0.861 0.011 78.598 0.000 0.861 0.861
## shame_mns2bwht 0.925 0.007 125.731 0.000 0.925 0.925
## sham_rcstndncs 0.902 0.009 100.668 0.000 0.902 0.902
## guilt_racism 0.896 0.008 108.815 0.000 0.896 0.896
## guilt_inequlty 0.872 0.009 92.527 0.000 0.872 0.872
## guilt_treatmnt 0.874 0.009 94.933 0.000 0.874 0.874
## guilt_behavior 0.891 0.008 105.144 0.000 0.891 0.891
## img_shm_dsgrcd 0.712 0.016 44.520 0.000 0.712 0.712
## image_shm_hwsn 0.796 0.012 63.932 0.000 0.796 0.796
## imag_shm_hmltd 0.643 0.019 34.127 0.000 0.643 0.643
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RR ~~
## MORAL 0.000 0.000 0.000
## GUILT 0.000 0.000 0.000
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
## MORAL ~~
## GUILT 0.000 0.000 0.000
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
## GUILT ~~
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
## IMAGE ~~
## General 0.000 0.000 0.000
##
## 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_deserve 0.000 0.000 0.000
## .rr_slavery 0.000 0.000 0.000
## .revsham_ntshmd 0.000 0.000 0.000
## .shame_racistmn 0.000 0.000 0.000
## .shame_mns2bwht 0.000 0.000 0.000
## .sham_rcstndncs 0.000 0.000 0.000
## .guilt_racism 0.000 0.000 0.000
## .guilt_inequlty 0.000 0.000 0.000
## .guilt_treatmnt 0.000 0.000 0.000
## .guilt_behavior 0.000 0.000 0.000
## .img_shm_dsgrcd 0.000 0.000 0.000
## .image_shm_hwsn 0.000 0.000 0.000
## .imag_shm_hmltd 0.000 0.000 0.000
## RR 0.000 0.000 0.000
## MORAL 0.000 0.000 0.000
## GUILT 0.000 0.000 0.000
## IMAGE 0.000 0.000 0.000
## General 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## revrr_favrs|t1 -1.120 0.052 -21.600 0.000 -1.120 -1.120
## revrr_favrs|t2 -0.552 0.043 -12.729 0.000 -0.552 -0.552
## revrr_favrs|t3 -0.170 0.041 -4.114 0.000 -0.170 -0.170
## revrr_favrs|t4 0.443 0.042 10.417 0.000 0.443 0.443
## rvrr_tryhrdr|1 -1.426 0.060 -23.616 0.000 -1.426 -1.426
## rvrr_tryhrdr|2 -0.823 0.046 -17.724 0.000 -0.823 -0.823
## rvrr_tryhrdr|3 -0.428 0.042 -10.094 0.000 -0.428 -0.428
## rvrr_tryhrdr|4 0.183 0.041 4.441 0.000 0.183 0.183
## rr_deserve|t1 -1.397 0.059 -23.514 0.000 -1.397 -1.397
## rr_deserve|t2 -0.873 0.047 -18.500 0.000 -0.873 -0.873
## rr_deserve|t3 -0.347 0.042 -8.281 0.000 -0.347 -0.347
## rr_deserve|t4 0.350 0.042 8.346 0.000 0.350 0.350
## rr_slavery|t1 -1.310 0.057 -23.097 0.000 -1.310 -1.310
## rr_slavery|t2 -0.869 0.047 -18.441 0.000 -0.869 -0.869
## rr_slavery|t3 -0.558 0.043 -12.857 0.000 -0.558 -0.558
## rr_slavery|t4 0.118 0.041 2.874 0.004 0.118 0.118
## rvshm_ntshmd|1 -1.419 0.060 -23.592 0.000 -1.419 -1.419
## rvshm_ntshmd|2 -0.850 0.047 -18.144 0.000 -0.850 -0.850
## rvshm_ntshmd|3 -0.539 0.043 -12.473 0.000 -0.539 -0.539
## rvshm_ntshmd|4 0.132 0.041 3.201 0.001 0.132 0.132
## rvshm_ntshmd|5 0.428 0.042 10.094 0.000 0.428 0.428
## rvshm_ntshmd|6 0.942 0.048 19.491 0.000 0.942 0.942
## sham_rcstmn|t1 -1.390 0.059 -23.486 0.000 -1.390 -1.390
## sham_rcstmn|t2 -0.930 0.048 -19.318 0.000 -0.930 -0.930
## sham_rcstmn|t3 -0.695 0.045 -15.511 0.000 -0.695 -0.695
## sham_rcstmn|t4 -0.425 0.042 -10.030 0.000 -0.425 -0.425
## sham_rcstmn|t5 0.080 0.041 1.960 0.050 0.080 0.080
## sham_rcstmn|t6 0.674 0.045 15.136 0.000 0.674 0.674
## shm_mns2bwht|1 -1.145 0.052 -21.846 0.000 -1.145 -1.145
## shm_mns2bwht|2 -0.722 0.045 -16.009 0.000 -0.722 -0.722
## shm_mns2bwht|3 -0.555 0.043 -12.793 0.000 -0.555 -0.555
## shm_mns2bwht|4 -0.257 0.041 -6.200 0.000 -0.257 -0.257
## shm_mns2bwht|5 0.224 0.041 5.419 0.000 0.224 0.224
## shm_mns2bwht|6 0.740 0.045 16.319 0.000 0.740 0.740
## shm_rcstndnc|1 -1.397 0.059 -23.514 0.000 -1.397 -1.397
## shm_rcstndnc|2 -1.047 0.050 -20.823 0.000 -1.047 -1.047
## shm_rcstndnc|3 -0.842 0.047 -18.024 0.000 -0.842 -0.842
## shm_rcstndnc|4 -0.542 0.043 -12.537 0.000 -0.542 -0.542
## shm_rcstndnc|5 -0.038 0.041 -0.915 0.360 -0.038 -0.038
## shm_rcstndnc|6 0.561 0.043 12.921 0.000 0.561 0.561
## guilt_racsm|t1 -0.913 0.048 -19.087 0.000 -0.913 -0.913
## guilt_racsm|t2 -0.376 0.042 -8.929 0.000 -0.376 -0.376
## guilt_racsm|t3 -0.170 0.041 -4.114 0.000 -0.170 -0.170
## guilt_racsm|t4 0.107 0.041 2.613 0.009 0.107 0.107
## guilt_racsm|t5 0.688 0.045 15.386 0.000 0.688 0.688
## guilt_racsm|t6 1.310 0.057 23.097 0.000 1.310 1.310
## guilt_nqlty|t1 -1.193 0.054 -22.270 0.000 -1.193 -1.193
## guilt_nqlty|t2 -0.747 0.045 -16.442 0.000 -0.747 -0.747
## guilt_nqlty|t3 -0.487 0.043 -11.383 0.000 -0.487 -0.487
## guilt_nqlty|t4 -0.224 0.041 -5.419 0.000 -0.224 -0.224
## guilt_nqlty|t5 0.313 0.042 7.502 0.000 0.313 0.313
## guilt_nqlty|t6 0.985 0.049 20.057 0.000 0.985 0.985
## gult_trtmnt|t1 -1.177 0.053 -22.132 0.000 -1.177 -1.177
## gult_trtmnt|t2 -0.750 0.045 -16.504 0.000 -0.750 -0.750
## gult_trtmnt|t3 -0.545 0.043 -12.601 0.000 -0.545 -0.545
## gult_trtmnt|t4 -0.271 0.042 -6.526 0.000 -0.271 -0.271
## gult_trtmnt|t5 0.260 0.041 6.266 0.000 0.260 0.260
## gult_trtmnt|t6 0.850 0.047 18.144 0.000 0.850 0.850
## guilt_behvr|t1 -1.057 0.050 -20.929 0.000 -1.057 -1.057
## guilt_behvr|t2 -0.654 0.044 -14.759 0.000 -0.654 -0.654
## guilt_behvr|t3 -0.437 0.042 -10.288 0.000 -0.437 -0.437
## guilt_behvr|t4 -0.208 0.041 -5.028 0.000 -0.208 -0.208
## guilt_behvr|t5 0.319 0.042 7.632 0.000 0.319 0.319
## guilt_behvr|t6 0.985 0.049 20.057 0.000 0.985 0.985
## img_shm_dsgr|1 -1.255 0.055 -22.748 0.000 -1.255 -1.255
## img_shm_dsgr|2 -0.743 0.045 -16.380 0.000 -0.743 -0.743
## img_shm_dsgr|3 -0.524 0.043 -12.153 0.000 -0.524 -0.524
## img_shm_dsgr|4 -0.110 0.041 -2.678 0.007 -0.110 -0.110
## img_shm_dsgr|5 0.475 0.043 11.126 0.000 0.475 0.475
## img_shm_dsgr|6 1.156 0.053 21.943 0.000 1.156 1.156
## img_shm_hwsn|1 -1.209 0.054 -22.405 0.000 -1.209 -1.209
## img_shm_hwsn|2 -0.719 0.045 -15.947 0.000 -0.719 -0.719
## img_shm_hwsn|3 -0.490 0.043 -11.447 0.000 -0.490 -0.490
## img_shm_hwsn|4 -0.097 0.041 -2.352 0.019 -0.097 -0.097
## img_shm_hwsn|5 0.545 0.043 12.601 0.000 0.545 0.545
## img_shm_hwsn|6 1.232 0.055 22.580 0.000 1.232 1.232
## img_shm_hmlt|1 -1.071 0.051 -21.087 0.000 -1.071 -1.071
## img_shm_hmlt|2 -0.505 0.043 -11.769 0.000 -0.505 -0.505
## img_shm_hmlt|3 -0.213 0.041 -5.158 0.000 -0.213 -0.213
## img_shm_hmlt|4 0.219 0.041 5.288 0.000 0.219 0.219
## img_shm_hmlt|5 0.790 0.046 17.178 0.000 0.790 0.790
## img_shm_hmlt|6 1.419 0.060 23.592 0.000 1.419 1.419
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .revrr_favors 0.141 0.141 0.141
## .revrr_tryhardr 0.169 0.169 0.169
## .rr_deserve 0.259 0.259 0.259
## .rr_slavery 0.269 0.269 0.269
## .revsham_ntshmd 0.470 0.470 0.470
## .shame_racistmn 0.237 0.237 0.237
## .shame_mns2bwht 0.064 0.064 0.064
## .sham_rcstndncs 0.186 0.186 0.186
## .guilt_racism 0.153 0.153 0.153
## .guilt_inequlty 0.139 0.139 0.139
## .guilt_treatmnt 0.078 0.078 0.078
## .guilt_behavior 0.125 0.125 0.125
## .img_shm_dsgrcd 0.248 0.248 0.248
## .image_shm_hwsn 0.126 0.126 0.126
## .imag_shm_hmltd 0.260 0.260 0.260
## RR 1.000 1.000 1.000
## MORAL 1.000 1.000 1.000
## GUILT 1.000 1.000 1.000
## IMAGE 1.000 1.000 1.000
## General 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_deserve 1.000 1.000 1.000
## rr_slavery 1.000 1.000 1.000
## revsham_ntshmd 1.000 1.000 1.000
## shame_racistmn 1.000 1.000 1.000
## shame_mns2bwht 1.000 1.000 1.000
## sham_rcstndncs 1.000 1.000 1.000
## guilt_racism 1.000 1.000 1.000
## guilt_inequlty 1.000 1.000 1.000
## guilt_treatmnt 1.000 1.000 1.000
## guilt_behavior 1.000 1.000 1.000
## img_shm_dsgrcd 1.000 1.000 1.000
## image_shm_hwsn 1.000 1.000 1.000
## imag_shm_hmltd 1.000 1.000 1.000For the bifactor model, \(\omega_t\) is 0.981, \(\omega_h\) is 0.918, the relative \(\omega\) is 0.936 and the factor correlation is 0.958 with an H of 0.973, PUC of 0.800 and an FDI of 0.986, with 62.8% of total variance general, 19.5% unique and 78% of the common variance general. The RR, MORAL, GUILT, and IMAGE have \(\omega_{hs}\), H, FDI, total variance and explained common variance of 0.383/0.672/0.820/0.087/0.108, 0.024/0.138/0.372/0.010/0.012, 0.102/0.303/0.551/0.026/0.032 and 0.315/0.530/0.728/0.054/0.067. It seems that the IMAGE and RR factors are independently interpretable but these measures are still overwhelmingly general.
Four
ZGRunCGFC.fit <- cfa(ZGModCGF, data = data, group = "ideo", std.lv = T, orthogonal = F, ordered = c("wpa_advantages", "wpa_opensdoors", "wpa_easier", "shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'ideo' 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
## (= -2.772286e-15) is smaller than zero. This may be a symptom that
## the model is not identified.ZGRunCGFM.fit <- cfa(ZGModCGF, data = data, group = "ideo", std.lv = F, orthogonal = F, group.equal = "loadings", ordered = c("wpa_advantages", "wpa_opensdoors", "wpa_easier", "shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'ideo' 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
## (= 1.071160e-14) is close to zero. This may be a symptom that the
## model is not identified.ZGRunCGFS.fit <- cfa(ZGModCGF, data = data, group = "ideo", std.lv = F, orthogonal = F, group.equal = c("loadings", "intercepts"), ordered = c("wpa_advantages", "wpa_opensdoors", "wpa_easier", "shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'ideo' contains missing valuesZGRunCGFF.fit <- cfa(ZGModCGF, data = data, group = "ideo", std.lv = F, orthogonal = F, group.equal = c("loadings", "intercepts", "residuals"), ordered = c("wpa_advantages", "wpa_opensdoors", "wpa_easier", "shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "revshame_notashamed", "revrr_favors", "revrr_tryharder"))## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'ideo' contains missing valuesZGRunCGFLA.fit <- cfa(ZGModCGF, data = data, group = "ideo", std.lv = T, orthogonal = F, group.equal = c("loadings", "intercepts", "residuals", "means"), ordered = c("wpa_advantages", "wpa_opensdoors", "wpa_easier", "shame_racistmean", "shame_means2bewhite", "shame_racistendencies", "guilt_racism", "guilt_inequality", "guilt_treatment", "guilt_behavior", "image_shame_disgraced", "image_shame_howseen", "image_shame_humiliated", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "revshame_notashamed", "revrr_favors", "revrr_tryharder"), control = list(rel.tol = 1e-4), check.gradient = F)## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: group variable 'ideo' contains missing valuesround(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 775.710 1216.318 1152.456 1157.736 8774.630
## df 522.000 552.000 722.000 724.000 736.000
## npar 444.000 414.000 244.000 242.000 230.000
## cfi.scaled 0.978 0.981 0.975 0.975 0.863
## rmsea 0.040 0.063 0.044 0.044 0.190
## rmsea.ci.lower 0.034 0.058 0.040 0.040 0.186
## rmsea.ci.upper 0.046 0.068 0.049 0.049 0.193
## srmr 0.044 0.057 0.047 0.047 0.049There may be some violations of metric invariance but there do not appear to be any for scalar or strict invariance. The means by group are certainly not equivalent.
Five
ZGWPDiscFA <- '
RR =~ revrr_favors + revrr_tryharder
DISC =~ rr_slavery + rr_deserve + racineq_discrim + disc_blacks + nodisc_equalincomes
WP =~ wpa_advantages + wpa_opensdoors + wpa_easier
General =~ RR + DISC + WP'
ZGRunWPDiscFA <- cfa(ZGWPDiscFA, data = data, std.lv = T, ordered = c("wpa_advantages", "wpa_opensdoors", "wpa_easier", "rr_slavery", "rr_deserve", "disc_blacks", "nodisc_equalincomes", "revshame_notashamed", "revrr_favors", "revrr_tryharder"), control = list(rel.tol = 1e-4), check.gradient = F)
summary(ZGRunWPDiscFA, stand = T, fit = T)## 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
## General =~
## 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
## General 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
## General 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\(\omega_t\) is 0.960, \(\omega_h\) is 0.952, the relative \(\omega\) is 0.992 and the factor correlation is 0.976, H is 0.960, PUC is 0.689, FDI is 0.980, 68.8% of total variance is general, 97% of common variance is general, and total uniqueness is 29.1%. The RR, DISC and WP factors have \(\omega_{hs}\) values of 0.038, <0.001 and 0.058 respectively (likely somewhat higher in a bifactor model), H of 0.063, <0.001 and 0.133, FDIs of 0.252, 0.004 and 0.364, and they explain 0.7%, <0.01% and 1.5% of the total variance, or 0.9%, <0.01% and 2.1% of the common variance, respectively (numbers are rounded).
References
Paternoster, R., Brame, R., Mazerolle, P., & Piquero, A. (1998). Using the Correct Statistical Test for the Equality of Regression Coefficients. Criminology, 36(4), 859–866. https://doi.org/10.1111/j.1745-9125.1998.tb01268.x