=========== TRUE MODELS =========== 1 MG configural: random loadings + random intercepts 2 MG metric: invariant loadings, random intercepts 3 MG scalar: fully invariant
4 ML configural: between loadings tilted (g != 0), theta_B > 0 5 ML metric: cross-level invariance holds, theta_B > 0 6 ML full: cross-level invariance, theta_B ~ 0
7 ML metric + loadings correlated with factor means (kappa = .5) 8 ML full + intercepts correlated with factor means
=========== ABSOLUTE FIT (means over replications) =========== dgp model n_rep converged_pct admissible_pct chisq_rej_pct cfi cfi_sd rmsea rmsea_sd srmr srmr_w srmr_b good_fit_pct mg_configural mg_configural 208 96.6 17.3 7.0 0.999 0.001 0.010 0.010 0.029 NaN NaN 100.0 mg_metric mg_configural 208 100.0 95.2 12.0 0.999 0.001 0.010 0.010 0.028 NaN NaN 100.0 mg_scalar mg_configural 208 100.0 92.3 11.1 0.999 0.001 0.011 0.010 0.029 NaN NaN 100.0 ml_configural mg_configural 208 97.6 13.0 9.9 0.999 0.002 0.010 0.010 0.029 NaN NaN 100.0 ml_metric mg_configural 208 97.6 13.5 10.8 0.999 0.001 0.009 0.010 0.029 NaN NaN 100.0 ml_full mg_configural 208 100.0 87.5 9.6 0.999 0.001 0.011 0.010 0.029 NaN NaN 100.0 ml_metric_bcorr mg_configural 209 87.1 0.0 8.2 0.999 0.001 0.009 0.010 0.030 NaN NaN 100.0 ml_full_gcorr mg_configural 209 100.0 91.9 12.0 0.999 0.002 0.011 0.011 0.029 NaN NaN 100.0 mg_configural mg_metric 208 100.0 96.2 100.0 0.905 0.011 0.105 0.006 0.083 NaN NaN 0.0 mg_metric mg_metric 208 100.0 100.0 8.7 0.999 0.002 0.009 0.009 0.041 NaN NaN 100.0 mg_scalar mg_metric 208 100.0 100.0 10.6 0.998 0.002 0.010 0.009 0.041 NaN NaN 100.0 ml_configural mg_metric 208 100.0 94.2 100.0 0.904 0.011 0.105 0.006 0.084 NaN NaN 0.0 ml_metric mg_metric 208 100.0 94.7 100.0 0.903 0.011 0.106 0.006 0.085 NaN NaN 0.0 ml_full mg_metric 208 100.0 100.0 12.5 0.998 0.002 0.011 0.009 0.041 NaN NaN 100.0 ml_metric_bcorr mg_metric 209 100.0 5.3 100.0 0.866 0.015 0.121 0.007 0.100 NaN NaN 0.0 ml_full_gcorr mg_metric 209 100.0 100.0 14.8 0.998 0.002 0.011 0.010 0.041 NaN NaN 100.0 mg_configural mg_scalar 208 100.0 76.4 100.0 0.589 0.036 0.189 0.008 0.145 NaN NaN 0.0 mg_metric mg_scalar 208 100.0 100.0 100.0 0.712 0.028 0.161 0.008 0.112 NaN NaN 0.0 mg_scalar mg_scalar 208 100.0 100.0 10.1 0.998 0.002 0.009 0.008 0.046 NaN NaN 100.0 ml_configural mg_scalar 208 100.0 1.0 100.0 0.558 0.034 0.196 0.007 0.160 NaN NaN 0.0 ml_metric mg_scalar 208 100.0 76.0 100.0 0.588 0.036 0.189 0.008 0.146 NaN NaN 0.0 ml_full mg_scalar 208 100.0 100.0 100.0 0.947 0.007 0.069 0.005 0.060 NaN NaN 1.9 ml_metric_bcorr mg_scalar 209 100.0 0.5 100.0 0.494 0.044 0.204 0.008 0.174 NaN NaN 0.0 ml_full_gcorr mg_scalar 209 100.0 92.8 100.0 0.933 0.007 0.078 0.004 0.072 NaN NaN 0.0 mg_configural ml_configural 208 100.0 96.6 9.1 1.000 0.000 0.003 0.003 0.064 0.005 0.059 100.0 mg_metric ml_configural 208 100.0 97.1 5.8 1.000 0.000 0.003 0.003 0.062 0.004 0.057 100.0 mg_scalar ml_configural 208 100.0 0.0 1.9 1.000 0.000 0.001 0.002 0.021 0.005 0.016 100.0 ml_configural ml_configural 208 100.0 60.6 11.1 1.000 0.000 0.003 0.003 0.074 0.005 0.069 100.0 ml_metric ml_configural 208 100.0 95.2 5.8 1.000 0.000 0.003 0.003 0.065 0.005 0.060 100.0 ml_full ml_configural 208 100.0 98.1 7.7 1.000 0.000 0.002 0.003 0.036 0.004 0.031 100.0 ml_metric_bcorr ml_configural 209 98.1 59.8 26.3 0.999 0.001 0.005 0.004 0.075 0.006 0.069 100.0 ml_full_gcorr ml_configural 209 100.0 0.0 0.5 1.000 0.000 0.001 0.002 0.039 0.005 0.034 100.0 mg_configural ml_crosslevel 208 100.0 100.0 10.1 1.000 0.000 0.003 0.003 0.072 0.005 0.067 100.0 mg_metric ml_crosslevel 208 100.0 100.0 5.8 1.000 0.000 0.003 0.003 0.067 0.004 0.063 100.0 mg_scalar ml_crosslevel 208 100.0 0.0 2.4 1.000 0.000 0.001 0.002 0.021 0.005 0.016 100.0 ml_configural ml_crosslevel 208 100.0 100.0 96.2 0.998 0.001 0.012 0.003 0.132 0.005 0.127 100.0 ml_metric ml_crosslevel 208 100.0 100.0 7.2 1.000 0.000 0.003 0.003 0.072 0.005 0.067 100.0 ml_full ml_crosslevel 208 100.0 100.0 7.7 1.000 0.000 0.002 0.003 0.036 0.004 0.031 100.0 ml_metric_bcorr ml_crosslevel 209 100.0 100.0 48.3 0.999 0.001 0.007 0.004 0.106 0.006 0.101 100.0 ml_full_gcorr ml_crosslevel 209 100.0 0.0 100.0 0.979 0.002 0.039 0.002 0.314 0.005 0.309 100.0 mg_configural ml_full 208 100.0 100.0 100.0 0.680 0.038 0.127 0.007 0.252 0.027 0.226 0.0 mg_metric ml_full 208 100.0 100.0 100.0 0.731 0.031 0.121 0.007 0.227 0.024 0.203 0.0 mg_scalar ml_full 208 100.0 100.0 1.0 1.000 0.000 0.001 0.001 0.021 0.005 0.016 100.0 ml_configural ml_full 208 100.0 88.9 100.0 0.636 0.038 0.135 0.007 0.370 0.067 0.303 0.0 ml_metric ml_full 208 100.0 100.0 100.0 0.680 0.041 0.127 0.008 0.248 0.027 0.221 0.0 ml_full ml_full 208 100.0 100.0 100.0 0.970 0.005 0.041 0.004 0.062 0.006 0.056 100.0 ml_metric_bcorr ml_full 209 100.0 89.0 100.0 0.572 0.056 0.138 0.008 0.376 0.047 0.329 0.0 ml_full_gcorr ml_full 209 100.0 100.0 100.0 0.936 0.007 0.060 0.003 0.073 0.043 0.030 1.4
=========== NESTED COMPARISONS ===========
chen_fail_pct / rutsvet_fail_pct = % of replications where the constraint is rejected
dgp comparison n_rep d_chisq df lrt_rej_pct mg_configural mg_configural -> mg_metric 208 1500.8 196 100.0
mg_metric mg_configural -> mg_metric 208 199.4 196 6.7
mg_scalar mg_configural -> mg_metric 208 199.2 196 7.7 ml_configural mg_configural -> mg_metric 208 1512.8 196 100.0
ml_metric mg_configural -> mg_metric 208 1530.9 196 100.0
ml_full mg_configural -> mg_metric 208 201.4 196 8.2 ml_metric_bcorr mg_configural -> mg_metric 209 1947.9 196 100.0 ml_full_gcorr mg_configural -> mg_metric 209 202.9 196 9.1 mg_configural mg_metric -> mg_scalar 208 4569.8 196 100.0
mg_metric mg_metric -> mg_scalar 208 4280.3 196 100.0
mg_scalar mg_metric -> mg_scalar 208 197.9 196 6.7 ml_configural mg_metric -> mg_scalar 208 4957.3 196 100.0
ml_metric mg_metric -> mg_scalar 208 4552.8 196 100.0
ml_full mg_metric -> mg_scalar 208 938.2 196 100.0 ml_metric_bcorr mg_metric -> mg_scalar 209 5073.1 196 100.0 ml_full_gcorr mg_metric -> mg_scalar 209 1141.3 196 100.0 mg_configural ml_configural -> ml_crosslevel 208 4.6 4 7.2
mg_metric ml_configural -> ml_crosslevel 208 4.2 4 5.8
mg_scalar ml_configural -> ml_crosslevel 208 3.9 4 5.3 ml_configural ml_configural -> ml_crosslevel 208 34.2 4 99.5
ml_metric ml_configural -> ml_crosslevel 208 4.8 4 9.6
ml_full ml_configural -> ml_crosslevel 208 3.6 4 3.4 ml_metric_bcorr ml_configural -> ml_crosslevel 209 10.5 4 44.9 ml_full_gcorr ml_configural -> ml_crosslevel 209 315.6 4 100.0 mg_configural ml_crosslevel -> ml_full 208 4200.3 6 100.0
mg_metric ml_crosslevel -> ml_full 208 3844.2 6 100.0
mg_scalar ml_crosslevel -> ml_full 208 5.8 6 1.4 ml_configural ml_crosslevel -> ml_full 208 4708.7 6 100.0
ml_metric ml_crosslevel -> ml_full 208 4194.8 6 100.0
ml_full ml_crosslevel -> ml_full 208 444.8 6 100.0 ml_metric_bcorr ml_crosslevel -> ml_full 209 4994.1 6 100.0 ml_full_gcorr ml_crosslevel -> ml_full 209 637.3 6 100.0 d_cfi d_rmsea d_srmr chen_fail_pct rutsvet_fail_pct 0.0937 0.0946 0.0544 100.0 100.0 0.0003 -0.0008 0.0123 1.0 0.0 0.0003 -0.0011 0.0122 1.4 0.0 0.0951 0.0950 0.0547 100.0 100.0 0.0957 0.0964 0.0555 100.0 100.0 0.0005 -0.0006 0.0123 1.9 0.0 0.1327 0.1124 0.0702 100.0 100.0 0.0005 0.0001 0.0124 1.9 0.0 0.3164 0.0846 0.0617 100.0 100.0 0.2868 0.1514 0.0711 100.0 100.0 0.0002 -0.0010 0.0047 0.0 2.9 0.3459 0.0906 0.0757 100.0 100.0 0.3150 0.0836 0.0615 100.0 100.0 0.0516 0.0581 0.0187 100.0 100.0 0.3722 0.0834 0.0743 100.0 100.0 0.0657 0.0671 0.0310 100.0 100.0 0.0000 0.0000 0.0078 1.4 0.0 0.0000 0.0000 0.0054 0.5 0.0 0.0000 0.0001 -0.0001 0.0 0.0 0.0022 0.0091 0.0577 85.6 0.0 0.0001 0.0001 0.0073 1.0 0.0 0.0000 -0.0002 0.0001 0.0 0.0 0.0005 0.0018 0.0306 42.4 0.0 0.0207 0.0384 0.2747 100.0 99.0 0.3196 0.1236 0.1584 100.0 100.0 0.2692 0.1188 0.1400 100.0 100.0 0.0000 -0.0002 0.0000 0.0 0.0 0.3610 0.1224 0.1760 100.0 100.0 0.3196 0.1239 0.1537 100.0 100.0 0.0301 0.0387 0.0245 100.0 100.0 0.4269 0.1316 0.2282 100.0 100.0 0.0429 0.0209 -0.2787 100.0 100.0