Model | n | χ^{2} | Scaling correction factor | Mean-adjusted χ^{2}* | df | P | CFI | RMSEA (90% CI) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Five-factor | ||||||||||||||||
White males | 274 | 176.916 | 171.053 | 94 | 0.000 | 0.892 | 0.055 (0.041-0.068) | |||||||||
White females | 291 | 182.742 | 154.442 | 94 | 0.000 | 0.914 | 0.047 (0.033-0.060) | |||||||||
Black males | 195 | 119.911 | 96.601 | 94 | 0.407 | 0.994 | 0.012 (0.000-0.040) | |||||||||
Black females | 653 | 244.121 | 213.081 | 94 | 0.000 | 0.912 | 0.044 (0.036-0.052) | |||||||||
Five-factor and two correlated errors | ||||||||||||||||
White males | 274 | 126.920 | 123.250 | 92 | 0.016 | 0.956 | 0.035 (0.016-0.050) | |||||||||
White females | 291 | 141.781 | 121.686 | 92 | 0.021 | 0.958 | 0.033 (0.014-0.048) | |||||||||
Black males | 195 | 110.253 | 90.348 | 92 | 0.529 | 0.999 | 0.000 (0.000-0.037) | |||||||||
Black females | 653 | 187.851 | 164.390 | 92 | 0.000 | 0.947 | 0.035 (0.026-0.043) | |||||||||
1. Unconstrained | 1,413 | 566.809 | 1.14 | 497.715 | 368 | 0.000 | 0.959 | 0.016 (0.012-0.019) | ||||||||
2. Equal factor loadings | 1,413 | 650.201 | 1.19 | 546.768 | 401 | 0.000 | 0.954 | 0.016 (0.012-0.019) | ||||||||
3. Equal factor loadings with rcc_low constraint released | 1,413 | 614.380 | 1.19 | 518.120 | 398 | 0.000 | 0.962 | 0.015 (0.011-0.018) | ||||||||
Model comparisons | χ^{2}_{diff} | Difference df | Difference test scaling correction factor | Mean-adjusted χ^{2}_{diff}^{†} | P | |||||||||||
1 vs 2 | 83.392 | 33 | 1.75 | 47.635 | 0.048 | |||||||||||
1 vs 3 | 47.571 | 30 | 1.76 | 27.000 | 0.623 |
Abbreviations: df, degrees of freedom; scf, scaling correction factor; dtscf, difference test scaling correction factor; RMSEA, root mean square error of approximation.
↵* The mean-adjusted χ^{2} is used when the outcome variables has a non-normal distribution. Satorra and Bentler (61) showed that if the usual normal-theory χ^{2} test statistic is divided by a scaling correction factor, the scaled statistic better approximates a χ^{2} distribution.
↵† The difference between two mean-adjusted χ^{2} for nested models does not follow a χ^{2} distribution. Satorra and Bentler (66) showed that the following equation for the mean-adjusted difference statistic, which incorporates a difference test scaling correction factor, does follow a χ^{2} distribution. Mean-adjusted χ^{2}_{diff} = (χ ^{2}_{nested} (χ ^{2}_{nested} − χ ^{2}_{comparison}) / dtscf. dtscf = (df_{nested} × scf_{nested} − df_{comparison} × scf_{comparison}) / (df_{nested} − df_{comparison}).