Table 4. Fit Indices for Multi-group Confirmatory Factor Analysis Evaluating Measurement Invariance of the Single-factor Structure Including the Four Intelligence Subtests Across Individuals With and Without a Migration Background.
| Model | df | χ2 | CFI | Mc | RMSEA | 90% CI | Δdf | Δχ2 | ΔCFI | ΔMc | Small diff p |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 Configural invariance | 3 | 11.506 | .986 | .993 | .067 | [.029, .110] | – | – | – | – | – |
| 2 Metric invariance | 6 | 16.481 | .983 | .992 | .053 | [.023, .084] | – | – | – | – | – |
| 2 versus 1 | – | – | – | – | – | – | 3 | 4.975 | .003 | .001 | .174 |
| 3 Scalar invariance | 9 | 29.839 | .965 | .984 | .061 | [.037, .085] | – | – | – | – | – |
| 3 versus 2 | – | – | – | – | – | – | 3 | 13.358 | .018 | .008 | .271 |
| 4 Residual invariance | 13 | 62.525 | .918 | .962 | .078 | [.059, .098] | – | – | – | – | – |
| 4 versus 2 | – | – | – | – | – | – | 4 | 32.686 | .047 | .022 | .181 |
| 5 Factor variancesa | 10 | 38.824 | .952 | .977 | .068 | [.046, .091] | – | – | – | – | – |
| 5 versus 2 | – | – | – | – | – | – | 1 | 8.985 | .013 | .007 | .270 |
| 6 Factor meansa | 10 | 150.616 | .766 | .895 | .149 | [.129, .171] | – | – | – | – | – |
| 6 versus 2 | – | – | – | – | – | – | 1 | 120.777 | .199 | .089 | .034 |
Note. NTotal = 632, NWithout migration background = 316, NWith migration background = 316. CFI = Comparative Fit Index; Mc = McDonald’s Noncentrality Index; RMSEA = root mean square error of approximation; CI = confidence interval.
a Factor variance invariance and factor mean invariance were calculated at the level of measurement invariance, as scalar invariance did not hold.