Table 3.
Summary of nested and difference model testing results
| NestedTest | H0 (Nested)(ep–df) | H1 (Compare)(ep–df) | Models nested?Fit function | H0 Fit indices | H1 Fit indices | Chi-square Difference TestGoodness-of-fit Differences |
|---|---|---|---|---|---|---|
| 1 | Single Factor (66–170) |
Higher Order (71–165) |
Yes ε = 0.00000002 |
χ2 = 2621.48 (170) p < .001 CFI = 0.760 TLI = 0.732 RMSEA = 0.127 (.123-.131) |
χ2 = 817.28 (165) p < .001 CFI = 0.936 TLI = 0.926 RMSEA = 0.066 (.062-.071) |
χ2diff = 1048.23 (5) p < .001 ΔCFI = 0.176 ΔTLI = 0.194 ΔRMSEA = – 0.061 |
| 2 | Single Factor (66–170) |
Corr. 5 Factor (76–160) |
Yes ε = 0.00000000 |
χ2 = 2621.48 (170) p < .001 CFI = 0.760 TLI = 0.732 RMSEA = 0.127 (.123-.131) |
χ2 = 789.98 (160) p < .001 CFI = 0.938 TLI = 0.927 RMSEA = 0.066 (.062-.071) |
χ2diff = 909.23 (10) p < .001 ΔCFI = 0.178 ΔTLI = 0.195 ΔRMSEA = – 0.061 |
| 3 | Single Factor (66–170) |
Bifactor (96–140) |
Yes ε = 0.00000000 |
χ2 = 2621.48 (170) p < .001 CFI = 0.760 TLI = 0.732 RMSEA = 0.127 (.123-.131) |
χ2 = 313.36 (140) p < .001 CFI = 0.983 TLI = 0.977 RMSEA = 0.037 (.032-.043) |
χ2diff = 1465.09 (30) p < .001 ΔCFI = 0.223 ΔTLI = 0.245 ΔRMSEA = – 0.090 |
| 4 | Higher Order (71–165) |
Corr. 5 Factor (76–160) |
Yes ε = 0.00000000 |
χ2 = 817.28 (165) p < .001 CFI = 0.936 TLI = 0.926 RMSEA = 0.066 (.062-.071) |
χ2 = 789.98 (160) p < .001 CFI = 0.938 TLI = 0.927 RMSEA = 0.066 (.062-.071) |
χ2diff = 38.45 (5) p < .001 ΔCFI = 0.002 ΔTLI = 0.001 ΔRMSEA = 0.000 |
| 5 | Higher Order (71–165) |
Bifactor (96–140) |
Yes ε = 0.00000000 |
χ2 = 817.28 (165) p < .001 CFI = 0.936 TLI = 0.926 RMSEA = 0.066 (.062-.071) |
χ2 = 313.36 (140) p < .001 CFI = 0.983 TLI = 0.977 RMSEA = 0.037 (.032-.043) |
χ2diff = 348.46 (25) p < .001 ΔCFI = 0.047 ΔTLI = 0.051 ΔRMSEA = – 0.029 |
| 6 | Corr. 5 Factor (76–160) |
Bifactor (96–140) |
Yes ε = 0.00000000 |
χ2 = 789.98 (160) p < .001 CFI = 0.938 TLI = 0.927 RMSEA = 0.066 (.062-.071) |
χ2 = 313.36 (140) p < .001 CFI = 0.983 TLI = 0.977 RMSEA = 0.037 (.032-.043) |
χ2diff = 327.82 (20) p < .001 ΔCFI = 0.045 ΔTLI = 0.050 ΔRMSEA = – 0.029 |
H0 = designated nested model (restricted: fewer parameters), H1 = designated comparison model (unrestricted: more parameters). ep = number of estimated parameters, df = number of degrees of freedom, χ2 = chi-square of model fit, CFI = goodness-of-fit comparative fit index, TLI = goodness-of-fit Tucker–Lewis fit index, RMSEA = Root mean square error of approximation index, χ2diff = chi-square difference test, ΔCFI = comparative goodness-of-fit index difference (H1 – H0), ΔTLI = Tucker–Lewis goodness-of-fit index difference (H1 – H0), ΔRMSEA = Root mean square error of approximation index difference (H1 – H0).