Table 7.
Goodness-of-fit comparison between nested models.
| Difference between Models | First Revision of Hypothetical Model (R1) | Second Revision of Hypothetical Model (R2) | ||||
|---|---|---|---|---|---|---|
| Δχ2 | Δdf | p | Δχ2 | Δdf | p | |
| UC−MW | 0.148 | 2 | 0.929 | 0.007 | 2 | 0.997 |
| UC−SW | 6.967 | 6 | 0.324 | 1.472 | 4 | 0.832 |
| UC−SC | 24.241 | 7 | 0.001 | 2.219 | 5 | 0.818 |
| UC−SR | 26.292 | 10 | 0.003 | 5.095 | 7 | 0.648 |
| UC−MR | 33.827 | 13 | 0.001 | 13.294 | 10 | 0.208 |
| MW−SW | 6.819 | 4 | 0.146 | 1.465 | 2 | 0.481 |
| MW−SC | 24.093 | 5 | <0.001 | 2.212 | 3 | 0.530 |
| MW−SR | 26.144 | 8 | 0.001 | 5.088 | 5 | 0.405 |
| MW−MR | 33.679 | 11 | <0.001 | 13.287 | 8 | 0.102 |
| SW−SC | 17.274 | 1 | <0.001 | 0.746 | 1 | 0.388 |
| SW−SR | 19.325 | 4 | 0.001 | 3.622 | 3 | 0.305 |
| SW−MR | 26.86 | 7 | <0.001 | 11.821 | 6 | 0.066 |
| SC−SR | 2.051 | 3 | 0.562 | 2.876 | 2 | 0.237 |
| SC−MR | 9.585 | 6 | 0.143 | 11.075 | 5 | 0.050 |
| SR−MR | 7.535 | 3 | 0.057 | 8.199 | 3 | 0.042 |
Note. Nested models in constraints: UC = Unconstrained model, MW = model with constraints on the measurement weights, SW = model with constraints on the structural weights, SC = model with constrains on the structural covariances, SR = model with constrains on the structural residuals, and MR = model with constraints on measurement residuals. Statistic: Δχ2 = chi-square difference test statistic, Δdf = difference between degrees of freedom of the two models being compared, and p = probability value of chi-square difference statistic under null hypothesis of equality of goodness of fit between the two models being compared.