Table 1.
Overview over analysis models used for overall model fit evaluation by means of χ2 tests and for evaluation of single interaction effects by means of χ2 difference tests for complete MSEM models and for partially saturated models (PS) at the within-group (Ws) or at the between-group (Bs) level.
| Population model | Type I error | Power |
|---|---|---|
| χ2 TEST | ||
| M_WIBI | WIBI | W0BI |
| PS_WIBs | WIB0 | |
| PS_WsBI | PS_W0Bs | |
| PS_WsB0 | ||
| χ2 DIFFERENCE TEST | ||
| M_W0B0 | W0B0 vs. WIBI | |
| PS_W0Bs vs. PS_WIBs | ||
| PS_WsB0 vs. PS_WsBI | ||
| M_WIB0 | W0B0 vs. WIB0 | |
| PS_W0Bs vs. PS_WIBs | ||
| M_W0BI | W0B0 vs. W0BI | |
| PS_WsB0 vs. PS_WsBI | ||
Population models are denoted by M, analysis models are denoted by their respective within- or between-levels (W, B), I indicates an interaction effect at the within- or between-group level (WI, BI), 0 indicates a missing interaction effect (W0, B0), PS are partially saturated analysis models at the within- or between-level (Ws, Bs). Misspecified models with either an interaction effect added to a linear model or an existing interaction effect fixed to zero are in italics.