Table 5 Measurement invariance testing steps [33]
Test for | Interpretation | Model constraints |
|---|---|---|
Configural invariance | Tests for the assumption of the same underlying factor structure in all subgroups, i.e., the overall model fits the data similarly well in all subgroups | No specific constraints are imposed on the estimated parameters. |
Metric invariance | Tests whether the same constructs are measured across subgroups, i.e., whether respondents in different subgroups attribute the same meaning to the respective motivation factors | • Factor loadings estimated freely but constrained to equality in the subgroups |
Scalar invariance | Tests whether subgroups can be compared on their mean scores or whether subgroups score systematically different (at the same underlying level of motivation) for certain items | • Factor loadings estimated freely but constrained to equality in the subgroups • Item intercepts estimated freely but constrained to equality in the subgroups |
Residual variance invariance | Tests whether the proportion of contamination by other constructs as measured by the different items (i.e., variance that is not explained by the intended factors) is equal across groups and whether measurements are thus fully comparable across groups | • Factor loadings estimated freely but constrained to equality in the subgroups • Item intercepts estimated freely but constrained to equality in the subgroups • Item residual variances estimated freely but constrained to equality in subgroups |