Testing measurement Invariance with ordinal categorical Items

Cross populations/groups comparisons of measurement scales requires testing measurement invariance of the scales under study. Very often, linear multi-group confirmatory factor analysis (CFA) is applied to assess measurement invariance even the items/indicators of constructs are ordinal categorical measures. Simulation studies provide evidence that treating ordinal measures as continuous measures may be alright in single-group CFA, if the ordinal measures have at least five response categories and don’t have excessive skewness and/or kurtosis; but it is inappropriate in multi-group modeling. While both Bottom-up and Top-down approaches are proposed for testing measurement invariance of scales with ordered-categorical items, Top-down approach seems preferable in practice. This presentation demonstrates how to apply the Top-down approach to test measurement invariance of scales with ordinal categorical items. The Ohio (n=248) and Kentucky (n=225) samples from a multi-site natural history study of rural illicit drug users are used to test measurement invariance of the Brief Symptom Inventory (BSI-18). The model results show that the item thresholds and factor loadings of the three factors (somatization, depression, and anxiety) are all invariant between the drug using populations located in the two Middle West states in the U.S. However, the structural parameters (e.g., means and variances of the three factors) significantly vary across the populations.