Collapsing Categorical Variables and Measurement Invariance. Issue 5 (3rd September 2019) - Rutkowski, Leslie; Svetina, Dubravka; Liaw, Yuan-Ling
Abstract : Cross-cultural comparisons of latent variable means demands equivalent loadings and intercepts or thresholds. Although equivalence generally emphasizes items as originally designed, researchers sometimes modify response options in categorical items. For example, substantive research interests drive decisions to reduce the number of item categories. Further, categorical multiple-group confirmatory factor analysis (MG-CFA) methods generally require that the number of indicator categories is equal across groups; however, categories with few observations in at least one group can cause challenges. In the current paper, we examine the impact of collapsing ordinal response categories in MG-CFA. An empirical analysis and a complementary simulation study suggested meaningful impacts on model fit due to collapsing categories. We also found reduced scale reliability, measured as a function of Fisher's information. Our findings further illustrated artifactual fit improvement, pointing to the possibility of data dredging for improved model-data consistency in challenging invariance contexts with large numbers of groups.