Selecting the number of clusters in Mixture Multigroup Structural Equation Modeling

Behavioral scientists often use Multigroup Structural Equation Modeling (MG-SEM) to compare groups in terms of their relations among latent variables (LV) —also called 'structural relations'. Since LVs are indirectly measured via questionnaire items, one should evaluate to what extent their measurement is invariant before comparing their structural relations. To efficiently compare many groups, the recently proposed Mixture Multigroup SEM (MMG-SEM) clusters groups based on their structural relations while accounting for measurement (non-)invariance. MMG-SEM requires the user to select the optimal number of clusters for the empirical data at hand. Various approaches have been developed to address this problem for related methods, but no definitive answer exists on which is best. This paper aims to find the best-performing model selection approach for MMG-SEM through an extensive simulation study. Specifically, we compared five information criteria and the convex hull procedure and included empirically realistic conditions that affect the clusters' separability.