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 latent variables (LVs) relations - also called 'structural relations'. Since LVs are measured indirectly, measurement invariance must be evaluated before comparing structural relations. To efficiently compare many groups, the recently proposed Mixture MG-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 data at hand. Various approaches address this problem, but no definitive answer exists on which is best. This paper aims to find the best-performing model selection approach for MMG-SEM through a simulation study by comparing five information criteria and the convex hull procedure and including empirically realistic conditions affecting the clusters' separability. No universally best measure was found, but based on our results, we recommend using the convex hull combined with another measure (e.g., AIC) when selecting the number of clusters.