Covariate inclusion in factor mixture modeling: Evaluating one-step and three-step approaches under model misspecification and overfitting.

Factor mixture modeling (FMM) has been increasingly used in behavioral and social sciences to examine unobserved population heterogeneity. Covariates (e.g., gender, race) are often included in FMM to help understand the formation and characterization of latent subgroups or classes. This Monte Carlo simulation study evaluated the performance of one-step and three-step approaches to covariate inclusion across three scenarios, i.e., correct specification (study 1), model misspecification (study 2), and model overfitting (study 3), in terms of direct covariate effects on factors. Results showed that the performance of these two approaches was comparable when class separation was large and the specification of covariate effect was correct. However, one-step FMM had better class enumeration than the three-step approach when class separation was poor, and was more robust to the misspecification or overfitting concerning direct covariate effects. Recommendations regarding covariate inclusion approaches are provided herein depending on class separation and sample size. Large sample size (1000 or more) and the use of sample size-adjusted BIC (saBIC) in class enumeration are recommended.