Incorporating machine learning into factor mixture modeling: Identification of covariate interactions to explain population heterogeneity

Factor mixture modeling (FMM) has been widely adopted in health and behavioral sciences to examine unobserved population heterogeneity. Covariates are often included in FMM as predictors of the latent class membership via multinomial logistic regression to help understand the formation and characterization of population heterogeneity. However, interaction effects among covariates have received considerably less attention, which might be attributable to the fact that interaction effects cannot be identified in a straightforward fashion. This study demonstrated the utility of structural equation model or SEM trees as an exploratory method to automatically search for covariate interactions that might explain heterogeneity in FMM. That is, following FMM analyses, SEM trees are conducted to identify covariate interactions. Next, latent class membership is regressed on the covariate interactions as well as all main effects of covariates. This approach was demonstrated using the Traumatic Brain Injury Model System National Database.