Interpreting and Testing Interactions in Conditional Mixture Models

Mixture modeling applications in psychology often include covariates to explain class membership and aid in construct validation of the latent classification variable. These applications tend to use between-class models involving only main effects of predictors. However, a variety of developmental theories posit interactions among risk and protective variables in predicting membership in trajectory classes or behavioral symptom profiles. This article bridges this disconnect between substantive theory and methodological practice by presenting and comparing two approaches for testing interactive effects of predictors on class membership: product term (PT) and multiple group (MG) approaches. For each approach, we discuss alternative interpretation strategies involving predicted probabilities and odds ratios; we also discuss when the approaches provide equivalent inferences. Published longitudinal and cross-sectional mixture model applications that had originally allowed for only additive effects on class membership are re-analyzed to illustrate the testing and interpretation of interactive effects on class membership using both PT and MG approaches.