Extensions of Auxiliary Variable Approaches for the Investigation of Mediation, Moderation, and Conditional Effects in Mixture Models

Person-centered analyses and mixture models, such as latent profile analyses (LPA), are becoming increasingly common in the organizational literature. However, common usage of LPA rarely extends to the estimation of moderation, conditional effects, and mediation within a single model. This can affect the accuracy of parameter estimates, and it interferes with development and investigation of complex theories. The current study provides an overview of systematic approaches that allows researchers to investigate models involving moderation, conditional effects on outcomes, and mediation. Using M plus, we offer an accessible method of testing complex statistical models that are auxiliary to the focal mixture model. We provide syntax for typical moderation, conditional effects, and mediation hypotheses, and we provide a detailed explanation of the procedures. We demonstrate these procedures with applications involving the five-factor model (FFM) of personality and several additional variables that comprise complex auxiliary statistical models. The pedagogical approach offered by this research will facilitate future theoretical developments and empirical advancements in the use of person-centered analyses.