A General Approach to Modeling Latent Variable Interactions and Nonlinear Effects

Interaction effects are prevalent in the behavioral sciences, particularly in psychology, where they are used to investigate the influences on human behavior by various factors. Methodological advancements have been made to model interaction effects in latent variable models. Traditional approaches like product indicator methods have limitations such as complexity, lack of parsimony, and applicability only to continuous data. Alternatively, the general interaction model and estimators have emerged but remain limited. This paper proposes a factored regression framework for estimating latent variable interactions and nonlinear effects. For example, I illustrate how to estimate latent by latent, latent by manifest, and three-way latent interactions. Additionally, I show how to probe the interactions with graphical diagnostics. This new approach offers flexibility in modeling complex structures, accommodating various data types, and including missing data on any variable. This framework is implemented in Blimp software, offering an accessible and user-friendly syntax for specifying the models. Through examples and syntax excerpts, this article demonstrates how to apply the factored regression approach to estimate latent interactions, making them more accessible to a broader audience in behavioral research.