A Factored Regression Approach to Modeling Latent Variable Interactions and Nonlinear Effects

Interaction effects are common in the behavioral sciences, especially in psychology, as they help explore how various factors influence human behavior. This paper introduces a factored regression framework designed to estimate latent variable interactions and nonlinear effects, providing a flexible approach for modeling complex data structures, accommodating diverse data types, and handling missing data on any variable. The factored regression framework also allows graphical diagnostics to probe interactions effectively. Monte Carlo simulations were conducted to compare the performance of factored regression with existing maximum likelihood methods, such as latent moderated structural equations and product indicators. Results indicate that factored regression performs comparably to, if not better than, these traditional methods. The factored regression framework is implemented in Blimp software, offering an accessible and user-friendly syntax for specifying the models. Through practical examples and syntax excerpts, this article demonstrates the application of factored regression for estimating latent interactions, making it more approachable for a wide audience in behavioral research.