Testing and Interpreting Latent Variable Interactions Using the semTools Package

Abstract

Examining interactions among predictors is an important part of a developing research program. Estimating interactions using latent variables provides additional power to detect effects over testing interactions in regression. However, when predictors are modeled as latent variables, estimating and testing interactions requires additional steps beyond the models used for regression. We review methods of estimating and testing latent variable interactions with a focus on product indicator methods. Product indicator methods of examining latent interactions provide an accurate method to estimate and test latent interactions and can be implemented in any latent variable modeling software package. Significant latent interactions require additional steps (plotting and probing) to interpret interaction effects. We demonstrate how these methods can be easily implemented using functions in the semTools package with models fit using the lavaan package in R, and we illustrate how these methods work using an applied example concerning teacher stress and testing.