Estimating individual-level interaction effects in multilevel models: a Monte Carlo simulation study with application

Moderated multiple regression provides a useful framework for understanding moderator variables. These variables can also be examined within multilevel datasets, although the literature is not clear on the best way to assess data for significant moderating effects, particularly within a multilevel modeling framework. This study explores potential ways to test moderation at the individual level (level one) within a 2-level multilevel modeling framework, with varying effect sizes, cluster sizes, and numbers of clusters. The study examines five potential methods for testing interaction effects: the Wald test, F-test, likelihood ratio test, Bayesian information criterion (BIC), and Akaike information criterion (AIC). For each method, the simulation study examines Type I error rates and power. Following the simulation study, an applied study uses real data to assess interaction effects using the same five methods. Results indicate that the Wald test, F-test, and likelihood ratio test all perform similarly in terms of Type I error rates and power. Type I error rates for the AIC are more liberal, and for the BIC typically more conservative. A four-step procedure for applied researchers interested in examining interaction effects in multi-level models is provided.