Moderated Multiple Regression, Spurious Interaction Effects, and IRT

Abstract

Two Monte Carlo studies were conducted to explore the Type I error rates in moderated multiple regression (MMR) of observed scores and estimated latent trait scores from a two-parameter logistic item response theory (IRT) model. The results of both studies showed that MMR Type I error rates were substantially higher than the nominal alpha levels when scale scores were composed of summed binary item responses (e.g., true/false, yes/no, disagree/agree items). Performing the regression analyses on estimated trait scores (Θ̂) from a two-parameter logistic model improved the error detection rates considerably. That is, the Type I error rates for spurious interaction effects were similar to the nominal alpha levels under most conditions. These findings suggest that IRT provides a viable means of controlling an important source of spurious interactions in data sets that are well characterized by IRT models.