Misleading Heuristics and Moderated Multiple Regression Models

TLDR

Moderated multiple regression models capture how the effect of one predictor on an outcome varies with another predictor by including an interaction term, a technique widely used in fields such as marketing. The authors contend that heuristics developed for ordinary multiple regression are often incorrectly generalized to moderated models, leading to misleading coefficient interpretations and flawed analyses. Through theoretical arguments and simulated data, they illustrate these pitfalls, explain how misapplications arise, and propose best practices for estimating, testing, and interpreting moderated regression models.

Abstract

Moderated multiple regression models allow the simple relationship between the dependent variable and an independent variable to depend on the level of another independent variable. The moderated relationship, often referred to as the interaction, is modeled by including a product term as an additional independent variable. Moderated relationships are central to marketing (e.g., Does the effect of promotion on sales depend on the market segment?). Multiple regression models not including a product term are widely used and well understood. The authors argue that researchers have derived from this simpler type of multiple regression several data analysis heuristics that, when inappropriately generalized to moderated multiple regression, can result in faulty interpretations of model coefficients and incorrect statistical analyses. Using theoretical arguments and constructed data sets, the authors describe these heuristics, discuss how they may easily be misapplied, and suggest some good practices for estimating, testing, and interpreting regression models that include moderated relationships.