Misleading heuristics and moderated multiple regression models

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.