Interaction effects may actually be nonlinear effects in disguise: A review of the problem and potential solutions

It is common in addictions research for statistical analyses to include interaction effects to test moderation hypotheses. Far less commonly do researchers consider the possibility that a given predictor may exert a nonlinear effect on the outcome. This lack of attention to the possible nonlinear effects of individual predictors is problematic because it may result in identification of entirely spurious interactions with other, correlated predictors. Given the commonplace practice of testing interactions, and the rarity of testing nonlinear effects, we speculate that some of the significant interactions reported in the literature may actually be spurious, reflecting only the misspecification of nonlinear effects. We outline the mathematical reasons for this problem using the relatively simple case of a quadratic regression model. Within this context, prior research by Busemeyer and Jones (1983) clearly demonstrated that quadratic effects of individual predictors can masquerade as interaction effects between correlated predictors. Furthermore, the explosive growth of mediation, moderation, and moderated mediation analyses in behavioral research makes this issue especially relevant for researchers of addiction. In this article, we (1) call further attention to the potential problems of omitting nonlinear effects in linear regression, (2) extend these findings to the more complex moderated mediation model, and (3) provide practical recommendations for applied researchers for differentiating nonlinear from interactive effects.