Should Moderated Regressions Include or Exclude Quadratic Terms? Present Both! Then Apply Our Linear Algebraic Analysis to Identify the Preferable Specification

Abstract

Organizational research increasingly tests moderated relationships using multiple regression with interaction terms. Most research does so with little concern regarding curvilinear relationships. But methodologists have established that omitting quadratic terms of correlated primary variables may create false interaction positives (type 1 errors). If dependent variables are generated by the canonical process where fully specified regressions satisfy the Gauss-Markov assumptions, including quadratics solves the problem. But our empirical analysis of published organizational research suggests that dependent variables are often generated by processes where, even with quadratics included, regression analyses will remain Gauss-Markov non-compliant. In such cases, our linear algebraic analysis demonstrates that including quadratics—even those motivated by compelling theory—may exacerbate rather than mitigate the incidence of false interaction positives. The interaction coefficient may substantially change its magnitude and even flip sign once quadratics are included, and not necessarily for the better. We encourage researchers to present two full sets of results when testing moderating hypotheses—one with, and one without, quadratic terms. Researchers should then answer five questions developed here in order to determine the preferable set of results.