Curvilinear Moderation—A More Complete Examination of Moderation Effects in Behavioral Sciences - Li, Johnson Ching-Hong (Frontiers in Applied Mathematics and Statistics, 2018)
In behavioral sciences, researchers often examine whether any linear moderations exist in their studies. That is, they evaluate the extent (i.e., magnitude, direction) to which a linear effect of a predictor X (e.g., cognitive ability) on a criterion Y (e.g., performance) may differ across the levels of a moderator M (e.g., gender). In that case, researchers often run a liner regression analysis for examining this moderation (e.g., gender by ability). Despite its popularity, linear moderation is insufficient for researchers to understand complex human phenomena. Curvilinear moderation is a data-analytic technique that identifies whether a predictor X and a criterion Y form a non-linear relationship, and how this relationship may differ across the levels of a moderator M. I describe eight common types of curvilinear moderation that are typically not addressed in the literature and propose an algorithm for detecting them. Using a Monte Carlo simulation, I show that the conventional linear regression analysis inappropriately and mistakenly flags a significant main effect of the moderator (M), but this effect is appropriately signaled as a significant curvilinear moderation effect (i.e., X by M) using my proposed algorithms. Misidentification of moderation effects poses serious threats to the accuracy of theory and model testing. Researchers can use curvilinear moderation analysis to avoid this problem and correctly detect curvilinear moderation in their studies.