Revisiting shape and moderation effects in curvilinear models

Abstract

Testing hypotheses using curvilinear models in the form of U-shaped, inverted U-shaped or S-shaped relationships has increased considerably over the last decade. However, researchers in the field continue to make common mistakes in analysing such models; for example, ignoring important steps in validating the shape (e.g. U-shape) of a curvilinear relationship, or failing to properly test for different types of moderation. In this paper, following Haans, Pieters, and He (2016), we aim to provide clear guidelines on how to properly test and theorize for shape and moderation effects in curvilinear models. We provide illustrations from different contexts, including U-, inverted U- and S-shaped relationships. We also describe a new procedure that simplifies the process of testing within such contexts. The simplification works for both theoretical derivations as well as for the computation of marginal and moderation effects and curvature.