Moderation in Response Surface Analysis: Current Shortcomings, Recommendations, and Software

Management scholars are often interested in congruence effects, which they analyze using polynomial regressions and response surface analyses. They also more and more frequently conduct moderation analyses of these polynomial regressions to understand how response surfaces change as a function of a third variable. Our review of the literature in management and applied psychology that tested moderation of response surface models reveals three shortcomings of the current practices: (1) hypotheses regarding moderation are more specific than what a general incremental variance test can assess, (2) probing and interpreting simple effects relies on a p-value heuristic – where a difference between conditional effects is assumed when an effect is significant at one level but not at another, and (3) there is no methodological guidance on how to assess moderation by congruence (i.e., cases where the effect of a variable is contingent on the degree of congruence between two other variables). To address these shortcomings, we (a) introduce indices of response surface moderation to directly test in what way a response surface shape changes as a function of a moderator, (b) we further detail how to analyze moderation by congruence, and (c) we wrote a user-friendly statistical program that facilitates conducting and interpreting moderation of congruence effects, and moderation by congruence effects.