Simplifying response surface analysis : proposing a new model specification

Researchers in psychology are often interested in questions of whether the magnitude of the similarity or difference between two measures or variables is related to an outcome of interest. These types of questions usually address theoretical issues in psychology that are linked with optimization. Such questions, for example, are whether a certain extent of similarity or difference between two constructs predicts the optimal levels of dyadic satisfaction, attraction, relationships, intrapersonal consistency; or what are the ideal levels of similarity or difference of person-environment fit on health outcomes, just to name a few. Methods such as difference scores and distance measures have been proposed and are commonly used to examine such research questions. However, these measures, when used in isolation, are restrictive and make strong modeling assumptions. More recently, response surface analysis (RSA) methods have been adapted to provide more modeling flexibility and less restrictive models to examine questions of whether (dis)similarity are related to outcomes of interest. The RSA model uses two predictors instead of one which preserves data dimensionality and allows each predictor to have both linear, curvilinear, and interactive relationship with the outcome. Given the functionality and utility of RSA, we advocate its use in similarity research while proposing to conceptualize the modeling of (dis)similarity measures in a simpler way for researchers who currently use or plan to use RSA to address such questions. We propose that researchers use an average (A) and a half of a difference (D) instead of the two original predictors. This new model specification has several advantages. First, it helps researchers to define (dis)similarity coefficients, the parameters that researchers of this topic are truly interested in, more precisely. Second, this new model specification utilizes two orthogonal variables, unlike the original model that uses two predictors that are mostly correlated with each other, thus avoiding multicollinearity issues altogether. Third, this usage allows researchers to interpret (dis)similarity coefficients on a response surface graph more easily. We demonstrated the incremental benefits of the proposed reparameterization approach through mathematical proofs and an empirical example.Arts, Faculty ofPsychology, Department ofGraduat