Polynomial Regression with Response Surface Analysis

Polynomial regression with response surface analysis is the methodological gold standard for testing congruence, fit, and agreement hypotheses in organizational behavior, introduced by Jeffrey Edwards and Mark Parry in 1993. It replaces the once-common practice of subtracting two scores and regressing the outcome on that difference, a practice that conflates several distinct effects and discards information. Instead, the two component variables are entered together with their squares and cross-product, and the resulting equation is interpreted as a three-dimensional surface relating the two predictors to the outcome. Edwards and Parry showed that difference scores impose untestable and usually false constraints, and that the polynomial approach recovers the constrained model as a special case while exposing far richer patterns. Shanock and colleagues' 2010 tutorial made the method accessible by providing surface coefficients, tests, and plotting tools. The technique is now standard wherever person-environment fit and rater agreement are studied.