Further Insight and Additional Inference Methods for Polynomial Regression Applied to the Analysis of Congruence

In their seminal paper, Edwards and Parry (1993) presented the polynomial regression as a better alternative to applying difference score in the study of congruence. While this method is increasingly applied in congruence research, its complexity relative to other methods for assessing congruence (e.g., difference score methods) was one of the main claims against its use. The objective of this work is to gain additional insight into the use of polynomial regression in the area of social and behavioral sciences. First, we elaborate on the meaning and the inference based on the coefficients obtained by applying polynomial regression and explain the mathematical terms that are used to describe response surfaces. Then, we introduce additional inference methods and illustrate their application on a real life example from the area of supportive exchanges, using data collected by the Smithers Institute at Cornell University (supported by the National Institute on Alcohol Abuse and Alcoholism). Our work is aimed to provide a guide to researchers who apply polynomial regression in order to assess the effect of congruence between two constructs and enable better understanding and interpretation of the results obtained.