Polynomial regression analysis and response surface methodology in leadership research

Congruence has served as an important research framework for many leadership research topics. Perhaps the most frequently used methodological/statistical approach for testing the congruence framework is polynomial regression analysis (PRA) with response surface methodology (RSM). As this approach was introduced to organizational sciences more than two decades ago, we can now identify the main issues with the use of this approach in leadership research. To systematically investigate these issues, we first review how PRA and RSM have been used in various leadership studies. We then review the levels-of-analysis and rater model assumptions prevalent in PRA in terms of multilevel techniques, choice of centering options, and issues of endogeneity. Finally, to better understand the inconsistencies and variabilities that exist in leadership research, we review the use of two main RSM features and summarize additional statistical techniques for assessment in this realm. Overall, we aim to promote the rigorousness of this methodology within the study of congruence in leadership research by enhancing its capability in theory testing and building.