# Polynomial Regression with Response Surface Analysis: A Powerful Approach for Examining Moderation and Overcoming Limitations of Difference Scores

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## Abstract

Polynomial regression with response surface analysis is a sophisticated statistical approach that has become increasingly popular in multisource feedback research (e.g., self-observer rating discrepancy). The approach allows researchers to examine the extent to which combinations of two predictor variables relate to an outcome variable, particularly in the case when the discrepancy (difference) between the two predictor variables is a central consideration. We believe this approach has potential for application to a wide variety of research questions. To enhance interest and use of this technique, we provide ideas for future research directions that might benefit from the application of this analytic tool. We also walk through a step-by-step example of how to conduct polynomial regression and response surface analysis and provide all the tools you will need to do the analyses and graph the results (including SPSS syntax, formulas, and a downloadable Excel spreadsheet). Our example involves how discrepancies in perceived supervisor and organizational support relate to affective commitment. Finally, we discuss how this approach is a better, more informative alternative to difference scores and can be applied to the examination of two-way interactions in moderated regression.

## Keywords

Polynomial regression Response surface analysis Two-way interactions Job attitudes Research methods## Notes

### Acknowledgment

This research was supported, in part, by funds from the University of North Carolina at Charlotte.

## References

- Aiken, L. S., & West, S. G. (1991).
*Multiple regression: Testing and interpreting interactions*. Newbury Park, CA: Sage.Google Scholar - Aselage, J., & Eisenberger, R. (2003). Perceived organizational support and psychological contracts: A theoretical integration.
*Journal of Organizational Behavior,**24*, 491–509.CrossRefGoogle Scholar - Atwater, L. E., Ostroff, C., Yammarino, F. J., & Fleenor, J. W. (1998). Self-other agreement: Does it really matter?
*Personnel Psychology,**51*, 577–598.CrossRefGoogle Scholar - Box, G. E. P., & Draper, N. R. (1987).
*Empirical model-building and response surfaces*. New York: Wiley.Google Scholar - Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003).
*Applied multiple regression/correlation analysis for the behavioral sciences*. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar - Edwards, J. R. (1994). The study of congruence in organizational behavior research: Critique and proposed alternative.
*Organizational Behavior and Human Decision Processes,**58*, 51–100.CrossRefGoogle Scholar - Edwards, J. R. (1995). Alternatives to difference scores as dependent variables in the study of congruence in organizational research.
*Organizational Behavior and Human Decision Processes,**64*, 307–324.CrossRefGoogle Scholar - Edwards, J. R. (2007). Polynomial regression and response surface methodology. In C. Ostroff & T. A. Judge (Eds.),
*Perspectives on organizational fit*(pp. 361–372). San Francisco: Jossey-Bass.Google Scholar - Edwards, J. R., & Parry, M. E. (1993). On the use of polynomial regression equations as an alternative to difference scores in organizational research.
*Academy of Management Journal,**36*, 1577–1613.CrossRefGoogle Scholar - Eisenberger, R., Huntington, R., Hutchison, S., & Sowa, D. (1986). Perceived organizational support.
*Journal of Applied Psychology,**71*, 500–507.CrossRefGoogle Scholar - Fleenor, J. W., McCauley, C. D., & Brutus, S. (1996). Self-other rating agreement and leader effectiveness.
*Leadership Quarterly,**7*, 487–506.CrossRefGoogle Scholar - Gentry, W. A., Hannum, K. M., Ekelund, B. Z., & de Jong, A. (2007). A study of the discrepancy between self- and observer-ratings on managerial derailment characteristics of European managers.
*European Journal of Work and Organizational Psychology,**16*, 295–325.CrossRefGoogle Scholar - Gentry, W. A., Yip, J., & Hannum, K. M. (in press). Self-observer rating discrepancies of managers in Asia: A study of derailment characteristics and behaviors in Southern and Confucian Asia.
*International Journal of Selection and Assessment.*Google Scholar - Gibson, C. B., Cooper, C. D., & Conger, J. A. (2009). Do you see what we see? The complex effects of perceptual distance between leaders and teams.
*Journal of Applied Psychology,**94*, 62–76.PubMedCrossRefGoogle Scholar - Harris, M. M., Ansaal, F., & Lievens, F. (2008). Keeping up with the Joneses: A field study of the relationships among upward, lateral, and downward comparisons and pay level satisfaction.
*Journal of Applied Psychology,**93*, 665–673.PubMedCrossRefGoogle Scholar - Kottke, J. L., & Sharafinski, C. E. (1988). Measuring perceived supervisory and organizational support.
*Educational and Psychological Measurement,**48*, 1075–1079.CrossRefGoogle Scholar - Meyer, J. P., & Allen, N. J. (1997).
*Commitment in the workplace: Theory research and application*. Thousand Oaks: Sage Publications.Google Scholar - Ostroff, C., Atwater, L. E., & Feinberg, B. J. (2004). Understanding self-other agreement: A look at rater and ratee characteristics, context, and outcomes.
*Personnel Psychology,**57*, 333–375.CrossRefGoogle Scholar - Rhoades, L., & Eisenberger, R. (2002). Perceived organizational support: A review of the literature.
*Journal of Applied Psychology,**87*, 698–714.PubMedCrossRefGoogle Scholar - Rhoades, L., Eisenberger, R., & Armeli, S. (2001). Affective commitment to the organization: The contribution to perceived organizational support.
*Journal of Applied Psychology,**86*, 825–836.PubMedCrossRefGoogle Scholar - Tabachnick, B. G., & Fidell, L. S. (2007).
*Using Multivariate Statistics*(5th ed.). Boston: Allyn and Bacon.Google Scholar - Yammarino, F. J., & Atwater, L. E. (1997). Do managers see themselves as others see them? Implications of self-other rating agreement for human resources management.
*Organizational Dynamics,**25*, 35–44.CrossRefGoogle Scholar

## References to Consult for More Information about Response Surface Analysis

- Edwards, J. R. (2002). Alternatives to difference scores: Polynomial regression analysis and response surface methodology. In F. Drasgow & N. W. Schmitt (Eds.),
*Advances in measurement and data analysis*(pp. 350–400). San Francisco: Jossey-Bass.Google Scholar - Atwater, L., Waldman, D., Ostroff, C., Robie, C., & Johnson, K. M. (2005). Self-other agreement: Comparing its relationship with performance in the U.S and Europe.
*International Journal of Selection and Assessment,**13*, 25–40.CrossRefGoogle Scholar