In This Article Polynomial Regression and Response Surface Analysis

  • Introduction
  • Conceptual Advantages
  • Method
  • Congruence (Person-Environment Fit)
  • Leadership
  • Individual Characteristics
  • Mediation, Moderation, and Polynomial Regression
  • Multilevel Polynomial Regression
  • Organizational Constructs
  • Psychological Contracts
  • Ratings and Feedback
  • Teams and Groups
  • Non-management Articles

Management Polynomial Regression and Response Surface Analysis
by
Lisa Schurer Lambert, Greg F. Hardt
  • LAST MODIFIED: 28 March 2018
  • DOI: 10.1093/obo/9780199846740-0133

Introduction

Polynomial regression and response surface methodology combines multiple regression relating two independent variables to a dependent variable, with a comprehensive framework for testing and interpreting the features of resulting three-dimensional graphed relationships. Previously utilized in various disciplines including agriculture, audio and speech, chemistry, economics, and forestry, polynomial regression and response surface methodology were introduced to managerial sciences by Edwards and Parry 1993. Specifically, the method was applied to avoid the limitations of difference scores (i.e., measure of agreement, fit, or similarity between two components or variables) used in studies of congruence (e.g., fit or similarity between two constructs such as the person and the environment in Person-Environment fit (P-E)). Difference scores represent the relationship between two measures with a single score, reducing an inherently three-dimensional relationship between three measures to two dimensions. Polynomial regression enables comprehensive tests of congruence as well as more complex relationships which difference scores cannot represent. Response surface methodology is used to describe, interpret, and test polynomial regression results including nuanced three-dimensional relationships, statistical constraints, and constraints implied by hypotheses.

  • Edwards, J. R., and M. E. Parry. “On the Use of Polynomial Regression Equations as an Alternative to Difference Scores in Oganizational Research.” Academy of Management Journal 36 (1993): 1577–1613.

    DOI: 10.2307/256822E-mail Citation »

    Seminal article presenting response surface methodology as an interpretive framework for polynomial regression. Polynomial regression is used to re-analyze data from a well-known P-E study investigating the relationships between subordinate values and supervisor values with organizational commitment; between job demands and job decision latitude with strain; between actual job enrichment and desired job enrichment with work motivation; and between own pay received and other’s pay received with propensity to leave.

Conceptual Advantages

Potential methodological problems with difference scores include reduced reliability, inherent ambiguity in interpretation (i.e., conceptually distinct constructs are measured and combined into a single score), confounding of effects (i.e., the individual effects of component measures on outcomes cannot be assessed when combined into one score), and imposing untested statistical constraints (i.e., constraints on effects which are imposed by difference scores but are not typically tested empirically). To address these methodological problems, Edwards 2002 advocated estimating a polynomial regression equation that includes the first-order effects of both independent variables (X, Y) along with their squared terms (X2, Y2) and the product term (XY) in order to represent moderating effects of the variables, as shown in the following equation: Z = b0 + b1X + b2Y + b3X2 + b4XY+ b5Y2 + e. The estimated regression coefficients (b0, b1, b2, b3, b4, b5) are used to plot a three-dimensional surface that captures the predicted value of the dependent variable (Z) at every combination of the two independent variables. The resulting response surface can be interpreted and tested for constraints and correspondence to hypotheses by applying response surface methodology. Although initially applied in managerial research to questions of congruence, polynomial regression and response surface methodology can be appropriate for testing the joint effect of any two independent variables on a dependent variable.

  • Edwards, J. R. “Alternatives to Difference Scores: Polynomial Regression and Response Surface Methodology.” In Advances in Measurement and Data Analysis. Edited by F. Drasgow and N. W. Schmitt, 350–400. San Francisco: Jossey-Bass, 2002.

    E-mail Citation »

    Presentation of analysis based on polynomial regression and response surface methodology as an alternative to analysis based on difference scores. Discussion covered numerous methodological problems of difference scores, how polynomial regression addresses these issues, and testing hypotheses using response surface methodology. Detailed example is included.

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