Polynomial Regression and Measurement Error

Abstract

Many of the phenomena of interest in information systems (IS) research are nonlinear, and it has consequently been recognized that by applying linear statistical models (e.g., linear regression), we may ignore important aspects of these phenomena. To address this issue, IS researchers are increasingly applying nonlinear models to their datasets. One popular analytical technique for the modeling and analysis of nonlinear relationships is polynomial regression, which in its simplest form fits a "U-shaped" curve to the data. However, the use of polynomial regression can be problematic when the independent variables are contaminated with measurement error, and the implications of error can be more severe than in linear models. In this research, we discuss a number of techniques that can be used for modeling polynomial relationships while simultaneously taking measurement error into account and examine their performance by using a simulation study. In addition, we discuss the use of marginal and response surface plots as interpretational aides when evaluating the results of polynomial models and showcase their use through a practical example using a well-known dataset. Our results clearly indicate that the use of a linear regression analysis for this kind of model is problematic, and we provide a set of recommendations for future IS research practice.