Testing the Form of Theoretical Models by Relaxing Assumptions: Comparing Parametric and Nonparametric Models
44 Pages Posted: 20 Oct 2012 Last revised: 16 Aug 2013
Date Written: October 19, 2012
One of the most fundamental assumptions in parametric statistical analysis is that the parametric model correctly captures the form of relationships being modeled. A key example is traditional multiple linear regression, where each partial regression function is assumed to be linear. This assumption is rarely explicitly tested in organizational research, partially because statistical approaches for testing the assumption are not widely known. We present methods to test this assumption by relaxing it. We discuss both fully nonparametric techniques and the more restrictive additive model, which relaxes only the assumption of linearity, compared to linear regression. We demonstrate how to fit both hypothesized linear models and equivalent additive models. We illustrate how to compare these models to determine whether the regression functions are truly linear. We discuss the strengths and limitations of nonparametric regression and additive models and advocate for more general use of these techniques in analysis of organizational data.
Keywords: statistical assumptions, theory testing, validation
JEL Classification: C14, M12
Suggested Citation: Suggested Citation