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

See all articles by Seth M. Spain

Seth M. Spain

Concordia University - JMSB

Kristin Sotak

State University of New York (SUNY) at Binghamton - School of Management

Joey Tsai

SUNY at Binghamton - School of Management

P. Harms

University of Nebraska at Lincoln

Sean Hannah

Wake Forest University - Schools of Business

Date Written: October 19, 2012

Abstract

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

Spain, Seth Michael and Sotak, Kristin and Tsai, Joey and Harms, P. and Hannah, Sean, Testing the Form of Theoretical Models by Relaxing Assumptions: Comparing Parametric and Nonparametric Models (October 19, 2012). Available at SSRN: https://ssrn.com/abstract=2164297 or http://dx.doi.org/10.2139/ssrn.2164297

Seth Michael Spain (Contact Author)

Concordia University - JMSB ( email )

1455 de Maisonneuve Blvd. West
Montreal, QC H3G 1M8
Canada

Kristin Sotak

State University of New York (SUNY) at Binghamton - School of Management ( email )

Binghamton, NY 13902-6001
United States

Joey Tsai

SUNY at Binghamton - School of Management

Binghamton, NY 13902-6001
United States

P. Harms

University of Nebraska at Lincoln ( email )

Lincoln, NE 68588
United States

Sean Hannah

Wake Forest University - Schools of Business

P.O. Box 7659
Winston-Salem, NC 27109-7285
United States

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