An Unbiased Model Comparison Test Using Cross-Validation

36 Pages Posted: 22 Feb 2011

See all articles by Bruce A. Desmarais

Bruce A. Desmarais

Pennsylvania State University

Jeffrey J. Harden

University of Colorado at Boulder - Department of Political Science

Date Written: February 21, 2011

Abstract

Political scientists often consider multiple empirical models of the same process. When these models are parametric and non-nested, the null hypothesis that two models fit the data equally well is commonly tested using methods introduced by Vuong (1989) and Clarke (2003, 2007). The objective of each is to compare the Kullback-Leibler Divergence (KLD) of the two models from the true model that generated the data. In this research note we show that both of these tests are based upon a biased estimator of the KLD, the individual log-likelihood contributions, and that the Clarke test is not proven to be consistent for the difference in KLDs. As a solution, we derive a test based upon cross-validated log-likelihood contributions, which represent an unbiased KLD estimate.

Keywords: Model Selection, Cross-Validation, Kullback-Leibler Divergence, Vuong Test, Clarke Test, Linear Regression, Ordinary Least Squares, Robust Regression

Suggested Citation

Desmarais, Bruce A. and Harden, Jeffrey J., An Unbiased Model Comparison Test Using Cross-Validation (February 21, 2011). Available at SSRN: https://ssrn.com/abstract=1765845 or http://dx.doi.org/10.2139/ssrn.1765845

Bruce A. Desmarais

Pennsylvania State University ( email )

University Park, State College, PA 16801
United States

HOME PAGE: http://sites.psu.edu/desmaraisgroup

Jeffrey J. Harden (Contact Author)

University of Colorado at Boulder - Department of Political Science ( email )

333 UCB
Boulder, CO 80309-0333
United States

HOME PAGE: http://spot.colorado.edu/~jeha9919/

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