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Linear Models with Outliers: Choosing between Conditional-Mean and Conditional-Median Methods

Published online by Cambridge University Press:  25 January 2021

Jeffrey J. Harden  and
Bruce A. Desmarais
Jeffrey J. Harden*
Affiliation:
University of North Carolina at Chapel Hill, USA
Bruce A. Desmarais
Affiliation:
University of Massachusetts–Amherst, USA
*
Jeffrey J. Harden, University of North Carolina at Chapel Hill, Department of Political Science, 312 Hamilton Hall, CB #3265, Chapel Hill, NC 27599 Email: jjharden@unc.edu
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Abstract

State politics researchers commonly employ ordinary least squares (OLS) regression or one of its variants to test linear hypotheses. However, OLS is easily influenced by outliers and thus can produce misleading results when the error term distribution has heavy tails. Here we demonstrate that median regression (MR), an alternative to OLS that conditions the median of the dependent variable (rather than the mean) on the independent variables, can be a solution to this problem. Then we propose and validate a hypothesis test that applied researchers can use to select between OLS and MR in a given sample of data. Finally, we present two examples from state politics research in which (1) the test selects MR over OLS and (2) differences in results between the two methods could lead to different substantive inferences. We conclude that MR and the test we propose can improve linear models in state politics research.

Keywords

outlierslinear modelsordinary least squaresmedian regressioncross-validation
Type
Research Article
Information
State Politics & Policy Quarterly , Volume 11 , Issue 4 , December 2011 , pp. 371 - 389
Copyright
Copyright © The Author(s) 2011

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