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

Jeffrey J. Harden, Bruce A. Desmarais, Jr.

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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.

Original languageEnglish (US)
Pages (from-to)371-389
Number of pages19
JournalState Politics and Policy Quarterly
Volume11
Issue number4
DOIs
StatePublished - Dec 1 2011

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All Science Journal Classification (ASJC) codes

  • Arts and Humanities (miscellaneous)
  • Political Science and International Relations

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