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Biometrika Advance Access originally published online on August 5, 2007
Biometrika 2007 94(3):755-759; doi:10.1093/biomet/asm046
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Copyright © 2007 Biometrika Trust

Miscellanea

On a generalization of a result of W. G. Cochran

D. R. Cox

Nuffield College, Oxford OX1 1NF, U.K.

david.cox{at}nuffield.ox.ac.uk

Received for publication 1 September 2006. Revision received 1 December 2006.
  Abstract

A relationship due to W.G. Cochran showing the effect on least squares regression coefficients of marginalizing over or conditioning on an explanatory variable is generalized to quantile regression coefficients. The condition under which conditioning does not induce interaction or effect reversal is shown. Examples are given. The discussion is simplest when all variables are continuous; the extension to discrete variables is outlined.

Key Words: Conditioning • Least squares regression • Marginalizing • Nonlinear regression • Probit model • Proportional hazards model • Quantile regression


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