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October 2003 Dimension reduction for the conditional mean in regressions with categorical predictors
Bing Li, R. Dennis Cook, Francesca Chiaromonte
Ann. Statist. 31(5): 1636-1668 (October 2003). DOI: 10.1214/aos/1065705121


Consider the regression of a response Y on a vector of quantitative predictors $\X$ and a categorical predictor W. In this article we describe a first method for reducing the dimension of $\X$ without loss of information on the conditional mean $\mathrm{E}(Y|\X,W)$ and without requiring a prespecified parametric model. The method, which allows for, but does not require, parametric versions of the subpopulation mean functions $\mathrm{E}(Y|\X,W=w)$, includes a procedure for inference about the dimension of $\X$ after reduction. This work integrates previous studies on dimension reduction for the conditional mean $\mathrm{E}(Y|\X)$ in the absence of categorical predictors and dimension reduction for the full conditional distribution of $Y|(\X,W)$. The methodology we describe may be particularly useful for constructing low-dimensional summary plots to aid in model-building at the outset of an analysis. Our proposals provide an often parsimonious alternative to the standard technique of modeling with interaction terms to adapt a mean function for different subpopulations determined by the levels of W. Examples illustrating this and other aspects of the development are presented.


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Bing Li. R. Dennis Cook. Francesca Chiaromonte. "Dimension reduction for the conditional mean in regressions with categorical predictors." Ann. Statist. 31 (5) 1636 - 1668, October 2003.


Published: October 2003
First available in Project Euclid: 9 October 2003

zbMATH: 1042.62037
MathSciNet: MR2012828
Digital Object Identifier: 10.1214/aos/1065705121

Primary: 62G08
Secondary: 62G09 , 62H05

Keywords: Analysis of covariance , central subspace , graphics , OLS , pHd , SAVE , SIR

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 5 • October 2003
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