Dimension reduction for the conditional mean in regressions with categorical predictors

Li, Bing ; Cook, R. Dennis ; Chiaromonte, Francesca

Ann. Statist., Tome 31 (2003) no. 1, p. 1636-1668 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 2003-10-14
Classification:  Analysis of covariance,  central subspace,  graphics,  OLS,  SIR,  PHD,  SAVE,  62G08,  62G09,  62H05