This paper, which is scheduled to appear in the December 1999
issue of JASA, adapts and extends many methods discussed in Regression
Graphics to regressions with a binary response. Several methods --
SIR, SAVE, pHd, and DOC -- are studied.
This paper, which has been accepted for publication in
JASA, describes how dimension reduction subspaces
respond to outliers and mixtures in regression. The general
conclusion is that methods such as SIR and SAVE can
capture outliers and regression mixtures without the need to prespecify
a parametric model.
Sliced average variance estimation (SAVE)
is a method for constructing sufficient summary plots
in regressions with many predictors. It was discussed
briefly on page 250 of Regression Graphics.
Methodological aspects of SAVE are described in this article.
The application of dimension reduction methods for the estimation of sufficient
summary plots in discriminant analysis is discussed in this paper.
In addition, a new permutation test for structural dimension is described.
Arc code for the permutation test,
which works with many methods like SIR, SAVE, and pHd,
is available here .
A method of forcing an elliptically contoured predictor
distribution is discussed in Section 8.4 of Regression Grapics.
This file contains Arc code for determining the weights when the
target predictor
distribution is normal.
This link takes you to Arc code for SIR when the response is bivariate.
Regression Graphics (218-220, 265-266) contains a discussion
of the bivariate version of SIR, as does the following paper on using Arc for
dimension reduction.
This document describes how many of the methods discussed in
Regression Graphics are implemented in Arc, including
reweighting and bivariate SIR.
Emphasis is on the methods not described in Applied Regression Including
Computing and Graphics . New results like the permutation
test are discussed as well.
This link takes you to Arc code written by Efstathia Bura for parametric
inverse regression (PIR). The idea behind PIR was mentioned in
Section 11.6 of Regression Graphics where it is
mis-characterized as a parametric version of SIR. PIR is developed in
the paper Estimating the structural dimension
of regressions via parametric inverse regression which it to appear in
JRSSB.
This paper, which is due to appear in
JASA, compares and contrasts the standard SIR chi-squared test for dimension with an alternative weighted chi-squared test that requires fewer conditions.
This paper introduces dimension reduction ideas for the mean function in
regression. This leads to the central mean subspace, which is similar to
the central subspace, except the focus is on the conditional mean. It is
scheduled to appear in the Annals.
This paper introduces the idea of and population
foundations for partial dimension reduction,
reducing the dimension of a selected collection of continuous or
many-valued predictors while conditioning on the rest of the
predictors. SIR is generalized to partial
dimension reduction. The Arc add-on
PartialSIR.lsp produces a new item in the
Graph&Fit menu that implements partial SIR for the constant covariance
case. Brief comments in the code are given at the start of the file.
This paper introduces the idea of testing regression predictors in
sufficient dimension reduction. A general context for testing is
given along with a specific implementation based on SIR.
It is scheduled to appear in the Annals. The Arc add-on
SIR-PredTests.lsp produces a new item in a
SIR model menu that implements selected tests, allowing for the
dimension of the central subspace to be specified or not.
Brief comments in the code are given at the start of the
file.