Dimension Reduction in Binary Response Regression

R. Dennis Cook, Hakbae Lee

Research output: Contribution to journalArticle

95 Citations (Scopus)

Abstract

The idea of dimension reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a prespecified model. Focusing on the central subspace, we investigate such “sufficient” dimension reduction in regressions with a binary response. Three existing methods—sliced inverse regression, principal Hessian direction, and sliced average variance estimation—and one new method—difference of covariances—are studied for their ability to estimate the central subspace and produce sufficient summary plots. Combining these numerical methods with the graphical methods proposed earlier by Cook leads to a novel paradigm for the analysis of binary response regressions.

Original languageEnglish
Pages (from-to)1187-1200
Number of pages14
JournalJournal of the American Statistical Association
Volume94
Issue number448
DOIs
Publication statusPublished - 1999 Dec 1

Fingerprint

Binary Response
Dimension Reduction
Central Subspace
Regression
Inverse Regression
Sufficient Dimension Reduction
Graphical Methods
Paradigm
Numerical Methods
Sufficient
Estimate
Binary response
Dimension reduction
Model

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

@article{bea4d8992b9944da910e0ad5593ddc36,
title = "Dimension Reduction in Binary Response Regression",
abstract = "The idea of dimension reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a prespecified model. Focusing on the central subspace, we investigate such “sufficient” dimension reduction in regressions with a binary response. Three existing methods—sliced inverse regression, principal Hessian direction, and sliced average variance estimation—and one new method—difference of covariances—are studied for their ability to estimate the central subspace and produce sufficient summary plots. Combining these numerical methods with the graphical methods proposed earlier by Cook leads to a novel paradigm for the analysis of binary response regressions.",
author = "Cook, {R. Dennis} and Hakbae Lee",
year = "1999",
month = "12",
day = "1",
doi = "10.1080/01621459.1999.10473873",
language = "English",
volume = "94",
pages = "1187--1200",
journal = "Journal of the American Statistical Association",
issn = "0162-1459",
publisher = "Taylor and Francis Ltd.",
number = "448",

}

Dimension Reduction in Binary Response Regression. / Cook, R. Dennis; Lee, Hakbae.

In: Journal of the American Statistical Association, Vol. 94, No. 448, 01.12.1999, p. 1187-1200.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Dimension Reduction in Binary Response Regression

AU - Cook, R. Dennis

AU - Lee, Hakbae

PY - 1999/12/1

Y1 - 1999/12/1

N2 - The idea of dimension reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a prespecified model. Focusing on the central subspace, we investigate such “sufficient” dimension reduction in regressions with a binary response. Three existing methods—sliced inverse regression, principal Hessian direction, and sliced average variance estimation—and one new method—difference of covariances—are studied for their ability to estimate the central subspace and produce sufficient summary plots. Combining these numerical methods with the graphical methods proposed earlier by Cook leads to a novel paradigm for the analysis of binary response regressions.

AB - The idea of dimension reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a prespecified model. Focusing on the central subspace, we investigate such “sufficient” dimension reduction in regressions with a binary response. Three existing methods—sliced inverse regression, principal Hessian direction, and sliced average variance estimation—and one new method—difference of covariances—are studied for their ability to estimate the central subspace and produce sufficient summary plots. Combining these numerical methods with the graphical methods proposed earlier by Cook leads to a novel paradigm for the analysis of binary response regressions.

UR - http://www.scopus.com/inward/record.url?scp=0442278036&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0442278036&partnerID=8YFLogxK

U2 - 10.1080/01621459.1999.10473873

DO - 10.1080/01621459.1999.10473873

M3 - Article

VL - 94

SP - 1187

EP - 1200

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 448

ER -