Dimension Reduction in Binary Response Regression

• Published in: Journal of the American Statistical Association Vol. 94; no. 448; pp. 1187 - 1200
• Main Authors: Cook, R. Dennis, Lee, Hakbae
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis Group 01.12.1999; American Statistical Association; Taylor & Francis Ltd
• Subjects: Binary system; Covariance; Covariance matrices; Dimension-reduction subspace; Dimensionality reduction; Eigenvalues; Exact sciences and technology; Inference; Inference from stochastic processes; time series analysis; Linear combinations of chi-squared variables; Linear inference, regression; Linear regression; Mathematical vectors; Mathematics; Matrices; P values; Principal Hessian direction; Probability and statistics; Regression analysis; Regression graphics; Sciences and techniques of general use; Sliced average variance estimation; Sliced inverse regression; Statistical variance; Statistics; Theory and Methods; Statistical regression; Reduction method; Graphic method; Covariance analysis; Variance analysis; Information theory
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.1999.10473873

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.