Dimension Reduction in Binary Response Regression

R. Dennis Cook, Hakbae Lee

Research output: Contribution to journalArticlepeer-review

118 Scopus citations


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 (US)
Pages (from-to)1187-1200
Number of pages14
JournalJournal of the American Statistical Association
Issue number448
StatePublished - Dec 1 1999


  • Dimension-reduction subspace
  • Linear combinations of chi-squared variables
  • Principal Hessian direction
  • Regression graphics
  • Sliced average variance estimation
  • Sliced inverse regression


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