Dimension reduction in binary response regression

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.