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Dimension reduction in binary response regression
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DOI：10.2307/2669934.png)
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Abstract
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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.
Keywords:
dimension-reduction subspace
linear combinations of chi-squared variables
regression graphics
sliced inverse regression
principal Hessian direction
sliced average variance estimation
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