Dimension reduction in binary response regression: A joint modeling approach

Abstract

Categorical responses cause no conceptual complications for dimension reduction in regression, but the performance of some methods may suffer in this context and hence supervised dimension reduction in practice must recognize the nature of the response. Using a continuous latent variable to represent an unobserved response underlying the binary response, a joint model is proposed for dimension reduction in binary regression. The minimal sufficient linear reduction is obtained, and an efficient expectation maximization algorithm is developed for carrying out maximum likelihood estimation. Simulated examples and an application to a dataset concerning the identification of handwritten digits are presented to compare the performance of the proposed method with that of existing methods.