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.

中文翻译：

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二元响应回归中的降维：联合建模方法

摘要 分类响应不会导致回归降维的概念复杂化，但某些方法的性能可能会在这种情况下受到影响，因此实践中的监督降维必须认识到响应的性质。使用连续的潜在变量来表示基于二元响应的未观察到的响应，提出了用于二元回归中降维的联合模型。获得了最小的充分线性约简，并开发了一种有效的期望最大化算法来进行最大似然估计。提供了模拟示例和对有关手写数字识别的数据集的应用，以比较所提出方法与现有方法的性能。