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This paper models categorical data with two or multiple responses, focusingon the interactions between responses. We propose an efficient iterativeprocedure based on sufficient dimension reduction. We study the theoreticalguarantees of the proposed method under the two- and multiple-response models,demonstrating the uniqueness of the proposed estimator and with the highprobability that the proposed method recovers the oracle least squaresestimators. For data analysis, we demonstrate that the proposed method isefficient in the multiple-response model and performs better than some existingmethods built in the multiple-response models. We apply this modeling and theproposed method to an adult dataset and right heart catheterization dataset andobtain meaningful results.

Dimension reduction of high-dimension categorical data with two or multiple responses considering interactions between responses