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

Abstract

This paper focuses on modeling the categorical data with two or multiple responses. We study the interactions between the responses and propose an efficient iterative procedure based on sufficient dimension reduction. We show that the proposed method reaches the local and global dimension reduction efficiency. The theoretical guarantees of the method are provided under the two- and multiple-response models. We demonstrate the uniqueness of the proposed estimator, further, we prove that the iteration converges to the oracle least squares solution in the first two and q steps for the two- and multiple-response model, respectively. For data analysis, the proposed method is efficient in the multiple-response model and performs better than some existing methods built in the multiple-response models. We apply this modeling and the proposed method to an adult dataset and a right heart catheterization dataset. Results show that both datasets are suitable for the multiple-response model and the proposed method always performs better than the compared methods.