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

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