This paper models categorical data with two or multiple responses, focusing on the interactions between responses. We propose an efficient iterative procedure based on sufficient dimension reduction. We study the theoretical guarantees of the proposed method under the two- and multiple-response models, demonstrating the uniqueness of the proposed estimator and with the high probability that the proposed method recovers the oracle least squares estimators. For data analysis, we demonstrate that 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 right heart catheterization dataset and obtain meaningful results.

翻译：本文用两种或多种答复的绝对数据模型,以两种或多种答复的相互作用为重点。我们提议了一个基于充分减少维度的高效迭代程序。我们研究了两个和多种答复模式下拟议方法的理论保障,显示了拟议估算器的独特性,并表明拟议方法极有可能恢复最小孔径估计器。关于数据分析,我们证明拟议方法在多重反应模式中是有效的,并比多反应模式中建立的某些现有方法表现得更好。我们将这一模型和拟议方法应用于成人数据集和右心导管数据集,并获得有意义的结果。