Ordinal response model is a popular and commonly used regression for ordered categorical data in a wide range of fields such as medicine and social sciences. However, it is empirically known that the existence of ``outliers'', combinations of the ordered categorical response and covariates that are heterogeneous compared to other pairs, makes the inference with the ordinal response model unreliable. In this article, we prove that the posterior distribution in the ordinal response model does not satisfy the posterior robustness with any link functions, i.e., the posterior cannot ignore the influence of large outliers. Furthermore, to achieve robust Bayesian inference in the ordinal response model, this article defines general posteriors in the ordinal response model with two robust divergences (the density-power and $\gamma$-divergences) based on the framework of the general posterior inference. We also provide an algorithm for generating posterior samples from the proposed posteriors. The robustness of the proposed methods against outliers is clarified from the posterior robustness and the index of robustness based on the Fisher-Rao metric. Through numerical experiments on artificial data and two real datasets, we show that the proposed methods perform better than the ordinary bayesian methods with and without outliers in the data for various link functions.

翻译：有序响应模型是医学和社会科学等广泛领域中用于有序分类数据的常用回归模型。然而，经验表明，“异常值”（即与其他配对相比具有异质性的有序分类响应与协变量的组合）的存在使得有序响应模型的推断不可靠。本文证明，在任何链接函数下，有序响应模型中的后验分布均不满足后验鲁棒性，即后验无法忽略大异常值的影响。此外，为了实现有序响应模型中的鲁棒贝叶斯推断，本文基于一般后验推断框架，使用两种鲁棒散度（密度功率散度和γ-散度）定义了有序响应模型中的一般后验。我们还提供了一种从所提出的后验中生成后验样本的算法。通过后验鲁棒性和基于Fisher-Rao度量的鲁棒性指数，阐明了所提出方法对异常值的鲁棒性。通过对人工数据和两个真实数据集的数值实验，我们表明，在各种链接函数下，所提出方法在数据存在和不存在异常值的情况下均优于普通贝叶斯方法。