We develop a nonparametric Bayesian modeling approach to ordinal regression based on priors placed directly on the discrete distribution of the ordinal responses. The prior probability models are built from a structured mixture of multinomial distributions. We leverage a continuation-ratio logits representation to formulate the mixture kernel, with mixture weights defined through the logit stick-breaking process that incorporates the covariates through a linear function. The implied regression functions for the response probabilities can be expressed as weighted sums of parametric regression functions, with covariate-dependent weights. Thus, the modeling approach achieves flexible ordinal regression relationships, avoiding linearity or additivity assumptions in the covariate effects. Model flexibility is formally explored through the Kullback-Leibler support of the prior probability model. A key model feature is that the parameters for both the mixture kernel and the mixture weights can be associated with a continuation-ratio logits regression structure. Hence, an efficient and relatively easy to implement posterior simulation method can be designed, using P\'olya-Gamma data augmentation. Moreover, the model is built from a conditional independence structure for category-specific parameters, which results in additional computational efficiency gains through partial parallel sampling. In addition to the general mixture structure, we study simplified model versions that incorporate covariate dependence only in the mixture kernel parameters or only in the mixture weights. For all proposed models, we discuss approaches to prior specification and develop Markov chain Monte Carlo methods for posterior simulation. The methodology is illustrated with several synthetic and real data examples.

翻译：我们提出一种基于非参数贝叶斯建模的序数回归方法，该方法将先验直接置于序数响应的离散分布之上。先验概率模型通过多项分布的结构化混合构建。我们利用续比对数几率表示来构建混合核函数，其中混合权重通过包含协变量线性函数的对数几率棍子断裂过程定义。响应概率的隐含回归函数可表示为含协变量依赖权重的参数回归函数的加权和。因此，该建模方法实现了灵活的序数回归关系，避免了协变量效应中的线性或可加性假设。通过先验概率模型的库尔贝克-莱布勒支撑集，正式探讨了模型的灵活性。模型的关键特征在于混合核函数与混合权重的参数均可与续比对数几率回归结构关联。由此，可采用Pólya-Gamma数据增广法设计高效且易于实现的后验模拟方法。此外，模型基于类别特定参数的条件独立结构构建，通过部分并行采样进一步获得计算效率提升。除通用混合结构外，我们还研究了仅在混合核参数或仅在混合权重中引入协变量依赖的简化模型版本。针对所有提出的模型，我们讨论了先验规范方法，并开发了用于后验模拟的马尔可夫链蒙特卡洛方法。该方法通过多个合成数据与真实数据实例进行验证。