Structured Mixture of Continuation-Ratio Logits Models for Ordinal Regression

• 成果类型: Article; Early Access
• 署名作者: Kang, Jizhou; Kottas, Athanasios
• 署名单位: University of California System; University of California Santa Cruz
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2689641
• 发表日期: 2026-07-31
• 关键词: Bayesian Nonparametrics; Dependent Dirichlet process; Logit stick-breaking prior; Markov Chain Monte Carlo; Polya-Gamma data augmentation; Dirichlet process; bayesian-analysis; inference; binary

摘要

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 the 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 the continuation-ratio logits regression structure. Hence, an efficient and relatively easy to implement posterior simulation method can be designed, using P & oacute;lya-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. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.