Scalable and Robust Regression Models for Continuous Proportional Data

• 成果类型: Article; Early Access
• 署名作者: Lee, Changwoo J.; Dahl, Benjamin K.; Ovaskainen, Otso; Dunson, David B.
• 署名单位: Duke University; University of Jyvaskyla
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2626081
• 发表日期: 2026-05-13
• 关键词: Bayesian; data augmentation; Generalized Linear Model; Latent Gaussian model; Markov Chain Monte Carlo; beta regression; scale; inference; ecology

摘要

Beta regression is used routinely for continuous proportional data, but it often encounters practical issues such as a lack of robustness to misspecification of the beta distribution and sensitivity to outliers. We develop an improved class of generalized linear models starting with the continuous binomial (cobin) distribution and further extending to dispersion mixtures of cobin distributions (micobin). The proposed cobin regression and micobin regression models have attractive robustness, computation, and flexibility properties. A key innovation is the Kolmogorov-Gamma data augmentation scheme, which facilitates Gibbs sampling for Bayesian computation, including in hierarchical cases involving nested, longitudinal, or spatial data. We demonstrate robustness, ability to handle responses exactly at the boundary (0 or 1), and computational efficiency relative to beta regression in simulation experiments and through analysis of the benthic macroinvertebrate multimetric index of U.S. lakes using lake watershed covariates. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.