A new specification of generalized linear models for categorical responses

• 成果类型: Article
• 署名作者: Peyhardi, J.; Trottier, C.; Guedon, Y.
• 署名单位: Universite de Montpellier; Universite de Montpellier; Universite Paul-Valery
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asv042
• 发表日期: 2015
• 页码: 889906
• 关键词: regression-models

摘要

Many regression models for categorical responses have been introduced, motivated by different paradigms, but it is difficult to compare them because of their different specifications. In this paper we propose a unified specification of regression models for categorical responses, based on a decomposition of the link function into an inverse continuous cumulative distribution function and a ratio of probabilities. This allows us to define a new family of reference models for nominal responses, comparable to the families of adjacent, cumulative and sequential models for ordinal responses. A new equivalence between cumulative and sequential models is shown. Invariances under permutations of the categories are studied for each family of models. We introduce a reversibility property that distinguishes adjacent and cumulative models from sequential models. The new family of reference models is tested on three benchmark classification datasets.