A new specification of generalized linear models for categorical responses
针对分类响应变量的回归模型因设定不同而难以比较，本文提出一种基于连接函数分解的统一设定，定义了名义响应变量的新参考模型族，并在三个基准分类数据集上进行了测试。
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.