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A new specification of generalized linear models for categorical responses

Peyhardi J., Trottier C., Guédon Y.. 2015. Biometrika, 102 (4) : p. 889-906.

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. (Résumé d'auteur)

Thématique : Méthodes mathématiques et statistiques

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