A new specification of generalized linear models for categorical responses

Jean Peyhardi 1, * Catherine Trottier 2, 3 Yann Guédon 4, 1
* Corresponding author
1 VIRTUAL PLANTS - Modeling plant morphogenesis at different scales, from genes to phenotype
UMR AGAP - Amélioration génétique et adaptation des plantes méditerranéennes et tropicales, INRA - Institut National de la Recherche Agronomique, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : 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.
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Submitted on : Tuesday, December 8, 2015 - 3:35:47 PM
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Jean Peyhardi, Catherine Trottier, Yann Guédon. A new specification of generalized linear models for categorical responses. Biometrika, Oxford University Press (OUP), 2015, 102 (4), pp.889-906. ⟨10.1093/biomet/asv042⟩. ⟨hal-01240023⟩



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