Séance Séminaire

Séminaire de Probabilités et Statistique

A new specification of generalized linear models for categorical data

Many regression models for categorical data have been introduced in different applied fields, motivated by different paradigms, but resulting in a lack of unification in their specification. Therefore these models are difficult to compare and their appropriateness with respect to category ordering assumption is questionable. The first contribution is to unify classical regression models for categorical response variables, whether nominal or ordinal. This unification relies mainly on a decomposition of the link function in two parts: an inverse continuous cdf and a ratio of probabilities. This framework allows us to define a new family of models for nominal data, comparable to the cumulative, sequential and adjacent families of models for ordinal data. We finally propose a classification of GLMs for categorical data along a nominal/ordinal scale.