Statistical Modelling 16 (4) (2016), 297–321
Partitioned conditional generalized linear models for categorical responses
Jean Peyhardi
Institut Montpelliérain Alexander Grothendieck,
Université de Montpellier,
34095 Montpellier,
France
e-mail: jean.peyhardi@umontpellier.fr
and
CIRAD,
Amélioration Génétique et Adaptation des Plantes, and Inria,
Virtual Plants,
34095 Montpellier,
France
Catherine Trottier
Institut Montpelliérain Alexander Grothendieck,
Université Paul-Valéry Montpellier,
34199 Montpellier,
France
Yann Guédon
CIRAD,
Amélioration Génétique et Adaptation des Plantes, and Inria,
Virtual Plants,
34095 Montpellier,
France
Abstract:
In categorical data analysis, several regression models have been proposed for hierarchically structured responses, such as the nested logit model, the two-step model or the partitioned conditional model for partially ordered set. The specifications of these models are heterogeneous and they have been formally defined for only two or three levels in the hierarchy. Here, we introduce the class of partitioned conditional generalized linear models (PCGLMs) that encompasses all these models and is defined for any number of levels in the hierarchy. The hierarchical structure of these models is fully specified by a partition tree of categories. Using the genericity of the recently introduced $(\boldsymbol{r}, F, \boldsymbol{Z}) $
specification of generalized linear models (GLMs) for categorical responses, it is possible to use different link functions and explanatory variables for each partitioning step. PCGLMs thus constitute a very flexible framework for modelling hierarchically structured categorical responses including partially ordered responses.
Keywords:
Specification of GLMs; Hasse diagram; Hierarchical structure among categories; partially ordered variable; partition tree.
Downloads:
Supplementary material in
pdf file.
back