Partitioned conditional generalized linear models for categorical data

TL;DR

This paper introduces partitioned conditional generalized linear models (PCGLMs) that can handle hierarchical categorical data with any number of levels, extending existing models to more complex structures.

Contribution

The paper proposes a new class of PCGLMs that generalize hierarchical models to any number of levels and types of categorical responses, using a partition tree framework.

Findings

PCGLMs can model complex hierarchical categorical data.

The models accommodate nominal, ordinal, and partially-ordered responses.

Flexible structure allows for broader application in categorical data analysis.

Abstract

In categorical data analysis, several regression models have been proposed for hierarchically-structured response variables, e.g. the nested logit model. But 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) defined for any numbers of levels. The hierarchical structure of these models is fully specified by a partition tree of categories. Using the genericity of the (r,F,Z) specification, the PCGLM can handle nominal, ordinal but also partially-ordered response variables.