Splitting models for multivariate count data

TL;DR

This paper introduces a new class of splitting distributions for multivariate count data, unifying and extending existing models, and demonstrating their advantages through practical examples.

Contribution

It defines criteria for multivariate discrete distributions and introduces splitting distributions that encompass and extend traditional multivariate count models.

Findings

Splitting distributions unify various multivariate count models.

They simplify analysis, inference, and interpretation.

The approach is demonstrated on three real datasets.

Abstract

Considering discrete models, the univariate framework has been studied in depth compared to the multivariate one. This paper first proposes two criteria to define a sensu stricto multivariate discrete distribution. It then introduces the class of splitting distributions that encompasses all usual multivariate discrete distributions (multinomial, negative multinomial, multivariate hypergeometric, multivariate neg- ative hypergeometric, etc . . . ) and contains several new. Many advantages derive from the compound aspect of split- ting distributions. It simplifies the study of their characteris- tics, inferences, interpretations and extensions to regression models. Moreover, splitting models can be estimated only by combining existing methods, as illustrated on three datasets with reproducible studies.