  Multivariate count data are defined as the number of items of different
categories issued from sampling within a population, which individuals are
grouped into categories. The analysis of multivariate count data is a recurrent
and crucial issue in numerous modelling problems, particularly in the fields of
biology and ecology (where the data can represent, for example, children counts
associated with multitype branching processes), sociology and econometrics. We
focus on I) Identifying categories that appear simultaneously, or on the
contrary that are mutually exclusive. This is achieved by identifying
conditional independence relationships between the variables; II)Building
parsimonious parametric models consistent with these relationships; III)
Characterising and testing the effects of covariates on the joint distribution
of the counts. To achieve these goals, we propose an approach based on
graphical probabilistic models, and more specifically partially directed
acyclic graphs.
