  The problem of overdispersion in multivariate count data is a challenging
issue. Nowadays, it covers a central role mainly due to the relevance of modern
technologies data, such as Next Generation Sequencing and textual data from the
web or digital collections. This work presents a comprehensive analysis of the
likelihood-based models for extra-variation data proposed in the scientific
literature. Particular attention will be paid to the models feasible for
high-dimensional data. A new approach together with its parametric-estimation
procedure is proposed. It is a deeper version of the Dirichlet-Multinomial
distribution and it leads to important results allowing to get a better
approximation of the observed variability. A significative comparison of these
models is made through two different simulation studies that both confirm that
the new model considered in this work allows to achieve the best results.
