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.
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