Dealing with overdispersion in multivariate count data

The problem of overdispersion in multivariate count data is a challenging issue. It covers a central role mainly due to the relevance of modern technology-based data, such as Next Generation Sequencing and textual data from the web or digital collections. A comprehensive analysis of the likelihood-based models for extra-variation data is presented. Particular attention is paid to the models feasible for high-dimensional data. A new approach together with its parametric-estimation procedure is proposed. It can be viewed as 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 the proposed model and existing strategies is made through two different simulation studies and an empirical data set, that confirm a better capability to describe overdispersion.