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The analysis of comorbidity is an open and complex research Field in the branch of psychiatry, where clinical experience and several studies suggest that the relation among the psychiatric disorders may have etiological and treatment implications. In this paper, we are interested in applying latent feature modeling to Find the latent structure behind the psychiatric disorders that can help to examine and explain the relationships among them. To this end, we use the large amount of information collected in the National Epidemiologic Survey on Alcohol and Related Conditions (NESARC) database and propose to model these data using a nonparametric latent model based on the Indian BuFiet Process (IBP). Due to the discrete nature of the data, we First need to adapt the observation model for discrete random variables. We propose a generative model in which the observations are drawn from a multinomial-logit distribution given the IBP matrix. The implementation of an eFicient Gibbs sampler is accomplished using the Laplace approximation, which allows integrating out the weighting factors of the multinomial-logit likelihood model. We also provide a variational inference algorithm for this model, which provides a complementary (and less expensive in terms of computational complexity) alternative to the Gibbs sampler allowing us to deal with a larger number of data. Finally, we use the model to analyze comorbidity among the psychiatric disorders diagnosed by experts from the NESARC database.