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. ; Francisco J. R. Ruiz is supported by an FPU fellowship from the Spanish Ministry of Education (AP2010-5333), Isabel Valera is supported by the Plan Regional-Programas I+D of Comunidad de Madrid (AGES-CM S2010/BMD-2422), Fernando P erez-Cruz has been partially supported by a Salvador de Madariaga grant, and Carlos Blanco acknowledges NIH grants (DA019606 and DA023200) and the New York State Psychiatric Institute for their support. The authors also acknowledge the support of Ministerio de Ciencia e Innovación of Spain (projects DEIPRO TEC2009-14504-C02-00, ALCIT TEC2012-38800-C03-01, and program Consolider-Ingenio 2010 CSD2008-00010 COMONSENS). This work was also supported by the European Union 7th Framework Programme through the Marie Curie Initial Training Network \Machine Learning for Personalized Medicine" MLPM2012, Grant No. 316861.