Authors: Sanjeena Dang, Drew Neish, Stephen Bak, Zeny Feng

The human gut microbiome is a source of great genetic and metabolic diversity. Microbiome samples which share similar biota compositions are known as enterotypes. Exploring the relationship between biological/environmental covariates and the taxonomic composition of the gut microbial community can shed light on the enterotype structure. Dirichlet-multinomial models have been previously suggested to investigate this relationship, however these models did not account for any latent group structure. Here, a finite mixture of Dirichlet-multinomial regression models is proposed and illustrated. These models allow for accounting for the enterotype structure and allow for a probabilistic investigation of the relationship between bacterial abundance and biological/environmental covariates within each inferred enterotype. Furthermore, a generalization of these models is also proposed that can incorporate the concomitant effect of the covariates on the resulting mixing proportions.