Multivariate count data is ubiquitous in many areas of research including the physical, biological, and social sciences. These data are traditionally modeled with the Dirichlet Multinomial distribution (DM). A new, more flexible Dirichlet-Tree Multinomial (DTM) model is gaining in popularity. Here, we consider Bayesian DTM regression models. Our…

Drawing valid inferences from modern measurement models is contingent upon a good fit of the data to the model. Violations of model-data fit have numerous consequences, limiting the usefulness and applicability of the model. As Bayesian estimation is becoming more common, understanding the Bayesian approaches for evaluating model-data fit models…