  The Latent Dirichlet Allocation (LDA) model is a popular method for creating
mixed-membership clusters. Despite having been originally developed for text
analysis, LDA has been used for a wide range of other applications. We propose
a new formulation for the LDA model which incorporates covariates. In this
model, a negative binomial regression is embedded within LDA, enabling
straight-forward interpretation of the regression coefficients and the analysis
of the quantity of cluster-specific elements in each sampling units (instead of
the analysis being focused on modeling the proportion of each cluster, as in
Structural Topic Models). We use slice sampling within a Gibbs sampling
algorithm to estimate model parameters. We rely on simulations to show how our
algorithm is able to successfully retrieve the true parameter values and the
ability to make predictions for the abundance matrix using the information
given by the covariates. The model is illustrated using real data sets from
three different areas: text-mining of Coronavirus articles, analysis of grocery
shopping baskets, and ecology of tree species on Barro Colorado Island
(Panama). This model allows the identification of mixed-membership clusters in
discrete data and provides inference on the relationship between covariates and
the abundance of these clusters.
