  Characterizing the shared memberships of individuals in a classification
scheme poses severe interpretability issues, even when using a moderate number
of classes (say 4). Mixed membership models quantify this phenomenon, but they
typically focus on goodness-of-fit more than on interpretable inference. To
achieve a good numerical fit, these models may in fact require many extreme
profiles, making the results difficult to interpret. We introduce a new class
of multivariate mixed membership models that, when variables can be partitioned
into subject-matter based domains, can provide a good fit to the data using
fewer profiles than standard formulations. The proposed model explicitly
accounts for the blocks of variables corresponding to the distinct domains
along with a cross-domain correlation structure, which provides new information
about shared membership of individuals in a complex classification scheme. We
specify a multivariate logistic normal distribution for the membership vectors,
which allows easy introduction of auxiliary information leveraging a latent
multivariate logistic regression. A Bayesian approach to inference, relying on
P\'olya gamma data augmentation, facilitates efficient posterior computation
via Markov Chain Monte Carlo. We apply this methodology to a spatially explicit
study of malaria risk over time on the Brazilian Amazon frontier.
