MULTIVARIATE MIXED MEMBERSHIP MODELING: INFERRING DOMAIN-SPECIFIC RISK PROFILES

• 成果类型: Article
• 署名作者: Russo, Massimiliano; Singer, Burton H.; Dunson, David B.
• 署名单位: Harvard University; Harvard Medical School; State University System of Florida; University of Florida; State University System of Florida; University of Florida; Duke University
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/21-AOAS1496
• 发表日期: 2022
• 页码: 391-413
• 关键词: inference; malaria; amazon

摘要

Characterizing the shared memberships of individuals in a classification scheme poses severe interpretability issues, even when using a moderate number of classes (say four). 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 Polya 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.