Interpretability and A Priori Constraints in Mixed Membership Models

• Activity Number: 54
• Type: Invited
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Burton Singer* and Marcia Castro
• Companies: University of Florida and Harvard University
• Keywords: Interpretability ; Shared membership ; Multi-level Model

Abstract

Interpreting shared membership in a mixed-membership model places the investigator in a difficult position, as standard estimation strategies produce a large number K, almost always greater than 6, of ideal profiles that represent best fitting representations of the data while at the same time making it impossible to interpret what membership in say 4 or more profiles actually means. This conflict between statistical goodness-of-fit and subject-matter-based interpretability of shared membership cannot usually be resolved using conventional mixed-membership models. We show by introducing multi-level mixed membership models, each level containing a small number of ideal profiles, to describe a population according to responses focused on distinct subject matter domains, and at the same time time producing a vector of correlated grade of membership scores for the individuals, interpretation of shared memberships across the distinct subject matter domains becomes feasible. Deciding on what constitutes a good model requires tradeoffs between statistical goodness-of fit criteria and frequently non-quantifiable subject matter based interpretation.