A New Bayesian Partial Membership Model for Soft Clustering with Mixed Outcomes

• Activity Number: 622
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jonathan Gruhl*+ and Elena Erosheva and Paul K Crane
• Companies: University of Washington and University of Washington and University of Washington
• Keywords: Individual-level mixture models ; Soft clustering ; Extended rank likelihood ; Multivariate data ; Markov chain Monte Carlo

Abstract

In the context of soft clustering, we propose an individual-level mixture model for multivariate mixed outcome data that may combine binary, ordinal, continuous, count and other types of non-nominal outcomes. In contrast to classical mixture models, individual-level mixtures allow for mixed membership in one or more classes (Erosheva and Fienberg, 2005). Our model extends the Bayesian partial membership model of Heller, Williamson and Ghahramani (2008) but takes a semiparametric approach for accommodating mixed outcomes by relying on the extended rank likelihood (Hoff, 2007). This approach affords us great flexibility in modeling multivariate data of arbitrary type without having to specify outcome distributions. We rely on Gibbs and Hybrid Monte Carlo sampling methods for estimation and demonstrate the model both on simulated data and on player data from the 2010-2011 NBA season to determine individual playing styles. A second example uses cognitive testing data from a study of dementia and we compare our results to qualitative classifications made by substantive experts. In addition, we compare and contrast the mixed membership and the partial membership approaches.