Grade of Membership and Latent Structure Models with Applications to Disability Survey Data

• Activity Number: 282
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2003 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Stat. Sciences
• Author(s): Elena A. Erosheva*+
• Companies: University of Washington
• Keywords: data augmentation ; Gibbs sampler ; GoM ; latent class ; Metropolis-Hastings

Abstract

Binary or multiple-choice response data are abundant in the social sciences. This type of data can be recorded in a contingency table, which quickly becomes sparse as the number of variables goes up. Standard modeling methods such as log-linear models are often not appropriate in this case. This work examines a relatively new latent structure model for multivariate discrete data, the Grade of Membership (GoM) model. The model assumes that each individual observation has a partial membership in each of the basis subpopulations. The partial membership assumption is expressed through a convex structure of individual response probabilities. Representing the GoM model as a constrained latent class model naturally leads to a Bayesian estimation framework. The Bayesian approach is employed to analyze a subset of functional disability data from the National Long Term Care survey to illustrate using the GoM model for describing the structure of discrete data. Finally, a framework for the general class of partial membership models is developed which unifies the GoM model and two other partial membership models that recently appeared in the genetics and the machine learning literatures.