Bayesian Estimation of the Grade of Membership Model
Erosheva Elena A. · 2003
Abstract The Grade of Membership model first appeared in the context of medical diagnosis problem in the 1970s. As a latent structure model for discrete response data, it deals with individual heterogeneity by introducing a set of extreme profiles and individual membership scores for each extreme profile. Existing estimation methods for the GoM model are maximum-likelihood based. Models closely related to the GoM have recently appeared in the genetics and machine learning literatures. We consider a Bayesian estimation approach based on the latent class representation of the GoM model. Augmenting data by the latent class indicators allows us to obtain posterior distribution of the model parameters via a Gibbs sampler, when model hyperparameters are known, or via a Metropolis- Hastings algorithm within the Gibbs, when they are unknown. We illustrate the estimation method on a subset of a disability survey data for the case of two extreme profiles.