ABSTRACT
CONTENTS 6.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 6.2 Functional Disability Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.3 Full Versus Partial Membership . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6.4 Bayesian Estimation of the GoM Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 6.5 Analysis and Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 6.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
This paper draws on the ideas of full versus partial membership in statistical modelling. We focus on the particular form of the latter, the Grade of Membership (GoM) model, which was developed in the 1970s in the context of medical diagnosis. Other examples of partial membership models include Probabilistic Latent Semantic Analysis and the Latent Dirichlet Allocation model, developed in machine learning; and a genetics clustering model for multilocus genotype data. All these models represent individuals as having partial membership in several subpopulations.
