The Use of Grade-of-Membership Techniques to Estimate Regression Relationships

Abstract

In this paper we describe the use of grade-of-membership (GOM) models to estimate multivariate regression relationships between multiple sets of discrete variables. A GOM model is a semiparametric latent structure model that represents state variables as a continuous mixture of fuzzy classes. The use of fuzzy classes allows representation of individual heterogeneity. We present conditions for identifiability and consistency of GOM estimators, and we present the generalization to conditionally dependent sets of variables, each represented by their own set of latent fuzzy classes. We discuss similarities and differences between GOM models and other latent structure models such as LISREL (and recent variants in which the observed variables may be discretely distributed). Finally we present an example from the 1982 and 1984 National Long Term Care Surveys, which found that health-service utilization is determined by medical conditions and functional status and that resources, attitudes, and behaviors act as mediating variables