Describing disability through individual-level mixture models for multivariate binary data

TL;DR

This paper develops a Bayesian mixture modeling approach using Grade of Membership models to analyze multivariate binary disability data, providing detailed individual disability profiles relevant for policy planning.

Contribution

It introduces a novel Bayesian estimation method for individual-level mixture models, establishing their equivalence with population models, applied to disability data analysis.

Findings

Effective modeling of disability profiles at the individual level

Bayesian estimation via MCMC for complex mixture models

Insights into disability patterns in elderly populations

Abstract

Data on functional disability are of widespread policy interest in the United States, especially with respect to planning for Medicare and Social Security for a growing population of elderly adults. We consider an extract of functional disability data from the National Long Term Care Survey (NLTCS) and attempt to develop disability profiles using variations of the Grade of Membership (GoM) model. We first describe GoM as an individual-level mixture model that allows individuals to have partial membership in several mixture components simultaneously. We then prove the equivalence between individual-level and population-level mixture models, and use this property to develop a Markov Chain Monte Carlo algorithm for Bayesian estimation of the model. We use our approach to analyze functional disability data from the NLTCS.