Longitudinal mixed membership models with applications to disability survey data

When analyzing longitudinal data we need to balance our understanding of individual variability with the production of meaningful and interpretable summaries of overall population tendencies. This is especially true when those in the target population are known to be heterogeneous in their progression over time due to unobserved individual traits. Additional complications arise when the data are discrete and multivariate. I propose a new family of models to analyze such data by combining features from a version of the cross-sectional Grade of Membership Model (Woodbury et al., 1978; Erosheva et al., 2007) and from the longitudinal Multivariate Latent Trajectory Model (Connor, 2006). This new family of models works by considering individuals to be combinations of a small number of "ideal" or "extreme" classes. By describing the ways each of these extreme classes evolves over time we are able to describe distinct general tendencies. At the same time, by considering individuals to be individual-level mixtures of these profiles, we are able to handle complex forms of heterogeneity.;I apply my method to data from the National Long Term Care Survey (NLTCS), a longitudinal survey with six completed waves aimed to assess the state and characteristics of disability among U.S. citizens age 65 and above. I develop a full Bayesian specification and estimation methods based on Markov Chain Monte Carlo sampling, as well as several extensions to the basic methods to handle specific aspects of the NLTCS and to be able to answer relevant questions about the differences between disability patterns across different generations and the interplay between disability dynamics and survival times.