This application seeks support for an investigation of the statistical properties of the Grade of Membership (GoM) models now in widespread use for the analysis of survey data on health status and disability for the elderly. Interpretation of results from analyses using these models and adoption of the models by a wider user community of gerontologists, demographers, and statisticians have been hindered by a lack of visualizable, fully-analyzed examples. This research project focuses on so-called """"""""conditional"""""""" GoM models which generate """"""""GoM"""""""" scores"""""""" for individual survey respondents -- these are the form of GoM models commonly employed in applications. The project concentrates on GoM models which supply 2 or 3-dimensional representations of data sets starting with 3 to 8 dichotomous variables. These low-dimensional cases permit both rigorous analysis and geometric presentation, supplying a repertory of examples of the different possible behaviors of the models. The project will proceed to a study of the robustness and sensitivity of GoM models to violations of the assumptions, working from artificially-constructed data sets based on variables from the AHEAD Survey and other national surveys on the elderly population.
