The GoM Model: Latent Class Representation and Implications for Bayesian Estimation"

Survey data in the social and health sciences contain answers to a number of yes/no or multiple choice questions (items) for each sampled person. The resulting data form a multidimensional contingency table where each cell entry is the number of observed responses corresponding to a particular discrete response pattern. When the items represent a broad underlying concept, such as disability, it is often useful to consider the use of statistical methods that capture that concept. Latent structure models allow for statistical inference about subject or item parameters, or both.

A relatively new latent structure model, Grade of Membership (GoM), deals with individual heterogeneity by introducing a set of extreme profiles and a vector of individual membership scores for each extreme profile for each individual. We show that the GoM model can simultaneously be thought of as being a multivariate latent trait model and a constrained latent class model. We treat the membership scores as coming from a known distribution and estimate the extreme profiles by using a Gibbs sampler algorithm