  We present a Bayesian model for estimating the joint distribution of
multivariate categorical data when units are nested within groups. Such data
arise frequently in social science settings, for example, people living in
households. The model assumes that (i) each group is a member of a group-level
latent class, and (ii) each unit is a member of a unit-level latent class
nested within its group-level latent class. This structure allows the model to
capture dependence among units in the same group. It also facilitates
simultaneous modeling of variables at both group and unit levels. We develop a
version of the model that assigns zero probability to groups and units with
physically impossible combinations of variables. We apply the model to estimate
multivariate relationships in a subset of the American Community Survey. Using
the estimated model, we generate synthetic household data that could be
disseminated as redacted public use files with high analytic validity and low
disclosure risks. Supplementary materials for this article are available
online.
