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 fa- cilitates 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 Ameri- can Community Survey. Using the estimated model, we generate synthetic household data that could be disseminated as redacted public use les. Supplementary materials for this article are available online. … Nested Dirichlet Process Mixture of Products of Multinomial Distributions (NDPMPM) google

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