Dirichlet Process Mixture Models for Nested Unordered Categorical Data

• Activity Number: 484
• Type: Topic Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Government Statistics Section
• Author(s): Jingchen Hu* and Jerry Reiter and Quanli Wang
• Companies: Duke University and Duke University and Duke University

Abstract

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, the Census Bureau's American Community Survey comprises 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 entirely synthetic household data that could be disseminated as redacted public use files with high analytic validity and low disclosure risks.