  We present an approach for imputation of missing items in multivariate
categorical data nested within households. The approach relies on a latent
class model that (i) allows for household level and individual level variables,
(ii) ensures that impossible household configurations have zero probability in
the model, and (iii) can preserve multivariate distributions both within
households and across households. We present a Gibbs sampler for estimating the
model and generating imputations. We also describe strategies for improving the
computational efficiency of the model estimation. We illustrate the performance
of the approach with data that mimic the variables collected in typical
population censuses.
