  We present a nonparametric Bayesian joint model for multivariate continuous
and categorical variables, with the intention of developing a flexible engine
for multiple imputation of missing values. The model fuses Dirichlet process
mixtures of multinomial distributions for categorical variables with Dirichlet
process mixtures of multivariate normal distributions for continuous variables.
We incorporate dependence between the continuous and categorical variables by
(i) modeling the means of the normal distributions as component-specific
functions of the categorical variables and (ii) forming distinct mixture
components for the categorical and continuous data with probabilities that are
linked via a hierarchical model. This structure allows the model to capture
complex dependencies between the categorical and continuous data with minimal
tuning by the analyst. We apply the model to impute missing values due to item
nonresponse in an evaluation of the redesign of the Survey of Income and
Program Participation (SIPP). The goal is to compare estimates from a field
test with the new design to estimates from selected individuals from a panel
collected under the old design. We show that accounting for the missing data
changes some conclusions about the comparability of the distributions in the
two datasets. We also perform an extensive repeated sampling simulation using
similar data from complete cases in an existing SIPP panel, comparing our
proposed model to a default application of multiple imputation by chained
equations. Imputations based on the proposed model tend to have better repeated
sampling properties than the default application of chained equations in this
realistic setting.
