Multiple Imputation of Missing Categorical and Continuous Values via Bayesian Mixture Models With Local Dependence

ABSTRACT

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 (1) modeling the means of the normal distributions as component-specific functions of the categorical variables and (2) 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. Supplementary materials for this article are available online.

KEYWORDS:

• Hierarchical mixture model
• Missing data
• Nonparametric Bayes
• Stick-breaking process

Supplementary Materials

Additional simulations and MCMC details Results of two additional simulation studies (one under MCAR, and one evaluating a general location model under MAR) as well as details of the MCMC algorithm to fit the HCMM-LD. (.pdf)

R package MixedDataImpute Containing an implementation of the HCMM-LD as well as the population used in the simulation studies (.tar.gz)

Funding

This work was supported by grants from the National Science Foundation (SES-11-31897, SES-1130706 and DMS-1043903). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Census Bureau or National Science Foundation.