Bayesian Simultaneous Edit and Imputation for Multivariate Categorical Data

In categorical data, it is typically the case that some combinations of variables are theoretically impossible, such as a three year old child who is married or a man who is pregnant. In practice, however, reported values often include such structural zeros due to, for example, respondent mistakes or data processing errors. To purge data of such errors, many statistical organizations use a process known as edit-imputation. The basic idea is first to select reported values to change according to some heuristic or loss function, and second to replace those values with plausible imputations. This two-stage process typically does not fully utilize information in the data when determining locations of errors, nor does it appropriately reflect uncertainty resulting from the edits and imputations. We present an approach that integrates editing and imputation for categorical microdata with structural zeros. We rely on a Bayesian hierarchical model that includes (i) a Dirichlet process mixture of multinomial distributions as the model for the underlying true values of the data, with support restricted to the set of theoretically possible combinations, (ii) a model for latent indicators of the values that are in error, and (iii) a model for the reported responses for values in error. We illustrate this integrated approach using simulation studies with data from the 2000 U. S. census, and compare it to a two-stage edit-imputation routine. Supplementary material is available online.