Bayesian non‐parametric generation of fully synthetic multivariate categorical data in the presence of structural zeros

Statistical agencies are increasingly adopting synthetic data methods for disseminating microdata without compromising the privacy of respondents. Crucial to the implementation of these approaches are flexible models, able to capture the nuances of the multivariate structure in the original data. In the case of multivariate categorical data, preserving this multivariate structure also often involves satisfying constraints in the form of combinations of responses that cannot logically be present in any data set—like married toddlers or pregnant men—also known as structural zeros. Ignoring structural zeros can result in both logically inconsistent synthetic data and biased estimates. Here we propose the use of a Bayesian non‐parametric method for generating discrete multivariate synthetic data subject to structural zeros. This method can preserve complex multivariate relationships between variables, can be applied to high dimensional data sets with massive collections of structural zeros, requires minimal tuning from the user and is computationally efficient. We demonstrate our approach by synthesizing an extract of 17 variables from the 2000 US census. Our method produces synthetic samples with high analytic utility and low disclosure risk.