  When seeking to release public use files for confidential data, statistical
agencies can generate fully synthetic data. We propose an approach for making
fully synthetic data from surveys collected with complex sampling designs. Our
approach adheres to the general strategy proposed by Rubin (1993).
Specifically, we generate pseudo-populations by applying the weighted finite
population Bayesian bootstrap to account for survey weights, take simple random
samples from those pseudo-populations, estimate synthesis models using these
simple random samples, and release simulated data drawn from the models as
public use files. To facilitate variance estimation, we use the framework of
multiple imputation with two data generation strategies. In the first, we
generate multiple data sets from each simple random sample. In the second, we
generate a single synthetic data set from each simple random sample. We present
multiple imputation combining rules for each setting. We illustrate the
repeated sampling properties of the combining rules via simulation studies,
including comparisons with synthetic data generation based on pseudo-likelihood
methods. We apply the proposed methods to a subset of data from the American
Community Survey.
