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.
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 the
public use files. We use the framework of multiple imputation to enable
variance estimation using two data generation strategies. In the first, we
generate multiple data sets from each simple random sample, whereas 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
each approach and the repeated sampling properties of the combining rules using
simulation studies