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In this paper we develop likelihood-based finite sample inference based on singly imputed partially synthetic data, when the original data follow either a multivariate normal or a multiple linear regression model. We assume that the synthetic data are generated by using the plug-in sampling method, where unknown parameters in the data model are set equal to observed values of their point estimators based on the original data, and synthetic data are drawn from this estimated version of the model. Empirical studies are presented to show that the proposed methods do indeed perform as the theory predicts, and to compare the proposed methods for singly imputed synthetic data with the combining rules that are used to analyze multiply imputed partially synthetic data. Some theoretical comparisons between singly and multiply imputed partially synthetic data inference are also provided. A data analysis example and disclosure risk evaluation of singly and multiply imputed partially synthetic data is presented based on public use data from the Current Population Survey. We discuss the specific conditions under which the proposed methodology will yield valid inference, and evaluate the performance of the methodology when certain conditions do not hold. We outline some ways to extend the proposed methodology for certain scenarios where the required set of conditions do not hold.
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