Inference for Multivariate Regression Model based on synthetic data generated under Fixed-Posterior Predictive Sampling: comparison with Plug-in Sampling

TL;DR

This paper develops exact likelihood-based inference methods for multivariate regression models using synthetic data generated by Fixed-Posterior Predictive Sampling, comparing it with Plug-in Sampling and discussing privacy measures.

Contribution

It introduces a new Fixed-Posterior Predictive Sampling method for synthetic data, enabling exact inference for single imputation, filling a gap in existing literature.

Findings

FPPS agrees with PPS in single imputation

Simulation studies compare FPPS with Plug-in Sampling

Privacy measures are analyzed and contrasted

Abstract

The authors derive likelihood-based exact inference methods for the multivariate regression model, for singly imputed synthetic data generated via Posterior Predictive Sampling (PPS) and for multiply imputed synthetic data generated via a newly proposed sampling method, which the authors call Fixed-Posterior Predictive Sampling (FPPS). In the single imputation case, our proposed FPPS method concurs with the usual Posterior Predictive Sampling (PPS) method, thus filling the gap in the existing literature where inferential methods are only available for multiple imputation. Simulation studies compare the results obtained with those for the exact test procedures under the Plug-in Sampling method, obtained by the same authors. Measures of privacy are discussed and compared with the measures derived for the Plug-in Sampling method. An application using U.S.\ 2000 Current Population Survey data is discussed.