Finite Sample Inference for Multiply Imputed Synthetic Data under a Multiple Linear Regression Model

Abstract

In this article, we develop finite sample inference based on multiply imputed synthetic data generated under the multiple linear regression model. We consider two methods of generating the synthetic data, namely posterior predictive sampling and plug-in sampling. Simulation results are presented to confirm that the proposed methodology performs as the theory predicts and to numerically compare the proposed methodology with the current state-of-the-art procedures for analysing multiply imputed partially synthetic data. AMS 2000 subject classification: 62F10, 62F25, 62J05