Inference for multivariate regression model based on multiply imputed synthetic data generated via posterior predictive sampling

The recent popularity of the use of synthetic data as a Statistical Disclosure Control technique has enabled the development of several methods of generating and analyzing such data, but almost always relying in asymptotic distributions and in consequence being not adequate for small sample datasets. Thus, a likelihood-based exact inference procedure is derived for the matrix of regression coefficients of the multivariate regression model, for multiply imputed synthetic data generated via Posterior Predictive Sampling. Since it is based in exact distributions this procedure may even be used in small sample datasets. Simulation studies compare the results obtained from the proposed exact inferential procedure with the results obtained from an adaptation of Reiters combination rule to multiply imputed synthetic datasets and an application to the 2000 Current Population Survey is discussed.