Bayesian Regression Analysis with Linked and Duplicated Data

We introduce a Bayesian methodology for performing record linkage and regression analysis using the resulting matched units in a k lists framework with possible duplications. We frame the record linkage process into a formal statistical model which comprises both the matching variables and other variables included at the inferential stage. This way, the researcher is able to account for the matching process uncertainty in inferential procedures based on probabilistically linked data, and at the same time, he/she is also able to generate a feedback propagation of uncertainty between the working statistical model and the record linkage stage. We argue that the feedback effect is essential to eliminate potential biases that could characterize the resulting post-linkage inference. The feedback effect is also able to improve record linkage performances. Practical implementation of the procedure is based on standard Bayesian computational techniques. Although the methodology is quite general, we have restricted our analysis to the popular and important case of multiple linear regression set-up for expository convenience.