Regression Analysis After Bipartite Bayesian Record Linkage

Abstract

In many settings, a data curator links records from two files to produce a dataset that is shared with secondary analysts. These analysts can use the linked file to estimate models of interest such as regressions. This two-stage approach does not necessarily account for the uncertainty in the model parameters that results from uncertainty in the linkages. Further, it does not leverage the relationships among the non-linking variables in the two files to help identify incorrect linkages. We propose a multiple imputation framework to address these shortcomings. First, we use a bipartite Bayesian record linkage model to generate multiple plausible linked datasets. This model does not use the non-linking variables. Second, we presume each linked file comprises a mixture of true links and false links. We estimate the mixture model using an EM algorithm that leverages the information provided by the non-linking variables. We combine point and variance estimates of the regression parameters in each plausible linked file via multiple imputation inferences. Using simulation studies of linear regressions, we demonstrate that the mixture modeling approach can have desirable repeated sampling properties. We illustrate the mixture modeling approach using Bayesian record linkage of data from the Survey on Household Income and Wealth, examining a regression involving the persistence of income.