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Many analyses require linking records from two databases comprisingoverlapping sets of individuals. In the absence of unique identifiers, thelinkage procedure often involves matching on a set of categorical variables,such as demographics, common to both files. Typically, however, the resultingmatches are inexact: some cross-classifications of the matching variables donot generate unique links across files. Further, the variables used formatching can be subject to reporting errors, which introduce additionaluncertainty in analyses. We present a Bayesian file matching methodologydesigned to estimate regression models and match records simultaneously whencategorical variables used for matching are subject to errors. The methodrelies on a hierarchical model that includes (1) the regression of interestinvolving variables from the two files given a vector indicating the links, (2)a model for the linking vector given the true values of the variables used formatching, (3) a model for reported values of the variables used for matchinggiven their true values, and (4) a model for the true values of the variablesused for matching. We describe algorithms for sampling from the posteriordistribution of the model. We illustrate the methodology using artificial dataand data from education records in the state of North Carolina.

Regression Modeling and File Matching Using Possibly Erroneous Matching Variables