Regression Modeling and File Matching Using Possibly Erroneous Matching Variables

ABSTRACT

Many analyses require linking records from two databases comprising overlapping sets of individuals. In the absence of unique identifiers, the linkage procedure often involves matching on a set of categorical variables, such as demographics, common to both files. Typically, however, the resulting matches are inexact: some cross-classifications of the matching variables do not generate unique links across files. Further, the variables used for matching can be subject to reporting errors, which introduce additional uncertainty in analyses. We present a Bayesian file matching methodology designed to estimate regression models and match records simultaneously when categorical variables used for matching are subject to errors. The method relies on a hierarchical model that includes (1) the regression of interest involving 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 for matching, (3) a model for reported values of the variables used for matching given their true values, and (4) a model for the true values of the variables used for matching. We describe algorithms for sampling from the posterior distribution of the model. We illustrate the methodology using artificial data and data from education records in the state of North Carolina.

KEYWORDS:

• Fusion
• Imputation
• Mixture
• Record linkage

Supplementary Materials

All simulations are conducted using R (R Core Team 2017b). The major packages involved are NPBayesImpute (Wang et al. 2016), foreign (R Core Team 2017a), mvtnorm (Genz et al. 2017), MASS (Venables and Ripley 2002), permute (Simpson 2016), LearnBayes (Albert 2014), ggplot2 (Wickham 2009), plotrix (J 2006), and nnet (Venables and Ripley 2002). All code and data for conducting the simulations in Section 4, as well as the code used to run the simulations in Section 5, can be downloaded at https://github.com/nmd16/BLASE. For information on obtaining access to confidential data from the NCERDC, see https://childandfamilypolicy.duke.edu/research/nc-education-data-center/.

Acknowledgments

This work was supported by NSF Grant SES 1131897, and by the Duke University Energy Initiative Energy Research Seed Fund, with cofunding from the Information Initiative at Duke. Data was provided by the North Carolina Education Research Data Center (NCERDC).

Additional information

Funding

National Science Foundation [SES 1131897].