Bias reduction for correlated linkage error

Linked data sets are often multi-linked, i.e. they are created by matching records from three or more data sources. In such cases, probability-based methods for record linkage may lead to correlated linkage errors. Furthermore, it is often the case that not all records can be linked, due to the linking procedure not being able to find suitable matches in at least one of the data sources. This can be simply because the data source is a sample, and so does not contain the requisite matching records. More generally, however, the probability algorithm used to create the matches may not be able to find another record that meets the minimum criterion for matching. In this paper we develop methods for carrying out regression analysis using multilinked data that allow for both correlated linkage error as well as unlinked records. We also investigate the role of auxiliary information in this process, focussing on the situation where marginal distribution information from the data sets being linked is available. Our simulation results show that recently published bias reduction methods based on an assumption of independent linkage errors can lead to insufficient bias correction in the correlated case, and that a modified approach which allows for correlated linkage errors is superior. We also show that auxiliary marginal information about the data sets being linked can help further reduce the bias due to both non-linkage and linkage errors.