Correcting for linkage errors in contingency tables—A cautionary tale

Record linkage aims to bring records together from two or more files that belong to the same statistical entity. Naïvely treating a linked file as if there are no linkage errors may lead to biased inference. We present two general approaches for compensating for linkage error when calculating and analysing a two-way contingency table for categorical data, and study the following question: under what conditions can a compensation approach improve on the naïve approach, where linkage error is not compensated for? To this end, we compare estimation errors, bias, variance and mean square error for the naïve approach and two compensation approaches by means of an analytical study as well as a simulation study.