Estimation Using the Generalised Weight Share Method: The Case of Record Linkage

More and more, databases are combined using record linkage methods to increase the amount of available information. When there is no unique identifier to perform the matching, a probabilistic linkage is used. A record on the first file is linked to a record on the second file with a certain probability, and then a decision is made on whether this link is a true link or not. This process usually requires a certain amount of manual resolution that is costly in terms of time and employees. Also, this process often leads to a complex linkage. That is, the linkage between the two databases is not necessarily one-to-one, but can rather be many-to-one, one-to-many, or many-to-many. Two databases combined using record linkage can be seen as two populations linked together. We consider in this paper the problem of producing estimates for one of the populations (the target population) using a sample selected from the other one. We assume that the two populations have been linked together using probabilistic record linkage. To solve the estimation problem issued from a complex linkage between the population where the sample is selected and the target population, Lavallée (1995) suggested the use of the Generalised Weight Share Method (GWSM). This method is an extension of the Weight Share Method presented by Ernst (1989) in the context of longitudinal household surveys. The paper will first provide a brief overview of record linkage. Secondly, the GWSM will be described. Thirdly, the GWSM will be adapted to provide three different approaches that take into account linkage weights issued from record linkage. These approaches will be: (1) use all non-zero links with their respective linkage weights; (2) use all non-zero links above a given threshold; and (3) choose the links randomly using Bernoulli trials. For each of the approaches, an unbiased estimator of a total will be presented together with a variance formula. Finally, some simulation results that compare the three proposed approaches to the Classical Approach (where the GWSM is used based on links established through a decision rule) will be presented.