A Generalized Fellegi--Sunter Framework for Multiple Record Linkage With Application to Homicide Record Systems

We present a probabilistic method for linking multiple datafiles. This task is not trivial in the absence of unique identifiers for the individuals recorded. This is a common scenario when linking census data to coverage measurement surveys for census coverage evaluation, and in general when multiple record systems need to be integrated for posterior analysis. Our method generalizes the Fellegi--Sunter theory for linking records from two datafiles and its modern implementations. The goal of multiple record linkage is to classify the record <italic>K</italic>-tuples coming from <italic>K</italic> datafiles according to the different matching patterns. Our method incorporates the transitivity of agreement in the computation of the data used to model matching probabilities. We use a mixture model to fit matching probabilities via maximum likelihood using the Expectation--Maximization algorithm. We present a method to decide the record <italic>K</italic>-tuples membership to the subsets of matching patterns and we prove its optimality. We apply our method to the integration of the three Colombian homicide record systems and perform a simulation study to explore the performance of the method under measurement error and different scenarios. The proposed method works well and opens new directions for future research.