  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 multiple record linkage goal is
to classify the record K-tuples coming from K 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 EM algorithm. We present a method to decide the record K-tuples
membership to the subsets of matching patterns and we prove its optimality. We
apply our method to the integration of three Colombian homicide record systems
and we perform a simulation study in order to explore the performance of the
method under measurement error and different scenarios. The proposed method
works well and opens some directions for future research.
