  In theory, the probabilistic linkage method provides two distinct advantages
over non-probabilistic methods, including minimal rates of linkage error and
accurate measures of these rates for data users. However, implementations can
fall short of these expectations either because the conditional independence
assumption is made, or because a model with interactions is used but lacks the
identification property. In official statistics, this is currently the main
challenge to the automated production and use of linked data. To address this
challenge, a new methodology is described for proper linkage problems, where
matched records may be identified with a probability that is bounded away from
zero, regardless of the population size. It models the number of neighbours of
a given record, i.e. the number of resembling records. To be specific, the
proposed model is a finite mixture where each component is the sum of a
Bernoulli variable with an independent Poisson variable. It has the
identification property and yields solutions for many longstanding problems,
including the evaluation of blocking criteria and the estimation of linkage
errors for probabilistic or non-probabilistic linkages, all without clerical
reviews or conditional independence assumptions. Thus it also enables
unsupervised machine learning solutions for record linkage problems.
