Glossary
Fellegi–Sunter model
The Fellegi–Sunter model classifies candidate record pairs using evidence from field agreements and disagreements.
Identity and entity resolution
The Fellegi–Sunter framework treats record linkage as a statistical decision problem. For each compared field, agreement or disagreement contributes evidence about whether a pair is a true match rather than a nonmatch. The combined comparison pattern supports classification into links, nonlinks and a region needing review. Its usefulness depends on estimated comparison distributions and the population to which they apply.
In practice, analysts choose informative fields and account for missing values, common names and correlated comparisons. Agreement on a rare identifier may carry more information than agreement on a common city. Thresholds express tolerated error trade-offs and should be calibrated for the actual decision. The framework does not make a pair true simply because a score crosses a line.
For organizations defending an identity decision, the comparison vector, thresholds and review outcome matter as much as the final link. They let an investigator see why two records were joined or kept apart. Record linkage is the task; the Fellegi–Sunter model is one way to assess pairs; blocking is a separate candidate-generation step.
Example
A Halden Therapeutics AG (fictional) pair agrees on a rare identifier but differs on a changed address; the evidence is assessed field by field.
The model in applied terms
The model compares two records field by field. For each field it asks whether the values agree, and it asks how likely that outcome is under two hypotheses: that the records belong to the same entity, and that they do not. The first probability is usually written m and the second u. For a surname, m is the probability that two records of the same person show the same surname, which is high but less than one because of typing errors and name changes, and u is the probability that two records of different people happen to share a surname, which is small for a rare surname and larger for a common one. Their ratio, usually expressed on a logarithmic scale as a match weight, measures how much agreement on that field counts in favour of a match. The Splink documentation presents this clearly with worked examples.
Weights from the fields are added, on the assumption that the fields are conditionally independent given the match status, to give a total score for the pair. Two thresholds divide the scores into three outcomes: link, possible link for clerical review, and non-link. The original 1969 paper by Fellegi and Sunter proved that, for given error rates, this rule minimises the share of pairs left for clerical review, which is why the three-way decision is a feature of the model and not an incidental choice.
Estimating the probabilities and its limits
The m and u values can be set from training pairs labelled by people or estimated without labels by expectation–maximisation, treating the match status as hidden; Winkler's survey of linkage research at the US Census Bureau covers estimation of this kind, and Enamorado and colleagues extend it to very large files. Unsupervised estimation works when the fields are informative and the proportion of matches in the candidate set is not tiny, and can fail otherwise; it should be checked against a reviewed sample.
The conditional independence assumption is the usual weak point. Postcode and city are not independent, and a surname change in a record may coincide with an address change. Correlated fields are counted twice, which makes scores overconfident. Remedies include dropping or combining correlated fields, modelling their joint outcomes, and calibrating the final score against reviewed pairs, as discussed under calibration. The match weight is evidence for a pair under a model; it is not a probability of a match unless the prior and the model have been checked.
A worked example
Suppose agreement on date of birth has m = 0.95 and u = 0.003, giving a match weight of about log2(0.95/0.003), which is roughly 8.3. Disagreement on date of birth has weight log2(0.05/0.997), which is about minus 4.3. Agreement on a very common surname has m = 0.9 and u = 0.04, weight about 4.5; on a rare one, u = 0.0005 gives a weight about 10.8. A pair that agrees on date of birth and a rare surname totals about 19, which is well above any reasonable upper threshold; a pair that agrees on date of birth and disagrees on a common surname totals about 8.3 minus 3.3, which is about 5 and would normally fall in the review band; a pair that agrees on a common surname and nothing else totals only about 4.5. These figures are illustrative, but they show why rare values are stronger evidence than common ones.
Related terms and boundaries
The model is the scoring core of record linkage and of probabilistic entity resolution, and it presupposes a candidate set of pairs, which is what blocking provides. Where its match weights are treated as confidences, the questions of source reliability arise in a different form: how far to trust each field's agreement, which is exactly what m and u express.
Checks a reviewer can run
Ask for the m and u values and how they were estimated. Check the conditional independence assumption by looking for correlated fields. Compare scores with reviewed pairs to see whether they behave as probabilities. Ask how the thresholds were chosen and what review volume they produce.
Common misreadings
- Assuming field comparisons are independent without checking.
- Treating a common-name match as strong evidence.
- Using scores without a review policy.
Appears in
- Deterministic vs probabilistic entity resolution
Deterministic rules make explicit match decisions; probabilistic methods estimate match likelihood from observed features.
References
- Fellegi and Sunter (1969), A Theory for Record Linkage, Journal of the American Statistical Association 64(328).
- Splink documentation, The Fellegi-Sunter model.
- Winkler (2006), Overview of Record Linkage and Current Research Directions, US Census Bureau.
- Enamorado, Fifield and Imai (2019), Using a Probabilistic Model to Assist Merging of Large-Scale Administrative Records, American Political Science Review 113(2).
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