Strategic Matching -- Tech Note #13
Estimating the Number of False Positive Matches
Applies to: CODES 2000 Version 2.1+, LinkSolv Version 2.2+.
Last updated:
Thursday October 21, 2004.
SUMMARY
The match weight calculated for a given record pair is the logarithm of the odds ratio for a true match given observed agreements and disagreements. Assuming a uniform prior probability distribution for a true match and given tabulated match weights, we can derive the posterior probability distribution that linked record pairs are true matches (see Tech Note #1). The Record Linkage Wizard includes a special function that makes this calculation straightforward. Summing the posterior probabilities over all tabulated record pairs gives the expected number of true positive matches among the tabulated pairs. Summing 1 minus the posterior probabilities gives the expected number of false positive matches.
PROCEDURE
First, complete the record linkage of interest, say CrashEMS, including merging the results from individual match passes. Make a note of the Total Matches parameter in your link specifications, say 9200.
Second, while still in the project database, click on Tables in the database window. Open Table A, say Crash (this table is an Access link to a table in another database). Make a note of the number of records, say 56689. Open Table B, say EMS. Make a note of the number of records, say 26089.
Third, click on Queries in the database window. Double click on Create query in Design view.
Fourth, close the Show Table dialog and select SQL from the View menu. Enter the following SQL command. The MatchProbability function is part of the Record Linkage Wizard. The CrashEMS table contains the merged list of linked record pairs and their match weights. It is referred to as the Match Pairs In Sets table for this match.
SELECT Sum(MatchProbability([MatchWeight],56689,26089,9200)) AS TruePositives,
Sum(1-MatchProbability([MatchWeight],56689,26089,9200)) AS FalsePositives
FROM CrashEMS;
Fifth, save and run the query. Note the number of true positives and false positives.