Strategic Matching -- Tech Note #1
Testing Linkage Feasibility:
A Manual Procedure
Applies to: All LinkSolv releases.
Last updated: Thursday August 23, 2001.
SUMMARY
It may be important to test whether a planned linkage is feasible -- that is, whether available match variables contain sufficient information to discriminate between true matched and unmatched record pairs with high probability. LinkSolv includes estimation tools which simplify this analysis but you can use the following manual procedure to test linkage feasibility at any time. You may need to do this to justify obtaining sensitive personal information such name or date of birth.
PROCEDURE
- Calculate the prior odds for a true match.
When linking two tables containing A and B records, respectively, and with expected total matched pairs approximately equal to M, the prior odds for a true match are
Prior Odds = M / ((A x B) - M)
- Establish a minimum acceptable posterior odds for a true match.
The minimum posterior odds for a true match should be high, say 9 to 1.
Posterior Odds = 9
- Calculate the minimum acceptable odds ratio.
Consequently, the minimum acceptable odds ratio (Posterior divided by Prior) for this match is
Minimum Odds Ratio = 9 / (M / ((A x B) - M))
- Calculate the agreement odds ratio for each match variable.
Observed agreements on each independent match variable contribute to the odds ratio in accordance with Bayes' Theorem. You can estimate the agreement odds ratio of each variable as A / f, where f is the observed modal frequency for that variable.
Agreement Odds Ratio = A / f
- Calculate the total agreement odds ratio for all match variables.
The cumulative effect on the total agreement odds ratio of agreements on all independent match variables is the product of the individual odds ratios. If this product exceeds the minimum odds ratio you estimated earlier, then the linkage is feasible.
EXAMPLE
Suppose A = 100,000, B = 5,000, and M = 5,000. Also, suppose Date of Birth, Sex, and Initials are available as independent match variables with modal frequencies of 10, 50,000, and 750, respectively. Then
Prior Odds = 5,000 / (100,000 x 5,000 - 5,000) = 1 / 99,999
Minimum Posterior Odds = 9
Minimum Odds Ratio = 9 / (1 / 99,999) = 899,991
For Date of Birth
Agreement Odds Ratio = 100,000 / 10 = 10,000
For Sex
Agreement Odds Ratio = 100,000 / 50,000 = 2
For Initials
Agreement Odds Ratio = 100,000 /750 = 133
Total for All Variables
Agreement Odds Ratio = 10,000 x 2 x 133 = 2,660,000
The total agreement odds ratio 2,660,000 is greater than the minimum acceptable odds ratio 899,991 so this match is feasible.
Suppose Date of Birth is not available, but Age is available with a modal frequency of 3,650. Then
For Age
Agreement Odds Ratio = 100,000 / 3,650 = 27
Total for All Variables
Agreement Odds Ratio = 27 x 2 x 133 = 7,182
The total agreement odds ratio 7,182 is less than the minimum acceptable odds ratio 899,991 so this match is not feasible.