How to prioritise recontacts Dan Hedlin Statistics Sweden & Stockholm University Situation • Suspect errors • Possible to make another observation of a unit • Cheaper to re-observe all items for a selected unit than the same number of items for several units • Must prioritise units • Able to predict true value • Issue: how to select observations for recontact EESW 2009 Stockholm 2 Solution: selective editing • • • • Widely used Large body of experience Meets requirements of quality enhancement and reduced response burden Although general problem, applications only in surveys and, to some extent, auditing EESW 2009 Stockholm 3 Form 1 Form 2 Item 1 Item 2 Sum of items 1 and 2 Item 3 EESW 2009 Stockholm 4 Form 1 Form 2 Item score 1 for form 2 Item 1 Item 2 Sum of items 1 and 2 Item score 3 for form 2 Item 3 Combined item scores for form 2, ’unit score’ EESW 2009 Stockholm 5 Item score • Common item score for item j in record k: ~ • • • kj wk ~ ykj zkj wk design weight ~ ykj predicted value zkj reported value EESW 2009 Stockholm 6 Item score • Common item score for item j in record k: ~ kj wk ~ ykj zkj Motivations • related to point estimate: difference between ‘true’ point estimate and ‘incorrect point estimate ~ • or ykj zkj as an estimate of square root of measurement variance EESW 2009 Stockholm 7 Unit score • What function of the item scores to form a unit score? • Let a item score be denoted by kj • … and a unit score by g γ k EESW 2009 Stockholm 8 Common unit score functions In the editing literature: p • Sum function: kj j 1 • Euclidean score: p 2 kj j 1 • Max function: max j kj EESW 2009 Stockholm 9 Outstanding issues in selective editing 1. Item score 2. Prediction of true value 3. Unit score 4. Nonresponse issues 5. Selection design (of forms) 6. Estimation of ‘total error’ Focus on choice of unit score EESW 2009 Stockholm 10 Unit scores unified by… 1 • Minkowski’s distance p g γk ; kj j 1 1 • Sum function if = 1 • Euclidean = 2 • Maximum function if EESW 2009 Stockholm infinity 11 Parametrised by Advantages • Unified unit score simplifies presentation and software implementation • Gives structure: orders the feasible choices …from smallest: = 1 …to largest: infinity EESW 2009 Stockholm 12 Three editing situations 1. Large errors remain in data, such as unit errors 2. No large errors, but may be bias due to many small errors in the same direction 3. Little bias, but may be many errors EESW 2009 Stockholm 13 Situation 3. Can show that if… • • Variance of error is Var Item score is ~ kj kj ~ ykj zkj 2 ~ wk ykj zkj Then Euclidean unit score optimal • The Euclidean unit score will minimise the sum of the variances of the remaining error in estimates of the total EESW 2009 Stockholm 14 ~ • However, ykj only prediction of true value • Can show that max function more robust to this prediction error than Euclidean function EESW 2009 Stockholm 15 Situation 2. Can show that if… • Bias contribution ~ ykj zkj Then no unit score optimal • The sum unit score will minimise the sum of the absolute values of the bias contributions, but not the bias However, sum unit score may be useful anyway in Situation 2 EESW 2009 Stockholm 16 Conclusion • The Euclidean and the max unit scores are good choices in Situation 3 • In Situation 2 one has to analyse the nature of the bias EESW 2009 Stockholm 17