Imputation in the 2001 Census

2. Imputation in the 2001 Census Robert Beatty NILS User Forum 11 December 2009

3. Coverage • How Census deals with • Missing households • Missing people within households • Incomplete returns

4. Coverage • Census is statutory • Census Act (Northern Ireland) 1969 • Penalties for non-compliance • Therefore counts everyone • Doesn’t it?

5. Coverage

6. Coverage

7. Coverage - international • Australia 2006 – 96% coverage • Don’t impute but adjust MYEs • New Zealand 2006 – 95% response rate • NZ imputed for non-response, but only on 4 key variables • Canada ‘adjust for non-responding households’ – need to know about occupied households

8. Adjustment issues • 1991 coverage – 98% • But inference about population? • Non-response not homogeneous • Young adults • Lower social class • Deprived areas

9. Coverage - 2001 • Acknowledge under-enumeration • 1991 Census 1,578k MYE 1,607k • Decision to adjust Census 2001 database • Objective – all Census outputs to fully reflect whole population • ‘One Number Census’ • Census = MYE

10. Coverage

11. Coverage - 2001 • ‘One Number Census’ method • Basic principle to use a large-scale Census Coverage Survey (CCS) to estimate under-enumeration in sampled areas • Apply survey estimates elsewhere

12. Census Coverage Survey • UK split into about 100 Estimation Areas (each about 0.5m population) • Three in Northern Ireland • About 200 postcodes / 3,000 households per Estimation Area • Three socio-economic strata within EA • Separate analysis in each strata within EA

13. Census Coverage Survey • Fieldwork about 3 weeks after Census day • Face to face interviews • Trained interviewers • Given map of postcode boundary • Asked to re-enumerate the postcode • Short questionnaire - coverage

14. Matching • Forms scanned into system • Special matching software developed • Database retrieval system • CCS returns carefully matched with Census returns – error rate estimated to be under 0.1 per cent

15. Dual System Estimator (DSE) • Use matched Census and CCS data • DSE estimates adjustment for those missed in both Census and CCS Counted By CCS Yes No Counted Yes n11 n10 n1+ By Census No n01n00n0+ n+1n+0n++ DSE estimate for the area (under certain assumptions): n++= n1+ n+1  n11

16. DSE : Simple ExampleFish pond • Day 1: Catch 950 fish, mark with a red dot. • Day 2: Catch 900 fish, mark with a blue dot. • Matched: 855 had blue and red dots. • Question – how many fish in the pond?

17. Dual System Estimator (DSE) Counted Day 2 Yes No Counted Yes 855 95 950 Day 1 No 45n00n0+ 900n+0n++ DSE estimate of the actual number of fish: n++= 950  900  855 = 1,000

18. Analysis • Separately for each age-sex group, within each stratum, within each EA • Apply DSE method to each sampling point (postcodes) within CCS area • Estimate function DSE = f(observed count) • Apply to all other sampling points within stratum (within EA), and aggregate

19. Ratio Estimation • Regression-type estimator • Each dot represents a CCS area • Use Census figure to estimate “true” figure

20. The One Number Census process

21. Imputing households • Use dummy forms as location • Use dummy forms as ‘constraint’? • Dependence on enumerators • Ireland 2006 – 15% of properties vacant

22. One Number Census outcome • 2001 Census response rate of 95% • 4.3% in wholly imputed households (mostly linked to dummy forms(3.0%)) • 0.4% additional people in already enumerated households • Imputed 80,000 people

23. Coverage

26. Response rates by age

27. Quality of returns • So far, considered non-respondents • Person & Household imputation • What about quality of returns actually made? • Decision taken to go for ‘complete’ returns • Item imputation

28. Edit and Impute - Edit • Limited number of ‘hard’ edits – can’t be married if aged under 16 • Larger number of ‘soft’ edits - quality

29. Edit and Impute - Impute • General principle of ‘complete’ data set • No ‘Not stated’ entries in outputs • Item imputation used • Donor imputation system • No different in principle to systems used in sample surveys

30. Edit and Impute - Impute • Level of item imputation differed by variable • Not applied to religion

31. Summary • Objective in 2001 that Census outputs should reflect whole population • Person and household imputation • 5% of persons imputed • Complete records generated for all returns through ‘item’ imputation

32. I told them in 1951 it was just you, me and the dog, but they keep coming back every 10 years to check.

33. Looking forward • Date for your diaries … • 27 March 2011

34. Any questions?

35. Usual residence definition • Historical – present on night • Most countries now ‘usually resident’ • Definitions do exist (UN) • 2001 – self-assessed • 2011 – instructions • ‘Intention to stay’