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

Coverage How Census deals with Missing households Missing people within households Incomplete returns

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

Coverage Population in thousands Published Census figure MYE 19911,5781,607

Coverage Population in thousands Published Census figure MYE 19911,578 (enumerated) 1,607 (best estimate)

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

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

Coverage 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

Coverage Population in thousands Published Census figure MYE 19911,578 (enumerated) 1, ,685 (adjusted) 1,689

Coverage ‘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

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

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

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

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 Yesn 11 n 10 n 1+ By Census Non 01 n 00 n 0+ n +1 n +0 n ++ DSE estimate for the area (under certain assumptions): n ++ = n 1+  n +1  n 11

DSE : Simple Example Fish 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?

Dual System Estimator (DSE) Counted Day 2 Yes No Counted Yes Day 1No45 n 00 n n +0 n ++ DSE estimate of the actual number of fish: n ++ = 950  900  855 = 1,000

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

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

The One Number Census process

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

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

Coverage Population in thousands Published Census figure MYE 19911,578 (enumerated) 1, ,685 (adjusted) 1,689

Response rates by age

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

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

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

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

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

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

Looking forward Date for your diaries … 27 March 2011

Any questions?

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