imputation in the 2001 census

Imputation in the 2001 CensusImputation in the 2001 Census

Robert Beatty

NILS User Forum

11 December 2009

CoverageCoverage

How Census deals withMissing householdsMissing people within householdsIncomplete returns

CoverageCoverage

Census is statutoryCensus Act (Northern Ireland) 1969Penalties for non-complianceTherefore counts everyoneDoesn’t it?

CoverageCoverage

Population in thousands

Published Census figure

MYE

1991 1,578 1,607

CoverageCoverage

Population in thousands

Published Census figure

MYE

1991 1,578

(enumerated)

1,607

(best estimate)

Coverage - internationalCoverage - international

Australia 2006 – 96% coverageDon’t impute but adjust MYEsNew Zealand 2006 – 95% response rateNZ imputed for non-response, but only on 4

key variablesCanada ‘adjust for non-responding

households’ – need to know about occupied households

Adjustment issuesAdjustment issues

1991 coverage – 98%But inference about population?Non-response not homogeneousYoung adultsLower social classDeprived areas

Coverage - 2001Coverage - 2001

Acknowledge under-enumeration1991 Census 1,578k MYE 1,607kDecision to adjust Census 2001 databaseObjective – all Census outputs to fully

reflect whole population‘One Number Census’Census = MYE

CoverageCoverage

Population in thousands

Published Census figure

MYE

1991 1,578

(enumerated)

1,607

2001 1,685

(adjusted)

1,689

Coverage - 2001Coverage - 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

Census Coverage SurveyCensus Coverage Survey

UK split into about 100 Estimation Areas (each about 0.5m population)

Three in Northern IrelandAbout 200 postcodes / 3,000 households per

Estimation AreaThree socio-economic strata within EASeparate analysis in each strata within EA

Census Coverage SurveyCensus Coverage Survey

Fieldwork about 3 weeks after Census dayFace to face interviewsTrained interviewersGiven map of postcode boundaryAsked to re-enumerate the postcodeShort questionnaire - coverage

MatchingMatching

Forms scanned into systemSpecial matching software developedDatabase retrieval systemCCS returns carefully matched with Census

returns – error rate estimated to be under 0.1 per cent

Dual System Estimator (DSE)Dual System Estimator (DSE) Use matched Census and CCS data DSE estimates adjustment for those missed in both

Census and CCSCounted By CCS

Yes No

Counted Yes n11 n10 n1+

By Census No n01 n00 n0+

n+1 n+0 n++

DSE estimate for the area (under certain assumptions):

n++ = n1+ n+1 n11

DSE : Simple ExampleDSE : Simple ExampleFish pondFish 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)Dual System Estimator (DSE)

Counted Day 2

Yes No

Counted Yes 855 95 950

Day 1 No 45 n00 n0+

900 n+0 n++

DSE estimate of the actual number of fish:

n++ = 950 900 855 = 1,000

AnalysisAnalysis

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 EstimationRatio Estimation

Regression-type estimator

Each dot represents a CCS area

Use Census figure to estimate “true” figure

Census

DSE

The One Number Census The One Number Census processprocess

CENSUS

CENSUS + CCS

ESTIMATE BY AGE AND SEX

FOR EA

EA ESTIMATES

ADJUSTED INDIVIDUAL AND

HOUSEHOLD DATA AND TABLES

NI POPULATION ESTIMATE

MATCHING

Quality Assurance

Dual System and regression estimation

CCS

QA

Imputation controlled to EA

estimates

Sum

Imputing householdsImputing households

Use dummy forms as locationUse dummy forms as ‘constraint’?Dependence on enumeratorsIreland 2006 – 15% of properties vacant

One Number Census outcomeOne 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 householdsImputed 80,000 people

CoverageCoverage

Population in thousands

Published Census figure

MYE

1991 1,578

(enumerated)

1,607

2001 1,685

(adjusted)

1,689

Distribution of LAD Level Underenumeration

0

10

20

30

40

50

60

70

80

Response Rate

Fre

qu

en

cy

Response rates by ageResponse rates by age

80

85

90

95

100

'0-4

'10-

14

'20-

24

'30-

34

'40-

44

'50-

54

'60-

64

'70-

74

'80-

84

age

male

female

Quality of returnsQuality of returns

So far, considered non-respondentsPerson & Household imputationWhat about quality of returns actually

made?Decision taken to go for ‘complete’ returnsItem imputation

Edit and Impute - EditEdit 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 - ImputeEdit and Impute - Impute

General principle of ‘complete’ data setNo ‘Not stated’ entries in outputsItem imputation usedDonor imputation systemNo different in principle to systems used in

sample surveys

Edit and Impute - ImputeEdit and Impute - Impute

Level of item imputation differed by variable

Not applied to religion

SummarySummary

Objective in 2001 that Census outputs should reflect whole population

Person and household imputation5% of persons imputedComplete 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 forwardLooking forward

Date for your diaries …27 March 2011

Any questions?Any questions?

Usual residence definitionUsual residence definition

Historical – present on nightMost countries now ‘usually resident’Definitions do exist (UN)2001 – self-assessed2011 – instructions‘Intention to stay’