Estimation & Adjustment in Census 2021

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Estimation & Adjustment
in Census 2021
Welcome
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Questions?
Visit www.sli.do and enter code 61866 to ask your questions
Technology problems?
Email sdr.stakeholder.engagement@ons.gov.uk
Starting at 10:15am
#Census2021

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Speakers
Gareth Powell
Project Lead for Census Estimation
Methodology
#Census2021 www.sli.do 61866

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Speakers
Viktor Račinskij
Methodologist – Census Estimation

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Speakers
Kirsten Piller
Methodologist – Census Adjustment

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Aims for this session:
• Explain why we estimate and adjust the census population
• Explore what an estimated and adjusted census database allows us
to produce
• Describe the statistical methods we will use to estimate and adjust
the census population in 2021
• Describe what our plans are for sharing the details of our methods

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Why are we running these webinars?
• To explain how the census works in collecting information
and producing great statistics
• To sign-post where more information is available
• To follow on from the material we published in October
• COVID response
• Statistical Design
• Findings from 2019 rehearsal

7 #Census2021 www.sli.do 61866

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Census 2021 Quality Targets
High quality, flexible,
timely, accessible census
statistics for users
94% overall
response
At least 80% in
every local authority
75% Online
Response
Minimise variability
in response
Support
completion

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Estimation and Adjustment
• How we account for non-response to the census
• Estimation creates key population totals, for each local
authority by age-sex group
• Adjustment takes these population estimates and makes
the record level database consistent

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Coverage Estimation in
Census 2021

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Overview of Estimation
• Even with a variety of strategies to maximise response, it is inevitable that
some people will not be counted, or counted in the wrong place
• Undercount error – a member of the target population is missing from
census
• Overcount error – a member of target population is counted in the wrong
location or counted twice
• In 2011 Census of England and Wales undercount was estimated to be 6%,
overcount – 0.6%
• Non-uniformly distributed across a population

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Census Coverage Estimation
• The process of estimating the coverage error corrected population size at
national and subnational levels
• Estimates for a range of domains such as age-sex, tenure, ethnicity, etc. by
local authority
• Individual and household populations
• Coverage error corrected census estimates have higher accuracy than the
raw census counts

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Raw census counts at the local authority level
in 2011 (estimated)

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What coverage error corrected population size
estimates may look like compared to raw counts

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Broad outline of estimation
• Census coverage survey conducted 6 weeks after the census
day, 1.5% of population sampled
• Census and the coverage survey data are matched
• Population size estimation
• Variance estimation

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Coverage estimation in 2011
• Data delivered in batches, estimation on groups of local authorities
(estimation areas)
• Census coverage survey
• ~1.5% of postcodes
• Stratified by local authority and hard-to-count index
• Sample in every local authority
• Two-stage cluster (output areas, postcodes)
• Optimal allocation with constraints
• Combination of the dual system, ratio and synthetic estimators used

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Data collection in Census 2021
• Online data collection means that the data are going to be
delivered quicker
• Estimation can be done using the data for the entirety of England
and Wales
• Different estimation approach based on the logistic / mixed
effects regression modelling

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Independent re-enumeration of a sample of the
population

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Independent re-enumeration of a sample of the
population: important points

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How (and why) the dual system estimator works
𝑇𝑜𝑡𝑎𝑙 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 = [𝑁𝑢𝑚𝑏𝑒𝑟 𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑡𝑜 𝑐𝑒𝑛𝑠𝑢𝑠] ∗
[𝐸𝑣𝑒𝑟𝑦𝑜𝑛𝑒 𝑖𝑛 𝐶𝐶𝑆]
[𝐼𝑛 𝑏𝑜𝑡ℎ 𝐶𝐶𝑆 𝑎𝑛𝑑 𝐶𝑒𝑛𝑠𝑢𝑠]
= 9 ∗
8
6
= 12

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How to go from sample to population?
Ratio estimator
[Population size] =[DSE estimate within sample]
[census count at population level]
[census count within a sample]
= 12 ∗
90
9
= 120

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Sampling error
Every CCS sample would be slightly different

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Variance Estimation
• Variance estimation quantifies the error around coverage error corrected estimates
• Gives confidence intervals for our estimates

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Estimating across many domains – Local
Authorities & characteristics

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Changes for 2021 – Regression based
modelling approach
• In 2011 we estimated domains separately
• In 2021 we will use a modelling approach to allow us to use all
domains at the same time
• This allows each of them to help in the estimation of all the others

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Changes for 2021 – Regression based
modelling approach
• Logistic or mixed effects logistic regression is used to estimate the
census response probability for an element (e.g. a person) in a local
authority with a set of characteristics
• Reduces variability of estimates and allows to reflect coverage
patterns and better meet assumptions of estimation
[𝑅𝑒𝑠𝑝𝑜𝑛𝑠𝑒 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦] =
1
1 + exp −[𝒙𝑇𝛽 + 𝒛𝑇𝜅 + 𝑢𝐿]

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Why regression?
• Doing estimation separately for each
domain loses some information as
domains can overlap
• E.g. if we estimate for all men ages 40-
44 in an area, we aren’t also using their
marital status
• We could break the estimation down
further – but groups would get too small

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Even better – use all variables and areas at once

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The rest of estimation
• Overcoverage estimation and correcting for overcoverage error is
conceptually similar
• Use the census to the coverage survey matching to establish the
cases of overcount within a sample
• Fit the logistic regression model to estimate the probability of correct
enumeration
• Apply it to adjust for overcoverage (downweight)
• Communal Establishments

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After Estimation
• Quality assurance using demographic analysis and admin data
• Record level totals aren’t the same as the estimates
• To get to small area multivariate outputs, need to impute record level
data – coverage adjustment

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Coverage Adjustment in
Census 2021

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Census Coverage Adjustment
• Coverage estimation process provides information on what types of persons
and households are estimated to have been missed
• Population estimates only broken down by characteristics associated with
non-response:
• age groups by sex, ethnicity, household size, hard to count index, activity
last week and tenure.

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Census Coverage Adjustment continued
• Adjustment process adds households and persons into the
census database
• Adjust so that it remains consistent with the population estimates
• Builds on previous census adjustment which began in the 2001
One-Number-Census approach
• Method for 2021 Census has changed, better meets population
estimates for all key variables

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Post-estimation
• Able to produce census outputs at any level and
for any breakdown of variables
• However, the census data does not account for
missed persons and households so outputs
would be biased
• Undercount does not usually occur uniformly
across all areas or other sub-groups of the
population such as age groups
Household ID Person ID Age Group
Census data

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Post-estimation continued
• Population size estimates available at
local authority (LA) level, by some key
characteristics
• For both person and household
characteristics
• Allows small area outputs and more
characteristic breakdowns
Population estimates

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2021 Census Coverage Adjustment Strategy
Stage 1: Impute missed households (with persons)
• Add household records into the census database – copy census
households from the database to meet the population estimates.
• Assign new geographical information (e.g. postcode)
Stage 2: Impute remaining characteristics
• Impute characteristics variables of the added records that aren’t
controlled for in the adjustment process.

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Shortfall in Population Estimates (Stage 1)
• However, we have a
shortfall for several
variable breakdowns by LA
– benchmarks
• When adding in
persons/households to
meet one characteristic’s
estimated shortfall, they
add to other characteristics
too
Example: LA counts of males aged 20-24
LA
Census
count
Population
estimate
Shortfall (target
amount to impute)
LA 1 650 800 150
LA 2 400 500 100
LA … … … …

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Selecting Records to Impute (Stage 1)
• In 2021, Combinatorial Optimisation (CO) will be used to select households.
• CO for adjustment process will involve the selection of a combination of
households from the census database that best fit the shortfall benchmarks.
• CO better meets these benchmarks; it performs well when controlling for all
of them simultaneously.

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Assigning Geographical Information (Stage 1)
• Need to assign a postcode to the imputed households
• Dummy forms provide us with records of addresses where unable to
enumerate, with basic information collected.
• Strong indicators of where usual resident households could exist.
• Assign imputed households a dummy form’s geographical information
• Dummy form has similar characteristics or is in small area with similar
characteristics
Household ID Person ID Age Group Postcode Output Area

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Post-adjustment Edit and Imputation (Stage 2)
• In Stage 2, imputation of the
remaining characteristic
variables will be completed
using CANadian Census
Edit and Imputation System
(CANCEIS).
Household ID Person ID Age Group … … … Postcode Output Area
Household ID Person ID Age Group … … … Postcode Output Area

Resulting Census Database
• Now can produce estimated census outputs that
account for missed persons and households
• And for more detailed breakdown/at lower
geographical level
• These outputs will aggregate to any other
outputs (e.g. LA or national level) as they are
from the same database
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Communal Establishments
• Communal Establishments (CEs) are dealt with separately to households in
adjustment
• In 2011, there were over 46,000 communal establishments with almost one
million residents in England and Wales
• Small CEs (7-49 beds) and large CEs (50+ beds) are adjusted separately
as different data informs the coverage of each in the census

Summary

Key points
• Improve the quality of the census results
• Final census results represent our best estimate of the whole
population, not just those we count
• Building on the successful approach used in 2001 and 2011
• Improvements to methods and quality
• The process is flexible and adaptable
• Thorough quality assurance throughout – including
Methodological Assurance Review Panel

References
• Overview of our design and plans for Census 2021
(further information is available from that document)
• We publish the papers reviewed by the Methodological
Assurance Review panel (MARP) on the UK Statistics
Authority website

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Estimation & Adjustment
in Census 2021
Any questions?
Visit www.sli.do and enter code 61866
Please complete our evaluation survey (we will email you a link) and let us know how we did.
If you have any questions email us on SDR.stakeholder.engagement@ons.gov.uk.
Want to learn more about the Census 2021 Statistical Design? Visit our website to find out
more about our other webinars.
#Census2021

Estimation & Adjustment in Census 2021

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