1. Some challenges for small area estimation
Dr Paul Williamson
Dept. of Geography & Planning

2. (1) What is Small Area Estimation?
Estimation of population characteristics for which a reliable direct survey estimate is unavailable/impractical
% of persons who are male at LSOA level
% of unemployed males who are ill at DISTRICT level

3. (2) Main SAE approaches Proxies Ecological regression
Find relationship between AREA-level Y and X(s) for areas sampled in survey
Assume applies to (non-sampled) areas, for which AREA-level X is known
E.g. ONS small area income estimates for MSOAs

4. Coefficient of
Variation
Big areas
(pop > 250k)
Small areas
(median pop. c 1k)

5. Known problems with Ecological Regression
Regression to the mean
Point estimate
Covariate dependent

6. Local ethnic distribution
Survey reweighting / calibration
Reweight survey data to fit local area constraints/margins...
Survey distribution
[age x ethnicity]
Local age distribution
Local ethnic distribution ?
...potentially weighting DOWN instead of up

7. Reweighting approaches:
IPF / raking/ Mostellerisation / Cross-Fratar / RAS etc../
Generalised Regression (GREG)
Integer linear programming methods
etc…
Known problems with reweighting approaches:
As per ecological regression…
BUT provides distributional rather than point estimates

8. Record-level imputation
Impute (estimate) missing data onto existing record level data
E.g. Impute income onto Census records given known individual attributes such as age and occupation
Known problems:
As per ecological regression, plus:
Requires record-level data with 100% local area coverage
BUT does provide distributional rather than point estimates

9. Geographical variation in interactions
(3) The limitations of SAE
Geographical variation in interactions
Other
White British
Not
Flat
Flat
Other
White British
Not
Flat
Correlation of
Accommodation type with Ethnicity
Flat

10. Geography MORE important
(Top 7)
Geography LESS important
(Bottom 7)

11. For the perfect estimate, need to know margins AND interactions

12. (4) Research Challenges
Ecological regression v. reweighting v. imputation
(deidentified) record-level linkage of census, survey and admin data
Understanding how interactions vary spatially
Quantifying estimate uncertainty
Better use of admin. data