methods for Small Area Estimation Dr Paul Williamson Centre for Spatial Demographics Research Dept of Geography amp Planning 1 Direct survey estimation a recap 3 Conventional SAE a recap ID: 638470
Download Presentation The PPT/PDF document "Spatial Microsimulation" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Spatial Microsimulation methods for Small Area Estimation
Dr Paul WilliamsonCentre for Spatial Demographics ResearchDept. of Geography & PlanningSlide2
(1) Direct survey estimation: a recapSlide3Slide4Slide5Slide6
(3) Conventional SAE: a recap
Ecological (Fay-Herriot) regressionFind 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
[ = ‘synthetic’ model-based estimate ]
E.g. ONS small area income estimates for MSOAsSlide7
Potential regression to the meanEstimates a point in distribution; not whole distribution
Possible solutionsFit separate models for separate points in the distribution …time consuming
Estimate the distribution using unit level imputation or the Empirical Best Predictor (‘World Bank’) approach
…BUT both require access to Census
microdata
Known problems with conventional SAE approachesSlide8
National/regional
Survey
distribution
[age
x
ethnicity]
Local
age
distribution
Local
ethnic
distribution
Calibrate (reweight) survey data to fit local area constraints/margins...
...BUT weighting DOWN instead of
up
= INDIRECT Survey Calibration
?
(4) ‘Spatial Microsimulation’:
an unconventional SAE approachSlide9Slide10Slide11
Spatial Microsimulation
SAE
Calibration WeightingSlide12
(5) Main approaches to Spatial MSM
Iterative P
roportional
F
itting / Raking
GREGWT
(Australian Bureau of Statistics) [MCS-r plus]
C
ombinatorial
O
ptimisationSlide13
IPFMCS-r/GREGWT
CO
Avoids convergence problems
No
No
Yes
Calibration weights close to initial weights
Yes
Yes
No
Optimisation problem
Min Discriminant Inf. between initial and final weights subject to exact fit to benchmarks and positive weightsMin Chi-sq distance between initial and final weights
subject to exact fit to benchmarks and positive weights
Min TAE or RSSZ between results and benchmarks subject to positive weightsOptimum Solution guaranteed? No No
NoDirect Integer-valued Solution Possible No
No YesSlide14
(6) A Spatial MSM exampleSlide15
2011 HSE ~ 10k respondentsSlide16
9 benchmark tables9 benchmark variables152 benchmark
constraints
Benchmark Tables
Source
Benchmark
constraints
BC1.
Origin
by
Tenure
LC4203EW
12
BC2.
Tenure
QS403EW
5
BC3.Marital status by Sex by Age
LC1108EW
50
BC4.Sex by AgeLC3302EW16BC5.Marital status by In-WorkLC6401EW
10BC6.Education
LC5103EW6BC7.
HRP Origin by Tenure by Age
LC4201EW36
BC8.
HRP In-Work by Tenure by Age
LC4601EW
12
BC9.
Area IMD (deprivation)
quintile
PHE table
5
Estimation problem
table comprising c. 96,000 cells (ignoring structural
zeros
)Slide17
Relative Error (%)
Linear Regression
Health
Mean
Deviation
Intercept
Slope
Adj. R-squared
Good
3.27
2.06
-66.58
1.04
0.986
Fair
20.44
16.34
46.790.80
0.793
Bad
14.1113.5310.200.950.850Slide18
(7) GREGWT v. COSlide19
(8) IPF v. CO
Target: Car ownership (2) x Tenure (3) (6 counts; 3%s) for residents at ward level
IPFSlide20
(9) ISC/SAE: a rapprochement?
ISC / Spatial Microsimulation is mathematically equivalent to…?…a GREG-like estimator (in most cases)……depending on the measure of fit to benchmarks and to original weights being maximizedSlide21
(a) Fitness for Purpose
If all you want is a point-estimate, then conventional SAE techniques are generally:Much easier to implementFasterBetter understood mathematically, with known variance etc.HOWEVER, if you want distributional estimate, then ISC could be a good solution
(10) The limitations of calibrationSlide22
(b) Precision/bias of ISC estimates currently unknownSlide23
(b) Real vs. Integer Weight solutions
Integer solutions required for:lifepath modelling (dynamic microsimulation)tax-benefit modellingadjustment of census for under/over enumeration
Finding ‘optimal’ integer solution is NP-hard, so currently only approximations are possibleSlide24
(d) Software
Off-the-shelf solutions exist for for IPF and GREG, but can be subject to convergence problemsExecutable and code for CO (in Fortran) available online or on request; or a stripped down version is available as an R package.Slide25
(e) The value-added of ISC
Type of interaction / distribution NSA UserConstrained (benchmarked)
Margin-constrained
Unconstrained
x
x
xSlide26
Local prior (n=373)
Regional prior (n=10)
Geodemographic prior (n=7)
Uniform prior (n=1)
% Misclassified
(f) Local sample is usually a poor priorSlide27
(g) Interactions vary spatially…
Correlation of
Accommodation type
with
Ethnicity
White British
Flat
Other
Not
Flat
White British
Flat
Other
Not
FlatSlide28
Geography MORE important
(Top 7)
Geography LESS important
(Bottom 7)
…but semi-predictably…Slide29
(11) Unresolved issues
‘Best’ calibration weighting approach/algorithm?What is the best prior?
‘The more constraints the better’; unless…?
Estimate precision/bias