What is … small area estimation
Dimitris BallasDepartment of GeographyUniversity of Sheffielde-mail: [email protected]://www.sheffield.ac.uk/geography/staff/ballas_dimitris
Outline
• Small area data sources• Why small area estimation?• Methodological approaches to small
area estimation• Spatial microsimulation• Policy relevance examples• Further reading and resources
(including web-links to free software)
Small area data sources: the census of population• Census data describe the state of the whole
nation, area by area – no other social survey has such comprehensive spatial coverage
• Extremely relevant for policy analysis – used by government in the allocation of billions of pounds of public expenditure
• Very valuable commercially – essential ingredients in marketing analysis and retail modelling
After Rees, P, Martin, D, Williamson, P (eds) (2002), The Census Data System, Chichester, Wiley
Neighbourhood statistics topics (http://www.neighbourhood.statistics.gov.uk ):Census of populationCrime and SafetyEconomic DeprivationEducation, Skills and TrainingHealth and CareHousingPhysical EnvironmentDeprivation and ClassificationIncome and LifestylesPopulation and Migration
Examples of more small area data sources
Why small area estimation?• Need for small area estimates of variables such as
income, poverty, wealth, health, fear of crime, healthy lifestyles…
• We know little about the interdependencies between household structure or type and their lifestyles at the small area level
• There is no ‘live’ geographical database of household types linked to earning capabilities (both earned and/or transfer payments) which can be used both to explore spatial variations in lifestyles and behaviour and to monitor the effects of changes in taxation, family credit, pensions, social security payments etc.
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• Policy makers need small area estimates• Academics need small area estimates• Public like small area estimates
– “What’s happening in my backyard”
Why small area estimation?
Policy relevance– socio-economic impact assessment– geographical impacts of social policy– what-if socio-spatial analysis
Small area estimation methods• Conduct a survey - very costly - confidentiality issues• Small area estimation methods can be applied to get
survey data down to small area level and to evaluate the spatial impacts of policies
• Various methodologies of small area estimation– Statistical approaches– Spatial microsimulation approaches
• Deterministic reweighting (IPF)• Probabilistic reweighting (CO)• Generalised linear regression (GREGWT)
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Methodological approaches to small area estimation
• Statistical approaches (more linked to statisticians)– Synthetic estimation– Multi-level modelling– Bayesian approaches
• Spatial microsimulation approaches (more linked to geographers)– Deterministic reweighting approaches (IPF)– Probabilistic reweighting approaches (combinatorial optimisation)– Generalised linear regression (GREGWT)
• But many links between the methodsFor a review of a recent effort to explore linkages between these two often separate sets of approaches see: http://www.ncrm.ac.uk/research/NMI/2012/smallarea.php
A very simple approach to generating indirect non-survey designed estimates
- Obtain small area total numbers from the census on variables that may be correlated with a ‘target variable (e.g. for income would be correlated with “occupational classification”)
- obtain information at the national, or sometimes regional level information on the same variable cross-tabulated by the census variable (e.g. earnings by occupational classification)
- multiply the known census totals by average value for each area
A model-based approach (Office for National Statistics, Heady et al., 2003)
• Estimating ‘average weekly household’ at the electoral ward level in England and Wales on the basis of the following predictors:
• the social class of the ward population; • Household type/composition• Regional/country indicators• the employment status of the ward population• the proportion of the ward population claiming DWP benefits;• the proportion of dwellings in each of the Council Tax bands in a ward• “The model-based approach is based on finding a relationship between
weekly household income (as measured in the Family Resources Survey (FRS)) and covariate information (usually from Census or administrative sources) for the wards that are represented in the Survey”
see http://www.neighbourhood.statistics.gov.uk/HTMLDocs/images/Model-Based_Income_Estimates%28V2%29_tcm97-51115.pdf
Spatial Microsimulation• A technique aiming at building large
scale data sets• Modelling at the microscale• A means of modelling real life events
by simulating the characteristics and actions of the individual units that make up the system where the events occur
What is microsimulation?
PERSON AHID PID AAGE12 SEX AJBSTAT … AHLLT AQFVOC ATENURE AJLSEG …
1 1000209 10002251 91 2 4 … 1 1 6 9 …
2 1000381 10004491 28 1 3 … 2 0 7 -8 …
3 1000381 10004521 26 1 3 … 2 0 7 -8 …
4 1000667 10007857 58 2 2 … 2 1 7 -8 …
5 1001221 10014578 54 2 1 … 2 0 2 -8 …
6 1001221 10014608 57 1 2 … 2 1 2 -8 …
7 1001418 10016813 36 1 1 … 2 1 3 -8 …
8 1001418 10016848 32 2 -7 … 2 -7 3 -7 …
9 1001418 10016872 10 1 -8 … -8 -8 3 -8 …
10 1001507 10017933 49 2 1 … 2 0 2 -8 …
11 1001507 10017968 46 1 2 … 2 0 2 -8 …
12 1001507 10017992 12 2 -8 … -8 -8 2 -8 …
Static spatial microsimulation• Reweighting probabilistic approaches, which
typically reweight an existing national microdata set to fit a geographical area description on the basis of random sampling and optimisation techniques
• Reweighting deterministic approaches, which reweight a non geographical population microdata set to fit small area descriptions, but without the use of random sampling procedures
• Synthetic probabilistic reconstruction models, which involve the use of random sampling
Static spatial microsimulation
PERSON AHID PID AAGE12 SEX AJBSTAT … AHLLT AQFVOC ATENURE AJLSEG …
1 1000209 10002251 91 2 4 … 1 1 6 9 …
2 1000381 10004491 28 1 3 … 2 0 7 -8 …
3 1000381 10004521 26 1 3 … 2 0 7 -8 …
4 1000667 10007857 58 2 2 … 2 1 7 -8 …
5 1001221 10014578 54 2 1 … 2 0 2 -8 …
6 1001221 10014608 57 1 2 … 2 1 2 -8 …
7 1001418 10016813 36 1 1 … 2 1 3 -8 …
8 1001418 10016848 32 2 -7 … 2 -7 3 -7 …
9 1001418 10016872 10 1 -8 … -8 -8 3 -8 …
10 1001507 10017933 49 2 1 … 2 0 2 -8 …
11 1001507 10017968 46 1 2 … 2 0 2 -8 …
12 1001507 10017992 12 2 -8 … -8 -8 2 -8 …
Static spatial microsimulation
Small area table 1 (household type)
Small area table 2 (number of cars)
Small area table 3 (tenure status)
Area 1 Area 1 Area 160 "married couple
households"10 no car 60 owner occupier
20 "Single-person households"
80 1 car 20 Local Authority or Housing association
20 "Other" 10 2+ cars 20 Rented privatelyArea 2 Area 2 Area 240 "married couple
households"40 no car 60 owner occupier
20 "Single-person households"
40 1 car 20 Local Authority or Housing association
40 "Other" 20 2+ cars 20 Rented privately
Tenure and car ownership example
Household car ownership characteristics
Household tenure characteristics
1 car
2+ cars
No car
Owner-occupier
LA/HA rented
Other
Simulation 27 24 49 39 17 44Census 50 20 30 60 10 30Absolute error
23 4 19 21 7 14
Combinatorial optimisation: simulated annealing
• Origins in thermodynamics• Metropolis et al. (1953) suggested an algorithm for the
efficient simulation of the evolution of a solid material to thermal equilibrium
• Annealing is a physical process in which a solid material is first melted in a heat bath and then it is cooled down slowly until it crystallises
• First used in a spatial microsimulation context by Williamson, P., Birkin, M., Rees, P. (1998), The estimation of population microdata by using data from small area statistics and samples of anonymised records, Environment and Planning A, 30, 785-816
Other methodologies
• Hill-climbing, genetic algorithms• Deterministic reweighting
approaches• Probabilistic synthetic
reconstruction techniques (IPF-based approaches)
age/sex male femaleunder-50 1 1over-50 2 1
Deterministic Reweighting the British Household Panel Survey (BHPS) - a simple example (1)
A hypothetical sample of individuals (list format)Individual sex age-group weight1st male over-50 12nd male over-50 13d male under-50 14th female over-50 15th female under-50 1
In tabular format:
age/sex male femaleunder-50 3 5over-50 3 1
Hypothetical Census data fora small area:
age/sex male femaleunder-50 1 1over-50 2 1
Reweighting the BHPS - a simple example (2)
Calculating a new weight, so that the sample will fit into the Census table
In tabular format:
age/sex male femaleunder-50 3 5over-50 3 1
Hypothetical Census data fora small area:
Individual sex age-group weight New weight 1st male over-50 1 1 x 3/2 = 1.5 2nd male over-50 1 1 x 3/2 = 1.5 3d male under-50 1 1 x 3/1 = 3 4th female over-50 1 1 x 1/1 = 1 5th female under-50 1 1x 5/1 = 5
Probabilistic synthetic reconstruction
After Birkin, M., Clarke, M. (1988), SYNTHESIS – a synthetic spatial informationsystem for urban and regional analysis: methods and examples, Environment and Planning A, 20, 1645-1671
Steps 1st 2nd … Last Age, sex and marital status and location (DED level) (given)
Age: 25 Sex: Male Marital Status: Single GeoCode: Leitrim Co., DED 001 Ballinamore
Age: 76 Sex: Female Marital Status: married GeoCode: Leitrim Co., DED 002 Cloverhill
… Age: 30 Sex: Male Marital Status: married GeoCode: Leitrim Co., DED 078 Rowan
Probability of hh of given age , sex and location (ED level) being at work
0.7 0.2 … 0.7
Random number 0.55 0.5 … 0.45 Economic activity assigned to hh on the basis of random sampling
At work Other (e.g. Retired)
… At work
Probability (conditional upon the above attributes) of hh being an employee in the Agriculture industry
0.6 … 0.2
Random number 0.4 … 0.6 Economic activity category assigned on the basis of random sampling
Employee in Agriculture
… Not an employee in Agriculture
… … … … …
SMILE model, after Ballas, D., Clarke, G. P., Wiemers, E., (2006) Spatial microsimulation for rural policy analysis in Ireland: The implications of CAP reforms for the national spatial strategy, Journal of Rural Studies, vol. 22, pp. 367-378 (doi:10.1016/j.jrurstud.2006.01.002)
Probabilistic synthetic reconstruction techniques
Dynamic spatial microsimulation
• Probabilistic dynamic models, which use event probabilities to project each individual in the simulated database into the future (e.g. using event conditional probabilities).
• Implicitly dynamic models, which use independent small area projections and then apply the static simulation methodologies to create small area microdata statically
Steps 1st 2nd … Last Age, sex and marital status and location (DED level) (given)
Age: 25 Sex: Male Marital Status: Single GeoCode: Leitrim Co., DED 001 Ballinamore
Age: 76 Sex: Female Marital Status: married GeoCode: Leitrim Co., DED 002 Cloverhill
… Age: 30 Sex: Male Marital Status: married GeoCode: Leitrim Co., DED 078 Rowan
Probability (conditional upon age, sex, location) of hh to migrate
0.30 0.05 … 0.26
Random number 0.2 0.4 … 0.4 Migration status assigned on the basis of random sampling
Migrant Non-migrant … Non-migrant
Probability (conditional upon age, sex, location) of hh to survive
0.9 0.5 0.8
Random number 0.5 0.4 … 0.4 Survival status Survived Deceased … Survived
Probabilistic dynamic models
after Ballas D , Clarke, G P, Wiemers, E, (2005) Building a dynamic spatial microsimulationmodel for Ireland , Population, Space and Place, 11, 157–172 (http://dx.doi.org/10.1002/psp.359)
SimBritain: combining Census data with the BHPS
Census of UK population:• 100% coverage• fine geographical detail• Small area data available
only in tabular format with limited variables to preserve confidentiality
• cross-sectional
British Household Panel Survey:
• sample size: more than 5,000 households
• Annual surveys (waves) since 1991
• Coarse geography• Household attrition
Ballas, D. , Clarke, G.P., Dorling, D., Eyre, H. and Rossiter, D., Thomas, B (2005) SimBritain: a spatial microsimulation approach to population dynamics, Population, Space and Place 11, 13–34 (http://dx.doi.org/10.1002/psp.351)
SimBritain modelling approach1. Establish a set of constraints2. Choose a spatially defined source population3. Repeatedly sample from source4. Adjust weightings to match first constraint5. Adjust weightings to match second constraint6. …7. Adjust weightings to match final constraint8. Go back to step 4 and repeat loop until
results converge9. Save weightings which define membership of
SimBritain
CONSTRAINT TABLESTABLE CATEGORY
Car Ownership no cars 1 car 2+ cars
Social Class affluent middle income less affluent
Demography 1 child 2+ children no children
Employment active retired inactive
Households married couple lone parent other
Tenure owner occupied council tenant other
How do we know it makes sense?
Average age se = 1.0 r squared = .760 beta = 1.22RR
cage
30
32
34
36
38
40
42
44
46
48
50
sage 30 32 34 36 38 40 42 44 46 48 50
How do we know it makes sense?
Long-term illness se = 1.7 r squared = .767 beta = 1.19
cill
0.00
0.05
0.10
0.15
0.20
0.25
0.30
sill 0.00 0.05 0.10 0.15 0.20 0.25 0.30
The potential of microsimulation for policy analysis Classifying households• Very poor: all households with income below 50% of the
median York income• Poor: all households with income more than 50% of the
median but lower than 75% of the median• Below-average: all households living on incomes higher
than 75% of the median but less than or equal to the median
• Above-average: all households living on incomes higher than the median and lower than 125% of the median
• Affluent: all households living on incomes above 125% of the median
Ballas, D., Clarke, G P, Dorling D, Rossiter, D. (2007), Using SimBritain to Modelthe Geographical Impact of National Government Policies,Geographical Analysis 39, pp.44-77 (doi:10.1111/j.1538-4632.2006.00695.x)
Very poor households 1991 2001 2011 2021
Households (% of all households in York) 17.2% 17.3% 17.8% 21.3%Individuals (% of all individuals in York) 14.7% 13.3% 13.7% 20.5%Children (% of all children in York) 21.8% 17.7% 18.6% 38.5%LLTI (as a % of all individuals in group) 9.0% 7.3% 5.4% 7.9%Elderly (over 64 years as a % of all individuals in group) 30.1% 32.0% 33.3% 44.2%Individuals in group with father's occupation: unskilled (%) 10.5% 6.8% 3.3% 15.1%Reporting anxiety and depression (% of all individuals in group) 10.6% 10.3% 7.4% 3.1%Reporting health problems with alcohol or drugs (% of all individuals in group) 0.9% 1.1% 0.3% 0.0%
Individuals who reported that they have no one to talk to 19.9% 23.8% 31.1% 31.5%
Living standards of very poor households
Working Families Tax Credits Amount in 2002-3
Adjusted for 1991
Couple or lone parent £60.00 £ 42.39 Child aged under 16 £26.35 £ 18.62 16-18 £27.20 £ 19.22 30 hours credit £11.65 £ 8.23 Disabled child credit £35.50 £ 25.08 Enhanced disability credit
Couple or lone parent £16.25 £ 11.48 Child £46.75 £ 33.03 Childcare credit One child 70% of up
to £13570% of up to £95.39
Two or more children 70% of up to £200
70% of up to £141.31
Additional partners in a polygamous marriage £22.70 £ 16.04
Using SimBritain to Model the Geographical Impact of National Government Policies
The estimated spatial impact in York
The estimated spatial impact in Wales
Further reading and resources (including software)• Combinatorial Optimisation software (including dummy dataset and associated
documentation) by Paul Williamson (University of Liverpool): http://pcwww.liv.ac.uk/~william/microdata/CO%20070615/CO_software.html
• Iterative Proportional Fitting and integerisation R code and data: Lovelace, R, Ballas D (2013), ‘Truncate, replicate, sample’: A method for creating integer weights for spatial microsimulation, Computers, Environment and Urban Systems, http://www.sciencedirect.com/science/article/pii/S0198971513000240 (open access article including publicly available R code and data)
• A recent review of the state of the art and research challenges by Adam Whitworth (University of Sheffield): Whitworth, A et al. (2013) Evaluations and improvements in small area estimation methodologies. Discussion Paper. NCRM http://www.ncrm.ac.uk/research/NMI/2012/smallarea.php and http://eprints.ncrm.ac.uk/3210/ ). This includes a Spatial Microsimulation R-Library by Dimitris Kavroudakis (University of the Aegean) including R code available from: http://www.shef.ac.uk/polopoly_fs/1.268326!/file/sms_Manual_v9.zip
• An introductory text to spatial microsimulation: Ballas, D., Rossiter, D, Thomas, B., Clarke G, Dorling D, (2005), Geography matters: simulating the local impacts of national social policies, Joseph Roundtree Foundation http://www.jrf.org.uk/sites/files/jrf/1859352669.pdf
• 2-day NCRM/TALISMAN course: An Introduction to Spatial Microsimulation Using R, 19-20 September 2014, University of Cambridge http://store.leeds.ac.uk/browse/extra_info.asp?compid=1&modid=2&deptid=9&catid=47&prodid=449