What is … small area estimation

1. What is … small area estimation Dimitris Ballas Department of Geography University of Sheffield e-mail: d.ballas@sheffield.ac.uk http://www.sheffield.ac.uk/geography/staff/ballas_dimitris

2. 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)

3. 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 • AfterRees, P, Martin, D, Williamson, P (eds) (2002), The Census Data System, Chichester, Wiley

4. Examples of more small area data sources Neighbourhood statistics topics (http://www.neighbourhood.statistics.gov.uk ): Census of population Crime and Safety Economic Deprivation Education, Skills and Training Health and Care Housing Physical Environment Deprivation and Classification Income and Lifestyles Population and Migration

5. 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.

6. Why small area estimation? • Policy makers need small area estimates • Academics need small area estimates • Public like small area estimates • “What’s happening in my backyard” Policy relevance • socio-economic impact assessment • geographical impacts of social policy • what-if socio-spatial analysis

7. 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)

8. 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 methods For 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

9. A very simple approach to generating indirect non-survey designedestimates • 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

10. 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” seehttp://www.neighbourhood.statistics.gov.uk/HTMLDocs/images/Model-Based_Income_Estimates%28V2%29_tcm97-51115.pdf

11. 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

12. What is microsimulation?

13. 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

14. Static spatial microsimulation

15. Static spatial microsimulation

16. Tenure and car ownership example

17. 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

18. Other methodologies • Hill-climbing, genetic algorithms • Deterministic reweighting approaches • Probabilistic synthetic reconstruction techniques (IPF-based approaches)

19. Deterministic Reweighting the British Household Panel Survey (BHPS) - a simple example (1) A hypothetical sample of individuals (list format) Hypothetical Census data for a small area: In tabular format:

20. Reweighting the BHPS - a simple example (2) Calculating a new weight, so that the sample will fit into the Census table Hypothetical Census data for a small area: In tabular format:

21. Probabilistic synthetic reconstruction After Birkin, M., Clarke, M. (1988), SYNTHESIS – a synthetic spatial information system for urban and regional analysis: methods and examples, Environment and Planning A, 20, 1645-1671

22. Probabilistic synthetic reconstruction techniques 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)

23. 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 microdatastatically

24. Probabilistic dynamic models after Ballas D , Clarke, G P, Wiemers, E, (2005) Building a dynamic spatial microsimulation model for Ireland , Population, Space and Place, 11, 157–172 (http://dx.doi.org/10.1002/psp.359)

25. 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)

26. SimBritain modelling approach • Establish a set of constraints • Choose a spatially defined source population • Repeatedly sample from source • Adjust weightings to match first constraint • Adjust weightings to match second constraint • … • Adjust weightings to match final constraint • Go back to step 4 and repeat loop until results converge • Save weightings which define membership of SimBritain

27. CONSTRAINT TABLES

28. How do we know it makes sense?

29. How do we know it makes sense?

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 Model the Geographical Impact of National Government Policies, Geographical Analysis 39, pp.44-77 (doi:10.1111/j.1538-4632.2006.00695.x)

31. Living standards of very poor households

32. 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 £135 70% 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

33. The estimated spatial impact in York

34. The estimated spatial impact in Wales

35. 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