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Small Area Estimation Programme Dr Alison Whitworth Outline • • History of SAE at ONS • Small Area Statistics Problem • Successful ONS experiences on Small Area Estimation SAE and Census Transformation • • Best use of administrative sources Lessons learned and challenges Small Area Statistics Problem Requirement for: • Comprehensive, timely and reliable information • Data for detailed geographical areas or subcategories But • Financial and operational constraints • Pressure to reduce survey sample sizes and respondent burden Solution! Borrow information from other related datasets • from similar areas, previous occasions Borrowing strength • Small area estimation methods: – Use statistical models that relate the survey data with auxiliary information (borrow strength) – Auxiliary information: administrative data or census data available for all areas/domains • Modelling procedure – Variableof interest -> survey data (Dependent variable) – Independent variables -> auxiliary data (covariates) • Model based estimates: – predicted values used for obtaining area/domain estimates Successful ONS experiences • Small Area Estimation at ONS begun as a research project in 1990s • Small Area Estimation Project (SAEP), 1998 • EURAREA, 2001-2004 • Applications: • Unemployment (GB)– annual LAD and PCA estimates updated quarterly • Mean Income (E&W) – ward/MSOA estimates 98/99, 01/02, 04/05 and 07/08 • Census – 2001 One Number Census, 2011 Mean household weekly income • SAEP method (Heady et al. 2003) • Estimates for Middle layer Super Output Area (MSOA) • Survey data: Family Resources Survey (clustered household sample survey) • Auxiliary data: Social benefit claimants, Income tax, data, council tax banding, Census variables …. • Linear regression model for log income • Uses unit level response and area level covariates 2011-2012 Official model-based MSOA estimates (England and Wales) £1,200 Upper confidence limit Net weekly income after housing costs (equivalised) Lower confidence limit £900 £600 £300 £0 Middle layer super output area (ranked by estimate) 95% Confidence Intervals for net income, equivalised, after housing costs Limitations of the ONS current approach (SAEP) for household income • Only allows for estimation of mean household income in each MSOA • User requirement for mean and percentiles estimates at lower level geographies Research in progress in the SAE Unit Examples : Estimation of Household Income Distribution for 2001 and 2011 Using the Empirical Best Predictor (EBP) Method Population Estimates by Local Authority and Ethnic Group Using Generalised Structure Preserving Estimators (GSPREE) Example 1: Household Income using EBP approach • Empirical Best Predictor (Molina and Rao, 2010) • Estimation of mean and percentiles of income and poverty measures under one framework • Unit level model (household & area level covariates) • Involves prediction of income for each household in the population • Requires access to household level census data in addition to survey data (non-census years?) 2001 EBP estimates North West and South East regions of England Income Distribution across four different MSOAs Coefficients of variation for income for five percentiles of the population 2001 EBP estimates North West and South East regions of England Conclusions • EBP approach seems promising • MSOA estimates of income distribution and poverty measures under one methodology Still more questions! • How to apply EBP approach in non-census years Example 2: Population by Ethnic Group using GSPREE Motivation: • National Statistician’s recommendation: make the best use of all available data in the production of population statistics. • Governments ambition: Censuses after 2021 be conducted using other sources of data… Census Transformation programme Research the potential use of administrative data and surveys to produce population, household and characteristic information currently provided in a Census. 14 Census Table Population by Local Authority and Ethnic Group England (March 2011) Local Authority White Mixed Asian Chinese Black Other Total Fareham 107959 1359 1200 467 357 239 111581 Southampton 203528 5678 16443 3449 5067 2717 236882 Portsmouth 181182 5467 9863 2611 3777 2156 205056 … … … … … … … 114819 10360 96392 8109 18629 5787 254096 64053 4758 54900 797 12115 3582 140205 … … … … … … … …. Tower Hamlets Slough ….. Data for Ethnic Group • 2011 Census estimates (Mar 2011) Proxy: Detailed cross tabulation but outdated • School Census (Jan 2014) Proxy: Detailed cross tabulation but age 5-15 only • Annual Population Survey (2014) Total population by ethnic group • Mid Year Population Estimates (2014) Total population by local authority Solution… • Combine administrative and census data with survey data to borrow strength and produce reliable estimate for each cell (domain) using GSPREE (Zhang and Chambers, 2004 and Luna-Hernandez, A, 2014). Data for Ethnic Group Census 2011 MYE 2014 White Mixed Dec 2014 School Census 107959 Fareham Southampton 203528 Portsmouth Fareham …. Southampton … Portsmouth Tower Hamlets …. Slough ….. Tower Hamlets … Slough ….. White Asian 5678 Other Total 1200 467 357 239 …….. 16443 3449 5067 2717 …….. 1359 Chinese Black Other 181182 5467 9863 2611 3777 2156 … … … … … … …… …… …… …… …… … … … … … 114819 10360 96392… 8109… 18629 5787 … … … … … … 64053 4758 54900 797 12115 3582 … … … … … … … … … … … … … … … … … … Mixed Chinese Black Asian … … … … … ……….. ………. APS July 2012 - June 2014 (weighted estimates) National total ………. ………. ………. ………. …..... … …….. ……… … Distribution of LA estimates by ethnic group, 2014 (England) Proportion of White – GSPREE & Census 1.0000 0.8000 Proportion 0.6000 White 2014 GSPREE White 2011 Census 0.4000 0.2000 0.0000 1 51 101 151 Local Authority 201 251 301 RMSE. LA by ethnic group, 2014 Fixed Effects GSPREE estimator (England) • Overall, GSPREE is successful in providing reliable estimates for most LAs. • However, non-negligible RMSEs (and CVs) are observed in some areas Conclusions • GSPREE shows good performance Small bias/RMSE in most LAs • Work in progress Validation study (1991/2001 Census) GSPREE: 2001 Census x 2011 data (APS, MYE, ESC) Validation: 2011 Census • Still more questions… Modelling strategy for more detailed categories Discuss alternatives to generate the synthetic population (bootstrap) Consider different attributes Academic support • Collaborative projects Structure Preserving Estimation (SPREE), • Expert advisory group Small area estimation • Funded research/ Bids e.g. NCRM • Conferences NCRM Bath (July) SAE Maastrict (Aug) Lessons learned • Good small area estimates depend on: – adequacy of the modelling procedures + covariates with good prediction power – model validation • Challenges: – ability to master the complexities of the required statistical theory – availability of relevant administrative/auxiliary data – capacity to overcome barriers for the acceptance of model based estimates as official statistics outputs 24 References Molina, I. and Rao, J. N. K. (2010). Small area estimation of poverty indicators. The Canadian Journal of Statistics 38, 369-385 Purcell, N. J. and Kish, L. (1980). Postcensal Estimates for Local Areas (or Domains). International Statistical Review, 48, 3-18. Zhang, L.C. and Chambers, R. (2004). Small area estimates for crossclassifications. Journal of the Royal Statistical Society, B, 66, 479– 496. Luna-Hernandez, A. (2014). On Small Area Estimation for Compositions Using Structure Preserving Models. Unpublished PhD upgrade document, Department of Social Statistics and Demography, University of Southampton.