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Guidelines on small area estimation for city statistics and other functional geographies 2019 edition Statistical requirements compendium 2018 edition 2018 MANUALS AND GUIDELINES Guidelines on small area estimation for city statistics and other functional geographics 2019 edition Manuscript completed in October 2019. Neither the European Commission nor any person acting on behalf of the Commission is responsible for the use that might be made of the following information. Luxembourg: Publications Office of the European Union, 2019 The European Commission is not liable for any consequence stemming from the reuse of this publication. © European Union, 2019 Reuse is authorised provided the source is acknowledged. The reuse policy of European Commission documents is regulated by Decision 2011/833/EU (OJ L 330, 14.12.2011, p. 39). For any use or reproduction of photos or other material that is not under the copyright of the European Union, permission must be sought directly from the copyright holders. For more information, please consult: https://ec.europa.eu/eurostat/about/policies/copyright Copyright for the cover photo: © Shutterstock/Ken Schulze The information and views set out in this publication are those of the author(s) and do not necessarily reflect the official opinion of the European Union. Neither the European Union institutions and bodies nor any person acting on their behalf may be held responsible for the use which may be made of the information contained therein. Collection: Manuals and guidelines Theme: General and regional statistics Print: ISBN 978-92-76-11708-7 ISSN 2363-197X doi:10.2785/822325 KS-GQ-19-011-EN-C PDF: ISBN 978-92-76-11709-4 ISSN 2315-0815 doi: 10.2785/763467 KS-GQ-19-011-EN-N Acknowledgements The authors would like to thank Bernhard Stefan Zins for providing his expertise in variance estimation for the AROPE indicator and the respective estimation routines. Further, we are grateful to the contract manager Britta Gauckler, Valeriya Angelova Tosheva and Gian Luigi Mazzi for providing important input to the project. Finally, we thank Jan Weymeirsch for assisting in the finalisation of the article and the project management team at GOPA for facilitating administrative tasks. Authors: Economic and Social Statistics Department Trier University, Faculty IV, Economics Ralf Münnich, Jan Pablo Burgard, Florian Ertz, Simon Lenau, Julia Manecke, Hariolf Merkle. Guidelines on small area estimation for city statistics and other functional geographies 3 Contents Contents 1 Introduction ........................................................................................................................... 7 1.1 Motivation .............................................................................................................................. 7 1.2 Additional information.......................................................................................................... 8 1.3 Scope ..................................................................................................................................... 8 2 Terms and basic definitions ................................................................................................ 9 3 Specification and evaluation of needs and resources .................................................... 11 3.1 Definition of target areas ................................................................................................... 11 3.2 Definition of target parameter............................................................................................ 12 3.3 Distinction of sampling designs ....................................................................................... 12 3.4 Definition of data availability ............................................................................................. 13 4 Implementation of small area estimation ......................................................................... 15 4.1 Choice of small area estimation approach ....................................................................... 15 4.2 Unit- versus area-level empirical best prediction ............................................................ 17 4.3 Auxiliary variables measured with (out) errors................................................................ 18 4.4 Testing for area-specific random effects ......................................................................... 18 4.5 Assurance of coherence .................................................................................................... 19 5 Model diagnostics and evaluation .................................................................................... 21 5.1 Model diagnostics .............................................................................................................. 21 5.2 Evaluation of approaches .................................................................................................. 22 6 Exemplary application ........................................................................................................ 24 7 References .......................................................................................................................... 35 8 Appendix ............................................................................................................................. 39 A.1 Design-based estimation ................................................................................................... 39 A.2 Model-assisted estimation ................................................................................................. 40 A.3 Model-based estimation ..................................................................................................... 40 A.3.1 Fay-Herriot estimator ......................................................................................................... 40 A.3.2 Battese-Harter-Fuller estimator ......................................................................................... 43 A.3.3 You-Rao estimator .............................................................................................................. 45 A.3.4 Measurement error model .................................................................................................. 47 Guidelines on small area estimation for city statistics and other functional geographies 4 Figures Figures Figure 1: Relation between direct estimator and Fay-Herriot estimator ......................................................... 28 Figure 2: Normal Q-Q-Plot of standardised residuals .................................................................................... 31 Figure 3: Fay-Herriot estimator in relation to standardised residuals ............................................................. 32 Figure 4: Efficiency gain through the Fay-Herriot estimator ........................................................................... 33 Guidelines on small area estimation for city statistics and other functional geographies 5 Abbreviations Abbreviations AES Adult Education Survey AIK Aikake Information Criterion AMELI Advanced Methodology for European Laeken Indicators AROPE At Risk Of Poverty or social Exclusion ARPR At Risk Of Poverty Rate BHF Battese-Harter-Fuller BLUP Best Linear Unbiased Predictor DOU Degree of Urbanization EBLUP Empirical Best Linear Unbiased Predictor FUAs Functional Urban Areas GOPA Gesellschaft für Organisation, Planung und Ausbildung mbH GREG Generalised Regression ICT Information and Communication Technology InGRID Inclusive Growth Research Infrastructure Diffusion ISCED International Standard Classification of Education LFS Labour Force Survey LWI Low Work Intensity NSI National Statistics Institute NUTS Nomenclature des Unités Territoriales Statistiques PSU Primary Sampling Unit REML Restricted Maximum Likelihood SAE Small Area Estimation SILC Survey on Income and Living Conditions SMD Severly Materially Deprivated SSU Second stage Sampling Units Guidelines on small area estimation for city statistics and other functional geographies 6 Introduction 1 1 Introduction 1 Introduction 1.1 Motivation The demand for reliable information on the level of cities and functional urban areas has increased significantly. However, the increasing need for detailed information in politics and economics is largely offset by unchanged or even lower budgets for data collection. Often, the sampling designs of social surveys are only designed for a reliable design-based estimation at the state or federal level due to maximum permissible sample sizes. By contrast, cities and functional urban areas are usually not incorporated in the sampling design and are, therefore, referred to as unplanned areas. As the relevant areas might have unplanned and, hence, random as well as small sample sizes, the estimation of the respective parameters of interest might be challenging. A direct design-weighted estimation method such as the well-known estimator by Horvitz and Thompson (1952), which includes only sampled units from each area of interest itself, might lead to unbiased estimates. However, unplanned and small sample sizes due to the disregard of cities and functional urban areas at the stage of designing the sample might result in imprecise estimates with large standard errors. It might even be the case that some areas of interest may not be sampled at all. Thus, the user needs often exceed the limits of traditional estimation methods. Small area estimation methods may be used to improve the quality of estimates
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