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A Guide to Small Area Estimation - Version 1.1 05/05/2006 6 Diagnostics For the Quality Small Area Estimates 62 6.1 Introduction 62 6.2 Diagnostics From Case Study 62 6.3 Assessment of Models Against Diagnostics 76 7 Communicating Quality to Users 78 7.1 Introduction 78 7.2 Sources of Error 80 7.3 Impact of Errors 83 7.4 Explanatory Notes 85 8 Summary 88 8.1 Points to Consider 88 8.2 What Areas of the ABS Provide Small Area Estimates 88 9 Frequently Asked Questions 90 APPENDICES 92 Appendix 1: List of Previous Small Area Work 92 Appendix 2: Technical Notes of Estimators 96 Appendix 3: SAS Datasets and Codes 100 Appendix 4: Diagnostics Graphs 101 Appendix 5: Explanatory Notes 103 Appendix 6: Quality Declaration 127 BIBLIOGRAPHY 139 LIST OF ACRONYMS 140 Australian Bureau of Statistics 4
A Guide to Small Area Estimation - Version 1.1 05/05/2006 1.1 What are Small Area Estimates? 1. Introduction Most ABS surveys are designed to provide statistically reliable, design based estimates only at the national and/or state/territory geographic levels. The sheer practical difficulties and cost of implementing and conducting sample surveys that would provide reliable estimates at levels finer than state/territory are generally prohibitive, both in terms of the increased sample size required and the added burden on providers of survey data (respondents). For purposes of this manual, small area estimation refers to methods of producing sufficiently reliable estimates for geographic areas that are too fine to obtain with precision, using direct survey estimation methods. By direct estimation we mean classical design based survey estimation methods (Saei and Chambers, 2003) that utilise only the sample units contained in each small area. Small area estimation methods are used to overcome the problem of small samples sizes to produce small area estimates that improve upon the quality of direct survey estimates obtained from the sample in each small area. The more sophisticated of these methods work by taking advantage of various relationships in the data, and involve, either implicitly or explicitly, a statistical model 1 to describe these relationships. (See Sections 4.1 & 4.2 for further discussion). Although conceptually similar, small domain estimates refers to those disaggregated to fine classificatory levels, such as by socioeconomic status, income, labour force status or industry. It is important to note that we have not undertaken any empirical study for small domain estimation methods for this manual, although intuitively we would expect that most techniques covered in this manual would still apply. The empirical analysis of this manual is based on knowledge and experience derived from only one empirical study, this being a study of the incidence of disability in Australia. This study uses data from the Survey of Disability, Ageing and Carers (SDAC) (see ABS (2003) for more details). 1 A statistical model is a mathematical representation of the relationship we assume to exist between the variable we are interested in predicting (known as the response or dependent variable) and other associated variables (known as the auxiliary, explanatory or independent variable). A model is then fitted to data that contains observed values for both the dependent variable and the auxiliary variables for each unit. The fitting process produces estimates of the model parameters such as intercepts and slopes. The unit here may be a person, a business or a small area itself, depending upon the level at which we wish to fit the model. The model also includes one or more error terms to describe the degree of stochastic or random variation with which predicted values for the response variable deviate from the observed values. Australian Bureau of Statistics 5
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SAE Manual Sections 1 to 4_1 (May 06).pdf - National Statistical ...

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