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Analysis of Survey Data Analysis of Survey Data. Edited by R. L. Chambers and C. J. Skinner Copyright ¶ 2003 John Wiley & Sons, Ltd. ISBN: 0-471-89987-9 WILEY SERIES IN SURVEY METHODOLOGY Established in part by WALTER A. SHEWHART AND SAMUEL S. WILKS Editors: Robert M. Groves, Graham Kalton, J. N. K. Rao, Norbert Schwarz, Christopher Skinner A complete list of the titles in this series appears at the end of this volume. Analysis of Survey Data Edited by R. L. CHAMBERS and C. J. SKINNER University of Southampton, UK Copyright # 2003 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (44) 1243 779777 Email (for orders and customer service enquiries): cs-books@wiley.co.uk Visit our Home Page on www.wileyeurope.com or www.wiley.com All Rights Reserved. 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ISBN 0-471-89987-9 (acid-free paper) 1. Mathematical statistics±Methodology. I. Chambers, R. L. (Ray L.) II. Skinner, C. J. III. Series. QA276 .A485 2003 001.4 H 22±dc21 2002033132 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 0 471 89987 9 Typeset in 10/12 pt Times by Kolam Information Services, Pvt. Ltd, Pondicherry, India Printed and bound in Great Britain by Biddles Ltd, Guildford, Surrey. This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production. To T. M. F. Smith Contents Preface xv List of Contributors xviii Chapter 1 Introduction 1 R. L. Chambers and C. J. Skinner 1.1. The analysis of survey data 1 1.2. Framework, terminology and specification of parameters 2 1.3. Statistical inference 6 1.4. Relation to Skinner, Holt and Smith (1989) 8 1.5. Outline of this book 9 PART A APPROACHES TO INFERENCE 11 Chapter 2 Introduction to Part A 13 R. L. Chambers 2.1. Introduction 13 2.2. Full information likelihood 14 2.3. Sample likelihood 20 2.4. Pseudo-likelihood 22 2.5. Pseudo-likelihood applied to analytic inference 23 2.6. Bayesian inference for sample surveys 26 2.7. Application of the likelihood principle in descriptive inference 27 Chapter 3 Design-based and Model-based Methods for Estimating Model Parameters 29 David A. Binder and Georgia R. Roberts 3.1. Choice of methods 29 3.2. Design-based and model-based linear estimators 31 3.2.1. Parameters of interest 32 3.2.2. Linear estimators 32 3.2.3. Properties of  b and  b 33 3.3. Design-based and total variances of linear estimators 34 3.3.1. Design-based and total variance of  b 34 3.3.2. Design-based mean squared error of  b and its model expectation 36 3.4. More complex estimators 37 3.4.1. Taylor linearisation of non-linear statistics 37 3.4.2. Ratio estimation 37 3.4.3. Non-linear statistics ± explicitly defined statistics 39 3.4.4. Non-linear statistics ± defined implicitly by score statistics 40 3.4.5. Total variance matrix of  b for non-negligible sampling fractions 42 3.5. Conditional model-based properties 42 3.5.1. Conditional model-based properties of  b 42 3.5.2. Conditional model-based expectations 43 3.5.3. Conditional model-based variance for  b and the use of estimating functions 43 3.6. Properties of methods when the assumed model is invalid 45 3.6.1. Critical model assumptions 45 3.6.2. Model-based properties of  b 45 3.6.3. Model-based properties of  b 46 3.6.4. Summary 47 3.7. Conclusion 48 Chapter 4 The Bayesian Approach to Sample Survey Inference 49 Roderick J. Little 4.1. Introduction 49 4.2. Modeling the selection mechanism 52 Chapter 5 Interpreting a Sample as Evidence about a Finite Population 59 Richard Royall 5.1. Introduction 59 5.2. The evidence in a sample from a finite population 62 5.2.1. Evidence about a probability 62 5.2.2. Evidence about a population proportion 62 5.2.3. The likelihood function for a population proportion or total 63 5.2.4. The probability of misleading evidence 65 5.2.5. Evidence about the average count in a finite population 66 5.2.6. Evidence about a population mean under a regression model 69 viii CONTENTS 5.3. Defining the likelihood function for a finite population 70 PART B CATEGORICAL RESPONSE DATA 73 Chapter 6 Introduction to Part B 75 C. J. Skinner 6.1. Introduction 75 6.2. Analysis of tabular data 76 6.2.1. One-way classification 76 6.2.2. Multi-way classifications and log±linear models 77 6.2.3. Logistic models for domain proportions 80 6.3. Analysis of unit-level data 81 6.3.1. Logistic regression 81 6.3.2. Some issues in weighting 83 Chapter 7 Analysis of Categorical Response Data from Complex Surveys: an Appraisal and Update 85 J. N. K. Rao and D. R. Thomas 7.1. Introduction 85 7.2. Fitting and testing log±linear models 86 7.2.1. Distribution of the Pearson and likelihood ratio statistics 86 7.2.2. Rao±Scott procedures 88 7.2.3. Wald tests of model fit and their variants 91 7.2.4. Tests based on the Bonferroni inequality 92 7.2.5. Fay's jackknifed tests 94 7.3. Finite sample studies 97 7.3.1. Independence tests under cluster sampling 97 7.3.2. Simulation results 98 7.3.3. Discussion and final recommendations 100 7.4. Analysis of domain proportions 101 7.5. Logistic regression with a binary response variable 104 7.6. Some extensions and applications 106 7.6.1. Classification errors 106 7.6.2. Biostatistical applications 107 7.6.3. Multiple response tables 108 Chapter 8 Fitting Logistic Regression Models in Case±Control Studies with Complex Sampling 109 Alastair Scott and Chris Wild 8.1. Introduction 109 CONTENTS ix 8.2. Simple case±control studies 111 8.3. Case±control studies with complex sampling 113 8.4. Efficiency 115 8.5. Robustness 117 8.6. Other approaches 120 PART C CONTINUOUS AND GENERAL RESPONSE DATA 123 Chapter 9 Introduction to Part C 125 R. L. Chambers 9.1. The design-based approach 125 9.2. The sample distribution approach 127 9.3. When to weight? 130 Chapter 10 Graphical Displays of Complex Survey Data through Kernel Smoothing 133 D. R. Bellhouse, C. M. Goia, and J. E. Stafford 10.1. Introduction 133 10.2. Basic methodology for histograms and smoothed binned data 134 10.3. Smoothed histograms from the Ontario Health Survey 138 10.4. Bias adjustment techniques 141 10.5. Local polynomial regression 146 10.6. Regression examples from the Ontario Health Survey 147 Chapter 11 Nonparametric Regression with Complex Survey Data 151 R. L. Chambers, A. H. Dorfman and M. Yu. Sverchkov 11.1. Introduction 151 11.2. Setting the scene 152 11.2.1. A key assumption 152 11.2.2. What are the data? 153 11.2.3. Informative sampling and ignorable sample designs 154 11.3. Reexpressing the regression function 155 11.3.1. Incorporating a covariate 156 11.3.2. Incorporating population information 157 11.4. Design-adjusted smoothing 158 11.4.1. Plug-in methods based on sample data only 158 11.4.2. Examples 159 x CONTENTS 11.4.3. Plug-in methods which use population information 160 11.4.4. The estimating equation approach 162 11.4.5. The bias calibration approach 163 11.5. Simulation results 163 11.6. To weight or not to weight? (With apologies to Smith, 1988) 170 11.7. Discussion 173 Chapter 12 Fitting Generalized Linear Models under Informative Sampling 175 Danny Pfeffermann and M. Yu. Sverchkov 12.1. Introduction 175 12.2. Population and sample distributions 177 12.2.1. Parametric distributions of sample data 177 12.2.2. Distinction between the sample and the randomization distributions 178 12.3. Inference under informative probability sampling 179 12.3.1. Estimating equations with application to the GLM 179 12.3.2. Estimation of E s (w t jx t ) 182 12.3.3. Testing the informativeness of the sampling process 183 12.4. Variance estimation 185 12.5. Simulation results 188 12.5.1. Generation of population and sample selection 188 12.5.2. Computations and results 189 12.6. Summary and extensions 194 PART D LONGITUDINAL DATA 197 Chapter 13 Introduction to Part D 199 C. J. Skinner 13.1. Introduction 199 13.2. Continuous response data 200 13.3. Discrete response data 202 Chapter 14 Random Effects Models for Longitudinal Survey Data 205 C. J. Skinner and D. J. Holmes 14.1. Introduction 205 CONTENTS xi [...]... strategy 16 .4.5 The effects of unobserved heterogeneity 207 210 213 218 2 21 2 21 222 225 230 232 232 234 235 236 236 238 239 239 2 41 245 245 246 249 2 51 252 253 254 255 255 255 255 256 257 259 263 CONTENTS 16 .5 Simulations of the effects of YTS 16 .5 .1 The effects of YTS participation 16 .5.2 Simulating a world without YTS 16 .6 Concluding remarks PART E Chapter 17 Chapter 18 Chapter 19 INCOMPLETE DATA Introduction... Duration or survival analysis 15 .5 .1 Non-parametric marginal survivor function estimation 15 .5.2 Parametric models 15 .5.3 Semi-parametric methods 15 .6 Analysis of event occurrences 15 .6 .1 Analysis of recurrent events 15 .6.2 Multiple event types 15 .7 Analysis of multi-state data 15 .8 Illustration 15 .9 Concluding remarks Applying Heterogeneous Transition Models in Labour Economics: the Role of Youth Training... Stephen Pudney 16 .1 Introduction 16 .2 YTS and the LCS dataset 16 .3 A correlated random effects transition model 16 .3 .1 Heterogeneity 16 .3.2 The initial state 16 .3.3 The transition model 16 .3.4 YTS spells 16 .3.5 Bunching of college durations 16 .3.6 Simulated maximum likelihood 16 .4 Estimation results 16 .4 .1 Model selection 16 .4.2 The heterogeneity distribution 16 .4.3 Duration dependence 16 .4.4 Simulation... Introduction R L Chambers and C J Skinner 1. 1 THE ANALYSIS OF SURVEY DATA the analysis of survey data Many statistical methods are now used to analyse sample survey data In particular, a wide range of generalisations of regression analysis, such as generalised linear modelling, event history analysis and multilevel modelling, are frequently applied to survey microdata These methods are usually formulated... L Chambers 17 .1 Introduction 17 .2 An example 17 .3 Survey inference under nonresponse 17 .4 A model-based approach to estimation under two-phase sampling 17 .5 Combining survey data and aggregate data in analysis Bayesian Methods for Unit and Item Nonresponse Roderick J Little 18 .1 Introduction and modeling framework 18 .2 Adjustment-cell models for unit nonresponse 18 .2 .1 Weighting methods 18 .2.2 Random... weight strata 18 .3 Item nonresponse 18 .3 .1 Introduction 18 .3.2 MI based on the predictive distribution of the missing variables 18 .4 Non-ignorable missing data 18 .5 Conclusion Estimation for Multiple Phase Samples Wayne A Fuller 19 .1 Introduction 19 .2 Regression estimation 19 .2 .1 Introduction 19 .2.2 Regression estimation for two-phase samples 19 .2.3 Three-phase samples 19 .2.4 Variance estimation 19 .2.5 Alternative...xii CONTENTS 14 .2 14 .3 14 .4 14 .5 Chapter 15 Chapter 16 A covariance structure approach A multilevel modelling approach An application: earnings of male employees in Great Britain Concluding remarks Event History Analysis and Longitudinal Surveys J F Lawless 15 .1 Introduction 15 .2 Event history models 15 .3 General observational issues 15 .4 Analytic inference from longitudinal survey data 15 .5 Duration... London School of Economics between 19 60 and 19 68 Their joint papers explored the foundations and advanced understanding of the role of models in inference from sample survey data, a key element of survey analysis Fred's review of the foundations of survey sampling in Smith (19 76), read to the Royal Statistical Society, was a landmark paper Fred moved to a lectureship position in the Department of Mathematics... Ottawa Ontario K1A 0T6 Canada C M Goia Department of Statistical and Actuarial Sciences University of Western Ontario London Ontario N6A 5B7 Canada R L Chambers Department of Social Statistics University of Southampton Southampton SO17 1BJ UK D J Holmes Department of Social Statistics University of Southampton Southampton SO17 1BJ UK A H Dorfman Office of Survey Methods Research Bureau of Labor Statistics... representations 19 .3 Regression estimation with imputation xiii 265 266 267 270 275 277 277 279 280 282 286 289 289 2 91 2 91 294 297 297 297 303 306 307 307 308 308 309 310 312 313 315 xiv CONTENTS 19 .4 19 .5 Chapter 20 Imputation procedures Example Analysis Combining Survey and Geographically Aggregated Data D G Steel, M Tranmer and D Holt 20 .1 Introduction and overview 20.2 Aggregate and survey data availability . Complex Survey Data 15 1 R. L. Chambers, A. H. Dorfman and M. Yu. Sverchkov 11 .1. Introduction 15 1 11 .2. Setting the scene 15 2 11 .2 .1. A key assumption 15 2 11 .2.2. What are the data? 15 3 11 .2.3 designs 15 4 11 .3. Reexpressing the regression function 15 5 11 .3 .1. Incorporating a covariate 15 6 11 .3.2. Incorporating population information 15 7 11 .4. Design-adjusted smoothing 15 8 11 .4 .1. Plug-in. data only 15 8 11 .4.2. Examples 15 9 x CONTENTS 11 .4.3. Plug-in methods which use population information 16 0 11 .4.4. The estimating equation approach 16 2 11 .4.5. The bias calibration approach 16 3 11 .5.