Model Assisted Survey Sampling

Transcription

1 Carl-Erik Sarndal Jan Wretman Bengt Swensson Model Assisted Survey Sampling Springer

2 Preface v PARTI Principles of Estimation for Finite Populations and Important Sampling Designs CHAPTER 1 Survey Sampling in Theory and Practice Surveys in Society Skeleton Outline of a Survey Probability Sampling Sampling Frame Area Frames and Similar Devices Target Population and Frame Population Survey Operations and Associated Sources of Error Planning a Survey and the Need for Total Survey Design Total Survey Design The Role of Statistical Theory in Survey Sampling 20 Exercises 22 CHAPTER 2 Basic Ideas in Estimation from Probability Samples Introduction Population, Sample, and Sample Selection Sampling Design Inclusion Probabilities The Notion of a Statistic The Sample Membership Indicators Estimators and Their Basic Statistical Properties 38 ix

3 x Contents 2.8 The n Estimator and Its Properties With-Replacement Sampling The Design Effect Confidence Intervals 55 Exercises 58 CHAPTER 3 Unbiased Estimation for Element Sampling Designs Introduction Bernoulli Sampling Simple Random Sampling Simple Random Sampling without Replacement Simple Random Sampling with Replacement Systematic Sampling Definitions and Main Result Controlling the Sample Size The Efficiency of Systematic Sampling Estimating the Variance Poisson Sampling Probability Proportional-to-Size Sampling Introduction nps Sampling pps Sampling Selection from Randomly Formed Groups Stratified Sampling Introduction Notation, Definitions, and Estimation Optimum Sample Allocation Alternative Allocations under STSI Sampling Sampling without Replacement versus Sampling with Replacement Alternative Estimators for Simple Random Sampling with Replacement The Design Effect of Simple Random Sampling with Replacement 112 Exercises 114 CHAPTER 4 Unbiased Estimation for Cluster Sampling and Sampling in Two 'or More Stages Introduction Single-Stage Cluster Sampling Introduction Simple Random Cluster Sampling Two-Stage Sampling Introduction Two-Stage Element Sampling Multistage Sampling Introduction and a General Result Three-Stage Element Sampling With-Replacement Sampling of PSUs 150

4 xi 4.6 Comparing Simplified Variance Estimators in Multistage Sampling 153 Exercises 154 CHAPTER 5 Introduction to More Complex Estimation Problems Introduction The Effect of Bias on Confidence Statements Consistency and Asymptotic Unbiasedness n Estimators for Several Variables of Study The Taylor Linearization Technique for Variance Estimation Estimation of a Ratio Estimation of a Population Mean Estimation of a Domain Mean Estimation of Variances and Covariances in a Finite Population Estimation of Regression Coefficients The Parameters of Interest Estimation of the Regression Coefficients Estimation of a Population Median Demonstration of Result ^ 205 Exercises 207 PART II Estimation through Linear Modeling, Using Auxiliary Variables CHAPTER 6 The Regression Estimator Introduction Auxiliary Variables The Difference Estimator Introducing the Regression Estimator Alternative Expressions for the Regression Estimator The Variance of the Regression Estimator Comments on the Role of the Model Optimal Coefficients for the Difference Estimator 239 Exercises 242 CHAPTER 7 Regression Estimators for Element Sampling Designs Introduction Preliminary Considerations The Common Ratio Model and the Ratio Estimator The Ratio Estimator under SI Sampling The Ratio Estimator under Other Designs Optimal Sampling Design for the n Weighted Ratio Estimator Alternative Ratio Models The Common Mean Model Models Involving Population Groups The Group Mean Model and the Poststratified Estimator The Group Ratio Model and the Separate Ratio Estimator 269

5 7.8 Simple Regression Models and Simple Regression Estimators Estimators Based on Multiple Regression Models Multiple Regression Models Analysis of Variance Models Conditional Confidence Intervals Conditional Analysis for BE Sampling Conditional Analysis for the Poststratification Estimator Regression Estimators for Variable-Size Sampling Designs A Class of Regression Estimators Regression Estimation of a Ratio of Population Totals 294 Exercises 297 CHAPTER 8 Regression Estimators for Cluster Sampling and Two-Stage Sampling Introduction ^ The Nature of the Auxiliary Information When Clusters of Elements Are Selected Comments on Variance and Variance Estimation in Two-Stage Sampling Regression Estimators Arising Out of Modeling at the Cluster Level The Common Ratio Model for Cluster Totals Estimation of the Population Mean When Clusters Are Sampled Design Effects for Single-Stage Cluster Sampling Stratified Clusters and Poststratified Clusters Regression Estimators Arising Out of Modeling at the Element Level Ratio Models for Elements The Group Ratio Model for Elements The Ratio Model Applied within a Single PSU 332 Exercises 333 PART III Further Questions in Design and Analysis of Surveys CHAPTER 9 Two-Phase Sampling Introduction 343 ' 9.2 Notation and Choice of Estimator The 7i* Estimator, Two-Phase Sampling for Stratification Auxiliary Variables for Selection in Two Phases Difference Estimators Regression Estimators for Two-Phase Sampling Stratified Bernoulli Sampling in Phase Two Sampling on Two Occasions Estimating the Current Total Estimating the Previous Total Estimating the Absolute Change and the Sum of the Totals 377 Exercises 379

6 xiii CHAPTER 10 Estimation for Domains Introduction The Background for Domain Estimation The Basic Estimation Methods for Domains Conditioning on the Domain Sample Size Regression Estimators for Domains A Ratio Model for Each Domain Group Models for Domains Problems Arising for Small Domains; Synthetic Estimation More on the Comparison of Two Domains 412 Exercises 413 CHAPTER 11 Variance Estimation ^ Introduction A Simplified Variance Estimator under Sampling without Replacement The Random Groups Technique Independent Random Groups Dependent Random Groups Balanced Half-Samples The Jackknife Technique The Bootstrap Concluding Remarks 444 Exercises 445 CHAPTER 12 Searching for Optimal Sampling Designs Introduction Model-Based Optimal Design for the General Regression Estimator Model-Based Optimal Design for the Group Mean Model Model-Based Stratified Sampling Applications of Model-Based Stratification Other Approaches to Efficient Stratification Allocation Problems in Stratified Random Sampling Allocation Problems in Two-Stage Sampling The n Estimator of the Population Total Estimation of the Population Mean Allocation in Two-Phase Sampling for Stratification A Further Comment on Mathematical Programming Sampling Design and Experimental Design 481 Exercises 481 CHAPTER 13 Further Statistical Techniques for Survey Data Introduction Finite Population Parameters in Multivariate Regression and Correlation Analysis 486

7 xiv Contents 13.3 The Effect of Sampling Design on a Statistical Analysis Variances and Estimated Variances for Complex Analyses Analysis of Categorical Data for Finite Populations Test of Homogeneity for Two Populations Testing Homogeneity for More than Two Finite Populations Discussion of Categorical Data Tests for Finite Populations Types of Inference When a Finite Population Is Sampled 513 Exercises 520 PART IV A Broader View of Errors in Surveys CHAPTER 14 Nonsampling Errors and Extensions of Probability Sampling Theory Introduction Historic Notes: The Evolution of the Probability Sampling Approach Measurable Sampling Designs Some Nonprobability Sampling Methods Model-Based Inference from Survey Samples Imperfections in the Survey Operations Ideal Conditions for the Probability Sampling Approach Extension of the Probability Sampling Approach Sampling Frames Frame Imperfections Estimation in the Presence of Frame Imperfections Multiple Frames Frame Construction and Maintenance Measurement and Data Collection Data Processing Nonresponse 551 Exercises 553 CHAPTER 15 Nonresponse Introduction Characteristics of Nonresponse Definition of Nonresponse Response Sets Lack of Unbiased Estimators Measuring Nonresponse Dealing with Nonresponse Planning of the Survey Callbacks and Follow-Ups Subsampling of Nonrespondents Randomized Response Perspectives on Nonresponse Estimation in the Presence of Unit Nonresponse Response Modeling 575

8 xv A Useful Response Model Estimators That Use Weighting Only Estimators That Use Weighting as Well as Auxiliary Variables Imputation 589 Exercises 595 CHAPTER 16 Measurement Errors Introduction On the Nature of Measurement Errors The Simple Measurement Model Decomposition of the Mean Square Error. ^ The Risk of Underestimating the Total Variance Repeated Measurements as a Tool in Variance Estimation Measurement Models Taking Interviewer Effects into Account Deterministic Assignment of Interviewers Random Assignment of Interviewers to Groups Interpenetrating Subsamples A Measurement Model with Sample-Dependent Moments 630 Exercises 634 CHAPTER 17 Quality Declarations for Survey Data Introduction Policies Concerning Information on Data Quality Statistics Canada's Policy on Informing Users of Data Quality and Methodology 641 Exercise 648 APPENDIX A Principles of Notation 649 APPENDIX B The MU284 Population 652 APPENDIX C The Clustered MU284 Population 660 APPENDIX D The CO 124 Population 662 References 666 Answers to Selected Exercises 680 Author Index 684 Subject Index 688