Comment: Struggles with Survey Weighting and Regression Modeling
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paper_title: Regression Analysis in Sample Surveys

paper_content:

Abstract Models are proposed as a basis for unbiased and biased estimation from sample survey data of a regression relation. Unbiased estimates of the variances and covariances of estimates of the regression coefficients are obtained for certain cases but do not appear to exist for all cases. It is suggested that past surveys, conducted mostly to obtain efficiently estimates of means and totals, be analyzed to yield estimates of regression relations, to obtain information needed in designing future surveys, and to test the adequacy of the proposed models.
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paper_title: A model-calibration approach to using complete auxiliary information from survey data

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Suppose that the finite population consists of N identifiable units. Associated with the ith unit are the study variable, yi, and a vector of auxiliary variables, xi. The values x1, x2,…, xN are known for the entire population (i.e., complete) but yi is known only if the ith unit is selected in the sample. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this article, a unified model-assisted framework has been attempted using a proposed model-calibration technique. The proposed model-calibration estimators can handle any linear or nonlinear working models and reduce to the conventional calibration estimators of Deville and Sarndal and/or the generalized regression estimators in the linear model case. The pseudoempirical maximum likelihood estimator of Chen and Sitter, when used in this setting, gives an estimator that is asymptotically equivalent to the model-calibration estimator but with positive weights. Some existing estimators ...
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paper_title: Estimation in Surveys with Nonresponse

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Preface. Chapter 1: Introduction. Chapter 2: The Survey and Its Imperfections. 2.1 The survey objective. 2.2 Sources of error in a survey. Chapter 3: General Principles to Assist Estimation. 3.1 Introduction. 3.2 The importance of auxiliary information. 3.3 Desirable features of an auxiliary vector. Chapter 4: The Use of Auxiliary Information under Ideal Conditions. 4.1 Introduction. 4.2 The Horvitz-Thompson estimator. 4.3 The generalized regression estimator. 4.4 Variance and variance estimation. 4.5 Examples of the generalized regression estimator. Chapter 5: Introduction to Estimation in the Presence of Nonresponse. 5.1 General background. 5.2 Errors caused by sampling and nonresponse. Appendix: Variance and mean squared error under nonresponse. Chapter 6: Weighting of Data in the Presence of Nonresponse. 6.1 Traditional approaches to weighting. 6.2 Auxiliary vectors and auxiliary information. 6.3 The calibration approach: some terminology. 6.4 Point estimation under the calibration approach. 6.5 Calibration estimators for domains. 6.6 Comments on the calibration approach. 6.7 Alternative sets of calibrated weights. 6.8 Properties of the calibrated weights. Chapter 7: Examples of Calibration Estimators. 7.1 Examples of familiar estimators for data with nonresponse. 7.2 The simplest auxiliary vector. 7.3 One-way classification. 7.4 A single quantitative auxiliary variable. 7.5 One-way classification combined with a quantitative variable. 7.6 Two-way classification. 7.7 A Monte Carlo simulation study. Chapter 8 The Combined Use of Sample Information and Population Information. 8.1 Options for the combined use of information. 8.2 An example of calibration with information at both levels. 8.3 A Monte Carlo simulation study of alternative calibration procedures. 8.4 Two-step procedures in practice. Chapter 9 Analysing the Bias due to Nonresponse. 9.1 Simple estimators and their nonresponse bias. 9.2 Finding an efficient grouping. 9.3 Further illustrations of the nonresponse bias. 9.4 A general expression for the bias of the calibration estimator. 9.5 Conditions for near-unbiasedness. 9.6 A review of concepts, terms and ideas. Appendix: Proof of Proposition 9.1. Chapter 10: Selecting the Most Relevant Auxiliary Information. 10.1 Discussion. 10.2 Guidelines for the construction of an auxiliary vector. 10.3 The prospects for near-zero bias with traditional estimators. 10.4 Further avenues towards a zero bias. 10.5 A further tool for reducing the bias. 10.6 The search for a powerful auxiliary vector. 10.7 Empirical illustrations of the indicators. 10.8 Literature review. Chapter 11: Variance and Variance Estimation. 11.1 Variance estimation for the calibration estimator. 11.2 An estimator for ideal conditions. 11.3 A useful relationship. 11.4 Variance estimation for the two-step A and two-step B procedures. 11.5 A simulation study of the variance estimation technique. 11.6 Computational aspects of point and variance estimation. Appendix: Properties of two-phase GREG estimator. Chapter 12: Imputation. 12.1 What is imputation? 12.2 Terminology. 12.3 Multiple study variables. 12.4 The full imputation approach. 12.5 The combined approach. 12.6 The full weighting approach. 12.7 Imputation by statistical rules. 12.8 Imputation by expert judgement or historical data. Chapter 13: Variance Estimation in the Presence of Imputation. 13.1 Issues in variance estimation under the full imputation approach. 13.2 An identity of combined and fully weighted approaches. 13.3 More on the risk of underestimating the variance. 13.4 A broader view of variance estimation for the combined approach. 13.5 Other issues arising with regard to item nonresponse. 13.6 Further comments on imputation. Appendix: Proof of Proposition 13.1. Chapter 14: Estimation Under Nonresponse and Frame Imperfections. 14.1 Introduction. 14.2 Estimation of the persister total. 14.3 Direct estimation of the target population total. 14.4 A case study. References. Index.
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Title: Comment: Struggles with Survey Weighting and Regression Modeling

Section 1: Introduction
Description 1: Introduce the topic of survey weighting and regression modeling, the debate between model-based and design-based approaches, and the evolving consensus.

Section 2: Importance of Accounting for Design
Description 2: Discuss the necessity of incorporating survey design in the modeling process and its practical applications, as well as the motivation behind maintaining certain desirable properties in model-based estimators.

Section 3: Disadvantages of Design-Based Approach
Description 3: Explain the perceived disadvantages of design-based model fitting and inference, such as the complexity and mysterious nature of weights, and the cumbersome nature of variance estimation.

Section 4: Advantages of Weighted Analysis
Description 4: Argue the distinct advantages of a weighted analysis, especially in terms of reducing analysis complexity from the perspective of statisticians using pre-weighted survey data.

Section 5: Division of Labor in Survey Analysis
Description 5: Describe the separation of tasks between survey statisticians and data analysts, the creation and use of survey weights, and how this division benefits both parties.

Section 6: Consistency of Weighted Estimators
Description 6: Discuss the design consistency of weighted estimators for population-level quantities and the consistency under joint design-response mechanisms despite limited formal theory.

Section 7: Confidentiality and Access to Data
Description 7: Highlight the confidentiality issues that limit data analysts' access to detailed variable information and the resulting challenges in building models that fully incorporate design effects.

Section 8: Complexity of Large-Scale Surveys
Description 8: Describe the complexities involved in accounting for various factors in large-scale surveys, such as stratification and imputation, and the associated challenges for data analysts.

Section 9: Solutions to Variance Estimation
Description 9: Address the solutions available for the more cumbersome variance estimation in weighted estimators, including the use of commercial software and replication weights.

Section 10: Integrating Design and Nonresponse Characteristics
Description 10: Explore the advantages and requirements of integrating design and nonresponse characteristics through explicit modeling in solving nonignorability problems.

Section 11: Recommendations for Future Developments
Description 11: Suggest possible future developments to improve the comfort level of data analysts with weighted analyses, including increased transparency in weight construction and better education on weighted analysis interpretation and methods.