# Multiple Imputation for Nonresponse in Surveys

John Wiley & Sons, Sep 25, 2009 - Mathematics - 258 pages
Demonstrates how nonresponse in sample surveys and censuses can be handled by replacing each missing value with two or more multiple imputations. Clearly illustrates the advantages of modern computing to such handle surveys, and demonstrates the benefit of this statistical technique for researchers who must analyze them. Also presents the background for Bayesian and frequentist theory. After establishing that only standard complete-data methods are needed to analyze a multiply-imputed set, the text evaluates procedures in general circumstances, outlining specific procedures for creating imputations in both the ignorable and nonignorable cases. Examples and exercises reinforce ideas, and the interplay of Bayesian and frequentist ideas presents a unified picture of modern statistics.

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### Contents

 1 INTRODUCTION 1 12 Examples of Surveys with Nonresponse 4 13 Properly Handling Nonresponse 7 14 Single Imputation 11 15 Multiple Imputation 15 16Numerical Example Using Multiple Imputation 19 17 Guidance for the Reader 22 Problems 23
 42 General Conditions for the RandomizationValidity of Infinitem RepeatedImputation Inferences 116 43 Examples of Proper and Improper Imputation Methods in a Simple Case with Ignorable Nonresponse 120 44 Further Discussion of Proper Imputation Methods 125 45 The Asymptotic Distribution of QmUm Bo for Proper Imputation Methods 128 46 Evaluations of Finitem Inferences with Scalar Estimands 132 47 Evaluation of Significance Levels from the Moment Based Statistics Dm and Dm with Multicomponent Estimands 137 48 Evaluation of Significance Levels Based on Repeated Significance Levels 144 Problems 148

 2 STATISTICAL BACKGROUND 27 22 Variables in the Finite Population 28 23 Probability Distributions and Related Calculations 31 24 Probability Specifications for Indicator Variables 35 25 Probability Specifications for X Y 39 26 Bayesian Inference for a Population Quantity 48 27 Interval Estimation 54 28 Bayesian Procedures for Constructing Interval Estimates Including Significance Levels and Point Estimates 59 29 Evaluating the Performance of Procedures 62 210 Similarity of Bayesian and RandomizationBased Inferences in Many Practical Cases 65 Problems 68 3 UNDERLYING BAYESIAN THEORY 75 32 Key Results for Analysis When the Multiple Imputations Are Repeated Draws from the Posterior Distribution of the Missing Values 81 33 Inference for Scalar Estimands from a Modest Number of Repeated CompletedData Means and Variances 87 34 Significance Levels for Multicomponent Estimands from a Modest Number of Repeated CompletedData Means and VarianceCovariance Matrices 94 35 Significance Levels from Repeated CompletedData Significance Levels 99 36 Relating the CompletedData and CompleteData Posterior Distributions When the Sampling Mechanism Is Ignorable 102 Problems 107 4 RANDOMIZATIONBASED EVALUATIONS 113
 5 PROCEDURES WITH IGNORABLE NONRESPONSE 154 52 Creating Imputed Values under an Explicit Model 160 53 Some Explicit Imputation Models with Univariate yi and Covariates 166 54 Monotone Patterns of Missingness in Multivariate Yi 170 55 Missing Social Security Benefits in the Current Population Survey 178 56 Beyond Monotone Missingness 186 Problems 195 6 PROCEDURES WITH NONIGNORABLE NONRESPONSE 202 62 Nonignorable Nonresponse with Univariate yl and No X i 205 63 Formal Tasks with Nonignorable Nonresponse 210 64 Illustrating Mixture Modeling Using Educational Testing Service Data 215 65 Illustrating Selection Modeling Using CPS Data 222 66 Extensions to Surveys with FollowUps 229 67 FollowUp Response in a Survey of Drinking Behavior Among Men of Retirement Age 234 Problems 240 REFERENCES 244 AUTHOR INDEX 251 SUBJECT INDEX 253 Copyright