## Multiple Imputation for Nonresponse in SurveysDemonstrates 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 |

244 | |

AUTHOR INDEX | 251 |

253 | |

### Common terms and phrases

Analysis approximately assume asymptotic average Bayesian inference beneﬁts Chapter complete-data statistics completed data set components conditional distribution covariates coverage deﬁned deﬁnition degrees of freedom distribution of Q draw drawn values estimand estimation task evaluated example ﬁnd ﬁnite ﬁrst ﬁxed followed-up nonrespondents fraction of missing hot-deck ignorable nonresponse imputation task imputed values inﬁnite interval estimate large samples linear regression matrix mean and variance missing data missing information missing values missingness model for nonresponse monotone pattern multiple imputations multiply-imputed data set multivariate nominal level nonignorable nonresponse notation observed values p-value parameters population posterior distribution posterior mean posterior probability prior distribution priori independent Prob{Q probability problem public-use data bases Q given random variable random-response randomization-based reference distribution repeated imputations repeated-imputation response mechanism Rina Rubin sampling mechanism satisﬁed Section signiﬁcance level simple random sample speciﬁcation standard complete-data standard errors Suppose survey Table tion unconfounded units univariate variance-covariance matrix Yobs