Multiple Imputation for Nonresponse in Surveys (eBook)

Donald B. Rubin , PhD, is a John L. Loeb Professor of Statistics at Harvard University in Cambridge, MA. He was named 2000-2001 Statistician of the Year by the Chicago Chapter of ASA. His research interests include causal inference in experiments and observational studies, developing and applying statistical models to data in a variety of scientific disciplines, and the application of Bayesian and empirical Bayesian techniques.

Tables and Figures.

Glossary.

1. Introduction.

1.1 Overview.

1.2 Examples of Surveys with Nonresponse.

1.3 Properly Handling Nonresponse.

1.4 Single Imputation.

1.5 Multiple Imputation.

1.6 Numerical Example Using Multiple Imputation.

1.7 Guidance for the Reader.

2. Statistical Background.

2.1 Introduction.

2.2 Variables in the Finite Population.

2.3 Probability Distributions and Related Calculations.

2.4 Probability Specifications for Indicator Variables.

2.5 Probability Specifications for (X,Y).

2.6 Bayesian Inference for a Population Quality.

2.7 Interval Estimation.

2.8 Bayesian Procedures for Constructing Interval Estimates,
Including Significance Levels and Point Estimates.

2.9 Evaluating the Performance of Procedures.

2.10 Similarity of Bayesian and Randomization-Based Inferences
in Many Practical Cases.

3. Underlying Bayesian Theory.

3.1 Introduction and Summary of Repeated-Imputation
Inferences.

3.2 Key Results for Analysis When the Multiple Imputations are
Repeated Draws from the Posterior Distribution of the Missing
Values.

3.3 Inference for Scalar Estimands from a Modest Number of
Repeated Completed-Data Means and Variances.

3.4 Significance Levels for Multicomponent Estimands from a
Modest Number of Repeated Completed-Data Means and
Variance-Covariance Matrices.

3.5 Significance Levels from Repeated Completed-Data
Significance Levels.

3.6 Relating the Completed-Data and Completed-Data Posterior
Distributions When the Sampling Mechanism is Ignorable.

4. Randomization-Based Evaluations.

4.1 Introduction.

4.2 General Conditions for the Randomization-Validity of
Infinite-m Repeated-Imputation Inferences.

4.3Examples of Proper and Improper Imputation Methods in a
Simple Case with Ignorable Nonresponse.

4.4 Further Discussion of Proper Imputation Methods.

4.5 The Asymptotic Distibution of
(&Qmacr;m,Ūm,Bm)
for Proper Imputation Methods.

4.6 Evaluations of Finite-m Inferences with Scalar
Estimands.

4.7 Evaluation of Significance Levels from the Moment-Based
Statistics Dm and &Dtilde;m with
Multicomponent Estimands.

4.8 Evaluation of Significance Levels Based on Repeated
Significance Levels.

5. Procedures with Ignorable Nonresponse.

5.1 Introduction.

5.2 Creating Imputed Values under an Explicit Model.

5.3 Some Explicit Imputation Models with Univariate
YI and Covariates.

5.4 Monotone Patterns of Missingness in Multivariate
YI.

5.5 Missing Social Security Benefits in the Current Population
Survey.

5.6 Beyond Monotone Missingness.

6. Procedures with Nonignorable Nonresponse.

6.1 Introduction.

6.2 Nonignorable Nonresponse with Univariate
YI and No XI.

6.3 Formal Tasks with Nonignorable Nonresponse.

6.4 Illustrating Mixture Modeling Using Educational Testing
Service Data.

6.5 Illustrating Selection Modeling Using CPS Data.

6.6 Extensions to Surveys with Follow-Ups.

6.7 Follow-Up Response in a Survey of Drinking Behavior Among
Men of Retirement Age.

References.

Author Index.

Subject Index.

Appendix I. Report Written for the Social Security
Administration in 1977.

Appendix II. Report Written for the Census Bureau in 1983.