Multiple Imputation for Nonresponse in Surveys

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 (Q_m,U_m,B_m) for Proper Imputation Methods

4.6 Evaluations of Finite-m Inferences with Scalar

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.