Statistical procedures for missing data have vastly improved, yet misconception and unsound practice still abound. The authors frame the missing-data problem, review methods, offer advice, and raise issues that remain unresolved. They clear up common misunderstandings regarding the missing at random (MAR) concept. They summarize the evidence against older procedures and, with few exceptions, discourage their use. They present, in both technical and practical language, 2 general approaches that come highly recommended: maximum likelihood (ML) and Bayesian multiple imputation (MI). Newer developments are discussed, including some for dealing with missing data that are not MAR. Although not yet in the mainstream, these procedures may eventually extend the ML and MI methods that currently represent the state of the art.

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Missing data: Our view of the state of the art.

In recent years, multiple imputation has emerged as a convenient and flexible paradigm for analysing data with missing values. Essential features of multiple imputation are reviewed, with answers to frequently asked questions about using the method in practice.

Multiple imputation: a primer:

It has long been customary to measure the adequacy of an estimator by the smallness of its mean squared error. The least squares estimators were studied by Gauss and by other authors later in the nineteenth century. A proof that the best unbiased estimator of a linear function of the means of a set of observed random variables is the least squares estimator was given by Markov [12], a modified version of whose proof is given by David and Neyman [4]. A slightly more general theorem is given by Aitken [1]. Fisher [5] indicated that for large samples the maximum likelihood estimator approximately minimizes the mean squared error when compared with other reasonable estimators. This paper will be concerned with optimum properties or failure of optimum properties of the natural estimator in certain special problems with the risk usually measured by the mean squared error or, in the case of several parameters, by a quadratic function of the estimators. We shall first mention some recent papers on this subject and then give some results, mostly unpublished, in greater detail.

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Estimation with Quadratic Loss

Basics Introduction The problem of missing data Concepts of MCAR, MAR and MNAR Simple solutions that do not (always) work Multiple imputation in a nutshell Goal of the book What the book does not cover Structure of the book Exercises Multiple imputation Historic overview Incomplete data concepts Why and when multiple imputation works Statistical intervals and tests Evaluation criteria When to use multiple imputation How many imputations? Exercises Univariate missing data How to generate multiple imputations Imputation under the normal linear normal Imputation under non-normal distributions Predictive mean matching Categorical data Other data types Classification and regression trees Multilevel data Non-ignorable methods Exercises Multivariate missing data Missing data pattern Issues in multivariate imputation Monotone data imputation Joint Modeling Fully Conditional Specification FCS and JM Conclusion Exercises Imputation in practice Overview of modeling choices Ignorable or non-ignorable? Model form and predictors Derived variables Algorithmic options Diagnostics Conclusion Exercises Analysis of imputed data What to do with the imputed data? Parameter pooling Statistical tests for multiple imputation Stepwise model selection Conclusion Exercises Case studies Measurement issues Too many columns Sensitivity analysis Correct prevalence estimates from self-reported data Enhancing comparability Exercises Selection issues Correcting for selective drop-out Correcting for non-response Exercises Longitudinal data Long and wide format SE Fireworks Disaster Study Time raster imputation Conclusion Exercises Extensions Conclusion Some dangers, some do's and some don'ts Reporting Other applications Future developments Exercises Appendices: Software R S-Plus Stata SAS SPSS Other software References Author Index Subject Index

Flexible Imputation of Missing Data

This article describes and evaluates a procedure for imputing missing values for a relatively complex data structure when the data are missing at random. The imputations are obtained by fitting a sequence of regression models and drawing values from the corresponding predictive distributions. The types of regression models used are linear, logistic, Poisson, generalized logit or a mixture of these depending on the type of variable being imputed. Two additional common features in the imputation process are incorporated: restriction to a relevant subpopulation for some variables and logical bounds or constraints for the imputed values. The restrictions involve subsetting the sample individuals that satisfy certain criteria while fitting the regression models. The bounds involve drawing values from a truncated predictive distribution. The development of this method was partly motivated by the analysis of two data sets which are used as illustrations. The sequential regression procedure is applied to perform multiple imputation analysis for the two applied problems. The sampling properties of inferences from multiply imputed data sets created using the sequential regression method are evaluated through simulated data sets.

A multivariate technique for multiply imputing missing values using a sequence of regression models

Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling

Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling.

Contributions to Probability and Statistics, Essays in Honor of Harold Hotelling.

Incomplete data in sample surveys

This is one of three volumes that represent the results of work undertaken by the Panel on Incomplete Data. The panel was set up in 1977 by the Committee on National Statistics within the Commission on Behavioral and Social Sciences and Education of the National Research Council in order to undertake a comprehensive review of the literature on survey incompleteness in sample surveys and to explore ways of improving the methods of dealing with it. The second volume contains the papers on theory and two bibliographies. An initial paper considers the historical perspective. Five papers are then presented on data collection dealing with callbacks follow-ups and repeated telephone calls; the impact of substitution on survey estimates; quota sampling; randomized response techniques; and handling missing data by network sampling. The next two papers focus on non-response and double sampling covering the randomization approach and the Bayesian approach. A section on weighting and imputation methods covers conceptual issues in the presence of non-response weighting adjustment for unit non-response hot-deck procedures and the use of multiple imputations to handle non-response. Sections are also included on imputation methodology concerning total survey error and on superpopulation models for non-response including both the ignorable case and the non-ignorable case. A selected annotated bibliography is provided with keywords and phrases available as an index; a separate unannotated bibliography deals with non-response and related topics. The primary geographic focus is on the United States.

William G. Madow

Papers

Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling

Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling.

Contributions to Probability and Statistics, Essays in Honor of Harold Hotelling.

Incomplete data in sample surveys

Incomplete data in sample surveys. Vol. 2: theory and bibliographies