Missing Data

Psychological Methods 2002, Vol. 7, No. 2, 147–177

Copyright 2002 by the American Psychological Association, Inc. 1082-989X/02/$5.00 DOI: 10.1037//1082-989X.7.2.147

Missing Data: Our View of the State of the Art
Joseph L. Schafer and John W. Graham
Pennsylvania State University Statistical procedures for missing data have vastly improved, yet misconception and unsound practice stillabound. 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 highlyrecommended: 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.

Why do missing data create such difficulty in scientific research? Because mostdata analysis procedures were not designed for them. Missingness is usually a nuisance, not the main focus of inquiry, but handling it in a principled manner raises conceptual difficulties and computational challenges. Lacking resources or even a theoretical framework, researchers, methodologists, and software developers resort to editing the data to lend an appearance of completeness.Unfortunately, ad hoc edits may do more harm than good, producing answers that are biased, inefficient (lacking in power), and unreliable.

Purposes of This Article
This article’s intended audience and purposes are varied. For the novice, we review the available methods and describe their strengths and limitations. For those already familiar with missing-data issues, we seek to fill gaps in understandingand highlight recent developments in this rapidly changing field. For

Joseph L. Schafer, Department of Statistics and the Methodology Center, Pennsylvania State University; John W. Graham, Department of Biobehavioral Health, Pennsylvania State University. This research was supported by National Institute on Drug Abuse Grant 1-P50-DA10075. Correspondence concerning this article should beaddressed to Joseph L. Schafer, The Methodology Center, Pennsylvania State University, Henderson S-159, University Park, Pennsylvania 16802. E-mail: jls@stat.psu.edu

methodologists, we hope to stimulate thoughtful discussion and point to important areas for new research. One of our main reasons for writing this article is to familiarize researchers with these newer techniques and encourage them toapply these methods in their own work. In the remainder of this article, we describe criteria by which missing-data procedures should be evaluated. Fundamental concepts, such as the distribution of missingness and the notion of missing at random (MAR), are presented in nontechnical fashion. Older procedures, including case deletion and single imputation, are reviewed and assessed. We then review andcompare modern procedures of maximum likelihood (ML) and multiple imputation (MI), describing their strengths and limitations. Finally, we describe new techniques that attempt to relax distributional assumptions and methods that do not assume that missing data are MAR. In general, we emphasize and recommend two approaches. The first is ML estimation based on all available data; the second isBayesian MI. Readers who are not yet familiar with these techniques may wish to see step-by-step illustrations of how to apply them to real data. Such examples have already been published, and space limitations do not allow us to repeat them here. Rather, we focus on the underlying motivation and principles and provide references so that interested readers may learn the specifics of applying them...