Analyses of multivariate data are frequently hampered by missing values. Until recently, the
only missing-data methods available to most data analysts have been relatively ad1 hoc practices
such as listwise deletion. Recent dramatic advances in theoretical and computational statistics,
however, have produced anew generation of flexible procedures with a sound statistical basis.
These procedures involve multiple imputation (Rubin, 1987), a simulation technique that
replaces each missing datum with a set of m > 1 plausible values. The m versions of the
complete data are analyzed by standard complete-data methods, and the results are combined
using simple rules to yield estimates, standard errors, and p-values that formally incorporate
missing-data uncertainty. New computational algorithms and software described in a recent
book (Schafer, 1997a) allow us to create proper multiple imputations in complex multivariate
settings. This article reviews the key ideas of multiple imputation, discusses the software programs currently available, and demonstrates their use on data from the Adolesc:ent Alcohol
prevention Trial (Hansen & Graham, 199 I).
Analyses of multivariate data are frequently hampered by missing values. Until recently, theonly missing-data methods available to most data analysts have been relatively ad1 hoc practicessuch as listwise deletion. Recent dramatic advances in theoretical and computational statistics,however, have produced anew generation of flexible procedures with a sound statistical basis.These procedures involve multiple imputation (Rubin, 1987), a simulation technique thatreplaces each missing datum with a set of m > 1 plausible values. The m versions of thecomplete data are analyzed by standard complete-data methods, and the results are combinedusing simple rules to yield estimates, standard errors, and p-values that formally incorporatemissing-data uncertainty. New computational algorithms and software described in a recentbook (Schafer, 1997a) allow us to create proper multiple imputations in complex multivariatesettings. This article reviews the key ideas of multiple imputation, discusses the software programs currently available, and demonstrates their use on data from the Adolesc:ent Alcoholprevention Trial (Hansen & Graham, 199 I).
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