This paper reviews recent advances in missing data research using graphical models to represent multivariate dependencies. We first examine the limitations of traditional frameworks from three different perspectives: . We then show how procedures based on graphical models can overcome these limitations and provide meaningful performance guarantees even when data are Missing Not At Random (MNAR). In particular, we identify conditions that guarantee consistent estimation in broad categories of missing data problems, and derive procedures for implementing this estimation. Finally we derive testable implications for missing data models in both MAR (Missing At Random) and MNAR categories.
Another approach to handling missing data is imputation: substituting a reasonable guess for each missing value . A simple example is , in which all missing observations of variable @math are substituted with the mean of all observed values of @math . Hot-deck imputation, cold-deck imputation , regression imputation ( @cite_54 ) and Multiple Imputation are examples of popular imputation procedures. Among these techniques, regression imputation guarantees consistent estimates for MAR data ( @cite_4 ). While many other imputation techniques are attractive in practice, performance guarantees (eg: convergence and unbiasedness) are based primarily on simulation experiments.
@cite_54 @cite_4
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What is done with missing data? Does the missingness mechanism matter? Is it a good idea to just use the default options in the major statistical packages? Even some highly trained statisticians do this, so can the non-statistician analysing their own data cope with some of the better techniques for handling missing data? This paper shows how the mean and standard deviation are affected by different methods of imputation, given different missingness mechanisms. Better options than the standard default options are available in the major statistical software, offering the chance to 'do the right thing' to the statistical and non-statistical community alike. Missing data analyses have received considerable recent attention in the methodological literature, and two “modern” methods, multiple imputation and maximum likelihood estimation, are recommended. The goals of this article are to (a) provide an overview of missing-data theory, maximum likelihood estimation, and multiple imputation; (b) conduct a methodological review of missing-data reporting practices in 23 applied research journals; and (c) provide a demonstration of multiple imputation and maximum likelihood estimation using the Longitudinal Study of American Youth data. The results indicated that explicit discussions of missing data increased substantially between 1999 and 2003, but the use of maximum likelihood estimation or multiple imputation was rare; the studies relied almost exclusively on listwise and pairwise deletion.