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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Hot deck imputation is a procedure in which missing items are replaced with values from respondents. A model supporting such procedures is the model in which response probabilities are assumed equal within imputation cells. An efficient version of hot deck imputation is described for the cell response model and a computationally efficient variance estimator is given. An approximation to the fully efficient procedure in which a small number of values are imputed for each nonrespondent is described. Variance estimation procedures are illustrated in a Monte Carlo study. Hot deck imputation is a method for handling missing data in which each missing value is replaced with an observed response from a "similar" unit. Despite being used extensively in practice, the theory is not as well developed as that of other imputation methods. We have found that no consensus exists as to the best way to apply the hot deck and obtain inferences from the completed data set. Here we review different forms of the hot deck and existing research on its statistical properties. We describe applications of the hot deck currently in use, including the U.S. Census Bureau's hot deck for the Current Population Survey (CPS). We also provide an extended example of variations of the hot deck applied to the third National Health and Nutrition Examination Survey (NHANES III). Some potential areas for future research are highlighted. Copyright (c) 2010 The Authors. Journal compilation (c) 2010 International Statistical Institute. Covariate data which are missing or measured with error form the subject of a growing body of statistical literature. Parametric methods have not been widely adopted, quite possibly due to the necessity of specifying the form of a 'nuisance function' not required for complete data analysis, and the non-robustness of the methods to mis-specification. A non-parametric counterpart of multiple imputation, known as 'hot deck', was proposed by Rubin (1987) and has been used by the Census Bureau to complete public-use databases. However, inference using this method has not been possible due to the distribution theory not being available. Recently, it has been shown that the hot deck estimator has the same asymptotic distribution as the 'mean score' estimator, so that inference using hot deck is now possible. The method is intuitively appealing and easily implemented. Furthermore, it accommodates missingness which depends on outcome, which is an important generalization of many currently available methods. In this paper, the hot deck multiple imputation method is explained, its asymptotic distribution presented and its application to data analysis demonstrated by an example. 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.