Statistical Analysis with Missing Data., 3rd Edition

4Single Imputation Methods

4.1 Introduction

Both complete-case and available-case analyses make no use of units with Y_j missing when estimating either the marginal distribution of Y_j or measures of covariation between Y_j and other variables. Intuitively, this is a mistake. Suppose a unit with Y_j (e.g., height) missing has the value of another variable Y_k (e.g., weight) that is highly correlated with Y_j. It is tempting to predict the missing value of Y_j from Y_k and then to include the filled-in (or imputed) value in analyses involving Y_j. We now discuss methods that impute (that is fill in) the values of variables that are missing. These methods can be applied to impute one value for each missing variable (single imputation), or to impute more than one value (multiple imputation), to allow appropriate assessment of imputation uncertainty.

Imputation is a general and flexible method for handling missing data problems. However, it has pitfalls. In the words of Dempster and Rubin (1983):

The idea of imputation is both seductive and dangerous. It is seductive because it can lull the user into the pleasurable state of believing that the data are complete after all, and it is dangerous because it lumps together situations where the problem is sufficiently minor that it can be legitimately handled in this way and situations where standard estimators applied to the real and imputed data have substantial biases.

Imputations should be conceptualized as draws from a predictive distribution ...