Multiple Imputation for Missing Data: Concepts and New Development (Version 9.0)

Multiple imputation provides a useful strategy for dealing with data sets with missing values. Instead of filling in a single value for each missing value, Rubin’s (1987) multiple imputation procedure replaces each missing value with a set of plausible values that represent the uncertainty about the right value to impute. These multiply imputed data sets are then analyzed by using standard procedures for complete data and combining the results from these analyses. No matter which complete-data analysis is used, the process of combining results from different imputed data sets is essentially the same. This results in valid statistical inferences that properly reflect the uncertainty due to missing values. This paper reviews methods for analyzing missing data, including basic concepts and applications of multiple imputation techniques. The paper presents SASprocedures, PROC MI and PROC MIANALYZE, for creating multiple imputations for incomplete multivariate data and for analyzing results from multiply imputed data sets. The MI and MIANALYZE procedures, which were introduced as experimental software in Releases 8.1 and 8.2, are production software in Version 9.0. The syntax and examples in this paper apply to Version 9.0. The following enhancements have been made to the MI procedure in Version 9.0: • A new REGPMM option in the MONOTONE statement and a new PMM option in the MCMC statement request the predicted mean matching method for imputation. This method imputes an observed value which is closest to the predicted value from the simulated regression model for each missing value. • A flexible model specification in the MONOTONE statement allows a different set of covariates to be specified for each imputed variable. The following changes and enhancements have been made to the MIANALYZE procedure in Version 9.0: • A new MODELEFFECTS statement allows you to specify the effects in the data set to be analyzed. This statement replaces the VAR statement, which was used in Releases 8.1 and 8.2. • A new STDERR statement provides standard errors associated with effects in the MODELEFFECTS statement. The statement can be used for univariate inference when the input DATA= data set contains both parameter estimates and standard errors as variables. • A new TEST statement tests linear hypotheses about the parameters. This paper also describes new experimental features in Version 9.0 for specification of classification variables in the MI and MIANALYZE procedures. Introduction Most SAS statistical procedures exclude observations with any missing variable values from the analysis. These observations are called incomplete cases. While using only complete cases has its simplicity, you lose information in the incomplete cases. This approach also ignores the possible systematic difference between the complete cases and incomplete cases, and the resulting inference may not be applicable to the population of all cases, especially with a smaller number of complete cases. Some SAS procedures use all the available cases in an analysis, that is, cases with available information. For example, PROC CORR estimates a variable mean by using all cases with nonmissing values on this variable, ignoring the possible missing values in other variables. PROC CORR also estimates a correlation by using all cases with nonmissing values for this pair of variables. This may make better use of the available data, but the resulting correlation matrix may not be positive definite. Another strategy is single imputation, in which you substitute a value for each missing value. Standard statistical procedures for complete data analysis can then be used with the filled-in data set. For example, each missing value can be imputed from the variable mean of the complete cases. This approach treats missing values as if they were known in the complete-data analyses. Single imputation does not reflect the uncertainty about the predictions of the unknown missing values, and the resulting estimated variances of the parameter estimates will be biased toward zero.