# Overview: MIANALYZE Procedure

The MIANALYZE procedure combines the results of the analyses of imputations and generates valid statistical inferences. Multiple imputation provides a useful strategy for analyzing data sets with missing values. Instead of filling in a single value for each missing value, Rubin’s (1976, 1987) multiple imputation strategy replaces each missing value with a set of plausible values that represent the uncertainty about the right value to impute.

Multiple imputation inference involves three distinct phases:

1. The missing data are filled in m times to generate m complete data sets.

2. The m complete data sets are analyzed using standard statistical analyses.

3. The results from the m complete data sets are combined to produce inferential results.

A companion procedure, PROC MI, creates multiply imputed data sets for incomplete multivariate data. It uses methods that incorporate appropriate variability across the m imputations.

The analyses of imputations are obtained by using standard SAS procedures (such as PROC REG) for complete data. No matter which complete-data analysis is used, the process of combining results from different imputed data sets is essentially the same and results in valid statistical inferences that properly reflect the uncertainty due to missing values. These results of analyses are combined in the MIANALYZE procedure to derive valid inferences.

The MIANALYZE procedure reads parameter estimates and associated standard errors or covariance matrix that are computed by the standard statistical procedure for each imputed data set. The MIANALYZE procedure then derives valid univariate inference for these parameters. With an additional assumption about the population between and within imputation covariance matrices, multivariate inference based on Wald tests can also be derived.

The MODELEFFECTS statement lists the effects to be analyzed, and the CLASS statement lists the classification variables in the MODELEFFECTS statement. The variables in the MODELEFFECTS statement that are not specified in a CLASS statement are assumed to be continuous.

When each effect in the MODELEFFECTS statement is a continuous variable by itself, a STDERR statement specifies the standard errors when both parameter estimates and associated standard errors are stored as variables in the same data set.

For some parameters of interest, you can use TEST statements to test linear hypotheses about the parameters. For others, it is not straightforward to compute estimates and associated covariance matrices with standard statistical SAS procedures. Examples include correlation coefficients between two variables and ratios of variable means. These special cases are described in the section Examples of the Complete-Data Inferences.