Analysis of Variance from Multiply Imputed Data Sets

The analysis of variance is a popular method used in many scientific applications. There are standard software for handling unbalanced data due to missing values in the outcome/dependent variable. The analysis becomes difficult when the missing values are in predictors. Multiple imputation is an increasingly popular method for handling such incomplete data. This approach involves replacing the missing set of values by more than one plausible set of values, preferably generated from their posterior predictive distribution given the observed data. Each plausible set of imputed values when combined with the observed set of values results in a completed data. Each completed data set is analyzed separately and the point estimates and their standard errors are combined to form a single inference. Many analysis of variance models may be formulated as regression models and then apply the standard multiple imputation combining rules. This is often not possible when the design is complex involving repeated measures and/or nested, random or interaction effects. It may be more convenient to directly combine the analysis of variance tables generated from each completed data to test appropriate hypotheses. This paper develops a combining rule for the completed data mean squares. Approximate F -tests are developed and evaluated using the actual and simulated data sets. The method is extended to comparison of regression models using partial F-tests in multiple linear regression analysis or the deviance statistics in fitting regression models using the Generalized Estimating Equations.