Combination rules for homoscedastic and heteroscedastic MANOVA models from multiply imputed datasets

Classical MANOVA tests do not pose any difficulty when the assumptions on which they are based are satisfied, while the modified Brown-Forsythe (MBF) procedure has low sensitivity to the lack of multivariate normality and homogeneity of covariance matrices. Both methods assume complete data for all subjects. In this paper, we present combination rules for the MANOVA and MBF procedures with multiply imputed datasets. These rules are illustrated by pooling the results obtained with a two-factor multivariate design after applying the two approaches to each of the imputed datasets when the covariance matrices were equal (MI-MANOVA) and when the covariance matrices were unequal (MI-MBF). A Monte-Carlo study was carried out to compare the proposed solution, in terms of type I error rates and statistical power, with the MANOVA and MBF approaches without missing data, and with listwise deletion of missing data followed by the MANOVA approach (LD-MANOVA) and listwise deletion followed by the MBF procedure (LD-MBF). Simulations showed that the type I error rates in all analyses on datasets with missing values (with or without imputation) were well controlled. We also found that the MI-MANOVA approach was substantially more powerful than LD-MANOVA. Moreover, the power of the MI-MANOVA was generally comparable to that of its complete data counterpart. Similar results were obtained for the MI-MBF procedure when covariance matrices were unequal. We conclude, based on the current evidence, that the solution presented performs well and could be of practical use. We illustrate the application of combination rules using a real dataset.