MANOVA versus mixed models: Comparing approaches to modeling within-subject dependence

Abstract

For inferential purposes such as hypothesis testing or confidence interval calculations, analysis of repeated measures data needs to account for within-subject dependence of observations. Multivariate analysis of variance (MANOVA) is a suitable traditional technique for this purpose. It assumes an unconstrained within-subject covariance matrix and balanced data. However, the so-called mixedmodel approach is a viable alternative to analyzing this type of data, because its underlying statistical assumptions are equivalent to the MANOVA model. While MANOVA is the classical approach, the mixed-model methodology, although by now implemented in all major statistical software packages, still is a relatively recent statistical development. The equivalence of both approaches to analyzing repeated measures data has frequently been noted in the literature. Nevertheless, in terms of test-statistics both approaches differ. While in large samples the test-statistics are essentially equivalent, their small sample behavior is not well known. In this article, we investigate by computer simulation the performance of several test-statistics calculated either from the MANOVA or the mixed-model approach for testing the interaction hypothesis with balanced data.