Modeling Group-Level Repeated Measurements of Neuroimaging Data Using the Univariate General Linear Model

Group-level repeated measurements are common in neuroimaging, yet their analysis remains complex. Although a variety of specialized tools now exist, it is surprising that to-date there has been no clear discussion of how repeated-measurements can be analyzed appropriately using the standard general linear model approach, as implemented in software such as SPM and FSL. This is particularly surprising given that these implementations necessitate the use of multiple models, even for seemingly conventional analyses, and that without care it is very easy to specify contrasts that do not correctly test the effects of interest. Despite this, interest in fitting these types of models using conventional tools has been growing in the neuroimaging community. As such it has become even more important to elucidate the correct means of doing so. To begin, this paper will discuss the key concept of the expected mean squares (EMS) for defining suitable F-ratios for testing hypotheses. Once this is understood, the logic of specifying correct repeated measurements models in the GLM should be clear. The ancillary issue of specifying suitable contrast weights in these designs will also be discussed, providing a complimentary perspective on the EMS. A set of steps will then be given alongside an example of specifying a 3-way repeated-measures ANOVA in SPM. Equivalency of the results compared to other statistical software will be demonstrated. Additional issues, such as the inclusion of continuous covariates and the assumption of sphericity, will also be discussed. The hope is that this paper will provide some clarity on this confusing topic, giving researchers the confidence to correctly specify these forms of models within traditional neuroimaging analysis tools.