Effect of initial fMRI data modeling on the connectivity reported between brain areas.
Nearly all neuroimaging data analysis rests upon some form of variance partitioning. Conventional analyses, with a general linear model (GLM), partition the variance in the measured response variable into partitions described by a design matrix of explanatory variables. This approach can also be adopted in the initial modeling of the data in studies using data-led methods to summarize functional connectivity, such as principle component analysis, or studies of effective connectivity, using for example structural equation modeling. The point made in this technical note is that the partition of the original time series has to be precisely described to qualify the sources of variations that are taken into account. For conventional analyses using the GLM, the partition investigated corresponds to the subspaces of the design matrix that are tested. However, in the analyses of functional and effective connectivity, the particular subspaces considered are not always specified explicitly. Here we show that selecting different subspaces, or variance partitions, can have a profound effect, both qualitatively and quantitatively, on the sample covariances and the ensuing inferences about connectivity. We will illustrate this using simulated data that include condition and block-related effects and their interactions. We will use these three subspaces to show how the correlation between two voxels depends on which sub-partitions are examined. We will also show how the partition of the design matrix influences the resulting correlation matrix observed when studying correlations between error terms. We will finally demonstrate, quantitatively, the effect of the variance partitions considered on the correlations between two regions using a real fMRI study of biological motion.