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MainIntroductionGranger causality mapping is a technique which explores directed influences (effective connectivity) between distinct regions in fMRI data. See Roebroeck, Formisano, Goebel (Neuroimage 25(1):23042, 2005) for a detailed description of the technique. In short, a Granger Causality Map (GCM) is computed with respect to a single selected reference region, and maps both sources of influence to the reference region and targets of influence from the reference region over the brain. Justifying its name, GCM makes use of the concept of Granger causality to define what 'influence' or 'causality' means in the context of fMRI timeseries. A (discrete) timeseries X[t] is said to Granger cause a (discrete) timeseries Y[t], if the past of X improves the prediction of the current value of Y, given that all other relevant sources of influence (at the very least Y's own past) have been taken into account. Analogously, and independently, Granger causality from Y to X can be defined. Finally, instantaneous influence (correlation) between X and Y is said to exist when values X[t] improve predictions of contemporaneous values Y[t] (or vice versa, instantaneous correlation is symmetric), taking into account all other relevant sources of influence (at the very least the past of both X and Y). Temporal information in the data is used to define the existence and direction of influences without a directed graph model of assumed regional connections. These definitions can be applied to fMRI timeseries with the use of Vector AutoRegressive (VAR) models.The GCMPlugin maps influence (effective connectivity) over the brain for a given reference region by repeatedly (for every voxel in a volume) pairing the timecourse of the reference region with the timecourse of a voxel and computing the three influence terms:
