Granger Causality Analysis
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We provide two programs, 3dGC.R and 1dGC.R, for Granger causality analysis via multivariate (or vector) auto-regressive modeling. First, the limitation of VAR analysis: If the data aren't sampled fine enough in temporal space, it may present false paths in the model. In other words the repetition time (TR) of the FMRI design should be small enough to catch the network evolution in the context of the experiment.
To detect the connectivities in a network we basically need to continuously sample a system long enough to have a reasonable representation of the network evolution. If we stop sampling the system continuously, we lose the capability to catch the connectivity at those break points. The methodology should work well with resting-state data since there is not much concern about data extraction and confounding effects, such as tasks of no interest, except for physiological noises. For context-dependent experiment, things could be a little complicated. In block designs with blocks of relatively long duration, you could extract the time points of those blocks, which might be tricky, and then feed them into the causality model. In rapid event-related designs it might be OK to keep the whole time series by regressing out those tasks/conditions of no interest if we can assume that the network is on almost all the time. However it is most likely problematic to apply the program to a slow event-related experiment from this perspective.
Other than the above necessities, the success of VAR analysis also relies on the assumptions from the modeling perspective: linearity of the system, stationarity (invariance of mean, variance and autocovariance) of the data, Gaussian residuals with positive definite contemporaneous covariance matrix, no serial correlation in individual residual time series, etc.
