Granger Causality

We employed Granger causality (GC) to characterize causal interactions among LFP time series from the recorded regions. GC is based on the Wiener-Granger concept of causality⁶¹. First, if knowledge of the past of a time series A improves the prediction of the future of another time series B better than what could be accomplished by knowing the past of B alone, then signal A “Granger-causes” signal B. This statistical concept is increasingly popular in the neuroscience community and offers a directional measure of neural functional connectivity. We used the multivariate Granger causality (MVGC) Matlab toolbox provided by Barnett and Seth⁴⁴ to calculate the multivariate conditional GC in the frequency domain over time, which is more appropriate for neural time series.

First, we fit a multivariate autoregressive (MVAR) model to the LFP data from the 4 regions studied in all trials, using the ordinary least squares method with model order estimated by the Akaike Information Criterion (limited to 20). Next, we obtained a MVAR model and calculated the autocovariance sequence for each sliding window (150 ms length, 10 ms step), which was then used to calculate the pairwise-conditional frequency-domain MVGC. The GC results was standard scored by the baseline (−3 s to −1 s) of each frequency. We considered as significant values those higher than baseline mean plus two times its standard deviation. The spectral GC maps were smoothed with a Gaussian filter (mask size = [20 70], standard deviation sigma = 30).