Granger Causality Analysis (GCA)

 Dear REST experts, 

 Thank you for your development of useful software. I have some questions about GCA. I am planning to use this software to analyze my fMRI data during the simple reward task (TR = 2 sec).

1. What is the difference between simple x2y model and autoregressive model? Output data was very different each other.
2. In Granger Causality Analysis Readme file, there is the sentence said 'The right FIC showed significantly positive causal effect on the dorsal anterior cingulate cortex (dACC) (Fig. 1a). This result is consistent with that in a previous study (Sridharan et al., 2008). Interestingly, the dACC showed significantly negative effect on the right FIC (Fig. 1b)'. Is that mean that there are reciprocal connection? 

3.  In Granger Causality Analysis Readme file, you use one-sample t-tests in order to generate group level maps. Some studies use empirical null distribution because Granger methods are non-negative and they could not use theoretical null distributions such as one-sample t-test, which are based on a Gaussian distribution. Which one is the appropriate way to get the group level map.

Thank you in advance.
Yous sincerely, 
Yuki Sakai

Dear Sakai,
These are my own opinions of the following questions:
1. The model of x2y is consisted with two parts: the past value of x and the past value of y itself. The model of autoregression contains only past value of y.
2. I think the results indicated what you thought. I agree with you. But it is unpublished.
3. The one sample t-tests were performed on the normal-distributed regression coefficients. As for the F values one residual, you need to transform them into normal distributed values, firstly. The F values are likely to be chi2-distributed (Geweke, 1984). There are some methods to transform a chi2-distributed value into normal-distributed value. You can use chi2-tests, of course. Recently, we examined the transformed F value and found that they are normal-distributed in over 75% voxels (unpublished).

I hope my reply could help.
Zang Zhen-Xiang