[FieldTrip] Non-Parametric Conditional Granger Causality
Per Arnold Lysne
lysne at unm.edu
Mon Jun 9 22:04:38 CEST 2014
Hello,
I am trying to use non-parametric Granger spectral decomposition on a simple, artificial MVAR system:
x(t) = 0.80*x(t-1) - 0.50*x(t-2) + 0.40*z(t-1)
y(t) = 0.53*y(t-1) - 0.80*y(t-2)
z(t) = 0.50*z(t-1) - 0.20*z(t-2) + 0.50*y(t-1)
This example system is drawn from Dhamala, Rangarajan, & Ding, 2008, NeuroImage, where is it used to demonstrate "prima facie", or erroneous conclusions about causality when the conditional decomposition is not used (i.e. in the system itself y->z->x, but an additional link y->x is seen when the non-conditional granger calculation is used).
In my code and output included below, the Fourier power and non-conditional Granger output are as expected, but the conditional Granger output appears to be uniformly near zero.
The only difference between the two cases in my code is the setting of a single parameter passed to ft_connectivityanalsysis, cfg.granger.conditional being 'no' and 'yes' in the respective cases.
My apologies if I have missed an archived post addressing this issue, as this is quite likely to be an error on my part. Alternatively, I do not recognize the calculation being performed in blockwise_conditionalgranger.m. If someone has a reference to this, I may be able to figure this out myself (I am working from Chen, Bressler, & Ding, 2006, "Frequency decomposition of conditional Granger causality and application to multivariate neural field potential data", Journal of Neuroscience Methods).
Thank you for your help,
Per A. Lysne
University of New Mexico
lysne at unm.edu<mailto:lysne at unm.edu>
The first image is the Fourier power spectra of the system (abs applied to complex-valued cross-power). The second image is the non-conditional Granger decomposition, and the third image the conditional Granger. My convention for plotting is "row-causes-column". Results are generated using 100 trials of 300 samples apiece with an assumed sampling frequency of 200 Hz. Software is Matlab R2012a, Student Edition, and my Fieldtrip download is dated 6/3/2014. The code which generated these images is attached.
[cid:898dbd0d-1330-430a-8327-bd9a95f2b7fe]
[cid:889457b8-d09d-4655-bac6-e3da92b8be20][cid:f640ae0e-d04f-451c-87ab-0f93aaa79870]
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