# [FieldTrip] Non-Parametric Conditional Granger Causality

jan-mathijs schoffelen jan.schoffelen at donders.ru.nl
Tue Jun 10 10:15:57 CEST 2014

```Dear Per,

Thanks for sending along the very clear code, makes it easy to run and verify ;-).
I think that it went quite OK. Using conditional Granger in this example would hopefully leading to the conclusion Z is Granger-causing X and Y is Granger-causing Z. Your fourier_granger variable (with conditioning) shows just that. The thing is, that the magnitude for some reason are much larger than the y-axis scale you chose for visualization. If you do a plot(fourier_granger.freq, fourier_granger.grangerspctrm), youâ€™ll see that there are 2 lines that show non-zero values.

Best wishes,
Jan-Mathijs

On Jun 9, 2014, at 10:04 PM, Per Arnold Lysne <lysne at unm.edu> wrote:

> 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
>
>
>
>
> 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.
>
>
> <MVAR2.Spectra.jpg>
> <MVAR2.NonCondGranger.jpg><MVAR2.CondGranger.jpg>
> <pal_test_ft_granger_cond.m>_______________________________________________
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Jan-Mathijs Schoffelen, MD PhD

Donders Institute for Brain, Cognition and Behaviour,
Centre for Cognitive Neuroimaging,

Max Planck Institute for Psycholinguistics,
Nijmegen, The Netherlands

J.Schoffelen at donders.ru.nl
Telephone: +31-24-3614793

http://www.hettaligebrein.nl

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