[FieldTrip] Non-Parametric Conditional Granger Causality

[jan-mathijs schoffelen]

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), you’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,
Radboud University Nijmegen, The Netherlands

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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