[FieldTrip] Granger Causality / MVAR modelling problem

[Schoffelen, J.M. (Jan Mathijs)]

Dear Daniel,

Indeed, it does not make much sense to try and make a MMVAR (Massively Multivariate AutoRegressive) model like this….
The number of ‘independent’ dimensions in your data is at most the number of EEG electrodes minus 1. Unless you find a way to meaningfully and dramatically reduce the number of nodes, the estimation procedure does not make sense to me. You may want to consider a massive pairwise decomposition (i.e. do the estimation multiple times, for each pair of nodes to be considered), although this might suffer from:

1) mis-interpretation due to non-observed common input into both nodes (which I think is not a very big problem), but some esteemed colleagues might disagree with this.

2) mis-estimation of the model due to violation of the AR assumptions due to residual instantaneous (and additive) leakage from second (the other source in the pair) and third party (distant sources) sources. This would require an ARMA model (or an equivalent state space model), both of which are not straightforward to estimate. (that is: people who claim that these methods should be used do not seem to be very much inclined to share their knowledge in easy-to-use and robust code (nudge-nudge).

Best wishes,
Jan-Mathijs

On 22 May 2019, at 11:39, Velden, Daniel <daniel.velden at med.uni-goettingen.de<mailto:daniel.velden at med.uni-goettingen.de>> wrote:

Dear community,

I am working on resting-state EEG data with around 40 trials per subject, each trial with a length of 10 seconds (sfrequency= 150Hz). This data is preprocessed using fieldtrip functions (Low-, Highpass filtering, ICA etc.) and then source reconstructed with the LCMV beamformer to 2338 source points on the individual subjects cortex.

Now I want to estimate Granger Causality (GC) for all of the 2338 source points, which requires mvar models of each subjects data. Here I use the “BioSig” toolkit with the default Vieira-Morf algorithm to remodel my data. While modelling most of my matrices are very badly conditioned with rcond’s of e-18 and lower.

After modelling it is necessary to choose the best fitting model order. So I calculate the Akaike and Bayesian Information criterion (AIC, BIC). But the AIC and BIC results are all “Inf” or “-Inf”, since the determinate of the noisecovariance results in that.

So does anyone else came across this issue? My presumption is, that the enormous amount of 2338 source/signals unavoidably results in badly conditioned matrices, since the number of comparisons/predictions that need to be made is too high and the algorithm assumes that every source/signal takes a role in every prediction of every value, therefore resulting in very small values for each ar-coefficient.

I appreciate any comment and/or contribution to that topic.

Greetings and all the best,
Daniel van de Velden

------------------------------------------------

Daniel van de Velden (M.Sc.) || PhD candidate
Wissenschaftlicher Mitarbeiter
Klinik für Klinische Neurophysiologie
Georg-August-Universität Göttingen
Robert-Koch.Str. 40, 37075 Göttingen
Tel. 0551- 39-65106

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