[FieldTrip] Phase Slope Index: How to choose bandwidth

Hähnke, Daniel daniel.haehnke at tum.de
Tue Mar 8 10:57:26 CET 2016 

Hi Sandhy,

that’s interesting. Can you describe how you found out about the bandwidth being narrower for lower frequencies? When I read the code, I had the impression that the bandwidth parameter is used once to calculate one bandwidth parameter in frequency bins that is subsequently used for the whole spectrum.

Best,

Daniel

On 07.03.2016, at 17:09, Prasandhya Astagiri Yusuf <prasandhya.a.yusuf at gmail.com<mailto:prasandhya.a.yusuf at gmail.com>> wrote:

Hi Daniel and Jan-Mathis,

since I also have tried to play around with PSI, I have an additional issue regarding the frequency bandwidth configuration.

I found that with using linear equidistant frequency bins, the low frequency oscillation has narrower bandwidth compared to high frequencies. So if I took 5 Hz frequency bandwidth and compute the PSI to check the low frequency (i.e alpha) coupling direction, low frequency coupling may not have sufficient neighboring frequencies. In some cases PSI could also mixed up both the positive and negative phase slope, then the summation result from n-frequency bins can be spuriously positive or negative.

Regarding the mixing of slope information, possibly this is one of methodological disadvantage. But for fairer frequency slope summation, I also have the same thought whether the logarithmic frequency step might be more proper in computing PSI..

Please someone correct me if I am wrong in interpreting these, I am trying to figure out how FieldTrip's PSI works.

Thanks!

Best,
Sandhy

-----------
Prasandhya A. Yusuf
PhD student

Medizinische Hochschule Hannover
VIANNA - Institute of AudioNeuroTechnology



On Mon, Mar 7, 2016 at 1:04 PM, Hähnke, Daniel <daniel.haehnke at tum.de<mailto:daniel.haehnke at tum.de>> wrote:
Hi Jan-Mathijs,

thanks for sharing your thoughts about problems with using non-equidistant frequency bins.

Also thanks for pointing out the possible problems in Granger causality. I actually computed the GC using non-parametric factorization and equidistant frequency bins, since the code gives an error if you don’t. As I wrote, these values from equidistant frequency bins look pretty similar to those PSI values from non-equidistant frequency bins.

Best,

Daniel


On 07.03.2016, at 10:02, Schoffelen, J.M. (Jan Mathijs) <jan.schoffelen at donders.ru.nl<mailto:jan.schoffelen at donders.ru.nl>> wrote:

Hi Daniel,

I am not an expert on PSI theory either, and here I would like to stay on the safe side. Even if it may be possible to vary the number of integration bins across frequencies, and include some normalisation step on top if it, I think it is very tricky, and rather won’t support this. The normalisation is probably quite arbitrary, because it could also involve some extrapolation of the underlying coherence spectrum. Also, using non equidistant frequency spacing increases the risk of the user having specified frequency specific smoothing, which further complicates integration of phase and coherence estimates across neighbouring frequency bins. Long story short, I will build in an explicit check about equidistance of frequency bins in ft_connectivityanalysis, to return an explicit error if this is not the case. This update will be a general clean up of the psi functionality, which also will include better error handling if the user happens to forget the bandwidth argument in the cfg. This will address bug 3084 on bugzilla.fieldtriptoolbox.org<http://bugzilla.fieldtriptoolbox.org/>.

While I am at it, you mentioned that your psi results look very much like the Granger you have computed. I am not sure how you have computed the Granger causality, but (if you have used non parametric factorisation of the cod matrix to get your spectral transfer matrices) it may be relevant to know that it is incorrect to compute it from freq data with non-equidistant frequency bins. The non-parametric spectral factorisation code assumes the data to be represented on equidistant frequency bins.

Best,
Jan-Mathijs



On 02 Mar 2016, at 15:08, Hähnke, Daniel <daniel.haehnke at tum.de<mailto:daniel.haehnke at tum.de>> wrote:

Hi Jan-Mathijs,

never underestimate the creativity of scientists ;)

Why do you think I can’t expect meaningful results from using logarithmically spaced frequency bins? At least when comparing my Granger results with the PSI values, they look pretty similar.
I know that the phase slope is dependent on the step size between frequencies, so I could miss or aberrantly pick up non-monotonicity in the phase slope if I use non-equidistant bins.
But if I assume that the slope changes monotonically across frequencies (which, if I’m not mistaken, is also assumed for equidistant frequency bins), a normalization by the bandwidth should be possible.

Please correct me if I’m wrong. I’m obviously no expert in PSI theory and would be glad to learn more.

Best,

Daniel

On 02.03.2016, at 14:05, Schoffelen, J.M. (Jan Mathijs) <jan.schoffelen at donders.ru.nl<mailto:jan.schoffelen at donders.ru.nl>> wrote:

Hi Daniel
I have never in my life considered that people would be so creative as to expect meaningful results when inputting the function with logarithmically spaced frequency bins. I should have known better, but I would be strongly in favour of checking for equidistant frequency bins, and if not: throw an error. I am opposed to using ‘bins’ as a unit, because FieldTrip should work wherever possible with physical units, rather than with unit-less units.

Best,
Jan-Mathijs


On 02 Mar 2016, at 13:13, Hähnke, Daniel <daniel.haehnke at tum.de<mailto:daniel.haehnke at tum.de>> wrote:

Hi all,

since only a few people seem to be using the PSI, I went into the code to see what it actually does. I would like to point out that there are some issues with the current implementation if you’re using logarithmically spaced frequency axes.

The parameter cfg.bandwidth (in Hz) is used to calculate the number of frequency bins that is used to calculate the PSI. This calculation, however, is only done once using the frequency from the lowest frequency bin. If the chosen bandwidth is not an integer multiple of a frequency bin step, this computation leads to a changed bandwidth.
If your frequency axis is not evenly spaced this leads to various bandwidths across the frequency axis, since the code only uses a fixed number of frequency bins across which to compute the PSI.

I think it would be useful to change the cfg.bandwidth input from Hz to number of bins. Also, people should be aware of the fact that the PSI value is correlated with the bandwidth. So, if you use a logarithmically spaced frequency axis, you should normalize your PSI values by the bandwidth corresponding to each frequency bin.

Best,

Daniel

On 01.03.2016, at 11:51, Hähnke, Daniel <daniel.haehnke at tum.de<mailto:daniel.haehnke at tum.de>> wrote:

Dear FieldTrip users,

I currently want to double-check the results I got from a non-parametric Granger-causality  analysis with another measure of directed communication, phase slope index.
However, after having read Nolte et al.’s paper from 2008 that introduced the PSI, I still don’t understand how to best choose the parameter cfg.bandwidth.

I tried out different values and got something qualitatively very similar to my Granger results. But this is rather fitting the parameter to the Granger results and kind of undermines my purpose of double-checking.

Furthermore, I am using a logarithmic (to base 2) frequency axis. Consequently, my frequency bins are not evenly spaced. I have the feeling that I would rather need different bandwidths for the individual frequency bins.

Does anyone know how to objectively choose the bandwidth parameter?

Best,

Daniel
--
Daniel Hähnke
PhD student

Technische Universität München
Institute of Neuroscience
Translational NeuroCognition Laboratory
Biedersteiner Straße 29, Bau 601
80802 Munich
Germany

Email: daniel.haehnke at tum.de<mailto:daniel.haehnke at tum.de>
Phone: +49 89 4140 3356<tel:%2B49%2089%204140%203356>


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