# [FieldTrip] Phase Slope Index: How to choose bandwidth

Prasandhya Astagiri Yusuf prasandhya.a.yusuf at gmail.com
Wed Mar 9 09:49:07 CET 2016

```Hi Daniel,
I mean it is known that the EEG bands have different frequency bandwidth,
like:

- Theta 4-7 Hz -> 4 Hz bandwidth
- Alpha 8-15 Hz -> 8 Hz bandwidth
- Beta 16-31 Hz -> 16 Hz bandwidth

So in my opinion, I think it's not really fair to have (in example) 5 Hz
bandwidth configuration in measuring PSI for Theta, even Delta, since it
(probably) mixed other oscillation band together.

In Field Trip's PSI, I found that the cross spectra S(f) are multiplied
with the conjugate cross spectra of the neighboring-higher-frequency bin
S*((f+1) to have phase lag difference between neighboring frequency bins
(or yields frequency slope if divided by the frequency resolution). Then it
sums together the results within 2 Hz above and 2 Hz below (for 5 Hz
bandwidth example). Finally it takes the imaginary part from the result.

If the phase lag difference between neighboring frequency bins (or the
frequency slope) are consistent for all results within this 5 Hz bandwidth,
then it yields high value. If they are inconsistent, they should not yield
high value. But what if the result is quite high that we then interpret as
a directionality, but it was only due to mixed up of positive and negative
values..? I still cannot answer this one. Maybe someone could help.

Best,

Sandhy

On Tue, Mar 8, 2016 at 10:57 AM, Hähnke, Daniel <daniel.haehnke at tum.de>
wrote:

> 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> 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>
> wrote:
>
>> Hi Jan-Mathijs,
>>
>> 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> 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.
>>
>> 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> 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
>>
>> Best,
>>
>> Daniel
>>
>> On 02.03.2016, at 14:05, Schoffelen, J.M. (Jan Mathijs) <
>> 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> 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> 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
>> Phone: +49 89 4140 3356
>>
>>
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