We are running analyses on resting state MEG data and we are finding negative values in the weighted phase lag index (wpli) measure. We have also run this data using the phase lag index (PLI) measure and do not see any values below zero. I thought that both the PLI and WPLI should be defined from 0 to 1. Although the negative values tend to be small, we are seeing this across many subjects.
I don't know the implementation in MNE, but, as far as I know, the WPLI
ranges between between -1 and 1 (see Fig. 1C in Vinck, Neuroimage 2011).
The same is for the imaginary coherence (Nolte, Clin Neurophysiol 2004).
The strength of phase-synchronization can be indexed by the magnitude
(or squared value) of the WPLI.
bye
Andrea
Le 14-Jun-17 ? 7:51 PM, Eric Larson a ?crit :
Yes it looks like WPLI should be bounded by 0 and 1. Can you open an
MNE issue so we can look into it further?
Eric
We are running analyses on resting state MEG data and we are
finding negative values in the weighted phase lag index (wpli)
measure. We have also run this data using the phase lag index
(PLI) measure and do not see any values below zero. I thought
that both the PLI and WPLI should be defined from 0 to 1.
Although the negative values tend to be small, we are seeing this
across many subjects.
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Fig1C shows the individual vectors and how they're weighted -- I was
looking at Eq.8 which defines WPLI, and the paragraph that followed where
they state that 0 ? ? ? 1 holds (due to the absolute value operations in
the numerator and denominator). But maybe there is more to it or you don't
need to take the absolute value of the expectation in the numerator, in
which case it could be -1 ? ? ? 1, is that what you have in mind...?
When you get a chance, could you try to share some data (as small as
possible) and a small code snippet (using coherence-computing routines)
that show this problem to the related MNE issue I opened
<https://github.com/mne-tools/mne-python/issues/4319>?
Hopefully this helps rather than compounds your problem, but this also occurs when computing the debiased squared wpli, where there should undoubtedly be no negative values (unless the debiasing does something strange that I'm not aware of), just FYI. Generally, any negative values are small just as Jeff sees. However, out of a group of 57 subjects that I ran this on, I got a minimum value of -0.3954, which isn't all that small. I only mention this in case it is some shared routine between the wpli and wpli2_debiased that is generating these negative values. Hopefully the data you get from Jeff is enough to figure out what's going on, but I can supply more if need be.
this also occurs when computing the debiased squared wpli, where there
should undoubtedly be no negative values (unless the debiasing does
something strange that I'm not aware of), just FYI.
From what I recall the debiasing can indeed produce (generally small)
negative values, so that at least I would expect. From Vinck et al., 2011:
If the WPLI exceeds the PLI, then the debiased WPLI-square estimator will
be negatively biased for small sample sizes.
The WPLI, however, doesn't have this characteristic, and from what I've
seen in a brief look at the MNE code, I'm not sure where it could come from
(based on where we use abs()). So a minimal example would help us track it
down.
this also occurs when computing the debiased squared wpli, where
there should undoubtedly be no negative values (unless the
debiasing does something strange that I'm not aware of), just FYI.
From what I recall the debiasing can indeed produce (generally small)
negative values, so that at least I would expect. From Vinck et al., 2011:
If the WPLI exceeds the PLI, then the debiased WPLI-square
estimator will be negatively biased for small sample sizes.
The WPLI, however, doesn't have this characteristic, and from what
I've seen in a brief look at the MNE code, I'm not sure where it could
come from (based on where we use abs()). So a minimal example would
help us track it down.
Eric
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I'm not sure whether to respond here or to that Digest email that just got sent out, but Jeff appears to also be using the 'wpli2_debiased' method, according to the chunks of code that just got sent out:
And Eric seems to be correct that these values can indeed be negative. If you look at Fig. 12 of Vinck et. al 2011, their color mapping spans from -0.2 to 0.6, with the two bias measure (unbiased PLI2 and debased WPLI2) both appearing to reach negative values compared to the direct PLI2. So, if Jeff is truly using 'wpli2_debiased' as his method just as I am (as the code suggests), then there should be no bug.