[Mne_analysis] Computing regression on sensor data then transforming to source space
Teon Brooks
teon at nyu.edu
Tue Feb 25 01:14:56 EST 2014
Hi,
Thank you Don, Hari and everyone else for your input and insight to my
question. I think it made for a very productive discussion and I now have a
better understanding of the things to consider when doing this.
Best,
Teon
On Friday, February 21, 2014, Krieger, Donald N.
<kriegerd at upmc.edu<javascript:_e(%7B%7D,'cvml','kriegerd at upmc.edu');>>
wrote:
> Thanks, Hari, for posting back and making it clear.
> I agree with your points to the extent that I follow them.
> I am pretty hazy about the effects of differing variances across the
> sensor measurements or the Betas computed from them on the MNE projections
> into the source space.
> Because of that and because the idea of applying regression across single
> trials on an independent task relevant variable is quite interesting and, I
> think promising, I had been thinking about applying it in the source space.
> If that works for a simple ANOVA, the means would represent mean
> neuroelectric currents and a statistical finding of a difference between
> two task conditions would imply that that source was differentially
> activated under the two conditions. That's what fMRI is about for
> neurovascular activity but with MEG, differential neuroelectric activation
> is much closer to what we conceive the brain is doing to accomplish the
> task.
>
> Our group has had success in generating 3D maps of differential activation
> using an even simpler chi-square test on a counting measure. Our first
> results just appeared in an open access journal: Intl J Advd Comp Sci (4)1:
> 15-25, 2014. But parametric statistics applied to dipole amplitude
> estimates has far greater potential statistical power. This discussion has
> spurred me to consider how to use that approach to amplify the power of
> those results.
>
> Thanks again.
>
> Regards,
>
> Don
>
> Don Krieger, Ph.D.
> Department of Neurological Surgery
> University of Pittsburgh
> (412)648-9654 Office
> (412)521-4431 Cell/Text
>
>
> > -----Original Message-----
> > From: Hari Bharadwaj [mailto:hari at nmr.mgh.harvard.edu]
> > Sent: Friday, February 21, 2014 9:36 AM
> > To: Krieger, Donald N.
> > Cc: mne_analysis at nmr.mgh.harvard.edu
> > Subject: Re: [Mne_analysis] Computing regression on sensor data then
> > transforming to source space
> >
> > Hi Donald,
> > Just to clarify, I did not intend to suggest that the betas in
> sensor and
> > source would be equal or equivalent... Apologies for any confusion
> caused..
> > What I meant in (A) below, was that the following would give identical
> > results if the regression is linear:
> > (1) computing beta values on sensor data (1 sensor at a time separately
> )
> > and computing the inverse solution with these beta values to get "source
> > beta" values..
> > (2) computing inverse solution of the original MEG data and then
> computing
> > "source beta" values directly by fitting the regression (1 source at a
> > time)...The "source betas" in the two cases are what I think will be
> identical.
> >
> > Regarding the noise variance, the discussion that I articulated was
> with the
> > problem of source estimation in mind. Hence it was about specifying the
> > noise covariance matrix for MNE (which was Denis's concern, I think)
> rather
> > than about statistical inference on the betas. The assertion is that if
> the
> > regression/ANOVA model is simple enough such that the sensor betas are
> > linear combinations across trials (or trial groups) AND if the weights
> for the
> > linear combination are normalized, then the noise covariance in the
> betas is
> > the same as the noise covariance of the original trials (or trial
> groups) that
> > went into its calculation (and hence the originally planned scaling of
> noise
> > covariance for MNE purposes would still be appropriate). I too, only
> > thought about the regression/ANOVA as being done on one sensor at a time
> > or one source at a time... Even with this relatively simple "mass
> univariate"
> > approach, if the model being fit is complex or has many terms the
> > relationship between the variance of the noise in the beta values and the
> > variance of the noise in original MEG/EEG data gets complicated and
> inverse
> > estimation could suffer.
> >
> > How to do parametric inference in source or sensor space by correctly
> > accounting for across sensor or across source variance inhomogeneities
> is a
> > whole issue on its own and is likely one with many complexities. If I
> > understand correctly, that is the question you have posed?
> >
> > Best,
> > Hari
> >
> > Hari Bharadwaj
> > PhD Candidate, Biomedical Engineering,
> > Auditory Neuroscience Laboratory
> > Boston University, Boston, MA 02215
> >
> > Martinos Center for Biomedical Imaging,
> > Massachusetts General Hospital
> > Charlestown, MA 02129
> >
> > hari at nmr.mgh.harvard.edu
> > Ph: 734-883-5954
> >
> > > On Feb 21, 2014, at 7:26 AM, "Krieger, Donald N." <kriegerd at upmc.edu>
> > wrote:
> > >
> > > Hi everyone,
> > >
> > > First with regards the continuing discussion of regression models which
> > include both scaled and categorical variables, etc.: There are general
> > purpose open sources statistical packages, e.g. R, which implement ANOVA,
> > ANCOVA, MANCOVA, etc. in the general linear model format, i.e. the one
> > we are discussing. It therefore might be worth evaluating one or more of
> > them for development of python wrappers which use them to do the
> > regressions we are discussing.
> > >
> > > Second with regards both the equivalent variance discussion and the
> > assertion of the equivalence of computing the Betas in sensor or source
> > space: Perhaps I am misunderstanding. I had just assumed that the
> > regression on an independent variable was to be for one sensor at a time.
> > Thus in the statistical framework the problem could be handled as a
> > MANOVA with the sensor measures being multiple dependent variables or
> > as a repeated measures ANOVA where the sensor measures are repeated
> > measures. In neither case though would regression on the independent
> > variable against a source be conceptually equivalent or give the same
> > answer. i.e. against a linear combination of the sensors,
> > >
> > > For the MANOVA approach, the regression against each sensor is handled
> > separately. So I think that at least the differences in variances
> across the
> > sensors don't matter. What do you think? I don't write with the voice
> of
> > authority here and would like to understand this.
> > >
> > > Don
> > >
> > > Don Krieger, Ph.D.
> > > Department of Neurological Surgery
> > > University of Pittsburgh
> > > (412)648-9654 Office
> > > (412)521-4431 Cell/Text
> > >
> > > ________________________________________
> > > From: mne_analysis-bounces at nmr.mgh.harvard.edu
> > > [mne_analysis-bounces at nmr.mgh.harvard.edu] on behalf of Hari
> > Bharadwaj
> > > [hari at nmr.mgh.harvard.edu]
> > > Sent: Thursday, February 20, 2014 10:57 AM
> > > To: Denis-Alexander Engemann
> > > Cc: mne_analysis at nmr.mgh.harvard.edu
> > > Subject: Re: [Mne_analysis] Computing regression on sensor data then
> > > transforming to source space
> > >
> > > Hi Denis et al.,
> > > It appears to me that there are two separate issues being confused
> > > here and perhaps there will be some clarity if we talk through it:
> > >
> > > (A) Whether to compute "betas" in sensor-space or source-space:
> > > This is not really a difficult question within the MNE or other
> > > linear inverse solution framework. Because, for a given inverse
> > > operator (let's call it M), computing betas in sensor or source space
> > > should lead to identical results unless the statistical model being
> > > fitted to compute the betas is somehow non-linear.
> > >
> > > (B) Choice of the noise model used to compute the operator M:
> > > This issue is more subtle and important and does not depend on the
> > > sequence in wh
--
--
Teon
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