[Mne_analysis] Computing regression on sensor data then transforming to source space
Alexandre Gramfort
alexandre.gramfort at telecom-paristech.fr
Thu Feb 20 01:57:31 EST 2014
hi Don,
thanks a lot for sharing these insights.
Although I get the idea of what you suggest, I am not sure
I would be able to perfectly replicate this analysis.
Do you happen to have a script you could share?
Also can you give the full ref from which the figure is extracted?
thanks again
Best,
Alex
On Wed, Feb 19, 2014 at 8:30 PM, Krieger, Donald N. <kriegerd at upmc.edu> wrote:
> Dear Teon,
>
>
>
> You have raised several interesting questions on which I would like to
> expand.
>
> Hari responded to several technical issues, viz. (1) constraints on what you
> do to retain the validity of your subsequent projection into source space
> and (2) weighting the regression to compensate for unequal numbers of trials
> for different levels of the independent variable.
>
>
>
> Here are some points about the meaning of what you are doing and about the
> technical issues.
>
> (1) If the independent variable is scaled rather than a 0/1 dummy, i.e.
> has multiple numeric levels, then your regression is asking a specific
> quantitative question about the amplitude of the magnetic field/source, i.e.
> is the amplitude a linear function of the independent variable? If for
> example the variable takes values n and 2n, you are asking: "Is the
> amplitude for the "2n" trials double what it is for the "n" trials?
>
> (2) I think it's reasonable to assume that many of the sources
> contributing to the magnetic field have nothing to do with the task.
> Although you are working with single trial data, your regression across the
> trials is collapsing the data in a generalized version of averaging. That
> helps attenuate the contributions to the field of unrelated sources. But if
> (a) there was a way up front to define regions of interest within the brain
> which you think are involved in the task, and (b) if the linear hypothesis
> you are testing is true, you should do better by doing the projection first
> and then doing the regression on the vertices within one ROI at a time. In
> that way you take advantage of the signal space separation capabilities of
> your projection operation to isolate the sources you think are involved. If
> you want to get formal statistics from your regression, you must find a way
> to adjust the degrees of freedom since presumably the source estimates from
> nearby vertices lack independence.
>
> (3) Multidimensional regression: I presume that you are doing your
> regression for a single time point, tau. Or perhaps you are averaging the
> amplitude values centered on the peak. In either case you get a single
> number for each magnetic field sensor for each trial. Instead you could use
> multiple points about the center of a peak and use a low order polynomial of
> tau multiplied by your original independent variable. Note that averaging
> is equivalent to using a zero-order polynomial. If you use say 21 data
> points centered on the peak, you increase your degrees of freedom by quite a
> lot. Of course your 21 data points lack independence but you still are
> using more information to do the regression.
>
> (4) The more important additional variable is along the time axis for
> the sequence of trials. If you use a polynomial function for that, any
> non-zero Beta other than the zero-order one represents a nonstationarity in
> your measurements. This is rarely assessed but with humans doing a task is
> always a concern and it's interesting too. The attached figure illustrates
> ideas (3) and (4) with evoked potential data.
>
>
>
> I hope I'm understanding you correctly and that this is helpful.
>
>
>
> Regards,
>
>
>
> 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
> [mailto:mne_analysis-bounces at nmr.mgh.harvard.edu] On Behalf Of Teon Brooks
> Sent: Wednesday, February 19, 2014 12:34 AM
> To: mne_analysis at nmr.mgh.harvard.edu
> Subject: [Mne_analysis] Computing regression on sensor data then
> transforming to source space
>
>
>
> Hi MNE listserv,
>
>
>
> I have single-trial data that I would like to regress a predictor (let's say
> word frequency) on it and then compute a source estimate. I'm planning to
> use mne-python to do this computation. I was wondering if I could do the
> regression over single trial sensor data first, get the beta values for each
> sensor over time, and then compute the source estimate as if it were an
> evoked object.
>
>
>
> My presumption is that it should be fine if the source transformation is
> linear. The other option would be to source transform the data then do the
> regression but the problem with doing this first is that computing the
> source estimates is more demanding on memory (say about 1000 trials with the
> around 5000 sources over 600-800ms of time). It would be more efficient if
> this computation could be done first if it is not computationally ill.
>
>
>
> What are your thoughts?
>
>
>
> Best,
>
> --
>
> teon
>
>
>
>
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