[Mne_analysis] Computing regression on sensor data then transforming to source space

[Krieger, Donald N.]

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> [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<mailto: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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