On my MEG data, I detected activity that is sensitive to two regressors in sensor space using linear regression. I source projected the beta values obtained in using a minimum-norm beamformer to determine the source responsible for the target-activity. My first question is can I do source projection from beta values or not? and why?
My second question concerns the way I do source projection and linear regression: either I compute linear regression on sensor space and then I project on source space, or I project single-trial activity on source space, and then I compute linear regression. I observed similar results in both cases, but (i) computation time for the first option is much faster, and (ii) I found that source projected the beta values led to an increase in the signal-to-noise ratio (SNR) of our results in comparison to compute the beta from source activity. Do you know why the SNR is higher in one condition in comparison to the other? Do you think that computing the beta from the source activity is more correct than source-projecting the beta values computed in the sensor space? and why?
Both approaches are correct because linear regression applies a linear transform to the sensor data, and source projection is just another linear transform. That said, the source projection linear kernel is optimized (in terms of SNR) for sensor data. It is hard to predict what would be the effect of applying it on beta coefficients, which in essence correspond to a higher-SNR (filtered) version of the data: It might actually do what you describe, which is an overestimation of the SNR wrt what is actually present in the sensor data.
Apologies for resurrecting this old thread, but I want to do something similar and double check whether the approach makes sense.
On the scalp level, I'm computing regressions between each EEG datapoint (i.e. each sample and channel of each single trial) and a behavioral variable. The resulting beta values yield some interesting spatial and temporal patterns, which I would like to localize at source level. Can I treat the betas the same way as raw amplitudes and perform a dSPM or sLORETA sourceloc with them?
I'm asking since I read on other brainstorm threads that source localization is not correct after Laplacian transform, as '...the minimum norm estimates requires the EEG in the original physical units.' (quote from Francois) and 'The source maps can only be legitimately obtained with the original sensor data. Doing otherwise would violate the physics of forward/inverse modeling and yield invalid results.' (quote from Sylvain)
Can I treat the betas the same way as raw amplitudes and perform a dSPM or sLORETA sourceloc with them?
No, you can't apply the Brainstorm inverse routines to anything but MEG, EEG or NIRS signals. Multiplying regression coefficients with the inverse models computed with Brainstorm will not give any meaningful results.
Thanks so much for your quick and helpful reply!
I would have 2 short follow up questions:
1.In that case, I assume a workaround (although computationally very expensive) would be to first perform a source inversion of the EEG signal, and then compute the regressions at source level?
2. What about arithmetic differences in EEG amplitude between 2 conditions? These are not 'actual' EEG signals anymore and might have very different statistical properties than the original data. is it also problematic to compute sources for such condition differences?
In that case, I assume a workaround (although computationally very expensive) would be to first perform a source inversion of the EEG signal, and then compute the regressions at source level?
You could try that, maybe using a few ROIs (not all the thousands of source time series).
But you probably would not obtain better results that the EEG directly. Maybe you'd get better results by using the two information in parallel, e.g. using your regression results to identify when you have elements of interest in the brain response, and visualizing the estimate sources at this latency.
What about arithmetic differences in EEG amplitude between 2 conditions? These are not 'actual' EEG signals anymore and might have very different statistical properties than the original data. is it also problematic to compute sources for such condition differences?
The subtraction is a linear operation, that can be permuted with the linear Minimum Norm source estimation: MNE(A)-MNE(B) = MNE(A-B).