Hi there,
I have a question regarding how best to statistically compare two
conditions. So far I have only being comparing between 2 conditions
using ROIs and comparing current estimates over time. However, I'd also
like to see the difference between two conditions across the whole
brain. I was wondering what the best approach to this was (Ideally
ending up with a dSPM map of condition1 - conditon2).
Any help on this would be appreciated
Thanks,
Alex Clarke
Why not first subtract one average response from the other and then
localize?
Because you are distorting the dipolar topographies when you do a
subtraction at the sensor level. The resulting data is likely contain
field patterns which do not relate to the leadfields of the actual
sources that gave rise to the data. Thus, any source reconstruction
which relies on lead field models, i.e. minimum norm, will give spurious
results.
-Padraig
Yury Petrov wrote:
I didn't understand Padraig's arguments. Minimum norm is a linear
method. This means that the same as for the forward matrix the inverse
matrix is calculated irrespective of the actual signals measured,
except for the noise covariance term. So if you add the noise
covariance matrices for the two conditions and feed the resulting
"difference" covariance matrix to the inverse routine, it will only
change the signal to noise ratios in the trivial way. But the matrix
will remain essentially the same, and the topography of the solution
should not be "distorted".
Not necessarily - the sensors pick up signals from multiple
generators following the superposition principle. This basically is
the sum of the products leadfield L_ij times dipole moment p_j plus
noise forming the magnetic induction B_i at sensor i
B_i = L_ij *p_j + n
If you subtract two field B1 and B2 and they share a common generator
- this one is excluded in sensor space. In theory this works
perfectly well in absence of noise.
Practically speaking this concept works pretty good for certain EEG
components like the ERN which is the difference between incorrect and
correct responses.
"Distortions" usually come from the noise term and generators not
being active in both conditions, or differently active in both
conditions. Additionally you have source model related distortions
e.g. regularisation.
So it depends mostly on your signal to noise ratio if it is wise to
subtract fields in sensor space or not.
It also depends on how accurate you can position the MEG helmet in
headframe coordinates across conditions, subjects, ...
If that can not be done reliably don't even think about subtraction
in sensor space. You just add additional variance to your data.
-Christian
Because you are distorting the dipolar topographies when you do a
subtraction at the sensor level. The resulting data is likely
contain field patterns which do not relate to the leadfields of the
actual sources that gave rise to the data. Thus, any source
reconstruction which relies on lead field models, i.e. minimum
norm, will give spurious results.-Padraig
Yury Petrov wrote:
Why not first subtract one average response from the other and
then localize?Hi there,
I have a question regarding how best to statistically compare
two conditions. So far I have only being comparing between 2
conditions using ROIs and comparing current estimates over time.
However, I'd also like to see the difference between two
conditions across the whole brain. I was wondering what the best
approach to this was (Ideally ending up with a dSPM map of
condition1 - conditon2).Any help on this would be appreciated
Thanks,
Alex Clarke
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Mne_analysis Info Page_______________________________________________
Mne_analysis mailing list
Mne_analysis at nmr.mgh.harvard.edu
Mne_analysis Info Page--
P?draig Kitterick
Graduate Student
Department of Psychology
University of York
Heslington
York YO10 5DD
UKTel: +44 (0) 1904 43 2883
Email: p.kitterick at psych.york.ac.uk_______________________________________________
Mne_analysis mailing list
Mne_analysis at nmr.mgh.harvard.edu
Mne_analysis Info Page
Christian Wienbruch
University of Konstanz
Clinical Psychology
Fach D27
78457 Konstanz
Christian.Wienbruch at uni-konstanz.de
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If one cannot assume similar source configurations in the two conditions
to be compared, presuming that any noise is constant and equivalent, is
it safe to say that subtraction would result in distorted data
('distorted' not the best choice of words but my vocabulary has failed
me today!), or at least data which would be difficult to interpret?
Thanks,
P.
Christian Wienbruch wrote:
Well you are right - that's what we see all the time. Even if you do
subtraction of incorrect and correct response to get the ERN - which
works well for a subset of EEG sensors in fronto-central locations -
in other regions not involved in the error processing you get
patterns difficult to interpret.
But condition comparisons or subtractions in source space must not
necessarily be more accurate - in case of minimum norm you "smear"
the currents following a mathematical minimization criterion - "the
minimum norm". Who says that the brain does work that way in a
particular task - minimizing the current. So it is difficult to say
what works best in terms of "best physiological model".
At that point - I usually don't care that much about the "most
accurate source localization" any more and look what is the best
measure to differentiate (e.g. conditions, groups) - once you've
ruled out all the trivial effects you've got a good chance to see
correlates of physiological differences. And if you can replicate
that I would call it "a reliable, valuable correlate", which does not
necessarily mean "true generator". It is rather a reasonable solution
from the infinite amount of inverse solutions, which is probably all
what we can expect in psychophysiology anyway.
Christian
If one cannot assume similar source configurations in the two
conditions to be compared, presuming that any noise is constant and
equivalent, is it safe to say that subtraction would result in
distorted data ('distorted' not the best choice of words but my
vocabulary has failed me today!), or at least data which would be
difficult to interpret?Thanks,
P.
Christian Wienbruch wrote:
Not necessarily - the sensors pick up signals from multiple
generators following the superposition principle. This basically
is the sum of the products leadfield L_ij times dipole moment p_j
plus noise forming the magnetic induction B_i at sensor iB_i = L_ij *p_j + n
If you subtract two field B1 and B2 and they share a common
generator - this one is excluded in sensor space. In theory this
works perfectly well in absence of noise.
Practically speaking this concept works pretty good for certain
EEG components like the ERN which is the difference between
incorrect and correct responses."Distortions" usually come from the noise term and generators not
being active in both conditions, or differently active in both
conditions. Additionally you have source model related distortions
e.g. regularisation.
So it depends mostly on your signal to noise ratio if it is wise
to subtract fields in sensor space or not.It also depends on how accurate you can position the MEG helmet in
headframe coordinates across conditions, subjects, ...
If that can not be done reliably don't even think about
subtraction in sensor space. You just add additional variance to
your data.-Christian
Because you are distorting the dipolar topographies when you do a
subtraction at the sensor level. The resulting data is likely
contain field patterns which do not relate to the leadfields of
the actual sources that gave rise to the data. Thus, any source
reconstruction which relies on lead field models, i.e. minimum
norm, will give spurious results.-Padraig
Yury Petrov wrote:
Why not first subtract one average response from the other and
then localize?Hi there,
I have a question regarding how best to statistically compare
two conditions. So far I have only being comparing between 2
conditions using ROIs and comparing current estimates over
time. However, I'd also like to see the difference between two
conditions across the whole brain. I was wondering what the
best approach to this was (Ideally ending up with a dSPM map
of condition1 - conditon2).Any help on this would be appreciated
Thanks,
Alex Clarke
_______________________________________________
Mne_analysis mailing list
Mne_analysis at nmr.mgh.harvard.edu
<mailto:Mne_analysis at nmr.mgh.harvard.edu>
Mne_analysis Info Page_______________________________________________
Mne_analysis mailing list
Mne_analysis at nmr.mgh.harvard.edu
<mailto:Mne_analysis at nmr.mgh.harvard.edu>
Mne_analysis Info Page--
P?draig Kitterick
Graduate Student
Department of Psychology
University of York
Heslington
York YO10 5DD
UKTel: +44 (0) 1904 43 2883
Email: p.kitterick at psych.york.ac.uk
<mailto:p.kitterick at psych.york.ac.uk>_______________________________________________
Mne_analysis mailing list
Mne_analysis at nmr.mgh.harvard.edu
<mailto:Mne_analysis at nmr.mgh.harvard.edu>
Mne_analysis Info PageChristian Wienbruch
University of Konstanz
Clinical Psychology
Fach D27
78457 KonstanzChristian.Wienbruch at uni-konstanz.de
<mailto:Christian.Wienbruch at uni-konstanz.de>--
P?draig Kitterick
Graduate Student
Department of Psychology
University of York
Heslington
York YO10 5DD
UKTel: +44 (0) 1904 43 2883
Email: p.kitterick at psych.york.ac.uk
Christian Wienbruch
University of Konstanz
Clinical Psychology
Fach D27
78457 Konstanz
Christian.Wienbruch at uni-konstanz.de
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Thanks Christian. This is really helpful. It is so challenging to fully
understand the limitations of what one is comparing, and how all of the
analysis steps up to that point have contributed to any effects that one
finds...
But it wouldn't be as much fun if it was easy 
-Padraig
Christian Wienbruch wrote:
You can ignore my comment. I was mistakenly thinking of non-linear
dipole fits. The solution for the difference data should be identical to
the difference between the solutions for the individual conditions as
long as the same regularisation parameter and noise covariance matrices
are used for both conditions so that the inverse operator is identical
in all cases.
-P
Yury Petrov wrote:
Hi Alex
For what it is worth, I thought about these kinds of questions some time ago
and presented a talk that was supposed to open up further discussion and
debate. The PDF of that talk is here:
http://www.nmr.mgh.harvard.edu/~daniel/links/presentation/stats_on_roi.pdf
It includes some basics on the mathematics and assumptions inherent in them.
Then the talk veers into the speculative with some thoughts on newer
possible methods for comparing conditions when you have multiple subjects
and multiple conditions.
I am still interested in developing these questions further, so let me know
if these ideas are helpful.
Daniel
Daniel, first of all, thanks for the great MNE review. Some typos that
I noticed:
page 30: remove Gaussian source distributions
page 33: theorm -> theorem
I find the MNE derivation based on Bayesian max-likelihood method
(e.g. in the Inverse Problem Theory book below) both simpler and more
satisfactory. In particular, it makes the nature of the MNE
assumptions much more explicit.
http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/Books/index.html
I don't see what's 'not cool' with subtracting dSPMs for two
conditions. dSPM is, essentially, a singnal-to-noise ratio. Assuming
that your noise was the same in both conditions (i.e. the same noise
covariance matrix) we just subtract signals, right?
Yury
Thank you for your comments. That textbook you mentioned looks very good.
Thank you for the link.
On the subject of subtracting F statistics, the more I think about it, the
more I wonder if it was premature for me to issue that blanket statement
that such a technique does not make statistical sense. Perhaps Yury, you are
right and we are simply looking at the difference in SNR for some cases.
The things that worry me still are:
- if a dipole were to rotate in a fixed position with a fixed amplitude,
what would that do in the subtraction case?
- when subtracting these F statistics, no account is made for temporal
relationships. So if I take the subtraction of two different time points
from the same source with a sinusoidal signal that are out of phase by 180
degrees, wouldn't this seem like one time point is more "significant" than
the other, when in fact you are looking at different phases of the same
thing?
- If the noise is not the same (i.e. when comparing two different sources),
what is the meaning of the subtraction? Does it relate to significance of
effect, or merely SNR due to anatomy/physics?
Maybe I am just too new to the field and am asking questions that have been
well picked over already. Anyone who can see where I went astray, please
feel free to chime in and straighten me out.
Daniel
- if a dipole were to rotate in a fixed position with a fixed
amplitude, what would that do in the subtraction case?
Daniel, you are right, this difference will be lost. But to me it
seems more reasonable to subtract electrode signals for the two
conditions first, then localize and do the F statistics on the
difference signal. So, for example, if a given dipole just changed its
orientation from inward in cond 1 to outward in cond 2, and you
subtract averaged potentials for cond 1 from cond 2, then the
difference will be localized as twice the outward current at the
dipole location.
- when subtracting these F statistics, no account is made for
temporal relationships. So if I take the subtraction of two
different time points from the same source with a sinusoidal signal
that are out of phase by 180 degrees, wouldn't this seem like one
time point is more "significant" than the other, when in fact you
are looking at different phases of the same thing?
Are you talking about comparing steady-state recordings in frequency/
phase domain? For regular ERPs the F statistics is calculated for each
timepoint in the recording, right? Of course, my assumption is that
one subtracts the conditions for the same timepoints.
- If the noise is not the same (i.e. when comparing two different
sources), what is the meaning of the subtraction? Does it relate to
significance of effect, or merely SNR due to anatomy/physics?
You are right. However, most experiments are done by running
interleaved conditions, each condition for 10 - 20 trials within the
same run of 15 - 60 minutes long. So the noise covariance should be
the same for all conditions. Also, in my (little) experience, the
difference in noise covariance matrices between different EEG
experiments is not that significant, given that you are using the same
head and the same net. It is probably even less significant for MEG,
where the electrode and magnetometer locations are fixed on the
helmet, and the environmental noise is, generally, better controlled.
It is important, of course, to multiply the noise covariance matrix by
2 (or really add the two covariance matrices) when doing F statistics
on difference signals.
Yury
Dear Daniel,
I was rereading your excellent dSPM intro, and have the following
degrees of freedom (DoF) question: what is the right number of DoF for
the noise in the F denominator? You say the number of the "baseline"
timepoints x 3. Where does this number of baseline timepoints come
from? Shouldn't it be just 3 (just as for the numerator), because we
add three variances? Also, if it was really not 3, then the correct F
value wouldn't be simply F = signal^2/noise^2 but F = signal^2 / 3 /
noise^2 / DoF_noise, i.e. the numerator and denominator would have to
be normalized by their respective DoFs, right?
Thanks,
Yury