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SPM  March 2009

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Subject:

Re: How do regressors compete for variance if not orthogonalized?

From:

"Dorian P." <[log in to unmask]>

Reply-To:

Dorian P.

Date:

Mon, 9 Mar 2009 12:15:49 +0100

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (189 lines)

Dear SPMers,

First, thanks to Cyril and the other participants who were interested
on the topic. I found a solution to the orthogonalization problem
which would like to discuss with you.

First commenting out the spm_orth line in (1) spm_get_ons.m and (2)
spm_fMRI_design.m doesn't seem a good idea because vectors are not
even normalized. Reaction times have values ranging 1-5000 while other
regressors have values ranging 1-5. As far as I know this may
compromise seriously the results (they did in my case).

A solution can be simply to normalize without orthogonalizing but I
followed another procedure. I orthogonalized  each pmod regressor with
its main condition (instead of serially in sequence). Another thread
also talks about it:
https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind0811&L=SPM&P=R3144

To do this I modified orthogonalization procedure like this.:
#####################################################
function X = spm_orthonlyfirst(X,OPT)
try
    OPT;
catch
    OPT = 'pad';
end

% recursive GM orthogonalisation
%--------------------------------------------------------------------------
sw = warning('off','all');
[n m] = size(X);
i     = find(any(X));
X     = X(:,i);
try
    x     = X(:,1);
    x1     = X(:,1); %  ---------------------- added
    j     = 1;
    for i = 2:size(X,2)
        D = X(:,i);
        % ---------------------- removed %  D = D - x*(inv(x'*x)*x'*D);
	  D = D - x1*(inv(x1'*x1)*x1'*D); % ---------------------- added
        if norm(D,1) > exp(-32)
            x          = [x D];
            j(end + 1) = i;
        end
    end
catch
    x     = zeros(n,0);
    j     = [];
end
warning(sw);

% and normalisation, if requested
%--------------------------------------------------------------------------
switch OPT
    case{'pad'}
        X      = zeros(n,m);
        X(:,j) = x;
    otherwise
        X      = spm_en(x);
end
----------------------------------------------------------------
#########################################################

Can somebody please confirm this is correct?


Then, I would appreciate some references on why common variability
between non-orthogonalized regressors is lost... Or how signal is
assigned to one regressor instead of the other? This would be useful
to sustain my results.

And, does anybody know where (in which file) SPM adds the 2nd order
regressor of a parametric modulation? We need to make a strange design
where modulations are not orthogonalized but different orders are. So
we can create groups of concurrent modulations A(1st, 2nd), B(1st,
2nd), who can explain as much as possible variability on their own.


Any kind of comment or help is greatly appreciated.


Dorian.








2009/3/4 Amitai Shenhav <[log in to unmask]>:
> Hi Cyril and Dorian,
>
> Thanks so much for the input (and the great references). I take your point
> that using this optimized approach will necessarily entangle effects of RT
> into subsequent parametric measures so is unlikely to allow for an explicit
> control over its effect prior to subsequent othogonalization.
>
> Thanks again for indulging my curiosity!
>
> Amitai
>
> On Wed, Mar 4, 2009 at 10:56 AM, Dorian P. <[log in to unmask]> wrote:
>>
>> Dear Cyril and Amitai,
>>
>> Just so support Cyril's answer. In a variable epoch approach you are
>> dealing with HRF duration, not amplitude. Alternatively, in a
>> parametric modulation you are dealing with amplitude changes, not
>> length. The paper above and these ones:
>> http://www.columbia.edu/cu/psychology/tor/Posters/grinband_HBM06.pdf
>> http://www.fmri.org/pdfs/RT%20in%20fMRI.pdf
>>
>> show that RTs has to do more with HRF length, instead of amplitude.
>> Their method is better to capture RTs regressors. However optimizing
>> the model to check RTs and then trying te remove them with a
>> parametric modulation will have the opposite effect. The modulation
>> will catch much less variability in amplitude because it's actually
>> explained in length. Then the following regressors will have a lot of
>> RTs effect (even though orthogonalized) because it is inherent to the
>> model and cannot be removed.
>>
>> Hope I'm right and this helps.
>> Regards.
>> Dorian
>>
>> 2009/3/4 cyril pernet <[log in to unmask]>:
>> > Hi Amitai
>> >>
>> >> Hi Cyril,
>> >>
>> >>    There was a recent paper, in neuroimage I think, where RT of each
>> >>    trials was used to model the hrf (instead of 0 modeling an
>> >>    inpulse) and this model was compared with a standard approach (1
>> >>    column for the regressor + modulation by RT) -- clearly it was
>> >>    better to directly 'modulate' the 1st regressor, but it may not
>> >>    always be possible to do so ..  cannot think of anything else here
>> >> ...
>> >>
>> >>
>> >> I would love to get the reference for the paper you mentioned if you
>> >> happen to have any more information about it.
>> >
>> > Dorian pointing me the paper I was referring to
>> >
>> > Grinband et al, Detection of time-varying signals in event-related
>> > fMRI designs, NeuroImage, Volume 43, Issue 3, 15 November 2008
>> >
>> > (http://www.sciencedirect.com/science/article/B6WNP-4T77G33-4/2/cc5ef4a8e9fbff5b4a99bd5f05663bf9)
>> >
>> >
>> >> Also, when the discussion is raised over the use of variable duration
>> >> HRF
>> >> and utilizing an RT regressor, they are generally suggested as
>> >> alternatives
>> >> to one another. Is there a concern regarding the use of both of these
>> >> in
>> >> unison (i.e., modeling the HRF with trial-specific RTs and then
>> >> regressing
>> >> out RT before adding additional parametric regressors)?
>> >>
>> > well you would model the hrf using RT so that it accommodates natural
>> > cognitive and motor related variations in the neural dynamic - of course
>> > you
>> > may loose some info regarding the sensorial/perceptive processing which
>> > would not vary according to this.. - anyway; now you try to regress out
>> > RT
>> > for each trial - how would you do that? even if you could, what would
>> > that
>> > mean? remember that the 1st part in about making a model of the hrf with
>> > variation in shape (time and amplitude) then you would try to regress
>> > out
>> > something like the amplitude or so ?? I'm really unsure about all this
>> > ...
>> > sorry
>> >
>> > cyril
>> >
>> >
>> >
>> >
>> > --
>> > The University of Edinburgh is a charitable body, registered in
>> > Scotland, with registration number SC005336.
>> >
>
>

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