Dear Cedric,
>I have a couple of questions regarding the parametric modulations. After
>specifying the weights for each parametric modulator, I took a look at
>the time domain regressors that are effectively created by SPM2 (?Review
>design? option), and I noticed that the weights for each of the stimulus
>for the parametric modulators were not the same as the ones I specified.
>Typically when you have one condition and two parametric modulators, the
>weights of both parametric modulators are mean corrected, and the
>weights of the 2nd modulator are orthogonalized with respect to the
>first parametric modulator (Is that correct? If so, what is the
>orthogonalization method used?). I also noticed that all the regressor
>have a different amplitude ? how is that amplitude calculated?
All stimulus functions are orthogonalized (within trial-type) in spm_get_ons
% orthogonalize inputs
%---------------------------------------------------------------
u = spm_orth(u);
spm_orth uses a Gram-Schmidt scheme
% recursive orthogonalization of basis functions
% FORMAT x = spm_orth(X)
%
% serial orthogionalization starting with the first column
%_______________________________________________________________________
% @(#)spm_orth.m 2.1 Karl Friston 02/02/07
x = X(:,1);
for i = 2:size(X,2)
D = X(:,i);
D = D - x*(pinv(x)*D);
if any(D)
x = [x D];
end
end
The amplitude of the stimulus functions is not changed, other than by
removing components that can be predicted by the 'subordinate' stimulus
functions.
>Next, I specified a 2nd design where I switched the order of the two
>regressors (the model still remains the same). Although this will create
>a different design matrix (now my ?first? parametric regressor is
>orthogonalized with respect to the ?second? one), the statistical
>activation map should not change. But that is not what I got: the main
>activated areas remained the same, but individual voxels had different
>t-values. That really confused me: should I not get exactly the same
>results in both cases? Or does the order of the regressors matter?
The order does matter because there is no unique orthogonalization
that does not depend on some ordering. The first parameter estimate
will not change with orthogonalization, but the second will. When you
switch the order you reveal this change. The orthogonalization was
introduced primarily to enable orthogonal polynomial expansions of
the parametric effect. If you want to switch it off, simply comment
out the call to spm_orth in spm_get_ons.
I hope this helps - Karl
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