Hello, it seems to me that requireing the design matrix to be perfectly
orthogonal within trial type (which occurs in spm_fMRI_design() on line
286) causes an issue when combined with rapid events and FIR models. for
example, take the following code:
>> temp=[eye(5);zeros(9,5)];
>> temp2=[zeros(4,5);eye(5);eye(5)];
>> test=temp+temp2
test =
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
1 0 0 0 1
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
this would represent an FIR model of order 5, where the 2nd trial is
spaced only 4 TRs after the 1st. Because this spacing is less than the
order, they two collums are not perfectly orthogonal...
>> spm_orth(test)
ans =
1 0 0 0 -.33
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
1 0 0 0 .66
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
1 0 0 0 -.33
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
These distortions carry through to the final design matrix.
Is there a good reason why spm needs to make and FIR set perfectly
orthogonal? Wouldn't jittering the trial separation be enough to achieve
accurate estimations of the betas? The consequence of the current
behavior would seem to be an inflation of the betas for the early
ordered FIR covariates, which would lead to a an inaccurate estimation
of HRF shape.
-Kevin Hill
--
Kevin T. Hill
Ph.D. Candidate
Lee Miller's Lab
Center for Mind and Brain
University of California, Davis
(530) 297-4426
http://mindbrain.ucdavis.edu/content/Labs/Miller/
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