Hi Josee
> I have read several threads (and a couple papers) on the use of temporal and dispersion derivatives, but would like to clarify how derivatives are included in/applied to a model.
>
ok I'll try to answer - hopefully if all ok Rik won't have to answer
this .. :-P
> 1. Are there multiple HRFs tested at each voxel (e.g.., the canonical HRF, time-modulated HRFs and/or dispersion-modulated HRFs)? If so, is it possible that different HRFs would be retained for different voxels (e.g., the canonical HRF for voxel A and a time-modulated HRF for voxel B)?
>
yes it creates 3 regressors per conditions ie 3 different models of
response; for each voxel the 3 regressors are fitted to the data (so
data are explained by a linear mixture of the 3) but yes it possible
that data in one voxel data are better explained by the hrf, in another
voxel better explained by a derivative
> 2. Or are the derivatives regressors in the model for the HRF, i.e., variables that can account for and thus reduce error/variance, much like a covariate? This would imply that only one HRF is modeled at each voxel, but time- and dispersion-related variance between voxels is taken into account in the model, correct?
>
well yes and no ; yes having 3 regressors now will reduce your error and
yes/no as you can look at the effect of each regressor (everything that
you through in the model accounts for some variance) - also note that
because these are basis functions they are orthogonal to each other and
therefore derivatives only explain some variance above what is explained
by the hrf only (unless you use this in a block design which mixes
things up ... search for an old e-mail from J Andersson)
> 3. If derivatives are error-reducing regressors, why are they represented as independent columns (1 for time, 1 for dispersion, for each condition) in the design matrix? Relatedly, when F-contrasting 2 conditions (say, A and B), why is it necessary to explicitly include the derivatives in the contrast specification (e.g.: 1 1 1 -1 -1 -1 for the A minus B contrast)?
>
as explained above they form 3 regressors so they make 3 columns in X -
the F contrast has to oppose basis functions one by one ie [1 0 0 -1 0
0;0 1 0 0 -1 0;0 0 1 0 0 -1] otherwise you are looking for a combination
of vectors that explain different things (amplitude, latency,
dispersion) using different rows means find voxels where A and B differ
for the hrf and/or the latency and/or the dispersion - the contrast you
entered mixes all together (like averaging amplitude+latency+dispersion)
> 4. Lastly, is there any reason derivatives should NOT be included in a 1st-level analysis (testing for fixed effects in a small group of subjects, n=5)?
>
I cannot think of any - seems a good idea to me ...
Cyril
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