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Steve - thanks for your reply.
With the help of Darren Gitelman, I have figured out where we went wrong.
Our data was a very good, bad example, of how to design an fMRI experiment - if anyone wants to use the figures I sent to illustrate that, feel free :)
I'll try and answer your points though:
>
> If each run is 10*3 = 30 s, why use a HPF with a cutoff of 128 s?
>
We used the recommended formula of 2 x (A + B) x TR, where A (10) and B (10) are the number of scans for the two conditions. However, that would probably make more sense if the scans were in the *same session*, I concede, but they were in separate sessions.
> I can't tell exactly what the regressors are.
>
> Are the regressors
> (1) the effect of convolving entire blocks (which are entire
> sessions) with the HRF (for each type, A and R), and
> (2) session effects?
Yes, and yes.
> That's what it looks like to me (except that I would have
> thought the rightmost session effect regressors to be only 1
> or 0, whereas in the grayscale schematic they don't look
> perfectly white in the light blocks).
I'm not sure how SPM2 models confounds. However, when you run the mouse over the design matrix it appears that the values in the session-specific confound blocks relate to individual scans - I'm guessing they represent the mean value or each. However, you are right - the end and start of the confound blocks seem to "overshoot" the data between second and second-last scans. I don't know why! (Unlike in the modeled condition-specific regressors, where there's the expected initial undershoot, followed by an overshoot)
> If so, the problem as I see it is that if you take a boxcar
> representing one of the blocks---which is also one of the
> sessions---and convolve it with the (canonical) HRF, you'll
> get "almost" another boxcar back. Not quite, because there
> is some lead-in and lead-out at the edges of the block. (If
> you take a really long block, longer than the characteristic
> time of the HRF, and convolve it with the HRF, this would be
> much clearer.)
I agree, but prescribing the design in this manner was appropriate as each session only contains one condition (block) so a boxcar regressor was appropriate.
> That means for any given session, the regressor formed from
> the session (convolved with the HRF) isn't all that
> dissimilar from the regressor equal to the block effect.
Exactly.
> That's a problem, because then the regressors are highly
> confounded. If you conduct t-tests, you "miss out" on
> variance. A good reference in the context of neuroimaging is
> Andrade et al., "Ambiguous Results in Functional Neuroimaging
> Data Analysis Due to Covariate Correlation,"
> _NeuroImage_ 10, 483-6 (1999). (This is also mentioned in
> stats books, e.g. Netter et al.'s book on linear models,
> though you have to hunt to find it.)
>
> And to the extent the regressors are not the same, you're
> just measuring the "edge effect" of the lead-in and -out of
> convolving with the hemodynamic response, which isn't right
> from a modeling point of view (IMO).
Thanks a lot for your help - I'll look up that reference!
Regards - Mike