Hello Cornelius,
The negative beta weight at t-1 means that in order to best fit the
actual signal something had to be subtracted from the response estimated
by the t-2 beta weight (and vice verse for the region with the inverse
pattern).  What you are observing is the model simply finding the best
fit to the actual response, given the regressors that you've supplied.
It is very difficult to meaningfully interpret the individual beta
weights of highly correlated regressors -- the results are unstable and
can be changed dramatically by just subtle changes in the underlying
data.  What is the correlation of t-2, t-1, and t0 regressors?

cheers,
-Mike H.

On Fri, 2010-04-23 at 11:34 +0200, Cornelius Werner wrote:
> Dear list,
> 
> I am somewhat puzzled by a review I got and really can't wrap my head
> around this. Perhaps this is because I am just a physician - maybe you
> can help me see the error of my ways :-)
> 
> We performed an fMRI experiment by scanning a patient population. They
> exhibited frequent spontaneous behavior, which we recorded and entered
> into the GLM as the first regressor. As we were interested in
> preparatory brain activity, we added two more regressors, preceding
> the behavioral regressor by one and two seconds, respectively, each
> with one second duration. Events were frequent enough and jittered
> enough to allow for some sort of rapid event-related design.
> This of course resulted in a design with three quite correlated
> regressors (lets say t-2, t-1 and t0). Thus, we did not model
> derivatives. The design matrix itself was still judged to be estimable
> by FSL. While I am aware that using such a setup in a whole-brain
> analysis in theory can yield strange results, we did obtain quite
> reasonable activations, corrected for multiple comparisons with voxel
> z>2.0 and p=0.05. Our results are anatomically meaningful and
> replicate (in part) previous observations.
> 
> Crucially, in one of these activations, we see a significant positive
> beta weight at t-2, a negative beta weight at t-1, and no effect at
> t0. Another region shows the inverse pattern. One reviewer pointed out
> that, according to the signal properties of the HRF, such a signal
> could not be possibly observed. This is what astounded me somewhat. I
> was of the opinion that the BOLD effect is at least assumed to be
> additive. Isn't that the prerequisite for linear contrasts? Our
> methods folks couldn't help me out on this, so I am really interested
> in a clarification on this matter.
> 
> Thank you very much!
> Cornelius
>