Dear Dan,
There's actually no problem with having correlated regressors in the GLM.
It is not uncommon.
The difficulty is just one of statistical power for estimating certain contrasts
but the GLM takes all that into account. Substituting other versions of the
regressors (e.g. A-B) does not help, as the statistics for the equivalent contrasts
would be exactly the same.
So I would recommend that you just put A and B in the design matrix and
work from there.
Note that excluding a regressor from a design matrix (and running a smaller
matrix) will give different results, even if there is no correlation. With correlation
these differences tend to get bigger. This is because the designs cannot be
made to be equivalent and so you cannot expect to get the same results.
All the best,
Mark
On 9 Dec 2011, at 22:25, Daniel CM wrote:
> Hopefully there is a simple answer to this design problem.
>
> We have two correlated parametric regressors, A and B. I would like to compare their contribution to the BOLD signal with each other (A - B), and between sessions (e.g. A session 1 - A session 2 …then B session 1 - B session 2). Obviously, I can not put A and B in the same GLM, so I am wondering if there is a trick to be done with contrasts, using simple linear algebra…
>
> The difference between the values of A and B is C.
>
> So A - B = C.
>
> Can one then include only A and C in a model (which are not correlated), and then calculate signal associated with B with a contrast that looks like: +1 A -1 C ?
>
> Likewise, include B and C in the model and calculate signal associated with A, by +1B and +1C ?
>
> Calculating A with a contrast vs. a single regressor seems to give very different results at the subject and group level. We would very much like to understand why… and if there is another way of doing this, we would be very happy to hear them.
>
> Any ideas?
>
> Cheers,
> Dan
>
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