Hi Jack,

well, your explanation is very helpful. Now I’m wondering how significant an interaction is, even if it is statistically valid, when it’s highly rank deficient with the main EVs. The main EVs are not or negligible correlated among themselves, however. Is there still a message in the interaction EVs, or should I rather remove them?

Thanks,
Georg

________________________________________
Von: FSL - FMRIB's Software Library [[log in to unmask]] im Auftrag von Jack Grinband [[log in to unmask]]
Gesendet: Dienstag, 2. Juni 2009 02:44
An: [log in to unmask]
Betreff: Re: [FSL] Orthogonalising interactions

Hi Georg,
It is very difficult to explain the meaning of voxels that are correlated to
the orthogonalized variable because orthogonalization changes its shape.  It
is thus no longer related to the psychological or physiological
variables/processes that were used to create it.  The orthogonalization
process is useful when you need to construct an optimal statistical model.
However, under most circumstances, one is more interested in constructing a
physiologically plausible model.  If it turns out that the variables of
interest are highly correlated, resulting in a rank deficient design matrix,
then it becomes necessary to change the experimental design such that those
variables are orthogonal or to limit your interpretation of the data i.e.
conclude that the activity can stem from either or both of the correlated
variables.
BTW, if you have a rank deficient matrix, the statistics are still valid.
However, they may not generalize across samples.
Hope this helps,

jack

On Tue, 2 Jun 2009 01:47:30 +0200, G. Homola
<[log in to unmask]> wrote:

>Hi All!
>
>Does it make sense to orthogonalise an interaction wrt the components (main
EVs) of that interaction? Is the regressor more or less plausible and
explainable then? To my mind orthogonalising is inevitable when the
interaction regressor is strongly correlated with the main EVs, else the
results become too ambiguous. On the other hand the more EVs I orthogonalise
with, the less probable it becomes to find activations with that regressor.
Is that right, or is there something really bad about orthogonalising
especially in combination with interactions I don’t take into consideration?
>
>Thanks in advance
>Georg