Dear FSL developers and experts,
I have a question concerning how orthogonalisation is done in FSL, and
in particular what happens when multiple (in my case two) regressors are
orthogonalised with respect to one another.
In FSL, when I orthogonalise one regressor (EV), say A, with respect to
another, B, then indeed A changes to A' so that A' is orthogonal to B. I
confirmed this by extracting the columns in question from the design.mat
file. This makes sense.
However, if I create another analysis in which I orthogonalise A with
respect to B *and* also orthogonalise B with respect to A, then
something happens that I don't understand. I expected that A would be
changed to some A'' and B would be changed to some B'', so that A'' and
B'' are orthogonal. However, what I find in the design.mat file is that
in that case, A is orthogonalised w.r.t B. but B is left unchanged. In
other words, B has retained all the shared variance between A and B. If
I swap the order of the EVs in the GUI, and, same as before,
orthogonalise both regressors with respect to one another, the result is
different: now A remains unchanged and B is orthogonalised w.r.t. A.
In other words, if I specify in the GUI that I want two EVs to be
orthogonalised w.r.t. one another, then really what seems to be
happening depends on the order of the EVs in the GUI, with the latter
being unchanged.
My question is: (1) did I observe this behaviour correctly, and (2) can
you explain why this makes sense? The pattern of findings that I
describe above was counter-intuitive to me, because I believed that by
orthogonalising both regressors with respect to one another, both
regressors would change in some symmetric way. Instead, only some of the
regressors change, and which those are depends on the order in which
they are entered into the design matrix.
I tried to find specifications of how FSL performs orthogonalisation,
but was unable to find any mathematical details, so this is why I
resorted to trying out these various items.
Thanks in advance for any explanations.
Best wishes and thanks for your work on developing FSL,
Floris
--
Floris van Vugt, Ph.D.
Motor Control Lab, Psychology Dept.
McGill University
1205 Dr. Penfield Ave
Stewart Biology Building
Montreal QC Canada H3A 1B1
www.florisvanvugt.com
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