JISCMail - FSL Archives

Hi,

Just to add to this.
There is no single way to orthogonalise two EVs with respect to each other, as it is not really well defined. So almost all packages will do it serially, as we do. This is not usually a problem though as it is very hard to find a scenario where you would ever want to orthogonalise two EVs wrt each other. In fact, we recommend strongly against orthogonalisation in general, as there are very limited circumstances when it gives a sensible answer, and in other cases it often returns a biased/invalid/unwanted/inflated result.

All the best,
Mark

On 18 Mar 2017, at 11:57, Anderson M. Winkler <[log in to unmask]<mailto:[log in to unmask]>> wrote:

Hi Floris,

Yes, of course, sorry. Well, now you have one more reason not to use orthogonalisation!

All the best,

Anderson

On 17 March 2017 at 14:54, Floris van Vugt <[log in to unmask]<mailto:[log in to unmask]>> wrote:
Hi Anderson,

Thanks for your reply, this is very helpful for me. I appreciate your suggestion to manually orthogonalise the regressors. One thing puzzles me still, which is that in my understanding Rb*A and Ra*B (using your definition of them) will actually be correlated by exactly the same amount as A and B are, just opposite signs. i.e. corr(A,B)=-corr(Rb*A,Ra*B). So I don't yet see how exactly the proposal helps. Am I missing something?

Thanks again and kind regards,
Floris

===

Hi Floris,

This is described in the FEAT manual: https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/FEAT/UserGuide#Appendix_B:_Design_Matrix_Rules

If this isn't the behaviour you'd like, one possible alternative is not do to the orthogonalisation, save the design, load it into Matlab/Octave (or R, etc), and do the orthogonalisation there by hand. Say you have the EVs A and B. You could replace A for Rb*A, and B for Ra*B, where Ra is the residual forming matrix due to A only, computed as I - A*inv(A'*A)*A', and I is the identity matrix (of size N, N=number of observations rows in the design matrix). Rb is computed similarly as I - B*inv(B'*B)*B'. Then include in the design the derivatives if needed (as indicated in the link above) and save.

I must say you may be disappointed, though. Like many people I have also looked into this and have convinced myself that orthogonalisation rarely pays off. Just use the design without it and you are safe.

All the best,

Anderson

On 15 March 2017 at 22:58, Floris van Vugt <[log in to unmask]> wrote:

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