Hi,

On 30 Jan 2007, at 20:14, Jaroslav Hlinka wrote:

> I want to make sure I understand to detail, since for me your  
> answers are
> in contrast (of kind [1 -1] :)) with how I have understood what I have
> read in the online randomise manual
> http://www.fmrib.ox.ac.uk/fsl/randomise/index.html:
>
> "If you have "confound regressors", randomise needs those to be  
> removed
> before continuing. Therefore, unlike with FEAT, you need to specify  
> these
> as a separate design matrix and use the -x option when calling  
> randomise;
> randomise then regresses these out of the data before continuing.
> !!!!!!Note that for THIS to make sense, your confounds and design of
> interest need to be orthogonal. In fact, in general in randomise, your
> regressors should be orthogonal to each other. !!!!!"

Right - sorry that the manual is 'confusing' (or maybe just plain  
wrong...) - we'll clean that up. I won't do it straight away though  
because the next version of randomise makes these issues MUCH easier  
conceptually and in practice.

The reason for moving confound regressors into a separate confound  
matrix was because _in permutation testing_ (as opposed to generic  
GLM) it has to be done that way (otherwise when you permute rows in  
the matrix the confound regressors aren't doing the right thing).

It makes no difference if the confound regressors are orthogonalised  
wrt each other.

It can make a difference whether the confound regressors are  
orthogonalised wrt the EV of interest in the main design. If you do  
this then you are moving all the shared variance into the EV of  
interest; you are saying that you trust that that part of the signal  
is real rather than confound (which in general would be dodgy).  
However if the different regressors are already fairly orthogonal  
then it won't make much difference either way.

In 'normal' GLM it doesn't make any difference to the stats of  
interest whether you orthogonalise the EVs of interest wrt the  
confounds or not. However, it _can_  make a difference whether the EV  
of interest is orthogonalised wrt the confound EV _when you are pre- 
regressing the confound as you do here with the -x option_. If you do  
not orthogonalise the EV of interest wrt the confound then the model  
fitting may be bad. You need to orthogonalise your EV of interest wrt  
the confound yourself before running randomise. Orthogonalising the  
EV of interest wrt the confound is the safe/conservative approach -  
you are assigning any signal that is shared between the confound and  
the EV of interest to the confound. However, again, if the different  
regressors are already fairly orthogonal then it won't make much  
difference either way.

In the next version of randomise, things get much easier. You no  
longer will have to setup a confound matrix, just include everything  
in one big matrix and setup the contrasts to ignore the confounds in  
the obvious way. The problem of making the permutation testing do the  
right thing is solved automatically for you by the program, by  
turning the EVs of interest and the contrast into a new effective  
single regressor, and forming a new associated orthogonal confound  
matrix. This confound is then pre-regressed out of the data before  
fitting the new effective EV to give the correct stats. This approach  
will resolve all the above issues, the only downside being that to do  
this correctly requires a new set of permutations for each contrast.  
We will also be adding in f-tests into the new version.

I _think_ the above answers all your questions below - apologies for  
the confusion and the confusing bit in the manual!

Cheers.


> My understanding of your answer is that:
> 1) The C matrix is going to be regressed out BOTH from X and Y by  
> using
> the –x option, that is, BOTH X and Y are going to be orthogonalised  
> with
> respect to C.  Explicitly, Y’=Y-Y*r(C,Y), where r(C,Y) takes the  
> cross-
> correlations AMONG columns of C into consideration.
>
> 2) for permutation testing, the EVs  in X have to be orthogonal
> (Is the reason to fulfil the exchangeability assumption. It is not the
> values of Y, but the combinations of X(EVs) values which are  
> permuted, and
> thus the permutation based distribution of X would not match the  
> initial
> one?)
>
> 2’) the constant CAN be included in the EVs (X), since it IS  
> orthogonal to
> any EV.
> (there I was a confused by simple linear algebra – in stats speech,  
> even
> variables X=[1,1,2,2] and Y=[1,2,2,1] are orthogonal (although
> XY=1+2+4+1=7), since their scalar product AFTER they are demeaned  
> is zero.
> Therefore constant is orthogonal to anything. Am I right?
> The constant can be as well included in C, or I can use –D option,  
> which
> would  demean X, Y and C, that is ALL of them, (so I do not have to  
> pre-
> demean any of the EVs nor confounds nor data)
>
> Nevertheless,
> I can imagine circumstances where the general orthogonality demand  
> would
> be right, (but it is probably not the case of how randomise works,  
> please
> tell me):
> 1) Demand for orthogonality of C to X might make sense if the –x  
> option
> would only regress C out of Y.
> Why do I think so?
> If C and X not orthogonal, then regressing C only from Y has not clear
> interpretation, while the other two sorts of “regressing out” would  
> make
> sense even in non-orthogonal C,X:
> regressing C only from X leads to computation of ‘part’ correlation  
> (of
> X,Y by correlating X’, Y - that makes some sense
> And regressing C from BOTH X and Y leads to ‘partial’ correlation –  
> which
> also makes some sense – and that is what I suppose the –x option  
> does, am
> I right?
> 2) Also the demand of orthogonality inside C would make sense, if  
> it the
> regressing out was based on simply computing and adding several
> independent corrections for every column of C based on the  
> correlation of
> that column with C.
>
> Thanks a lot for showing me way to light,
>
> looking for the next version of software with additional features,
>
> Jaroslav Hlinka
>
> PhD student
> Academic Radiology
> University of Nottingham
> [log in to unmask]


------------------------------------------------------------------------ 
---
Stephen M. Smith, Professor of Biomedical Engineering
Associate Director,  Oxford University FMRIB Centre

FMRIB, JR Hospital, Headington, Oxford  OX3 9DU, UK
+44 (0) 1865 222726  (fax 222717)
[log in to unmask]    http://www.fmrib.ox.ac.uk/~steve
------------------------------------------------------------------------ 
---