Hi Greg, 
 
Thank you very much for responding to my inquiries.  I have finished orthogonalizing B wrt A, and results hold as predicted.
 
I am interested in identifying voxels where signal is correlated with variable A after controlling for B and vice versa.  I haven't demeaned my EVs (variables A & B) because I'm interested in multiple regression results (vs. variables A & B as covariates whose variance I want to exclude from the group mean).  
 
The results generated by FSL seems to be the exact opposite of the results generated by R.  That is, the pattern of activation identified by FSL as associated with A is one that's identified to be associated with B by R, and vice versa.  We've taken signals for several points and tested them in SYSTAT, and SYSTAT results match R results exactly.  So we're not sure why FSL results differ.  Any insight or hypotheses you have that might shed light would be sincerely appreciated.
 
Thanks,
Lisa


I'm by no means one of the experts on FSL's GLM, but I've tried to research
these exact questions recently. I'll give you what I have learned. I'd
appreciate if the FSL GLM experts could jump in if necessary to fill in the
gaps or inaccuracies.

On Wed, 2 May 2007 01:02:28 +0100, Lisa Lu <[log in to unmask]> wrote:

>Hello,
>
>I am interested in mapping partial correlations between signal and 2
>variables.  Basically, I want to identify voxels at which my signal
>contains variance which can be explained by variable A after accounting
>for variance explained by variable B, and vice versa. 
>
>I have done this by setting
>EV1=variable A raw score (i.e., not demeaned) and
>EV2=variable B raw score (i.e., not demeaned). 


I believe that, because you do not have an EV explicitly coding the group
mean and you haven't demeaned these EVs, they can grab some variance related
to the group mean. Unless you have a really good reason not to demean, I
always demean all covariates just to be safe.


>To look at voxels where variable A is positivly correlated with signal
>after variance due to B is controlled, I set a contrast, [1 0].  To look
>at corresponding negative correlation, I set a contrast [-1 0].  To
>identify voxels where B is positively correlated with signal after A is
>controlled, [0 1], and [0 -1] for negative correlation.  If this is
>correct, what is the interpretation of my resulting maps?  Am I looking at
>voxels with significant semipartial correlation between signal and EV
>(i.e., variance contributed by B has been removed from error variance, vs.
>partial correlation, where variance contributed by B has been removed from
>both explained variance and error variance)?


FSL's GLM calculates the PE for each EV in the model with variance that can
be independently attributed to that EV and not to other EVs in the model.
Furthermore, I believe that varcopes (against which the t-test for each PE
is calculated) are related to the residual variance after removing variance
that can be explained by other EVs in the model. If these facts are true, in
the model that you've specified, the PEs are already analogous to partial
correlations: relationship between EV and signal after removing variance
attributed to other EVs from both the numerator and denominator of the t-test.

As an aside, I don't believe that this is the way that the GLM works in
general (e.g., in SAS and SPSS). I believe that PEs in the typical GLM are
analogous to semi-partial correlations, in which the significance of the PE
is tested against the total variance in the model, regardless of how many
PEs are present in the model.

GLM experts... clarify if necessary.



>I also repeated the above and orthogonized A wrt B.  Resulting contrast
>maps corresponding to A ([1 0] and [-1 0]) look exactly the same as
>without orthogonalizing.  Maps corresponding to B ([0 1] and [0 -1]) are
>slightly different although the pattern is similar.  Is this because the
>joint variance between A & B have now all gone into B? 


Yes, that's exactly why. The contrasts involving B will look identical in a
model with A orthog wrt B and in a model with B alone.


>Is it true that as
>maps corresponding to B now also contain variance that overlapped with A,
>it is inappropriate to interprete this map as voxels whose signal varied
>with B with effects of A controlled?


Correct. That's what the first model gave you.


>To look at voxels whose signal varied with B with effects of A controlled,
>I think I would need to orthogonize B wrt A.  Theoretically, when I do
>this, the resulting maps for B should look exactly like the results of the
>original, unorthogonalized analysis. 


A model in which B is orthogonalized wrt A will give you 1) B with effects
of A controlled and 2) A without controlling for B. However, as you now
know, it's not necessary to orthogonalize anything if you simply want to
control for all of the other variables in the model.


>I am testing this now, but would
>really like the experts' input regarding whether I have done the previous
>steps correctly, and if my interpretation are accurate.
>
>Thanks so much!
>Lisa
>
>
>Lisa Lu, Ph.D.
>Postdoctoral Fellow
>Laboratory of Neuro Imaging
>UCLA Dept of Neurology - #1 in NIH Funding
>David Geffen School of Medicine
>Neuroscience Research Building 1, Suite 225
>635 Charles Young Drive South
>Los Angeles, CA 90095-7334
>(310) 267-5555
>[log in to unmask]
>========================================================================