Hi guys.
Apart from a few details, FSL just implements a standard GLM.
When EVs covary, the rules say this: Only the orthogonal part of the
EVs is used to estimate the parameter estimate.
Hence orthogonalising A wrt B, has no effect on the PE for A, but
effects the PE for B.
This is the definition of orthogonalising in FSL; it may be different
in R, I am not sure.
Are you at the single subject level, or the group level?
At the group level, you need to model the mean.
Cheers
T
On 4 May 2007, at 21:26, Lisa Lu wrote:
> 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]
>> =====================================================================
>> ===
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