Hi Tim,
Thanks for your reminder to model the group mean. I've been reviewing my stats textbook, and now realize that it's necessary to model the group mean because this corresponds to the y-intercept in the regression equation.
Thanks,
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]
________________________________
From: FSL - FMRIB's Software Library on behalf of Tim Behrens
Sent: Fri 5/4/2007 11:36 PM
To: [log in to unmask]
Subject: Re: [FSL] orthogonalizing variables (computing partial correlations)
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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