Hi,
Just to add to this - there is also an effect on both the fit and
residuals if the EVs are correlated, since doing things in two
steps is not equivalent to doing it in one in this case. When
the EVs are correlated it is necessary to do it all in one GLM
in order to be really correct in all ways.
For the mathematically inclined you can see this with the
following example (using MATLAB notation):
x1=[1 0 0]'
x2=[0.5 1 0]'
y=[3 2 1]'
So that the combined solution is:
beta=pinv([x1 x2])*y
res=y-[x1 x2]*beta
While the separate solution is:
beta1=pinv(x1)*y
res1=y-x1*beta1
beta2=pinv(x2)*res1
res2=res1-x2*beta2
The results are:
beta=[2 2]'
versus
beta1=3
beta2=1.6
and
res=[0 0 1]'
versus
res1=[0 2 1]'
res2=[-0.8 0.4 1]'
So you can see the inconsistencies here.
The only way to make the methods consistent
is to orthogonalise the second-stage design matrix
with respect to the first. If you haven't done this
then you'll be in the situation above.
If your EVs (or design matrices) are already
orthogonal then it does not matter which way
you do things - they are all equivalent.
Hope this helps.
All the best,
Mark
On 19 Dec 2009, at 10:39, Stephen Smith wrote:
> Hi - I think your understanding is probably correct; the approaches
> are largely equivalent. The degrees of freedom will indeed be
> slightly different, with the include-condounds-within-main-model
> having the more correct DoF. Another possible difference may be
> that in the pre-confound-regression case you will have highpass-
> filtered the data but not the confound-model so it may not match as
> well as in the include-condounds-within-main-model case, where this
> will be dealt with correctly.
>
> Cheers.
>
>
> On 18 Dec 2009, at 22:48, Robert Kelly wrote:
>
>> Hello,
>>
>> I get slightly different results depending upon which of two
>> approaches I use
>> to denoise data.
>>
>> Approach 1: Use a 4D fMRI (preprocessed) image and the time course
>> of a
>> presumed noise source with fsl_regfilt to produce a denoised 4D
>> image.
>> Regress the denoised image against a task-related time course with
>> FEAT to
>> yield spatial maps of PE values and z-scores corresponding to task-
>> related
>> brain activation.
>>
>> Approach 2: Regress the first 4D image against the task-related
>> time course
>> with FEAT, adding the noise source time course to the EVs, but not
>> to the
>> Contrasts & F-tests (Its EV gets a zero).
>>
>> Both approaches yield similar results and both appear to improve the
>> sensitivity for detecting activation, but the corresponding spatial
>> map voxel
>> values generally differ up or down by amounts of about 1%, varying
>> from
>> nearly zero differences to differing by a few percent for some
>> voxels.
>>
>> I expected some slight differences in results due to differences in
>> degrees of
>> freedom or rounding errors, but I did not expect the differences to
>> be this
>> large. Do you have any idea what might account for the differences?
>>
>> Cheers,
>> Robert
>>
>
>
> ---------------------------------------------------------------------------
> 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
> ---------------------------------------------------------------------------
>
>
>
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