Dear Mike,
Smoothing the beta images, b, is not the same as smoothing the data, y.
If y = X b + e
then smoothing the data is equivalent to smoothing the beta's and
smoothing the error, e.
In SPMs Restricted Maximum Likelihood (ReML) parameter estimation
scheme, the autocovariance in the error is used in the estimation of
the betas. So, because the errors will be different so will the
estimated beta's.
Also, the spatial smoothness of the error fields is used to compute
the number of RESELs - so that statistical inference (using Random
Field Theory) as well as parameter estimation will be different.
In summary, there are reasons why the resullts should be different.
You could try smoothing the errors as well and then re-estimating
the beta's - but I imagine this is a beast to implement.
Best,
Will.
Mike Glabus wrote:
> I am currently applying the WLS method for motion correction proposed by
> Jorn Diedrichsen and Reza Shadmehr (Neuroimage,2005,27:3;624-634).
>
> One of the requirements for the application of WLS method is to derive a
> variance estimate on unsmoothed images. This means doing the SPM(2)
> analysis on the unsmoothed images then smoothing the beta images prior to
> deriving contrasts.
>
> However, I have noticed that, when testing this in a standard analysis to
> evaluate whether a smoothed image analysis is the same as an unsmoothed
> image/smoothed beta file analysis, the results are different. I applied
> the same FWHM of filter to the smoothed beta image analysis as for the
> analysis of the smoothed images (images were spatally normalized in both
> cases and hi-pass filtered at 128 seconds)
>
> Is there a particular reason why the results should be different? Should I
> use less smoothing when applied to beta images?
>
> Regards - MFG
>
>
--
William D. Penny
Wellcome Department of Imaging Neuroscience
University College London
12 Queen Square
London WC1N 3BG
Tel: 020 7833 7475
FAX: 020 7813 1420
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URL: http://www.fil.ion.ucl.ac.uk/~wpenny/
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