On Thu, 15 Sep 2005 11:50:49 -0400, =?iso-8859-1?Q?J=F6rn?= Diedrichsen
<[log in to unmask]> 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
>At 11:17 AM 9/15/2005 +0100, Will Penny wrote:
>>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:
>
>
>Dear Michael,
>As Will points out, smoothing beta images will result in an incorrect
>first-level (or fixed effects) inference, because your error-images were
>calculated on unsmoothed data and you it is not valid to just smooth
these
>as you would smooth betas.
>So what if you want to do your data analysis on unsmoothed data? Doing
this
>has a number of advantages, for example, you can use Robust regression
>using WLS. Furthermore, if you would like to project you functional data
>onto a surface representation, it is best not to smooth in the volume too
>much before projecting the data onto a surface, but to smooth after you
>projected onto the surface.
But smoothing after projecting doesn't respect the original geometry that
you had before you projected, unless you smooth in a very clever fashion
after you project.
>For these reasons I prefer doing the
>first-level analysis on unsmoothed, unnormalized data.
>To nonetheless get a within-subject inference, I recommend the doing a
>second-level (mixed effects) model within that subject: Depending on you
>task design, often you will have a repetition of similar condition across
>the experiment, for example trials in a event related design, task-blocks
>in a block design, or at least estimates from the same condition for each
Run.
>On the first level, I set up my design matrix, such that each of these
>trials, blocks, or runs has a own regressor and will get an own estimated
>beta-weight. Here I use WLS to exclude artifacts from the imaging data.
>Then I will smooth (and normalize) these beta-images and set up a
>second-level analysis within that subject, using the beta-images from the
>first level as the data. If trials or blocks are reasonably spaced, it is
>generally not too far of the truth to assume temporally independent data,
>so you can use ordinary least-squares, as you would in a between subject
>analysis.
>Compared to a fixed-effects model, this way of analyzing data within a
>participant will reduce your degrees of freedom, and therefor your
>p-values. However, this approach has two advantages:
>a. Your inference will be robust against violations of the temporal noise
>model (autocorrelation), that you assumed on the first level.
>b. You explicitly take the "true" repetition-by-repetition variability
into
>account, i.e. how consistent the hemodynamic changes were in this subject
>across different repetitions of the same activity.
>
>Hope this helps,
>
>Joern
>
>--------------------------------------------------------------------------
--------------
>Jörn Diedrichsen
>Department of Biomedical Engineering
>Johns Hopkins University
>720 Rutland Ave, 419 Traylor Building
>Baltimore, MD 21205-2195
>email: [log in to unmask]
>web: http://www.bme.jhu.edu/~jdiedric/
>fax: 410 614-9890
>phone: 410 614-8266
>========================================================================
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