>>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. 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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