Tom,
Thanks for your response. I liked the way you posed the question regarding
the global covariance estimation...
>I don't think anyone really believes
>that the nonsphericity/covariance is homogeneous over the brain, so
>the question is instead: If we have to assume a global covariance, for
>which voxels do we want the global estimate be most accurate?
From a purely pre-surgical perspective, I would answer: We want the
covariance estimate to be most accurate for the cluster(s) of interest.
Would it then make sense to make cluster specific estimates resulting in
several local covariance estimates instead of one global estimate? And if
we know our contrast of interest apriori (as is the case for most clinical
scans) would it be better to use a T-statistic to identify the voxels that
enter the covariance estimate?
For instance,
1) Perform OLS with T-based height and extent thresholds to identify
most-likely clusters
2) Pool covariances over individual clusters in the normal manner to
generate multiple V's
3) Perform WLS using cluster specific V's (with some metric,
neighest-neighbor perhaps, for deciding which V to use for voxels not
entering the covariance estimates)
I'm probably in over my head with this (overfitting perhaps???) but it would
seem like a logical extension to the SPM method at least for single-subject
settings.
-Brian
-----Original Message-----
From: Thomas E Nichols
To: Lenoski, Brian - SJHMC
Cc: [log in to unmask]
Sent: 6/26/2006 12:15 PM
Subject: Re: [SPM] Multi-Subject Realignment and Non-sphericity
implementation quest ions
Brian,
I'll answer your second question...
> 2) For determining the voxels that are "pooled" and enter the ReML
> calculation of hyperparameters, the code is somewhat hard to
> decipher. Is it correct to assume that the voxel is "significant"
> and enters "pooled" data (i.e. Cy) if:
>
> F(voxel) > F(p=0.001)
>
> where: F(p=0.001) is calculated using numerator and denominator
> d.o.f. as determined from design matrix (i.e. trace(X) and trace(R)
> respectively)
That's right.
> Also, is pooling "significant" voxels done for theoretical or
> computational reasons and would there be a reason not to just pool
> all in-mask voxels???
Theoretical/modeling reasons. I don't think anyone really believes
that the nonsphericity/covariance is homogeneous over the brain, so
the question is instead: If we have to assume a global covariance, for
which voxels do we want the global estimate be most accurate? SPM
says "we care about the voxels most likely to contain true signal,
those with P_F < 0.001 based on a preliminary OLS".
Honestly, I'm uneasy with a global covariance assumption. One small
thing I do to at least get a small sense of how this works, is that I
notice how many voxels are used in this estimate. In spm_spm.m,
around line 820 in SPM2 and around 860 in SPM5, I added the last line
below:
% normalize non-sphericity and save hyperparameters
%---------------------------------------------------------------
V = V*nScan/trace(V);
xVi.h = h;
xVi.s = s; % # vox contributing to
Cy
and then, manually, after the analysis is complete, I look at
SPM.xVi.s. If it is really tiny (say less than 20) I might worry
about the quality of the covariance estimate (not enough data). If s
is really huge, I might also worry, as then huge amounts of the brain
(which are probably heterogeneous) are being pooled to determine the
global estimate.
Hope this helps.
-Tom
-- Thomas Nichols -------------------- Department of
Biostatistics
http://www.sph.umich.edu/~nichols University of Michigan
[log in to unmask] 1420 Washington Heights
-------------------------------------- Ann Arbor, MI 48109-2029
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