I think it comes down to the infamous bias-variance tradeoff.
GLM Flex implements a partitioned error, which is safer (makes fewer assumptions about sphericity, particularly whether nonsphericity is uniform across voxels), but potentially less sensitive (if nonsphericity is modelled accurately, by being uniform across voxels).
Flexible factorial (ie SPM in general) uses a single pooled error, which is potentially less robust but can be more sensitive if nonsphericity assumptions are met.
Ie in crude terms, GLM-Flex has less bias but greater variance (ie less efficient); Flexible factorial has more bias but less variance (more efficient).
The problem is that it is difficult to test whether nonsphericity is uniform over voxels because it is difficult to estimate from only a few voxels - ie a "catch-22".
People have shown that autocorrelation of error in 1st-level fMRI timeseries models (one form of nonsphericity) does vary across voxels, but whether the same is true for 2nd-level ANOVAs on beta-images probably depends on the data, ie difficult to "prove" in general.
If you want to be safe (conservative), then GLM Flex may be best.
For more info, see:
http://www.mrc-cbu.cam.ac.uk/wp-content/uploads/2013/05/check_pooled_error.m
(or email me if you would like the PDF (book chapter) that explains this script).
R
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Professor Richard Henson
Director for Neuroimaging
MRC Cognition & Brain Sciences Unit
15 Chaucer Road
Cambridge, CB2 7EF
England
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URL: http://www.mrc-cbu.cam.ac.uk/people/rik.henson/personal
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-----Original Message-----
From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]] On Behalf Of H. Nebl
Sent: 14 November 2013 16:24
To: [log in to unmask]
Subject: [SPM] Flexible factorial - is it valid?
Dear everyone,
although there have been various discussions on this before, I would try one more time to find out about the validity of Flexible factorial designs as implemented in SPM. One potential issue is df, one issue is the pooled error term. The conclusion has often been that the interaction is valid, but the main effects are not. But is there any "proof"?
For example, I ran a 2x2 within-subject ANOVA, 16 subjects, with Flexible factorial (equal variance, independence no). According to xjview the F image for the interaction has 1,45 df. When running the same model with GLM Flex, the corresponding F image has 1,15 df?
Best,
Helmut
(and sorry for starting with this topic once again, but it seems to be necessary...)
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