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Subject:

Re: multiple sessions + subjects (flame, dofs, FE)

From:

Stephen Smith <[log in to unmask]>

Reply-To:

FSL - FMRIB's Software Library <[log in to unmask]>

Date:

Thu, 6 May 2004 10:02:28 +0100

Content-Type:

TEXT/PLAIN

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Parts/Attachments

TEXT/PLAIN (120 lines)

Hi,

> Wrt to FE:
> Doing fixed effects analysis, I have to calculate the requested "contrast"
> or mean effect from the copes:
> e.g.  avwmerge -t copes cope1 ... copeN
>  avwmaths copes -Tmean copes
> and get the adjusted variance image:
>  avwmerge -t varcopes varcope1 ... varcopeN
>  avwmaths varcopes -Tmean -div <Number of varcopes> varcopes
> Is this true only for t-contrasts? How would I do FE with F-tests?

Yep - more difficult with F-stat images.....not sure what the analytical
null distribution for FE-F is; an approximation would be to take the
zfstat images from first-level (f converted to z) and take the approximate
FE-Z at second-level with sum(z)/sqrt(n) BUT this is only approximate and
obviously doesn't make much sense if any of the z values in the sum are
negative.....

> Wrt to DOFs:
> Reading the technical reports, I actually thought flame is doing some
> trick to preserve more dof's. However, this is not the case? My dof's at
> any level would always be the number of input images minus number of EVs?

FLAME isn't directly seeking to expand the DOFs (eg by spatial
regularisation) but does estimate the "true" DOF after taking the FE
component of the "true" ME variance into account and fitting a t
distribution to the estimated ME parameter estimate posterior (including
allowing estimated DOF to vary and possibly increase).

> Wrt to demeaning of EVs:
> It is not completely clear to me why one have to demean an EV. Say I have
> a behavioral covariate 3 2 1. Demeaning it would change its values to 1 0 -
> 1. However, this should mean that voxels of the second image could take
> any value (and not in between the first and third image) to get a good fit
> of this EV. Am I missing something?

Nope - that's right, odd though it might seem. If you think about fitting
a straight line through 3 points (equally spaced on the x axis), the slope
isn't affected by the value of the middle point.

> Wrt to flame:
> As I am scripting all of my analysis, I noted one option that seems not to
> be documented: "fixed effects". Is this already working? I guess Hauke
> already asked: How to input F-tests into flame?

I'm not sure - if it is working, it certainly hasn't been tested much!
I'll let Mark Woolrich comment more on this.

WRT F - this is what Robin was asking a few days ago and similar to the
answer above - I'm afraid no-one's done the maths yet for F   ;-)

But - watch this space - in the next year or so we will be releasing new
methods for inference which may allow much more flexibility in what gets
fed into the inference (thresholding) - so this kind of thing should get
easier.

> Wrt to contrast masking:
> How do I implement this from the command line? Is it simply using avwmaths
> with the -mas option?

Yes - the contrast masking isn't doing any new stats - just binary
masking. Note that if you are writing your own analysis scripts it's worth
looking at fsl/tcl/feat.tcl to see what it does.

> And finally concerning my own study design:
> I have 4 subjects each with 3 sessions per day and 6 repetitions over a
> period of 6 weeks. I want to analyze the effect of a behavioral covariate
> which has been measured weekly (same day as functional scans). Having only
> one value of the covariate but 3 intra-day sessions I thought of putting
> these together using fixed effects analysis. Finally I wanted to put the
> (FE) copes/varcopes to a second but not third level for the following
> reason:
> - I do NOT want to generalize results to the population my subjects came
> from
> - it seems necessary to include inter-day variance
> - the covariate for one subject is all zero
> - I am having much more dof's
> Using a design like:
>
> subject1-week1: 1 0 0 0 -3
> subject1-week2: 1 0 0 0 -1
> ...
> subject2-week1: 0 1 0 0  2
> subject2-week2: 0 1 0 0  1
> ...
> subject4-week6: 0 0 0 1 -5
>
> with the first 4 colums being subject EVs and the last colums being the
> behavioral covariate, do I violate any statistical assumption (multiple
> sessions/subjects - at least not possible using SPM)? Would it be wise to
> define seperate groups for each subject (to get seperate variance
> estimates)?
> And finally, say something special has happened in one but none of the
> other measurements and I want to analyze where in the brain it came from ;-
> )) should this EV really look like -1 for each image but 23 for the
> outstanding event (with 24 measurements in total)?

If you are going to do "fixed effects" at the highest level you will need
to carry up all variances from all levels so that you can pool them. Your
design looks ok, as long as you CAN get FE working on a general design
matrix (though I suspect that FE in FLAME _isn't_ finished yet). But apart
from that, I don't think any of the described modelling/stats is dodgy.

WRT your outlier, that approach is indeed reasonable - in effect you're
subtracting the average of all the others from the outlier.

Cheers.



 Stephen M. Smith  DPhil
 Associate Director, FMRIB and Analysis Research Coordinator

 Oxford University Centre for Functional MRI of the Brain
 John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK
 +44 (0) 1865 222726  (fax 222717)

 [log in to unmask]  http://www.fmrib.ox.ac.uk/~steve

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