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Subject:

Re: Rank deficiency

From:

Mark Jenkinson <[log in to unmask]>

Reply-To:

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

Date:

Sat, 24 Jan 2004 23:30:30 +0000

Content-Type:

text/plain

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text/plain (88 lines)

Hi Heather,

Your original email looks to me like you are explicitly modeling
rest in EV-baseline (which is 1 in all the odd timepoints while
all other EVs are only non-zero at even timepoints).  In this
case, what you want to do is just drop this EV completely as
it does not add anything to your model.  The rest condition should
not be explicitly modeled in first level FEAT analyses.

(Technically the reason for this is that all data and EVs are demeaned
and hence it is not permissible to have EVs that add up to a constant,
non-zero mean: which in your case is achieved by
baseline + 1/30*EV30 + 1/10*EV10 + 1/40*EV40 + 1/20*EV20 + 1/50*EV50
= 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ... )

Also, I would recommend using a unit height for your other
EVs.  That is, make the non-zero entries equal to 1.0 not to
30 or 10 or whatever the force strength was.  Then you can
test for the mean effect with a contrast of [1 1 1 1 1] or a
linear effect with [-2 -1 0 1 2].  (Note that without normalizing the
height of the EVs, a linear effect would be more like [1 1 1 1 1] in
the contrast, and the mean would be complicated)

Individual force conditions can still be tested by contrasts like
[0 1 0 0 0] and you can still mask the mean effect with the individual
contrasts as Joe suggested.

Hope this makes things clear.
All the best,
        Mark




On Saturday, January 24, 2004, at 08:52  am, Joseph Devlin wrote:

> Dear Heather,
>
> If I understand your model setup correctly, you haven't explicitly
> modeled
> rest.  Instead you have one EV for each of the force conditions plus
> one
> for all force conditions together.  It is this latter EV that is
> causing
> rank deficiency.  The reason is that this "common force" EV is a linear
> combination of the individual force EVs:
>
> common = 1/10*EV1 + 1/20*EV2+1/30*EV3+1/40*EV4*1/50*EV5
>
> But the common force EV doesn't need to be included in the model to
> extract
> the information that you're interested in.  With just the 5 EVs, you
> can
> compute a main effect of force minus rest using the contrast [1 1 1 1
> 1].  If you mask this inclusively with each of the force conditions
> relative to rest, you will guarantee that your effect isn't coming
> from a
> subset of conditions and instead is present in each.  You can do this
> with
> avwmaths.
>
> Then you can look for parametrically changing force effects with
> whatever
> shape you are expecting.  FOr a linear change, you can use [-2 -1 0 1
> 2]
> and for a second-order effect you could use [4 1 0 1 4].  You should
> note,
> however, that since you have an odd number of conditions, each of these
> contrasts ignores the middle value (contrast weight of zero) so you'll
> have
> to plot out effect sizes in any area of interest to guarantee that the
> data
> meet your expectations.
>
> Good luck.
>
> Joe
>
> --------------------
> Joseph T. Devlin, Ph. D.
> FMRIB Centre, Dept. of Clinical Neurology
> University of Oxford
> John Radcliffe Hospital
> Headley Way, Headington
> Oxford OX3 9DU
> Phone: 01865 222 738
> Email:  [log in to unmask]

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