Dear Paul,
Sorry, I was forgetting that SPM99 tries to take account of this
problem. I must admit that I haven't used SPM99 for this purpose, so
I don't quite know how it works. I still don't think that it helps
you, for the following reason.
As I understand it, when you have two covariates, then the variance
modelled by these can be partitioned into three components:
1. variance which can only be explained by covariate A
2. variance which can be explained by either covariate,
3. variance which can only be explained by covariate B.
The way in which you specify your orthogonalization order (SPM99
prompts you for this after you have chosen your contrasts) will
influence the parameter estimate for one or other covariate, and I
have to confess that I cannot remember which way round it works, as I
find it a bit confusing. I think that the first contrast which you
specify is left unchanged (i.e. the same contrast is applied to the
same parameter estimates), but the second contrast is modified to
compensate for the fact that your parameter estimate is for
components 2 and 3 rather than just component 3. Thus your parameter
estimates stay the same, but you will see that the second (I think!)
contrast now looks slightly different, and includes non-zero values
even for some of the covariates which only appeared in the first
contrast when they were originally specified.
However, regardless of the implementation, I think that the idea is
that you are ascribing the variance which can be modelled by either
covariate (component 2 above) to one or other. You don't actually
know which one it comes from, and there is no way to find out. You
could still be mislead in your situation. Thus, you might set things
up so that the common variance (component 2) is explained by
covariate B, when in reality it is entirely attributable to covariate
A. The remaining variance which can only be explained by covariate A
(component 1) is appropriately modelled by this covariate. Once
again you have a situation where variance which actually comes from
one condition appears to be attributable to a combination of both,
and so you have voxels showing up spuriously in your conjunction.
But I may be wrong about this. It may be that SPM99 discounts the
common variance (component 2), so that the conjunction would now ask
whether the data from a voxel includes both 'component 1' and
'component 3' variance. If there is considerable co-linearity
between the contrasts, so that much of the variance is 'component 2',
then this test would obviously be rather insensitive, but I think
that the results might be meaningful even in your case. However, if
this is what SPM99 does, then I wouldn't have thought that it would
need to ask you for an orthogonalization order.
I hope that someone else will be able to give a more expert reply,
and tell you which of these SPM99 actually does. Some of the real
experts are away at the moment, though. If this question is
important, though, I would seriously consider doing another
experiment in which each condition has its own baseline, as described
before!
Best wishes,
Richard.
>Richard thanks for your reply. I suspected that there may be a problem with
>non-orthogonal contrasts but I did not fully understand. What is SPM doing
>when it "orthogonalizes" the contrasts in a conjunction? Does this
>have any meaning
>and why does it not account for the non-orthogonal nature of the contrasts?
>
>Thanks,
>Paul
>
>Richard Perry wrote:
>
>> Dear Paul,
>>
>> Your approach was quite reasonable, except that you have made the
>> assumption that the contrasts 1 0 and 0 -1 are orthogonal, and I
>> guess that this is probably not the case. (After all, when you have
>> stimulus A, presumably you can't also have stimulus B at the same
>> time?) If they are not orthogonal, then the conjunction which you
>> have tried is not really interpretable.
>>
>> To take an over simplistic example, imagine a situation in which
> > there were only two conditions, A and B, and these were both modelled
>> with box cars, and in fact the covariate for B was equal to that for
>> A multiplied by -1 and with +1 added (i.e. when A had ones, B had
>> zeros and when A had zeros, B had ones). In this overspecified
>> model, the same variance in voxels which were actually 'activated' by
>> condition A but not B could either be modelled using covariate A
>> (with a positive parameter estimate) or with covariate B (with a
>> negative parameter estimate). Many of these voxels would end up
>> being modelled by some combination of the two, and these would show
>> up in the both contrasts, 1 0 and 0 -1, and would therefore also show
>> up in the conjunction of these two, in spite of the fact that in this
>> example there is no response at all to B.
>>
>> Really to answer your question you need to have more conditions.
>> Ideally you should have condition A and its own baseline condition,
>> and condition B with its own baseline condition (you can't use the
>> same baseline for two conditions which you want to use for a
>> conjunction analysis). With these four covariates you could do the
>> conjunction of 1 -1 0 0 and 0 0 -1 1, and get a meaningful answer. I
>> guess that what you have ended up with, in your conjunction of 1 0
>> and 0 -1, are many more voxels than you expected. These are not
>> necessarily voxels in which 'areas of activation from one stimulus
>> overlap with inactivations from the other stimulus'; it may just be
>> telling you that your covariates are significantly co-linear.
>>
>> Best of luck,
>>
>> Richard.
>>
>
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--
from: Dr Richard Perry,
Clinical Research Fellow, Wellcome Department of Cognitive Neurology,
Darwin Building, University College London, Gower Street, London WC1E
6BT.
Tel: 0171 504 2187; e mail: [log in to unmask]
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