Richard and SPM users,

Thank you for your reply. I would like to repose this question giving more
details on my study design. I hope that if you are unable to answer me, other
experts will try.

I have designed my experiment based on human and animal physiology experiments.
I have a 3 condition epoch based fMRI study with the following conditions A, B,
and AB pseudorandomly ordered. I am unable to provide separate baselines for
each condition because this would present physiologic problems. My paradigm is
(as you suggested) non orthogonal. However, the co-linearity between the
contrasts is quite small. The greatest cosine is -0.13. Is it possible for SPM
to correct for this during the orthogonalization step? Also, there seems to be
questions about interpretation of orthogonalized conjunctions. After SPM
performs the orthogonalization step, it the conjunction interpretable?

If it is not possible to use conjunctions, is it valid to use masking for non
orthogonal contrasts and simply present my data in a descriptive rather than a
statistical manner. My interest is to demonstrate the areas where activations
from A overlap with deactivations from B and vise versa. I have performed both
conjunction and masking analyses with nearly identical results. I also find that
the main effects (i.e. 1 0 0, -1 0 0, 0 1 0 and 0 -1 0) support the conjunction
and masking results. I believe that the results are real but want to ensure that
I perform valid statistical analyses on the data.

Any help will be much appreciated.

Paul

Richard Perry wrote:

> 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.
>