Dear Joe
> >In fact the second-level analysis, used in SPM, assumes that the design
> >matrices are identical for each subject.
>
> I've seen this point mentioned before but I think I may have missed its
> importance. Does this mean that if you randomize the order of
> presentation across subjects then you cannot use an RFX because each
> subject has a different design matrix? I think this is rarely done in
> fMRI studies but it is normal practice for PET. I'm wondering whether
> this means that the assumptions underlying an RFX analysis are violated
> when analysing (typical) PET data.
The critical thing, about using the simple 2-stage analysis to implement
an exact RFX analysis in SPM, is that the contribution from the error
variance (Ce) at the 1st level is the same for each subject. This is
pinv(X)*Ce*pinv(X)'
where X is the 1st-level design matrix. Because
pinv(X)*Ce*pinv(X)' = pinv(X(i,:))*Ce*pinv(X(i,:))'
where i is any permuation of indices, randomizing the order of
conditions over subjects will have no effect. Indeed randomizing the
onset times of different trial types in fMRI will have no effect
(ignoring minor interactions with serial correlations). The only
situation where one should be careful is when the number of trials, in
X, varies substantially from subject to subject.
> Would it make a difference if one analysed a group of subjects (with
> different stimuli presentation ordering) using the 'conditions x subj'
> option before generating the subject-specific contrasts? In that
> case, each subject would be part of the same design matrix although the
> contrasts would come from independent (and different) subsets.
Yes. For PET one must always model the effects in a subject-separable
fashion (i.e. 'conditions x subj'). This is enforced in the fMRI setup
because each session is specified separately.
I hope this helps - Karl
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