Dear Darren,

At 00:59 27/10/98 -0600, you wrote:
| My question concerns the proper random effects statistics for performing
| conjunctions.

Interesting... never thought about this. I guess there are two obvious
possibilities: (a) A population level inference about a within-subect level
conjunction, and (b) a conjunction at the population level. An example of
the latter would be to find areas where two populations both activate (by
about the same amount). As for the former, I'm not sure it's technically
possible.

| In the Random Effects toolkit instructions Andrew suggest using
| Multi-subject different conditions analysis for examining main effects, and
| Multi-study different conditions analysis for examining interactions
| between different studies. In my own use of the Random effects kit I find
| that including more than 2 conditions in a Multi-subject analysis, even if
| those conditions are contrasted in pairs, doesn't seem to estimate the
| activations correctly.

Strictly speaking, you shouldn't put more than one (paired) comparison into
the second level of an SPM random effects comparison. With two conditions
and one (mean) scan per subjct per condition, the "multi-subject: different
conditions" test is a paired t-test. In adding further conditions you
implicitly assumme tha the model fits, i.e. that the residuals are
independant and identically Normally distributed. For this you gain degrees
of freedom. However, usually the independance criterion is not met in this
situation, since knowing something about how two conditions on each subject
deviate from the model can tell you something about the third. The
variance-covariance matrix has off-diagonal elements, i.e. is
non-spherical. The net result is that you have spurious aditional degrees
of freedom and therefore invalid inference.

There are non-sphericity corrections, but these would either have to be
comupted voxel by voxel (resulting in an SPM{t} with different degrees of
freedom at every voxel), or a "blanket" catch-all correction such as the
Greenhouse-Geiser correction would have to be used. The latter is
particularly severe, and for the relatively low numbers of conditions in
functional neuroimaging experiments you're probably better off just
assessing the two conditions of interest.

A final possibility is that the additional conditions are simply more
variable than the two under consideration, such that adding them to the
model biases the variance estimate leading to erroneous inference.

| If one was doing a conjunction analysis then I imagine one would use the
| Multi-study analysis to combine the 2 study types. Thus one is then faced
| with the curious condition whereby the activations seen in a conjunction
| (multi-study analysis) may not appear to reflect the individual main
| effects (multi-subject analysis). Is there a way out of this conundrum? Can
| one use the main effects within each study type as shown by the multi-study
| analysis??

I have to admit I'm not quite following what you're after here, although I
suspect that it's not possible! Can you give further details?

Hope this helps,

-andrew


+- Dr Andrew Holmes [log in to unmask]
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