Dear Kath,
>I have been thinking about the issue of testing conjunctions (across two
>contrasts) between groups at the second level in a random effects
analysis, and
>I am seeking some advice. From previous discussions, I understand that
>performing a conjunction (of two contrasts) is possible at the second
level, by
>taking two the con*.images for contrast, for each subject to the second
level,
>but in doing so you are making strong assumptions about the sphericity of the
>error terms.
Exactly.
>I understand from the documentation for SPM2b, that such issues of sphericity
>are addressed explicity (i.e., by modelling non-sphericity) and
that...."Using
>the non-sphericity option allows one to take up multiple contrasts from
the same
>subject to a second level, to emulate a mixed or random effects analysis."
Indeed.
>What I would like to do is compare the results of the conjunction of (A-B)
and
>(C-D) between groups (patients and controls), so if [p = patients, c =
>controls], this would equate to statistically comparing (A-B)p and (C-D)p vs
>(A-B)c and (C-D)c. I would like to know (a) areas commonly activated (in
>patients and controls) in the conjunction, and (b) areas differentially
>activated by controls and patients across the conjunction (i.e., areas
activated
>by patients not by controls in the conjunctin and the inverse, areas
activated
>by controls and not by patients in the conjunction). Is this type of analysis
>possible to do in SPM2b by modelling non-sphericity and how would I implement
>such an analysis?
Firstly, one cannot "compare the results of the conjunction" because a
conjunction
is already a [conjoint] comparison (i.e. you cannot compare a comparison).
I think what you want for:
(a) areas commonly activated (in patients and controls) in both (A-B) and
(B-C);
is a 4-way conjunction (A-B)p & (A-B)c & (C-D)p & (C-D)c
(b) areas differentially activated by controls and patients across the
conjunction;
is a conjunction of the group x task interactions (i.e. differential
activations).
This would be a conjunction ((A-B)p - (A-B)c) & ((C-D)p - (C-D)c)
These would be tested for by a conjunction of the contrasts
a) [1 0 0 0] & [0 1 0 0] & [0 0 1 0] & [0 0 0 1]
b) [1 -1 0 0] & [0 0 1 -1]
for a second level model with (A-B)p, (A-B)c, (C-D)p and (C-D)c as effects.
This
would simply involve creating the four con* images (two for each subject)
at the first
level and modelling non-sphericity at the second level. You do not have to
model
non-sphericity unless you think the activations are correlated within
subject or
they have different variabilities.
I hope this helps - Karl
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