Dear Gaspare,
> I need your help to select the appropriate analysis model for a 2x2
> factorial fMRI experiment, where 10 subjects performed an Activation
> (A) and a Baseline (B) task, with stimuli delivered either in the
> visual (v) or in the tactile (t) modality.
>
> I've specified and estimated separate subject-specific models, entering
> 4 conditions (Av Bv At Bt), modeled as box-cars (convolved with hrf),
> and tested for the main effect of task (1 -1 1 -1) and the interaction
> task x modality (1 -1 -1 1 and -1 1 1 -1). I then entered the contrast
> images into a 2nd level random-effect analysis (one sample t-test).
>
> The problem is the following: since I am interested in finding regions
> which are activated by task A vs. B to the same degree in the two
> modalities, this should be more properly tested by a conjunction
> analysis (i.e. the conjunction between the "simple effects" of task in
> the two modalities: 1 -1 0 0 and 0 0 1 -1), rather than by the "main
> effect" contrast (1 -1 1 -1). With the conjunction approach, regions
> where interactions occur should be discarded from the results.
>
> But: - If I do the conjunction analysis at the 1st (subject-specific)
> stage, I do not obtain any contrast image to enter at the 2nd
> (random-effects) stage. - On the other hand, I can't imagine an easy
> way to do the conjunction analysis at the 2nd level, for example using
> "simple effects" contrast images. Is there any? - If not, I could
> build a big multi-subject fixed-effects model and test for the
> conjunction between 1 -1 0 0 1 -1 0 0 ... (repeated for all subjects)
> and 0 0 1 -1 0 0 1 -1 ... (again repeated for all subjects). In this
> case, however, I understand that my inference would be limited to the
> subjects studied, because this is a fixed-effects approach.
This is an interesting issue which we have been wrestling with as
well. One approach would be to take estimates of the simple main
effects to the second level (e.g with contrasts 1 -1 0 0, 0 0 1 -1) and
model these seperately (using 'multiple regression' in 'Basic models'
and [0,...0, 1,...1] for the first regressor and [1,...1 0,...0,] for
the second). A conjunction of second level contrasts [0 1 and 1 0]
should give you what you are after. The assumption you are making here
is that the simple main effects have the same error variance and are
independent of subject (i.e. show sphericity).
Perhaps others would like to comment on, or qualify, this?
I hope this helps - Karl
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