Dear Jerome,
> The outline of the problem are that we have a 4 x 3 design with a
> block design fMRI experiment; 4 movement durations, 3 movement
> frequencies for finger tapping. We have used the random effect model
> in SPM to create activation maps (voxel level, then cluster level) at
> each of the 12 conditions. Inspection of the data yields the
> impression that there are interactions between duration and frequency
> in certain brain areas (for example primary motor cortex and
> cerebellum). With Jean-Baptisite Poline, we tried to implement an F
> test to determine the interaction effects, but Zito's been stumped by
> a number of issues (again he knows the details, better than me).
There are a number of approaches to this depending on whether you want to
do a fixed effect analysis or random effect analysis.
The simplest would be to formulate the interactions in terms of
contrasts, an creating SPM{t} at the first level, or taking the
contrast images (one per subject) to the second level, for a RFX
analysis (one sample t-test). This is simple if you expect the
interaction to be linear i.e. increasing duration has a linear or
monotonic effect on frequency-evoked responses. I imagine this to be
the case for the ranges you have chosen. The contrast testing for this
interaction is effectively the contrasts for the monotonc effects of
frequnecy and duration multiplied by each other.
i.e. for each subjects 12 epoch-related regrwssors
D1F1 D1F2 D1F3 D2F1 D2F2 D2F3 D3F1 D3F2 D3F3 D4F1 D4F2 D4F3
-1 0 1 -1 0 1 -1 0 1 -1 0 1 = main effect
of Frequency
-1.5 -1.5 -1.5 -0.5 -0.5 -0.5 0.5 0.5 0.5 1.5 1.5 1.5 = main effect
of Duration
1.5 0 -1.5 0.5 0 -0.5 -0.5 0 0.5 -1.5 0 1.5 = interaction
(and the negative of this). Note that some cells have a contrast weight
of zero, which is a waste. A slightly more efficient approach would be
to model the main effects and interaction directly by parametrically
modulating a movement-related box-car regressor. Here the contrast weight
vectors enter at the specification of the design matrix (modulating a
single 'movement' regssor, three times, to give four regressors:
Movement Frequency Duration FrequencyxDuration
the contrast is now simply 0 0 0 1 (amd 0 0 0 -1).
This approach can be extended to model nonlinear or second order effects
but I would use a first order model initially.
I ope this helps - Karl
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|