Dear SPMers,
in our study we manipulated two parameters independently in three levels. For instance, intensity (low, medium, high) and speed (slow, medium, fast) of a single stimulus (thus, 9 conditions plus resting baseline). To assess the effects of each parameter, we modelled all trials as one single condition with two parametrics (SPM5) and then we could test for each parameter by a 0 1 0 0 ... contrast. However, how would it be possible to detect areas which show an interaction between intensity and speed?
If we would have only two parameters, I would have used an interaction contrast such as (fast/high - fast/low) - (slow/high - slow/low). However, this would not incorporate the intermediate levels of the parametric manipulation.
The only other thing I could think of would be derived from linear regression methodology. Create 9 conditions and let the interaction be the product of the two conditions:
cond intensity speed interaction
1 low (-1) slow (-1) +1
2 low (-1) med (0) 0
3 low (-1) fast (+1) -1
4 med (0) slow (-1) 0
5 med (0) med (0) 0
6 med (0) fast (+1) 0
7 high (+1) slow (-1) -1
8 high (+1) med (0) 0
9 high (+1) fast (+1) 1
With these 9 conditions one could test using the following contrasts:
linear increase of activity with intensity: -1 -1 -1 0 0 0 1 1 1 (first column)
linear increase of activity with speed: -1 0 1 -1 0 1 -1 0 1 (second column)
interaction of intensity and speed: +1 0 -1 0 0 0 -1 - +1 (third column)
However, this sounds rather complicated and I'm not sure whether this would be the best/right way to do this analysis. In particular, as the "complicated" contrast in column three is identical to the easy suggestion mentioned above :-) (as if only two factors were present). In this case I'm wondering whether it was of any advantage to include a third, intermediate, condition...
Any comments are greatly aprreciated!
Thanks a lot &
Kind Regards,
Andre
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