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I guess here is the answer from Karl Friston :)
The only porblem is that we don't usually have a baseline condition collected.  
Neither SPM gives a baseline, SPM gives only "contrasts". 
Additionally, what's the baseline for the brain in real life..?
 


Dear Andre,


I'm looking for a paper which I'm very (but not 100%) sure was by you.
I just can't find it and I didn't get an answer via the SPM mailing
list. However, the issue is quite important for me.

The paper dealt with interaction contrasts and made the statement that
activation in each task can be subdivided into a task unspecific
component and a task specific component. Because of this the following
contrast would not be meaningful

A B C
1 -1 -1
An example would be a dual-task, where A is the dual-task, and B and C
are the individual component tasks the dual-task consists of. The aim is
to test whether there is additional (=over-additive) activation in A as
compared to the sum of B and C.
(BTW, I'm not even sure whether this contrast is mathematically valid)

In fact, the definition of a contrast (a weighted mixture of parameter 
estimates) is that it is estimable. This means if you can estimate it, it is 
valid (and SPM will tell you if you cannot).


In this example, the task unspecific effect would have been subtracted
twice from A. To circumvent this, it was suggested in the paper to
estimate the task unspecific effect by a resting baseline and add it to
condition A (in this example the dual-task). This would result in a
classical 2x2 interaction contrast:
A B C Base
1 -1 -1 1

Yes, this would be the way to establish over-additive effects, under a linear 
model. Imagine the following task analysis

A causes activation with the following components:

n    - non-specific
b    - B-specific
c    - C-specific
cxb - superadditive (interaction)

so:

A = n + b + c + cxb
B = n + b
C = n + c
B = n

The contrast weights  1 -1 -1     give A - B - C        =  cxb - n, while 
the contrast  weights  1 -1 -1  1 give A - B - C + B =  cxb , which is the 
superadditive effect.



I would greatly appreciate any hints what paper this was, and any other
comments on the logic of testing for (over-)additive activations.


The closest I remember is: 

http://www.fil.ion.ucl.ac.uk/~karl/The%20Trouble%20with%20Cognitive%
20Subtraction.pdf 


Note that there was a brief literature on superadditive effects in multi-sensory 
integration 
designs that addressed more ad -hoc definitions of superactivity of the form A 
> B & A > B, which 
implicitly appeal to nonlinear (ceiling-effect) models.


I hope this helps :) - Karl