Dear SPM- and DCM experts,

I am currently working on a way to describe functional hemispheric  
dominance by means of connectivity. Following the example of Frässle  
et al. (2016, “mechanisms of hemispheric lateralization: …”) I want to  
compare intrinsic and modulatory (fMRI-)DCM parameters from both  
hemispheres. More precisely, I aim to assign a value to each of my  
subjects in a fashion close to the lateralization index often used for  
activation magnitude or cluster size, i.e. (left - right)/(left +  
right). It turns out, however, that there are some obstacles inherent  
to my approach which I am going to describe in the following:

The main issue preventing me from simply applying the classic LI to  
DCM parameters here is that this only works for two positive values.  
In the case of DCM parameters, the LI should be suitable for two  
negative parameters as well (by inversion of the result’s sign), but  
it is certainly not suited for one positive and one negative parameter  
and yields results outside the limits of -1 and +1. While computing  
the difference between a positive and a negative parameter would work  
perfectly fine (numerator), the problem seems to be the normalization  
(denominator), meaning I am now left with the evaluation of how big  
this difference is in relative terms.

I have tried transforming sets of parameters of interest across all  
subjects into a positive range to prevent negative values and then  
computing the classic LI. However, it seems inappropriate to just  
treat the most negative/positive parameter or basically any arbitrary  
value as the limits of this set. Additionally, this results in smaller  
normalization terms for parameters that were negative before  
transformation and larger ones for parameters that were positive  
before transformation. Therefore, I abandoned this approach in favor  
of a more promising one.

This time I transformed each subject’s entire set of parameters (A, B  
and C) into a common size. I did that by shrinking or stretching each  
set (preserving proportionality within the set) so that the average  
absolute parameter size is equal across all subjects. This essentially  
serves as a sample-dependent normalization so that the simple  
difference of one subject’s two parameters of interest should now  
serve as a comparable measure of lateralization in the context of this  
sample.

However, for this procedure I am assuming that the absolute size of a  
DCM parameter is not clearly interpretable per se or between subjects  
but only when comparing it with other parameters from the same  
subject/DCM. To my knowledge there is no rule of thumb on what is a  
small, medium, or big parameter of effective connectivity (is there?),  
which leads me to believe that it differs from one DCM to another. To  
me, this also corresponds with the fact that in some DCMs I find the  
parameters in general to be pretty large and in others rather small,  
while showing related connectivity patterns.

A brief example:
Let’s say I have inverted a DCM with 3 regions in each hemisphere and  
many connections between and within both hemispheres and now I am  
interested in the lateralization of the intrinsic connectivity from  
left to right area M1 (“l2r”) and from right to left area M1 (“r2l”).  
Both subject X and subject Y have l2r = 1.0 and r2l = 0.5 implying a  
stronger intrinsic information transfer towards the right M1. However,  
subject X’s parameters in general are large while subject Y’s are  
small. Let’s say subject X’s average absolute parameter size is 0.9  
and subject Y’s is only 0.3.
Am I now correct in assuming that the two parameters of interest  
should be considered more powerful within subject Y’s set of  
parameters? And if yes, is it adequate to assume that they are in fact  
about 3 times more powerful (0.9/0.3 = 3) and that this also applies  
to the difference ((1.0 – 0.5)*3 = 1.5)? Or am I better off just  
interpreting the absolute difference (1.0 – 0.5 = 0.5 in both cases)  
regardless of each subject’s average parameter size?

I am well aware that this form of normalization is quite different  
from the one applied in the classic LI, but I could not find any  
simple solutions in the literature or by myself. I have applied my  
normalization approach to a large sample of simulated DCM parameters  
(10,000 subjects x 38 parameters) and correlated the resulting  
differences with the classic LI for cases where both parameters of  
interest share the same sign (allowing the classic LI to yield valid  
results), Pearson’s r was ~ .88. When using the unnormalized  
differences instead, r drops to ~ .76, suggesting that I should go  
with the normalized differences instead of the “raw” differences to  
better approximate the classic LI. However, my knowledge regarding the  
interpretation of DCM-parameters is still somewhat limited, so I hope  
you can provide me with some insights. Any help would be greatly  
appreciated! Thanks in advance!

Best regards,
Rafael Maleki