I am now involved in a project examining the nonlinear effects of effective connectivity. For our fMRI data, I have constructed several nonlinear DCM models as well as regular bilinear DCM models. Unfortunately, the model comparison procedure always give higher evidence for the bilinear models, even though I have evidence from the physiophysiological interaction analysis that there might be a nonnlinear modulation effect. So I started to think whether it is appropriate to directly compare nonlinear DCMs to the bilinear DCMs. 

 

 

To my understand, I think model A and B should have same model evidence, because all the zero parameters of DCM.d will not accounted in model complexity. However, when I compared model A and B using model comparison procedure, model A was always better than model B. I want to ask that why model A is better than model B in this circumstance? And is it reasonable to use model B as a control bilinear model when I want to illustrate nonlinear effects of some nonlinear DCMs? 

 

 

That is interesting. You are absolutely right that the two models should have the same evidence – in theory.   However, the use of a nonlinear DCM requires a slightly more elaborate integration scheme (because the states need to be updated more frequently - because they change connectivity):

 

% specify parameters for spm_int_D (ensuring updates every second or so)

%--------------------------------------------------------------------------

if DCM.options.nonlinear

    M.IS     = 'spm_int_D';

    M.nsteps = round(max(Y.dt,1));

    M.states = 1:n;

else

    M.IS     = 'spm_int';

end

 

This means that the model predictions will be slightly different and that models A and B are (in effect) different. I think it is a very good idea to compare nonlinear models with and without non-zero D parameters (i.e. use model B as a null nonlinear model). This ensures the same integration scheme is used for both.

 

I suspect that, in the absence of nonlinear coupling effects, the standard integration scheme is slightly more accurate – this may be why model A has greater evidence than model B.

 

I hope this helps.

 

With very best wishes and Happy New Year – Karl