Dear DCM experts,

I hope you could help us with some insight concerning some weird behaviour during DCM model inversion that we have observed.

We apply bilinear DCM for fMRI on event-related data from 2 prefrontal regions in a decision-making task. We use one of the main conditions as "direct input" (via the C-matrix) and its 1st parametric modulation as "modulatory input" (via the B-matrix). We apply the default EM algorithm for model inversion.

Being an ER design, it's not optimal for DCM and we also initially had "flat-line" fits in most of our subjects using the default DCM settings (DCM 10). 

We then changed the hyper-priors on mean and covariance on observed responses from the default M.hE = 0 and M.hC = 1 to M.hE = 4 and M.hC = exp(-8) where we still had flat-line fits. At M.hE = 8 and M.hC = exp(-10) we had fitting (ie pure noise was no longer the "best" model of data).

We tried also M.hE = 10 and M.hC = exp(-12) and here we found that the "observed response" plotted via the spm_nlsi_GN script began to drift from around zero to around 10 in 2 subjects (and resulting in very good % variance explained on 80-90 %)-- please see the attached slide with screenshots from time-step 6 to time-step 124 of the same model fitted to (suppossedly) the same data from one of the subjects. We used the default HP filter at 128 at 1st level analysis. Out of 4 models in our model-space, it was only in one of the models that we saw this drift.

Looking at the script spm_nlsi_GN the plotting of "observed response" is based on, as I understand it, the prediction (f) + the prediction error (e). (A question aside: why is observed data calculated in this way iteratively, rather than using the eigenvariate from the DCM.Y.y ?)

So, the drift must have something to do with this way of depicting the observed response.

But it leads us to wonder whether the results using non-default hyper-priors (including less extreme ones) are trustworthy in general- as stated, the drift was noticeable in 2 subjects out of 16, but we worry whether in other subjects this has lead to flawed results also because of smaller drifts that were unnoticed. Is it a phenomenon that arises because we choose rather extreme hyper-priors and could we still use, say M.hE = 8 and M.hC=exp(-10) where this drift was not observed in this subject? 

Thanks a lot for your time and help!

Best regards, Brian Haagensen