Dear Tali,
Regarding your first question - how, in general, additional parameters could reduce the variance explained by a model. It's easy to think of a case where adding a parameter could reduce explained variance. Say I add an A-matrix connection parameter to a DCM which is not there in the biological system, and this additional connection disrupts the dynamics of the whole network. Call this the 'full' model. It will give lower explained variance than a nested model without this erroneous connection.
Keep in mind that explained variance is just the correlation between your predicted timeseries and the observed timeseries. It is not a robust measure of model fit as it doesn't take the complexity of the model (effective number of parameters) into account. I like to use explained variance as a sanity check - to confirm that my predicted timeseries "look like" my observed data rather than, say, having flat-lined. But we don't use it for model comparison for the reason I explained (free energy deals with this by reflecting the accuracy minus complexity).
As for post-hoc DCM. It's not clear whether the 16 models on which you performed full estimation were the same models as those on which you used post-hoc? Post-hoc DCM disables parameters (by setting their prior variance to 0) where doing so won't make much difference to the model evidence. That is, where the evidence of the full and reduced model is approximately the same. If you're finding a difference between full estimation and post-hoc on the same models, it could be that the model estimation in one approach is falling into a local minimum and not finding the optimal solution.
Best,
Peter.
Peter Zeidman, PhD
Methods Group
Wellcome Trust Centre for Neuroimaging
12 Queen Square
London WC1N 3BG
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-----Original Message-----
From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]] On Behalf Of Tali Bitan
Sent: 23 June 2014 20:35
To: [log in to unmask]
Subject: [SPM] Variance explain by DCM
Dear DCM experts
Previous posts suggested to look at the variance explained by models in DCM (DCM.R - in using DCM Diagnostics or spm_dcm_fMRI_check) as an indication for model convergence in DCM_post_hoc. As far as I understand this assumes that the variance explained by the full model is the upper limit for the the variance explained by any reduced model.
We have now specified and inverted 16 DCM models to use in a standard BMS (not post-hoc). When looking at the variance explained by these models we find that in some individuals, there are models that explain more variance than the full model.
My question is:
1) How can that be possible? How can the inclusion of additional parameters reduce the variance explained by the model?
2) If this is possible - how can this criterion (variance explained by the full model) be used as exclusionary criterion for participants from DCM_post_hoc?
Thanks
Tali Bitan
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