Dear Klaas, Darren, Rik, Chris et al,

Can I revisit the issue of disconnected regions in DCM models (archive # 045837) for your opinion. It is a common question about DCM and model selection. We agree that for comparisons of model evidences the same data are required in all models, which means that for DCM of fMRI (unlike M/EEG) the same regions must exist in all models. There are three cases one may wish to compare:

Case A: all regions are connected by one or more paths, and subject to network perturbation from driving inputs (directly or indirectly). A ‘normal’ model by current practice in other words, with variations on model structure comparable in terms of their Free energy. These variations include differences in intrinsic and modulatory influences, but always with all nodes connected to the main network. So far so good.

Case B: the regions fall into two groups or sub-networks, each with internal connections and subject to driving inputs (Rik’s question 1 below). Chris’ accepted case B as “modelling 2 parallel and independent processes a single model” ,provided that each component network had driving inputs. DCM then opimtises parameters jointly over both parts. An obvious case would be to compare models with and without inter-hemispheric connections between homologous regions, thereby connecting or disconnecting symmetrical intra-hemispheric networks.

Case C: all but one region are interconnected, and subject to driving inputs. One region is not connected to the rest of the network (Rik’s question 2 below). Case C is the problem.  I look forward to the extended version of klaas’ recent answer (below) but note the comment on this issue last year (archive # 040700) that “Technically, your approach is fine, but one may debate whether it is conceptually sensible.”  

If the disconnected region has driving inputs, but no afferents from the rest of the network, then it seems to be a special type of case B (a very limited parallel network) and therefore technically and conceptually ok.

However, if the disconnected region is wholly unexplained (no driving inputs and no afferents) then two things happen.  First, the model has no means to explain the activity of the region, and therefore the model accuracy would be very poor (lowering F: Darren and Chris’ points). The reduced complexity in the model that disconnects this region would elevate F slightly, but may be not enough to outweigh a wholly unexplained time series (an empirical issue). The Second problem is the loss of validity of the network model. Of the vast potential model space, we choose a subspace of say 2-50 models to compare, and base this selection of models on face-, structural- and predictive- validity of the models. The models are justified on their neurobiological plausibility, and theoretical relevance.  An active but wholly disconnected region without driving inputs or afferents is inexplicable within DCM and  implausible biologically (for the activity to be task related, not including spontaneous activity, epilepsy etc).

In summary, a model may include a region that lacks intrinsic connections with other parts of the network, provided that the model includes a potential explanation of the activity of the isolated region (e.g. driving inputs, or using stochastic DCM). DCM will then indicate whether adding intrinsic connections to the main network increases F (as evidence for an enriched, fully connected model). But, this is not an inference about whether the region is “missing”, since it was not missing from either model. It cannot be used to add or subtract regions from the model (in contrast to say GOF indices in iterative model building in SEM).

Is this a fair summary under current DCM?

Best wishes,

James

Dear Darren
Apologies for a brief reply (due to lack of time).  This question is relevant for any hypothesis-driven modeling approach, not only DCM.  In all brevity, my answer would be that simply comparing the evidence of two models in which a region X is connected vs. disconnected to the rest of the system is not sufficient to establish whether or not X is "missing" in the reduced model.  Instead, what one would need to do is to compute the evidence for the reduced model under presence vs. absence of the changes in system dynamics that *would have been induced in the reduced system* had X been allowed to interact with it.  More details on this (hopefully) soon  ;-)
All the best,
Klaas

Christophe and others,

I would like to get further clarification on #2 below- is it ok to have disconnected regions and to compare the models.
So if I understand what you are saying it is OK to disconnect regions and then test that model vs. ones with that region connected? I guess these models would be considered to have the "same data" even though the region was disconnected?
I understand the disconnected region wouldn't have any activity since it isn't being driven by anything, but I presume this would be reflected in a reduced free energy term?
Would it be possible to use the change in the free energy term to decide if a region truly belonged in the model?
Darren

On Thu, Mar 17, 2011 at 9:11 AM, Christophe Phillips <[log in to unmask]> wrote:

Hi Rik,
Let me have a go at your questions.
See interleaved text here under.
Le 17/03/2011 11:09, Rik Henson a écrit :

Dear DCMers –

 A few, hopefully simple questions for DCM(10) for fMRI:

 1. Does it make sense to have a model with 4 regions, in which 2 regions within each of 2 pairs are interconnected, but there are no connections across pairs (ie, two “isolated” subnetworks; eg, with regions E1<->E2 F1<->F2, DCM.a = [1 1 0 0; 1 1 0 0; 0 0 1 1; 0 0 1 1])?

Yes it does.
You're "simply" modelling 2 parrallel and independent processes a single model.

2. A related question to above: does it make sense to compare the free energy of two models, one in which a region is “isolated”  (ie has no connections apart from a self-connection) with one in which it has connections to other regions? And could this be used to ask whether that region needs to be in the model? (I realise one cannot use the free energy to compare models with different regions – ie different data – but wonder whether this approach could be a useful heuristic answer to that question?).

The residual term of the isolated region will be its own signal (no drive -> flat modelled activity).
So your question would rather be: is the activity in my last/isolated region better explained, or not, when it is driven by the rest of the network? The model comparison will thus be between a simple model where the activity of one area is not explained at all, and another one with an extra parameter and a bit more signal explained.
This doesn't really answer your question whether the region should (or not) be part of the network though...
I would say that choice of regions to include in the model is more empirical: you should include the areas necessary to build a model which models as accurately as possible (or  sufficiently realistically) the "brain function" you want to study.