Dear Gus
> 1. I have a patient sample and a control sample that Id like to compare. Is it appropriate/valid to perform the first-level model estimations using the Full+BMR PEB option on the two groups separately (ie one GCM per group), and then concatenate these two estimated GCMs for the second-level PEB analysis (which includes the 1 -1 group regressor)?
No, I don't think this would be ideal. The spm_dcm_peb_fit function (which underlies the Full+BMR PEB option) will draw subjects' parameter estimates towards the group mean, where local minima exist. To do that separately for each group could bias your future inferences towards group difference. Is there a particular reason you want to do this?
> 2. Is it possible/meaningful to compare the fitness of PEB models? That is, I have a single full DCM model per subject that I search using PEB to prune connections, and would be interested to make the determination for example that a PEB model which includes age as a regressor fits better/worse than a PEB model without age included? On this note, is the PEB-resulting BMA.F an indicator of the model evidence of the reduced model, and thus if exp(BMA.F) is 0 then the BMA model may not be fitting/explaining the data very well?
Yes - comparing group level models (PEBs) based on their free energy is an important part of the framework. One option is to ask which combination of connections best explains your data - that's the search option you mentioned in the batch editor (implemented in spm_dcm_peb_bmc.m). Another option is to ask which combination of regressors (e.g. with or without age) best explains your data. You could do this yourself by comparing the free energies (PEB.F) of the different PEB models. Or you could use the function spm_dcm_bmc_peb.m (not to be confused with the one above!) which will compare all combinations of your behavioural regressors. This doesn't yet have a GUI, but give it a go - I'm happy to provide further guidance on interpreting the results if it's not clear.
Model comparisons on PEBs, performed using the PEB framework, will also produce a Bayesian Model Average (BMA). The BMA can either be over competing PEBs that you specify, or via an exhaustive search as you mentioned. I would not recommend using the BMA.F to perform further model comparisons.
> 3. Is it possible to recover subject-level parameters following the second-level PEB search? For example, if I see a strong evidence of a group difference for a particular connection, and wanted look at the group-averages, where would I find the Hz values for each subject (the BMA only appears to be storing sample means, unless Im missing where they are stored)?
Having used the BMA search to establish the group difference, you might indeed want to plot the DCM connections' strengths. In particular, you can plot the DCM connection strengths you would have got, if the DCMs had been estimated with group-level priors. The GUI doesn't provide this yet, but you can easily do it with a script:
[PEB, GCM_updated] = spm_dcm_peb(GCM, M, fields);
The structure GCM_updated contains all the subjects' DCMs, with the expected value (GCM{i}.Ep) and covariance (GCM{i}.Cp) of each parameter in subject i. For further details of scripting PEB (details of the M and fields parameters), see https://en.wikibooks.org/wiki/SPM/Parametric_Empirical_Bayes_(PEB) . Note that we don't currently have a facility to update the DCMs with priors set after performing the model search, although this could be implemented in principle.
Do let me know if you have any further questions.
Best
Peter
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