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Dear Marco

In your example experiment, you have three levels – let’s call them the within-session level (one factor: conditionA vs conditionB), the between-session level (session1 vs session2) and the between-subject level (this is just the group mean across subjects, as you have no other covariates). For simplicity, I’ll assume that at the within-subject level, the subject is always either in conditionA or conditionB.

Here are two options for how to model this:

Option 1: One PEB model

- Model all the within-session and between-session effects at the first level (in the GLMs / DCMs). So in your GLM for any given subject, you’ll concatenate runs and include a regressor modelling the effect of condition A, and a regressor modelling the effect of session (e.g. a column vector with value 0 for each MRI volume in run 1, and value 1 for each MRI volume in run 2).

- Specify and estimate a DCM for each subject, with the onsets of condition A as the driving input. Include the session regressor from the GLM as the modulatory input (B-matrix) – so in your model, you’re explicitly parametrising the effect of session on particular connections. I would not explicitly include the interaction term in the DCM – because you get this for free (in DCM, the modulatory input is only in play with the driving input is on).

- Take the B-matrix parameters representing the regions-specific session effects to the group level, by summarising them in a second level Bayesian GLM (PEB model), with just a column of ones as the design matrix.

Option 2: PEB-of-PEBs

- Create 2 DCMs per subject: one for each run.

- For each subject, create a subject-specific PEB model with their two DCMs as input. E.g.

PEB_subject1 = spm_dcm_peb([‘GCM_subject1_session1.mat’; ‘GCM_subject1_session2.mat’],X2)

The design matrix X2 will have two columns, representing the commonalities across sessions [1 1]’ and the difference between sessions [1 -1]’.

- Take the parameters from the previous step up to the third level. In other words, you’ll form a 3^rd level PEB model summarising the parameters of the subject-specific parameters. To do this you would type:

PEB_group = spm_dcm_peb(PEBs, X3),

where PEBs is a vertical cell array containing each subject-specific PEBs. Design matrix X3 is just a column of ones. This third level model now has parameters representing the group average (across subjects) of the commonalities across sessions and the differences between sessions.

In my opinion, the second option is more elegant, because it recapitulates the structure of your experiment. However, I expect it would be less sensitive. The DCM estimation will have far less data to work with when estimating the parameters, and I expect in practise, you’ll end up with less efficient estimators overall. But I’d be interested to here if that’s correct :-)

All the best

Peter

From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]] On Behalf Of marco tettamanti
Sent: 10 October 2018 10:36
To: [log in to unmask]
Subject: Re: [SPM] PEB model comparisons - spm_dcm_bmc_peb and spm_dcm_peb_bmc

Dear Peter,
I take the chance to jump into this discussion with a follow-up question on your very clear explanation:
Regarding the specification of covariates within the PEB Design Matrix, is it the case that for spm_dcm_bmc_peb.m - but also for spm_dcm_peb_bmc.m - one could model not just between-subjects but also within-subjects effects?
Say, for instance a 2x2 within-subjects design, with one group of subjects, each scanned twice under two experimental conditions:
Covariate 1: Main effect of Group
Covariate 2: Main effect of Factor1: Session1 vs. Session2
Covariate 3: Main effect of Factor2: ConditionA vs. ConditionB
Covariate 4: Interaction Factor1 X Factor2

Thank you and very best wishes,
Marco

On 09/10/2018 12:19, Zeidman, Peter wrote:

Dear Marta

Thanks for your question about how spm_dcm_bmc_peb.m works. First, to clarify something potentially confusing about the naming of the functions – which you may have already worked out:

The function spm_dcm_peb_bmc.m compares the evidence for different reduced (nested) PEB models, in which different combinations of parameters are switched off relating to specific DCM connections. For example, you might use this function to compare the full PEB model against the reduced PEB model in which all parameters relating to the connection from hippocampus to thalamus have been switched off.

By contrast, the function spm_dcm_bmc_peb.m asks which combination of connectivity parameters provides the best estimate of between-subject effects (e.g. age or clinical scores). In other words, it scores every combination of connectivity structures and regressors (covariates). So you could use this function to ask which combination of connections underlie a particular diagnostic test or a mixture of tests.

Which function you use will depend on whether your question is primarily about connections or covariates.

Overview of spm_dcm_bmc_peb

The function performs the following set of steps. For each first level connectivity structure (DCM), it computes a Bayesian GLM (PEB model). It then compares the evidence for each PEB model against reduced models in which combinations of parameters have been switched off. Specifically, it will switch off connections relating to Covariate 1, Covariate 2, Covariate 3… and all mixtures of covariates, for example Covariate 1 AND Covariate 2, Covariate 1 AND Covariate 3. You will end up with a score (free energy) for each combination of connectivity patterns and regressors.

The resulting figure for an example analysis is shown, attached. I’ll walk you through it, and highlight matrix K that you were asking about –

-          Middle right panel (‘Design matrix’). This is the between-subjects design matrix used in the PEB model. I had 30 subjects and 3 regressors – group mean, diagnosis and age. In all plots, white = 1 and black = 0.

-          Bottom right panel (‘Model space’). The 3 regressors above give rise to 4 combinations or mixtures of regressors. These are referred to 2^nd level models, shown here. For example, model 1 has all three regressors switched on, model 2 has regressors 1 and 2 but not regressor 3 switched on, etc. This is matrix K – with one row per 2^nd level model and one column per regressor.

-          Middle left panel (‘Posterior probabilities’) shows the joint probability of PEB models fitted to each of the DCMs (columns) with each of the mixtures of regressors (rows). This shows that the best explanation for the group level data is the first DCM with the second mixture of covariates (mean and diagnosis, but not age). The corresponding free energies are shown in the bottom left panel.

-          Top left and top right panels (‘First level’ and ‘Second level’). This shows the same information as the middle left panel, but marginalised (summed) over rows and columns. So from the top left panel, it’s clear that connectivity structures 1 and 2 are the best, and from the top right, it’s clear that mixture of regressors number 2 is the clear winner.

Hope that helps

Peter

From: Gandolla Marta [mailto:[log in to unmask]]
Sent: 08 October 2018 12:15
To: Zeidman, Peter <[log in to unmask]>
Cc: Lorenzo Niero <[log in to unmask]>
Subject: Bayesian model reduction and empirical Bayes for group (DCM) studies

Dear Peter,

this is Marta Gandolla from Politecnico di Milano, and I'm writing you as you are indicated as corresponding author for the paper mentioned in the subject, published on 2016.

We are currently replicating your approach with our data, however, we would need a confirmation from you.

With respect to 2nd level analysis, the code select itself in independece the model space order (function spm_dcm_bmc_peb).

By reading your paper and information found here and there, we concluded that the model space is indicated in the variable BMC.K, where we can find on the columns the specified second level regressors, and in the rows the models.

We would be greatful if you could confirm or detail our interpretation of the output of your paper.

All the best,

Marta

--

Marta Gandolla

Post-Doc Research Fellow
NEARlab - NeuroEngineering And medical Robotics Laboratory
http://www.nearlab.polimi.it/
Dipartimento di Elettronica, Informazione e Bioingegneria - DEIB
Politecnico di Milano

phone: +39 02-2399-9509
fax: +39 02-2399-9003

--

Marco Tettamanti, Ph.D.

Nuclear Medicine Department & Division of Neuroscience

IRCCS San Raffaele Scientific Institute

Via Olgettina 58

I-20132 Milano, Italy

Phone ++39-02-26434888

Fax ++39-02-26434892

Email: [log in to unmask]

Skype: mtettamanti

http://scholar.google.it/citations?user=x4qQl4AAAAAJ

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