Dear Sara
Returning to your second question, how to accommodate repeated measures in the second level of your three-level design. Another way to model this, which would not require per-subject regressors, would be to rotate your existing analysis design as follows. Create 6 separate second level PEBs with a single regressor (constant) in each:
1. PEB of pre-stimulus anodal
2. PEB of post-stimulus anodal
3. PEB of pre-stimulus cathodal
4. PEB of post-stimulus cathodal
5. PEB of pre-stimulus sham
6. PEB of post-stimulus sham
Then create one third level PEB, applied to the parameters all six of the above. There are various to specify the design matrix. For instance, you could model the mean and pre vs post for each condition:
X=[1 -1 0 0
1 1 0 0
1 0 -1 0
1 0 1 0
1 0 0 -1
1 0 0 1]
Of course, you can select which design is best by comparing the free energy, stored in PEB.F at the highest level of the design (note, do not use BMA.F).
Best
Peter
-----Original Message-----
From: Zeidman, Peter
Sent: 13 November 2019 14:19
To: Sara C <[log in to unmask]>
Cc: [log in to unmask]
Subject: RE: [SPM] Interpreting interaction results (PEB framework)
Dear Sara
Ah I now see that you're already using the PEB-of-PEBs approach :-) To remind myself of your design. At the first level you've got DCMs pre- and post-stimulation for each subject, where the stimulation can be anodal, cathodal or sham. At the second level you've got three PEB models: anodal, cathodal and sham. In each PEB model, you have two regressors of interest: the mean and pre vs post stimulation. You then have a third level (PEB) model, fitted to the two parameters from each second-level model. Your third level design matrix has separate regressors for each of the three conditions.
That all looks good in your script. The only thing that I can imagine is wrong is that the third level PEB model is specified as:
PEBvs_shamA = spm_dcm_peb(PEBall,M,field);
Where field = {'A'}. I think, however, the parameters going up to third level might be losing the name 'A'. To work round this, please could you re-run this using:
% Count the parameters going from the second to the third level np = length(PEBanodalA.Pnames) * length(PEBanodalA.Xnames);
% Run PEB on those parameters
PEBinteractionA = spm_dcm_peb(PEBall,M,1:np);
I would be interested to hear if that resolves the problem. There should then be 18 parameters in PEBvs_shamA.
Best
Peter
-----Original Message-----
From: Sara C <[log in to unmask]>
Sent: 13 November 2019 11:49
To: Zeidman, Peter <[log in to unmask]>
Subject: Re: [SPM] Interpreting interaction results (PEB framework)
Dear Peter,
Sorry to bother you again, we are trying to implement the design you suggested but we have doubts due to the results we are getting. More specifically, in a previous email you said this:
"To recap, you've got three 2nd level PEBs (which I'll order anodal, cathodal, sham below), and from each one you're getting two parameters: mean of pre/post, and differences between pre/post.
The 3rd level regressors for the between-subjects design matrix will be: commonalities [1 1 1]', TMS vs sham [1/3 1/3 -2/3]' and anodal vs cathodal [1 -1 0]'. This design matrix will automatically be replicated over 2nd level parameters, giving you the following regressors in your 3rd level PEB:
1. Commonalities of all 3 groups' pre/post mean (i.e. overall mean)
2. Commonalities of all 3 groups' pre/post difference (i.e. main effect of time)
3. TMS vs sham on the pre/post mean (i.e. the main effect of TMS vs sham)
4. TMS vs sham on the pre/post difference (i.e. interaction of TMS and time)
5. Anodal vs cathodal on the pre/post mean (i.e. main effect of anodal/cathodal)
6. Anodal vs cathodal on the pre/post difference (i.e. interaction of anodal/cathodal and time) "
However, when we look at the results from this PEB-of-PEBs using spm_dcm_peb_review(BMA,GCM) we only get 3 covariates, therefore we don't really know how we could get all those information (those 6 regressors you mentioned).
I attached here the script we used, perhaps if/when you have time you could give it a look to see if we are doing something wrong? Perhaps in the way we specify our GCMs?
We truly appreciate your help! Thank you very much.
Best regards,
Sara
On 29/10/2019, 11:20, "Zeidman, Peter" <[log in to unmask]> wrote:
Dear Sara
> 1) Do you think the design we tried is wrong? We did it that way because we are particularly interested in comparing each polarity against sham separately, because anodal and cathodal stimulation should exert very different (and, in theory, opposite) effects
Your design means that you can't compare anodal vs cathodal. E.g. if there's an effect of one of anodal vs sham and no effect of cathodal vs sham, you can't conclude there's a difference between anodal and cathodal (a difference in evidence is not evidence for a difference). Given you included them in the same experiment, I expect you want to compare them, so I'd put them in the same model. If you want sham to form the baseline, and get estimates of each TMS condition vs sham, you can code this using 3 regressors in your 3rd level PEB's between-subject design matrix:
Sham [1 1 1]'
Anodal vs sham [1 0 0]'
Cathodal vs sham [0 1 0]'
I.e. with this design, sham forms the intercept of the model. You could first use the design mentioned in my previous email to test for main effects and interactions, then use the design above to get separate estimates of each condition for plotting purposes (i.e. to understand your interaction).
> 2) Either with this new design or with the one we tried, would the procedure I described in the previous email be correct if we then want to look at the direction of the interaction (as in increase or decrease of excitation or inhibition)?
> I'm referring to this from my past email:
> "We tried performing 6 separate PEBs for each polarity and time, and saving the updated DCMs like this: [PEB,rGCM] =spm_dcm_peb(GCM,M,fields) We then averaged the values in GCM.Ep.A across participants and plotted them for each node of our A matrix to see the direction of change (e.g. changes between anodal and sham pre and post stimulation), but it seems like these values are not exactly concordant with what we see in the interaction results…is there a better way of doing it?"
> (So essentially I'm trying to understand how to interpret the final results)
The approach I mentioned above might give more consistent results than plotting the individual subjects' updated DCMs (although I agree that sounds sensible). There are various reasons why the individual subjects may look different to the PEB result - essentially, the parameters that best explain the group aren't necessarily the parameters that best explain the individuals.
Hope that helps
Peter
On 28/10/2019, 13:00, "Zeidman, Peter" <[log in to unmask]> wrote:
Dear Sara
I think you should simplify this so that you've just got one PEB-of-PEBs (I'll call that the 3rd level). To recap, you've got three 2nd level PEBs (which I'll order anodal, cathodal, sham below), and from each one you're getting two parameters: mean of pre/post, and differences between pre/post.
The 3rd level regressors for the between-subjects design matrix will be: commonalities [1 1 1]', TMS vs sham [1/3 1/3 -2/3]' and anodal vs cathodal [1 -1 0]'. This design matrix will automatically be replicated over 2nd level parameters, giving you the following regressors in your 3rd level PEB:
1. Commonalities of all 3 groups' pre/post mean (i.e. overall mean)
2. Commonalities of all 3 groups' pre/post difference (i.e. main effect of time)
3. TMS vs sham on the pre/post mean (i.e. the main effect of TMS vs sham)
4. TMS vs sham on the pre/post difference (i.e. interaction of TMS and time)
5. Anodal vs cathodal on the pre/post mean (i.e. main effect of anodal/cathodal)
6. Anodal vs cathodal on the pre/post difference (i.e. interaction of anodal/cathodal and time)
Hopefully this will be easier to interpret. Please let me know if anything remains unclear.
Best
Peter
-----Original Message-----
From: SPM (Statistical Parametric Mapping) <[log in to unmask]> On Behalf Of Sara Calzolari
Sent: 26 October 2019 10:39
To: [log in to unmask]
Subject: [SPM] Interpreting interaction results (PEB framework)
Dear DCM experts,
I have a question regarding the interpretation of PEB results when dealing with INTERACTIONS.
Here’s the context of the analysis:
We’ve applied 3 tDCS sessions to each participant (anodal, cathodal and sham) and scanned them PRE and POST tDCS stimulation in each session.
We wanted to compute the interaction of time (pre/post) and polarity of stimulation (anodal vs sham and cathodal vs sham).
Therefore, in our analysis we’ve performed:
3 first-level PEBs (one for anodal, one for cathodal, one for sham stimulation), in which the contrast is [-1 1] for scans Pre and Post stimulation
2 second-level PEBs, one for the contrast anodal vs sham [1 -1] and one for the contrast cathodal vs sham [1 -1] that take as input the first-level PEBs
The results of these two final PEBs should therefore be the interaction of time and polarity.
Now, we would like to interpret these results, and in particular we would like to understand the direction of the resulting changes in each node (e.g. result in one node shows a decrease in connectivity - is this a decrease in excitation or a decrease in inhibition?) I know we can’t infer that information from these results only, so my question is: how can we get information regarding the direction of these interaction effects?
We tried performing 6 separate PEBs for each polarity and time, and saving the updated DCMs like this: [PEB,rGCM] =spm_dcm_peb(GCM,M,fields) We then averaged the values in GCM.Ep.A across participants and plotted them for each node of our A matrix to see the direction of change (e.g. changes between anodal and sham pre and post stimulation), but it seems like these values are not exactly concordant with what we see in the interaction results…is there a better way of doing it?
NB: it’s resting-state data, so we have results for the A matrix only.
Many thanks for your help!
Best regards,
Sara
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