Dear Nofar
Sorry for the delay in getting back to you. In a follow-up email, you mentioned that you got a different answer on this question from Stefan Frässle. Revisiting your question, I agree that he was right and I was wrong :-)
To recap, you had three experimental conditions of interest where word stimuli were presented: ambiguous words 1 (ambig1), ambiguous words 2 (ambig2) and unambiguous words. You modelled these in the DCM as 'all words', ambig1 and ambig2, where 'all words' was driving and the others were modulatory. Because you had other unmodelled conditions in the experiment, sometimes the input was zero (i.e., there was an unmodelled implicit baseline). And you didn't mean-centre the inputs.
Therefore, as Stefan says, the response x for one region would be defined as:
dx/dt = ax + b{2}*u{2} + b{3}*u{3} + c*u{1}
Where I have used curly brackets to indicate the experimental condition: {1}=all words, {2}=ambig1, {3}=ambig2. When there was no word stimulus being presented, so u{1}=u{2}=u{3}=0, this reduces to:
dx/dt = ax
Therefore, the A-matrix parameters are the activity when no words from the three conditions of interest are being presented.
All the best
Peter
-----Original Message-----
From: Zeidman, Peter
Sent: 26 July 2021 15:21
To: Nofar <[log in to unmask]>; [log in to unmask]
Subject: RE: [SPM] DCM design and interpretation
Dear Nofar
> Our VOI’s were extracted from the original SPM.mat, that includes 11 conditions. Only 3 of these conditions are of interest for the DCM analysis: Unambig words, Ambig words1, Ambig words2. We therefore extracted the VOI’s while adjusting for the F-contrast that only includes these 3 conditions, namely: {1 0 0; 0 1 0; 0 0 1}.
Great.
> We then created a new SPM.mat that includes 3 conditions: 'All words' (including words from all 3 conditions of interest: Ambig1+ambig2+Unambig), ‘Ambig1’ and ‘Ambig2’.
> In the DCM model ‘All words’ served as the driving input (C matrix), and 'Ambig1' and 'Ambig 2' - were used as modulatory effects (B matrices).
Very good.
> 1. We did NOT mean-center the input matrix U. Can we interpret our A matrix as reflecting connectivity during the “neutral” times in our experiment (e.g. un-modeled null events)? Can we assume that it does not reflect connectivity during the other (8) conditions included in the original timeseries because we adjusted the VOI’s for the F contrast that only included the 3 relevant conditions?
In this case, we would interpret matrices B (ambig1, ambig2) as the connectivity during reading ambiguous words (1; 2) as compared to null event. Correct?
Almost - you would interpret matrix A as the connectivity during unambiguous trials. The B matrices are the connectivity during ambiguous trials, relative to the unambiguous trials, i.e. relative to the A-matrix (remember that in the equation for the neural model, the effective connectivity is the sum of the A and B matrices when the modulatory inputs are in play, whereas the effective connectivity is just matrix A when there are no modulatory inputs in play). If it's helpful - the interpretation is similar as it would be for your GLM.
> 2. If we want to estimate the difference in connectivity between reading ambiguous words (1 and 2) and unambiguous words, what would be the best way to do that?
> • Option A: add a 4th condition to the new SPM for ‘Unambig’, then use this regressor as another B matrix, and then compute contrasts comparing the difference between Ambig1-Unambig, and Ambig2-Unambig.
> • Option B: in the new SPM create 3 conditions: ‘Ambig1’, ‘Ambig2’, and ‘Ambig words’ (which includes the other 2 but does not model unambiguous words). In DCM include ‘Ambig words’ as a driving input (C matrix) and ‘Ambig1’ and ‘Ambig2’ in the B matrices. In this case, if we do NOT mean-centre the input the A matrix will reflect connectivity during Unambiguous words (because they were not included in the input matrix U), and the B matrices will reflect the difference between ambiguous and unambiguous words.
You don't need to - these are the B-matrix parameters you already have. Alternatively, if you really need a parameter for the main effect of ambiguity (ambiguous vs non-ambiguous), you could create a design matrix with (1) all words, (2) all ambiguous, (3) ambig2 (or ambig1 - but not both). The second condition can then be interpreted as ambiguous vs non-ambiguous, and then third condition can be interpreted as ambig2 vs ambig1. But as I said, you've already got separate parameters for each kind of ambiguous trial, so that may be sufficient.
All the best
Peter
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