Hi Marco,
I'm not a DCM expert, but I have some suggestions that might tide you over
until one of the DCM authors gets a chance to reply....see below

i) The GLM design matrix included, along with the 4 experimental
> conditions, a 5th regressors representing all stimuli of all conditions
> (i.e. conditions A1, A2, B1, and B2 merged). We called this regressor ALL.
>
> ii) VOIs were extracted from the t-Student main effect (A-B).
>
> iii) ALL was the driving input vector to the input region, whereas the 4
> individual experimental conditions were allowed to separately modulate
> all the intrinsic connections of the system.
>
> iv) With contrasts on the bilinear parameters of matrix B, we then
> assessed whether the individual connections were strengthened
> differentially for e.g. (A-B) or for (A1-A2)-(B1-B2).
>
> So much for our implementation. Now the reviewers' points:
>
> One reviewer points out that since the condition ALL is not orthogonal
> to the other regressors, this will affect the estimation of the
> t-contrast for the extraction of the VOIs (point ii above). The reviewer
> suggests to leave out the regressor ALL from the analysis. While we
> actually found minimal differences between the results of the GLM
> analysis with and without the regressor ALL, we are of course aware that
> this is a problem. However, we do not know how we should proceed. Our
> understanding is that modelling the 4 experimental conditions as
> separate inputs to the DCM model corresponds to asking a different
> question, based on the intrinsic connections (matrix A), and not on the
> bilinear parameters (matrix B). This is not what we want.
> The reviewer suggests that we should instead use the GLM model without
> the regressor ALL and "set the contrasts accordingly for the B and C
> vectors". We do not know what this means in practice.


Here it would probably help to take a look at Will Penny's example on the
spm website. I think that the best way to address you question (which is the
same as the example if I recall correctly) is to model your 2 x 2 factorial
DCM with 3 regressors: one including all sensory input, one including a main
effect ( e.g all A1 + all A2 trials) , and one an interaction (e.g. just all
A1 trials) .  Each regressors thus models a smaller and smaller subset of
the trials, and some trials are modelled twice or more.  This allows you to
set the first regressor ('photic') as a driving input to the system,
entering all the information to the system in one go.  You can then assess
the modulatory influence of your main effect regressor or your interaction
regressor on the connections in your DCM.  The 'comparison' with other
conditions is implicit in the fact that these become part of the baseline
for each regressor.

I can see 2 disadvantages in the approach you have taken so far.  1) by
modelling
all 4 conditions separately, and then adding the ALL regressor, I guess
your parameters are not uniquely specified, because you will have modelled
all trials exactly twice (have a look at the grey boxes below your design
matrix).  2) DCM is not really an exploratory connectivity technique.
Rather than assessing the modulatory influence of all your regressors on
*all* your connections, a better approach might be to make 2 models, one in
which the main effect regressors modulates the connections between your
regions of interest, and another in which the interaction regressor does
so.  You can then compare these models using Bayesian model comparison, to
address your precise question.


> Another reviewer, in turn, points out that our "DCM model is
> overmodeled" and suggests that we should "re-define the model such that
> (1) All [ALL?? (my note)] input is linked to the input region and (2)
> only (i) the main effect of A vs B, (ii) the main effect of 1 vs 2 and
> (iii) the interaction are entered as modulatory effects. Currently, the
> authors allow all four effects to modulate the connection strengths
> rendering an interpretation of the intrinsic connectivity and modulatory
> effects per se ambiguous."

I think this is similar to my suggestion above, except that the reviewer
suggests entering both main effects (A vs B e.g.. all A1 + A2 trials AND 1
vs 2 e.g. A1+B1 trials) as well as the interaction.

>
> As a minor point, our fMRI experiment included 9 separate sessions.
> Following previous suggestions on the spm-list, we modelled our GLM
> design matrix with 1 single super-session including all 9 time series,
> and included 9 additional confound regressors modelling the session
> effects.
> One reviewer suggested that we should instead average the results across
> sessions or concatenate the time-series of the sessions. The latter
> suggestion does not seem viable, since the length of the VOI time series
> would not correspond anymore to the size of the SPM.mat design matrix
> entered in the DCM model specification GUI.
> Are there any strong arguments against modelling "super-sessions" as we
> did?

I don't exactly know what you mean by a super-session if you don't mean
concatenation...but  as the reviewer points out, you can simply make a DCM
(and,  correspondingly, each VOI) for each session, and then easily average them following estimation,
although this might be a bit laborious if
you are using the GUI.  I know of no disadvantage to modelling all your
scans in a single session as long as you model between-session variance as
a nuisance...but then perhaps your reviewer knows of a reason that I don't
:)

read down to this point!), one reviewer
> argued against our choice of reporting connections at posterior
> probabilities of P>0.80, suggesting that we should instead use a more
> conventional threshold of P>0.95 or P>0.90.
> We understand that a threshold of P>0.80 is quite liberal. On the other
> hand, the intrinsic connections were all strongly significant (all
> P>0.95). With respect to matrix B, we wished to demonstrate that the
> functional integration within the specified neural system was greater
> for conditions A vs B. The contrasts on the bilinear terms showed that
> in all the connections within the system the direction of the modulatory
> effect was always in terms of a greater strength for conditions A than
> for conditions B. All the connections showed a P > 0.80, and no
> connection showed e.g. a P > 0.10, indicating a stronger connection
> strength for B vs A.
> The choice of the Bayesian threshold, although quite liberal, was
> therefore aimed at showing the overall direction of the modulatory
> effects (A>B). Is this fallacious statistical reasoning?
>
I will leave this to the Bayesians.  But just one point: as far as I am
aware, the fact that your intrinsic connections are or are not significant
is of little relevance for interpreting the statistical reliablity of your
modulatory connections.

good luck
Chris