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Dear Sunali,
If there is a clearly winning family then BMA is applied just to those models in that family. You can then proceed
with
parameter level inference.
If a parameter is absent from a model then during BMA it is assigned a value of zero. The more frequently that
model is selected in the BMA process (its selected in proportion to its evidence – see eq 27 in families paper) the more the BMA estimate of that parameter tends to zero.
Re inputs vs modulations – in the families paper the first question was – where does the input go ? family inference
was used to answer this. The answer being, input goes to region P. The question about the modulations was then restricted to those models for which the input went to region P.
Re your data. Perhaps you have 64 models for which the F-H connection is modulated, and 64 where the F-S connection
is modulated. You then have 2 families, and family inference tells you which is most likely.
Sorry for my very late email !
Best,
Will.
From:
Wadehra, Sunali [mailto:[log in to unmask]]
Sent: 28 November 2012 03:06
To: [log in to unmask]
Subject: Questions re: "Comparing Families of DCMs"
Dear Dr. Penny,
I am taking the liberty of emailing you, as your advice on a DCM-related question relevant to my current research would be highly valued.
By way of context, we have previously used DCM using a “best-model” approach (e.g., Diwadkar, Wadehra et al., Arch Gen Psychiatry, 2012)
where we selected the model with the highest evidence (model space of n=136), then making inferences regarding inter-group differences based on the Bayesian parameter averages from the winning model. This approach has yielded meaningful results. However, the
data set with which I am presently working (examining cortical-striatal-hippocampal interactions during associative learning in schizophrenia) may be better suited to Bayesian Model Averaging (Penny et al., 2010). Though your paper is extremely lucid, I am
having some challenges in adapting a BMA framework for my analyses.
My understanding is that in the paper you motivate a partitioning of models into disjoint subsets (p. 6) and then utilize a hierarchical
approach toward family level inference (p 8 & Table 2) before BMA to reach a final set of winning models associated with the specific partitioning related hypothesis (Figure 2).
I am a little unclear on how you make a transition from this approach to BMA of your chosen parameters? For example, it may be possible
that models in your subset do not share the same set of endogenous connections (though they share the same attribute on which they were assigned to the family). Thus, how is a parameter that may not be present in all models of a family explored?
Additionally, what was the rationale behind averaging only input parameters when the family-level BMS investigated in your paper investigate
both driving and modulatory inputs?
In our analyses, we are employing a model space to distinguish between hypotheses relating to the contextual modulation of frontal-striatal
and frontal-hippocampal pathways by learning. It is possible to construct disjoint model spaces associated with each of those hypotheses, but it is not clear to me how the parameter inference can accrue over the collective sets. For example, were we to splice
the families into frontal-striatal modulation for family level inference, models relating to frontal-hippocampal modulation would be distributed across the complimentary sets. The same would occur in the vice-versa case. It is possible that I am not understanding
some fundamental aspects of your approach.
I know you must be very busy but ventured to request your advice all the same. If there is some way that I can clarify what we are attempting,
I will be happy to provide you further detail and of course provide appropriate acknowledgement should we be able to submit our work for publication.
I look forward to your response.
Sincerely,
Sunali Wadehra,
Medical Student (Yr02)
Department of Psychiatry & Behavioral Neuroscience
Wayne State University School of Medicine
Detroit, MI USA