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Dear Ian,
The conditional dependencies among parameters can be high. Even between parameter pairs for A,B and C (excluding haemodynamic parameters) we have found correlations
up to -0.3, although most were in the range -.1 to 0.1. The extent of this dependency will vary considerably between tasks and models. However, for one task and one family of models, it is possible that an additional parameter makes little difference to the
model evidence. A corollary is that correlated parameters can, if taken individually, be unreliable (i.e. better not to use one as a dependent variable in secondary statistical tests of group effects).
In addition to Klaas’ reference you could also look at fig 6 in http://www.ncbi.nlm.nih.gov/pubmed/20056151
(based of course on http://www.ncbi.nlm.nih.gov/pubmed/17884583). This demonstrates that the correlations
among parameters are reproducible across different data sets for a given model and task, both within and between different subject groups, and the problem is not just an idiosyncratic result of a specific data set.
Best wishes,
James
From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]]
On Behalf Of Klaas Enno Stephan
Sent: 03 April 2011 11:03
To: [log in to unmask]
Subject: Re: [SPM] DCM-Conditional Dependencies
Dear Ian,
Normalizing the posterior covariance matrix DCM.Cp corresponds to transforming it into a posterior correlation matrix. Since the correlation coefficient is
corr = COV_xy / (SD_x * SD_y)
you need to
1. compute the (posterior) standard deviation for each parameter (this is the square root of its diagonal entry in DCM.Cp)
2. divide each element in DCM.Cp by the product of the (posterior) standard deviations of the respective parameters.
Note you will have zero/NaN elements for each connection or input that you disallowed in your model specification; this will . You can suppress MATLAB warnings by
warning off MATLAB:divideByZero
and remove NaNs using the isfinite command of MATLAB.
The order of the elements in DCM.Cp is the same as in DCM.Ep.
All the best
Klaas
PS. For an example of what you want to do, see Figure 6 in this paper:
http://www.ncbi.nlm.nih.gov/pubmed/17884583
Von: Ian Ballard <[log in to unmask]>
An: [log in to unmask]
Gesendet: Samstag, den 2. April 2011, 0:40:16 Uhr
Betreff: [SPM] DCM-Conditional Dependencies
SPM experts,
I am writing to inquire as to how one goes about investigating whether modulatory inputs showed conditional dependencies (see email correspondence below). Dr. Stephan suggests looking at the normalized posterior covariance matrix. First, how exactly do you
normalize the posterior covariance matrix? Second, how do you decipher which indices correspond to which connections? Are they the same as for the Ep vector? Any help would be greatly appreciated.
Thanks,
Ian
Error! Filename not specified.
AW: [SPM] DCM model comparison - strong bias for simple models
Dear Tali,
Karl has already addressed most of your issues. As he said, there are clear differences between your sets of models, i.e. the changes in intrinsic connections clearly made a difference in your case. Without knowing the structure of you models in detail, it
is difficult to predict why changes in modulatory inputs did not impact much on the model evidence in your case. If you added additional modulatory inputs it could be that these additional inputs showed conditional dependencies with existing modulatory inputs
(simply speaking: the effects explained by one input were partially explainable by another). You can look at the posterior covariance matrix (DCM.Cp) to check this; you should normalise this matrix to a posterior correlation matrix to get interpretable values.
Best wishes,
Klaas