Dear Hector,
> Dear Dr. Friston, sorry to bother you with this basic question but I am sur=
> e that you can help me. I am using fMRI time series to asses a model of eff=
> ective connectivity. I have three regions (x1, x2, x3) obtained from an ABA=
> BAB. paradigm. All of the regions are highly correlated:
>
> Correlation:
>
> x1 ,x2 == 0.85
>
> x1 ,x3 == 0.86
>
> x2 ,x3 == 0.81
>
> The anatomical model suggest the connectivity: x3== C1 x1 + C2 x2 + e
>
> Obviously, the variance in x3 could be explained by x1 or x2 by its own, so=
> when I try to compute the coefficients (using the first PC of the region)=
> one of them becomes very small. However if I made the regression separatel=
> y (x3== C1 x1 + e or x3== C2 x2 + e) the coefficients are almost the same. =
> I don't know how to model these relationships to reflect the real strength =
> of connections in the model.=20
I am afraid that you can only make an inference about the unique inputs
from x1 and x2 but not the common inputs (when you model only one input
the common input becomes unique and the regression coeficient is
suitably high). The simplest thing to do would be to orthogonalize x1
and x2. This makes the estimate of effective connecivity much more
efficient. In this case an orthogonalization scheme might be to create
two 'virtual' areas x1+x2 and x1-x1. The connection strength from
x1+x2 reflects the influence of both areas and the x1-x2 is the effect
of the difference.
> Another question is, which data I should use in the effective connectivity =
> analysis, i) the raw data of the most significant pixel, ii) the principal =
> component of the blob that defines the region, iii) the fitted and adjusted=
> response.
All three - I would use the principal component of the blob centered on
the most significant voxel. In spm_regions you should be able to
remove the confounds before computing the first eigenvariate. Do this
or the constant and drift terms will dominate.
With very best wishes,
karl
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