A while back I inquired as to how to obtain ANCOVA adjusted pixel values to make
a scatterplot against a co-variate of interest and obtain a true correlation
coefficient. Christian Buchel suggested the following
>
> The Z-scores SPM reports cannot easily be transformed into correlation
> coefficients. It is easier to get the adjusted data and do it
post-hoc: Go
> to results and plot the adjusted data. You will then find a variable y
in
> Matlab workspace. This matrix contains the adjusted (for globals,
subject
> effects) data. You can now look for the correlation between y and your
> behavioural data.
>
Jean-Baptise Poline then noted that:
>Just a short follow-up to Christian comment : make sure your covariates
>of interest are not correlated to the covariates of no interest before
>you apply Christian's procedure.
I am now faced with the following puzzling findings.
1) The ANCOVA adjusted pixel values extracted per Dr. Buchel's suggestion are
correlated with the global values (I am using modeled FDG images). I would have
expected that the ANCOVA procedure would have removed any correlation of the
pixel values with the global values.
2) The global values and the co-variate of interest are indeed correlated
I know from other postings that when the co-variate of interest and the
co-variate of no interest are correlated that one has to orthogonalize the
design matrix. But I am not sure how to go about doing this.
I am interested in correlating the change across conditions between the scans
and the co-variate of interest. As per previous postings by Andrew Holmes, I
have constructed a single mean centered covariate from the change scores of the
covariate, with the following formula
Baseline covariate = -1* (ChangeScore - Mean)/2 Treatment covariate = 1*
(ChangeScore - Mean)/2
The correlation between the change in globals and the change in this covariate
is about -0.71.
I would guess that to orthogonalize the design matrix one could regress the
co-variate of interest (as the dependent variable) against the co-variate of no
interest (as the independent variable). The residuals from the regression would
then become the new values for the co-variate of interest. Since I am
interested in the change across session I can see two ways of computing the new
values for the co-variate of interest.
1) Compute the residuals of the global vs. covariate for each condition
independently, then compute the change score of the residuals, and mean center
those change scores ?
OR
2) Compute the residuals of the change in globals vs. change in covariate, then
mean center the residuals as the new covariate
I would think the two approaches would yield similar results, although #2 seems
more intuitive to me.
Am I on the right track here ? Any help would be appreciated.
sg
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