Jesper,
Thanks for your explanation regarding calculation of ANCOVA adjusted values, and
the very clear description of the muddled situation regarding the merits of the
two normalization methods.
In order to calculate ANCOVA adjusted pixel values, you said
>simply to estimate a single beta for each voxel across all subjects. This
>means that you assume that a given voxel has the same behaviour with
>respect to changes in global flow for all subjects.
>...the global values are averaged across all subjects and scans to yield
>a global mean.
>...a single beta is estimated based on all scans of the study and
>Y(adj) = Y(actual) - beta(Scan Global - Global Mean)
This is what I originally though was the case. But it was unclear to me
whether all conditions were included in the calculation of the single beta for
each voxel. Since the ANCOVA model assumes that the regressions for each
condition have parallel slopes, and SPM does not explicitly test for homogenity
of slopes, the simpliest way to satisfy this condition is to calculate a single
beta for all conditions.
Say there are 7 subjects, with each subject getting 1 scan for each of two
condtions. This yields a total of 14 scans. Is the value of a given pixel for
all 14 scans regressed against the corresponding global value ? Similarly,
would the global mean be calculated by averaging all 14 global values ?
Second, you state that
> any subject specific effects will be subtracted from the
>adjusted values.
This suggests to me that the Y(adj) that is calculated by the formula above is
the classic ANCOVA least squares adjusted mean for a given pixel across all
subjects in a given condition. It is not clear, then, how to calculate the
subject specific effects to be subtracted from the adjusted value.
What I am trying to calculate is the ANCOVA adjusted value for each individual's
scan. I understand that if one plots by covariate in the RESULTS section of
SPM96, then query's MatLab for the 'y' vector, the output is a list of the
adjusted pixel values for each subject and scan. I am trying to calculate the
corresponding datapoints for the ROI data. The intent is to make the
normalization calculations consistent for the two data analysis approaches. In
the end I want to compare the scatterplots of the correlations with the
co-variate for SPM and ROI analysis.
Thanks for you help.
sg
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