Dear Steven,
>
>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.
>
You are absolutely correct here. A single beta is estimated for all
conditions. It is also true that the validity of this assumption is not
explicitly tested in SPM.
>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 ?
>
Yes, the values of a given voxel is regressed against the corresponding
global values. And yes, the global mean is calculated by averaging all 14
global values. Please note however that it is very unlikely that your
global values are orthogonal to your conditions (simply by chance) which
means that you will have to fit your entire model at once. Regressing the
voxel values onto the globals, adjusting for the global confound followed
by an ANOVA (which seems to be what you want to do) will give you different
results compared to an ANCOVA (which would be the sensible thing to do).
>
>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.
>
If all columns of the design matrix had been orthogonal (i.e. if the
globals were not included) the subject specific effects would simply have
been the averages across the two scans for each subject. Again, since you
include the globals you need to fit the entire model to get the proper
subject specific effects.
>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.
If all you want to compare is the ROI approach versus the pixel-by-pixel
approach and you want everything else to be identical, by far the simplest
would be to do as follows:
1. Get your ROI values into matlab organised as a matrix (e.g. Y) with one
row for each scan and one colum for each region.
2. Load the SPM.mat that you got from your SPM analysis
3. Create a matrix X = [H B G];
4. Solve in a least squares sense by
beta = pinv(X)*Y;
beta will now contain one column for each region with the parameter
estimates you are interested in, and you may subsequently use them to
calculate your adjusted values. Remember to enter your ROI values in the
same order that you entered your files in SPM though.
>In
>the end I want to compare the scatterplots of the correlations with the
>co-variate for SPM and ROI analysis.
>
Why?
>Thanks for you help.
Good luck Jesper
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