Dear Bruno,
Beta1>0 & Beta1>Beta2 & Beta1>Beta3.
Hello,
I am modeling the extent to which different stimulus-related features explain how the BOLD-baseline response varies across stimuli.
For the sake of the argument, let's assume that the baseline and covariates of no interest (e.g., head motion parameters) have already been filtered out of the data. Let's also assume that the features are perfectly orthogonal, i.e., not correlated.
As such, my first level model would be a multiple regression of the type:
BOLD = Beta1*Feature1+Beta2*Feature2+Beta3*Feature3+constant.
At the group level one thing I am interested in is where Beta is positive. To this purpose, I run one simple T-test for each of the features using the Beta images from each subject as dependent data.
My problem now concerns how to setup a more complex 2nd level model where I want to find those regions where, e.g.,:
Beta1>0 & Beta1>Beta2 & Beta1>Beta3.
Again for the sake of the argument, let's assume that the Betas for the different features are comparable (e.g., regressors have been standardized prior to entering the model).
So, what I am doing for the moment is:
[1] setup the following design matrix (N = n subjects):
Beta1 Beta2 Beta3
1 0 0 subj1
1 0 0 subj2
1 0 0 subj...
1 0 0 subjN
0 1 0 subj1
0 1 0 subj2
0 1 0 subj...
0 1 0 subjN
0 0 1 subj1
0 0 1 subj2
0 0 1 subj...
0 0 1 subjN
[2] set up these two contrasts:
c1:[1 0 0]
c2:[1 -1/2 -1/2]
[3] find those regions where both c1 and c2 are significant (or test the c1 & c2 conjunction).
Is this procedure correct? I am afraid, for example, of inflating the degrees of freedom.
Thank you for any feedback,
Bruno
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Bruno L. Giordano, PhD
Postdoctoral Research Fellow
CIRMMT – Schulich School of Music
555 Sherbrooke Street West
Montréal, QC H3A1E3
Canada
+1 514 398 4535, Ext. 00900 (voice)
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http://www.music.mcgill.ca/~bruno