Dear Bruno,

The model you propose for all the subjects seems fine, but if you want to test 

Beta1>0 & Beta1>Beta2 & Beta1>Beta3.

then the contrasts you want to define are 
[ 1  0  0 ]
[ 1 -1  0 ]
[ 1  0 -1 ]

and then take a conjunction of those three t-contrast.

*That* procedure would be correct, and as long as you tell SPM that you have repeated measures (i.e. don't just treat it as 3*N independent scans) you'll be fine.

-Tom

On Sat, May 22, 2010 at 4:58 PM, Bruno L. Giordano <[log in to unmask]> wrote:
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)
+1 514 398 2962 (fax)
http://www.music.mcgill.ca/~bruno



--
____________________________________________
Thomas Nichols, PhD
Principal Research Fellow, Head of Neuroimaging Statistics
Department of Statistics & Warwick Manufacturing Group
University of Warwick
Coventry  CV4 7AL
United Kingdom

Email: [log in to unmask]
Phone, Stats: +44 24761 51086, WMG: +44 24761 50752
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