Dear NBS experts, 

I'm experiencing some issues with my design matrix.

I need to compare three different groups, acquired with different MR scanners; thus, from what I understand, I should run on NBS an F-test, using center of acquisition as nuisance variable. 

I tried to set the design matrix as follow: 

1 1 0 0 1
1 1 0 0 1
1 0 1 0 2
1 0 1 0 2
1 0 0 1 3
1 0 0 1 3

Where, the 1st column is the intercept, 2nd the first group, 3rd second group, 4th third group, 5th column is MR scanner.
The contrast I used is: 

0 1 1 1 0

However, when I run the NBS with this design I get the "Rank deficient" warning. They suggested me to demean the nuisance variables (thus I get for example in the 6th column: center 1 --> -0.92969, center 2 --> 0.070312, center 3 --> 1.0703), but I always get the warning. 

I'm afraid I'm using the wrong design matrix for this purpose...Does anyone have any suggestion on how I should model it? How to put the nuisance variable related to the MR scanner? 

Thank you very much! 

All the best, 

Giulia