Hi everyone,

I need some help in order to set up a design matrix and the relative contrast.

I am analysing the data of a (rs-fmri) study that involved 5 groups of subjects. Each group has been acquired in two centres, but one of the two centre had a pretty substantial scanner update in between the acquisition (I know, I know...). For this reason we decided to set up the nuisance variables "centre" as if the groups were acquired in 3 different centres (or if you prefer as if they were acquired with 3 different scanning protocols).

Now, my problem arise from the fact that in the centre that had the upgrade, one group was only acquired BEFORE the upgrade.

As a first thing, I wanted to see if there was any effect of group, centre, and their interaction in the DMN and the fronto-parietal network.
To do so, I thought of using a design matrix "full factorial spm style", that is, 5*3 cell, representing the 15 possible combinations of levels of the two factors. However, is pretty evident that this is not a good solution, as one of the cell is empty, so that my group effect and interaction effect will be biased.

I thought that I could at least test for a main effect of centre and group, constructing the design matrix with 3 0/1  columns for centre plus 5 0/1 columns for group. In this context, the centre would be mainly a nuisance variable, i.e. my question would be "is there an effect of group after correcting for the fact that the groups have been acquired in 3 centres". However, I realized again that this would not work (I think), since the effect of one centre can not be calculated within one group.

Is there a way out of this mess that does not imply exclude the group that has no acquisition in one centre ?