Hi Ole,

This is not the correct setup for a within-subjects design. A column should be included for each subject to model there individual mean and the first column of 1's should be removed. Protcol can be removed if it is orthogonal with session. 

The 2nd design matrix is more correct. But the first colums of 1's should be removed and you may want to check whether Protocol is orthogonal to the other variates. 

NBS/FSL use a very similar modeling stategy. 

Andrew

Originally posted by Ole Jonas Böken:

Dear Prof. Zalesky,

Thank you for your quick reply! As a quick follow-up, we would like to clarify whether our design matrix adequately captures a paired design (last vs. first session) when including the covariates TSO and protocol.

Our current setup is:

Intercept, PrevsPost, TSO, Protocol
1, -1, -0.9964, 1
1, 1, 1.3098, 0
1, -1, -1.3889, 1
1, 1, 0.7455, 0

together with exchange blocks [1;1;2;2].

However, in FSL paired designs are typically modeled with additional subject-specific EVs to explicitly account for within-subject differences, leading to:

Intercept, PrevsPost, TSO, Protocol, EV1, EV2
1, -1, -0.9964, 1, 1, 0
1, 1, 1.3098, 0, 1, 0
1, -1, -1.3889, 1, 0, 1
1, 1, 0.7455, 0, 0, 1

This raised the question whether our first specification with exchange blocks already provides valid inference, or whether subject-specific EVs (as in the FSL approach) are required in addition.

Many thanks in advance.

Best,

Ole