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