Thank you Jeanette,
While digging further the question: "to orthogonalize or not to orthogonalize" I came across an interesting exchange on the topic with your involvement:
Actually Mark Jenkinson mentioned in it that possibly (not necessarly though) the only situation where othogonalization could be justified is when related covariates are used on a higher level:
This implies to my situation, but even in this case there is a workabout to avoid generally discouraged orthogonalization as Mark proposes:
"However, it
isn't really much more informative that doing the two t-contrasts and then an F-contrast (possibly with contrast masking to separate the positive and negative correlations in the F-contrast, which itself is unsigned). So even in this case it is a weak argument for orthogonalisation."
After your email and Mark's old remarks I think the problem of orthogonalization is more or less clarified for me. However I'm still struggling a bit with the concept of the overall mean and including it in the model, especially at the 2nd level.
In my case: I include a number of covariates in addion BOLD statistics from the 1st level. What is the meaning of this overall mean? I can see that as the name suggests it refers to varaibility attributable to all regressors: i.e. BOLD statistics AND covariates? Why is it necessary to take it into the model?
Iwo