More obvious to discuss the model.... for me... [Software]

posted by ElMaestro  – Denmark, 2022-11-10 01:34 (468 d 01:24 ago) – Posting: # 23359
Views: 1,452

Hi all,

The mixed model is for our purposes
Y= Xb + Zu + e

Z is the design matrix for the random effects expressed in u, typically the betweens.
Now, in BE if we decide to fit the model with an intercept in Z then obviously we will get a column of ones followed by a column with indices for either treatment A or treatment B, but not both. Under this model specification we are thus estimating the intercept (whose interpretation is not so straightforward if you ask me, but see Pharm Cat's example above) along with the betweens for A or B (implementation-dependent), but not both.
One the other hand, if we want to have separate variance estimates for A and B extracted directly from u once optimised, then we would make sure that the random effects are fit without intercept, implying Z without a column of ones, and Bob's your uncle.

I do not see any good arguments for fitting random effects with an intercept column in Z, but I do see arguments for doing it without. If the software takes care of everything from optimisation to generation of a CI behind the curtains, then there is no preference and software defaults will suffice whatever they are since the CI will be the same.

Pass or fail!

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