[R-meta] Alternative view of fixed effects in meta-regression

[Timothy MacKenzie]

Dear Colleagues,

I have some clarification questions.

In multilevel models, what do the fixed-effect coefficients exactly
predict? (change in the 'observed' effect yi for 1 unit of increase in
moderator X OR change in some form of 'true effect' [depending on the
random-part specification] for 1 unit of increase in moderator X)

The reason I ask this is the bottom of p.26 of this paper (
https://osf.io/4fe6u/). In this paper, Dr. Pustejovsky describes a 3-level
model (j cases in k studies):

                                       Rjk = Y0 + Y1(Age)jk + Vk + Ujk + ejk

Then, he interprets Age's fixed effect coefficient as: *"the difference in
average effect sizes between cases [level 2] that differ in age by one
year"*.

I wonder how this interpretation is possible and can be extended to other
models (see below)?

Say X is a continuous moderator that can vary between 'studies' and
'outcomes'. How can we apply Dr. Pustojuvsky's logic to the interpretation
of 'X' fixed coefficient separately in:

(A) 'rma.mv(yi ~ X, random=~1 | study)'
vs.
(B) 'rma.mv(yi ~ X, random=~1 | study/outcome)' differ?

Thank you very much,
Tim

	[[alternative HTML version deleted]]