[R-meta] Alternative view of fixed effects in meta-regression
Timothy MacKenzie
|@w|@wt @end|ng |rom gm@||@com
Sat Aug 21 16:08:44 CEST 2021
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
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