[R-meta] Definition of random effect in meta-regression vs multilevel modeling

Dear Fred,

I don't think you ever got a response to this question. I would say yes,
the meaning is the same, but there may be differences in the details /
implementation. For example, things like '~ 1 | id' work the same for lme()
and rma.mv(), but if you do

random = ~ var1 | var2

in lme(), then the var-cov matrix of the random effects is by default
assumed to be unstructured (or more precisely, it's assumed to be a
positive (semi-)definite matrix). In rma.mv(),

random = ~ var1 | var2

assumes a compound symmetric structure (struct="CS") by default (which can
be changed via the 'struct' argument). Also, in lme(), there can be one or
multiple variables on the left of |, some of which can also be numeric (for
'random slopes'), while in rma.mv() there can only be one variable on the
left of | and it must be a string/factor variable. In essence,

random = ~ var1 | var2, struct="UN"

in rma.mv() is equivalent to

random = ~ 0 + var1 | var2

in lme() and if struct="CS", then it is equivalent to

random = list(var2 = pdCompSymm(~ 0 + var1))

in lme() (assuming var1 is a string/factor variable). If you want the same
behavior as lme() (including the possibility of multiple variables on the
left | including numeric ones), you can use struct="GEN". Also, there are
some other structures in rma.mv() such as those for temporal/spatial
autocorrelation that do not have direct counterparts in lme() and that
behave a bit differently (one can model temporal/spatial autocorrelation in
the residuals in lme() models, but not in the random effects).

I hope this helps to clarify things.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:

r-sig-meta-analysis-bounces at r-project.org] On

Behalf Of Farzad Keyhan
Sent: Friday, 25 June, 2021 18:27
To: r-sig-meta-analysis at r-project.org
Subject: [R-meta] Definition of random effect in meta-regression vs

multilevel

modeling

Hello List Members,

In ordinary multilevel modeling, the question of what is a random effect
often revolves around whether to call the right side (here intercepts) or
left side (a grouping variable) of `|` in the following: `~ 1 | id`.

Question: Do terms like "random slopes" (e.g., `~ factor(time) | studyID`)
and "random intercepts" (e.g., `~ 1 | studyID`) have the same meaning in
multilevel/multivariate meta-regression modeling as they do in ordinary
multilevel modeling?

Thanks,
Fred