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

[Farzad Keyhan]

Dear Wolfgang,

Thank you very much for your informative response.

Have a great day,
Fred

On Thu, Jul 8, 2021 at 6:56 AM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> 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 using r-project.org] On
> >Behalf Of Farzad Keyhan
> >Sent: Friday, 25 June, 2021 18:27
> >To: r-sig-meta-analysis using 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
>

	[[alternative HTML version deleted]]