[R-meta] Studies that use several formulas to capture the same outcome

[Jack Solomon]

Many thanks, Wolfgang. So, any 'study-level' moderator that is meant to be
'random' needs to specified as crossed random-effect only, as it doesn't
vary in any grouping variable, correct?

If yes, then given that the coding of 'study' and 'formula' are similar,
does that mean
"~ 1 | study" itself is a crossed random-effect just like "~ 1 | formula"
is?

Many thanks, Jack

On Wed, Jul 7, 2021, 6:18 AM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> Since 'formula' does not vary within studies, ~ 1 | study/formula is
> adding the study-level random effect twice and hence is redundant. But if
> you want to 'generalize beyond the set of formulas used', then I would not
> add it as a moderator either. One could consider adding it as a crossed
> random effect, that is random = list(~ 1 | study, ~ 1 | formula).
>
> Best,
> Wolfgang
>
> >-----Original Message-----
> >From: R-sig-meta-analysis [mailto:
> r-sig-meta-analysis-bounces using r-project.org] On
> >Behalf Of Michael Dewey
> >Sent: Wednesday, 07 July, 2021 12:32
> >To: Jack Solomon; R meta
> >Subject: Re: [R-meta] Studies that use several formulas to capture the
> same
> >outcome
> >
> >Dear Jack
> >
> >My immediate reaction is to use it as a moderator. Am I missing some
> >problem you have identified?
> >
> >Michael
> >
> >On 07/07/2021 03:31, Jack Solomon wrote:
> >> Hello All,
> >>
> >> Studies in my study pool have used different formulas to capture the
> same
> >> construct. Ideally, I want to be able to generalize beyond the set of
> >> formulas used in my study pool.
> >>
> >> But, given the structure of my data (below), I wonder whether to use
> >> "formula" as a random effect nested (while it doesn't vary within
> studies)
> >> in studies or simply use "formula" as a study-level moderator?
> >> ```
> >> rma.mv(yi, vi, random = ~ 1 | study/formula)
> >> # OR
> >> rma.mv(yi ~ formula, vi, random = ~ 1 | study)
> >> ```
> >> Many thanks, Jack
> >>
> >> study  formula
> >> 1      2
> >> 1      2
> >> 2      1
> >> 2      1
> >> 3      1
> >> 4      2
> >> 4      2
>

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