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

[Viechtbauer, Wolfgang (SP)]

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