# [R-meta] Question about longitudinal that report multiple outcomes

Viechtbauer, Wolfgang (SP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Mon May 3 14:28:19 CEST 2021

```See again below for my responses.

Best,
Wolfgang

>-----Original Message-----
>From: Jack Solomon [mailto:kj.jsolomon using gmail.com]
>Sent: Friday, 30 April, 2021 1:44
>To: Viechtbauer, Wolfgang (SP)
>Cc: r-sig-meta-analysis using r-project.org
>Subject: Re: Question about longitudinal that report multiple outcomes
>
>Thank you Wolfgang. I realized I confused something in my previous email. I meant
>to say the following:
>
>1- If I wanted to fit the `non-multivariate` parametrization of "random = list(~
>outcome | study, ~ time| interaction(study,outcome))", then, would that have been:
>
>"random = ~ 1| study/outcome/time"?

This is the same as:

random = list(~ outcome | study, ~ time| interaction(study,outcome)), struct=c("CS","CS")

but the latter has one more superfluous parameter (i.e., the latter model is overparameterized), but the fit should be the same.

However, it is not the same as models such as:

random = list(~ outcome | study, ~ time| interaction(study,outcome)), struct=c("CS","AR")
random = list(~ outcome | study, ~ time| interaction(study,outcome)), struct=c("UN","AR")

>If yes, could I then use "time" as a fixed
>predictor as well? (If no, then, I think the multivariate parametrization is the
>only specification that allows "time" to be used both as random and fixed (=
>moderator), correct?)

This is not correct. One can use 'time' as fixed effect in various models and this is unrelated to whether one uses a multivariate parametrization.

>2- Imagine we only have "time", then, when would it be appropriate to use: "random
>= ~ 1| study/time/esID" [where "esID" is the row numbers]? and then could I use
>"time" as a fixed moderator?

If you have repeated observations of some outcome over time, then such a model assumes that the correlation does not depend on the distance in time between those observations. That is typically unrealistic, so I would not recommend this. Again, whether one can use 'time' as a fixed effect is an unrelated issue.

>Conclusion: If I intend to use "time" or "outcome" both as random and fixed (=
>moderator), we only should use the multivariate parametrization of the random
>effect in the "rma.mv()" syntax, correct?

As above.

>Thank you,
>Jack
>
>On Thu, Apr 29, 2021 at 3:08 AM Viechtbauer, Wolfgang (SP)
><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>
>Best,
>Wolfgang
>
>>-----Original Message-----
>>From: Jack Solomon [mailto:kj.jsolomon using gmail.com]
>>Sent: Thursday, 29 April, 2021 4:08
>>To: Viechtbauer, Wolfgang (SP)
>>Cc: r-sig-meta-analysis using r-project.org
>>Subject: Re: Question about longitudinal that report multiple outcomes
>>
>>Dear Wolfgang,
>>
>>Thank you so much for your response.
>>
>>Wolfgang: I can't quite parse your question. We are saying that the two 1.1
>>effects are dependent and that the two 1.2 effects are dependent and that the two
>>2.1 effects are dependent. But the two 1.1 effects are not correlated with any of
>>the other effects and so on. If this is what you meant, then yes.
>>
>>++++ My question is that shouldn't 1.1, and 1.1 be correlated with 1.2 and 1.2 as
>>they belong to "study 1"? Is n't the goal to let the effect sizes from each study
>>to be correlated with each other due to multiple outcomes and multiple time
>>points, and let the effect sizes from different studies to be uncorrelated with
>>each other due to being from independent studies?
>
>Yes, but that's not the purpose of the '~ time | interaction(study,outcome)' term
>which you asked about. This term allows for correlation among multiple effect
>sizes obtained over time from the same study and the same outcome. The correlation
>of different outcomes from the same study occurs via the '~ outcome | study' term.
>
>>++++ I imagine "~time | interaction(study,outcome)" is the same as "~time |
>>study/outcome", correct?
>
>If this would work in rma.mv() (which does not), then '~ time | study/outcome'
>should expand into the two terms '~ time | study' and '~ time |
>interaction(study,outcome)' (if we would assume the same behavior as in lme()), so
>this is not the same as only adding '~ time | interaction(study,outcome)' or
>list(~ outcome | study, ~ time | interaction(study,outcome).
>
>This aside, rma.mv() does not allow terms of the form '~ inner | outer1/outer2'.
>If you want to do this, then you have to do list(~ inner | outer1, ~ inner |
>interaction(outer1, outer2').
>
>> If yes, why not  jus "random = ~time |
>>study/outcome/esID", and instead creating "random = list(~ outcome | study, ~
>time
>>| study/outcome)"?
>
>Since the answer was no, I'll skip this.
>