[R-meta] Multivariate meta-analysis when "some studies" are multi-outcome

Viechtbauer, Wolfgang (SP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Tue Mar 16 11:22:44 CET 2021

Dear Simon,

At the very least, you should add random effects at the level of the studies and at the level of the estimates, so:

dat$estid <- 1:nrow(dat)

and then

random = ~ 1 | id / estid

For longitudinal data, one could also consider using some kind of autocorrelation structure for the estimates within studies. There are some examples here:


clubSandwich::impute_covariance_matrix() also allows for the construction of a V matrix with an autocorrelation structure.

If the different outcomes are meaningfully related across studies (i.e., outcome '1' stands for the same thing across all studies), then one could also consider using an unstructured var-cov matrix with correlated random effects for outcomes within studies. This would be akin to:



>-----Original Message-----
>From: Simon Harmel [mailto:sim.harmel using gmail.com]
>Sent: Monday, 15 March, 2021 17:31
>To: Viechtbauer, Wolfgang (SP)
>Cc: R meta
>Subject: Re: [R-meta] Multivariate meta-analysis when "some studies" are multi-
>Dear Prof. Viechtbauer,
>Many thanks for your response. I found the following particularly helpful
>So, I went from my initial model: `rma.mv(d, V = SE^2, mods = ~factor(outcome)-1,
>random= ~1|id, data = dat)`
>to now:
>`V <- clubSandwich::impute_covariance_matrix(vi = dat$SE^2, cluster = dat$id, r =
>`rma.mv(d, V = V, mods = ~factor(outcome)-1, random= ~1|id, data = dat)`
>However, what type of dependence is accounted for by the multilevel part (i.e.,
>`random= ~1|id`), and what type of dependence is accounted for by including the
>imputed variance-covariance matrix?
>Specifically, in my data, all primary studies (n=52) are longitudinal, 15 of them
>are multi-outcome, and almost all are multi-group treatments. Are all of these
>types of dependence reasonably accounted for?
>Many thanks for your consideration,
>On Mon, Mar 15, 2021 at 6:54 AM Viechtbauer, Wolfgang (SP)
><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>Hi Simon,
>I would suggest to search/browse the archives, as this kind of question has been
>discussed at various points in the past. The archives can be found here:
>There is no built-in search functionality for the archives, but one can restrict
>search engines to conduct searches at particular sites. For example, if you do a
>google search including
>you should only get 'hits' from the mailing list archives. The same should work
>with DuckDuckGo. Note sure about other engines.
>Note that search engines index the archives at semi-regular intervals, so the most
>recent posts will not show up this way, but those can be searched manually.
>>-----Original Message-----
>>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>>Behalf Of Simon Harmel
>>Sent: Saturday, 13 March, 2021 23:53
>>To: R meta
>>Subject: [R-meta] Multivariate meta-analysis when "some studies" are multi-
>>Dear All,
>>I'm conducting a meta-analysis where 15 out of 52 studies have used more
>>than one outcome variable. In addition, almost all studies include multiple
>>A shortened version (i.e., without moderators) of our dataset appears below
>>(`*id`=study id; `d`=effect size; `SE` = standard error; `outcome`=outcome
>>variable index*).
>>I was wondering what would be the appropriate modeling options for such a
>>I appreciate your expertise and consideration,
>>*#-- R data and code:*
>>dat <- read.csv("https://raw.githubusercontent.com/hkil/m/master/tst.csv")
>>rma.mv(d, V = SE^2, mods = ~factor(outcome)-1, random= ~1|id, data = dat)
>>## I'm assuming this would be an insufficient model

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