[R-meta] rma.mv: why some var components change but others don't across 2 models

[Viechtbauer, Wolfgang (SP)]

Dear Stefanou,

With the way you have 'outcome' coded, these two formulations are not equivalent. I believe this post discusses this:

https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2018-July/000896.html

Best,
Wolfgang

>-----Original Message-----
>From: Stefanou Revesz [mailto:stefanourevesz using gmail.com]
>Sent: Friday, 29 October, 2021 17:24
>To: R meta
>Cc: Viechtbauer, Wolfgang (SP)
>Subject: rma.mv: why some var components change but others don't across 2 models
>
>Dear Wolfgang and Expert List Members,
>
>Why `study` with 57 levels in model `res` gives `sigma^2.1 = 0.0200`
>but `study` with 57 levels in model `res2` gives `sigma^2.1  =
>0.0122`?
>(SAME LEVELS BUT DIFFERENT RESULTS)
>
>Why `outcome` with 4 levels in model `res` gives `sigma^2.2 = 0.0093`
>but `outcome` with 68 levels in model `res2` gives `sigma^2.2  =
>0.0093`?
>(DIFFERENT LEVELS BUT SAME RESULTS)
>
>For reproducibility, below are my data and code.
>
>Many thanks to you all,
>Stefanou
>
>m <- read.csv("https://raw.githubusercontent.com/fpqq/w/main/c.csv")
>
>res <- rma.mv(yi, vi, random = list(~ 1 | study, ~1|outcome, ~ 1 |
>measure), data=m)
>                    estim       sqrt  nlvls  fixed   factor
>sigma^2.1  0.0200  0.1415     57     no    study
>sigma^2.2  0.0093  0.0964      4     no  outcome
>sigma^2.3  0.0506  0.2249      7     no  measure
>
>res2 <- rma.mv(yi, vi, random = list(~ 1 | study/outcome, ~ 1 |
>measure), data=m)
>                    estim       sqrt  nlvls  fixed         factor
>sigma^2.1  0.0122  0.1105     57     no          study
>sigma^2.2  0.0093  0.0964     68     no  study/outcome
>sigma^2.3  0.0363  0.1904      7     no        measure