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

[Viechtbauer, Wolfgang (SP)]

The values are not exactly identical and it is coincidence that they end up looking that way when rounded to 4 decimal places. For example try:

res <- rma.mv(yi, vi, random = list(~ 1 | study, ~1 | outcome, ~ 1 | measure), data=m, subset=study <= 20)
res2 <- rma.mv(yi, vi, random = list(~ 1 | study/outcome, ~ 1 | measure), data=m, subset=study <= 20)

and they are rather different.

Best,
Wolfgang

>-----Original Message-----
>From: Stefanou Revesz [mailto:stefanourevesz using gmail.com]
>Sent: Saturday, 30 October, 2021 15:06
>To: Viechtbauer, Wolfgang (SP)
>Cc: R meta
>Subject: Re: rma.mv: why some var components change but others don't across 2
>models
>
>Dear Wolfgang,
>
>Thank you for your reply. I did check that previously. But my question is why
>'outcome' gives the same variance component across both res (with 4 levels) and
>res2 (with 68 levels) models?
>
>Thank you so much,
>Stefanou
>
>On Sat, Oct 30, 2021, 7:08 AM Viechtbauer, Wolfgang (SP)
><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>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