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

[Stefanou Revesz]

Wolfgang, you're a lifesaver! That's such a confusing coincidence!

As we inch toward the last few studies, the variance component for
'outcome' across `res` (fully crossed model), and `res2` (nested +
crossed model) get more and more similar.

Does this say anything about the data structure up to these last few
studies vs. that of the last few studies? (I'm still in shock, and
want to rationalize why this is happening to me)

res <- rma.mv(yi, vi, random = list(~ 1 | study, ~1 | outcome, ~ 1 |
measure), data=m, subset=study <= 54)
res2 <- rma.mv(yi, vi, random = list(~ 1 | study/outcome, ~ 1 |
measure), data=m, subset=study <= 54)

Stefanou

On Sat, Oct 30, 2021 at 11:03 AM Viechtbauer, Wolfgang (SP)
<wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>
> 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