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

[Viechtbauer, Wolfgang (SP)]

Unless the values of 'outcome' are meaningful and not just (essentially arbitrary) values to distinguish different rows, using something like '~ 1 | outcome' makes no sense. For example, say the coding looks like this:

study outcome yi vi
1     1       .  .
1     2       .  .
2     1       .  .
2     2       .  .
2     3       .  .
3     1       .  .
...

'~ 1 | study / outcome' makes sense to allow for between- and within-study heterogeneity. But unless a "1" for outcome in study 1 represents the same type of outcome as "1" is study 2 and 3, 'list(~ 1 | study, ~ 1 | outcome') makes no sense. If the numbers or values are only used to distinguish different outcomes within the same study but carry no inherent meaning beyond that, then one could just as well have coded the studies as:

study outcome yi vi
1     1       .  .
1     2       .  .
2     3       .  .
2     4       .  .
2     5       .  .
3     6       .  .
...

and '~ 1 | study / outcome' would give identical results to the previous coding, but 'list(~ 1 | study, ~ 1 | outcome') would not. In fact, with the second coding, '~ 1 | study / outcome' and 'list(~ 1 | study, ~ 1 | outcome') are identical (because the second coding is implicitly creating the same nesting that '~ 1 | study / outcome' implies).

Regardless of the coding, '~ 1 | study / outcome' and '~ outcome | study' with struct="CS" is identical (strictly speaking, the latter allows for a negative correlation and if so, then the equivalence breaks down, but let's not get into this). Structures like "HCS" and "UN" only make sense again when the values of 'outcome' are inherently meaningful and not just arbitrary identifiers.

Best,
Wolfgang

>-----Original Message-----
>From: Stefanou Revesz [mailto:stefanourevesz using gmail.com]
>Sent: Monday, 01 November, 2021 17:20
>To: Viechtbauer, Wolfgang (SP)
>Cc: R meta
>Subject: Re: rma.mv: why some var components change but others don't across 2
>models
>
>Thanks! Feel free to ignore this, but I don't think it has come up on
>the mailing list before.
>
>If I use: list(~ 1 | study, ~1|outcome, ~ 1 | measure), then
>everything else aside, it means I believe that there are inherent
>differences in 'outcome' that would necessitate disentangling
>'outcome' effects from those of study and measure (crossing outcome
>with study and measure).
>
>On the other hand, I can use list(~ outcome | study, ~ 1 | measure),
>struct="UN" which again adheres to the belief that there are inherent
>differences in 'outcome' without necessitating disentangling 'outcome'
>effects from those of study and measure (outcome nested in study).
>
>What's the difference between the two strategies above, and why I
>never see: list(~ 1 | study, ~1|outcome) in the archives (all I see is
>either '~1|study/outcome' or its multivariate reparametrization '~
>outcome | study'?
>
>Stefanou