[R-meta] Difference between "GEN" and "UN" in metafor

[Farzad Keyhan]

Hello All,

I guess my own question was misplaced when I was answering this question:
https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2021-August/003079.html.

So, here is my own question for Wolfgang, I understand that for say
`outcome` with K levels, random = ~ outcome | study, struct="UN" creates
correlated random effects with K variances and K*(K-1)/2 covariances in
each `study`.

Also, for struct="UN", `outcome` has to be a factor.

But apparently struct="GEN" can also be used with both numeric and
non-numeric variables and apparently with multiple variables on the left of
the vertical bar `|` e.g., `outcome + var2 | id` (not sure if `||` or `
outcome * var2  | study` are also handled?).

First, for the same factor variable (say `outcome` a binary one), what is
the difference in the interpretation of random effects and the correlation
estimates in:

random = ~  outcome | study, struct="UN"

VERSUS

random = ~  outcome | study, struct="GEN"

Second, for a numeric variable (say `AGE`), what is the interpretation of
random effects and the correlation estimates in:

random = ~ AGE | study, struct="GEN"

Thank you,
Fred

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