[R-meta] random part in meta-regression vs. that in multilevel models

Dear Jack,

See below for my responses.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:

r-sig-meta-analysis-bounces at r-project.org] On

Behalf Of Jack Solomon
Sent: Wednesday, 17 March, 2021 22:01
To: r-sig-meta-analysis at r-project.org
Subject: [R-meta] random part in meta-regression vs. that in multilevel

models

Hello List Members,

**First, I have always thought it is illegitimate to add random-effects

for

something that has not been estimated in the fixed part of the model.  For
example:

`lme4::lmer(math ~ female*minority + (ses | sch.id), data = data)` is
illegitimate because `ses` has not been estimated in the fixed part.

It's perfectly fine to do this if one is willing to assume that the mean
slope of ses is 0. Often, this is not an appropriate assumption but I would
not say this is illegitimate.

This reminds me of the common trope that one should never add an
interaction to a model without also adding the corresponding main effects.
One can come up with perfectly valid arguments where this is not necessary
under certain circumstances. For example, suppose I have conducted a
randomized study where I measured people in two groups twice, once pre and
once post treatment. Assume the data are in this format:

person group post y
1      T     0    .
1      T     1    .
2      C     0    .
2      C     1    .
...

I assume the meaning of these variables is self-evident. Then

y ~ post + post:group

is a perfectly valid model as far as I am concerned. It assumes that there
is no pre-treatment group difference (since the model does not include a
group 'main effect'), but for a randomized study, any pre-treatment group
difference would be due to chance anyway, so why estimate a pre-treatment
group difference that must be in reality, by definition, 0?

So this is a model that includes the post:group interaction, but not all
corresponding main effects. Is this wrong? Not to me at least. I might not
use this model for other reasons - for example, to avoid discussions with
reviewers who will claim that one MUST ALWAYS include all main effects
corresponding to an interaction <sigh> - but that's a different issue.

But I frequently see multilevel meta-regression models where intercept is
dropped (~0+...) from the fixed part but at the same time it is added to
the random part.  For example:

metafor::rma.mv(es ~ 0+outcome, V, random= ~1|id/outcome, data = data)

Assuming 'outcome' is a factor/character variable, es ~ 0+outcome is just
a reparameterization of es ~ outcome and ultimately those are two identical
models.

Coincidentally, since you brought this up: I run roughly weekly live
streams where I discuss R and stats and the session tonight will cover this
in detail (not in the context of meta-analysis or multilevel modeling, but
the same idea applies). If you are interested, see:

https://www.wvbauer.com/doku.php/live_streams

These live streams are completely free, no registration required, just
click on the link and start watching at 5pm CET.

So, why is this ok in meta-regression?

Yes, in this particular case for sure.

**Second, I have always thought that `outcome` is treated as a categorical
predictor and thus appearing only to the **left** of `|`.  For example:

lme4::lmer(es ~0+outcome + (0 + outcome | id), data = data)

But I frequently see multilevel meta-regression models where outcome is
treated as a categorical predictor AND a **grouping variable** thus
appearing only to the **right** of `|`.  For example:

metafor::rma.mv(es ~ 0+outcome, V, random= ~1|id/outcome, data = data)

So, why is this ok in meta-regression?

See: https://www.metafor-project.org/doku.php/analyses:konstantopoulos2011
which discusses how these two may be completely analogous parameterizations
of the same model, if a certain var-cov structure is assumed for 'outcome |
id' (that's not the case above for lmer(), since it automatically will use
an unstructured var-cov matrix for 'outcome | id', but rma.mv() or
nlme::lme() allow specification of different structures, struct="CS" being
the default in for the former).

I don't know how many times I have posted the konstantopoulos2011 link
above on this mailing list, but I can highly recommend it for anybody who
is doing a multilevel meta-analysis (I got curious; a google search with
'site:https://stat.ethz.ch/pipermail/r-sig-meta-analysis/
analyses:konstantopoulos2011' suggests 101 times ... plus a few more times
today!).

Anyway, I hope this helps to clarify some things.

Many thanks for your support,
Jack