[R-meta] Random effects in MA

[Viechtbauer, Wolfgang (SP)]

Hi Emily,

There are many more districts than those included in this meta-analysis. So, while I assume the districts in the dataset are not a random sample from the larger population of districts, it is still a subset. And we do not just want to say something about *these* districts, but the larger population.

This aside, the question of when to treat something as fixed versus random is not an easy one. An interesting discussion about this can be found in this paper:

Gelman, A. (2005). Analysis of variance: Why it is more important than ever. Annals of Statistics, 33(1), 1-53.

See section 6. It discusses 5 different way of defining fixed vs. random effects, which are, at least partly, incompatible. So, there isn't really a consensus on this issue anyway.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Emily Russell
Sent: Tuesday, 10 July, 2018 10:47
To: r-sig-meta-analysis using r-project.org
Subject: [R-meta] Random effects in MA

Dear All

I was wondering about the definition of 'random effects' in the contexts of a mixed-effects model.  The example in the metafor manual using the Konstantopoulos (2011) data  has a fixed number of districts each of which have a number of studies conducted within them.  The random = ~ 1 | district/study fits a random effect at the study and district level:

res.ml <- rma.mv<http://finzi.psych.upenn.edu/library/metafor/html/rma.mv.html>(yi, vi, random = ~ 1 | district/study, data<http://stat.ethz.ch/R-manual/R-devel/library/utils/html/data.html>=dat)

What I don't understand is how districts can be a random variable, as presumably we have a fixed and known number of them and don't want to make more general inferences about districts; does that not make districts a fixed-effect?

I fear I may be missing something obvious so apologies if it is!

Emily