[R-meta] metafor: non-normal meta-regression and random effects within meta-regression?

[Viechtbauer, Wolfgang (SP)]

Hi Roy,

The short answer: No, metafor does not allow for non-Gaussian distributions (well, there is rma.glmm() for binomial and Poisson data, but that's something different than what you are asking about).

Longer answer: For what part of the model do you want to use non-Gaussian distributions? For the sampling errors of the estimates and/or for the random effects? I do not know anything about animal home ranges, but the estimates used in meta-analyses are typically averages of some kind and (sometimes with a suitable transformation) have a (at least approximately) normal sampling distribution thanks to the CLT (this can break down in small samples or extreme cases, for which rma.glmm() provides methods for count data that may be more suitable then).

We typically also assume normal random effects, but more out of convenience (i.e., the math just simplifies a lot then) than strong theory. For certain random effects, one could argue that they reflect the sum of many small (and independent) perturbations, which would lead to normality again due to the CLT. But that may not hold, so there are models with non-normal (e.g., t or mixtures of normals) random effects. See, for example, the metaplus package.

If you want something completely customizable in terms of the models, you probably should look into fully Bayesian models (e.g., Stan/rstan). The brms package makes the use of such models very accessible. You should be able to specify known sampling variances there as well.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Roy Averill-Murray
Sent: Wednesday, 16 January, 2019 20:22
To: R-sig-meta-analysis using r-project.org
Subject: [R-meta] metafor: non-normal meta-regression and random effects within meta-regression?

I've been reading about meta-analysis and the metafor package and have two
quick questions for which I have not yet found answers:

Is it possible for the predictor model in a meta-regression to be based on
non-Gaussian distributions? For example, I am analyzing animal home ranges,
which are distributed within (0, inf), so (before looking into
meta-regression) I have been estimating GLMs on the home range point
estimates with a gamma distribution. I have not yet applied metafor to my
analysis with a Gaussian regression, but when I ignore v_i in the
individual home ranges, gamma models fit better than Gaussian.

Separately, I am conducting a similar analysis in which the response
variable is again home range size, but repeated for individuals in multiple
years. To date, I have been using GLMM with a gamma distribution and animal
ID as a random effect (plus other fixed effects). Can I include individual
as a random effect in a meta-regression, do I simply include "year" as a
fixed effect (with the within- and between-individual variation combined in
tau^2?), or something else?

I'm surprised that I have not been able to find anyone else addressing
these questions (beginning with meta-regression of home range sizes in the
first place) in the ecological literature. Thanks for any input,

Roy Averill-Murray