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

Roy Averill-Murray roy@ver|||murr@y @end|ng |rom gm@||@com
Thu Jan 17 18:18:47 CET 2019

To clarify the home range models I am investigating, below is the glm
model, ignoring the variances in subject-specific home range estimates.
"AKDE" is the home range estimate, which is bounded by (0, inf), hence the
use of "family = Gamma." I was hoping to include this relationship in the
moderator formula when I add the v_i for AKDE.

glm(AKDE ~ Sex, family = Gamma(link = "log"), data = TotHR)

Here's a corresponding model that looks at annual home ranges, which are
repeated among individuals (ID).

glmmTMB(AKDE ~ Sex*Drought + (1 | ID), family = Gamma(link = "log"), data =

I'll begin by seeing how the first model looks in metafor under the
assumption that the AKDE ~ Sex relationship is Normal.

Message: 1

> Date: Thu, 17 Jan 2019 09:42:08 +0000
> From: "Viechtbauer, Wolfgang (SP)"
>         <wolfgang.viechtbauer using maastrichtuniversity.nl>
> To: Roy Averill-Murray <royaverillmurray using gmail.com>,
>         "R-sig-meta-analysis using r-project.org"
>         <R-sig-meta-analysis using r-project.org>
> Subject: Re: [R-meta] metafor: non-normal meta-regression and random
>         effects within meta-regression?
> Message-ID: <2d134912775d401694ee4f3f659b7d79 using UM-MAIL3214.unimaas.nl>
> Content-Type: text/plain; charset="us-ascii"
> 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
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