Accounting for nonindependent effect sizes in meta-analysis

Dear all,

I am currently undertaking an ecological meta-analysis using brms but I am struggling to figure out how best to account for nonindependent effect sizes appropriately.

To provide a brief overview of the dataset:

I have effect sizes (log response ratio and variance components) for three measures of ecosystem function (A, B and C) due to the presence (treatment) or absence (control) of different insect species. It should be noted that the three measures of function are correlated and they are often measured in the same ‘individuals’ (not people, let’s call them ecological individuals’.

Now, quite a few studies generated multiple effect sizes, from:
i) assessing one or more functions by multiple insect species, or
ii) repeated measures of one or more functions by the same species, or
iii) a mixture of both i) and ii)

This leads to a dataset of 196 effect sizes from 44 studies.

To start, I fitted the following meta-analytic model:

bf(yi|se(sei,sigma=TRUE) ~ function+(1|study),

I have been able to account for phylogenetic nonindependence among insect species by generating a phylogenetic correlation matrix from a phylogenetic tree along with a species random effect.

i.e. `bf(yi|se(sei,sigma=TRUE) ~ function+(1|study)+(1|species),
               cov_ranef = list(“species” = A))`

yi = effect size
sei = standard error of effect size
function = ecosystem function (factor, three levels)
study = publication id (factor, 44 levels)
species = insect species (factor, 30 levels)
A = phylogenetic vcv matrix

I am wondering if anyone has any advice about how I can also account for nonindependence arising from repeated measures of function by the same species in a given study? As well as the fact that each aspect of function is correlated within each study?

Any help would be much appreciated. I am happy to provide a copy of the dataset if that will aid in answering this question.

Stay safe out there

  • Operating System: MacOS Mojave
  • brms Version: 2.12.0

You could start by adding more “random effects” for instance a random effect denoting the species within studies so that those correlations are taken into account via the random effects structure.

To model that “function” might have varying effects across studies, you could replace (1 | study) by (function | study) for instance, which would also model the correlations between those different varying effects.