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[R-meta] Dear Wolfgang

@Ji: I don't have immediate answers to your questions, but I just want to raise another point, since you mentioned that there are often multiple estimates for the same site over time, for many sites (some of which I suspect may be close to each other spatially), and for many species.

In principle, an appropriately formulated model should be able to automatically account for these things. Let me give a simple analogy. Suppose I want to know if group A has higher/lower blood pressure than group B. I measure the blood pressure of the individuals in group A once. In group B, I have the same number of individuals but measure their blood pressure 100 times. I obviously cannot just run a t-test here, treating the repeated measurements from group B as if there are 100 times as many people in that group. An appropriately formulated multilevel / mixed-effects model however will account for the (presumably) very high correlation in the repeated measurements for the same individual and effectively downweight these repeated measurements.

The same idea applies to meta-analysis. I can formulate models that allow for dependency/correlation in multiple estimates for the same site over time and that allow for spatial correlation in sites (depending on close together they are). In fact, I was recently involved in a meta-analysis on fish abundance data where we accounted for the spatial correlation in the estimates:

Maire, A., Thierry, E., Viechtbauer, W., & Daufresne, M. (2019). Poleward shift in large-river fish communities detected with a novel meta-analysis framework. Freshwater Biology, 64(6), 1143-1156.

In this case, the estimates were slopes (for some measure over time), so we did not have to deal with temporal correlation in the estimates (except when computing the slopes and corresponding standard errors themselves). But based on this paper, I actually added spatial correlation structures to the rma.mv() function (this is in the 'devel' version). See:

https://wviechtb.github.io/metafor/reference/rma.mv.html

and search for "For outcomes that have a known spatial configuration".

The rma.mv() function also allows for adding random effects to account for serial/auto correlation in estimates. This is relevant to account for dependency in multiple estimates from the same site over time.

Inclusion of different species also raises the possibility of phylogenetic correlations. rma.mv() yet again has you covered here. One can add random effects for species with and without a corresponding correlation matrix derived from a phylogeny.

The tricky part is of course coming up with an 'appropriately formulated model'. You are stepping into cutting-edge territory here, so good luck on this one! ;)

Best,
Wolfgang