[R-meta] phylogenetic information in both moderator and random part of rma.mv?

[Sigurd Einum]

Dear Wolfgang, thank you for these insights! This clarified for me the way effects of class and phylogeny (within class) is partitioned in the model! 
When I fit the two models you suggested (see below), AICc is lower for mod2 (with delta AICc > 2). My interpretation of your reply, i.e. that the effect of phylogeny is an empirical question, is that since there is little evidence for a phylogenetic signal within classes for this data set, mod2 (i.e. treating the species as independent observations as long as I account for the random species effect (1|species)) is appropriate when estimating the class effect. 

mod1 <- rma.mv(lambda, sampvar,mods = ~ Class, random = list(~ 1 | study, ~ 1 | species, ~ 1 | phylo),
               R = list(phylo = A), data = Final.data, sparse = TRUE, method = "REML")

mod2 <- rma.mv(lambda, sampvar,mods = ~ Class, random = list(~ 1 | study, ~ 1 | species),
                                   data = Final.data, sparse = TRUE, method = "REML")

Best wishes,
Sigurd


>-----Original Message-----
>From: Viechtbauer, Wolfgang (NP)
><wolfgang.viechtbauer using maastrichtuniversity.nl>
>Sent: Thursday, September 29, 2022 4:59 PM
>To: r-sig-meta-analysis using r-project.org
>Cc: Sigurd Einum <sigurd.einum using ntnu.no>
>Subject: RE: phylogenetic information in both moderator and random part of
>rma.mv?
>
>Dear Sigurd,
>
>I do not know enough about the specifics of the application to say whether
>comparing the model with versus without phylogeny is sufficient to conclude
>something about evolutionary divergence.
>
>However, let me make a few comments (I am also basing some comments here
>on what you wrote to me initially in an email before redirecting you to this
>mailing list for further discussions):
>
>So you fitted a mixed-effects model with lme() of the form:
>
>lme(Y ~ Class, random = ~ 1 | species, data=Final.data, method="ML")
>
>(or maybe including weights = varFixed(~ sampvar)) and found 'Class' to be
>relevant (regardless of whether this means: large coefficient, statistically
>significant, sufficiently larger value of the information criterion compared to a
>null model). Then you fitted the model below (where you are accounting for
>phylogeny) and now the support for the relevance of 'Class' disappears or is
>considerably weaker. I hope this summarizes the issue.
>
>First, I would ask: Have you compared the lme() model with this?
>
>rma.mv(Y, sampvar, mods = ~ Class, random = ~ 1 | species, data = Final.data,
>sparse = TRUE, method = "ML")
>
>Note that this is not exactly the same model as what lme() fits as explained here:
>
>https://www.metafor-project.org/doku.php/tips:rma_vs_lm_lme_lmer
>
>This aside, it is quite possible that the relevance / effect / significance of 'Class'
>changes when accounting for the phylogeny, because this accounts for the
>potential dependence of the outcome due to similarities between species in a
>different way than just including species itself as a random effect.
>
>Now does it make sense to include Class as a moderator while also including
>random effects for species? I would say yes. Class is a broader category, so the
>species random effect accounts for heterogeneity within classes (and the fixed
>effect for class allows the average of all species belonging to the same class to
>differ from that of other classes). And whether the values of this random effect
>are correlated or not (as predicted by the phylogeny) is an empirical question. So
>if the model with phylogeny fits better, then I would go with that.
>
>Best,
>Wolfgang
>
>>-----Original Message-----
>>From: R-sig-meta-analysis
>>[mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Sigurd
>>Einum
>>Sent: Wednesday, 28 September, 2022 21:04
>>To: r-sig-meta-analysis using r-project.org
>>Subject: [R-meta] phylogenetic information in both moderator and random
>>part of rma.mv?
>>
>>Dear list,
>>
>>I want to test for evolutionary divergence (among ectothermic animals)
>>in a single trait Y. My first approach to this was to test for
>>divergence among taxonomic classes (specifically amphibians, reptiles,
>>insects, fish, and crustaceans). I compiled data on several species per
>>class, and multiple estimates of Y per species (from different
>>experiments), and analysed the data using a traditional mixed effects
>>model (lme), with species as a random effect and taxonomic class as fixed
>effect.
>>
>>However, one reviewer suggested I should control for phylogeny (without
>>being more specific). So I built a tree for these species (using
>>package rotl), made it ultrametric (using compute.brlen in package
>>ape), and computed the variance- covariance matrix A from this (using
>>vcv from package ape). I then created a variable phylo to distinguish
>>the phylogenetic component from the non- phlylogenetic species random
>effect, and used metafor to fit the model:
>>
>>rma.mv(Y, sampvar,mods = ~ Class, random = list(~ 1 | species, ~ 1 | phylo),
>>               R = list(phylo = A), data = Final.data, sparse = TRUE,
>>method =
>>"ML")
>>
>>(sampvar is the sampling variance associated with each estimate of Y)
>>
>>However, now I have started doubting whether this model makes sense,
>>i.e. to estimate an effect of taxonomic class (which in essence is a
>>phylogenetic effect) while simultaneously modelling a random effect of
>>phylogeny. Would an appropriate alternative be to not have class as a
>>moderator, but rather compare fits of models with and without the
>>phylogenetic variance-covariance matrix. If the model including
>>phylogeny is better than one without it, can I conclude that there is evolutionary
>divergence in this trait?
>>
>>Any advice anyone might have on this would be much appreciated!
>>
>>Best wishes
>>Sigurd Einum