[R-meta] multilevel bivariate metaanalysis in the presence of phylogenetic correlation

[Sigurd Einum]

Dear all, I have a question regarding multilevel bivariate metaanalysis in the presence of a known correlation structure (phylogenetic relatedness) using metafor.

Each study has one or more experiments ( "id"), where each experiment has estimates of two different parameters ("trait", ARR and lambda), together with their variances and covariances (providing variance-covariance matrix for the errors in the parameter estimates, V). Experiments are done on different species, and I have a phylogeny which is used to create the phylogenetic variance-covariance matrix.

One potential model I thought could be possible to use, which I thought would allow for different phylogenetic correlations for the different outcomes, as well as different species-level random effects (independent of phylogeny) for the two traits:
mod1 <- rma.mv(yi = yi, V = V, mods = ~trait,  data = new_data, random = list(~ 1 | study, ~1|id, ~ trait | species,~ trait | phylo), R = list(phylo = A))

However, this gives the warning: Argument 'R' specified, but list name(s) not in 'random'.
So, on the one hand this suggests to me that the phylogenetic variance-covariance matrix is ignored, and that phylo here is treated as a species random effect independent of phylogenetic correlation ("species" and "phylo" in new_data are identical species names). However, on the other hand the model output does give separate estimates for the two levels:


Multivariate Meta-Analysis Model (k = 394; method: REML)

     logLik     Deviance          AIC          BIC         AICc
-37620.5596   75241.1192   75269.1192   75324.5733   75270.2452

Variance Components:

            estim    sqrt  nlvls  fixed  factor
sigma^2.1  0.0001  0.0079     37     no   study
sigma^2.2  0.0007  0.0265    197     no      id

outer factor: species (nlvls = 77)
inner factor: trait   (nlvls = 2)

            estim    sqrt  k.lvl  fixed   level
tau^2.1    0.0121  0.1100    197     no     ARR
tau^2.2    0.0001  0.0117    197     no  lambda

        rho.ARR  rho.lmbd    ARR  lmbd
ARR           1                -    77
lambda  -0.9852         1     no     -

outer factor: phylo (nlvls = 77)
inner factor: trait (nlvls = 2)

              estim    sqrt  k.lvl  fixed   level
gamma^2.1    0.0099  0.0994    197     no     ARR
gamma^2.2    0.0002  0.0155    197     no  lambda

        phi.ARR  phi.lmbd    ARR  lmbd
ARR           1   -0.4692      -    77
lambda  -0.4692         1     no     -

Test for Residual Heterogeneity:
QE(df = 388) = 8590750.5336, p-val < .0001

Test of Moderators (coefficients 1:6):
QM(df = 6) = 34669.2288, p-val < .0001

So, my questions are
(1) which of these interpretations are correct? If the model does include the phylogenetic correlation structure, (2) is the value -0.4692 the phylogenetic correlation between the two traits? (3) What does the value -0.9852 from the trait|species term represent? And (4) how do one calculate I2 for such a model (I could only find examples from models that are either multilevel or bivariate, and not both at the same time?)

Any insights will be appreciated!
Best wishes,
Sigurd


Prof. Sigurd Einum
Dept. Biology, NTNU, Norway
https://www.ntnu.no/ansatte/sigurd.einum


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