[R-meta] testing for and visualizing correlation between dependent traits in bivariate meta-analysis

[Viechtbauer, Wolfgang (NP)]

Hi Sigurd,

Thanks for the fully reproducible code/data.

As for the difference between the parameter estimates from the model and computations based on the random effects, you will find some discussions of this in the archives. A quick search yielded:

https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2023-May/004627.html

but I vaguely remember other threads where this has come up (not in connection with the correlation, but the variance).

For you data, I examined the species-level standardized residuals:

rstandard(mod1, cluster=new_data$species)$cluster

and the Cook's distances:

cds <- cooks.distance(mod1, cluster=new_data$species)
par(mar=c(4,12,2,2))
barplot(cds, horiz=TRUE, las=1, xlab="Cook's Distance")

I would start by checking what is going with the data for these species.

Best,
Wolfgang

> -----Original Message-----
> From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> On Behalf
> Of Sigurd Einum via R-sig-meta-analysis
> Sent: Thursday, October 31, 2024 09:56
> To: R-sig-meta-analysis using r-project.org
> Cc: Sigurd Einum <sigurd.einum using ntnu.no>
> Subject: [R-meta] testing for and visualizing correlation between dependent
> traits in bivariate meta-analysis
>
> I have a data set where two traits (lambda and lFC.inf) are measured
> simultaneously in different species, and the same species may be observed in
> more than one experiment. I apply a bivariate model to these data, where I want
> to check whether the two traits are correlated across species (e.g. does species
> that have a large value for one trait have a small value for the other). For
> this, I compare two models with struct ="UN" or struct = "DIAG", using AICc.
> This gives strong support for the model with struct = "UN", with an estimated
> negative correlation of -0.71.
>
> I want to visualize this pattern, and naively thought that I could just obtain
> the species-level random effects for lambda and lFC.inf from this model
> (obtained using ranef) and make a plot between them. However, this plot shows a
> very (unrealistic) tight relationship, and the negative correlation between
> these is considerably stronger (-0.94) than what the model estimated.
> Interestingly, when I do the same for the model with struct = "DIAG", the
> correlation becomes more similar to the one estimated in the model (-0.67).
>
> So my questions are (1) is my interpretation of the model comparison correct?
> and (2) how do I best visualize the result in a figure?
>
> See below for script.
> Any input on this would be greatly appreciated.
>
> Best,
> Sigurd Einum