I want to perform a meta analysis (in R) on the effect of temperature on two outcomes; reproduction and lifespan. It is believed that temperature has a quadratic effect on reproduction but has a cubic effect on lifespan. I want to model both of these outcomes simultaneously because I have data from many studies where the reproduction and lifespan of the same individuals are recorded.
Is it possible to include both of these non-linear structures in the same meta-analytical model?
So far I have ran these models separately i.e.
** for reproduction:** meta_reproduction^2 <- rma.mv(es, VCV_shared, mod= ~ poly(treattemp, degree=2, raw=TRUE), random= list(~ 1|study_code, ~1|obs), test = "t", dfs = "contain", data= rdata, method= "REML")
**for lifespan: ** meta_lifespan^3 <- rma.mv(es, VCV_shared, mod= ~ poly(treattemp, degree=3, raw=TRUE), random= list(~ 1|study_code, ~1|obs), test = "t", dfs = "contain", data= rdata, method= "REML")
In each case the es and vcv_shared are the effect sizes and covariance matrix for reproduction and lifespan respectively.
However, I would like to include these in the same model so I can incorporate the fact that the same individuals are used in each experiment for reproduction and longevity outcomes.
It is possible to us outcome (i.e. reproduction/lifespan) as a fixed effect, but I wouldn't be able to have quadratic for reproduction and a cubic structure for lifespan that way.
I was thinking there might be some way to linearise both effect sizes?
Any advice is welcome.
Thanks, Fay