[R-meta] test different levels of a random effect

[James Pustejovsky]

Hi Yefeng,

Yefeng, for your aim (1), whether an estimate associated with a certain
species is significantly different from 0 (in the sense of P value), I like
what Wolfgang suggested of using the BLUPs to determine the species for
which there is evidence of non-zero effect. A challenge is determining
whether/how to do some sort of familywise error or false discovery rate
control, since you'd be running 345 hypothesis tests.

For your aim (2), whether any two of such species-specific estimates of
interest are different, if you are looking for a way to test the *joint*
null hypothesis that all species-specific estimates are equal (i.e., that
there are no differences between the effects for any pair of species), then
it seems like the most direct route would be to test that the species.id
variance component is equal to zero. You could do this with a likelihood
ratio test comparing the model with species.id random effects to the model
without such random effects.

James

James

On Wed, Nov 20, 2024 at 11:59 AM Viechtbauer, Wolfgang (NP) via
R-sig-meta-analysis <r-sig-meta-analysis using r-project.org> wrote:

> Dear Yefeng,
>
> Trying to estimate 345 different variance components in approach 2. seems
> quite ambitious to me.
>
> As for 1., it is worth pointing out that using fixed versus random effects
> for species is somewhat similar, except that the estimates you get from
> using random effects exhibit a natural shrinkage effect. This can be nicely
> visualized as follows:
>
> res1 <- rma.mv(yi, V, random = list(~ 1 | study.id, ~ 1 | effect.size.id,
> ~ 1 | species.id), data=dat, sparse = TRUE)
> res2 <- rma.mv(yi, V, mods = ~ species.id - 1, random = list(~ 1 |
> study.id, ~ 1 | effect.size.id), data=dat, sparse = TRUE)
>
> plot(coef(res2), coef(res1) + ranef(res1)$species.id$intrcpt, pch=21,
> bg="gray",
>      xlab="Fixed Species Effects", ylab="Random Species Effects",
>      xlim=c(-1,3), ylim=c(-1,3),
>      panel.first={abline(0,1);
>                   abline(h=coef(res1), lty="dotted");
>                   abline(v=coef(res1), lty="dotted")})
>
> If you install the latest 'devel' version of metafor, you can use:
>
> ranef(res1, vcov=TRUE)
>
> to obtain also the full var-cov matrices of the BLUPs of the random
> effects. Then one could test pairs of species against each other while
> accounting for the covariance:
>
> sub <- ranef(res1, vcov=TRUE)
> sub$pred <- sub$pred$species.id[1:2,]
> sub$vcov <- sub$vcov$species.id[1:2,1:2]
> sub
>
> rma.mv(intrcpt, V=sub$vcov, mods = c(0,1), data=sub$pred)
>
> Best,
> Wolfgang
>
> > -----Original Message-----
> > From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org>
> On Behalf
> > Of Yefeng Yang via R-sig-meta-analysis
> > Sent: Friday, November 15, 2024 05:16
> > To: r-sig-meta-analysis using r-project.org
> > Cc: Yefeng Yang <yefeng.yang1 using unsw.edu.au>
> > Subject: [R-meta] test different levels of a random effect
> >
> > Dear community,
> >
> > My question might look weird. Let me explain my question using a concert
> > example.
> >
> > Dat.moura2021 in metadata package contains 457 studies on assortative
> mating in
> > 345 species.
> > library(metafor)
> > dat <- dat.moura2021$dat
> >
> > ### calculate r-to-z transformed correlations and corresponding sampling
> > variances
> > dat <- escalc(measure="ZCOR", ri=ri, ni=ni, data=dat)
> > ### assume that the effect sizes within studies are correlated with
> rho=0.6
> > V <- vcalc(vi, cluster=study.id, obs=effect.size.id, data=dat, rho=0.6)
> > ### fit a model with study identity, observation, and species as random
> effects
> > res <- rma.mv(yi, V, random = list(~ 1 | study.id, ~ 1 | effect.size.id,
> ~ 1 |
> > species.id), data=dat, sparse = T)
> >
> > In this specific dataset, I want to know whether (1) an estimate
> associated with
> > a certain species is significantly different from 0 (in the sense of P
> value),
> > and (2) whether any two of such species-specific estimates of interest
> are
> > different.
> >
> > 1. A natural solution that occurs to me is to add the species variable
> (in our
> > case, species.id) as a predictor rather than a random effect, and we
> can do
> > subsequent test of factors and linear combinations of parameters.
> > ### add species.id as a predictor
> > res2 <- rma.mv(yi, V, mods = ~ species.id - 1, random = list(~ 1 |
> study.id, ~ 1
> > | effect.size.id), data=dat, sparse = T)
> >
> > This has a potential issue that model res2 is likely to be
> overparameterized. Of
> > course, we can check the likelihood profile of each parameter estimate to
> > confirm whether each estimate is identifiable. But this takes a long
> time to do
> > so. Importantly, species.id should be a random effect rather than a
> fixed
> > effect.
> >
> > 2. A second approach is similar to the first one but has a slightly
> different
> > assumption. A normal regression model assumes homogeneous variance
> (tau^2)
> > across different levels of a predictor. But species.id has 345 levels.
> It is not
> > very reasonable to assume all 345 species share a common heterogeneity.
> To relax
> > this assumption, we can use a subgroup random effects model, which was
> proposed
> > in Pustejovsky, J. E., & Tipton, E. (2022)
> >
> > ### fit a subgroup random effects model
> > V_subgroup <- vcalc(vi, cluster=study.id, subgroup=species.id, data=dat,
> > rho=0.6)
> > res3 <- rma.mv(yi, V_subgroup, mods = ~ species.id - 1, random = list(~
> > species.id | study.id), struct = "DIAG", data=dat, sparse = T)
> > ### add effect size id as an additional random effect
> > res4 <- rma.mv(yi, V_subgroup, mods = ~ species.id - 1, random = list(~
> > species.id | study.id, ~ 1 | effect.size.id), struct = "DIAG",
> data=dat, sparse
> > = T)
> >
> > I do not know which one (res3 vs. res4) is better
> >
> > 3. We can sum up the intercept (or fixed effect) and random effect
> estimates of
> > species.id of the model object res to get the species-specific
> estimates. Then,
> > we use the Wald-type method to test the species-specific estimates and
> > difference between them.
> >
> > ### get species's random effect estimate
> > res_ranef <- ranef(res)
> > ### combine with the fixed effect estimate
> > est <- data.frame(species = rownames(res_ranef$species.id),
> >                   beta = res$beta[1] + res_ranef$species.id$intrcpt,
> >                   se = sqrt(res$se[1]^2 + res_ranef$species.id$se^2))
> >
> > But this approach will ignore the covariance between different species.
> >
> > I would be grateful if anyone can provide insights into (1) which
> approaches
> > above is preferrable, and (2) if none of them is valid,  can you help
> find a
> > solution?
> >
> > Best,
> > Yefeng
>
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