[R-meta] Multi-level model accounting for within-cluster correlation

[Dr. Guido Schwarzer]

Hi,

In statistical consulting, a Master's student asked me whether the following R code is correct to conduct a multi-level meta-analysis:

## assume that the effect sizes within studies are correlated with rho = 0.6
V <- vcalc(vi, cluster = cluster_id, obs = study_id, data = dat, rho = 0.6)
## fit multilevel model using this approximate V matrix
res1 <- rma.mv(yi, V, random = ~ 1 | cluster_id / study_id, data = dat)

To my understanding, the advantage of a multi-level model is that no assumption on the within-cluster correlation is required / the correlation must no be specified, i.e., the model would be
res2 <- rma.mv(yi, vi, random = ~ 1 | cluster_id / study_id, data = dat)

Am I correct?

And, if so, does the above model using the block diagonal covariance matrix V make any sense?

Best,
Guido