[R-meta] Notable difference between treditional and bootstrap 95% CI for sigma2: which one is preffered?

[towhidi]

Dear all,

I am working on a dataset with a multilevel structure: 185 SMDs, nested 
in 108 outcomes, nested in 41 comparisons (to address multiarmed trials) 
nested in 34 studies (random = ~1 | 
stud_id/cont_id/outcome_id/occasion).

For some of the sigma^2 values, the CI from confint() is largely 
different from the bootstrap CI, e.g., for a sigma^2 = .04, the upper 
limit from confint() is .38, while the boot CI upper limit is .21.

(1) What does this difference imply?

(2) When such differences exist between traditional and boot CIs, Which 
one is more reliable?

For calculating boot CI I used the following:

sim <- simulate(res, nsim=300)
sav <- lapply(sim, function(x) {
tmp <- try(rma.mv(x, vi, data = dat, random = res$random), silent=TRUE)
if (inherits(tmp, "try-error")) {
next
} else {
tmp
}})

sigma2.l4 <- sapply(sav, function(x) x$sigma2[2])

quantile(sigma2.l4, c(0.025, .975))

Of note, I have checked the profile plot and there seemed to be no 
convergence problem.

I also have another related question:
(3) Is the general formula for I^2 for multilevel models 
(https://www.metafor-project.org/doku.php/tips:i2_multilevel_multivariate) 
can be applied to RVE without any modifications?

Thank you.


-- 
Ali Zia-Tohidi MSc
Clinical Psychology
University of Tehran