[R-meta] confidence interval for I^2 in multilevel model

[Porter, Kyle]

Hello all,

I am using metafor to calculate an I^2 analogue for a multilevel random effects meta-regression as described at http://www.metafor-project.org/doku.php/tips:i2_multilevel_multivariate

I would like help in calculating a 95% confidence interval for this derivation of I^2.

Specifically, I am using the code taken below from the website to generalize the concept of I^2 to a clustered/multilevel model.

(the text below is taken from http://www.metafor-project.org/doku.php/tips:i2_multilevel_multivariate):
Based on the discussion above, it is now very easy to generalize the concept of I2 to such a model (see also Nakagawa & Santos, 2012). That is, we can first compute:

W <- diag(1/dat$vi)
X <- model.matrix(res)
P <- W - W %*% X %*% solve(t(X) %*% W %*% X) %*% t(X) %*% W
100 * sum(res$sigma2) / (sum(res$sigma2) + (res$k-res$p)/sum(diag(P)))


My specific application is as follows (the outcome is a single proportion):

PPV_prevdat <- escalc(measure="PAS", data=PPV_prev, xi=TP, ni=posTest)

mvregAll <- rma.mv(data=PPV_prevdat, yi, vi, method="REML", random = ~ 1 | ID, struct="DIAG", mods = ~ factor(Bethesda) + factor(Blinded) + prev +factor(NRAS12_13) + factor(HRAS12_13) + factor(KRAS61))

w <- diag(1/PPV_prevdat$vi)
x <- model.matrix(mvregAll)
P <- w - w %*% x %*% solve(t(x) %*% w %*% x) %*% t(x) %*% w
100 * sum(mvregAll$sigma2) / (sum(mvregAll$sigma2) + (mvregAll$k-mvregAll$p)/sum(diag(P)))

Any help/suggestion is appreciated.

Thank you,
Kyle Porter