### load data
dat <- get(data(dat.pritz1997))
### computation of "weighted average" in Zhou et al. (1999), Table IV
dat <- escalc(measure="PR", xi=xi, ni=ni, data=dat, add=0)
theta.hat <- sum(dat$ni * dat$yi) / sum(dat$ni)
se.theta.hat <- sqrt(sum(dat$ni^2 * dat$vi) / sum(dat$ni)^2)
ci.lb <- theta.hat - 1.96*se.theta.hat
ci.ub <- theta.hat + 1.96*se.theta.hat
round(c(estimate = theta.hat, se = se.theta.hat, ci.lb = ci.lb, ci.ub = ci.ub), 4)
### random-effects model with raw proportions
dat <- escalc(measure="PR", xi=xi, ni=ni, data=dat)
res <- rma(yi, vi, data=dat)
predict(res)
### random-effects model with logit transformed proportions
dat <- escalc(measure="PLO", xi=xi, ni=ni, data=dat)
res <- rma(yi, vi, data=dat)
predict(res, transf=transf.ilogit)
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