[R-meta] sd of blups vs tau in RE model

[Yefeng Yang]

Dear experts,


I kindly request your guidance in resolving my matter.

To simplify my query, I would like to focus solely on the random-effects model for now. My question pertains to the conceptual equivalence between the tau (standard deviation of the mean/overall effect) and the standard deviation of the study-specific effects within the studies included in a meta-analysis. Some researchers refer to these study-specific effects as BLUPs.

To explore this further, I conducted an analysis using a specific dataset in metafor. However, my findings seem to suggest otherwise. I present a reproducible example below for your reference:

# calculate es and var
dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)

# RE model
res <- rma(yi, vi, data=dat)

# calculate blups
blup_value <- blup(res)

# test whether the overall effect from res is equal to the simple mean of blup_value
res$beta[1] # -0.7145323
mean(blup_value$pred) # -0.7145323

We see the two values are equal.

# test whether tau from res is equal to the var of blup_value
sqrt(res$tau2) # 0.5596815
sd(blup_value$pred) # 0.4816293

We see the two values are not equal and seem to have a big gap.
Any comments and insights?

Best,
Yefeng



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