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

Hi both,

I happen to come across a paper, which can answer both of your comments.

Eq. 1 and the following Eqs. show the derivation of the equivalence
mentioned by my earlier email.

Wang C C, Lee W C. A simple method to estimate prediction intervals and
predictive distributions: summarizing meta?analyses beyond means and
confidence intervals[J]. Research Synthesis Methods, 2019, 10(2): 255-266.


Best,
Yefeng
------------------------------
*From:* James Pustejovsky <jepusto at gmail.com>
*Sent:* Friday, 30 June 2023 13:08
*To:* Yefeng Yang <yefeng.yang1 at unsw.edu.au>
*Cc:* R Special Interest Group for Meta-Analysis <
r-sig-meta-analysis at r-project.org>
*Subject:* Re: [R-meta] sd of blups vs tau in RE model


 Thanks for your clarification. Your explanations are very clear.
Actually, the SD of BLUPs and tau will converge when the within-study
replicates are getting large.


Can you say more about this? Is this claim based on simulations or
something? I see the intuition, but it also seems like this property might
depend not only on the within-study replicates all being large, but also on
their _relative_ sizes.