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

[James Pustejovsky]

The approximations there are predicated on k (the number of studies) being
large enough that the estimated heterogeneity (tau-hat) converges to the
true heterogeneity parameter.

On Thu, Jun 29, 2023 at 11:29 PM Yefeng Yang <yefeng.yang1 using unsw.edu.au>
wrote:

> 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 using gmail.com>
> *Sent:* Friday, 30 June 2023 13:08
> *To:* Yefeng Yang <yefeng.yang1 using unsw.edu.au>
> *Cc:* R Special Interest Group for Meta-Analysis <
> r-sig-meta-analysis using 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.
>
>

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