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

[Reza Norouzian]

Yefeng,

Another question/comment that I hear when I distinguish between
statistics (sd, correlation etc.) hand-calculated from BLUPs and and
their counterparts estimated directly by the model (which is not
conditioned on observed data) is that given that the BLUPs are
conditioned on observed data and don't necessarily reflect the
population, then would it be possible or make sense to, for example,
construct a confidence interval for a statistic (sd, correlation etc.)
hand-calculate from BLUPs.


On Thu, Jun 29, 2023 at 8:48 PM Yefeng Yang via R-sig-meta-analysis
<r-sig-meta-analysis using r-project.org> wrote:
>
> Hi James,
>
> 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.
>
> A quick update for you:  I investigated KDE a little bit using density() in R. It seems to work well with BLUPs - it can show the empirical distribution without relying on normal distribution assumption. There is an augment in density() that can be used to tune smoothing bandwidth, although this parameter can not be tuned directly in density().
>
>
> Also appreciate your comments, Reza.
>
> Best,
> Yefeng
> ________________________________
> From: James Pustejovsky <jepusto using gmail.com>
> Sent: Friday, 30 June 2023 11:26
> 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
>
>
>
>
>   1.   Would you like to explain a bit "the SD of the BLUPs is not the same thing as the SD of the population distribution". Conceptually, I thought they are the same - both representing the marginal distribution after accounting for sampling error.
>
>  The BLUPs are estimates of study-specific effects. Say that the population consists of effect sizes for all the people on the listserv. We estimate a meta-analysis using effect size estimates from you, me, Wolfgang, and Gerta. The BLUPs are then estimates of the true effects for you, me, Wolfgang, and Gerta. They're not estimating a feature of the population distribution, they're estimating a feature of the effects for the observed meta-analysts. Thus, there's no reason that the SD of the effects from you, me, Wolfgang, and Gerta should be exactly the same as the SD of the population of all the meta-analysts on the listserv.
>
>   1.  If I use some dispersion-relevant stats derived from the distribution of BLUPs to represent the heterogeneity, is it reasonable?
>
> Maybe? I would think it depends on the specific statistics. This is kind of what I was getting at with my comment about the kernel density estimator.
>
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