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

[James Pustejovsky]

>    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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