[R-meta] mixed-effects and moderators

[Fred Oswald]

This is very heartening, thank you Reza!

On my end, I should have provided you all with a reproducible example...I
was relying on a graduate student's screenshots of their output and should
have gone back to the original data.

Really appreciate your time and support here!

Best,
Fred

Fred Oswald
workforce.rice.edu | @FredOswald <https://twitter.com/FredOswald> | calendar
<http://workforce.rice.edu/contact/>


On Wed, Oct 20, 2021 at 7:58 PM Reza Norouzian <rnorouzian using gmail.com> wrote:

> Hello Fred,
>
> Not sure how your data looks, but here is a reproducible example where
> the two methods do match.
>
> Best,
> Reza
>
> dat <- dat.bcg
> dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat)
>
> res1 <- rma(yi, vi, data=dat)
> res2 <- rma(yi, vi, mods = ~ ablat, data=dat)
>
> (R2 <- (res1$tau2 - res2$tau2) / res1$tau2)
>
> (`METHOD ONE` <- res1$tau2 - res2$tau2 )
> # [1] 0.2368886
> (`METHOD TWO` <- res2$tau2 * (R2 / (1-R2)))
> # [1] 0.2368886
>
> On Wed, Oct 20, 2021 at 7:34 PM Fred Oswald <foswald using rice.edu> wrote:
> >
> > Your response was very helpful, thank you, Reza!
> >
> > METHOD ONE
> > As a simple approach, you could estimate tau^2_moderators by subtracting
> > (a) tau^2_residual reported in the mixed-effects model (with moderators)
> > from (b) tau^2 total reported in the random effects model (no
> moderators).
> >
> > METHOD TWO
> > You also could get it from R2 and the residual tau^2  reported in the
> > mixed-effects model (with moderators), because:
> >
> > R2 = (tau^2_total - tau^2_res)/tau^2_total
> > (see page 251 here:
> > https://cran.r-project.org/web/packages/metafor/metafor.pdf)
> >
> > and that's the same thing as saying
> > R2 = tau^2_moderators / (tau^2_moderators + tau^2_res)
> >
> > Rearranging the above, we get:
> > tau^2_moderators = tau^2res * R2 / (1 - R2)
> >
> > The estimate of tau^2_moderators from method one vs. method two above is
> > not the same for me (close, but not the same) - maybe in part due to
> > rounding error, I'm not sure.
> >
> > Thanks again.
> >
> > Best,
> > Fred
> >
> > Fred Oswald
> > workforce.rice.edu | @FredOswald <https://twitter.com/FredOswald> |
> calendar
> > <http://workforce.rice.edu/contact/>
> >
> >
> > On Mon, Oct 18, 2021 at 9:21 PM Reza Norouzian <rnorouzian using gmail.com>
> wrote:
> >
> > > Hello Fred,
> > >
> > > I believe the following should be very helpful:
> > >
> https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2021-October/003447.html
> > >
> > > Kind regards,
> > > Reza
> > >
> > > On Mon, Oct 18, 2021 at 8:57 PM Fred Oswald <foswald using rice.edu> wrote:
> > >
> > >> Hello, and apologies if this has been addressed before: For a
> > >> mixed-effects
> > >> model in metafor, how does one estimate the amount of heterogeneity
> > >> accounted for by continuous moderators (tau^2_mod)? Maybe use the
> > >> closed-form D-L estimate from Q_M?
> > >>
> > >> Otherwise, deriving this from the output is not obvious to me (e.g.,
> I2 is
> > >> based on tau^2_res, and R2 assumed fixed effects).
> > >>
> > >> Also, presumably tau^2_total = tau^2_mod + tau^2_res…yes?
> > >>
> > >> Thank you for any support!
> > >>
> > >> Best,
> > >> Fred Oswald
> > >>
> > >> Website | https://workforce.rice.edu
> > >> Calendar | https://tinyurl.com/foswald
> > >> Twitter  | @FredOswald
> > >> Future of Work  | https://tinyurl.com/futureworking
> > >> --
> > >> Best,
> > >> Fred Oswald
> > >>
> > >> Website | https://workforce.rice.edu
> > >> Calendar | https://tinyurl.com/foswald
> > >> Twitter  | @FredOswald
> > >> Future of Work  | https://tinyurl.com/futureworking
> > >>
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> > >>
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> > >>
> > >
> >
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