[R-meta] mixed-effects and moderators

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 at 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> |

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<http://workforce.rice.edu/contact/>


On Mon, Oct 18, 2021 at 9:21 PM Reza Norouzian <rnorouzian at 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 at 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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