[R-meta] mixed-effects and moderators

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/>

[R-meta] mixed-effects and moderators

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