[R-meta] mixed-effects and moderators

[Fred Oswald]

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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