[R-meta] Questions about the use of metaprop for the pooling of proportions

[Dr. Gerta Rücker]

Hi all

Am 08.03.2022 um 23:19 schrieb Viechtbauer, Wolfgang (SP):
> Happy to see other people spending time at 11pm thinking about this kind of stuff :)
Yes. That's typical mathematicians' behaviour.
> If we want to be really precise, the MLE of the logit-transformed true proportion is qlogis((sum r_i)/(sum n_i)) for the logistic regression model with a logit link, but since MLEs are invariant under transformations, so plogis(qlogis((sum r_i)/(sum n_i))) = (sum r_i)/(sum n_i)) is the MLE of the true proportion. In fact, this is neatly demonstrated by fitting the logistic regression with an identity link (do we even call this 'logistic' regression?!?):
>
> coef(glm(out1/n ~ 1, weights = n, family = binomial(link = "identity")))
>
> That all of this happens 'automagically' is really a neat feature of logistic regression.

Nice!

Good night then :)

Gerta