[R-meta] Questions about the use of metaprop for the pooling of proportions
Dr. Gerta Rücker
ruecker @end|ng |rom |mb|@un|-|re|burg@de
Tue Mar 8 23:36:24 CET 2022
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.
Good night then :)
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