Dear Statalisters,

I am thinking of fitting a fractional response or beta regression for Y on X, for a dataset which looks something like:
Identifier Numerator Denominator Y X1 X2
1 1000 2000 0.5 1 1
2 2000 3000 0.666667 2 3
3 3000 4000 0.75 3 5
4 4000 5000 0.8 4 7
5 5000 6000 0.833333 5 9
6 6000 7000 0.857143 6 11
7 7000 8000 0.875 7 13
8 8000 9000 0.888889 8 15
9 9000 10000 0.9 9 17

However, to me, it seems intuitive to assign more "weight" to observations where the sample size and/or number of events is larger. For example, it just seems to make sense that Observation 9 should contribute more weight to the analysis as it has 10000 observations and therefore should have the greatest precision / narrowest confidence intervals (if we were to compute the 95% CI of the proportion). Meaning to say that the confidence intervals around the proportion 9000/10000 is smaller than the confidence intervals around a proportion of say, 1000/2000.

In line with the above intuition, I was thinking of assigning inverse variance or inverse-SE weights to the analysis, by computing the SE of the logit of Y.

But I am also conscientious of the fact that I have not found any references to support such an approach..

I was hoping to get some expert advice if you are aware of any statistical theory / simulation papers which might support my above methodology...

Thanks in advance!
Best regards,
Nicholas Syn