st: How is confidence interval calculated in weighted GLM in Stata?

["Tan, Ji (GRS, Wuhan)" <Ji.Tan@towerswatson.com>]

Say in a simple Poisson regression,  EYi= λi=Oi*exp(β)
Log likelihood function is  So  And Fisher Score algorithm gives: This is in line with Stata.

However,  in the weighted case, log likelihood function changes to , ,
I  find Stata does not follow this numerically. So would anyone kindly explain this to me?

Thanks.

Regards,
Ji







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