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

 From "Tan, Ji (GRS, Wuhan)" To "statalist@hsphsun2.harvard.edu" Subject RE: st: How is confidence interval calculated in weighted GLM in Stata? Date Sat, 1 May 2010 09:46:16 +0800

```Sorry I did not know the convention here, and Thanks for the reference, while I don't have immediate access to. Let me rewrite in plain text:

Say in a simple Poisson regression,  E(Yi)=ui=Oi*exp(b), Log likelihood function is {sum (Yi*b-ui)}, when we add weighting wi, it became {sum wi(Yi*b-ui)}, The estimation of b is {(sum wi*Yi)/(sum wi*Oi)}, and the Fisher Score algorithm gives its distribution as N(b, (sum wi^2*ui)/(sum wi*ui)^2).

However, this calculation only agree with Stata when we have equal weights, i.e. all the wi are the same. So would anyone kindly explain this to me?

Best regards,
Ji

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Maarten buis
Sent: Friday, April 30, 2010 8:02 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: How is confidence interval calculated in weighted GLM in Stata?

--- On Fri, 30/4/10, Tan, Ji (GRS, Wuhan) wrote:
> Say in a simple Poisson regression,  EYi= i=Oi*exp()
> 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?

You can only sent plain text and no attachments to
the statalist, so your message got hopelessly
garbled. So I can't answer you question directly,
I can only give you some literature recomendations:

James W. Hardin and Joseph M. Hilbe "Generalized
Linear Models and Extensions, second edition.
College Station, TX: Stata Press.
<http://www.stata-press.com/books/glmext.html>

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------

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