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# Re: st: Weights in Poisson regression

 From Hideto Koizumi <[email protected]> To [email protected] Subject Re: st: Weights in Poisson regression Date Tue, 22 Oct 2013 11:32:18 -0400

```Thank you very much Steve for your prompt detailed response and
providing the reference!
I will look into the paper.

Kindest regards,
Hideto

On Mon, Oct 21, 2013 at 11:35 PM, Steve Samuels <[email protected]> wrote:
>
> Correction:
>
> An analytic weight is proportional to the inverse of the observation
> variance, not to the variance itself.
>
>
>
> I should have added the obvious, that for the Poisson problem, variance
> = expected count  = Poisson parameter ("lambda") x population.
>
>
> Hideto:
>
> Your proposal would amount to double weighting. Maximum likelihood for
> Poisson regression is already equivalent to a generalized weighted least
> squares problem, with an analytic weight equal to the (estimated)
> variance of each observation. (Charnes et al., 1976). Note that
> county population (the exposure) is not the estimated variance and so
> would be suboptimal, even for the generalized regression.
>
> Reference:
>
> Charnes, Abraham, EL Frome, and Po-Lung Yu. 1976. The equivalence of
> generalized least squares and maximum likelihood estimates in the
> exponential family. Journal of the American Statistical Association 71,
> no. 353: 169-171.
>
>
> Steve
> [email protected]
>
> On Oct 21, 2013, at 11:45 AM, Hideto Koizumi wrote:
>
> Hi,
> Does anyone know how to use population at the unit of analysis (e.g.,
> population within each county of Connecticut) as weights in Poisson
> regression with an exposure variable (i.e., population of each county
> itself)? I wanted to simply use analytic weights but Poisson doesn't
> allow it due to its non-linear functional form. Anyone knows how to
> deal with this or knows any paper along this line?
>
> I would very much appreciate any input!
>
> Kindest regards,
> Hideto Koizumi
> ----------------------------------------
> Innovations for Poverty Action
> World Bank
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```