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# Re: st: Weights in Poisson regression

 From Steve Samuels <[email protected]> To [email protected] Subject Re: st: Weights in Poisson regression Date Mon, 21 Oct 2013 23:35:40 -0400

```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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