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From | Hideto Koizumi <hkoizumi@poverty-action.org> |
To | statalist@hsphsun2.harvard.edu |
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 <sjsamuels@gmail.com> 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 > sjsamuels@gmail.com > > 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 > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/