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From |
Maarten Buis <maartenlbuis@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: robust poisson regression vs. glm with log link |

Date |
Wed, 24 Aug 2011 10:10:43 +0200 |

On Tue, Aug 23, 2011 at 8:03 PM, Dimitriy V. Masterov wrote: > William Gould has a new post on the NEC blog about how Poisson > regression with vce(robust) is a better alternative to log-linear > regression: > > http://blog.stata.com/2011/08/22/use-poisson-rather-than-regress-tell-a-friend/#disqus_thread > > I can't seem to comment there, so I hope I can post my questions here > to get some insight. First, how does the robust Poisson model perform > relative to glm with a log link function? Are there ways to get the > elasticities from the poisson and/or glm coefficients? You can get exactly the same estimates and standard errors by also specifying the -family(poisson)- option. If you leave that option out you are using a different variance function, in this case constant variance. The logic comes from the quasi-likelihood tradition, which has found that one can make a function that has very similar properties to the likelihood function by just specifying how the mean depends on the explanatory variables (the link-function) and how the variance depends on that mean (the variance function). If all we want to do is see how the mean changes when the explanatory variables change, than there is an asymptotic argument that all that has to be correctly specified is this mean function. In finite samples the variance function may still matter, and that is why quite some attention is typically spent on also checking the variance function and why -glm- allows various variance functions (-family()-). See for example: James W. Hardin and Joseph M. Hilbe (2007) Generalized Linear Models and Extensions, second edition. College Station: Stata Press. or McCullagh, Peter; Nelder, John (1989). Generalized Linear Models, Second Edition. Boca Raton: Chapman and Hall/CRC. If you wish to explore those properties than I often find simulation to be very illuminating, in addition to reading about those techniques. Below is a quick set-up of how I would start with such a simulation. For getting a reliable idea about the coverage I would use more iterations: If the models works exactly as planned than we would expect only 50 rejections of the true hypothesis out of a 1000 iterations, and it is the deviations from that number 50 that decides how wrong or right the coverage is. With 20,000 iterations you would expect a 1000 rejections of the true hypothesis, giving you much more opportunity to detect deviations. Then the aim would be to explore how well the model works and when it brakes down by trying out a set of scenarios, e.g. different sample sizes. *------------------ begin example ----------------------- program drop _all program define sim, rclass drop _all sysuse nlsw88 gen y = exp(5 + .06*grade + 0.1*ttl_exp - /// 0.002*ttl_exp*ttl_exp + rnormal(0, 1.041) ) poisson y c.ttl_exp##c.ttl_exp grade, vce(robust) return scalar b_p = _b[grade] return scalar se_p = _se[grade] glm y c.ttl_exp##c.ttl_exp grade, link(log) vce(robust) return scalar b_g = _b[grade] return scalar se_g = _se[grade] end simulate b_p=r(b_p) se_p=r(se_p) /// b_g=r(b_g) se_g=r(se_g) , /// reps(1000) : sim simsum b*, se(se*) true(.06) mcse *----------------- end example ----------------------------- (For more on examples I sent to the Statalist see: http://www.maartenbuis.nl/example_faq ) This simulation requires Ian White's -simsum- package, which is described in Ian White (2010) "simsum: Analyses of simulation studies including Monte Carlo error" The Stata Journal, 10(3): 369-385. You can install it by typing in Stata -ssc install simsum-. Hope this helps, Maarten -------------------------- Maarten L. Buis Institut fuer Soziologie Universitaet Tuebingen Wilhelmstrasse 36 72074 Tuebingen Germany http://www.maartenbuis.nl -------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: robust poisson regression vs. glm with log link***From:*"Dimitriy V. Masterov" <dvmaster@gmail.com>

**Re: st: robust poisson regression vs. glm with log link***From:*Maarten Buis <maartenlbuis@gmail.com>

**References**:**st: robust poisson regression vs. glm with log link***From:*"Dimitriy V. Masterov" <dvmaster@gmail.com>

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