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From |
Cameron McIntosh <cnm100@hotmail.com> |

To |
STATA LIST <statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: Model for Poisson-shaped distribution but with non-count data |

Date |
Tue, 6 Dec 2011 16:41:13 -0500 |

You might also consider a Bayesian multilevel model with a gamma prior: Griffin, J.E., & Brown, P.J. (2010). Inference with normal-gamma prior distributions in regression problems. Bayesian Analysis, 5(1), 171-188.http://ba.stat.cmu.edu/journal/2010/vol05/issue01/griffin2.pdf Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models. Bayesian Analysis, 1(3), 515–533.http://www.stat.columbia.edu/~gelman/research/published/taumain.pdf Lambert, P.C., Sutton, A.J., Burton, P.R., Abrams, K.R., & Jones, D.R. (2005). How vague is vague? A simulation study of the impact of theuse of vague prior distributions in MCMC using WinBUGS. Statistics in Medicine, 24, 2401–2428.http://www.yaroslavvb.com/papers/lambert-how.pdf Browne W.J., & Draper, D. (2006). A comparison of Bayesian and likelihood-based methods for fitting multilevel models. Bayesian Analysis, 1(3), 473–514.http://ba.stat.cmu.edu/journal/2006/vol01/issue03/draper2.pdf Cam > Date: Tue, 6 Dec 2011 12:48:35 -0800 > Subject: Re: st: Model for Poisson-shaped distribution but with non-count data > From: ogallupe@gmail.com > To: statalist@hsphsun2.harvard.edu > > Thank you for the input, Cam, Paul, Paul, Nick, David, and Bill. > > You have given me some very good options to consider. > > Regarding Cam's earlier question, the multimodality only surfaces when > the DV is transformed using lnskew0. It is not an issue using the raw > version. > > All the best. > > Owen > > On Tue, Dec 6, 2011 at 9:34 AM, William Gould, StataCorp LP > <wgould@stata.com> wrote: > > David Hoaglin <dchoaglin@gmail.com>, in reference to the blog entry > > "Use Poisson Rather Than Regress, Tell a Friend" at > > > > http://blog.stata.com/2011/08/22/use-poisson-rather-than-regress-tell-a-friend/ > > > > wrote, > > > >> [..] I did not see any > >> mention of the fact that the Poisson distribution is discrete. In the > >> limit (as the mean of the distribution becomes large), that matters > >> less, but one would need to view the possible data values as discrete. > >> > >> Some of the equations in the blog are not quite correct. For example, > >> since Poisson regression is a form of generalized linear model, the > >> linear predictor is fitted to log(E(y)), rather than to log(y). The > >> random component of the GLM is a Poisson distribution. > > > > I'm concerned that someone might interpret what David wrote to mean > > > > 1. There may be practical problems using -poisson- to run > > log-linear regressions, depending on whether the LHS variable > > contains noninteger values. > > > > 2. There may be theoretical problems using -poisson- to run > > log-linear regressions. > > > > Neither would be true. My short-and-quick response is, > > > > 1. -poisson- can handle non-discrete (non-integer) data values. > > Left-hand-side values do not have to be large to ammelorate any > > problem. > > > > 2. The formulas in the blog are as intended and are correct. > > > > Let me explain. > > > > > > Concerning #1, -poisson- does not round values when run on noninteger > > data. Instead, it gives the warning message "you are responsible for > > interpreation of noncount dep. variable." > > > > An implication of that is that the objective function with non-integer > > data may not be a true likelihood function. Actually, I suspect that > > it is, but that's irrelevant because we in the blog entry are doing M > > estimation and I recommended you obtain standard errors using the > > -vce(robust)- option. > > > > When -poisson- calculates the likelihood value associated with a > > noninteger value, it does that using the standard formulas, but > > substituting the Gamma function for factorial function. That is > > appropriate for M estimation. > > > > This generalization means that you can run -poisson- using a LHS > > variable with noninteger values and there will be no problems. All > > the values, in fact, can even be less than 1! Whether you run on y, > > y/10, y/100, y/1000, ..., all that will change will be the intercept. > > > > > > Concerning #2, the formulas written in the blog entry imply that > > log(E(y)) = a + b*X. It is true that I did write > > > > y = exp(a + b*X + e) > > > > and that implies more than merely log(E(y)) = a + b*X. I did that > > because I was starting with the log-linear regression problem. > > The purpose of the blog entry is to show that -poisson- could be > > used as an alternative to linear regression on the ln(y). > > > > -- Bill > > wgould@stata.com > > * > > * 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/ > > * > * 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/ * * 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/

**References**:**Re: st: Model for Poisson-shaped distribution but with non-count data***From:*"William Gould, StataCorp LP" <wgould@stata.com>

**Re: st: Model for Poisson-shaped distribution but with non-count data***From:*Owen Gallupe <ogallupe@gmail.com>

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