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Date:         Wed, 22 Nov 2006 13:54:40 -0800
Reply-To:     Dale McLerran <stringplayer_2@YAHOO.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Dale McLerran <stringplayer_2@YAHOO.COM>
Subject:      Re: poisson regression
In-Reply-To:  <>
Content-Type: text/plain; charset=iso-8859-1

--- Jeff <zhujp98@GMAIL.COM> wrote:

> I have poisson regression model. > I express it as > Log(P(Y=y))=b0+b1x1+b2x2+b3x3; > > My question is this the right expression for poisson regression? > > and how to interpret b1? > Thanks. > > Jeff >


Your regression function is not a standard model, and for good reason. I would note that if you have positive slope values, then for sufficiently large X1 (or X2 or X3), the value of Log(p(Y=y)) may exceed 0. In that case, the value of p(Y=y)>1. That is not a very satisfactory model, is it?

For Poisson regression, one usually assumes that

log(mu) = b0 + b1*X1 + ... + bk*Xk


mu = exp(b0 + b1*X1 + ... + bk*Xk)

where mu is the expected value of the response. The log link shown above is the canonical form of the link function for a Poisson response. Note that mu>0 when we use the log link function. Since the r.v. Y takes on nonnegative values, it is fitting that our estimate of the mean be constrained to be nonnegative, and this is accomplished when we employ the log link.

Fitting the Poisson regression involves modelling the mean such that the estimated density model provides the best possible match to the observed response probability structure. Exactly how this is done is beyond what I have time (or space) to write here. You might get further understanding by reading the details section for the GENMOD procedure.


--------------------------------------- Dale McLerran Fred Hutchinson Cancer Research Center mailto: Ph: (206) 667-2926 Fax: (206) 667-5977 ---------------------------------------

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