```Date: Thu, 11 Mar 2004 06:27:53 -0800 Reply-To: Dale McLerran Sender: "SAS(r) Discussion" From: Dale McLerran Subject: Re: zero truncated poisson regression Comments: To: Andrew Haywood Content-Type: text/plain; charset=us-ascii Andrew, I was mulling over my response from yesterday and realized that I kind of got ahead of myself at one point. I indicated that > The probability function for the zero-truncated Poisson distribution > is > > p(y) = exp(-Xbeta)*(Xbeta**y)/(y!) / > (1 - exp(-Xbeta)*(Xbeta**0)*(0!)) > = exp(-Xbeta)*(Xbeta**y)/(y!) / (1 - exp(-Xbeta)) > = -Xbeta + y*log(Xbeta) - log(y!) - log(1 - exp(-Xbeta)) This last line is incorrect, of course. I was anticipating the log-likelihood function which the nlmixed procedure would solve. Thus, I should have written: p(y) = exp(-Xbeta)*(Xbeta**y)/(y!) / (1 - exp(-Xbeta)*(Xbeta**0)*(0!)) = exp(-Xbeta)*(Xbeta**y)/(y!) / (1 - exp(-Xbeta)) and the log-likelihood function is ll(y) = -Xbeta + y*log(Xbeta) - log(y!) - log(1 - exp(-Xbeta)) The remainder of the post should be OK. > As you suggest, nlmixed allows one to solve the likelihood function. > > proc nlmixed data=mydata; > Xbeta = beta0 + x1*beta1 + x2*beta2 + ... + x*beta; > loglike = -Xbeta + y*log(Xbeta) - lgamma(y+1) - > log(1 - exp(-Xbeta)); > model y ~ general(loglike); > run; Just felt that I should set the record straight. Dale ===== --------------------------------------- Dale McLerran Fred Hutchinson Cancer Research Center mailto: dmclerra@fhcrc.org Ph: (206) 667-2926 Fax: (206) 667-5977 --------------------------------------- __________________________________ Do you Yahoo!? Yahoo! Search - Find what you’re looking for faster http://search.yahoo.com ```

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