Date:         Tue, 5 Mar 2002 13:41:02 -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: Genmod and Positive Poisson
In-Reply-To:  <C0E2F977298CD411883100A024B2F510C8CDD6@uel-pdc.uel.br>
Content-Type: text/plain; charset=us-ascii

Silvano,

What is the Positive Poisson distribution?  How does it arise?  If
a Positive Poisson distribution is a Poisson distribution with zero
values censored so that the probability function could be written as

  p(y) = exp(-Xbeta)*(Xbeta**y)/(y!) / (1 -
exp(-Xbeta)*(Xbeta**0)*(0!))
       = exp(-Xbeta)*(Xbeta**y)/(y!) / (1 - exp(-Xbeta))

then you could use the nlmixed procedure in version 8.x of SAS to
fit the model without having to specify deviance and variance
functions.  All that you need to specify for nlmixed to work is the
likelihood function.  The following syntax should fit the model:

proc nlmixed data=mydata;
  Xbeta = beta0 + x1*beta1 + x2*beta2 + ... + x<k>*beta<k>;
  p_y = exp(-Xbeta)*(Xbeta**y)/(fact(y)) / (1 - exp(-Xbeta));
  loglike = log(p_y);
  model y ~ general(loglike);
run;


If my assumption about the probability function of the Positive
Poisson distribution is incorrect, then simply modify the probability
function to provide the correct form.  And please respond to the
first couple of questions above.  I really would like to know just
what this distribution is and how it occurs.

Dale


--- Silvano Cesar da Costa <silvano@UEL.BR> wrote:
> Hi,
>
> I'm trying fit Positive Poisson using Genmod.
> The statements are:
>
> Proc Genmod;
>  class ini cult;
>    m = _mean_;
>    a = m/(1-exp(-m));
>    y = _resp_;
>    d = 2 * (y * log(y/a) + log( (exp(a)-1)/(exp(y)-1)));
>    variance var = a * (1 + m -a);
>    deviance dev = d ;
>  model nbrotos = ini|cult / link=log type1 type3;
> run;
>
> but, I'm not sure if was correct.
>
> Someone can help me.
>
> Thanks,
>
> Silvano.


=====
---------------------------------------
Dale McLerran
Fred Hutchinson Cancer Research Center
mailto: dmclerra@fhcrc.org
Ph:  (206) 667-2926
Fax: (206) 667-5977
---------------------------------------

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