Nick,
Just to relate my experience in such case:
- Number of prdt purchased follow a Poisson distribution :
log(P(N))=N*log(lambda)-logfact(N+1)-log(exp(lambda)-1))
log(lambda)=B*X
- Purchase incidence (prob. of purchase at least one) : p=1-exp(-exp(C*X))
Gombertz rather than Logit form --> log(-log(1-P))=C*X so if C==B,
log(1-P)=-lambda probability of no purchase under the Poisson count
process..
I always include the same variables in the binary and count process, and
test whether B=C (the variables have same effect over both processes)
Just compare the joint model (binary�count) with the complete Poisson
model..
What I always found (more than 15 product categories), B=C was
systematically & strongly rejected
-----Message d'origine-----
De : [email protected]
[mailto:[email protected]]De la part de
Theodoropoulos, N.
Envoy� : vendredi 28 novembre 2003 17:06
� : [email protected]
Objet : st: zero inflated poisson model
Hi Statalisters,
I am using a zero inflated poisson model (zip) and it is not clear to me if
I have to incorporate in the two processes (count data process and binary
process) the same explanatory variables.
Green (2000, page 298) suggests that the covariates between the two
processes need not be the same.
Long (1997, p. 243) suggests that in the Zip (t) model the z's and the x's
are the same, and the parameters in the logit process are assumed to be a
scalar multiple of the parameters in the poisson process. However, he
suggests that while the Zip(t) model reduces the number of parameters, it is
difficult to imagine a social science application in which one would expect
the parameters in the binary process to be a simple multiple of the
parameters in the poisson process. The differences between the beta's and
the gamma's parameters may be of substantive interest.
I have been experimented by including the same covariates in the poisson
process and in the logit process as well as discriminate between them. The
magnitudes of the coefficients as well as their signs change and depend on
the number of covariates I include in the binary process.
My question is the following: Is there a general rule for what variables one
should include in the logit process and what variables to include in the
poisson process, or one should just experiment?
Any suggestions?
Thanks in advance,
Nick
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