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st: zero inflated poisson model
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?
Thanks in advance,
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