st: Mixed Poisson models with degenerate conditional distribution for a given value of a covariate

[Alexander Limonov <alexlimonov@yahoo.com>]

Hi Statalist,

I have a general statistical question (although there's also a question of how to implement the answer in Stata...).

I'm working with a count data-generating process where the dependent variable is restricted to 0, if one of the covariates (let's say it's nonnegative and discrete) is 0. This occurs in a nontrivial number of cases. Otherwise, the dependent variable may be assumed to follow any conditional discrete distribution of your choice, but Poisson could be a start.

My understanding is that there exists a class of models, namely zero-inflated Poisson models, that allow for something like that, but there, the probability of obtaining a 0 as a response (due to the non-Poisson component, that is), while potentially conditional on the same covariates as the Poisson response, appears to be normally modeled using a logit link.

(The situation seems like censoring, but I don't know what relevant censored count models exist...)

The questions:

-Does the ZIP model fit the process I'm describing, and what modifications are necessary? 

-If yes, is there a way to "hack" this together with existing Stata procedures? 

-If no, what model would be appropriate?

Best,

Alexander Limonov


      
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