How to run a truncated and inflated Poisson model in R?

Question

My data doesn't contain any zeros. The minimum value for my outcome, y, is 1 and that is the value that is inflated. My objective is to run a truncated and inflated Poisson regression model using R.

I already know how to separate way each regression zero truncated and zero inflated. I want to know how to combine the two conditions into one model.

Thanks for you help.

Answer 1

For zero inflated models or zero-hurdle models, the standard approach is to use pscl package. I also wrote a package fitting that kind of models here but it is not yet mature and fully tested. Unless you have voluminous data, I still recommend you to use pscl that is more flexible, robust and documented.

For zero-truncated models, you can have a look at the VGML::vglm function. You might find useful information here .

Note that you are not doing the same distributional assumption so you won't need the same estimation data. Given the description of your dataset, I think you are looking for a zero-truncated model (since you do not observe zeros). With zero-inflated models, you decompose your observed pattern into zeros generated by a selection model and others generated by a count data model. This doesn't look to be a pattern consistent with your dataset.