[R] Zero-inflated neg.bin. model and pscl package

[Ben Bolker]

Simone Vincenzi <svincenz <at> nemo.unipr.it> writes:

> I don't understand from the sentence in the pscl guide "Zero-inflated count
> models are a type of two-component mixture model, with a component for zero
> counts, and the other component for the positive counts" if:
> a)to get true estimate of the relative mean abundance, the model multiply
> the relative mean abundance at a site by the probability that the relative
> mean abundance at a site is generated through a negative binomial
> distribution, as proposed by Lambert (Technometrics, 1992). By using this
> kind of mixture model, zeros arise from one or two processes and their
> related covariates. 
> b) we have two independent models, where the first part is a binary outcome
> model and the second one is a negative binomial model, assuming that zeros
> arise from a single process and set of covariates, as proposed by Dobbie and
> Welsh (Austr.N.Z.J.Stat., 2001)
> 
> Thanks
> 
> Simone Vincenzi
> PhD student in Ecology, University of Parma, Italy
> 
 
  From your descriptions and a quick look at the two papers you cite,
my main conclusion is that I don't really think these are actually
different models -- just different descriptions of the same statistical
model.
  Digging into the code in the package and looking at
?zeroinfl shows that the package is fitting a binomial
model for the probability of a structural zero and
a Poisson or negative binomial for the result otherwise ...
you can specify covariates for both models.

  As a minor point: both references you cite actually focus
on ZI Poisson (not NB) regression models, although Dobbie and
Welsh do allow for overdispersion ...

  hope that helps
   Ben Bolker