I've fit a dataset using the zeroinfl model with a poisson regression. I'm having trouble understanding why it is that when I use the predict function, all of the values are non-zero. I know that I have an excess of 0 counts, and that this model fits my data much better than the regular poisson regression. Can anyone explain to me what this model is actually doing? I have a good background in statistics, and I read the manual, but I still don't understand exactly how this regression model is working. As a note, I'm using this model with all default optional parameters.
Here is the explanation I found in the manual:
"Zero-inflated count models are two-component mixture models combining a point mass at zero with a proper count distribution. Thus, there are two sources of zeros: zeros may come from both the point mass and from the count component. Usually the count model is a Poisson or negative binomial regression (with log link). The geometric distribution is a special case of the negative binomial with size parameter equal to 1. For modeling the unobserved state (zero vs. count), a binary model is used that captures the probability of zero inflation. in the simplest case only with an intercept but potentially containing regressors. For this zero-inflation model, a binomial model with different links can be used, typically logit or probit. The formula can be used to specify both components of the model: If a formula of type y ~ x1 + x2 is supplied, then the same regressors are employed in both components. This is equivalent to y ~ x1 + x2 | x1 + x2. Of course, a different set of regressors could be specified for the count and zero-inflation component, e.g., y ~ x1 + x2 | z1 + z2 + z3 giving the count data model y ~ x1 + x2 conditional on (|) the zero-inflation model y ~ z1 + z2 + z3. A simple inflation model where all zero counts have the same probability of belonging to the zero component can by specified by the formula y ~ x1 + x2 | 1."
So, are there really two models, or is this just two models combined into one?
