[R] Zero-inflated regression models: predicting no 0s

[Achim Zeileis]

On Thu, 2 Jun 2011, geojs wrote:

> Thanks for the quick reply, 
>
> I understand that the predict(zip1A, type = "response") command is computing
> the fitted_means and these are different than the probabilities
> predict(zip1A, type = "prob").

Yes. One evaluates the probability density function, and the other one the 
expectation from this density.

> Although, according to Martin (2005), the highest probabilities do not 
> simply lead to the true count estimates: "to get the true estimate of 
> relative mean abundance from the ZIP one must multiply the estimated 
> relative mean number of individuals at a site by the probability that 
> the relative mean number of individuals at a site is generated through a 
> Poisson distribution."

I haven't checked that paper but I suspect that this is a verbal 
description of the fitted mean of a zero-inflated Poisson distribution. 
See Equation 8 in the JSS paper that introduces hurdle/zeroinfl.

> I initially thought that the predicted mean and the observed count could 
> be compared to estimate the fit of the model,

They can be. But then - not surprisingly - you only assess the fit of the 
mean. (E.g., you do not assess the ability to predict the number of zeros, 
and you do not assess potential overdispersion etc.)
Z

> but now I am not sure what to think with Martin (2005) statement.
>
> Thank you for your help, 
>
> JM
>
> Martin, T.G. et al. (2005) Zero tolerance ecology: improving ecological
> inference by modelling the source of zero observations, Ecology Letters,
> Volume 8, Issue 11, pages 1235?1246.
>
>
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