I am trying to decide if zero inflated poisson is appropriate for my data vs. a Poisson hurdle model.
In background reading between the two I've run across a statement saying that a zero inflated model attempts to distinguish between true zeros and excess zeros. I'm having a problem understanding what is the different between those two zeros.
Can anyone explain what those two types of zeros mean in the context of zero inflated modeling?
I only know what I've read, but I believe the difference is that excess zeros are zeros where there could not be any events, while true zeros occur where there could have been an event, but there was none. For example, people coming into a bank: during business hours, there might be a period of time when zero customers entered the bank (true zero), but when the bank is closed, you will always get zeros (excess zeros) and since the bank is closed more than it is open you will get a lot of excess zeros.
The book by Zuur et al Mixed Effects Models and Extension in Ecology with R provides extensive explanations of ZIP models of various sorts. They state that "zeros due to design, survey, or observer error are...called false zeros or false negatives [or, I believe, the excess zeros you are talking about]. In a perfect world, we should not have them. The structural zeros are called positive zeros, true zeros, or true negatives." (page 271). They continue to discuss how a hurdle model handles these different kinds of zeros differently than a zero-inflated model.
I think of this as a mixture of two distributions. The excess zeros as those zeroes in excess of what could be produced by a particular process (e.g. poisson or negative binomial). So, there is a zero present in the data by a certain probablity and if not zero, then it's value is governed by the processs (e.g. poisson or negative binomial), where it could also be zero again of course by that process. Am curious if I am off base and I am sure someone will point this out.
