7.5 Zero-Inflated and hurdle models
When counting things, like cars on a road, stars in the sky, moles on your skin, or virtually anything else, one option is to not count a thing, that is, to get zero. The number zero can generally occur for many reasons; we get a zero because we were counting red cars and a red car did not go down the street or because we missed it. If we use a Poisson or NegativeBinomial distribution to model such data, we will notice that the model generates fewer zeros compared to the data. How do we fix that? We may try to address the exact cause of our model predicting fewer zeros than the observed and include that factor in the model. But, as is often the case, it may be enough, and simpler, to assume that we have a mixture of two processes:
One modeled by a discrete distribution with probability
One giving extra zeros with probability 1 −
In some texts, you will find that represents the extra zeros instead of 1 − . This is not a big deal;...
