Zero Inflated Poisson Regression

Zero Inflated Poisson (ZIP) regression is a new model for count data with excess zeros. A highly reliable manufacturing process, for example, may be in a perfect state (zero defects) a fraction of the time and in an imperfect state that gives both zero and positive counts the rest of the time. In medical applications, there may be a class of people immune to a disease and a class susceptible to the disease. Both the mean in the imperfect state and the probability of being in the perfect (or immune) state are allowed to depend on covariates. In many applications, as the probability of perfection decreases the mean in the imperfect state increases. The computations are not straightforward when the parameters are related, however. But if the two sets of parameters are allowed to vary independently and the probability of zero and the imperfect mean are parametrized appropriately, maximum likelihood estimates are easy to compute. Statistical theory then shows how to transform maximum likelihood estimates for the more general, independent parameter case into maximum likelihood estimates for the more parsimonious, dependent parameter case. ZIP regression will be applied to some quality control data.