Modelling excess zeros in count data: A new perspective on modelling approaches
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We consider models underlying regression analysis of count data in which the observed frequency of zero counts is unusually large, typically with respect to the Poisson distribution. We focus on two alternative modelling approaches: Over-Dispersion (OD) models, and Zero-Inflation (ZI) models, both of which can be seen as generalisations of the Poisson distribution; we refer to these as Implicit and Explicit ZI models, respectively. Although sometimes seen as competing approaches, they can be complementary; OD is a consequence of ZI modelling, and ZI is a by-product of OD modelling. The central objective in such analyses is often concerned with inference on the effect of covariates on the mean, in light of the excess of zeros in the counts. The contribution of our paper is to focus on models for different types of ZI, some of which can only be generated by explicit ZI modelling; and on their characterisation by considering the induced probability of a zero as a function of the zero probability of a base distribution (usually Poisson). We develop the underlying theory for univariate counts. The perspective highlights some of the difficulties encountered in distinguishing the alternative modelling options.
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