Models for count data with many zeros

Poisson regression models provide a standard framework for the analysis of count data. In practice, however, count data are often overdispersed relative to the Poisson distribution. One frequent manifestation of overdispersion is that the incidence of zero counts is greater than expected for the Poisson distribution and this is of interest because zero counts frequently have special status. For example, in counting disease lesions on plants, a plant may have no lesions either because it is resistant to the disease, or simply because no disease spores have landed on it. This is the distinction between structural zeros, which are inevitable, and sampling zeros, which occur by chance. In recent years there has been considerable interest in models for count data that allow for excess zeros, particularly in the econometric literature. These models complement more conventional models for overdispersion that concentrate on modelling the variance-mean relationship correctly. Application areas are diverse and have included manufacturing defects (Lambert, 1992), patent applications (Crepon & Duguet, 1997), road safety (Miaou, 1994), species abundance (Welsh et al., 1996; Faddy, 1998), medical consultations