A flexible GEV link for zero inflated conway Maxwell Poisson regression with a case study on motor vehicle crashes

This paper introduces a new flexible link for zero inflated Conway Maxwell Poisson (COMPoisson) distribution. Zero inflated Poisson regression has been widely used for modeling rare events with excess zeros. In recent years, the zero inflated Conway Maxwell Poisson regression has been proposed. The advantage of COM-Poisson is its ability to handle both under- and over-dispersion through controlling one special parameter in the distribution, which makes it more flexible than current frequently used models, i.e., Poisson and Negative Binomial. The usual link function for zero inflated models is the logit link, which assumes the response curve between covariates and the probability of zeros is symmetric. This assumption is not always true. To add more flexibility, we propose a new flexible link function for the zero inflated Conway Maxwell Poisson regression, the generalized extreme value (GEV) model, which can capture different skewness with a shape parameter. Thus we can let data tell the skewness of the link function. Simulation studies and an application on traffic accident data are conducted to show the flexibility of our proposed model against the commonly used models.