Poisson Beta Regression for Count Data With an Application to Hospital Length of Stay Data

There has been growing awareness recently that conventional models for count data, such as the Negative Binomial model and zero inflated models, often yield poor fit and sub-optimal performance when applied to real-world count data problems. In response, a new, more flexible model for count data, the Poisson-Beta model, has started to attract attention. The Poisson-Beta model is a Poisson mixture where the underlying mixing distribution is a scaled Beta density. However, because its density function cannot be expressed in closed form, its use has been limited to very simple applications such as parameter estimation. This work presents a method of overcoming the computational complexity issues associated with the Poisson-Beta density to allow its application to problems of far greater complexity, enabling it to be used to model response variables in multivariate regression. This work additionally demonstrates that Poisson-Beta regression compares favorably to a range of commonly used regression models for count response data, achieving narrower confidence intervals and superior power.