Bootstrapping generalized linear models to accommodate overdispersed count data

When modelling counts or rates using Poisson regression, it is common to find overdispersion in data. Overdispersed count data is prevalent in a variety of applied research areas such as ecology and finance when the variance of the response is higher than the Poisson distribution allows. While there are models that are capable of handling data of this nature, conducting inference when presented with overdispersed data poses some challenges. Classical parametric approaches to inference may fail to be reliable when computing bounds for confidence regions as the mean-variance assumption of the Poisson distribution may not be satisfied. Bootstrap approaches are a viable alternative and we explore the performance of the one-step residual and wild bootstrap as a means to perform inference for regression parameters. Furthermore, we adopt an analytic approach to bootstrapping that is able to accommodate overdispersion, while being preferable from an efficiency perspective.

In Statistical Papers