A Distance-Based Statistic for Goodness-of-Fit Assessment

The modelling of count data in real world scenarios often requires models that address over-dispersion. Within the generalized linear modeling framework, various over-dispersion models are available as extensions of the basic Poisson model. Graphical assessment of goodness-of-fit commonly involves half-normal plots, for which a simulated envelope can be added to aid interpretation. The simulated envelope is such that, under a well-fitted model, the majority of points should fall within its bounds. Nonetheless, closely related models tend to produce very similar graphs. Here, we propose an objective statistic based on half-normal plots with a simulated envelope to aid goodness-of-fit assessment.