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

Jayakumari, Darshana; Einbeck, Jochen; Hinde, John; Moral, Rafael A.

Abstract

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.

Citation

Jayakumari, D., Einbeck, J., Hinde, J., & Moral, R. A. (2024). A Distance-Based Statistic for Goodness-of-Fit Assessment. In J. Einbeck, H. Maeng, E. Ogundimu, & K. Perrakis (Eds.), Developments in Statistical Modelling (263-268). Springer. https://doi.org/10.1007/978-3-031-65723-8_40

• Online Publication Date: Jul 12, 2024
• Publication Date: Jul 12, 2024
• Deposit Date: Aug 28, 2024
• Publicly Available Date: Jul 13, 2025
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Pages: 263-268
• Series Title: Contributions to Statistics
• Book Title: Developments in Statistical Modelling
• ISBN: 9783031657221
• DOI: https://doi.org/10.1007/978-3-031-65723-8_40
• Keywords: Count data, Half-normal plot, Model selection
• Public URL: https://durham-repository.worktribe.com/output/2772172
• Additional Information: Conference Name: International Workshop on Statistical Modelling; Conference City: Durham; Conference Country: United Kingdom; Conference Year: 2024; Conference Start Date: 14 July 2024; Conference End Date: 19 July 2024; Conference URL: https://maths.dur.ac.uk/iwsm2024/