Modeling highly dispersed crash data with sichel GAMLSS: An alternative approach to traditional methods

This research examines the application of Sichel (SI) generalized additive models for location, scale, and shape (GAMLSS) in addressing the challenge of modeling highly dispersed crash data. The Sichel distribution, which combines the Poisson distribution with the generalized inverse Gaussian distribution, is particularly suited for modeling data with significant dispersion, where traditional models often prove inadequate. The primary objective of this study was to assess the performance of the Sichel GAMLSS in comparison with the widely-used Negative Binomial (NB) generalized linear model (GLM). To achieve this, the study developed and evaluated NB, zero-inflated NB (ZINB), Poisson inverse Gaussian (PIG) and SI models using two crash datasets characterized by high dispersion. The first dataset comprises crash data from 338 rural interstate road sections in Indiana, while the second dataset includes crash data from undivided 4-lane rural road segments in Texas. The models were compared using a range of goodness-of-fit criteria. Results demonstrate that the Sichel GAMLSS offers a better fit than the NB, ZINB and PIG GLMs for the datasets analyzed. Moreover, the Sichel model provides advantageous statistical properties, such as a long-term mean that is never zero and a variance function driven by a two-parameter dispersion mechanism. Therefore, the SI GAMLSS presents itself as a promising alternative to the traditional NB GLMs for the analysis of highly dispersed crash datasets.