A semi-nonparametric Poisson regression model for analyzing motor vehicle crash data

Area of Science:

• Transportation Safety
• Statistical Modeling
• Econometrics

Background:

• Motor vehicle crash frequency on rural highways is a significant transportation safety concern.
• Higher driving speeds on rural roads contribute to crash severity.
• Traditional models like Negative Binomial (NB) may not fully capture the complexity of crash data.

Purpose of the Study:

• To develop and evaluate a semi-nonparametric Poisson regression model for analyzing motor vehicle crash frequency.
• To assess the model's ability to accommodate flexible distributions of unobserved heterogeneity.
• To compare the performance of the proposed model against traditional methods like the NB model.

Main Methods:

• Development of a semi-nonparametric Poisson regression model.
• Utilizing a flexible semi-nonparametric (SNP) distribution for unobserved heterogeneity.
• Conducting simulation experiments to test the SNP distribution's mimicry capabilities.
• Empirical estimation and comparison with the Negative Binomial (NB) model.

Main Results:

• The SNP distribution effectively mimics various distributions, including normal, log-gamma, bimodal, and trimodal.
• The semi-nonparametric model demonstrates improved model precision and goodness-of-fit compared to the NB model.
• The SNP model captures potential multimodality in unobserved heterogeneity, offering better insights into crash data structure.
• A significant difference was found in the coefficient for lane width between the SNP and NB models.

Conclusions:

• The semi-nonparametric Poisson regression model offers superior statistical performance for analyzing rural highway crash data.
• The flexibility of the SNP distribution enhances understanding of crash data, particularly unobserved heterogeneity.
• The NB model may overestimate the impact of factors like lane width on crash frequency reduction.