Functional forms of the negative binomial models in safety performance functions for rural two-lane intersections

Area of Science:

• Traffic Safety Engineering
• Statistical Modeling

Background:

• Safety Performance Functions (SPFs) are vital for estimating intersection crashes and identifying sites for safety improvements.
• Existing Negative Binomial (NB) models have limitations in accurately predicting crash frequencies at rural two-lane intersections.

Purpose of the Study:

• To evaluate different functional forms of Negative Binomial (NB) models (NB-1, NB-2, NB-P) for estimating SPFs by crash type.
• To assess the impact of parameterizing the over-dispersion parameter using traffic volume data.
• To compare model goodness-of-fit and prediction accuracy for rural two-lane intersection types (3ST, 4ST, 4SG).

Main Methods:

• Applied NB-1, NB-2, and NB-P models to estimate SPFs for various crash types at three rural intersection types.
• Utilized major and minor road Annual Average Daily Traffic (AADT) as predictors for SPF estimation and over-dispersion parameter.
• Compared models based on goodness-of-fit statistics and crash prediction performance.

Main Results:

• The NB-P model demonstrated superior goodness-of-fit compared to NB-1 and NB-2 for most crash and intersection types due to its flexible variance structure.
• The over-dispersion parameter is dependent on the defined variance structure and varies across intersections; it can be effectively estimated using major and minor road AADT.
• The NB-P model with parameterized over-dispersion better captures data heterogeneity and slightly improves crash prediction accuracy, particularly for 3ST and 4SG intersections.

Conclusions:

• The NB-P model with a parameterized over-dispersion factor is recommended for developing intersection SPFs.
• This approach provides more unbiased parameter estimates and enhances crash prediction accuracy for rural two-lane intersections.
• Accurate SPFs are essential for effective traffic safety management and targeted infrastructure improvements.