Bayesian analysis of multivariate crash counts using copulas

Area of Science:

• Road safety research
• Statistical modeling
• Transportation engineering

Background:

• Jointly modeling correlated multivariate crash counts is crucial for understanding road safety.
• Existing models like multivariate Poisson and negative binomial regression have limitations in capturing complex dependencies.
• Roadway characteristics and environmental factors influence crash counts by severity and type.

Purpose of the Study:

• To introduce more general copula-based multivariate count regression models.
• To incorporate dependence among multivariate crash counts using copulas for correlated random effects.
• To provide a flexible framework for analyzing road safety data with complex correlation structures.

Main Methods:

• Developed copula-based multivariate count regression models within a Bayesian framework.
• Modeled multivariate random effects using copulas to capture dependence.
• Applied the proposed method to crash count data from 451 unsignalized intersections in California.

Main Results:

• The proposed copula-based models flexibly account for overdispersion and general correlation structures (positive and negative).
• These models encompass previously suggested methods like multivariate Poisson-Gamma mixture and Poisson-Lognormal regression.
• Demonstrated the model's utility with real-world crash data across five severity levels.

Conclusions:

• Copula-based multivariate count regression models offer a powerful and flexible approach for road safety analysis.
• These models effectively handle complex dependencies and overdispersion in crash data.
• The methodology provides a unified framework for various multivariate count models in road safety research.