Finite mixture Negative Binomial-Lindley for modeling heterogeneous crash data with many zero observations

Area of Science:

• Traffic Safety Research
• Statistical Modeling
• Transportation Engineering

Background:

• Crash data often exhibit high dispersion, numerous zero counts, and long tails, challenging traditional Negative Binomial (NB) models.
• Existing Negative Binomial-Lindley (NB-L) models offer improvements but may not fully capture heterogeneity in crash data from multiple subpopulations.
• Finite mixture models are effective for analyzing data from heterogeneous populations.

Purpose of the Study:

• To derive and characterize the Finite Mixture Negative Binomial-Lindley (FMNB-L) model for analyzing crash data with dispersion, zero-inflation, and long tails.
• To assess the FMNB-L model's ability to identify underlying subpopulations within crash data.
• To apply the FMNB-L model to Texas four-lane freeway crash data and compare its performance against existing models.

Main Methods:

• Derivation and theoretical analysis of the Finite Mixture Negative Binomial-Lindley (FMNB-L) model.
• Simulation studies to demonstrate the model's capability in identifying subpopulations.
• Application of the FMNB-L model to Texas freeway crash data, comparing goodness-of-fit with NB, NB-L, and finite mixture NB models.

Main Results:

• The FMNB-L model successfully identified two distinct subpopulations within the analyzed crash data.
• The FMNB-L model demonstrated a significantly superior fit compared to the Negative Binomial (NB), Negative Binomial-Lindley (NB-L), and finite mixture NB models.
• The model's performance was validated through simulation studies and application to real-world Texas freeway crash data.

Conclusions:

• The Finite Mixture Negative Binomial-Lindley (FMNB-L) model is a robust tool for analyzing complex crash data characterized by high dispersion, zero-inflation, and long tails.
• The FMNB-L model effectively accounts for population heterogeneity by identifying distinct subpopulations, leading to improved model fit.
• This advanced statistical approach offers enhanced insights for traffic safety analysis and intervention strategies.