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The negative binomial-Lindley generalized linear model: characteristics and application using crash data.

Srinivas Reddy Geedipally1, Dominique Lord, Soma Sekhar Dhavala

  • 1Texas Transportation Institute, Texas A&M University, 3135 TAMU, College Station, TX 77843-3135, United States. srinivas-g@ttimail.tamu.edu

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Summary
This summary is machine-generated.

A new Negative Binomial-Lindley generalized linear model (NB-L GLM) effectively analyzes traffic crash data with excess zeros and high dispersion. This model outperforms traditional Negative Binomial and zero-inflated models for complex crash datasets.

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Area of Science:

  • Transportation Safety
  • Statistical Modeling
  • Traffic Engineering

Background:

  • Crash data often exhibits excess zeros and high dispersion, challenging traditional statistical models like Poisson and Negative Binomial (NB).
  • Existing models struggle with datasets where many sites have no observed crashes and a long tail of high crash counts.
  • The Negative Binomial-Lindley (NB-L) distribution offers a potential solution for count data with excess zeros.

Purpose of the Study:

  • To apply and evaluate a NB generalized linear model with Lindley mixed effects (NB-L GLM) for traffic crash data analysis.
  • To assess the model's performance on simulated and observed datasets, particularly those with excess zeros and high dispersion.
  • To compare the NB-L GLM against established NB and zero-inflated models.

Main Methods:

  • Development and application of a NB generalized linear model with Lindley mixed effects (NB-L GLM).
  • Utilized simulated data to demonstrate the model's general performance characteristics.
  • Applied the NB-L GLM to two real-world traffic crash datasets, one with a significant number of zeros.

Main Results:

  • The NB-L GLM demonstrated superior performance compared to NB and zero-inflated models.
  • The model's effectiveness was evident in datasets characterized by a large number of zeros and a long tail.
  • The NB-L GLM also showed advantages when analyzing highly dispersed crash data.

Conclusions:

  • The NB-L GLM is a robust and superior alternative for analyzing traffic crash data, especially when dealing with excess zeros and high dispersion.
  • This advanced statistical approach improves the accuracy and reliability of traffic safety analyses.
  • The findings suggest wider adoption of the NB-L GLM for transportation safety research involving complex count data.