Estimating Dispersion Parameter of Negative Binomial Distribution for Analysis of Crash Data: Bootstrapped Maximum Likelihood Method

The objective of this study is to improve the estimation of the dispersion parameter of the negative binomial distribution for modeling motor vehicle collisions. The negative binomial distribution is widely used to model count data such as traffic crash data, which often exhibit low sample mean values and small sample sizes. Under such situations, the most commonly used methods for estimating the dispersion parameter—the method of moment and the maximum likelihood estimate—may become inaccurate and unstable. A bootstrapped maximum likelihood method is proposed to improve the estimation of the dispersion parameter. The proposed method combines the technique of bootstrap resampling with the maximum likelihood estimation method to obtain better estimates of the dispersion parameter. The performance of the bootstrapped maximum likelihood estimate is compared with the method of moment and the maximum likelihood estimates through Monte Carlo simulations. To validate the simulation results, the methods are applied to observed data collected at four-leg unsignalized intersections in Toronto, Ontario, Canada. Overall, the results show that the proposed bootstrap maximum likelihood method produces smaller biases and more stable estimates. The improvements are more pronounced with small samples and low sample means.

• Record URL:
  https://doi.org/10.3141/2019-03
• 
• Summary URL:
  http://scholar.google.com/scholar_lookup?title=Estimating+Dispersion+Parameter+of+Negative+Binomial+Distribution+for+Analysis+of+Crash+Data%3a+Bootstrapped+Maximum+Likelihood+Method&author=Y.+Zhang&author=Z.+Ye&author=D.+Lord&publication_year=2007
• Availability:
  • Find a library where document is available. Order URL: http://worldcat.org/isbn/9780309104463
• Authors:
  • Zhang, Yunlong
  • Ye, Zhirui
  • Lord, Dominique
• Publication Date: 2007

Language

• English

Media Info

• Media Type: Print
• Features: Figures; References; Tables;
• Pagination: pp 15-21
• Monograph Title: Statistical Methods, Safety Data, Analysis, and Evaluation 2007
• Serial:
  • Transportation Research Record: Journal of the Transportation Research Board
  • Issue Number: 2019
  • Publisher: Transportation Research Board
  • ISSN: 0361-1981

Subject/Index Terms

• TRT Terms: Binomial distributions; Crash data; Crashes; Dispersion (Statistics); Highway safety; Maximum likelihood method; Monte Carlo method; Poisson distributions; Simulation; Statistical analysis
• Uncontrolled Terms: Bootstrap maximum likelihood method
• Subject Areas: Data and Information Technology; Highways; Safety and Human Factors; I81: Accident Statistics;

Filing Info

• Accession Number: 01045014
• Record Type: Publication
• ISBN: 9780309104463
• Files: TRIS, TRB, ATRI
• Created Date: Feb 8 2007 7:12PM