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Empirical Bayes estimates of finite mixture of negative binomial regression models and its application to highway safety

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  • Yajie Zou
  • John E. Ash
  • Byung-Jung Park
  • Dominique Lord
  • Lingtao Wu

Abstract

The empirical Bayes (EB) method is commonly used by transportation safety analysts for conducting different types of safety analyses, such as before–after studies and hotspot analyses. To date, most implementations of the EB method have been applied using a negative binomial (NB) model, as it can easily accommodate the overdispersion commonly observed in crash data. Recent studies have shown that a generalized finite mixture of NB models with K mixture components (GFMNB-K) can also be used to model crash data subjected to overdispersion and generally offers better statistical performance than the traditional NB model. So far, nobody has developed how the EB method could be used with finite mixtures of NB models. The main objective of this study is therefore to use a GFMNB-K model in the calculation of EB estimates. Specifically, GFMNB-K models with varying weight parameters are developed to analyze crash data from Indiana and Texas. The main finding shows that the rankings produced by the NB and GFMNB-2 models for hotspot identification are often quite different, and this was especially noticeable with the Texas dataset. Finally, a simulation study designed to examine which model formulation can better identify the hotspot is recommended as our future research.

Suggested Citation

  • Yajie Zou & John E. Ash & Byung-Jung Park & Dominique Lord & Lingtao Wu, 2018. "Empirical Bayes estimates of finite mixture of negative binomial regression models and its application to highway safety," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(9), pages 1652-1669, July.
    • Handle: RePEc:taf:japsta:v:45:y:2018:i:9:p:1652-1669
    DOI: 10.1080/02664763.2017.1389863
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    Cited by:

    1. Chen Xu & Decun Dong & Dongxiu Ou & Changxi Ma, 2019. "Time-of-Day Control Double-Order Optimization of Traffic Safety and Data-Driven Intersections," IJERPH, MDPI, vol. 16(5), pages 1-18, March.
    2. Ruone Zhang & Xin Ye & Ke Wang & Dongjin Li & Jiayu Zhu, 2019. "Development of Commute Mode Choice Model by Integrating Actively and Passively Collected Travel Data," Sustainability, MDPI, vol. 11(10), pages 1-15, May.
    3. Luo, Qiang & Yuan, Jie & Chen, Xinqiang & Wu, Shubo & Qu, Zhijian & Tang, Jinjun, 2019. "Analyzing start-up time headway distribution characteristics at signalized intersections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    4. Jingjing Xu & Behram Wali & Xiaobing Li & Jiaqi Yang, 2019. "Injury Severity and Contributing Driver Actions in Passenger Vehicle–Truck Collisions," IJERPH, MDPI, vol. 16(19), pages 1-16, September.
    5. Lukuman Wahab & Haobin Jiang, 2019. "A comparative study on machine learning based algorithms for prediction of motorcycle crash severity," PLOS ONE, Public Library of Science, vol. 14(4), pages 1-17, April.
    6. Medury, Aditya PhD & Vlachogiannis, Dimitris & Grembek, Offer PhD, 2020. "Assessing the Variation of Curbside Safety at the City Block Level," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt46n9669d, Institute of Transportation Studies, UC Berkeley.
    7. Qian Duan & Xin Ye & Jian Li & Ke Wang, 2020. "Empirical Modeling Analysis of Potential Commute Demand for Carsharing in Shanghai, China," Sustainability, MDPI, vol. 12(2), pages 1-18, January.
    8. Xiaoyong Tang & Xiaoyi Liao, 2018. "Application-aware deadline constraint job scheduling mechanism on large-scale computational grid," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-19, November.
    9. Changxi Ma & Dong Yang & Jibiao Zhou & Zhongxiang Feng & Quan Yuan, 2019. "Risk Riding Behaviors of Urban E-Bikes: A Literature Review," IJERPH, MDPI, vol. 16(13), pages 1-18, June.
    10. Muhammad Wisal Khattak & Hans De Backer & Pieter De Winne & Tom Brijs & Ali Pirdavani, 2024. "Comparative Evaluation of Crash Hotspot Identification Methods: Empirical Bayes vs. Potential for Safety Improvement Using Variants of Negative Binomial Models," Sustainability, MDPI, vol. 16(4), pages 1-22, February.
    11. Yichuan Peng & Yuming Jiang & Jian Lu & Yajie Zou, 2018. "Examining the effect of adverse weather on road transportation using weather and traffic sensors," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-14, October.
    12. Yajie Zou & Xinzhi Zhong & Jinjun Tang & Xin Ye & Lingtao Wu & Muhammad Ijaz & Yinhai Wang, 2019. "A Copula-Based Approach for Accommodating the Underreporting Effect in Wildlife‒Vehicle Crash Analysis," Sustainability, MDPI, vol. 11(2), pages 1-13, January.
    13. Xin Guan & Xin Ye & Cheng Shi & Yajie Zou, 2019. "A Multivariate Modeling Analysis of Commuters’ Non-Work Activity Allocations in Xiaoshan District of Hangzhou, China," Sustainability, MDPI, vol. 11(20), pages 1-19, October.

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