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Extension of the Application of Conway‐Maxwell‐Poisson Models: Analyzing Traffic Crash Data Exhibiting Underdispersion

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  • Dominique Lord
  • Srinivas Reddy Geedipally
  • Seth D. Guikema

Abstract

The objective of this article is to evaluate the performance of the COM‐Poisson GLM for analyzing crash data exhibiting underdispersion (when conditional on the mean). The COM‐Poisson distribution, originally developed in 1962, has recently been reintroduced by statisticians for analyzing count data subjected to either over‐ or underdispersion. Over the last year, the COM‐Poisson GLM has been evaluated in the context of crash data analysis and it has been shown that the model performs as well as the Poisson‐gamma model for crash data exhibiting overdispersion. To accomplish the objective of this study, several COM‐Poisson models were estimated using crash data collected at 162 railway‐highway crossings in South Korea between 1998 and 2002. This data set has been shown to exhibit underdispersion when models linking crash data to various explanatory variables are estimated. The modeling results were compared to those produced from the Poisson and gamma probability models documented in a previous published study. The results of this research show that the COM‐Poisson GLM can handle crash data when the modeling output shows signs of underdispersion. Finally, they also show that the model proposed in this study provides better statistical performance than the gamma probability and the traditional Poisson models, at least for this data set.

Suggested Citation

  • Dominique Lord & Srinivas Reddy Geedipally & Seth D. Guikema, 2010. "Extension of the Application of Conway‐Maxwell‐Poisson Models: Analyzing Traffic Crash Data Exhibiting Underdispersion," Risk Analysis, John Wiley & Sons, vol. 30(8), pages 1268-1276, August.
    • Handle: RePEc:wly:riskan:v:30:y:2010:i:8:p:1268-1276
    DOI: 10.1111/j.1539-6924.2010.01417.x
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    References listed on IDEAS

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    1. Seth D. Guikema & Jeremy P. Goffelt, 2008. "A Flexible Count Data Regression Model for Risk Analysis," Risk Analysis, John Wiley & Sons, vol. 28(1), pages 213-223, February.
    2. Galit Shmueli & Thomas P. Minka & Joseph B. Kadane & Sharad Borle & Peter Boatwright, 2005. "A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 127-142, January.
    3. Boatwright, Peter & Borle, Sharad & Kadane, Joseph B., 2003. "A Model of the Joint Distribution of Purchase Quantity and Timing," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 564-572, January.
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    Cited by:

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    2. S. Hadi Khazraee & Antonio Jose Sáez‐Castillo & Srinivas Reddy Geedipally & Dominique Lord, 2015. "Application of the Hyper‐Poisson Generalized Linear Model for Analyzing Motor Vehicle Crashes," Risk Analysis, John Wiley & Sons, vol. 35(5), pages 919-930, May.
    3. Darcy Steeg Morris & Kimberly F. Sellers, 2022. "A Flexible Mixed Model for Clustered Count Data," Stats, MDPI, vol. 5(1), pages 1-18, January.
    4. Royce A. Francis & Srinivas Reddy Geedipally & Seth D. Guikema & Soma Sekhar Dhavala & Dominique Lord & Sarah LaRocca, 2012. "Characterizing the Performance of the Conway‐Maxwell Poisson Generalized Linear Model," Risk Analysis, John Wiley & Sons, vol. 32(1), pages 167-183, January.
    5. Jinxian Weng & Qiang Meng & David Z. W. Wang, 2013. "Tree‐Based Logistic Regression Approach for Work Zone Casualty Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 33(3), pages 493-504, March.
    6. Meena Badade & T. V. Ramanathan, 2022. "Probabilistic Frontier Regression Models for Count Type Output Data," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 235-260, September.
    7. Sunecher Yuvraj & Mamode Khan Naushad & Jowaheer Vandna, 2019. "Modelling with Dispersed Bivariate Moving Average Processes," Journal of Time Series Econometrics, De Gruyter, vol. 11(1), pages 1-19, January.
    8. Hwachyi Wang & S. K. Jason Chang & Hans De Backer & Dirk Lauwers & Philippe De Maeyer, 2019. "Integrating Spatial and Temporal Approaches for Explaining Bicycle Crashes in High-Risk Areas in Antwerp (Belgium)," Sustainability, MDPI, vol. 11(13), pages 1-28, July.
    9. Zeng, Qiang & Wen, Huiying & Huang, Helai & Wang, Jie & Lee, Jinwoo, 2020. "Analysis of crash frequency using a Bayesian underreporting count model with spatial correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

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