Characteristics-based heuristics to select a logical distribution between the Poisson-gamma and the Poisson-lognormal for crash data modelling

References

• Aguero-Valverde, J. 2013. “Full Bayes Poisson Gamma, Poisson Lognormal, and Zero Inflated Random Effects Models: Comparing the Precision of Crash Frequency Estimates.” Accident Analysis & Prevention 50: 289–297. doi: 10.1016/j.aap.2012.04.019
   PubMed Web of Science ®Google Scholar
• Aguero-Valverde, J., and P. P. Jovanis. 2008. “Analysis of Road Crash Frequency with Spatial Models.” Transportation Research Record: Journal of the Transportation Research Board 2061: 55–63. doi: 10.3141/2061-07
   Web of Science ®Google Scholar
• Breiman, L. 2001. “Random Forests.” Machine Learning 45 (1): 5–32. doi: 10.1023/A:1010933404324
   Web of Science ®Google Scholar
• Breiman, L., J. H. Friedman, R. A. Olshen, and C. J. Stone. 1984. Classification and Regression Trees. Monterey, CA: Wadsworth & Brooks/Cole Advanced Books & Software. ISBN 978-0-412-04841-8.
   Google Scholar
• Geedipally, S. R., D. Lord, and S. S. Dhavala. 2012. “The Negative Binomial-Lindley Generalized Linear Model: Characteristics and Application Using Crash Data.” Accident Analysis & Prevention 45: 258–265. doi: 10.1016/j.aap.2011.07.012
   PubMed Web of Science ®Google Scholar
• Geedipally, S. R., M. Shirazi, and D. Lord. 2017. “Exploring the Need for Region-specific Calibration Factors.” Transportation Research Record: Journal of the Transportation Research Board 2636, 73–79. doi: 10.3141/2636-09
   Google Scholar
• Gonzales-Barron, U., and F. Butler. 2011. “A Comparison between the Discrete Poisson-gamma and Poisson-lognormal Distributions to Characterise Microbial Counts in Foods.” Food Control 22 (8): 1279–1286. doi: 10.1016/j.foodcont.2011.01.029
   Web of Science ®Google Scholar
• Hastie, T., R. Tibshirani, and J. Friedman. 2001. The Elements of Statistical Learning. New York: Springer.
   Google Scholar
• James, G., D. Witten, T. Hastie, and R. Tibshirani. 2013. An Introduction to Statistical Learning (Vol. 6). New York: Springer.
   Google Scholar
• Khazraee, S. H., V. Johnson, and D. Lord. 2018. “Bayesian Poisson Hierarchical Models for Crash Data Analysis: Investigating the Impact of Model Choice on Site-specific Predictions.” Accident Analysis & Prevention 117: 181–195. doi: 10.1016/j.aap.2018.04.016
   PubMed Web of Science ®Google Scholar
• Lord, D. 2006. “Modeling Motor Vehicle Crashes Using Poisson-gamma Models: Examining the Effects of low Sample Mean Values and Small Sample Size on the Estimation of the Fixed Dispersion Parameter.” Accident Analysis & Prevention 38 (4): 751–766. doi: 10.1016/j.aap.2006.02.001
   PubMed Web of Science ®Google Scholar
• Lord, D., and S. R. Geedipally. 2011. “The Negative Binomial–Lindley Distribution as a Tool for Analyzing Crash Data Characterized by a Large Amount of Zeros.” Accident Analysis & Prevention 43 (5): 1738–1742. doi: 10.1016/j.aap.2011.04.004
   PubMed Web of Science ®Google Scholar
• Lord, D., S. R. Geedipally, and M. Shirazi. 2016. Improved Guidelines for Estimating the Highway Safety Manual Calibration Factors. ATLAS-2015-10.
   Google Scholar
• Lord, D., and F. Mannering. 2010. “The Statistical Analysis of Crash-frequency Data: A Review and Assessment of Methodological Alternatives.” Transportation Research Part A: Policy and Practice 44 (5): 291–305.
   Web of Science ®Google Scholar
• Lord, D., and L. F. Miranda-Moreno. 2008. “Effects of Low Sample Mean Values and Small Sample Size on the Estimation of the Fixed Dispersion Parameter of Poisson-gamma Models for Modeling Motor Vehicle Crashes: A Bayesian Perspective.” Safety Science 46 (5): 751–770. doi: 10.1016/j.ssci.2007.03.005
   Web of Science ®Google Scholar
• Mannering, F. L., and C. R. Bhat. 2014. “Analytic Methods in Accident Research: Methodological Frontier and Future Directions.” Analytic Methods in Accident Research 1: 1–22. doi: 10.1016/j.amar.2013.09.001
   Google Scholar
• Miaou, S. P., and D. Lord. 2003. “Modeling Traffic Crash-flow Relationships for Intersections: Dispersion Parameter, Functional form, and Bayes Versus Empirical Bayes Methods.” Transportation Research Record: Journal of the Transportation Research Board 1840 (1): 31–40. doi: 10.3141/1840-04
   Google Scholar
• Qin, X., J. N. Ivan, and N. Ravishanker. 2004. “Selecting Exposure Measures in Crash Rate Prediction for Two-lane Highway Segments.” Accident Analysis and Prevention 36 (2): 183–191. doi: 10.1016/S0001-4575(02)00148-3
   PubMed Web of Science ®Google Scholar
• Shaon, M. R. R., X. Qin, M. Shirazi, D. Lord, and S. R. Geedipally. 2018. “Developing a Random Parameters Negative Binomial-Lindley Model to Analyze Highly Over-dispersed Crash Count Data.” Analytic Methods in Accident Research 18: 33–44. doi: 10.1016/j.amar.2018.04.002
   Web of Science ®Google Scholar
• Shirazi, M., S. S. Dhavala, D. Lord, and S. R. Geedipally. 2017. “A Methodology to Design Heuristics for Model Selection Based on the Characteristics of Data: Application to Investigate When the Negative Binomial Lindley (NB-L) is Preferred Over the Negative Binomial (NB).” Accident Analysis & Prevention 107: 186–194. doi: 10.1016/j.aap.2017.07.002
   PubMed Web of Science ®Google Scholar
• Shirazi, M., S. R. Geedipally, and D. Lord. 2017. “A Monte-Carlo Simulation Analysis for Evaluating the Severity Distribution Functions (SDFs) Calibration Methodology and Determining the Minimum Sample-size Requirements.” Accident Analysis & Prevention 98 (2017): 303–311. doi: 10.1016/j.aap.2016.10.004
   PubMedGoogle Scholar
• Shirazi, M., S. R. Geedipally, and D. Lord. 2017c. “A Procedure to Determine When Safety Performance Functions Should be Recalibrated.” Journal of Transportation Safety & Security 9 (4): 457–469. doi: 10.1080/19439962.2016.1240734
   Web of Science ®Google Scholar
• Shirazi, M., D. Lord, S. S. Dhavala, and S. R. Geedipally. 2016. “A Semiparametric Negative Binomial Generalized Linear Model for Modeling Over Dispersed Count Data with a Heavy Tail: Characteristics and Applications to Crash Data.” Accident Analysis & Prevention 91: 10–18. doi: 10.1016/j.aap.2016.02.020
   PubMed Web of Science ®Google Scholar
• Shirazi, M., D. Lord, and S. R. Geedipally. 2016. “Sample-size Guidelines for Recalibrating Crash Prediction Models: Recommendations for the Highway Safety Manual.” Accident Analysis & Prevention 93: 160–168. doi: 10.1016/j.aap.2016.04.011
   PubMed Web of Science ®Google Scholar