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

References

• J. Aguero-Valverde and P.P. Jovanis, Analysis of road crash frequency with spatial models, Transport. Res. Rec.: J. Transport. Res. Board 2061 (2008), pp. 55–63. doi: 10.3141/2061-07
   Web of Science ®Google Scholar
• C. Chen, G. Zhang, Z. Qian, R.A. Tarefder, and Z. Tian, Investigating driver injury severity patterns in rollover crashes using support vector machine models, Accid. Anal. Prev. 90 (2016), pp. 128–139. doi: 10.1016/j.aap.2016.02.011
   PubMed Web of Science ®Google Scholar
• L. Cheng, S.R. Geedipally, and D. Lord, The Poisson–Weibull generalized linear model for analyzing motor vehicle crash data, Saf. Sci. 54 (2013), pp. 38–42. doi: 10.1016/j.ssci.2012.11.002
   Web of Science ®Google Scholar
• W. Cheng and S. Washington, New criteria for evaluating methods of identifying hot spots, Transport. Res. Rec.: J. Transport. Res. Board 2083 (2008), pp. 76–85. doi: 10.3141/2083-09
   Web of Science ®Google Scholar
• W. Cheng and S.P. Washington, Experimental evaluation of hotspot identification methods, Accid. Anal. Prev. 37 (2005), pp. 870–881. doi: 10.1016/j.aap.2005.04.015
   PubMed Web of Science ®Google Scholar
• R.D. Connors, M. Maher, A. Wood, L. Mountain, and K. Ropkins, Methodology for fitting and updating predictive accident models with trend, Accid. Anal. Prev. 56 (2013), pp. 82–94. doi: 10.1016/j.aap.2013.03.009
   PubMed Web of Science ®Google Scholar
• C. Ding, X. Ma, Y. Wang, and Y. Wang, Exploring the influential factors in incident clearance time: Disentangling causation from self-selection bias, Accid. Anal. Prev. 85 (2015), pp. 58–65. doi: 10.1016/j.aap.2015.08.024
   PubMed Web of Science ®Google Scholar
• N. Eluru, M. Bagheri, L.F. Miranda-Moreno, and L. Fu, A latent class modeling approach for identifying vehicle driver injury severity factors at highway-railway crossings, Accid. Anal. Prev. 47 (2012), pp. 119–127. doi: 10.1016/j.aap.2012.01.027
   PubMed Web of Science ®Google Scholar
• S. Frühwirth-Schnatter, Finite Mixture and Markov Switching Models, Springer Science & Business Media, New York, 2006.
   Google Scholar
• S.R. Geedipally, D. Lord, and S.S. Dhavala, The negative binomial-Lindley generalized linear model: Characteristics and application using crash data, Accid. Anal. Prev. 45 (2012), pp. 258–265. doi: 10.1016/j.aap.2011.07.012
   PubMed Web of Science ®Google Scholar
• M. Gharib, Two characterisations of a gamma mixture distribution, Bull. Aust. Math. Soc. 52 (1995), pp. 353–358. doi: 10.1017/S0004972700014842
   Web of Science ®Google Scholar
• E. Hauer, Empirical Bayes approach to the estimation of “unsafety”: The multivariate regression method, Accid. Anal. Prev. 24 (1992), pp. 457–477. doi: 10.1016/0001-4575(92)90056-O
   PubMed Web of Science ®Google Scholar
• E. Hauer, Observational Before/After Studies in Road Safety, Pergamon Press, Elsevier Science Ltd., Oxford, 1997.
   Google Scholar
• E. Hauer, D. Harwood, F. Council, and M. Griffith, Estimating safety by the empirical Bayes method: A tutorial, Transport. Res. Rec.: J. Transport. Res. Board 1784 (2002), pp. 126–131. doi: 10.3141/1784-16
   Google Scholar
• E. Hauer, J.C. Ng, and J. Lovell, Estimation of safety at signalized intersections (with discussion and closure), Transport. Res. Rec.: J. Transport. Res. Board 1185 (1988), pp. 48–61.
   Google Scholar
• D.A. Hensher and W.H. Greene, The mixed logit model: The state of practice, Transportation 30 (2003), pp. 133–176. doi: 10.1023/A:1022558715350
   Web of Science ®Google Scholar
• J. Jun, Understanding the variability of speed distributions under mixed traffic conditions caused by holiday traffic, Transport. Res. Part C: Emer. Technol. 18 (2010), pp. 599–610. doi: 10.1016/j.trc.2009.12.005
   Web of Science ®Google Scholar
• D. Lord, S.R. Geedipally, B.N. Persaud, S.P. Washington, I. Van Schalkwyk, J.N. Ivan, C. Lyon, and T. Jonsson, Methodology to predict the safety performance of rural multilane highways, 2008.
   Google Scholar
• D. Lord and P.-F. Kuo, Examining the effects of site selection criteria for evaluating the effectiveness of traffic safety countermeasures, Accid. Anal. Prev. 47 (2012), pp. 52–63. doi: 10.1016/j.aap.2011.12.008
   PubMed Web of Science ®Google Scholar
• D. Lord and F. Mannering, The statistical analysis of crash-frequency data: A review and assessment of methodological alternatives, Transport. Res. Part A: Policy Pract. 44 (2010), pp. 291–305.
   Web of Science ®Google Scholar
• F.L. Mannering and C.R. Bhat, Analytic methods in accident research: Methodological frontier and future directions, Anal. Methods Accid. Res. 1 (2014), pp. 1–22. doi: 10.1016/j.amar.2013.09.001
   Google Scholar
• F.L. Mannering, V. Shankar, and C.R. Bhat, Unobserved heterogeneity and the statistical analysis of highway accident data, Anal. Methods Accid. Res. 11 (2016), pp. 1–16. doi: 10.1016/j.amar.2016.04.001
   Web of Science ®Google Scholar
• G. Maycock and R.D. Hall, Accidents at 4-arm roundabouts. TRRL Laboratory Report 1120, Transportation and Road Research Laboratory, Crowthorne, UK, 1984.
   Google Scholar
• G. Mclachlan and D. Peel, Finite Mixture Models, John Wiley & Sons, New York, 2000.
   Google Scholar
• L. Miranda-Moreno, L. Fu, F. Saccomanno, and A. Labbe, Alternative risk models for ranking locations for safety improvement, Transport. Res. Rec.: J. Transport. Res. Board 1908 (2005), pp. 1–8. doi: 10.3141/1908-01
   Google Scholar
• O. Muralidharan, An empirical Bayes mixture method for effect size and false discovery rate estimation, Ann. Appl. Stat. 4 (2010), pp. 422–438. doi: 10.1214/09-AOAS276
   Web of Science ®Google Scholar
• B.-J. Park and D. Lord, Application of finite mixture models for vehicle crash data analysis, Accid. Anal. Prev. 41 (2009), pp. 683–691. doi: 10.1016/j.aap.2009.03.007
   PubMed Web of Science ®Google Scholar
• B.-J. Park, D. Lord, and C. Lee, Finite mixture modeling for vehicle crash data with application to hotspot identification, Accid. Anal. Prev. 71 (2014), pp. 319–326. doi: 10.1016/j.aap.2014.05.030
   PubMed Web of Science ®Google Scholar
• B.-J. Park, D. Lord, and L. Wu, Finite mixture modeling approach for developing crash modification factors in highway safety analysis, Accid. Anal. Prev. 97 (2016), pp. 274–287. doi: 10.1016/j.aap.2016.10.023
   PubMed Web of Science ®Google Scholar
• E.S. Park, P.J. Carlson, R.J. Porter, and C.K. Andersen, Safety effects of wider edge lines on rural, two-lane highways, Accid. Anal. Prev. 48 (2012), pp. 317–325. doi: 10.1016/j.aap.2012.01.028
   PubMed Web of Science ®Google Scholar
• Y. Peng, D. Lord, and Y. Zou, Applying the generalized waring model for investigating sources of variance in motor vehicle crash analysis, Accid. Anal. Prev. 73 (2014), pp. 20–26. doi: 10.1016/j.aap.2014.07.031
   PubMed Web of Science ®Google Scholar
• B. Persaud, B. Lan, C. Lyon, and R. Bhim, Comparison of empirical Bayes and full Bayes approaches for before–after road safety evaluations, Accid. Anal. Prev. 42 (2010), pp. 38–43. doi: 10.1016/j.aap.2009.06.028
   PubMed Web of Science ®Google Scholar
• R. Rigby and D. Stasinopoulos, A Flexible Regression Approach Using GAMLSS in R, London Metropolitan University, London, 2009.
   Google Scholar
• J. Tang, F. Liu, Y. Zou, W. Zhang, and Y. Wang, An improved fuzzy neural network for traffic speed prediction considering periodic characteristic, IEEE Trans. Int. Transport. Sys. 18 (2017), pp. 2340–2350. doi:doi: 10.1109/TITS.2016.2643005.
   Google Scholar
• P. Vangala, D. Lord, and S.R. Geedipally, Exploring the application of the negative binomial–generalized exponential model for analyzing traffic crash data with excess zeros, Anal. Methods Accid. Res., 7 (2015), pp. 29–36. doi: 10.1016/j.amar.2015.06.001
   Web of Science ®Google Scholar
• S.P. Washington, M.G. Karlaftis, and F.L. Mannering, Statistical and Econometric Methods for Transportation Data Analysis, 2nd ed., Chapman Hall/CRC, Boca Raton, 2011.
   Google Scholar
• L. Wu, D. Lord, and Y. Zou, Validation of crash modification factors derived from cross-sectional studies with regression models, Transport. Res. Rec.: J. Transport. Res. Board 2514 (2015), pp. 88–96. doi: 10.3141/2514-10
   Web of Science ®Google Scholar
• L. Wu, Y. Zou, and D. Lord, Comparison of Sichel and negative binomial models in hot spot identification, Transport. Res. Rec.: J. Transport. Res. Board 2460 (2014), pp. 107–116. doi: 10.3141/2460-12
   Web of Science ®Google Scholar
• Y. Xiong and F.L. Mannering, The heterogeneous effects of guardian supervision on adolescent driver-injury severities: A finite-mixture random-parameters approach, Transport. Res. Part B: Methodol. 49 (2013), pp. 39–54. doi: 10.1016/j.trb.2013.01.002
   Web of Science ®Google Scholar
• S. Yasmin, N. Eluru, C.R. Bhat, and R. Tay, A latent segmentation based generalized ordered logit model to examine factors influencing driver injury severity, Anal. Methods Accid. Res. 1 (2014), pp. 23–38. doi: 10.1016/j.amar.2013.10.002
   Google Scholar
• L. Zha, D. Lord, and Y. Zou, The Poisson inverse Gaussian (PIG) generalized linear regression model for analyzing motor vehicle crash data, J. Transport. Saf. Secur. 8 (2014), pp. 18–35. doi: 10.1080/19439962.2014.977502
   Web of Science ®Google Scholar
• Y. Zou, D. Lord, Y. Zhang, and Y. Peng, Comparison of Sichel and negative binomial models in estimating empirical Bayes estimates, Transport. Res. Rec.: J. Transport. Res. Board 2392 (2013), pp. 11–21. doi: 10.3141/2392-02
   Web of Science ®Google Scholar
• Y. Zou, J. Tang, L. Wu, K. Henrickson, and Y. Wang, Quantile analysis of factors influencing the time taken to clear road traffic incidents, Pro. ICE – Transport. 170 (2017), pp. 296–304.
   Google Scholar
• Y. Zou, H. Yang, Y. Zhang, J. Tang, and W. Zhang, Mixture modeling of freeway speed and headway data using multivariate skew-t distributions, Transportmetrica A: Transport Sci. 13 (2017), pp. 657–678. doi: 10.1080/23249935.2017.1318973
   Web of Science ®Google Scholar
• Y. Zou, Y. Zhang, and D. Lord, Application of finite mixture of negative binomial regression models with varying weight parameters for vehicle crash data analysis, Accid. Anal. Prev. 50 (2013), pp. 1042–1051. doi: 10.1016/j.aap.2012.08.004
   PubMed Web of Science ®Google Scholar
• Y. Zou, Y. Zhang, and D. Lord, Analyzing different functional forms of the varying weight parameter for finite mixture of negative binomial regression models, Anal. Methods Accid. Res. 1 (2014), pp. 39–52. doi: 10.1016/j.amar.2013.11.001
   Google Scholar