Bayesian Poisson hierarchical models for crash data analysis: Investigating the impact of model choice on site-specific predictions

Accident Analysis and Prevention

Volumn 117, Issue , 2018, Pages 181-195

  Khazraee, S Hadi ^a   Johnson, Valen ^b   Lord, Dominique ^c  

^a UBER TECHNOLOGIES INC   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

^c Department of Electrical and Computer Engineering   (United States)

Author keywords

Bayesian model; Model choice; Poisson hierarchical; Poisson inverse gamma; Site specific prediction

Indexed keywords

ACCIDENTS; BAYESIAN NETWORKS; CODES (SYMBOLS); DATA HANDLING; HIERARCHICAL SYSTEMS; INFORMATION ANALYSIS; REGRESSION ANALYSIS;

BAYESIAN MODEL; MODEL CHOICE; POISSON HIERARCHICAL; POISSON-INVERSE GAMMA; SITE-SPECIFIC;

FORECASTING;

BAYES THEOREM; COMPARATIVE STUDY; HUMAN; INDIANA; MICHIGAN; POISSON DISTRIBUTION; PREVENTION AND CONTROL; REPRODUCIBILITY; STATISTICAL MODEL; STATISTICS AND NUMERICAL DATA; TEXAS; TRAFFIC ACCIDENT;

ACCIDENTS, TRAFFIC; BAYES THEOREM; HUMANS; INDIANA; MICHIGAN; MODELS, STATISTICAL; POISSON DISTRIBUTION; REPRODUCIBILITY OF RESULTS; TEXAS;

EID: 85046171454     PISSN: 00014575     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aap.2018.04.016     Document Type: Article

References (68)

1. AASHTO, Highway Safety Manual. 1st ed., 2010, American Association of State and Highway Transportation Officials, Washington, D.C.
2. Aguero-Valverde, J., Jovanis, P.P., Analysis of road crash frequency with spatial models. Transp. Res. Rec. 2061 (2008), 55–63.
3. Aguero-Valverde, J., Full Bayes Poisson gamma, Poisson lognormal, and zero inflated random effects models: comparing the precision of crash frequency estimates. Accid. Anal. Prev. 50 (2013), 289–297.
4. Bonneson, J.A., McCoy, P.T., Estimation of safety at two-way stop-controlled intersections on rural highways. Transp. Res. Rec. 1401 (1993), 83–89.
5. Carlin, B.P., Comment on article by Celeux et al. Bayesian Anal. 1 (2006), 675–676.
6. Carriquiry, A., Pawlovich, M.D., From Empirical Bayes to Full Bayes: Methods for Analyzing Traffic Safety Data. 2004 (Accessed 7 March 2014) http://www.iowadot.gov/crashanalysis/pdfs/eb_fb_comparison_whitepaper_october2004.pdf.
7. Celeux, G., Forbes, F., Robert, C.P., Titterington, D.M., Deviance information criteria for missing data models (with discussion). Bayesian Anal. 1 (2006), 651–706.
8. Chib, S., Marginal likelihood from the Gibbs output. J. Am. Stat. Assoc. 90 (1995), 1313–1321.
9. Davis, G.A., Yang, S., Bayesian identification of high-risk intersections for older drivers via Gibbs sampling. Transp. Res. Rec. 1746 (2001), 84–89.
10. Daziano, R.A., Miranda-Moreno, L., Heydari, S., Computational Bayesian statistics in transportation modeling: from road safety analysis to discrete transport reviews. J. Transp. Rev. 33:5 (2013), 570–592.
11. El-Basyouny, K., Sayed, T., Collision prediction models using multivariate poisson-lognormal regression. Accid. Anal. Prev. 41 (2009), 820–828.
12. Fitzpatrick, K., Park, E.S., Safety effectiveness of HAWK pedestrian treatment. Transp. Res. Rec. 2140 (2009), 214–223.
13. Geedipally, S.R., Lord, D., Dhavala, S.S., The negative binomial-Lindley generalized linear model: characteristics and application using crash data. Accid. Anal. Prev. 45:2 (2012), 258–265.
14. Geedipally, S.R., Lord, D., Dhavala, S.S., A caution about using the deviance information criterion while modeling traffic crashes. Saf. Sci. 62 (2013), 495–498.
15. Gelfand, A.E., Smith, A.F.M., Sampling-based approaches to calculating marginal densities. J. Am. Stat. Assoc. 85 (1990), 398–409.
16. Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., Rubin, D.B., Bayesian Data Analysis. third edition, 2013, Chapman and Hall/CRC, New York.
17. Gelman, A., Meng, X.-L., Simulating normalizing constants: from importance sampling to bridge sampling to path sampling. Stat. Sci. 13 (1998), 163–185.
18. Goldstein, H., Multilevel Statistical Models. 4th ed., 2010, John Wiley & Sons, West Sussex, England.
19. Han, C., Carlin, B.P., Markov chain Monte Carlo methods for computing Bayes factors: a comparative review. J. Am. Stat. Assoc. 96 (2001), 1122–1132.
20. Harwood, D.W., Bauer, K.M., Potts, I.B., Torbic, D.J., Richard, K.R., Kohlman Rabbani, E.R., Hauer, E., Elefteriadou, L., Safety Effectiveness of Intersection Left- and Right-Turn Lanes, Report No. FHWA-RD-02-089., 2002, Federal Highway Administration (FHWA), Washington, D.C.
21. Hauer, E., Persaud, B.N., A common bias in before and after accident comparisons and its elimination. Transp. Res. Rec. 905 (1983), 164–174.
22. Hauer, E., On the estimation of the expected number of accidents. Accid. Anal. Prev. 18 (1986), 1–12.
23. Hauer, E., Ng, J.C.N., Lovell, J., Estimation of safety at signalized intersections. Transp. Res. Rec. 1185 (1989), 48–61.
24. Hauer, E., Empirical Bayes approach to the estimation of unsafety: the multivariate regression approach. Accid. Anal. Prev. 24:5 (1992), 456–478.
25. Hauer, E., Observational Before–After Studies in Road Safety: Estimating the Effect of Highway and Traffic Engineering Measures on Road Safety. 1997, Pergamon Press, Elsevier Science, Ltd., Oxford, United Kingdom.
26. Hauer, E., Overdispersion in modeling accidents on road sections and in empirical Bayes estimation. Accid. Anal. Prev. 33:6 (2001), 799–808.
27. Heydecker, B.G., Wu, J., Identification of sites for accident remedial work by Bayesian statistical methods: an example of uncertain inference. Adv. Eng. Softw. 32 (2001), 859–869.
28. Hinde, J., Compound Poisson regression models. Gilchrist, R., (eds.) GLIM 82: Proceedings of the International Conference on Generalized Linear Models, 1982, Springer-Verlag, New York.
29. Khazraee, S.H., Full Bayesian Poisson-Hierarchical Models for Crash Data Analysis: Investigating the Impact of Model Choice on Site-Specific Predictions. PhD Dissertation. 2016, Department of Civil Engineering, Texas A&M University, College Station, Texas.
30. Lee, P., Bayesian Statistics: An Introduction. 4th ed., 2012, John Wiley & Sons, West Sussex, England.
31. Lord, D., Geedipally, S.R., Persaud, B.N., Washington, S.P., van Schalkwyk, I., Ivan, J.N., Lyon, C., Jonsson, T., Methodology for Estimating the Safety Performance of Multilane Rural Highways. NCHRP Web-Only Document 126. 2008, National Cooperation Highway Research Program, Washington, D.C.
32. Lord, D., Mannering, F., The statistical analysis of crash-frequency data: a review and assessment of methodological alternatives. Transp. Res. Part A 44 (2010), 291–305.
33. Lord, D., Miranda-Moreno, L.F., 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. Saf. Sci. 46:5 (2008), 751–770.
34. Lord, D., Park, P.Y.-J., Investigating the effects of the fixed and varying dispersion parameters of Poisson-gamma models on empirical Bayes estimates. Accid. Anal. Prev. 40:4 (2008), 1441–1457.
35. Lord, D., Washington, S.P., Ivan, J.N., Poisson, Poisson-gamma and zero inflated regression models of motor vehicle crashes: balancing statistical fit and theory. Accid. Anal. Prev. 37:1 (2005), 35–46.
36. Ma, J., Kockelman, K., Damien, P., A multivariate Poisson-lognormal regression model for prediction of crash counts by severity, using Bayesian methods. Accid. Anal. Prev. 40 (2008), 964–975.
37. Mannering, F.L., Bhat, C.R., Analytic methods in accident research: methodological frontier and future directions. Anal. Methods Accid. Res. 1 (2014), 1–22.
38. Mannering, F.L., Shankar, V., Bhat, C.R., Unobserved heterogeneity and the statistical analysis of highway accident data. Anal. Methods Accid. Res. 11 (2016), 1–16.
39. Maycock, G., Hall, R.D., Accidents at Four-Arm Roundabouts. Laboratory Report LR 1120., 1984, Transport Research Laboratory, Crowthorne, Berkshire, U.K.
40. Meng, X.-L., Vaida, F., What's missing for DIC with missing data? (Comment on article by Celeux et al.). Bayesian Anal. 1 (2006), 687–698.
41. Miaou, S.P., Lord, D., Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus empirical Bayes. Transp. Res. Rec. 1840 (2003), 31–40.
42. Miaou, S.-P., Song, J.J., Mallick, B.K., Roadway traffic crash mapping: a space time modeling approach. J. Transp. Stat. 6:1 (2003), 33–57.
43. Miaou, S.-P., Song, J.J., Bayesian ranking of sites for engineering safety improvements: decision parameter, treatability concept, statistical criterion and spatial dependence. Accid. Anal. Prev. 37:4 (2005), 699–720.
44. Miller, Comparison of hierarchical Bayesian models for overdispersed count data using DIC and Bayes’ factors. Biometrics 65 (2009), 962–969.
45. Miranda-Moreno, L.F., Fu, L., Saccomanno, F.F., Labbe, A., Alternative risk models for ranking locations for safety improvement. Transp. Res. Rec. 1908 (2005), 1–8.
46. Mitra, S., Washington, S., On the nature of over-dispersion in motor vehicle crash prediction models. Accid. Anal. Prev. 39 (2006), 459–468.
47. MRC Biostatistics Unit, Cambridge Biomedical Campus. DIC: Deviance Information Criterion. http://www.mrc-bsu.cam.ac.uk/software/bugs/the-bugs-project-dic. (Accessed 3 April 2016).
48. Park, E.S., Lord, D., Multivariate Poisson-lognormal models for jointly modeling crash frequency by severity. Transp. Res. Rec.: J. Transp. Res. Board. 2019 (2007), 1–6.
49. Park, E.S., Park, J., Lomax, T.J., A fully Bayesian multivariate approach to before-after safety evaluation. Accid. Anal. Prev. 42 (2010), 1118–1127.
50. Persaud, B.N., Do traffic signals affect safety? Some methodological issues. Transp. Res. Rec. 1185 (1988), 37–47.
51. Persaud, B., Lyon, C., Nguyen, T., Empirical Bayes procedure for ranking sites for safety investigation by potential for safety improvement. Transp. Res. Rec. 1665 (1999), 7–12.
52. Persaud, B., Lyon, C., Empirical Bayes before–after safety studies: lessons learned from two decades of experience and future directions. Accid. Anal. Prev. 39 (2007), 546–555.
53. Plummer, M., Comment on article by Celeux et al. Bayesian Anal. 1 (2006), 681–686.
54. Poch, M., Mannering, F.L., Negative binomial analysis of intersection accident frequency. J. Transp. Eng. 122:2 (1996), 105–113.
55. Schluter, P.J., Deely, J.J., Nicholson, A.J., Ranking and selecting motor vehicle accident sites by using a hierarchical Bayesian model. Statistician 46 (1997), 293–316.
56. Shirazi, M., Dhavala, S.S., Lord, D., Geedipally, S.R., A methodology to design heuristics for model selection based on characteristics of data: application to investigate when negative binomial Lindley (NB-L) is preferred over negative binomial (NB). Accid. Anal. Prev. 107 (2017), 186–194.
57. th Annual Meeting of the Transportation Research Board, Washington, D.C, 2018.
58. Shirazi, M., Lord, D., Dhavala, S.S., Geedipally, S.R., A semiparametric negative binomial generalized linear model for modeling over dispersed count data with a heavy tail: characteristics and applications to crash data. Accid. Anal. Prev. 91 (2016), 10–18.
59. Sinharay, S., Stern, H.S., Posterior predictive model checking in hierarchical models. J. Stat. Plan. Inference 111 (2003), 209–221.
60. Spiegelhalter, D.J., Best, N.G., Carlin, B.P., van der Linde, A., Bayesian measures of model complexity and fit. J. R. Stat. Soc. Ser. B 64 (2002), 583–640.
61. Spiegelhalter, D.J., Thomas, A., Best, N.G., Lun, D., WinBUGS Version 1.4.3 User Manual. 2003, MRC Biostatistics Unit, Cambridge http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/manual14.pdf.
62. Tanner, M., Wong, W., The calculation of posterior distributions by data augmentation (with discussion). J. Am. Stat. Assoc. 82 (1987), 528–550.
63. Vangala, P., Lord, D., Geedipally, S.R., Exploring the application of the negative binomial-generalized exponential model for analyzing traffic crash data with excess zeros. Anal. Methods Accid. Res. 7 (2015), 29–36.
64. Vogt, A., Bared, J., Accident models for two-lane rural segments and intersections. Transp. Res. Rec. 1635 (1998), 18–29.
65. Washington, S.P., Karlaftis, M., Mannering, F.L., Statistical and Econometric Methods for Transportation Data Analysis. 2nd ed., 2010, Chapman and Hall, Boca Raton.
66. Yang, M., Rasbash, J., Goldstein, H., Barbosa, M., MLwiN Macros for Advanced Multilevel Modelling. Version 2.0a. 1999, Multilevel Models Project, Institute of Education, University of London, UK http://www.bris.ac.uk/cmm/software/mlwin/download/d-1-10/advmacma.pdf.
67. Zha, L., Lord, D., Zhou, Y., The Poisson inverse Gaussian (PIG) generalized linear regression model for analyzing motor vehicle crash data. J. Transp. Saf. Secur. 8:1 (2016), 18–35.
68. Zou, Y., Lord, D., Zhang, Y., Analyzing Highly Dispersed Crash Data Using the Sichel Generalized Additive Models for Location, Scale and Shape. Working Paper. 2012, Zachry Department of Civil Engineering, Texas A&M University, College Station, TX https://ceprofs.civil.tamu.edu/dlord/Papers/Zou_et_al_Sichel_GAMLSS.pdf.