A negative binomial crash sum model for time invariant heterogeneity in panel crash data: Some insights

Analytic Methods in Accident Research

Volumn 14, Issue , 2017, Pages 1-9

  Mothafer, Ghasak I M A ^a   Yamamoto, Toshiyuki ^a   Shankar, Venkataraman N ^b  

^a NAGOYA UNIVERSITY   (Japan)

^b The Pennsylvania State University   (United States)

Author keywords

Negative binomial (NB); Random effects; Random effects Poisson gamma (REPG); Time invariant heterogeneity; Types of crashes

Indexed keywords

NORMAL DISTRIBUTION; POISSON DISTRIBUTION;

NEGATIVE BINOMIAL; POISSON GAMMAS; RANDOM EFFECTS; TIME INVARIANTS; TYPES OF CRASHES;

RANDOM PROCESSES;

EID: 85009841213     PISSN: 22136657     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amar.2016.12.003     Document Type: Article

References (54)

1. Anastasopoulos, P.C., Random parameters multivariate Tobit and zero-inflated count data models: addressing unobserved and zero-state heterogeneity in accident injury-severity rate and frequency analysis. Analytic Methods in Accident Research 11 (2016), 17–32.
2. Anastasopoulos, P., Mannering, F.L., A note on modeling vehicle-accident frequencies with random-parameters count models. Accident Analysis and Prevention 41:1 (2009), 153–159.
3. Anastasopoulos, P.C., Mannering, F.L., The effect of speed limits on drivers’ choice of speed: a random parameters seemingly unrelated equations approach. Analytic Methods in Accident Research 10 (2016), 1–11.
4. Anastasopoulos, P.C., Sarwar, M.T., Shankar, V.N., Safety-oriented pavement performance thresholds: accounting for unobserved heterogeneity in a multi-objective optimization and goal programming approach. Analytic Methods in Accident Research 12 (2016), 35–47.
5. Baltagi, B., Econometric Analysis of Panel Data. 2008, John Wiley and Sons.
6. Barua, S., El-Basyouny, K., Islam, M.T., Multivariate random parameters collision count data models with spatial heterogeneity. Analytic Methods in Accident Research 9 (2016), 1–15.
7. Behnood, A., Mannering, F.L., The temporal stability of factors affecting driver-injury severities in single-vehicle crashes: some empirical evidence. Analytic Methods in Accident Research 8 (2015), 7–32.
8. Behnood, A., Mannering, F.L., An empirical assessment of the effects of economic recessions on pedestrian-injury crashes using mixed and latent-class models. Analytic Methods in Accident Research 12 (2016), 1–17.
9. Behnood, A., Roshandeh, A.M., Mannering, F.L., Latent class analysis of the effects of age, gender, and alcohol consumption on driver-injury severities. Analytic Methods in Accident Research 3 (2014), 56–91.
10. Bhargava, A., Franzini, L., Narendranathan, W., Serial correlation and the fixed effects model. The Review of Economic Studies 49:4 (1982), 533–549.
11. Bonnans, J.F., Gilbert, J.C., Lemaréchal, C., Sagastizábal, C.A., Numerical Optimization: Theoretical and Practical Aspects. 2006, Springer Science & Business Media.
12. Cameron, A.C., Trivedi, P.K., Essentials of count data regression. Baltagi, B.H., (eds.) A Companion to Theoretical Econometrics, 2001, 331–348.
13. Cameron, A.C., Trivedi, P.K., Microeconometrics: Methods and Applications. 2005, Cambridge University Press.
14. Cameron, A.C., Trivedi, P.K., Regression Analysis of Count Data. 2013, Cambridge University Press.
15. Chin, H.C., Quddus, M.A., Applying the random effect negative binomial model to examine traffic accident occurrence at signalized intersections. Accident Analysis and Prevention 35:2 (2003), 253–259.
16. Chiou, Y.C., Fu, C., Modeling crash frequency and severity with spatiotemporal dependence. Analytic Methods in Accident Research 5 (2015), 43–58.
17. Chiou, Y.C., Fu, C., Chih-Wei, H., Incorporating spatial dependence in simultaneously modeling crash frequency and severity. Analytic Methods in Accident Research 2 (2014), 1–11.
18. Coruh, E., Bilgic, A., Tortum, A., Accident analysis with the random parameters negative binomial panel count data model. Analytic Methods in Accident Research 7 (2015), 37–49.
19. Dong, C., Clarke, D.B., Yan, X., Khattak, A., Huang, B., Multivariate random-parameters zero-inflated negative binomial regression model: an application to estimate crash frequencies at intersections. Accident Analysis and Prevention 70 (2014), 320–329.
20. Dong, C., Clarke, D.B., Nambisan, S.S., Huang, B., Analyzing injury crashes using random-parameter bivariate regression models. Transportmetrica A: Transport Science, 2016, 1–7.
21. Godambe, V.P., An optimum property of regular maximum likelihood estimation. The Annals of Mathematical Statistics 31:4 (1960), 1208–1211.
22. Green, W.H., Econometric Analysis. 2003, Pearson Education India.
23. Hausman, J.A., Hall, B., Griliches, Z., Econometric models for count data with an application to the patents R&D relationship. Econometrica 52:4 (1984), 909–938.
24. Heydari, S., Fu, L., Joseph, L., Miranda-Moreno, L.F., Bayesian nonparametric modeling in transportation safety studies: applications in univariate and multivariate settings. Analytic Methods in Accident Research 12 (2016), 18–34.
25. Hong, J., Shankar, V.N., Venkataraman, N., A spatially autoregressive and heteroskedastic space-time pedestrian exposure modeling framework with spatial lags and endogenous network topologies. Analytic Methods in Accident Research 10 (2016), 26–46.
26. Ivan, J.N., Wang, C., Bernardo, N.R., Explaining two-lane highway crash rates using land use and hourly exposure. Accident Analysis and Prevention 32:6 (2000), 787–795.
27. Kuha, J., AIC and BIC comparisons of assumptions and performance. Sociological Methods and Research 33:2 (2004), 188–229.
28. Kumara, S., Chin, H., Study of fatal traffic accidents in Asia Pacific countries. Transportation Research Record: Journal of the Transportation Research Board 1897 (2004), 43–47.
29. Law, T.H., Noland, R.B., Evans, A.W., Factors associated with the relationship between motorcycle deaths and economic growth. Accident Analysis and Prevention 41:2 (2009), 234–240.
30. Lord, D., The Prediction of Accidents on Digital Networks: Characteristics and Issues Related to the Application of Accident Prediction Models. (Doctoral dissertation), 2000, University of Toronto.
31. Lord, D., Mannering, F., The statistical analysis of crash-frequency data: a review and assessment of methodological alternatives. Transportation Research Part A: Policy and Practice 44:5 (2010), 291–305.
32. 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. Accident Analysis and Prevention 37:1 (2005), 35–46.
33. Lyon, C., Oh, J., Persaud, B., Washington, S., Bared, J., Empirical investigation of interactive highway safety design model accident prediction algorithm: Rural intersections. Transportation Research Record: Journal of the Transportation Research Board 1840 (2003), 78–86.
34. Ma, J., Kockelman, K.M., Damien, P., A multivariate Poisson-lognormal regression model for prediction of crash counts by severity, using Bayesian methods. Accident Analysis and Prevention 40:3 (2008), 964–975.
35. Malyshkina, N.V., Mannering, F.L., Tarko, A.P., Markov switching negative binomial models: an application to vehicle accident frequencies. Accident Analysis and Prevention 41:2 (2009), 217–226.
36. Mannering, F.L., Bhat, C.R., Analytic methods in accident research: methodological frontier and future directions. Analytic Methods in Accident Research 1 (2014), 1–22.
37. Mannering, F., Shankar, V., Bhat, C., Unobserved heterogeneity and the statistical analysis of highway accident data. Analytic Methods in Accident Research 11 (2016), 1–16.
38. Miaou, S.P., Lord, D., 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 (2003), 31–40.
39. Miaou, S.P., Song, J.J., Bayesian ranking of sites for engineering safety improvements: decision parameter, treatability concept, statistical criterion, and spatial dependence. Accident Analysis and Prevention 37:4 (2005), 699–720.
40. Mothafer, G.I., Yamamoto, T., Shankar, V.N., Evaluating crash type covariances and roadway geometric marginal effects using the multivariate Poisson gamma mixture model. Analytic Methods in Accident Research 9 (2016), 16–26.
41. Norros, I., Kuusela, P., Innamaa, S., Pilli-Sihvola, E., Rajamäki, R., The Palm distribution of traffic conditions and its application to accident risk assessment. Analytic Methods in Accident Research 12 (2016), 48–65.
42. Park, B.J., Lord, D., Application of finite mixture models for vehicle crash data analysis. Accident Analysis and Prevention 41:4 (2009), 683–691.
43. Quddus, M.A., Time series count data models: an empirical application to traffic accidents. Accident Analysis and Prevention 40:5 (2008), 1732–1741.
44. Russo, B.J., Savolainen, P.T., Schneider, W.H., Anastasopoulos, P.C., Comparison of factors affecting injury severity in angle collisions by fault status using a random parameters bivariate ordered probit model. Analytic Methods in Accident Research 2 (2014), 21–29.
45. Sarwar, M.T., Anastasopoulos, P.C., The effect of long term non-invasive pavement deterioration on accident injury-severity rates: a seemingly unrelated and multivariate equations approach. Analytic Methods in Accident Research 13 (2017), 1–15.
46. Serhiyenko, V., Mamun, S.A., Ivan, J.N., Ravishanker, N., Fast Bayesian inference for modeling multivariate crash counts. Analytic Methods in Accident Research 9 (2016), 44–53.
47. Shankar, V., Mannering, F., Barfield, W., Effect of roadway geometrics and environmental factors on rural freeway accident frequencies. Accident Analysis and Prevention 27:3 (1995), 371–389.
48. Shankar, V., Milton, J., Mannering, F., Modeling accident frequencies as zero-altered probability processes: an empirical inquiry. Accident Analysis and Prevention 29:6 (1997), 829–837.
49. Shankar, V., Albin, R., Milton, J., Mannering, F., Evaluating median crossover likelihoods with clustered accident counts: an empirical inquiry using the random effects negative binomial model. Transportation Research Record: Journal of the Transportation Research Board 1635 (1998), 44–48.
50. Sittikariya, S., Shankar, V.N., Shyu, M.B., Chayanan, S., Accounting for serial correlation in count models of traffic safety. Journal of the Eastern Asia Society for Transportation Studies 6 (2005), 3645–3657.
51. Stata Corp LP, Stata Statistical Software Release 9. 2005, Stata Press Publication.
52. Ulfarsson, G., Shankar, V., Accident count model based on multiyear cross-sectional roadway data with serial correlation. Transportation Research Record: Journal of the Transportation Research Board 1840 (2003), 193–197.
53. Venkataraman, N., Shankar, V., Ulfarsson, G.F., Deptuch, D., A heterogeneity-in-means count model for evaluating the effects of interchange type on heterogeneous influences of interstate geometrics on crash frequencies. Analytic Methods in Accident Research 2 (2014), 12–20.
54. Zeng, Q., Huang, H., Pei, X., Wong, S.C., Modeling nonlinear relationship between crash frequency by severity and contributing factors by neural networks. Analytic Methods in Accident Research 10 (2016), 12–25.