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 and Prevention

Volumn 38, Issue 4, 2006, Pages 751-766

  Lord, Dominique ^a  

^a Texas AandM University   (United States)

Author keywords

Empirical Bayes; Low sample mean values; Poisson gamma; Small sample size; Statistical models

Indexed keywords

MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD ESTIMATION; PARAMETER ESTIMATION; POISSON EQUATION; PROBABILISTIC LOGICS; STATISTICAL METHODS;

EMPIRICAL BAYES; LOW SAMPLE MEAN VALUES; POISSON-GAMMA; SMALL SAMPLE SIZE; STATISTICAL MODELS;

GROUND VEHICLES;

ALGORITHM; ARTICLE; CONFIDENCE INTERVAL; HUMAN; POISSON DISTRIBUTION; SAMPLE SIZE; STATISTICAL MODEL; STATISTICS; TRAFFIC ACCIDENT;

ACCIDENTS, TRAFFIC; ALGORITHMS; CONFIDENCE INTERVALS; HUMANS; MODELS, STATISTICAL; POISSON DISTRIBUTION; SAMPLE SIZE;

EID: 33747691081     PISSN: 00014575     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aap.2006.02.001     Document Type: Article

References (65)

1. Abbess C., Jarett D., and Wright C.C. Accidents at blackspots: estimating the effectiveness of remedial treatment. With special reference to the "regression-to-mean" effect. Traffic Eng. Control 22 10 (1981) 535-542
2. Abdel-Aty M., and Addella M.F. Linking roadway geometrics and real-time traffic characteristics to model daytime freeway crashes: generalized estimating equations for correlated data. Transport. Res. Rec. 1897 (2004) 106-115
3. Anscombe F.J. Sampling theory of the negative binomial and logarithmic series distributions. Biometrika 36 (1950) 358-382
4. Cameron, A.C., 2005. Personal communication. College Station, TX.
5. Cameron A.C., and Trivedi P.K. Econometric models based on count data: comparisons and applications of some estimators and tests. J. Appl. Econom. 1 (1986) 29-53
6. Cameron A.C., and Trivedi P.K. Regression-based tests for overdispersion in the Poisson model. J. Econom. 46 (1990) 347-364
7. Cameron A.C., and Trivedi P.K. Regression Analysis of Count Data (1998), Cambridge University Press, Cambridge, UK
8. Clark S.J., and Perry J.N. Estimation of the negative binomial parameter κ: by Maximum Quasi-Likelihood. Biometrics 45 (1989) 309-316
9. Davidian M., and Carroll R.J. A note on extended Quasi-likelihood. J. Roy. Stat. Soc.: Ser. B 82 (1987) 1079-1091
10. Dean C.B. Modified pseudo-likelihood estimator of the overdispersion parameter in Poisson mixture models. J. Appl. Stat. 21 6 (1994) 523-532
11. Federal Highway Administration. Module 1 - Network Screening. SafetyAnalyst: Software Tools for Safety Management of Specific Highway Sites (2003), U.S. Department of Transportation, Washington, DC. http://www.safetyanalyst.org/whitepapers/module1.pdf (web page: http://www.safetyanalyst.org/whitepapers/module1.pdf, accessed on June 10, 2005)
12. Fisher R.A. The negative binomial distribution. Ann. Eugenics 11 (1941) 182-187
13. Fletcher R. A new approach to variable metric algorithms. Comput. J. 13 (1970) 317-322
14. Fridstrøm L., Ifver J., Ingebrigtsen S., Kulmala R., and Thomsen L.K. Measuring the contribution of randomness, exposure, weather, and daylight to the variation in road accident counts. Accident Anal. Prev. 27 1 (1995) 1-20
15. Gourieroux C., Monfort A., and Trognon A. Pseudo maximum likelihood methods: theory. Econometrika 52 (1984) 681-700
16. Gourieroux C., Monfort A., and Trognon A. Pseudo maximum likelihood methods: application. Econometrika 52 (1984) 701-720
17. Gourieroux C., and Visser M. A count data model with unobserved heterogeneity. J. Econom. 79 (1986) 247-268
18. Hauer E. Identification of sites with promise. Transport. Res. Rec. 1542 (1996) 54-60
19. Hauer E. Observational Before-After Studies in Road Safety: Estimating the Effect of Highway and Traffic Engineering Measures on Road Safety (1997), Elsevier Science Ltd., Oxford
20. Hauer E., and Persaud B.P. Problem of identifying hazardous locations using accident data. Transport. Res. Rec. 975 (1984) 36-43
21. Hauer E., Council F.M., and Mohammedshah Y. Safety models for urban four-lane undivided road segments. Transport. Res. Rec. 1897 (2004) 96-105
22. Hauer E., Ng J.C.N., and Lovell J. Estimation of safety at signalized intersections. Transport. Res. Rec. 1185 (1988) 48-61
23. Heydecker B.G., and Wu J. Identification of sites for road accident remedial work by Bayesian statistical methods: an example of uncertain inference. Adv. Eng. Softw. 32 (2001) 859-869
24. Ivan J.N., Wang C., and Bernardo N.R. Explaining two-lane highway crash rates using land use and hourly exposure. Accident Anal. Prev. 32 6 (2000) 787-795
25. Kononov J., and Allery B.K. Explicit consideration of safety in transportation planning and project scoping. Transport. Res. Rec. 1897 (2004) 116-125
26. Kulmala R. Safety at Rural Three- and Four-Arm Junctions: Development and Applications of Accident Prediction Models (1995), VTT Publications 233, Technical Research Centre of Finland, Espoo
27. Kumara S.S.P., and Chin H.C. Study of fatal traffic accidents in Asia Pacific countries. Transport. Res. Rec. (1897) 43-47
28. Kumara S.S.P., Chin H.C., and Weerakoon W.M.S.B. Identification of accident causal factors and prediction of hazardousness of intersection approaches. Transport. Res. Rec. 1840 (2003) 116-122
29. Lawless J.F. Negative binomial and mixed Poisson regression. Can. J. Stat. 15 3 (1987) 209-225
30. Lee F. Specification test for Poisson regression models. Int. Econ. Rev. 27 (1986) 689-706
31. Lord, D., 2000. The prediction of accidents on digital networks: characteristics and issues related to the application of accident prediction models. Ph.D. Dissertation. Department of Civil Engineering, University of Toronto, Toronto, Ontario.
32. Lord D., and Bonneson J.A. Calibration of predictive models for estimating the safety of ramp design configurations. Transport. Res. Rec. 1908 (2005) 88-95
33. Lord D., Manar A., and Vizioli A. Modeling crash-flow-density and crash-flow-V/C ratio for rural and urban freeway segments. Accident Anal. Prev. 37 1 (2005) 185-199
34. Lord D., and Persaud B.N. Accident prediction models with and without trend: application of the generalized estimating equations procedure. Transport. Res. Rec. 1717 (2000) 102-108
35. Lord D., Washington S.P., and Ivan J.N. Poisson, Poisson-gamma and zero inflated regression models of motor vehicle crashes: balancing statistical fit and theory. Accident Anal. Prev. 37 1 (2005) 35-46
36. Lord, D., Miranda-Moreno, L.F., 2006. Effects of Low Sample Mean Values and Small Sample Size on the Estimation of the Dispersion Parameter of Poisson-gamma Models: A Bayesian Perspective. Working Paper. Zachry Department of Civil Engineering, Texas A&M University, College Station, TX.
37. Lyon C., Oh J., Persaud B.N., Washington S.P., and Bared J. Empirical investigation of the IHSDM accident prediction algorithm for rural intersections. Transport. Res. Rec. 1840 (2003) 78-86
38. Maher M.J., and Summersgill I. A comprehensive methodology for the fitting predictive accident models. Accident Anal. Prev. 28 3 (1996) 281-296
39. Maycock, G., Hall, R.D., 1984. Accidents at 4-arm roundabouts. TRRL Laboratory Report 1120. Transportation and Road Research Laboratory, Crowthorne, Bershire.
40. McCullagh P., and Nelder J.A. Generalized Linear Models. 2nd ed. (1989), Chapman and Hall, London, UK
41. Miaou S.-P., and Lord D. Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus empirical Bayes. Transport. Res. Rec. 1840 (2003) 31-40
42. Miaou S.-P., and Song J.J. Bayesian ranking of sites for engineering safety improvements: Decision parameter, treatability concept, statistical criterion and spatial dependence. Accident Anal. Prev. 37 4 (2005) 699-720
43. Morris C.N. Fitting Hierarchical Models. Proceedings of the Workshop on Statistics and Epidemiology: Environment and Health. Minneapolis, MN (1997). http://www.ima.umn.edu/summerstat/week6.html (web page: http://www.ima.umn.edu/summerstat/week6.html#wk6tue, accessed on January 3, 2006)
44. Myers R.H., Montgomery D.C., and Vining G.G. Generalized Linear Models: With Applications in Engineering and the Sciences (2002), Wiley Publishing Co., New York, NY
45. Noland R.B., and Quddus M.A. Analysis of pedestrian and bicycle casualties with regional panel data. Transport. Res. Rec. 1897 (2004) 43-47
46. Oh J., Lyon C., Washington S.P., Persaud B.N., and Bared J. Validation of the FHWA crash models for rural intersections: lessons learned. Transport. Res. Rec. 1840 (2003) 41-49
47. In: Payne R.W. (Ed). The Guide to Genstat (2000), Lawes Agricultural Trust, Rothamsted Experimental Station, Oxford, UK
48. Persaud B.N., and Dzbik L. Accident prediction models for freeways. Transport. Res. Rec. 1401 (1993) 55-60
49. Persaud B.N., Bahar G., Mollett C.J., and Lyon C. Safety evaluation of permanent raised snow-plowable pavement markers. Transport. Res. Rec. 1897 (2004) 148-163
50. Persaud B.N., Lord D., and Palminaso J. Issues of calibration and transferability in developing accident prediction models for urban intersections. Transport. Res. Rec. 1784 (2002) 57-64
51. Piegorsch W.W. Maximum likelihood estimation for the negative binomial dispersion parameter. Biometrics 46 (1990) 863-867
52. Pieters E.P., Gates C.E., Martin J.H., and Sterling W.L. Small-sample comparison of different estimators of negative binomial parameters. Biometrics 33 (1977) 718-723
53. Poch M., and Mannering F.L. Negative binomial analysis of intersection-accident frequency. J. Transport. Eng. 122 2 (1996) 105-113
54. Qin X., Ivan J.N., and Ravishankar N. Selecting exposure measures in crash rate prediction for two-lane highway segments. Accident Anal. Prev. 36 2 (2004) 183-191
55. Ross G.J.S., and Preece D.A. The negative binomial distribution. The Statistician 34 (1985) 323-661
56. SAS Institute Inc. Version 9 of the SAS System for Windows (2002), SAS Institute Inc., Cary, NC
57. Shenton L.R., and Wallington P.A. The bias of moment estimators with an application to the negative binomial. Biometrika (1962) 193-204
58. Spiegelhalter, D.J., Thomas, A., Best, N.G., Lun, D., 2003. WinBUGS Version 1.4.1 User Manual. MRC Biostatistics Unit, Cambridge. Available from http://www.mrc-bsu.cam.ac.uk/bugs/welcome.shtml.
59. Tarko A.P., and Kanodia M. Effective and fair identification of hazardous locations. Transport. Res. Rec. 1897 (2004) 64-70
60. Toft N., Innocent G.T., Mellor D.J., and Reid S.W.J. The Gamma-Poisson model as a statistical method to determine if micro-organisms are randomly distributed in a food matrix. Food Microbiol. 23 1 (2006) 90-94
61. Walsh G.R. Methods of Optimization (1975), Wiley Publishing Co., London, UK
62. Willson L.J., Folks J.L., and Young J.H. Multistage estimation compared with sample-size estimation of the negative binomial κ. Biometrics 40 (1984) 109-117
63. Willson L.J., Folks J.L., and Young J.H. Complete sufficiency and maximum likelihood estimation for the two-parameter negative binomial distribution. Metrika 33 (1984) 349-362
64. Wood G.R. Generalised linear accident models and goodness of fit testing. Accident Anal. Prev. 34 4 (2002) 417-427
65. Wood G.R. Confidence and prediction intervals for generalized linear accident models. Accident Anal. Prev. 37 2 (2005) 267-273