Applying the Generalized Waring model for investigating sources of variance in motor vehicle crash analysis

Accident Analysis and Prevention

Volumn 73, Issue , 2014, Pages 20-26

  Peng, Yichuan ^a   Lord, Dominique ^b   Zou, Yajie ^b  

^a UNIVERSITY OF CENTRAL FLORIDA   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Crash modeling; Generalized Waring model; Liability; Negative binomial model; Over dispersion; Proneness; Randomness

Indexed keywords

ACCIDENT PREVENTION; PRODUCT LIABILITY; SAFETY ENGINEERING;

CRASH MODELING; NEGATIVE BINOMIAL MODELS; OVER DISPERSION; PRONENESS; RANDOMNESS; GENERALIZED;

RANDOM PROCESSES; PRODUCT LIABILITY;

ANALYSIS OF VARIANCE; MOTOR VEHICLE; STATISTICAL MODEL; STATISTICS AND NUMERICAL DATA; TRAFFIC ACCIDENT; UNITED STATES;

ACCIDENTS, TRAFFIC; ANALYSIS OF VARIANCE; MODELS, STATISTICAL; MOTOR VEHICLES; TEXAS;

EID: 84906836605     PISSN: 00014575     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aap.2014.07.031     Document Type: Article

References (46)

1. AASHTO Highway Safety Manual first ed. 2010 American Association of State Highway and Transportation Officials Washington, DC
2. P. Anastasopoulos, and F. Mannering A note on modeling vehicle-accident frequencies with random-parameters count models Accid. Anal. Prevent. 41 2009 153 159
3. A. Cameron, and P.K. Trivedi Regression Analysis of Count Data Econometric Society Monographs, vol. 30 1998 Cambridge University Press Cambridge
4. M. Castro, R. Paleti, and C.R. Bhat A latent variable representation of count data models to accommodate spatial and temporal dependence: application to predicting crash frequency at intersections Transport. Res. Part B 46 2012 253 272
5. M. Castro, R. Paleti, and C.R. Bhat A spatial generalized ordered response model to examine highway crash injury severity Accid. Anal. Prevent. 52 2013 188 203
6. L. Cheng, S.R. Geedipally, and D. Lord Examining the Poisson-Weibull generalized linear model for analyzing crash data Safety Sci. 54 2013 38 42
7. R.D. Connors, M. Maher, A. Wood, L. Mountain, and K. Ropkins Methodology for fitting and updating predictive accident models with trend Accid. Anal. Prevent. 56 2013 82 94
8. N. Eluru, M. Bagheri, L. Miranda-Moreno, and L. Fu A latent class modelling approach for identifying vehicle driver injury severity factors at highway-railway crossings Accid. Anal. Prevent. 47 2012 119 127
9. E. Chen, and A. Tarko Modeling safety of highway work zones with random parameters and random effects models Anal. Methods Accid. Res. 1 2014 86 95
10. S.R. Geedipally, D. Lord, and S.S. Dhavala The negative-binomial- generalized-lindley generalized linear model: characteristics and application using crash data Accid. Anal. Prevent. 45 2012 258 265
11. S.R. Geedipally, D. Lord, and B.-J. Park Analyzing different parameterizations of the varying dispersion parameter as a function of segment length Transport. Res. Rec. 2103 2009 108 118
12. S.R. Geedipally, S. Patil, and D. Lord Examining methods for estimating crash counts according to their collision type Transport. Res. Rec. 2165 2010 12 20
13. C.A. Gourieroux, and M. Visser A count data model with unobserved heterogeneity J. Econom. 79 1986 247 268
14. M. Greenwood, and G.U. Yule An enquiry into the nature of frequency distributions representative of multiple happenings, with special reference to multiple attacks of disease or repeated accidents J.R. Statist. Soc. 83 1920 255 279
15. E. Hauer Overdispersion in modelling accidents on road sections and in empirical bayes estimation Accid. Anal. Prevent. 33 6 2001 799 808 (Pubitemid 32798109)
16. J.O. Irwin The generalized waring distribution applied to accident theory J. R. Stat. Soc. Ser. A 131 2 1968 205 225
17. H.M. John, and K.F. Kurtis Numerical Methods Using Matlab fourth ed. 2004
18. D. Lord, and S.R. Geedipally Models for analyzing count data with a lot of zeros Presented at the Annual Joint Statistical Meeting, American Statistical Association, August 2-7, 2014 Boston, MA 2014
19. D. Lord, and J.A. Bonneson Calibration of predictive models for estimating the safety of ramp design configurations Transport. Res. Rec. 1908 2005 88 95 (Pubitemid 43240313)
20. D. Lord, and F. Mannering The statistical analysis of crash-frequency data: a review and assessment of methodological alternatives Transport. Res. - Part A 44 5 2010 291 305
21. D. Lord, and L.F. Miranda-Moreno 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 Sci. 46 5 2008 751 770 (Pubitemid 351707761)
22. D. Lord, and P.Y-J. Park Investigating the effects of the fixed and varying dispersion parameters of Poisson-gamma models on empirical Bayes estimates Accid. Anal. Prevent. 40 2008 1441 1457
23. D. Lord, S.P. Washington, and J.N. Ivan Poisson, Poisson-gamma and zero inflated regression models of motor vehicle crashes: balancing statistical fit and theory Accid. Anal. Prevent. 37 2005 35 46
24. D. Lord, S.P. Washington, and J.N. Ivan Further notes on the application of zero inflated models in highway safety Accid. Anal. Prevent. 39 2007 53 57 (Pubitemid 44740242)
25. M. Maher, and L. Mountain The sensitivity of estimates of regression to the mean Accid. Anal. Prevent. 41 2009 861 868
26. N.V. Malyshkina, F.L. Mannering, and A.P. Tarko Markov switching Negative Binomial models: an application to vehicle accident frequencies Accid. Anal. Prevent. 41 2 2009 217 226
27. F. Mannering, and C.R. Bhat Analytic methods in accident research: Methodological frontier and future directions Anal. Methods Accid. Res. 1 2014 1 22
28. S.-P. Miaou, and D. Lord Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus Empirical Bayes Transport. Res. Rec. 1840 2003 31 40
29. S.-P. Miaou, and J.J. Song Bayesian ranking of sites for engineering safety improvements: Decision parameter, treatability concept, statistical criterion, and spatial dependence Accid. Anal. Prevent. 37 2005 699 720 (Pubitemid 40753442)
30. S.P. Miaou, J.J. Song, and B.K. Mallick Roadway traffic crash mapping: a space-time modeling approach J. Transport. Stat. 6 2003 33 57
31. E.M. Newbold A contribution to the study of the human factor in the causation of accidents Indust. Health Res. Board Rep. 1925 34
32. E.M. Newbold Applications of the statistics of repeated events, particularly to industrial accidents J.R. Statist. Soc. 90 1927 487 547
33. B.-J. Park, and D. Lord Adjustment for the maximum likelihood estimate of the Negative Binomial dispersion parameter Transport. Res. Rec. 2061 2008 9 19
34. B.-J. Park, and D. Lord Application of finite mixture models for vehicle crash data analysis Accid. Anal. Prevent. 41 2009 683 691
35. K. Poormeta On the modelling of overdispersion of counts Statistica Neerlandica 53 1 1999 5 20
36. R Development Core Team R: A language and environment for statistical computing R Foundation for Statistical Computing, Vienna, Austria 2007
37. J. Rodríguez-Avi, A. Conde-Sánchez, A.J. Sáez-Castillo, M.J. Olmo-Jiménez, and A.M. Martínez Rodríguez A generalized Waring regression model for count data Comput. Stat. Data Anal. 53 2009 3717 3725
38. J. Rodríguez-Avi, A. Conde-Sánchez, A.J. Sáez-Castillo, and M.J. Olmo-Jiménez A new generalization of the Waring distribution Comput. Stat. Data Anal. 51 12 2007 6138 6150 (Pubitemid 47135580)
39. Y. Shamsunnahar, E. Naveen, 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 2013 23 38
40. S.P. Washington, R.J. Cole, and S.B. Herbel European advanced driver training programs: reasons for optimism IATSS Res. 34 2 2011 72 79
41. Wu, L.; Lord, D.; Zou, Y.; 2014. Validation of CMFs Derived from Cross Sectional Studies using Regression Models. Zachry Department of Civil Engineering, Texas A&M University, College Station, TX (Paper submitted for publication).
42. E. Xekalaki The univariate generalized waring distribution in relation to accident theory: Proneness, spells or contagion Biometrics 39 4 1983 887 895 (Pubitemid 14268533)
43. Y. Xiong, and F. Mannering The heteroscedastic effects of guardian supervision on adolescent driver-injury severities: a finite mixture-random parameters approach Transport. Res. Part B 49 2013 39 54
44. S. Yasmin, N. Eluru, and S.V. Ukkusuri Alternative Ordered Response Frameworks for Examining Pedestrian Injury Severity in New York City J. Transport. Safety Secur. 6 4 2013 275 300
45. Y. Zou, D. Lord, Y. Zhang, and Y. Peng Comparison of Sichel and Negative Binomial models in estimating empirical Bayes estimates Transport. Res. Rec. 2392 2013 11 21
46. 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. Prevent. 50 2013 1042 1051