吉林大学学报(工学版) ›› 2015, Vol. 45 ›› Issue (3): 769-775.doi: 10.13229/j.cnki.jdxbgxb201503013

Previous Articles     Next Articles

Modeling of excess zeros issue in crash count andysis

XU Jian1, 2, SUN Lu1, 3   

  1. 1.School of Transportation, Southeast University, Nanjing, Jiangsu 210096, China;
    2.Center for Transportation Research, University of Texas at Austin, Austin 78712, USA;
    3. Department of Civil Engineering, Catholic University of America, Washington DC 20064, USA
  • Received:2013-08-12 Online:2015-05-01 Published:2015-05-01

PDF (PC)

474

Abstract: The performances of several mathematical models are evaluated for the investigation of the excess zeros issue in crash data analysis. These models include: zero-inflated Poisson and negative binomial models, multiple zero-inflated Poisson and negative binomial models, Poisson- and binomial-Lindley models. In the evaluation several goodness-of-fit measures are employed, including Deviance Information Criterion (DIC), Mean Absolute Deviance (MAD), Mean Square Predictive Error (MSPE), Maximum Cumulative Residual Plot Deviance (MCPD) and Cross-Validation assessment (CV). The evaluation is conducted based on the crash data sets of a state of USA in year 2010, and Markov chain and Monte Carlo methods are used. Statistic results show that Lindley models are preferred to multilevel zero-inflated models; among all the six models, the negative binomial-Lindley performs the best.

Key words: traffic and transportation safety engineering, crash count, zero-inflated models, multilevel zero-inflated models, Lindley models, goodness-of-fit

CLC Number: 

  • U491.31
[1] Lambert D. Zero-inflated poisson regression, with an application to defects in manufacturing[J]. Technometrics, 1992,34(1):1-14.
[2] Miaou, S. The relationship between truck accidents and geometric design of road sections: poisson versus negative binomial regressions[J]. Accident Analysis & Prevention,1994,26(4):471-482.
[3] Lee J, Mannering F L. Impact of roadside features on the frequency and severity of run-off-road accidents:an empirical analysis[J]. Accident Analysis & Prevention, 2002,34(2):349-361.
[4] Shankar V N, Ulfarsson G F, Pendyala R M, et al. Modeling crashes involving pedestrians and motorized traffic[J]. Safety Science,2003,41(7):627-640.
[5] Qin X, Ivan J N, Ravishankar N. Selecting exposure measures in crash rate prediction for two-lane highway segments[J]. Accident Analysis & Prevention,2004,36(2):183-191.
[6] Yan Xue-dong,Wang Bin,An Mei-wu, et al. Distinguishing between rural and urban road segment traffic safety based on zero-inflated negative binomial regression models[DB/OL]. [2013-01-18].http://www.hindawi.com/journals/ddns/2012/789140/.
[7] 马壮林,邵春福,胡大伟,等.高速公路交通事故起数时空分析模型[J]. 交通运输工程学报,2012,12(2):93-99.
Ma Zhuang-lin, Shao Chun-fu, Hu Da-wei, et al. Temporal-spatial analysis model of traffic accident frequency on expressway[J]. Journal of Traffic and Transportation Engineering, 2012, 12 (2): 93-99.
[8] Lee A H, Wang Kui, Scott J A, et al. Multi-level zero-inflated Poisson regression modeling of correlated count data with excess zeros[J]. Statistical Methods in Medical Research,2006,15(1):47-61.
[9] Moghimbeigi A,Eshraghian M R,Mohammad K,et al.Multilevel zero-inflated negative binomial regression modeling for over-dispersed count data with extra zeros[J].Journal of Applied Statistics,2008,35(10):1193-1202.
[10] Lindley D V. Fiducial distributions and Bayes' theorem[J]. Journal of the Royal Statistical Society,1958,20(1):102-107.
[11] Zamani H, Ismail N. Negative binomial-Lindley distribution and its application[J]. Journal of Mathematics and Statistics,2010,6(1):4-9.
[12] Lord D, Geedipally S R. The negative binomial-Lindley distribution as a tool for analyzing crash data characterized by a large amount of zeros[J]. Accident Analysis and Prevention,2011,43(5):1738-1742.
[13] Reddy G S, Lord D, Dhavala S S. The negative binomial-Lindley generalized linear model: Characteristics and application using crash data[J]. Accident Analysis & Prevention,2012,45(3):258-265.
[14] Miaou S.The relationship between truck accidents and geometric design of road sections:Poisson versus negative binomial regressions[J].Accident Analysis & Prevention,1994,26(4):471-482.
[15] Vuong Q H. Likelihood ratio tests for model selection and non-nested hypothesis[J]. Econometrica,1989,57(2),307-333.
[16] Oh J, Lyon C, Washington S P, et al. Validation of the FHWA crash models for rural intersections: lessons learned[C]∥Transportation Research Record, Transportation Research Board, National Research Council,Washington DC, 2003:41-49.
[17] Geedipally S R, Patil S, Lord D. Examination of methods for estimating crash counts according to their collision type[J]. Transportation Research Record, Transportation Research Board, National Research Council, Washington DC,2010:12-20.
[18] Huang H L,Chin H C.Modeling road traffic crashes with zero-inflation and site-specific random effects[J].Statistical Methods & Applications,2010,19(3):445-462.
[19] Thomas A, O'Hara B, Ligges U, et al. Making BUGS open[J]. R News,2006,6(1):12-17.
[1] SUN Lu, XU Jian, CUI Xiang-min. Panel data models for analysis and prediction of crash count [J]. 吉林大学学报(工学版), 2015, 45(6): 1771-1778.
[2] JIN Li-sheng, WANG Yan, LIU Jing-hua, WANG Ya-li, ZHENG Yi. Front vehicle detection based on Adaboost algorithm in daytime [J]. 吉林大学学报(工学版), 2014, 44(6): 1604-1608.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright © Journal of Jilin University(Engineering and Technology Edition), All Rights Reserved.
Tel: +86-431-85095297　Fax: +86-431-85094074　E-mail: xbgxb@jlu.edu.cn
Powered by Beijing Magtech Co. Ltd