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Modeling road traffic crashes with zero-inflation and site-specific random effects

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Abstract

Zero-inflated count models are increasingly employed in many fields in case of “zero-inflation”. In modeling road traffic crashes, it has also shown to be useful in obtaining a better model-fitting when zero crash counts are over-presented. However, the general specification of zero-inflated model can not account for the multilevel data structure in crash data, which may be an important source of over-dispersion. This paper examines zero-inflated Poisson regression with site-specific random effects (REZIP) with comparison to random effect Poisson model and standard zero-inflated poison model. A practical and flexible procedure, using Bayesian inference with Markov Chain Monte Carlo algorithm and cross-validation predictive density techniques, is applied for model calibration and suitability assessment. Using crash data in Singapore (1998–2005), the illustrative results demonstrate that the REZIP model may significantly improve the model-fitting and predictive performance of crash prediction models. This improvement can contribute to traffic safety management and engineering practices such as countermeasure design and safety evaluation of traffic treatments.

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References

  • Angers JF, Biswas A (2003) A Bayesian analysis of zero-inflated generalized Poisson model. Comput Stat Data Anal 42: 37–46

    Article  MATH  MathSciNet  Google Scholar 

  • Barron DN (1998) The analysis of count data: overdispersion and autocorrelation. Sociol Methodol 22: 179–219

    Article  Google Scholar 

  • Box EP, Hunter WG, Hunter JS (1978) Statistics for experimenters. Wiley, New York

    MATH  Google Scholar 

  • Brooks SP, Gelman A (1998) Alternative methods for monitoring convergence of iterative simulations. J Comput Graph Stat 7: 434–455

    Article  MathSciNet  Google Scholar 

  • Chin HC, Quddus MA (2003) Modeling count data with excess zeros. Sociol Methods Res 32(1): 90–116

    Article  MathSciNet  Google Scholar 

  • Gelfand AE, Smith AFM (1990) Sampling based approaches to calculating marginal densities. J Am Stat Assoc 85: 398–409

    Article  MATH  MathSciNet  Google Scholar 

  • Gelman A, Carlin JB, Stern HS (2003) Bayesian data analysis. 2nd edn. Chapman and Hall, New York

    Google Scholar 

  • Ghosh SK, Pabak M, Lu JC (2006) Bayesian analysis of zero-inflated regression models. J Stat Plan Inference 136: 1360–1375

    Article  MATH  Google Scholar 

  • Hall DB (2000) Zero-inflated Poisson and binomial regression with random effects: a case study. Biometrics 56: 1030–1039

    Article  MATH  MathSciNet  Google Scholar 

  • Haque MM, Chin HC, Huang H (2010) Applying Bayesian hierarchical models to examine motorcycle crashes at signalized intersections. Accid Anal Prev 42(1): 203–212

    Article  Google Scholar 

  • Hausman JC, Hall BH, Griliches Z (1984) Econometric models for count data with an application to the patents—Rand D relationship. Econometrica 52(4): 909–938

    Article  Google Scholar 

  • Hinde J (1982) Compound Poisson regression models. In: Gilchrist R (ed) GLIM 82: Proceedings of the international conference on generalized linear models. Springer, New York, pp 109–121

  • Huang H, Chin HC, Haque MM (2008) Severity of driver injury and vehicle damage in traffic crashes at intersections: Bayesian hierarchical analysis. Accid Anal Prev 40(1): 45–54

    Article  Google Scholar 

  • Huang H, Chin HC, Haque MM (2009) Empirical evaluation of alternative approaches in identifying crash hotspots: naive ranking, empirical Bayes and full Bayes. Transp Res Rec 2103: 32–41

    Article  Google Scholar 

  • Karen CHY, Kelvin KWY (2005) On modeling claim frequency data in general insurance with extra zero. Insur Math Econ 36: 153–163

    Article  MATH  Google Scholar 

  • Kulmala R (1995) Safety at rural three- and four-arm junctions: development and application of accident prediction models. Technical Research Center at Finland, VTT Publications, Espoo

    Google Scholar 

  • Kumara SSP, Chin HC (2003) Modeling accident occurrence at signalized tee intersections with special emphasis on excess zeros. Traffic Inj Prev 3(4): 53–57

    Article  Google Scholar 

  • Lambert D (1992) Zero-inflated Poisson regression with an application to defects in manufacturing. Technometrics 34: 1–14

    Article  MATH  Google Scholar 

  • Land KC, McCall PL, Nagin DS (1996) A comparison of Poisson, negative binomial and semiparametric mixed Poisson regressive models with empirical applications to criminal careers data. Sociol Methods Res 24: 387–442

    Article  Google Scholar 

  • Lawless JF (1987) Negative binomial and mixed Poisson regressions. Can J Stat 15: 209–225

    Article  MATH  MathSciNet  Google Scholar 

  • Lee AH, Stevenson MR, Wang K, Kelvin KWY (2002) Modeling young driver motor vehicle crashes: data with extra zeros. Accid Anal Prev 34: 515–521

    Article  Google Scholar 

  • Lee J, Mannering FL (2002) Impact of roadside features on the frequency and severity of run-off-road accidents: an empirical analysis. Accid Anal Prev 34(2): 349–361

    Article  Google Scholar 

  • Lord D, Washington SP, Ivan JN (2005) Poisson, Poisson-gamma and zero-inflated regression models for motor vehicle crashes: balancing statistical fit and theory. Accid Anal Prev 37: 35–46

    Article  Google Scholar 

  • Miaou SP (1994) The relationship between truck accidents and geometric design of road section: Poisson versus negative binomial regression. Accid Anal Prev 26(4): 471–482

    Article  Google Scholar 

  • Poch M, Mannering FL (1996) Negative binomial analysis of intersection accident frequencies. J Transp Eng 122(2): 105–113

    Article  Google Scholar 

  • Qin X, Ivan JN, Ravishanker N (2004) Selecting exposure measures in crash rate prediction for two-lane highway segments. Accid Anal Prev 36: 183–191

    Article  Google Scholar 

  • Shankar VN, Albin RB, Milton JC, Mannering FL (1998) Evaluation of median crossover likelihoods with clustered accident counts: an empirical inquiry using the random effect negative binomial model. Transp Res Rec 1635: 44–48

    Article  Google Scholar 

  • Shankar VN, Mannering FL, Barfield W (1995) Effect of roadway geometric and environmental factors on rural freeway accident frequencies. Accid Anal Prev 27(3): 371–389

    Article  Google Scholar 

  • Shankar VN, Milton JC, Mannering FL (1997) Modeling accident frequencies as zero-altered probability process: an empirical enquiry. Accid Anal Prev 29(6): 829–837

    Article  Google Scholar 

  • Shankar VN, Ulfarsson GF, Pendyala RM, Neberagal MB (2003) Modeling crashes involving pedestrians and motorized traffic. Saf Sci 41(7): 627–640

    Article  Google Scholar 

  • Spiegelhalter DJ, Thomas A, Best NG, Lunn D (2003) WinBUGS version 1.4.1 User Manual. MRC Biostatistics Unit, Cambridge

    Google Scholar 

  • Tanner M, Wong W (1987) The calculation of posterior distributions by data augmentation (with discussion). J Am Stat Assoc 82: 528–550

    Article  MATH  MathSciNet  Google Scholar 

  • Vehtari A, Lampinen J (2002) Bayesian model assessment and comparison using cross-validation predictive densities. Neural Comput 14: 2439–2468

    Article  MATH  Google Scholar 

  • Vieira AMC, Hinde JP, Demetrio CGB (2000) Zero-inflated proportion data models applied to a biological control assay. J Appl Stat 27(3): 373–389

    Article  MATH  Google Scholar 

  • Vogt A, Bared J (1998) Accident models for two-lane rural segments and intersections. Transp Res Rec 1635: 18–29

    Article  Google Scholar 

  • Vuong Q (1989) Likelihood ratio tests for model selection and non-nested hypothesis. Econometrica 57(2): 307–333

    Article  MATH  MathSciNet  Google Scholar 

  • Wang P (2001) Markov zero-inflated Poisson regression models for a time series of counts with excess zeros. J Appl Stat 28(5): 623–632

    Article  MATH  MathSciNet  Google Scholar 

  • Wang K, Lee AH, Kelvin KWY, Philip JW (2003) A bivariate zero-inflated Poisson regression model to analyze occupational injuries. Accid Anal Prev 35: 625–629

    Article  Google Scholar 

  • Xie M, He B, Goh TN (2001) Zero-inflated Poisson model in statistical process control. Comput Stat Data Anal 38: 191–201

    Article  MATH  MathSciNet  Google Scholar 

  • Yang CM (2003) A Bayesian hierarchical model for accident and injury surveillance. Accid Anal Prev 35: 91–102

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Central Florida, Orlando, FL, 32826, USA

    Helai Huang

  2. Department of Civil Engineering, National University of Singapore, Engineering Drive 2, EW1-04-02B, Singapore, 117576, Singapore

    Hong Chor Chin

Authors
  1. Helai Huang
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  2. Hong Chor Chin
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Correspondence to Helai Huang.

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Huang, H., Chin, H.C. Modeling road traffic crashes with zero-inflation and site-specific random effects. Stat Methods Appl 19, 445–462 (2010). https://doi.org/10.1007/s10260-010-0136-x

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