Abstract
In traditional identification of hot spots, often known as the sites with black spots or accident-prone locations, methodologies are developed based on the total number of accidents. These criteria provide no consideration of whether the accidents were caused or could be averted by road improvements. These traditional methods result in misidentification of locations that are not truly hazardous from a road safety authority perspective and consequently may lead to a misapplication of safety improvement funding. We consider a mixture of the zero-inflated Poisson and the Poisson regression models to analyze zero-inflated data sets drawn from traffic accident studies. Based on the membership probabilities, observations are well separated into two clusters. One is the ZIP cluster; the other is the standard Poisson cluster. A simulation study and real data analysis are performed to demonstrate model fitting performances of the proposed model. The Bayes factor and the Bayesian information criterion are used to compare the proposed model with several competing models. Ultimately, this model could detect accident-prone spots.
Similar content being viewed by others
References
Akman, V. E. and Raftery, A. E. (1986). “Bayes factors fornon-homogeneous poisson processes with vague prior information.” Journal of the Royal Statistical Society Series B, Vol. 48, No. 3, pp. 322–329.
Broet, P., Richardson, S., and Radvanyi, F. (2002). “Bayesian hierarchical model for identifying changes in gene expression from microarray experiments.” Journal of Computational Biology, Vol. 9, No. 4, pp. 671–683.
Brown, B., Farley, C., and Forgues, M. (1992). “Identification of dangerous highway locations: Results of Community Health Department study in Quebec.” In transportation research record, Transportation Research Board (TRB), National Research Council, Washington D.C., Vol. 1376, pp. 78–85.
Carson, J. and Mannering, F. L. (2001). “The effect of ice warning signs on ice-accident frequencies and severities.” Accident Analysis and Prevention, Vol. 33, No. 1, pp. 99–109.
Chang, Y. C. (2000). “Residuals analysis of the generalized linear models for longitudinal data.” Statistics in Medicine, Vol. 19, No. 10, pp. 1277–1293.
Chen, M. H. and Shao, Q. M. (1999). “Monte Carlo estimation of Bayesian credible and HPD intervals.” Journal of Computational and Graphical Statistics, Vol. 8, No. 1, pp. 69–92.
Cheng, W. and Washington, S. (2005). “Experimental evaluation of hotspot identification method.” Accident Analysis and Prevention, Vol. 37, No. 5, pp. 870–881.
Dahl, D. (2003). “Modeling differential gene expression using a dirichlet process mixture model.” Proc., 2003 Int. the American Statistical Association, Bayesian Statistical Sciences Section, Alexandria, VA: American Statistical Association.
Gelfand, A. E. and Smith, A. F. M. (1990). “Sampling based approaches to calculating marginal densities.” Journal of American Statistical Association, Vol. 85, No. 410, pp. 398–409.
Geman, S. and Geman, D. (1984). “Stochastic relaxation, gibbs distributions and the bayesian restoration of images.” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 6, No. 6, pp. 721–741.
Hadi, M. A., Aruldhas, J., Chow, L. F., and Wattleworth, J. A. (1995). “Estimating safety effects of cross-section design for various highway types using negative binomial regression.” Transportation Research Record, Vol. 1500, pp. 169–177.
Hammersley, J. M. and Handscomb, D. C. (1964). Monte carlo methods, Methuen, London.
Hauer, E., Harwood, D. W., Council, F. M., and Griffith, M. S. (2002). “Estimating safety by the empirical bayes method: A tutorial.” In transportation research record, Transportation Research Board (TRB), National Research Council, Journal of the Transportation Research Board, Vol. 1784, pp. 126–131.
Heydecker, B. G. and Wu, J. (2001). “Identification of sites for accident remedial work by Bayesian statistical methods: An example of uncertain inference.” Advances in Engineering Software, Vol. 32, No. 10, pp. 859–869.
Higle, J. L. and Hecht, M. B. (1989). “A comparison of techniques for the identification of hazardous locations.” Transportation Research Record, Vol. 1238, pp. 10–19.
Jang, H., Lee, S., and Kim, S. W. (2010). “Bayesian analysis for zero-inflated regression models with the power prior: Applications to road safety countermeasures.” Accident Analysis and Prevention, Vol. 42, No. 2, pp. 540–547.
Jeffreys, H. (1961). Theory of probability, Third Edition, Oxford University Press.
Joshua, S. and Garber, N. (1990). “Estimating truck accident rate and involvements using linear and poisson regression models.” Transportation planning and Technology, Vol. 15, No. 1, pp. 47–58.
Kass, R. E. and Raftery, A. (1995). “Bayesian factors.” Journal of the American Statistical Association, Vol. 90, No. 430, pp. 773–795.
Kim, D. G., Washington, S., and Oh, J. (2006). “Modeling crash types: New insights into the effects of covariates on crashes at rural intersections.” Journal of Transportation Engineering, Vol. 132, No. 4, pp. 282–292.
Lambert, D. (1992). “Zero-inflated poisson regression with an application to defects in manufacturing.” Technometrics, Vol. 34, No. 1, pp. 1–14.
Lee, J. and Mannering, F. L. (2002). “Impact of roadside features on the frequency and severity of run-off-roadway accidents: An empirical analysis.” Accident Analysis and Prevention, Vol. 34, No. 2, pp. 149–161.
Li, J., Abdelwahab, W., and Brown, G. (1994). “Joint effects of access and geometry on two-lane rural highway safety in British Columbia.” Canadian Journal of Civil Engineering, Vol. 21, No. 6, pp. 1012–1024.
Lindsay, B. G. (1995). Mixture models: Theory, geometry, and applications. in Institute of Matyematical Statistics, American Statistical Association.
Lord, D., Washington, S. P., and Ivan, J. N. (2005). “Poisson, Poissongamma and zero inflated regression models of motor vehicle crashes: Balancing statistical fit and theory.” Accident Analysis and Prevention, Vol. 37, No. 1, pp. 35–46.
Lord, D., Washington, S. P., and Ivan, J. N. (2007). “Further notes on the application of zero-inflated models in highway safety.” Accident Analysis and Prevention, Vol. 39, No. 1, pp. 53–57.
Mahal, D., Hakkert, A. S., and Phrasker, J. N. (1982). “A system for the allocation of safety resources on a road network.” Accident Analysis and Prevention, Vol. 14, No. 1, pp. 45–56
Malyshkina, N. V. and Mannering, F. L. (2010). “Zero-state Markov switching count-data models: An empirical assessment.” Accident Analysis and Prevention, Vol. 42, No. 1, pp. 122–130.
Mayora, J. M. P. and Rubio, R. L. (2003). “Relevant variables for crashrate prediction on spain’s two-lane rural roads.” Transportation Research Board 82nd Annual Meeting, Washington, D.C.
McCulloch, R. E. and Rossi, P. E. (1991). “A Bayesian approach to testing the arbitrage pricing theory.” Journal of Econometrics, Vol. 49, No. 1, pp. 141–168.
McLachlan, G. J. and Basford, K. E. (1988). Mixture models: Inference and applications to clustering, Marcel Dekker, New York.
McLachlan, G. J., Bean, R. W., and Peel, D. (2002). “A mixture modelbased approach to the clustering of microarray expression data.” Bioinformatics, Vol. 18, No. 3, pp. 413–422.
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). “Equations of state calculations by fast computing machines.” Journal of the Chemical Physics, Vol. 21, No. 6, pp. 1087–1091.
Miaou, S. P. (1994). “The relationship between truck accidents and geometric design of road sections: Poisson versus negative binomial regressions.” Accident Analysis and Prevention, Vol. 26, No. 4, pp. 471–482.
Miaou, S. P., Hu, P. S., Wright, T., Rathi, A. K., and Davis, S. C. (1992). “Relationship between truck accidents and highway geometric design: A poisson regression approach.” Transportation Research Record, Vol. 1376, pp. 10–18.
Milton, J. and Mannering, F. (1998). “The relationship among highway geometrics, traffic-related elements and motorvehicle accident frequencies.” Transportation, Vol. 25, No. 4, pp. 395–413.
Miranda-Moreno, L. F., Fu, L., Saccomanno, F., and Labbe, A. (2005). “Alternative risk models for ranking locations for safety improvemnet.” Transportation Research Record, Vol. 1908, pp. 1–13.
Miranda-Moreno, L. F., Labbe, A., and Fu, L. (2007). “Bayesian multiple testing procedures for hotspot identification.” Accident Analysis and Prevention, Vol. 39, No. 6, pp. 1192–1201.
Newton, M. A. and Raftery A. E. (1994). “Approximate Bayesian inference by the weighted likelihood bootstrap (with discussion).” Journal of the Royal Statistical Society Series B, Vol. 56, No. 1, pp. 3–48.
Ng, J. C. W. and Sayed, T. (2004). “Effect of geometric design consistency on road safety.” Canadian Journal of Civil Engineering, Vol. 31, No. 2, pp. 218–227.
Norden, N., Orlansky, J., and Jacobs, H. (1956). “Application of statistical quality-control techniques to analysis of highway accident data.” Highway Research Board (HRB), National Council, Washington D.C., Vol. 117, pp. 17–31.
Odgen, K. W. (1997). Safer roads: A guide to road safety engineering, Cambridge University Press.
Pan, W., Lin, J., and Le, C. T. (2002). “How many replicates of arrays are required to detect gene expression changes in microarray experiments? A mixture model approach.” Genome Biology, Vol. 3, No. 5, pp. 0022.1–0022.10.
Park, B. J. and Lord, D. (2009). “Application of finite mixture models for vehicle crash data analysis.” Accident Analysis and Prevention, Vol. 41, No. 4, pp. 683–691.
Park, B. J., Lord, D., and Hart, J. D. (2010). “Bias properties of Bayesian statistics in finite mixture of negative binomial regression models in crash data analysis.” Accident Analysis and Prevention, Vol. 42, No. 2, pp. 741–749.
Persaud B. N. and Hauer, E. (1984). “Comparison of two methods for de-biasing before and after accident studies.” Transportation Research Record, Vol. 975, pp. 43–49.
Petridou, E. and Moustak, M. (2000). “Human factors in the causation of road traffic crashes.” European Journal of Epidemiology, Vol. 16, No. 9, pp. 819–826.
Raftery, A. E. and Banfield, J. D. (1991). “Stopping the Gibbs sampler the use of morphology and other issues in spatial statistics.” Annals of the Institute of Statistical Mathematics, Vol. 43, No. 1, pp. 32–43.
Schwarz, G. (1978). “Estimating the dimension of a model.” The Annals of Statistics, Vol. 6, No. 2, pp. 461–464.
Shankar, V., Mannering, F. L., and Barfield, W. (1995). “Effect of roadway geometrics and environmental factors on rural freeway accident frequencies.” Accident Analysis and Prevention, Vol. 27, No. 3, pp. 371–389.
Shankar, V., Milton, J. C., and Mannering, F. L. (1997). “Modeling accident frequencies as zero-altered probability process: An empirical inquiry.” Accident Analysis and Prevention, Vol. 29, No. 6, pp. 829–837.
Smith, A. F. M. and Spiegelhalter, D. J. (1980). “Bayes factors and choice criteria for linear models.” Journal of the Royal Statistical Society Series B, Vol. 42, No. 2, pp. 213–220.
Spiegelhalter, D. J. and Smith, A. F. M. (1982). “Bayes factors for linear and log-linear models with vague prior information.” Journal of the Royal Statistical Society Series B, Vol. 44, No. 3, pp. 377–387.
Tadesse, M., Sha, N., and Vannucci, M. (2005). “Bayesian variable selection in clustering high-dimensional data.” Journal of the American Statistical Association, Vol. 100, No. 470, pp. 602–617.
Tamburri, T. N. and Smith, R. N. (1970). “The safety index: Method of evaluating and rating safety benefits.” In Highway Research Record, Highway Research Board (HRB), National Research Council, Washington D.C., Vol. 332, pp. 28–43.
Tarko, A. P., Sinha, K. C., and Farooq, O. (1996). “Methodology for identifying highway safety problem areas.” In Transportation Research Record, Transportation Research Board (TRB), National Research Council, Washington D.C., Vol. 1542, pp. 49–53.
Tunaru, R. (2002). “Hierarchical Bayesian models for multiple count data.” Austrailian Journal of Statistics, Vol. 31, No. 2, pp. 221–229.
Vogt, A. and Bared, J. G. (1998). Accident models for two-lane rural road: Segments and intersections, Report Number FHWA-RD-98-133, U.S., Department of Transportation, Federal Highway Administration, Washington, D.C.
Wright, C. C., Abbess, C. R., and Jarrett, D. F. (1988). “Estimating the regression to mean effect associated with road accident black spot treatment: Towards a more realistic approach.” Accident Analysis and Prevention, Vol. 20, No. 3, pp. 199–214.
Zeger, S. L. and Karlim, M. R. (1991). “Generalized linear models with random effect: A Gibbs sampling.” Journal of American Statistical Association, Vol. 86, No. 413, pp. 79–86.
Zhang, C. and Ivan, J. N. (2005). “Effects of geometric characteristics on head-on crash incidence on two-lane roads in connecticut.” Transportation Research Board 84th Annual Meeting, Washington, D.C.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chang, I., Kim, S.W. Modelling for identifying accident-prone spots: Bayesian approach with a Poisson mixture model. KSCE J Civ Eng 16, 441–449 (2012). https://doi.org/10.1007/s12205-012-1513-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-012-1513-9