DOI QR코드

DOI QR Code

Impact of Heterogeneous Dispersion Parameter on the Expected Crash Frequency

이질적 과분산계수가 기대 교통사고건수 추정에 미치는 영향

  • Received : 2014.08.11
  • Accepted : 2014.09.11
  • Published : 2014.09.30

Abstract

This study tested the hypothesis that the significance of the heterogeneous dispersion parameter in safety performance function (SPF) used to estimate the expected crashes is affected by the endogenous heterogeneous prior distributions, and analyzed the impacts of the mis-specified dispersion parameter on the evaluation results for traffic safety countermeasures. In particular, this study simulated the Poisson means based on the heterogeneous dispersion parameters and estimated the SPFs using both the negative binomial (NB) model and the heterogeneous negative binomial (HNB) model for analyzing the impacts of the model mis-specification on the mean and dispersion functions in SPF. In addition, this study analyzed the characteristics of errors in the crash reduction factors (CRFs) obtained when the two models are used to estimate the posterior means and variances, which are essentially estimated through the estimated hyper-parameters in the heterogeneous prior distributions. The simulation study results showed that a mis-estimation on the heterogeneous dispersion parameters through the NB model does not affect the coefficient of the mean functions, but the variances of the prior distribution are seriously mis-estimated when the NB model is used to develop SPFs without considering the heterogeneity in dispersion. Consequently, when the NB model is used erroneously to estimate the prior distributions with heterogeneous dispersion parameters, the mis-estimated posterior mean can produce large errors in CRFs up to 120%.

Keywords

dispersion parameter;Poisson-gamma mixture;crash frequency;heterogeneous negative binomial model

References

  1. B. G. Heydecker, J. Wu, "Identification of Sites for Road Accident Remedial Work by Bayesian Statistical Methods: An Example of Uncertain Inference", Advances in Engineering Software, Vol. 32, No. 10-11, pp. 859-869, 2001. DOI: http://dx.doi.org/10.1016/S0965-9978(01)00037-0 https://doi.org/10.1016/S0965-9978(01)00037-0
  2. K. El-Basyouny, T. Sayed, "Comparison of Two Negative Binomial Regression Techniques in developing Accident Prediction Models", Transportation Research Record 1950, pp. 9-16, 2006. DOI: http://dx.doi.org/10.3141/1950-02 https://doi.org/10.3141/1950-02
  3. S. Mitra, S. P. Washington, "On the Nature of Over-Dispersion in Motor Vehicle Crash Prediction Models", Accident Analysis and Prevention, Vol. 39, No. 3, pp. 459-468, 2007. DOI: http://dx.doi.org/10.1016/j.aap.2006.08.002 https://doi.org/10.1016/j.aap.2006.08.002
  4. S. R. Geedipally, D. Lord, "Effects of the Varying Dispersion Parameter of Poisson- gamma models on the Estimation of Confidence Intervals of Crash Prediction Model", Transportation Research Board 87th Annual Meeting, Washington, D.C., 2008.
  5. D. Lord, P. Y. Park, "Investigating the Effects of the Fixed and Varying Dispersion Parameters of Poisson-gamma Models on Empirical Bayes Estimates", Accident Analysis and Prevention, Vol. 40, No. 4, pp. 1441-1457, 2008. DOI: http://dx.doi.org/10.1016/j.aap.2008.03.014 https://doi.org/10.1016/j.aap.2008.03.014
  6. K. Shin, K. Choi, "Empirical Bayes Method in the Study of Traffic Safety via Heterogeneous Negative Binomial Model", Conference of Korean Society of Civil Engineers, Korean Society of Civil Engineers, pp. 54-57, 2009.
  7. E. Hauer, "Bias-by-Selection: Overestimation of the Effectiveness of Safety Countermeasures caused by the Process of Selection for Treatment", Accident Analysis and Prevention, Vol. 12, No. 2, pp. 113-117, 1980. DOI: http://dx.doi.org/10.1016/0001-4575(80)90049-4 https://doi.org/10.1016/0001-4575(80)90049-4
  8. E. Hauer, "Selection for Treatment as a Source of Bias in Before-and-After Studies," Traffic Engineering and Control, Vol. 21, pp. 419-421, 1980.
  9. Hauer E. Observational Before-After Studies in Road Safety: Estimating the Effect of Highway and Traffic Engineering Measures on Road Safety. Pergamon, 1997.
  10. K. Shin, "Comparative Study on the Estimation Methods of Traffic Crashes : Empirical Bayes Estimate vs. Observed Crash", Journal of Korean Society of Civil Engineers, Vol. 30, No. 5, pp. 453-459, 2010.
  11. K. Shin, "Assessing Estimation Methods of the Expected Crashes using Panel Traffic Crash Data", Journal of Korean Society of Transportation, Vol. 29, No. 1, pp. 103-111, 2011.
  12. Hilbe, J. M. Negative Binomial Regression. Cambridge University Press, 2007. DOI: http://dx.doi.org/10.1017/CBO9780511811852

Acknowledgement

Supported by : 경성대학교