- Volume 23 Issue 4
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Bayesian analysis for the bivariate Poisson regression model: Applications to road safety countermeasures
- Choe, Hyeong-Gu (Division of Applied Mathematics, Hanyang University) ;
- Lim, Joon-Beom (Department of Transportation Engineering, University of Seoul) ;
- Won, Yong-Ho (Division of Applied Mathematics, Hanyang University) ;
- Lee, Soo-Beom (Department of Transportation Engineering, University of Seoul) ;
- Kim, Seong-W. (Division of Applied Mathematics, Hanyang University)
- Received : 2012.06.20
- Accepted : 2012.07.23
- Published : 2012.07.31
We consider a bivariate Poisson regression model to analyze discrete count data when two dependent variables are present. We estimate the regression coefficients as sociated with several safety countermeasures. We use Markov chain and Monte Carlo techniques to execute some computations. A simulation and real data analysis are performed to demonstrate model fitting performances of the proposed model.
Supported by : National Research Foundation of Korea (NRF)
- Adamids, L. and Loukas, S. (1994). ML estimation in the bivariate Poisson distribution in the presence of missing values via the EM algorithm. Journal of Statistical Computation and Simulation, 50, 163-172. https://doi.org/10.1080/00949659408811608
- 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, 48, 322-329.
- Babkov, V. F. (1968). Road design and traffic safety. Traffic Engineering and Control, 236-239.
- Bijleveld, F. D. (2005). The covariance between the number of accidents and the number of victims in multivariate analysis of accident related outcomes. Accident Analysis & Prevention, 37, 591-600. https://doi.org/10.1016/j.aap.2005.01.004
- Garber, N. J. and Gadirau, R. (1988). Speed variance and its in uence on accidents, AAA Foundation for Traffic Safety, Washington, DC.
- Gelfand, A. E. and Smith, A. F. M. (1990). Sampling based approaches to calculating marginal densities. Journal of American Statistical Association, 85, 398-409. https://doi.org/10.1080/01621459.1990.10476213
- Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7, 457-472. https://doi.org/10.1214/ss/1177011136
- Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Transaction on Pattern Analysis and Machine Intelligence, 6, 721-741. https://doi.org/10.1109/TPAMI.1984.4767596
- Jovanis, P. P. and Chang, H. L. (1986). Modelling the relationship of accidents to miles travelled. Transportation Research Record, 1068, 42-51.
- Kim, D. and Jeong, H. C. (2006). Multivariate Poisson distribution generated via reduction from indepen- dent Poisson variates. Journal of the Korean Data & Information Science Society, 17, 953-961.
- Kim, D., Jeong, H. C. and Jung, B. C. (2006). On the multivariate Poisson distribution with specic covariance matrix. Journal of the Korean Data & Information Science Society, 17, 161-171.
- Lord, D. and Persaud, B. N. (2004). Estimating the safety performance of urban road transportation networks. Accident Analysis & Prevention, 36, 609-620. https://doi.org/10.1016/S0001-4575(03)00069-1
- Ma, J. and Kockelman, K. M. (2006). Bayesian multivariate Poisson regression for models of injury count, by severity. Transportation Research Record, 1950, 24-34. https://doi.org/10.3141/1950-04
- Papageorgiou, H. and Loukas, S. (1988). Conditional even point estimation for bivariate discrete distribu- tions. Communications in Statistics-Theory and Methods, 17, 3403-3412. https://doi.org/10.1080/03610928808829811
- Persaud, B. N. (1991). Estimating accident potential of Ontario road sections. Transportation Research Record, 1327, 47-53.
- Persaud, B. N. (1994). Accident prediction models for rural roads. Canadian Journal of Civil Engineering, 21, 547-554. https://doi.org/10.1139/l94-056
- Persaud, B. N. and Dzbik, L. (1993). Accident prediction models for freeways. Transportation Research Record, 1401, 55-60.
- 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, 42, 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, 44, 377-387.
- Tsionas, E. G. (2001). Bayesian multivariate Poisson regression. Communications in Statistics-Theory and Methods, 30, 243-255. https://doi.org/10.1081/STA-100002028
- Tunaru, R. (2002). Hierarchical Bayesian models for multiple count data. Austrian Journal of Statistics, 31, 221-229.
- Zeger, S. L. and Karim, M. R. (1991). Generalized linear models with random effect: A Gibbs sampling. Journal of the American Statistical Association, 86, 79-86. https://doi.org/10.1080/01621459.1991.10475006