Browse > Article
http://dx.doi.org/10.5351/KJAS.2008.21.4.603

Bayesian Analysis for the Zero-inflated Regression Models  

Jang, Hak-Jin (Division of Applied Mathematics, Hanyang University)
Kang, Yun-Hee (Division of Applied Mathematics, Hanyang University)
Lee, S. (Division of Transportation Engineering, The University of SEOUL)
Kim, Seong-W. (Division of Applied Mathematics, Hanyang University)
Publication Information
The Korean Journal of Applied Statistics / v.21, no.4, 2008 , pp. 603-613 More about this Journal
Abstract
We often encounter the situation that discrete count data have a large portion of zeros. In this case, it is not appropriate to analyze the data based on standard regression models such as the poisson or negative binomial regression models. In this article, we consider Bayesian analysis for two commonly used models. They are zero-inflated poisson and negative binomial regression models. We use the Bayes factor as a model selection tool and computation is proceeded via Markov chain Monte Carlo methods. Crash count data are analyzed to support theoretical results.
Keywords
Zero-inflated model; Bayesian model selection; Bayes factor; Markov chain Monte Carlo;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Joshua, S. C. and Garber, N. J. (1990). Estimating truck accident rate and involvements using linear and poisson regression models, Transportation Planning and Technology, 15, 41-58   DOI
2 McCulloch, R. and Rossi, P. E. (1991). A bayesian approach to testing the arbitrage pricing theory, Journal of Econometrics, 49, 141-168   DOI   ScienceOn
3 Miaou, S. P. and Lum, H. (1993). Modeling vehicle accidents and highway geometric design relationships, Accident Analysis and Prevention, 25, 689-709   DOI   ScienceOn
4 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, 29, 829-837   DOI   ScienceOn
5 Szabo, R. M. and Khoshgoftaar, T. M. (2000). Exploring a poisson regression fault model: A comparative study, Technical Report TR-CSE-00-56, Florida Atlantic University
6 Milton, J. C. and Mannering, F. L. (1998). The relationship among highway geometrics, traffic-related elements and motor-vehicle accident frequencies, Transportation, 25, 395-413   DOI   ScienceOn
7 Jeffreys, H. (1961). Theory of Probability, (Third edition), Oxford University Press, Oxford
8 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, 27, 371-389   DOI   ScienceOn
9 임아경, 오만숙 (2006). 영과잉 포아송 회귀모형에 대한 베이지안 추론: 구강위생 자료에의 적용, <응용통계연구>, 19, 505-519   과학기술학회마을   DOI
10 Newton, M. A. and Raftery, A. E. (1994). Approximate Bayesian inference with the weighted likelihood bootstrap, Journal of the Royal Statistical Society, Series B, 56, 3-48
11 Jovanis, P. P. and Chang, H. L. (1986). Modelling the relationship of accidents to miles traveled, Transportation Research Record, 1068, 42-51
12 Gelfand, A. E. and Smith, A. F. M. (1990). Sampling based approaches to calculating marginal densities, Journal of the America Statistical Association, 85, 389-409
13 Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741   DOI   ScienceOn
14 Poch, M. and Mannering, F. (1996). Negative binomial analysis of intersection-accident frequencies, Journal of Transportation Engineering, 122, 105-113   DOI   ScienceOn
15 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, 43, 32-43