Bayesian Analysis for the Zero-inflated Regression Models

- Journal title : Korean Journal of Applied Statistics
- Volume 21, Issue 4, 2008, pp.603-613
- Publisher : The Korean Statistical Society
- DOI : 10.5351/KJAS.2008.21.4.603

Title & Authors

Bayesian Analysis for the Zero-inflated Regression Models

Jang, Hak-Jin; Kang, Yun-Hee; Lee, S.; Kim, Seong-W.;

Jang, Hak-Jin; Kang, Yun-Hee; Lee, S.; Kim, Seong-W.;

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;

Language

Korean

Cited by

1.

COTS 하드웨어 컴포넌트 기반 임베디드 소프트웨어 신뢰성 모델링,구태완;백종문;

한국정보과학회논문지:소프트웨어및응용, 2009. vol.36. 8, pp.607-615

2.

허들모형에 대한 베이지안 추론,선지영;심정숙;정병철;

Journal of the Korean Data Analysis Society, 2014. vol.16. 4B, pp.1837-1847

References

1.

임아경, 오만숙 (2006). 영과잉 포아송 회귀모형에 대한 베이지안 추론: 구강위생 자료에의 적용, <응용통계연구>, 19, 505-519

2.

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

3.

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

4.

Jeffreys, H. (1961). Theory of Probability, (Third edition), Oxford University Press, Oxford

5.

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

6.

Jovanis, P. P. and Chang, H. L. (1986). Modelling the relationship of accidents to miles traveled, Transportation Research Record, 1068, 42-51

7.

McCulloch, R. and Rossi, P. E. (1991). A bayesian approach to testing the arbitrage pricing theory, Journal of Econometrics, 49, 141-168

8.

Miaou, S. P. and Lum, H. (1993). Modeling vehicle accidents and highway geometric design relationships, Accident Analysis and Prevention, 25, 689-709

9.

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

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.

Poch, M. and Mannering, F. (1996). Negative binomial analysis of intersection-accident frequencies, Journal of Transportation Engineering, 122, 105-113

12.

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

13.

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

14.

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

15.

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