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http://dx.doi.org/10.5351/KJAS.2011.24.5.951

Bayesian Inference for the Zero In ated Negative Binomial Regression Model  

Shim, Jung-Suk (Department of Statistics, University Of Seoul)
Lee, Dong-Hee (Department of Business Administration, Kyonggi University)
Jun, Byoung-Cheol (Department of Statistics, University Of Seoul)
Publication Information
The Korean Journal of Applied Statistics / v.24, no.5, 2011 , pp. 951-961 More about this Journal
Abstract
In this paper, we propose a Bayesian inference using the Markov Chain Monte Carlo(MCMC) method for the zero inflated negative binomial(ZINB) regression model. The proposed model allows the regression model for zero inflation probability as well as the regression model for the mean of the dependent variable. This extends the work of Jang et al. (2010) to the fully defiend ZINB regression model. In addition, we apply the proposed method to a real data example, and compare the efficiency with the zero inflated Poisson model using the DIC. Since the DIC of the ZINB is smaller than that of the ZIP, the ZINB model shows superior performance over the ZIP model in zero inflated count data with overdispersion.
Keywords
Bayesian Model Selection; Latent variable; ZINB(Zero-In ated Negative Binomial); MCMC (Markov Chain Monte Carlo);
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1 Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2002). Bayesian measures of model complexity and fit, Journal of the Royal Statistical Society: Series B, 64, 583-639.   DOI   ScienceOn
2 Winkelmann, R. (2003). Econometric Analysis of Count Data, Springer, New York.
3 Yau, K. K. W., Wang, K. and Lee, A. H. (2003). Zero-inflated negative binomial mixed regression modeling of over-dispersed count data with extra zeros, Biometrical, 45, 437-452.   DOI   ScienceOn
4 Ghosh, S. K., Mukhopadhyay, P. and Lu, J. (2006). Bayesian analysis of zero-inflated regression models, Journal of Statistical Planning and Inference, 136, 1360-1375.   DOI   ScienceOn
5 Gurmu, S. and Trivedi, P. K. (1996). Excess zeros in count models for recreational trips, Journal of Business and Economic Statistics, 14, 469-477.   DOI
6 Jang, H. J., Lee, S. B. and Kim, S. W. (2010). Bayesian analysis for zero-inflated regression models with the power prior: Aapplications to road safety countermeasures, Accident Analysis and Prevention, 42, 540-547.   DOI   ScienceOn
7 Kass, R. E. and Raftery, A. E. (1995). Bayes factors, Journal of the American Statistical Association, 90, 773-795.   DOI
8 Lambert, D. (1992). Zero-inflated poisson regression with an application to defects in manufacturing, Technometrics, 34, 1-14.   DOI   ScienceOn
9 Peter, D. H. (2009). A First Course in Bayesian Statistical Methods, Springer.
10 Ridout, M. S., Demetrio, C. G. B. and Hinde, J. P. (1998). Models for count data with many zeros, Proceedings of the XIX th International Biometrics Conference, Cape Town, Invited Papers, 179-192.
11 Ridout, M. S., Hinde, J. and Demetrio, C. G. B. (2001). A score test for testing a zero-inflated poisson regression model against zero-inflated negative binomial alternatives, Biometrics, 57, 219-223.   DOI   ScienceOn
12 Rodrigues, J. (2003). Bayesian analysis of zero-inflated distributions, Communications in Statistics, Theory and Methods, 32, 281-289.   DOI   ScienceOn
13 Seller, C., Stoll, J. R. and Chavas, J. P. (1985). Validation of empirical measures of welfare change: A comparison of nonmarket techniques, Land Economics, 61, 156-175.   DOI   ScienceOn
14 Congdon, P. (2005). Bayesian Models for Categorical Data, John Wiley & Sons, New York.
15 임아경, 오만숙 (2006). 영과잉 포아송 회귀모형에 대한 베이지안 추론: 구강 위생 자료에의 적용, <응용통계연구>, 16, 505-519.   과학기술학회마을   DOI   ScienceOn
16 장학진, 강윤희, 이수범, 김성욱 (2008). 영과잉 회귀모형에 대한 베이지안 분석, <응용통계연구>, 21, 603-613.   과학기술학회마을   DOI   ScienceOn
17 Cameron, A. C. and Trivedi, P. K. (1998). Regression Analysis of Count Data, Cambridge University Press, Cambridge.
18 Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (2004). Bayesian Data Analysis, Chapman & Hall, BocaRaton.