Bivariate Zero-Inflated Negative Binomial Regression Model with Heterogeneous Dispersions

서로 다른 산포를 허용하는 이변량 영과잉 음이항 회귀모형

  • Kim, Dong-Seok (Department of Mathematics, Kyonggi University) ;
  • Jeong, Seul-Gi (Department of Mathematics, Kyonggi University) ;
  • Lee, Dong-Hee (Department of Business Administration, Kyonggi University)
  • Received : 20110700
  • Accepted : 20110800
  • Published : 2011.09.30


We propose a new bivariate zero-inflated negative binomial regression model to allow heterogeneous dispersions. To show the performance of our proposed model, Health Care data in Deb and Trivedi (1997) are used to compare it with the other bivariate zero-inflated negative binomial model proposed by Wang (2003) that has a common dispersion between the two response variables. This empirical study shows better results from the views of log-likelihood and AIC.


  1. 이동희, 정병철 (2010). 코폴라를 활용한 이변량 제로팽창 일반화 포아송 회귀모형, Journal of the Korean Data Analysis Society, 12, 1473-1484.
  2. Cameron, A. C., Li, T., Trivedi, P. K. and Zimmer, D. M. (2004). Modelling the differences in counted outcomes using bivariate copula models with application to mismeasured counts, Econometrics Journal, 7, 566-584.
  3. Deb, P. and Trivedi, P. K. (1997). Demand for medical care by the elderly: A finite mixture approach, Journal of Applied Econometrics, 12, 313-336.<313::AID-JAE440>3.0.CO;2-G
  4. Dempster, A. P., Laird, N. M., Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discusiion), Journal of the Royal Statistical Society B, 39, 1-38.
  5. Gupta, P. L., Gupta, R. C. and Tripathi, R. C. (2004). Score test for zero inflated generalized Poisson regression model, Communications in Statistics - Theory and Methods, 33, 47-64.
  6. Gurmu, S. and Elder, J. (2000). Generalized bivariate Count data regression models, Economics Letters, 68, 31-36.
  7. Lee, J., Jung, B. C. and Jin, S. H. (2007). Tests for zero inflation in a bivariate zero-inflated Poisson model, Statistica Neerlandica, 63, 400-417.
  8. Li, C. S., Lu, J. C., Park, J., Kim, K., Brinkley, P. A. and Peterson, J. (1999). Multivariate zero-inflated Poisson models and their applications, Technometrics, 41, 29-38.
  9. Marshall, A. W. and Olkin, I. (1990). Multivariate distributions generated from mixtures of convolution and product families, In H.W. Block, A.R. Sampson and T.H. Savits(eds), Topics in Statistical Dependence, 372-393. IMS Lecture Notes - Monograph Series, 16.
  10. Munkin, M. K. and Trivedi, P. K. (1999). Simulated maximum likelihood estimation of multivariate mixed-Poisson regression models, with application, Econometrics Journal, 2, 29-48.
  11. So, S., Chun, H. and Jung, B. C. (2011). Bivariate negative binomial regression model with heterogeneous dispersions, Communications in Statistics - Theory and Methods, Submitted.
  12. Van den Broek, J. (1995). A score test for zero inflation in a Poisson distribution, Biometrics, 51, 738-743.
  13. Walhin, J. F. (2001). Bivariate ZIP models, Biometrical Journal, 43, 147-160.<147::AID-BIMJ147>3.0.CO;2-5
  14. Wang, K., Lee, A. H., Yau, K. K. W. and Carivick, P. J. W. (2003). A bivariate zero-inflated Poisson regression model to analyze occupational injuries, Accident Analysis and Prevention, 35, 625-629.
  15. Wang, P. (2003). A bivariate zero-inflated negative binomial regression model for count data with excess zeros, Economics Letters, 78, 373-378.