- Volume 25 Issue 5
Poisson regression and negative binomial regression are usually used to analyze counting data; however, these models are unsuitable for fit zero-inflated data that contain unexpected zero-valued observations. In this paper, we review the zero-inflated regression in which Bernoulli process and the counting process are hierarchically mixed. It is known that zero-inflated regression can efficiently model the over-dispersion problem. Vuong statistic is employed to compare performances of the zero-inflated models with other standard models.
Negative binomial regression;Poisson regression;Vuong statistic
- Agarwal, D. K., Gelfand, A. E. and Citron-Pousty, S. (2002). Zero-inflated models with application to spatial count data, Environmental and Ecological Statistics, 9, 341-355. https://doi.org/10.1023/A:1020910605990
- Cameron, A. C. and Trivedi, P. K. (1986). Econometric models based on count data: Comparisons and applications of some estimators and tests, Journal of Applied Econometrics, 1, 29-53. https://doi.org/10.1002/jae.3950010104
- Chernoff, H. (1954). On the distribution of the likelihood ratio, Annals of Mathematical Statistics, 25, 573-578. https://doi.org/10.1214/aoms/1177728725
- Choi, K., Kim, B., Bae, W., Jung, W. and Cho, Y. (2008). Developing the index of foodborne disease occurrence, The Korean Journal of Applied Statistics, 21, 649-658. https://doi.org/10.5351/KJAS.2008.21.4.649
- Lambert, D. (1992). Zero-inflated Poisson regression models with an application to defects in manufacturing, Technometrics, 34, 1-14. https://doi.org/10.2307/1269547
- Lawless, J. F. (1987). Negative binomial and mixed Poisson regression, The Canadian Journal of Statistics, 15, 209-225. https://doi.org/10.2307/3314912
- Miller, J. M. (2007). Comparing Poisson, Hurdle, and ZIP model t under varying degrees of skew and zero-inflation, University of Florida, DAI-A 68/06, Dec 2007.
- SAS Institute Inc. (2008). SAS/ETS User's Guide (Version 9.2, Chap.10, The COUNTREG Procedure), SAS Institute Inc., Cary, NC, USA
- Vuong, Q. (1989). Likelihood ratio tests for model selection and non-nested hypothesis, Econometrica, 57, 307-334. https://doi.org/10.2307/1912557