MODELING INSECT-EGG DATA WITH EXCESS ZEROS USING ZERO-INFLATED REGRESSION MODELS

Year 2010, Volume: 39 Issue: 2, 273 - 282, 01.02.2010

Abdullah Yesilova M. Bora Kaydan Yilmaz Kaya

Abstract

As zero-inflated observations occur very often in studies on plant protection, models taking into account zero-inflated observations are frequently required. Especially, zero-inflated observations occur in large numbers for insects whose post-oviposition period lasts long, or that generally lay their eggs during the first days of the oviposition period. For the data used in this study, 1114 (43.84%) of the 2541 observations were zero. In the selection of an appropriate regression model, zeroinflated negative binomial regression was chosen as the best model. In
all regression models, the day of laying and the three different hosts were seen to have a significant effect on daily egg numbers (p < 0.01).

Keywords

Zero-inflated count data, Overdispersion, Zero-inflated models, Hurdle models, 2000 AMS Classification: 91 G 70

MODELING INSECT-EGG DATA WITH EXCESS ZEROS USING ZERO-INFLATED REGRESSION MODELS

Abstract

References

• Agresti, A. Categorical Data Analysis (John and Wiley & Sons, Incorporation, New Jersey, Canada, 1997).
• Banik, S. and Kibria, B. M. G. On some discrete models and their comparisons: An empiri- cal comparative study, Proceedings of The 5th Sino-International Symposium on Probability, Statistics, and Quantitative Management KU/FGU/JUFE Taipei, Taiwan, ROC May 17, 41–56, 2008 (ICAQM/CDMS, 2008).
• B¨ohning, D. Zero-inflated Poisson models and C.A.MAN: A tutorial collection of evidence, Biometrical Journal 40(6), 833–843, 1998.
• B¨ohning, D., Dietz, E. and Schlattmann, P. The zero-inflated Poisson model and the de- cayed, missing and filled teeth index in dental epidemiology, Journal of Royal Statistical Society A 162, 195–209, 1999.
• Cameron, A. C. and Trivedi, P. K. Regression Analysis of Count Data (Cambridge University Press, New York, 1998).
• Cheung, Y. B.Zero-inflated models for regression analysis of count data: A study of growth and development, Statistics in Medicine 21, 1461–1469, 2002.
• Cox, R. Some remarks on overdispersion, Biometrika 70, 269–274, 1983.
• Dalrymple, M. L., Hudson, I. L and Ford, R. P. K. Finite mixture, zero-inflated Poisson and Hurdle models with application to SIDS, Computational Statistics & Data Analysis 41, 491–504, 2003.
• Frome, E. D., Kutner, M. H. and Beauchamp, J. J. Regression analysis of Poisson-distributed data, Journal of American Statistical Association 68 (344), 935–940, 1973.
• Hilbe, J. M. Negative Binomial Regression (Cambridge, UK, 2007).
• Jansakul, N. Fitting a zero-inflated negative binomial model via R, In: Proceedings 20th International Workshop on Statistical Modelling. Sidney, Australia, 277–284, 2005.
• Kaydan, M. B. and Kılın¸cer, N. Investigation on egg laying character of Phenacoccus aceris (Signoret) (Coccoidea:Hemiptera: Pseudococcidae) on different host plant species, Ankara University Journal of Agriculture 13 (3), 224–230, 2007.
• Khoshgoftaar, T. M., Gao, K. and Szabo, R. M. Comparing software fault predictions of pure and zero-inflated Poisson regression models, International Journal of Systems Science 36(9), 707–715, 2005.
• Kibria, B. M. G. Applications of some discrete regression models for count data, Pakistan Journal of Statistics and Operation Research, 2 (1), 1–16, 2006.
• Lambert, D. Zero-inflated Poisson regression, with an application to defects in manufac- turing. Technometrics 34(1), 1–13, 1992.
• Lawles, J. F. Negative binomial and mixed Poisson regression, The Canadian Journal of Statistcs 15 (3), 209–225, 1987.
• Lee, A. H., Wang, K. and Yau, K. K. W. Analysis of zero-inflated Poisson data incorporating extent of exposure, Biometrical Journal 43(7), 963–975, 2001.
• Long, J. S. and Freese, J. Regression Models for Categorical Depentent Variable Using Stata (Stata Press Publication, StataCorp LD Collage Station, Texas, USA , 2006).
• Ridout, M., Hinde, J. and Demetrio, C. G. B. A score test for a zero-inflated Poisson re- gression model against zero-inflated negative binomial alteratves, Biometrics 57, 219–233, 2001. [20] Rose, C. E., Martin, S. W., Wannemuehler, K. A. and Plikaytis, B. D. On the zero-inflated and Hurdle models for modelling vaccine adverse event count data, Journal of Biopharma- ceutical Statistics 16, 463–481, 2006.
• SAS. SAS/Stat Software Hangen and Enhanced (SAS Institute Incorporation, USA , 2007). [22] Senapati, S. K. and Ghose, S. K. Biology of the mealybug Planococcoides bengalensis Ghosh and Ghose (Homoptera: Pseudococcidae), Environment & Ecology 6, 648–652, 1998.
• Stokes, M. E., Davis, C. S. and Koch, G. G. Categorical Data Analysis Using the SAS System (John Wiley & Sons Incorporated, USA, 2000).
• Wang, P., Puterman, M. L., Cockburn, I. M. and Le, N. Mixed Poisson regression models with covariate dependent rates, Biometrics 52, 381–400, 1996.
• Yau, K. K. W. and Lee, A. H. Zero-inflated Poisson regression with random effects to eval- uate an occupational injury prevention programme, Statistics in Medicine 20, 2907–2920, 2001. [26] Yau, Z. Score Tests for Generalization and Zore-Inflation in Count Data Modeling (Un- published Ph.D. Dissertation, University of South Caroline, Columbia, 2002).
• Yesilova, A. The Use of Mixed Poisson Regression Models for Categorical Data in Biology (Unpublished Ph.D. Dissertation, Y¨uz¨unc¨u Yıl University, Van, Turkey, 2003).