Models

Year 2010, Volume: 23 Issue: 2, 131 - 136, 31.03.2010

Abdullah Yesılova , Yılmaz Kaya Barıs Kakı İsmail Kasap

Abstract

Analysis of Plant Protection Studies with Excess Zeros Using Zero-Inflated and Negative Binomial Hurdle Models

Abstract

In this study, the analysis of data with many zeros for plant protection area was carried out by using the models of Poisson Regression (PR), negative binomial (NB) regression, zero-inflated Poisson (ZIP) regression, zeroinflated negative binomial (ZINB) regression, and negative binomial hurdle (NBH) model. As zero-inflated observations are too much in the studies, done in the plant protection area; models considering zero-inflated observations are frequently required. Mites (Acari: Tetranychidae; Stigmaeidae), the basic material of this study, can reach to quite high amounts under convenient temperature (18-32°C temperature). The fact that deviance obtained from PR model together with Pearson Chi-square and deviance goodness of statistics came about quite higher than the value of (1) represented that there was an overdispersion in data set. In the selection of appropriate regression model, Akaiki information criteria and Bayesian information criteria were used. At the end of these information criteria, ZINB regression was chosen as the best model. In ZINB model, the effects of Zetzellia mali, temperature, and periods were significant on the total P. ulmi number (p<0.01), while applying insecticide was insignificant (p>0.05).

 

 Key Words: Zero-inflated data; overdispersion; Negative binomial Hurdle model; Zero-inflated models.

 

Keywords

Zero-inflated data, overdispersion, Negative binomial Hurdle model, Zero-inflated models

References

• Agresti, A., “Categorical Data Analysis”, New Jersey, Canada, John and Wiley & Sons Incorporation, (1997).
• Böhning, D., “Zero- Inflated Poisson Models and C. A. MAN. A Tutorial Collection of Evidence”, Biometrical Journal, 40(7): 833-843 (1998).
• Böhning, D., Dietz, E., Schlattmann, P., “The Zero-Inflated Poisson Model and the Decayed, Missing and Filled Teeth Index in Dental Epidemiology”, Journal of Royal Statistical Society A, 162: 195–209 (1999).
• Cameron, A.C., Trivedi, P.K., “Regression Analysis of Count Data”, New York, Cambridge University Pres, (1998). [5] 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., 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., Beauchamp, J.J. “Regression Analysis of Poisson- Distributed Data”, Association, 68(344): 935-940 (1973). American Statistical
• 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).
• Kasap, İ., Çobanoğlu, S., “Mite (Acari) Fauna in Apple Orchards of Around The Lake Van Basin of Turkey”, Türk. Entomol. Journal. 31 (1): 135-149 (2007).
• Khoshgoftaar, T.M., Gao, K., Szabo, R.M., “Comparing Software Fault Predictions of Pure and Zero- inflated Poisson Regression Models”, International Journal of Systems Science, 36(11): 705-715 (2005).
• Lambert, D., “Zero-Inflated Poisson Regression, with an Application to Defects in Manaufacturin”, 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., Yau, K.K.W., “Analysis of Zero-Inflated Poisson Data Incorporating Extent of Exposure”, Biometrical Journal, 43(8):963-975 (2001).
• Long, J.S., Freese, J., “Regression Models for Categorical Depentent Variable Using Stata”, A Stata Pres Publication, USA, (2006).
• McCullagh, P., Nelder, J.A., “Generalized Linear Models”. Second Edition, Chapmann and Hall, London, (1989).
• Ridout, M., Hinde, J., Demetrio, C.G.B., “A Score Test for a Zero-Inflated Poisson Regression Model Against Alteratves”. Biometrics, 57: 219-233 (2001). Negative Binomial
• Rose, C.E, Martin, S.W., Wannemuehler, K.A., Plikaytis, B.D., “On the of Zero-inflated and Hurdle Models for Medelling Vaccine Adverse event Count Data”, Journal of Biopharmaceutical Statistics, 16: 463-481(2006).
• SAS. SAS/Stat. Software, Hangen and Enhanced, USA: SAS, Institute. Incorporation (2007). [21] Stokes, M.E., Davis, C.S., Koch, G.G., “Categorical Data Analysis Using the SAS System”, USA; John and Wiley & Sons Incorporation (2000).
• Wang, P., Puterman, M.L., Cockburn, I.M., Le, N., “Mixed Poisson Regression Models with Covariate Dependent Rates”, Biometrics, 52: 381-400 (1996).
• Yau, K.K.W., Lee, A.H., “Zero-Inflated Poisson Regression with Random Effects to Evaluate an Occupational Injury Prevention Programme”, Statistics in Medicine, 20: 2907-2920 (2001).
• Yau, Z., “Score Tests for Generalization and Zore- Inflation in Count Data Modeling”, Unpublished Ph. D. Dissertation, University of South Caroline, Columbia (2006).
• Yeşilova, A., Kaki, B., Kasap, İ., “Regression methods Used in Modelling of Dependent Variable Obtained Data”,Journal of Statistical Research, 05:1-9 (2007). Zero-Inflated Count