Overdispersion study of poisson and zero-inflated poisson regression for some characteristics of the data on lamda, n, p
(1) * Lili Puspita Rahayu Mail (Ministry of Education and Culture of The Republic of Indonesia, Indonesia)
(2) Kusman Sadik Mail (Bogor Agriculture University, Indonesia)
(3) Indahwati Indahwati Mail (Bogor Agriculture University, Indonesia)
*corresponding author

Abstract


Poisson distribution is one of discrete distribution that is often used in modeling of rare events. The data obtained in form of counts with non-negative integers. One of analysis that is used in modeling count data is Poisson regression. Deviation of assumption that often occurs in the Poisson regression is overdispersion. Cause of overdispersion is an excess zero probability on the response variable. Solving model that be used to overcome of overdispersion is zero-inflated Poisson (ZIP) regression. The research aimed to develop a study of overdispersion for Poisson and ZIP regression on some characteristics of the data. Overdispersion on some characteristics of the data that were studied in this research are simulated by combining the parameter of Poisson distribution (λ), zero probability (p), and sample size (n) on the response variable then comparing the Poisson and ZIP regression models. Overdispersion study on data simulation showed that the larger λ, n, and p, the better is the model of ZIP than Poisson regression. The results of this simulation are also strengthened by the exploration of Pearson residual in Poisson and ZIP regression.

Keywords


Overdispersion; Poisson; Zero Inflated Poisson Regression; Simulation Data

   

DOI

https://doi.org/10.26555/ijain.v2i3.73 		      

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References


N. Jansakul and J. P. Hinde, “Score tests for zero-inflated Poisson models,” Comput. Stat. Data Anal., vol. 40, no. 1, pp. 75–96, 2002.

N. Ismail and A. A. Jemain, “Handling overdispersion with negative binomial and generalized Poisson regression models,” in Casualty Actuarial Society Forum, 2007, pp. 103–158.

M. Ridout, C. G. B. Demétrio, and J. Hinde, “Models for count data with many zeros,” in Proceedings of the XIXth international biometric conference, 1998, vol. 19, pp. 179–192.

D. Lambert, “Zero-inflated Poisson regression, with an application to defects in manufacturing,” Technometrics, vol. 34, no. 1, pp. 1–14, 1992.

M. Xie, B. He, and T. N. Goh, “Zero-inflated Poisson model in statistical process control,” Comput. Stat. Data Anal., vol. 38, no. 2, pp. 191–201, 2001.

S. Numna, “Analysis of extra zero counts using zero-inflated Poisson models,” Prince of Songkla University, 2009.

J. W. Hardin, J. M. Hilbe, and J. Hilbe, Generalized linear models and extensions. Stata press, 2007.

R. Savic and M. Lavielle, “Performance in population models for count data, part II: a new SAEM algorithm,” J. Pharmacokinet. Pharmacodyn., vol. 36, no. 4, pp. 367–379, 2009.

A. C. Cameron and P. K. Trivedi, Regression analysis of count data, vol. 53. Cambridge university press, 2013.

M. Flynn and L. A. Francis, “More flexible GLMs zero-inflated models and hybrid models,” Casualty Actuar. Soc, vol. 2009, pp. 148–224, 2009.

G. Casella and R. L. Berger, Statistical inference, vol. 2. Duxbury Pacific Grove, CA, 2002.




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