Zero Inflated Strict Arcsine Regression Model

Zero inflated strict arcsine model is a newly developed model which is found to be appropriate in modeling overdispersed count data. In this study, we extend zero inflated strict arcsine model to zero inflated strict arcsine regression model by taking into consideration the extra variability caused by extra zeros and covariates in count data. Maximum likelihood estimation method is used in estimating the parameters for this zero inflated strict arcsine regression model.

Authors:

• Y. N. Phang
• E. F. Loh

Keywords:

• Overdispersed count data
• maximum likelihood estimation
• simulated annealing.

References:

[1] M. Ridout, C. G. B. Demetrio, and J. Hinde, "Models for count with
many zeros", in: Invited Paper Presented at the 19th International
Biometric Conference, CapeTown, South Africa, 1998, 178.
[2] S. Gurmu and P. K. Trivedi, "Excess zeros in count models for
recreational trips", Journal of Business and Economic Statistics, 14,
1996, 469-477.
[3] K. K. W. Yau and K. C. H. Yip, "On modeling claim frequency data in
general insurance with extra zeros". Insurance: Mathematics and
Economics Vol. 36, Issue 2, 2005, 153-163.
[4] M. L. Dalrymple, I. L. Hudson, and R. P. K. Ford, "Finite mixture, zeroinflated
Poisson and hurdle models with application to SIDS",
Computational Statistics & Data Analysis, 41, 2003, 491-504
[5] R. Winkelmann, Econometric Analysis of Count Data. Springe Verlag,
Berlin, Heidelberg, 2008.
[6] R. Winkelmann, "Health care reform and the number of doctor visits -
An econometric analysis," Journal of Applied Econometrics 19, 2004,
455-472
[7] Y. N. Phang, "Statistical inference for a family of discrete distribution
with cubic variance functions", Unpublished PhD thesis, University
Malaya, Malaysia, 2007
[8] Y. N. Phang, and E. R. Loh. Proceedings: IASC 2008: Joint Meeting of
4th World Conference of the IASC and 6th Conference of the IASC and
6th conference of the Asian Regional Section of the IASC on
Computational Statistic and Data Analysis, Yokohama, Japan, 2008
[9] D.Lambert, "Zero-inflated Poisson regression, with an application to
random defects in manufacturing". Technometrics, 34, 1992, 1-14
[10] A. C. Cameron and P. K. Trivedi, "Regression analysis of count data".
Cambridge University Press. 1998
[11] D. B. Hall, "Zero inflated Poisson and binomial with random effects: a
case study," Biometrics, 56, 2000, 1030-1039
[12] D. Bohning, E. Dietz, P. Schlattman, L. Mendonca and U. Kirchner,
"The zero-inflated Poisson model and the decayed, missing and filled
teeth index in dental epidemiology". Journal of the Royal Statistical
Society, Series A, 1999,162-209
[13] K. K. W. Yau, K. Wang, and A. H.and Lee, "Zero-inflated negative
binomial mixed regression Modeling of overdispersed count data with
extra zeros". Biometrical Journal 45, 4, 2003, 437-452.
[14] F. Famoye and P. S. Karan, " Zero-Inflated Generalized Poisson
Regression Model with an Application to Domestic Violence Data," J of
Data Science 4, 2006, 117-130.
[15] A. C. Mehmet, "Zero-inflated regression models for modeling the effect
of air pollutants on hospital admissions", Polish Journal of Environment
Studies, Vol. 21, No. 3, 2012, 565-568.
[16] B. M. Golam Kibria, " Applicaations of some discrete regression models
for count data", Pakistan Journal of Statistics and Operation research,
Vol11 No. 1, 2006, 1-16.
[17] G. Letac and M. Mora, "Natural real exponential families with cubic
variance functions," The Annals of Statistics, 18, 1990, 1-37.
[18] C. C. Kokonendji and M. Khoudar, "On Strict Arcsine Distribution"
Communications in Statistics. Theory Methods,33(5), 2004, pg993-1006
[19] W. L. Goffe., G. Ferrier and, J. John Rogers, "Global optimization of
statistical functions with simulated annealing. Journal of Econometric,
60 (1/2), 1994, 65-100