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Zero inflated Poisson distribution in equidispersed data with excessive zeros

Author Affiliations

  • 1University of Botswana, Gaborone, Botswana
  • 2University of Botswana, Gaborone, Botswana

Res. J. Mathematical & Statistical Sci., Volume 8, Issue (1), Pages 31-34, January,12 (2020)

Abstract

From the literature, choosing the right model when the dependent variable is a count outcome remains a problem in literature. For count outcome variable with overdispersion due to excessive zero counts (zero inflation), Zero Inflated distributions such as Zero Inflated Poisson/Negative Binomial are usually considered to find better fitting models. Moreover, numerous studies suggested that if the data is characterized by equidispersion with signs of zero inflation, Zero Inflated Poisson (ZIP) distribution should be applied. Therefore, the aim of this paper is to investigate if ZIP distribution should substitute standard Poisson distribution if there are signs of zero inflation in equidispersed data. Equidispersed simulated and real life datasets with signs of zero inflation were used for the analysis. Evidence of equidispersion and zero inflation were tested and goodness-of-fit tests for both Poisson and ZIP distributions were obtained. Results revealed that for an equidispersed data with signs of zero inflation, standard Poisson performed better than ZIP distribution.

References

  1. Walters G.D. (2007)., Using poisson class regression to analyze count data in correctional and forensic psychology: A relatively old solution to a relatively new problem., Criminal Justice and Behavior, 34(12), 1659-1674.
  2. Long J.S. (1997)., Regression Models for Categorical and Limited Dependent Variables: Advanced Quantitative Techniques in the Social Sciences., Sage Publications, Thousand Oaks, 7.
  3. Muoka A.K., Waititu A. and Ngesa O.O. (2016)., Statistical models for count data., Science Journal of Applied Mathematics and Statistics, 4(6), 256-262.
  4. Ismail N. and Zamani H. (2013)., Estimation of claim count data using negative binomial, generalized poisson, zero-inflated negative binomial and zero-inflated generalized poisson regression models., In Casualty Actuarial Society E-Forum, 41, 1-28.
  5. Akın D. (2011)., Analysis of highway crash data by negative binomial and poisson regression models., Second International Symposium on Computing in Science and Engineering, Kusadasi, Izmir, Turkey, 1.
  6. Chen F., Chen S. and Ma X. (2016)., Crash frequency modeling using real-time environmental and traffic data and unbalanced panel data models., International journal of environmental research and public health, 13(6), 609.
  7. Dong C., Nambisan S.S., Richards S.H. and Ma Z. (2015)., Assessment of the effects of highway geometric design features on the frequency of truck involved crashes using bivariate regression., Transportation Research Part A: Policy and Practice, 75, 30-41.
  8. Yaacob W.F.W., Lazim M.A. and Wah Y.B. (2010)., A practical approach in modelling count data., In Proceedings of the Regional Conference on Statistical Sciences, Malaysia, 176-183.
  9. Edwin T. (2014)., Power series distributions and zero-infalted models., Doctorate Thesis. University of Nairobi.
  10. Perumean-Chaney S.E., Morgan C., McDowall D. and Aban I. (2013)., Zero-inflated and overdispersed: what′s one to do?., Journal of Statistical Computation and Simulation, 83(9), 1671-1683.
  11. Elhai J.D., Calhoun P.S. and Ford J.D. (2008)., Statistical procedures for analyzing mental health services data., Psychiatry research, 160(2), 129-136.
  12. Bortkiewicz L. (1898)., Das Gesetz der kleinen Zahlen., BG Teubner, Leipzig.
  13. Alam N. (2015)., Detecting Overdispersion in Count Data: Comparison of Tests., Doctorate Thesis. East West University.
  14. Dean C. and Lawless J.F. (1989)., Tests for detecting overdispersion in Poisson regression models., Journal of the American Statistical Association, 84(406), 467-472.
  15. Cameron A.C. and Trivedi P.K. (1990)., Regression-based tests for overdispersion in the Poisson model., Journal of econometrics, 46(3), 347-364.