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Mean regression model for the zero-truncated Poisson distribution and its generalization

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Listed:
  • Li, Xun-Jian
  • Sun, Yuan
  • Tian, Guo-Liang
  • Liang, Jiajuan
  • Shi, Jianhua

Abstract

Zero-truncated count data (e.g., days of staying in hospital; survival weeks of female patients with breast cancer) often arise in various fields such as medical studies. To model such data, the zero-truncated Poisson (ZTP) distribution is commonly utilized to investigate the relationship between the response counts and a set of covariates. For existing ZTP regression models, it is very hard to explain the regression coefficients β or it is quite difficult to perform a constrained optimization to calculate the maximum likelihood estimates (MLEs) of β. This paper aims to introduce a new mean regression model for the ZTP distribution with a clear interpretation about the regression coefficients. Because of a challenge that the original Poisson mean parameter λi cannot be expressed explicitly by the ZTP mean parameter μi, an embedded Newton–Raphson algorithm is developed to calculate the MLEs of regression coefficients. The construction of bootstrap confidence intervals is presented and three hypothesis tests (i.e., the likelihood ratio test, the Wald test and the score test) are considered. Furthermore, the ZTP mean regression model is generalized to the mean regression model for the k-truncated Poisson distribution. Simulation studies are conducted and two real data are analyzed to illustrate the proposed model and methods.

Suggested Citation

  • Li, Xun-Jian & Sun, Yuan & Tian, Guo-Liang & Liang, Jiajuan & Shi, Jianhua, 2023. "Mean regression model for the zero-truncated Poisson distribution and its generalization," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:csdana:v:179:y:2023:i:c:s0167947322002304
    DOI: 10.1016/j.csda.2022.107650
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    References listed on IDEAS

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    1. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273.
    2. M. Khorashadizadeh & A. H. Rezaei Roknabadi & G. R. Mohtashami Borzadaran, 2010. "Variance residual life function in discrete random ageing," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 67-75.
    3. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    4. Rainer Winkelmann, 2008. "Econometric Analysis of Count Data," Springer Books, Springer, edition 0, number 978-3-540-78389-3, December.
    5. Hausman, Jerry & Hall, Bronwyn H & Griliches, Zvi, 1984. "Econometric Models for Count Data with an Application to the Patents-R&D Relationship," Econometrica, Econometric Society, vol. 52(4), pages 909-938, July.
    6. Grogger, J T & Carson, Richard T, 1991. "Models for Truncated Counts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(3), pages 225-238, July-Sept.
    7. Gurmu, Shiferaw, 1991. "Tests for Detecting Overdispersion in the Positive Poisson Regression Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(2), pages 215-222, April.
    8. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    9. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    10. Gurmu, Shiferaw & Trivedi, Pravin K., 1992. "Overdispersion tests for truncated Poisson regression models," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 347-370.
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