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

Li，Xun Jian1; Sun，Yuan1; Tian，Guo Liang1,3; Liang，Jiajuan2; Shi，Jianhua3

2023-03-01

10.1016/j.csda.2022.107650

COMPUTATIONAL STATISTICS & DATA ANALYSIS   Impact Factor & Quartile

0167-9473

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 λ cannot be expressed explicitly by the ZTP mean parameter μ, 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.

Embedded Newton–Raphson algorithm k-truncated Poisson Mean regression Minorization–maximization algorithm Zero-truncated Poisson

English

First

National Natural Science Foundation of China[12171225];Natural Science Foundation of Fujian Province[2020J01794];

MATHEMATICS

2-s2.0-85140748505

Scopus

1.Department of Statistics and Data Science,Southern University of Science and Technology,Shenzhen,Guangdong Province,518055,China
2.Department of Statistics and Data Science,Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science,BNU–HKBU United International College,Zhuhai,Guangdong Province,519087,China
3.School of Mathematics and Statistics,Minnan Normal University,Zhangzhou,Fujian Province,363000,China

Li，Xun Jian,Sun，Yuan,Tian，Guo Liang,et al. Mean regression model for the zero-truncated Poisson distribution and its generalization[J]. COMPUTATIONAL STATISTICS & DATA ANALYSIS,2023,179.

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,179.

Li，Xun Jian,et al."Mean regression model for the zero-truncated Poisson distribution and its generalization".COMPUTATIONAL STATISTICS & DATA ANALYSIS 179(2023).