Generalization And Application Of Zero - Expansion Negative Binomial Regression Model

Count data exists in such domains as public health, actuarial science, agriculture, and so on. As the class of generalized linear models, however, Poisson regression is limited because it assumes the mean is equal to the variance and events are independent, which are quite difficult to achieve in practice. Furthermore, in certain circumstances there will be more or excess zeros than the Poisson regression model would predict, which is known as zero-inflated phenomenon. If so, zero-inflated model may function better in these cases. Currently, the ZIP model is preferably adopted to deal with a random event containing excess zero-inflated data in unit time.In practical applications, the other phenomenon concerning the zero-inflated data is as follows:1) the over-dispersion produced by non-zero counts data,2) the internal relevance of the longitudinal data3) the missing of the observationsTherefore, it is necessary to improve the ZIP regression model. And the present author will utilize the better-functioning ZI model to analyze the zero-inflated data in a practical and fitting way. This paper only focuses on phenomenon1) and2) mentioned above, leaving phenomenon3) for future study.The problem of over-dispersion can be solved by the fixed effect ZINB model, which is a statistical model based on NB II distribution. After the brief introduction to some background academic knowledge (like ZI data, development of the ZI model, etc.), the fixed effect ZINB model will be discussed systematically (including parameter estimation aspect, ZI parameter hypothesis testing aspect, over-dispersion hypothesis testing aspect and statistical diagnosis aspect). Then, the NBK distribution-based ZINBK model is to be studied from the same aspects, and the good or bad side of the fitting effect will be worked out respectively after the case study through NB, ZINB, and ZINBK model. Afterwards, the same research method and research process will apply to the random effect ZINKM model, and on this basis it can conclude the optical and worst of the fitting effect respectively (ZINB, ZIPM, ZINBM, ZINBKM). Finally, the paper will roughly describe and indicate how the relevant future study is to be conducted.