Statistical Research And Application Of Poisson Regression Model

Linear regression model is a hot issue in the research of the statistics, and it hasa wide range of applications in the economic, financial, medical, education and otherfields. However, in many cases, the linear regression model will be limited. Nelderand Wedderburn (1972) extended the linear regression model, and generalized linearmodel (GLM) was proposed, which can be applied to many fields of data analysisproblems. In addition to the classical linear regression model as a special case hasbeen widely applied in various fields, especially the Logistic model and Poissonmodel.In this paper, based on introductions of the definition,parameter estimation andparametric test of the classical Poisson regression model,, and this paper mainlyresearches on the Statistical diagnosis models by constructing the diagnosis statistics,and diagnosis index figure to look for strong influence points, and using the hatmatrix decomposition principle and mathematical statistics principle to explore neweffective diagnostic indicator diagram to determine strong influence points.At last,through the empirical analysis shows that the study is useful and effective.In the article, based on the semiparametric model of longitudinal data, thesemiparametric Poisson regression model of the longitudinal data is established,estimate the parameters in the model and study the information matrix of theparameters, meanwhile its calculation method is given, and we design the Newton--Raphson iteration algorithm for solving nonlinear equations, finally the estimate ofunknown parameters is obtained.