Some Discussions Of Nonlinear Logistic Regression Models

With the rapid development of modern society, more and more statistical models are widespread used to solve realistic questions in some important fields, such as economy、 epidemiologic research、medicinal valuation、clinical trials and so on. As a kind of frequently-used, Logistic regression model regression model is an analysis method which applied to all fields of epidemiology and medicine, it can explore some risk factors of disease, for example, and then predict the probability whether or not a certain disease happens according to the risk factors, and can estimate how the probability of somebody get the disease or be in a certain risk is. But there are some limitations under many circumstances, because there is a linear relationship between the independent variable and Logit (p) in Logistic regression model, or it become difficult to analysis the data which is independently and two-point distribution by used the traditional Logistic regression model. The statistics analysis method which is fit for this data is the extending of the traditional Logistic regression model. Nonlinear Logistic regression model is an extending form of the traditional Logistic regression model, and be contributed to perfect the theoretical foundation though the theoretical research. It can solve a large of society practical problems such as epidemiologic research and clinical trials.This paper researches the theoretical basis of the nonlinear Logistic regression model at first, and gives the parameter estimation of the model with method of maximum likelihood estimation. In second, the differential geometric approach to nonlinear Logistic regression model is used to establish the general connection between parameter confidence regions and the curvature of statistical models, and three types of formulations of the parameter and subset parameters are obtained in terms of curvature, and then derives stochastic expansion related to the maximum likelihood estimator as a basic tool to investigate the asymptotic. In addition, this paper researches the parameter estimation、confidence regions and stochastic expansions of the nonlinear mixed Logistic regression model. Finally, this paper systematically discussed statistical diagnosis of the nonlinear Logistic regression model by case deletion model (CDM) and mean-shift outlier model (MSOM), and derives the diagnostic statistics to distinguish strong influence points or the diagnosis of outliers, such as Score statistics, Cook distance, Pearson residuals and Likelihood distance, the case studies are given to illustrate our results.