Statistical Analysis On A Special Longitudinal Data Model

With the rapid development of science and technology, the theory and method of statistical analysis are continuously developed and improved. In the process of statistical analysis, it is a very important research topic to establish a mathematical model. Many complex systems usually contain uncertainty, then probabilistic and statistical models are often used, and hence the methods of statistical inference become the important analysis methods in systems analysis. Usually people used to use regression analysis to deal with these problems. The theory and methods of regression analysis develop rapidly. It is not only an important branch of statistics, but also widely used in all fields. The theory of regression analysis with the continuous development of longitudinal data on the regression model has become an important research topic, and in medical, engineering and other fields has been widely applied. In the process of statistical analysis, it is a very important research topic to establish a mathematical model. For example, the engineers of steelworks want to have a mathematical model about the process of steelmaking to implement computer automatic control; Weather researchers want to have a mathematical model about pneumatic, rainfall and winds to forecast weather; The experts on urban planning want to have a mathematical model about a large system including population, traffic, energy and pollution to provide the scientific data to help leadership to make urban development planning and decision-making.We discuss Longitudinal data of a special kind of non-linear random effects model, and because of the large value of the distribution of variables were analyzed, as well as non-linear random effects model of the impact analysis conducted in-depth discussions.In Chapter 2, we discussed the non-linear random effects model, and given the model estimates of fixed effects parameters as well as the Gauss-Newton iteration algorithm.Chapter 3 based on the study of non-linear random effects model parameter estimation , Systematically studied the effect of a random statistical diagnosis of non-linear model to study the impact of the model analysis, the mean shift model, Score statistic of outlier. At the same time, derived from the impact of the strong point of identification or diagnosis of abnormal point statistics such as the generalized Cook distance, likelihood distance, and by the residuals and students of residuals, leverage. And then discussed the local impact analysis, and conducted a case study. A real example illustrates that our method is available.