The Existence Of Random Effects For The Nonlinear Model With Right-Censored Data

With the rapid development of science and technology, the theory and method of system analysis are being increasingly and extensively used. Meanwhile, the theory of systems analysis is continuously developed and improved. Many complex systems usually contain uncertainly, then probabilistic and statistical models are often used, and hence the methods of statistical inference become the important analysis methods in systems analysis. Many system analysis researchers and statisticians have paid great attention to the random effect models because of their wide application. In this paper, We discusses the non-linear random effects model and right censored data model, and right-censored data with non-linear model of the existence of random effects were studied. Focus on likelihood ratio test and restricted likelihood ratio test. The main ideas of the paper are as follow:Chapter 2 describes the system using the maximum likelihood ratio test and restricted likelihood ratio test to test the existence of random effects for linear mixed model. And the random effects & statistics are given the estimated parameters.Chapter 3 introduces the non-linear random effects model of how the existence of the problem into a general linear mixed model of random effects of the problem there. Finally, examples illustrates that our method is available.Chapter 4 studies the nonlinear random effect models with censored data. Then the Laplace methods is employed to deal with these models. Based on this method, the fixed effect parameter estimates and Gauss-Newton formula are obtained.