Estimation For A Class Of Nonlinear Random Effect Model

Mixed effects model is an important tool for the analysis of correlated data,such as longitudinal data and repeated measurement data,it is also widely applied in finance,economy and other fields.In recent years,many scholars interested in mixed effects model.Partially linear model is special case of partially nonlinear model,we can combine the advantages of these models by studying the estimation problem of the partially nonlinear random effect model.And it will have a wider application prospect in the partially nonlinear random effect model.Usually,we use local method to deal with function item.But in this article,we use B-spline method to handle function item and it will make up the disadvantages of local method.We consider the estimation for a class of nonlinear random effect model.It in-cludes partially linear random effects model,partially nonlinear random effects model and partially nonlinear random effects model for longitudinal data.In order to estimate the link function,we propose generalized least square estimate(GLSE)and B-splines estimate methods.Further,we use the estimator and Gauss-Newton method to con-struct the estimation of parameter.Finally,we also consider the estimation for the variance components.The consistency and the asymptotic normality of the estimator will be given.A simulation study and real example will show the effectiveness of the methodology.