Empirical Likelihood Estimation For Partially Linear Mixed Effects Model With Longitudinal Data

Longitudinal data refers to the data collected by repeated measurement of each subject at different time points.Hence,data within the same subject is correlated.When modeling longitudinal data,we must take into account the dependencies within the group,otherwise it will reduce the efficiency of inference.Therefore,the mixed effects model with random effects is one of the common models when analyzing longitudinal data.Although it can be used to analyze the longitudinal data and has a strong ability to explain,excessive assumption of linear relationship between the response variable and covariates will lead to the estimation of the parameters of interest inconsistent easily.Therefore,Partial Linear Mixed Effects is formed by adding a semi-parametric component into the mixed effect model.PLMM include not only fixed and random effects,but also parametric and non-parametric parts.The model makes full use of the information of the data and has a good applicability and flexibility.Therefore,the model is widely used in the analysis of longitudinal data,and the research on the statistical inference of PLMM based on longitudinal data has certain theoretical significance and practical value.Specifically,the paper includes the following parts:The first chapter introduces the background and significance of the longitudinal data,and then discusses the background and estimate method of the model,finally introduces the development status and the inference process of the empirical likelihood method.The second chapter discusses the problem of parameter estimation in PLMM,and make use of generalized empirical likelihood method to estimate the parameters of the model.Therefore,we obtain the estimators of parametric component,nonparametric component and variance component.Besides,the large sample properties of the estimators are proved under certain conditions.The third chapter discusses the parameter estimation of Generalized Partial Linear Mixed Effects Model,and make use of generalized empirical likelihood method to estimate the parameters of the model.Therefore,we obtain the estimators of parametric component,nonparametric component and variance component.Besides,the large sample properties of the estimators are proved under certain conditions.The fourth chapter carries on the empirical analysis,and applies the above research method to the medical example of the child respiratory tract infection.Which is used to illustrate the validity of the proposed method.The fifth chapter summarizes the results of this study,the experience in the research process and the worthy of further study.The innovations of this paper are embodied in the following two aspects:(1)The generalized empirical likelihood method is used to study the statistical inference of generalized linear mixed effects model with longitudinal data for the first time,as well as the application range of the generalized empirical likelihood method is extended.(2)Considering the intragroup dependence of the longitudinal data,we add the covariance matrix of the group to construct the parameter statistics.Therefore,the generalized empirical log likelihood ratio function is obtained.The effectiveness of model statistical inference has been improved by taking into account the intragroup dependencies of data.