A New Profile Likelihood Estimation Method Based On Joint Mean-covariance Model

Longitudinal data are data obtained from the observation of the same individual at different time points,with inter group independence and intra group correlation.Considering the regression problem of longitudinal data,the maximum likelihood estimation of regression parameters can be obtained when the error density is known.However,in practical problems,the error density is usually unknown.The profile likelihood method can obtain consistent estimates of regression parameters when the error density is unknown,but it considers a static covariance matrix.Currently,the commonly used method for processing intra group correlations is the joint mean covariance model.In this paper,covariates are introduced to model the generalized autoregressive parameters and variance parameters in the joint mean covariance model,and a section likelihood estimation of the regression parameters is proposed using the idea of section likelihood.This method can incorporate time and covariate information into the covariance matrix structure and can handle non monotonic missing longitudinal data.This paper first introduces the definition and characteristics of longitudinal data,overview on present research situation and two models for processing longitudinal data.Then,a new section likelihood method for estimating regression parameters is proposed.The estimation of mean parameters,generalized autoregressive parameters and variance parameters are given under the joint mean covariance model in chapter 2.Firstly,the profile likelihood estimation of the mean parameter is obtained by maximizing the profile likelihood equation;Secondly,using the obtained estimates,the profile likelihood estimation of the generalized autoregressive parameters is obtained by maximizing the profile likelihood equation;Then,the section likelihood estimation obtained in the first two steps is used to bring into the generalized estimation equation to obtain the estimation of variance parameters;Finally,iterative algorithms for implementing mean parameters,generalized autoregressive parameters,and variance parameters are given.The chapter 3 verifies the performance of the new profile likelihood method in various situations by generating limited samples through random simulation,and compares it with the method used in Pan & Ye(2006).It is concluded that the new profile likelihood method has good robustness and antipollution ability.Finally,we selected calf weight data and lung function data from black HIV infected people in South Africa to apply to the new profile likelihood method,and compared the results to show that the new profile likelihood method has better performance.