Study On The Parameter Estimation And Model Selection Of Generalized Estimating Equations In Longitudinal Data Analysis

This paper focuses on the parameters and covariance estimation in generalized estimation equations in longitudinal data and the related problems of model selection.Firstly,in chapter 1 and chapter 2,the background knowledge of this paper and the research status are introduced.Starting from the longitudinal data,gradually transitioned to the linear model,generalized linear model and then to the generalized estimating equation.Then the basic solving method and general properties of the generalized estimating equation are introduced.Secondly,in Chapters 3,we discuss the problems of small sample covariance estimation proposed by Liang and Zeger?1986?.Actually,as shown by many researchers,the sandwich covariance estimator has been illustrated to exhibit considerable bias and underestimate the sampling variance of the regression parameter estimates in small samples,though it is robust to the misspecification of the working ICS of the response.In order to improve the small sample performances,several improved robust covariance estimators have been introduced in the literature.Westgate?2013?introduced an empirical covariance estimation for the variance inflation.This paper combines Westgate's?2013?and the various modified covariance estimators mentioned before,also introduces the five robust covariance estimates and estimates of various improvements based on these five robust variance estimates.Next,the approximate t-tests and F-tests based on various improved covariance estimators are discussed.In addition,numerical simulations demonstrate the performance of different covariance estimations.The Gaussian data and binomial data are simulated to show the performance of t-test and F-test with small correlation coefficient?0.2?and large correlation coefficient?0.5?.Simulation results show that the standard errors of the improved covariance estimators are much smaller than the Sandwich estimates while maintaining a smaller first-type error rate.At the same time,as the sample size increases,the standard error gradually decreases but is still better than the Sandwich estimation.In addition,the first type error converges to 0.05.Finally,in chapters 5,according to the proposed new robust covariance estimation,various new variable selection criterions are constructed and their performances are given through numerical simulations.Simulations show that the accuracy of the selection criterions for correct selection of criteria is increased after increasing the sample size.In addition,when the sample size increases to 100,the accuracy rate has reached 98.5%.Meanwhile,the accuracy of the selection of each criterion under the real structure of the first-order autocorrelation structure is slightly better than that of the real structure of exchangeable correlation structure.At the same time,when the correlation coefficient increases,the accuracy of judgment of each criterion will also increase,and the improved CIC_West-N's performance is excellent.Chapter 5 gives conclusions and outlook.