Longitudinal Data Analysis Using Generalized Estimating Equation With Random Effects

Linear mixed model is a common statistical model of longitudinal data,widely used in biomedicine,social economics,psychology and other fields.The parameter estimation of fixed effects and variance components is a hot issue in statistical research.Generalized estimating equation is a longitudinal data analysis method with good properties,the paper uses this method to study the parameter estimation of linear and generalized linear mixed model.The paper first introduces the research background and basic model theory of longitudinal data,and next discusses the application of generalized estimating equation method for a class of linear mixed models.For the random intercept model,establish the GEE under the exchangeable working correlation matrix to find the relationship between the variance components and the correlation coefficient.For the random coefficient model with two variance components,calculate the marginal mean and covariance matrix of the model and substitute them into the estimating equation.In addition,the statistical analysis of a class of Poisson random-effects models is achieved by the GEE method.Generalized estimating equations models the mean of the response variable.Consider that the mean of the response variables is affected by random effects,and the response variables of the same individual under random effects are independent of each other.First,the generalized estimating equation with random effects is established given the random effects,the mean function of response variable changes.Next,consider it as a random effect again.At this time,the equation contains random variable,the paper combines multiple imputation method to deal with it.Generally,it is assumed that the random effects follow a normal distribution with unknown variance.Consider using the product of a standard normal random number and standard deviation of random effects as the filling value.Obviously,the value is related to the estimation of the variance component,which can be combined with the estimation equation to establish an iterative process.This paper selects examples of longitudinal data for the example analysis of the above method,and the effectiveness is evaluated through simulation analysis.The average deviation and mean square error in the simulation results are within the acceptable range,which shows that the method used in this paper is feasible.