Robust Estimation Of Parameters In Generalized Linear Model With Longitudinal Data

Longitudinal data is widely applied in biomedicine,epidemiology and economics.It is obtained by repeated measurements at different time points of thesame individual,and has the characteristics of intra-group correlation and inter-group independence.However,due to the characteristics of repeated measurements of longitudinal data,missing values or outliers are easy to occur in practical research.Therefore,it is one of the hot topics in recent years to study the robust estimation of regression models based on the longitudinal data,and also has a strong practical significance.In this paper,we first investigate robust quadratic inference functions for generalized linear models with longitudinal data.A weighted exponential score function is applied to control the effect of outliers,and quadratic inference functions(QIF)are used to achieve a more efficient estimation.Under some regularity conditions,the resulting estimators are consistent and asymptotically normal distributed.Secondly,we consider the generalized estimation equation(GEE)in longitudinal linear regression models with monotone responses missing patterns.A weighted likelihood method is first proposed to obtain the robust estimation of the parameters involved in the missing model.Based on the robust generalized estimating equations(ERGEE),a robust inverse probability weighting generalized estimating equations(IPWGEE)is obtained to estimate the parameter with response dropouts.For the two groups of studies,the numerical simulation results show that there are still robust simulation results when many outliers are included and the working correlation matrix is misspecified,and the responses are missing.