Generalized Empirical Likelihood Inference in Generalized Linear Models for Longitudinal Data

In this article, the generalized linear model for longitudinal data is studied. A generalized empirical likelihood method is proposed by combining generalized estimating equations and quadratic inference functions based on the working correlation matrix. It is proved that the proposed generalized empirical likelihood ratios are asymptotically chi-squared under some suitable conditions, and hence it can be used to construct the confidence regions of the parameters. In addition, the maximum empirical likelihood estimates of parameters are obtained, and their asymptotic normalities are proved. Some simulations are undertaken to compare the generalized empirical likelihood and normal approximation-based method in terms of coverage accuracies and average areas/lengths of confidence regions/intervals. An example of a real data is used for illustrating our methods.