Analysis of longitudinal data with multiple levels of variation

Abstract

Longitudinal studies, in which subjects are measured repeatedly through time, play an important role in many areas of research. Often these longitudinal studies involve some complex experimental or sampling designs, which result in clustering or grouping between subjects, as well as serial correlation within subjects. The generalized estimating equation approach (GEE) is a method of parameter estimation that requires only a model for the mean of the data and the relationship between the mean and the variance. Traditionally GEE assumes independence between the subjects. When the independence assumption no longer holds, we modify the estimating equations for analysing longitudinal data with multiple levels of random variation. Simulation results show that the modified estimating equation method produces good estimates of the model parameters. Various bootstrap methods are assessed for making inference on the variance and the confidence intervals for the variance component and correlation parameter estimators, historically showing undercoverage. A new weighted estimating equation bootstrap, which uses different weight schemes for different parameter estimators, shows improved variance estimation and coverage probabilities for the variance component estimators. Non-normal errors are also discussed in the framework of the modified generalized estimating equations. The robust ML II estimators are generalized to fit the longitudinal data and the bootstrap estimators are revaluated in the context of the response contamination models. Finally the modified generalized estimating equation method, the robust estimating equation method and theirs corresponding bootstrap methods are implemented to two real datasets. Show more