Weighted composite quantile regression for longitudinal mixed effects models with application to AIDS studies

Abstract

In longitudinal data studies, a conjunct feature of the multitudinous statistical methods is to depict the conditional mean of outcome variable. However, the conditional mean is not the best measure of centrality which may be affected by outliers. As an available alterative, composite quantile regression (CQR) can result in robust estimation results even for non-normal error distributions in regression analysis instead of the least square estimation (LSE). In this paper, we develop a weighted CQR of longitudinal mixed model from a likelihood framework based on the composite asymmetric Laplace distribution (CALD). Using the mixture representation of the CALD, we establish the joint hierarchical likelihood of the model and achieve the iterative weighted least square estimators of unknown parameters via the MCEM (Monte Carlo Expectation Maximization) algorithm. Finally, the developed procedures are illustrated by Monte Carlo simulations and an AIDS (Acquired Immune Deficiency Syndrome) data analysis.