Composite Hierachical Linear Quantile Regression

Multilevel (hierarchical) modeling is a generalization of linear and generalized linear modeling in which regression coefcients are modeled through a model,whose parameters are also estimated from data.Multilevel model fails to fit well typically by the use of the EM algorithm once one of level error variance (like Cauchy distribution) tends to infinity.This paper proposes a composite multilevel to combine the nested structure of multilevel data and the robustness of the composite quantile regression,which greatly improves the efciency and precision of the estimation.The new approach,which is based on the Gauss-Seidel iteration and takes a full advantage of the composite quantile regression and multilevel models,still works well when the error variance tends to infinity.We show that even the error distribution is normal,the MSE of the estimation of composite multilevel quantile regression models nearly equals to mean regression.When the error distribution is not normal,our method still enjoys great advantages in terms of estimation efciency.