M-quantile regression for multivariate longitudinal data

We propose an M-quantile regression model for the analysis of multivariate continuous longitudinal data. M-quantile regression represents an appealing alternative to standard regression models, as it combines the robustness of quantile and the efficiency of expectile regression, detailing a picture of the response variable distribution. Discrete individual-specific random parameters are considered to account for both dependence within longitudinal profiles and association between multiple responses from the same sample unit. An extended version of the standard EM algorithm for mixed models is proposed to derive model parameter estimates.