Regression Coefficients Clustering for Longitudinal Data in the Presence of Heteroscedasticity

Regression coefficients clustering has gained increasing importance in various applications. However, most of the existing studies fail to accommodate skewed or asymmetrically distributed data with heteroscedasticity. In the context of longitudinal data, this paper investigates regression coefficients clustering by combining the asymmetric least squares loss with the multi-direction separation penalty method. The proposed method enables the identification of subgroups in which individuals share similar covariate effects, while allowing different important variables to be selected for different individuals. Meanwhile, the proposed method effectively addresses heteroscedasticity issues and captures more comprehensive distributional characteristics compared to ordinary least squares regression. The paper establishes theoretical properties, including the consistency of the estimator and its oracle property. To efficiently compute the proposed estimator, we develop an algorithm that combines cyclic coordinate descent with the alternating direction method of multipliers. Simulation studies and a practical example are provided to demonstrate the superiority of the proposed approach.