We propose a robust procedure to estimate a linear regression model with compositional and real-valued explanatory variables. The proposed procedure is designed to be robust against individual outlying cells in the data matrix (cellwise outliers), as well as entire outlying observations (rowwise outliers). Cellwise outliers are first filtered and then imputed by robust estimates. Afterwards, rowwise robust compositional regression is performed to obtain model coefficient estimates. Simulations show that the procedure generally outperforms a traditional rowwise-only robust regression method (MM-estimator). Moreover, our procedure yields better or comparable results to recently proposed cellwise robust regression methods (shooting S-estimator, 3-step regression) while it is preferable for interpretation through the use of appropriate coordinate systems for compositional data. An application to bio-environmental data reveals that the proposed procedure—compared to other regression methods—leads to conclusions that are best aligned with established scientific knowledge.

我们提出了一个鲁棒的程序来估计具有成分和实值解释变量的线性回归模型。拟议的过程旨在针对数据矩阵中的单个外围单元（信元异常值）以及整个外围观测值（行异常值）具有鲁棒性。首先过滤基于单元的离群值，然后通过可靠的估算来估算。之后，执行行稳健的成分回归以获得模型系数估计。仿真表明，该过程通常优于传统的仅行稳健回归方法（MM-estimator）。此外，与最近提出的细胞鲁棒回归方法（射击S估计器，3步回归），但最好通过使用适当的坐标系进行成分数据解释。对生物环境数据的一项应用表明，与其他回归方法相比，所提出的程序得出的结论与已建立的科学知识最为吻合。