Sliced inverse regression method for multivariate compositional data modeling

Compositional data modeling is of great practical importance, as exemplified by applications in economic and geochemical data analysis. In this study, we investigate the sliced inverse regression (SIR) procedure for multivariate compositional data with a scalar response. We can achieve dimension reduction for the original multivariate compositional data quickly and then conduct a regression on the dimensional-reduced compositions. It is documented that the proposed method is successful in detecting effective dimension reduction directions, which generalizes the theoretical framework of SIR to multivariate compositional data. Comprehensive simulation studies are conducted to evaluate the performance of the proposed SIR procedure and the simulation results show its feasibility and effectiveness. A real data application is finally used to illustrate the success of the proposed SIR-based method.