Expanding the Scope of Multivariate Regression Approaches in Cross-Omics Research

Abstract Recent technological advancements and developments have led to a dramatic increase in the amount of high-dimensional data and thus have increased the demand for proper and efficient multivariate regression methods. Numerous traditional multivariate approaches such as principal component analysis have been used broadly in various research areas, including investment analysis, image identification, and population genetic structure analysis. However, these common approaches have the limitations of ignoring the correlations between responses and a low variable selection efficiency. Therefore, in this article, we introduce the reduced rank regression method and its extensions, sparse reduced rank regression and subspace assisted regression with row sparsity, which hold potential to meet the above demands and thus improve the interpretability of regression models. We conducted a simulation study to evaluate their performance and compared them with several other variable selection methods. For different application scenarios, we also provide selection suggestions based on predictive ability and variable selection accuracy. Finally, to demonstrate the practical value of these methods in the field of microbiome research, we applied our chosen method to real population-level microbiome data, the results of which validated our method. Our method extensions provide valuable guidelines for future omics research, especially with respect to multivariate regression, and could pave the way for novel discoveries in microbiome and related research fields.