近年来科技的进步和发展使得高维数据急剧增加，研究人员对合适且有效的多元回归方法的需求也随之增长。许多传统的多元分析方法如主成分分析等已广泛应用于投资分析、图像识别和群体遗传结构分析等研究领域。然而，这些常见的方法存在其局限性，即忽略了响应之间的相关性和变量选择效率低的问题。因此，本文引入了降秩回归方法及其扩展形式——稀疏降秩回归和行稀疏的子空间辅助回归，这些方法有望满足上述需求，从而提高回归模型的可解释性。我们通过开展仿真研究来评估它们的效果，并将它们与其他几种变量选择方法进行比较。对于不同的应用场景，我们也提供了基于预测能力和变量选择精度的选择建议。最后，为了证明这些方法在微生物组研究领域的实用价值，我们将所选择的方法应用于实际种群水平的微生物组数据，结果验证了我们方法的有效性。该方法的扩展形式为未来的组学研究特别是多元回归研究提供了有价值的指导，并为微生物组学及其相关研究领域的新发现奠定了基础。

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.