<p>Complex systems usually feature interactions not only between pairwise entities but also among three or more entities. Hypergraph can effectively characterize these higher-order interactions. Meanwhile, all higher-order interactions can also be projected onto a number of lower-order interactions. Determining whether all higher-order interactions must be considered or if they can be approximated by lower-order interactions with minimal loss remains an open question. We propose a method to decompose higher-order structures in a stepwise way, thereby allowing to explore the impacts of hyperedges of any order. Experiments suggest that in some networks, incorporating higher-order interactions significantly enhances the accuracy of link prediction, while in others, the effect is insignificant. Therefore, the role of higher-order interactions varies in different types of networks. Overall, since the improvement in predictive accuracy provided by higher-order interactions is significant in some networks, we believe that the study of higher-order interactions is valuable.</p><p></p>