Link prediction suffers from the data sparsity problem. This paper presents and validates our hypothesis that, for sparse networks, incidence matrix factorization (IMF) could perform better than adjacency matrix factorization (AMF), which has been used in many previous studies. A key observation supporting the hypothesis is that IMF models a partially-observed graph more accurately than AMF. A technical challenge for validating our hypothesis is that, unlike AMF approach, there does not exist an obvious method to make predictions using a factorized incidence matrix. To this end, we newly develop an optimization-based link prediction method adopting IMF. We have conducted thorough experiments using synthetic and real-world datasets to investigate the relationship between the sparsity of a network and the performance of the aforementioned two methods. The experimental results show that IMF performs better than AMF as networks become sparser, which strongly validates our hypothesis.