From the individual to species level, it is common for animals to have connections with one another. These connections can exist in a variety of forms; from the social relationships within an animal society, to hybridisation between species. The structure of these connections in animal systems can be depicted using networks, often revealing non-trivial structure which can be biologically informative. Understanding the factors which drive the structure of animal networks can help us understand the costs and benefits of forming and maintaining relationships. Multivariate modelling provides a means to evaluate the relative contributions of a set of explanatory factors to a response variable. However, conventional modelling approaches use statistical tests which are unsuitable for the dependencies inherent in network and relational data. A solution to this problem is to use specialised models developed in the social sciences, which have a long history in modelling human social networks. Taking predictive multivariate models from the social sciences and applying them to animal networks is attractive given that current analytical approaches are predominantly descriptive. However, these models were developed for human social networks, where participants can self-identify relationships. In contrast, relationships between animals have to be inferred through observations of associations or interactions, which can introduce sampling bias and uncertainty to the data. Without appropriate care, these issues could lead us to make incorrect or overconfident conclusions about our data. In this thesis, we use an established network model, the multiple regression quadratic assignment procedure (MRQAP), and propose approaches to facilitate the application of this model in animal network studies. Through demonstrating these approaches on three animal systems, we make new biological findings and highlight the importance of considering data-sampling issues when analysing networks. Additionally, our approaches have wider applications to animal network studies where relationships are inferred through observing dyadic interactions.