Mathematics competency is fast becoming an essential requirement in ever greater parts of day-to-day work and life. Thus, creating strategies for improving mathematics learning in students is a major goal of education research. However, doing so requires an ability to look at many aspects of mathematics learning, such as demographics and psychological dispositions, in an integrated way as part of the same system. Large-scale assessments such as the Programme for International Student Assessment (PISA) provide an accessible and large volume of coherent data, and this gives researchers the opportunity to employ data-driven approaches to gain an overview of the system. For these reasons, we have used machine learning to explore the relationships between psychological dispositions and mathematical literacy in Australian 15-year-olds using the PISA 2012 data set. Our results from this strongly data-driven approach re-affirm the primacy of mathematics self-efficacy and highlight novel complex interactions between mathematics self-efficacy, mathematics anxiety and socio-economic status. In this paper, we demonstrate how education researchers can usefully employ data-driven modelling techniques to find complex non-linear relationships and novel interactions in a multidimensional data set.