Link prediction is one of the core problems in network and data science with widespread applications. While predicting pairwise nodal interactions (links) in network data has been investigated extensively, predicting higher-order interactions (higher-order links) is still not fully understood. Several approaches have been advocated to predict such higher-order interactions, but no principled method has been put forth to tackle this challenge so far. Cross-fertilizing ideas from Volterra series and linear structural equation models, the present paper introduces self-driven graph Volterra models that can capture higher-order interactions among nodal observables available in networked data. The novel model is validated for the higher-order link prediction task using real interaction data from social networks.@en