This paper introduces a novel conceptual foundation for Social Set Analysis, the Social Interaction Model. It contributes to the state-of-the-art theory in Big Social Data by extending the existing Social Data Model through proposal of an improved concept which is formally grounded in set theory and relational algebra. The concept of Interactions based on one initial Action between two social media Actors, and zero or many Reactions, all referencing the initial Action, is presented. Furthermore, temporal and spatial dimensions are included as a core component of the proposed model, thus streamlining data analytics tasks in the realm of Social Set Analysis. Key differences between the existing Social Data Model and the Social Interaction Model contributed in this paper are the inclusion of non-textual artifact content types, the unification of a previously bipartite Social Data Model, the deprecation of an empirically vague notion of Activities, and improved interoperability between data sources.