In most real-world applications, it is seldom the case that a given observable evolves independently of its environment. In social networks, users' behavior results from the people they interact with, news in their feed, or trending topics. In natural language, the meaning of phrases emerges from the combination of words. In general medicine, a diagnosis is established on the basis of the interaction of symptoms. Here, we propose a new model, the Interactive Mixed Membership Stochastic Block Model (IMMSBM), which investigates the role of interactions between entities (hashtags, words, memes, etc.) and quantifies their importance within the aforementioned corpora. We find that interactions play an important role in those corpora. In inference tasks, taking them into account leads to average relative changes with respect to non-interactive models of up to 150\% in the probability of an outcome. Furthermore, their role greatly improves the predictive power of the model. Our findings suggest that neglecting interactions when modeling real-world phenomena might lead to incorrect conclusions being drawn.