Engagement is a fuzzy concept. In the present work we operationalize engagement mechanistically by linking it directly to human behaviour and show that the construct of engagement can be used for shaping and interpreting data-driven methods. First we outline a formal framework for engagement modelling. Second we expanded on our previous work on theory-inspired data-driven approaches to better model the engagement process by proposing a new modelling technique, the Melchoir Model. Third, we illustrate how, through model comparison and inspection, we can link machine-learned models and underlying theoretical frameworks. Finally we discuss our results in light of a theory-driven hypothesis and highlight potential application of our work in industry.