Media is evolving from traditional linear narratives to personalised experiences, where control over information (or how it is presented) is given to individual audience members. Measuring and understanding audience engagement with this media is important in at least two ways: (1) a post-hoc understanding of how engaged audiences are with the content will help production teams learn from experience and improve future productions; (2), this type of media has potential for real-time measures of engagement to be used to enhance the user experience by adapting content on-the-fly. Engagement is typically measured by asking samples of users to self-report, which is time consuming and expensive. In some domains, however, interaction data have been used to infer engagement. Fortuitously, the nature of interactive media facilitates a much richer set of interaction data than traditional media; our research aims to understand if these data can be used to infer audience engagement. In this paper, we report a study using data captured from audience interactions with an interactive TV show to model and predict engagement. We find that temporal metrics, including overall time spent on the experience and the interval between events, are predictive of engagement. The results demonstrate that interaction data can be used to infer users engagement during and after an experience, and the proposed techniques are relevant to better understand audience preference and responses.