To help create more of an understanding on user engagement, this thesis proposes a model inspired by cognitive behaviour theory to explore user-to-user engagement on Twitter, in particular, factors that affect user engagement behaviour. Through case study and a novel model that combined machine learning and the cognitive-behaviour theory, this thesis examines tweets to determine how cognitive behaviour dynamics affect user engagement. The proposed model is evaluated on a dataset of tweets from 10 CEOs (n = 938). The results from the case study approach showed the content characteristics of these tweets such as sentiment analysis and subjectivity affectivity, but no clear idea on which factors affected engagement. The results from the proposed cognitive inspired machine learning model found that topics, emotions and cognitive perceptions play a role in affecting user-to-user engagement. The model predicts that higher engagement behaviours are motivated by topic and positive sentiments.