Unlabelled - Information is spread as individuals engage with other users in the underlying social network. Analysis of social engagements can therefore provide insights to understand the motivation behind how and why users engage with others in different activities. In this study, we aim to understand the driving factors behind four engagement types in Twitter, namely like, reply, retweet, and quote. We extensively analyze a diverse set of features that reflect user behaviors, as well as tweet attributes and semantics by natural language processing, including a deep learning language model, BERT. The performance of these features is assessed in a supervised task of engagement prediction by learning social engagements from over 14 million multilingual tweets. In the light of our experimental results, we find that users would engage with tweets based on text semantics and contents regardless of tweet author, yet popular and trusted authors could be important for reply and quote. Users who actively liked and retweeted in the past are likely to maintain this type of behavior in the future, while this trend is not seen in more complex types of engagements, reply, and quote. Moreover, users do not necessarily follow the behavior of other users with whom they have previously engaged. We further discuss the social insights obtained from the experimental results to understand better user behavior and social engagements in online social networks. Supplementary information - The online version contains supplementary material available at 10.1007/s13278-022-00872-1.