The rapid recent use of learning analytics (LA) in higher education, specifically during the COVID-19 pandemic, allows the monitoring of users' behavior while learning. Using LA may promote students' learning outcomes but also intrude into their privacy. This study aimed to explore students' behaviour and perceptions towards privacy and data protection when using LA for pedagogical needs, examine the privacy trade-off of students' willingness to share personal information in exchange for pedagogical benefits and understand the predicting variables for this privacy trade-off. A model was developed containing five groups of influencing variables (demographic data, perceptions, feelings, behaviour and awareness) on the privacy trade-off. A total of 1,014 students completed an online questionnaire. The results found that students do care about their privacy but are not aware of privacy and data protection regulations. They are willing to trade off privacy for pedagogical benefits, and they trust their academic institutions, but they want transparency. Age, a sense of security in the academic institution, behaviour, data misuse concern and institution management of students' personal information are the significant predictors for a privacy trade-off. It is important to engage students in the process as they are the main beneficiaries of LA and build trust between them and the institution.