Understanding students' privacy concerns is an essential first step toward effective privacy-enhancing practices in learning analytics (LA). In this study, we develop and validate a model to explore the students' privacy concerns (SPICE) regarding LA practice in higher education. The SPICE model considers "privacy concerns" as a central construct between two antecedents--perceived privacy risk and perceived privacy control, and two outcomes--trusting beliefs and non-self-disclosure behaviours. To validate the model, data through an online survey were collected, and 132 students from three Swedish universities participated in the study. Partial least square results show that the model accounts for high variance in privacy concerns, trusting beliefs, and non-self-disclosure behaviours. They also illustrate that students' perceived privacy risk is a firm predictor of their privacy concerns. The students' privacy concerns and perceived privacy risk were found to affect their non-self-disclosure behaviours. Finally, the results show that the students' perceptions of privacy control and privacy risks determine their trusting beliefs. The study results contribute to understand the relationships between students' privacy concerns, trust and non-self-disclosure behaviours in the LA context. A set of relevant implications for LA systems' design and privacy-enhancing practices' development in higher education is offered.