The utilization of learning analytics to identify at-risk students for early intervention has exhibited promising results. However, most predictive models utilized to address this issue have been based on non-probabilistic machine learning models. In response, this study incorporated probabilistic machine learning for two reasons: (1) to facilitate the inclusion of domain knowledge, and (2) to enable the quantification of uncertainty in model parameters and predictions. The study developed a five-stage, probabilistic logistic regression model to identify at-risk students at different stages throughout the academic calendar. Rather than predicting a student’s final or exam mark, the model was focused on predicting the at-risk probabilities for subsequent assessments—specifically, the probability of a student failing an upcoming assessment. The model incorporated student engagement data from Moodle, as well as demographic and student performance data. The study’s findings indicate that the significance and certainty of student engagement and demographic variables decreased after incorporating student-performance variables, such as assignments and tests. The most effective week for identifying at-risk students was found to be week 6, when the accuracy was 92.81%. Furthermore, the average level of uncertainty exhibited by the models decreased by 60% from stage 3 to 5, indicating more reliable predictions at later than earlier stages. The study highlights the potential of a probabilistic machine learning model to aid instructors and practitioners in identifying at-risk students, and thereby to enhance academic outcomes.

A Bayesian additive regression tree (BART) is a recent statistical method that blends ensemble learning with nonparametric regression. BART is constructed using a Bayesian approach, which provides the benefit of model-based prediction uncertainty, enhancing the reliability of predictions. This study proposes the development of a BART model with a binomial likelihood to predict the percentage of students retained in tutorial classes using attendance data sourced from a South African university database. The data consist of tutorial dates and encoded (anonymized) student numbers, which play a crucial role in deriving retention variables such as cohort age, active students, and retention rates. The proposed model is evaluated and benchmarked against the random forest regressor (RFR). The proposed BART model reported an average of 20% higher predictive performance compared to RFR across six error metrics, achieving an R-squared score of 0.9414. Furthermore, the study demonstrates the utility of the highest density interval (HDI) provided by the BART model, which can help in determining the best- and worst-case scenarios for student retention rate estimates. The significance of this study extends to multiple stakeholders within the educational sector. Educational institutions, administrators, and policymakers can benefit from this study by gaining insights into how future tutorship programme student retention rates can be predicted using predictive models. Furthermore, the foresight provided by the predicted student retention rates can aid in strategic resource allocation, facilitating more informed planning and budgeting for tutorship programmes.

The increasing use of virtual learning environments (VLEs) in recent years has transformed teaching and learning methods. Universities now combine VLEs with traditional classrooms to accommodate hybrid teaching and learning approaches. However, student engagement with VLEs varies, and universities lack the tools to effectively determine and analyse VLE engagement. Consequently, data-driven decision-making regarding VLE usage remains a challenge for universities. This study thus proposed a user-friendly web-based application, using a R shiny framework, to determine and understand student engagement levels in VLEs. In this study, two clustering methods, K-means and Gaussian Mixture Model (GMM) were compared, to identify the most effective method for the proposed application. The results indicated that GMM outperforms K-means by generating more accurate and comprehensive groupings of student engagement levels. One key advantage of the GMM method is its ability to capture uncertainty and provide probabilities of student membership in each level of engagement, which enhances its usefulness for decision-making. Furthermore, the GMM method achieves these outcomes efficiently, saving valuable learning time. This research holds significant implications for education by providing valuable guidance for the development of Educational Data Mining (EDM) applications. Universities can leverage these applications to gain deep insights into VLE usage and enhance their understanding of student engagement. By adopting this web-based application, educators and administrators can make informed decisions and tailor interventions to optimize student learning experiences within VLEs. Keywords: Virtual Learning Environments, Student Engagement, Clustering.