Leveraging Learning Analytics to Model Student Engagement in Graduate Statistics: A Problem-Based Learning Approach in Agricultural Education ^†

Graduate students often experience difficulties in learning statistics, particularly those who have limited mathematical backgrounds. In recent years, Learning Management Systems (LMS) and Problem-Based Learning (PBL) have been widely adopted to support instruction, yet little research has explored how these tools relate to learning outcomes using mixed methods design. Limited studies have employed machine learning methods such as clustering analysis in Learning Analytics (LA) to explore different behavior of clusters based on students log data. This study followed an explanatory sequential mixed methods design to examine student engagement patterns on Canvas and learning outcomes of students in a graduate-level statistics course. LMS log data and surveys were collected from 31 students, followed by interviews with 19 participants. K-means clustering revealed two groups: a high-performing group with lower LMS engagement and a low-performing group with higher LMS engagement. Six themes emerged from a thematic analysis of interview transcripts: behavioral differences in engagement, the role of assessment, emotional struggle, self-efficacy, knowledge or skill gain, and structured instructional support. Results indicated that low-performing students engaged more frequently and benefited from structured guidance and repeated exposure. High-performing students showed more proactive and consistent engagement habits. These findings highlight the importance of intentional course design that combines PBL with LMS features to support diverse learners.