Imputation Sensitivity and Robustness of Student Clustering in Higher Education Data

This paper investigates how different approaches to handling missing data shape the outcomes of unsupervised clustering in educational datasets. Three commonly used imputation algorithms – mean substitution, Random Forest and Multiple Imputation with Chain Equations (MICE) – were applied to student records from a Croatian higher education institution. The analysis included 461 students, with 46 (9.98%) missing values for study duration. Each dataset was analyzed individually using three clustering algorithms: K-means, Ward’s hierarchical clustering and Gaussian mixture model (GMM). The three imputation methods and three clustering algorithms produced nine algorithm-dataset combinations. Solutions containing between two and ten clusters were evaluated using the silhouette coefficient. It was also examined whether the different datasets produced numerically and substantively similar student clusters. The results show that different imputation choices have a pronounced impact on Ward’s hierarchical clustering, which selected ten clusters for MICE, six for Random Forest and four for Mean Replacement. On the other hand, K-means and GMM showed a high degree of robustness, consistently identifying the same number of clusters in all completed datasets – eight clusters for K-means and two for GMM. The analysis showed that when imputation was done with the mean value, all missing study durations were replaced with the same value. In contrast, Random Forest and Multiple Imputation by Chained Equations (MICE) estimated different study durations for each student, which preserved larger differences among the imputed values. Despite these methodological differences, several interpretable student profiles emerged repeatedly, including high-achieving students, long-studying older students, low-achieving early-leavers and students with moderate academic success. These results show that the effect of missing data processing on student grouping is algorithm-specific. Solutions based on centroids and mixtures were comparatively robust in this data set, while Ward’s hierarchical clustering produced different results since the imputation methods changed the calculated similarities between students. These results may benefit researchers working with unsupervised machine learning and incomplete educational data sets. Therefore, educational clustering analyses should examine whether different imputation methods produce the same number of clusters, and whether the resulting clusters represent similar groups of students.