Stratifying cognitive performance severity in higher education using a two level clustering approach

Cognitive ability distributions are multidimensional and may exhibit non-linear structure, which can limit centroid-based clustering. This study proposes a two-level spectral clustering framework for multivariate cognitive severity stratification using psychometric latent trait (theta) estimates of logical reasoning, verbal ability, and abstraction.. The complete sample (N = 36,830) was organised according to three latent ability estimates derived from logical reasoning, verbal ability, and abstraction. In the first stage, graph Laplacian–based spectral clustering identified three severity strata without assuming spherical cluster structure. The lowest-performing cluster (n = 13,252) was then refined in a second stage to obtain more detailed subgroups. Multivariate cluster separability was evaluated using PERMANOVA, showing significant differentiation among clusters (pseudo-F = 4687.0, R² = 0.2613, p = 0.01). Pairwise post hoc tests confirmed significant separation across all cluster pairs, with the strongest divergence between the lowest and highest strata (pseudo-F = 6156.5, R² = 0.3978, p = 0.01). NMDS with fitted vectors further indicated distinct contributions of abstraction, verbal ability, and logical reasoning to cluster separation. Rather than providing diagnostic labels, this study presents an interpretable and scalable unsupervised framework for identifying structured severity patterns in complex cognitive data.