Longitudinal tracking of students academic progress using model-based clustering

Abstract

Clustering methods have often been used to group similar students’ performance for tracking their academic progress. A typical approach is to group the students by treating the observations as accumulated average marks on several assessed subjects within a period of time. Here, similar characteristics of students are identified based on the overall variation of marks between the subjects but ignores the temporal aspect of students performance even though the assessments are carried out at different time points. Alternatively, such characteristics in the observations could be treated as a set of longitudinal data since the measurements consider time-spaced and repeated events. This paper aims to compare the output between these two different treatments of observations using Model-based Clustering (MBC). Specifically, the average observations are applied to the classical MBC whereas the longitudinal observations require some adjustment to the covariance matrix to cater for its longitudinal data structure. A synthetic data set generated based on some pre-university students’ marks on four science subjects from three series of continuous assessments are applied to the methods. The results show that the longitudinal observations on adjusted MBC produce a greater number of clusters that could characterise students’ progress with a better internal and external cluster quality compared to the average observations on classical MBC.