Modeling Nonlinear Ability Trajectories and Learner Heterogeneity in Online Learning: A Bayesian Nonparametric Dynamic IRT Framework

2026-06-13

AI Summary

Existing online learning analytics struggle to capture the nonlinear dynamics of student ability, often requiring a prespecified number of clusters and failing to effectively model the relationship between engagement behaviors and ability evolution. This work proposes a Bayesian nonparametric dynamic item response theory framework that employs B-spline basis functions to flexibly characterize the nonlinear influence of participation on ability drift. By incorporating a Mixture-of-Finite-Mixtures prior, the model automatically infers the number of latent learner subgroups, enabling unsupervised clustering and longitudinal tracking of individual ability trajectories. Applied to data from 198 undergraduate students in a statistics course, the model identified four distinct learner types—struggling-declining, low-stable, mainstream-stable, and high-improving—revealing highly stable ability trajectories and no significant predictive effect of participation volume on ability drift.

Abstract

Online learning has amplified the need to understand how student engagement patterns influence learning outcomes, particularly given the flexibility of technology-mediated environments. To address this, we propose a Bayesian nonparametric dynamic item response theory (IRT) framework that tracks within-individual ability trajectories across instructional units. The proposed model integrates B-spline basis expansions to capture nonlinear effects of engagement behaviors on ability drift, alongside a Mixture-of-Finite-Mixtures (MFM) prior to automatically determine the number of latent learner clusters. This framework overcomes three limitations in the existing literature: (1) rigid linearity assumptions in engagement-ability relationships, (2) dependence on pre-specified cluster counts, and (3) the inability to track longitudinal ability dynamics. We apply the model to longitudinal data from 198 undergraduates completing a 9-chapter introductory statistics course on CourseKata. The model automatically identified four distinct learner profiles: struggling-declining (11\%), low-stable (23\%), mainstream-stable (55\%), and high-improving (12\%). Results indicate that ability trajectories remained remarkably stable across chapters, and engagement quantity metrics did not significantly predict ability drift. These findings suggest that in introductory online statistics education, academic ability primarily reflects a stable pre-existing characteristic rather than a dynamically malleable course outcome. Ultimately, this framework offers a flexible tool for learner profiling to inform adaptive instructional design.

Problem

• nonlinear ability trajectories
• learner heterogeneity
• online learning
• longitudinal ability dynamics
• engagement-ability relationship

Innovation

• Bayesian nonparametrics
• dynamic item response theory
• B-spline basis expansion
• Mixture-of-Finite-Mixtures
• learner heterogeneity