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stat updates on arXiv.org

Simultaneous Monitoring of Shape and Surface Color via 4D Point Clouds: A Registration-free Approach A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint
Modeling Nonlinear Ability Trajectories and Learner Heter...
[Submitted on 14 Jun 2026] · 2026-06-16 · via stat updates on arXiv.org

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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.

Submission history

From: Guanyu Hu [view email]
[v1] Sun, 14 Jun 2026 00:45:53 UTC (75 KB)