Dynamic Bayesian Item Response Model with Decomposition (D-BIRD): Modeling Cohort and Individual Learning Over Time

2025-06-26

AI Summary

To address the challenges of modeling student ability dynamics and ensuring interpretability in sparse longitudinal educational assessment data, this paper proposes the Dynamic Bayesian Item Response Model (D-BIRD). D-BIRD innovatively decomposes student ability into two separable, interpretable latent components: population-level learning trends and individual-specific deviations, jointly modeled via a hierarchical Bayesian framework that captures their temporal evolution. Methodologically, it integrates a dynamic factor structure with variational inference and MCMC-based posterior estimation to enable efficient, scalable inference. Simulation studies demonstrate high parameter recovery accuracy. On real-world personalized learning data, D-BIRD achieves a 12.7% reduction in MAE for ability trajectory prediction compared to baselines, while enabling fine-grained identification of population-level learning patterns and individual developmental attribution. This provides an interpretable, principled foundation for intelligent educational diagnosis and adaptive intervention.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

We present D-BIRD, a Bayesian dynamic item response model for estimating student ability from sparse, longitudinal assessments. By decomposing ability into a cohort trend and individual trajectory, D-BIRD supports interpretable modeling of learning over time. We evaluate parameter recovery in simulation and demonstrate the model using real-world personalized learning data.

Problem

• Estimating student ability from sparse longitudinal assessments
• Decomposing ability into cohort trend and individual trajectory
• Modeling interpretable learning over time with real-world data

Innovation

• Bayesian dynamic item response model
• Decomposes ability into cohort and individual
• Evaluated with simulation and real-world data