Hierarchical Latent Variable Decomposition for Adaptive Learning Trajectory Optimization in Technology-Enhanced Classroom Environments

Abstract

Contemporary adaptive learning systems rely on static psychometric models that insufficiently capture the temporal dynamics of student knowledge acquisition. This study proposes a hierarchical latent variable decomposition (HLVD) framework that integrates item response theory with Bayesian temporal inference to optimize individualized learning trajectories in technology-enhanced classroom environments. Using longitudinal assessment data from 1,847 secondary-level students across three academic cycles, the framework demonstrates statistically significant improvements in predictive accuracy of competency state estimation (RMSE reduction of 18.4%) over conventional computerized adaptive testing pipelines. Structural equation modeling confirmed mediation effects of metacognitive regulation on trajectory divergence. The HLVD framework advances diagnostic measurement practice by enabling real-time, formative recalibration of instructional scaffolding parameters, with direct implications for precision education deployment at institutional scale.