A Recursive Stochastic Algorithm for Real-Time Online Parameter Estimation in Item Response Theory: Enhancing Computational Efficiency for Dynamic Educational Assessment
Year: 2025
Type: article
Abstract: Traditional large-scale educational data are typically static and updated periodically, making it difficult to capture the dynamic changes in real time. However, recent technological advancements allow online exam platforms to collect students’ response data in real time. While item response theory (IRT) estimation methods are widely recognized for their accuracy, they are primarily designed for offline environments. When real-time data continuously arrives and online parameter estimation is required, these methods become computationally impractical. To address this challenge, we propose a recursive stochastic algorithm, i.e., truncated average stochastic Newton algorithm (TASNA), for the efficient online parameter estimation within the IRT framework. This algorithm significantly improves computational efficiency compared to the expectation–maximization (EM) algorithm implemented in the mirt package in R . The algorithm offers a powerful alternative to the traditional offline EM method. Furthermore, we investigate the asymptotic properties of the algorithm, proving its almost sure convergence and asymptotic normality. Numerical experiments using both simulated and real data demonstrate the practicality of the proposed method.
Source: Psychometrika
Authors: Sainan Xu, Jing Lu, Jiwei Zhang
Institution: Northeast Normal University
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W7116895013