A modified expectation-maximization algorithm for accelerated item response theory model estimation with large datasets

Clinical Snapshot

Key Findings

• P Value: Not reported

• Effect Size: Up to 60% reduction in computation time with 40-item forms

• Primary Outcome: Convergence time reduction while maintaining parameter estimation accuracy

• Nnt Or Sensitivity: Consistent time reductions across all subset sizes with 54 items, variable performance with 36 items

• Confidence Interval: Not applicable for simulation study

Clinical Application

High feasibility for implementation in existing statistical software packages and operational testing programs Relevant to Australian educational assessment bodies like ACARA for NAPLAN, university admissions testing, and psychological assessment in clinical practice under AHPRA guidelines Educational testing organizations, psychological assessment developers, and researchers conducting large-scale IRT analyses

Abstract

The expectation-maximization (EM) algorithm is widely used for parameter estimation in item response theory (IRT) modeling. However, when applied to datasets with large numbers of individuals and items, the standard EM algorithm can be slow to converge, with computationally expensive E-steps. We propose a modified EM algorithm to accelerate estimation for unidimensional two-parameter logistic IRT models. The modified algorithm uses a two-stage structure with partial-step updating over data subsets to reduce convergence time, while maintaining comparable accuracy and precision. The first two simulation studies evaluated its performance relative to standard EM, focusing on convergence time, parameter recovery, and standard error estimation across varying subset sizes and item counts. The third study demonstrated its scalability and runtime advantage in a large-scale testing scenario involving one million respondents and 100 items. The fourth study evaluated robustness under departures from unidimensionality. The proposed algorithm showed time reductions under smaller subsets with 36 items, consistent reductions across all subset sizes with 54 items, and the largest reduction (60%) with 40-item forms constructed from 100 items, while maintaining comparable estimation performance. These results highlight the algorithm's potential for large-scale applications involving tens of thousands of respondents and moderate-to-large item pools, with modifications that can be integrated into existing EM routines. We conclude with directions for operational use and potential extensions to multidimensional IRT estimation.

References

1. 1.Feng, T., & Cai, L. (2026). A modified expectation-maximization algorithm for accelerated item response theory model estimation with large datasets. Behavior Research Methods. https://doi.org/10.1016/j.jpdc.2017.07.005