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

Tianying Feng1, Li Cai2

  • 1University of California, Los Angeles, 315 SEIS Building, Los Angeles, CA, 90095-1522, USA.

Behavior Research Methods
|April 21, 2026
PubMed
Summary
This summary is machine-generated.

A new modified expectation-maximization (EM) algorithm speeds up item response theory (IRT) modeling for large datasets. This faster EM algorithm maintains accuracy for parameter estimation in educational and psychological testing.

Keywords:
EM algorithmEstimationItem response theoryLarge data

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Area of Science:

  • Psychometrics
  • Statistical modeling
  • Educational measurement

Background:

  • The expectation-maximization (EM) algorithm is standard for item response theory (IRT) parameter estimation.
  • Standard EM can be computationally intensive and slow to converge with large datasets.

Purpose of the Study:

  • To develop and evaluate a modified EM algorithm for accelerated parameter estimation in unidimensional two-parameter logistic IRT models.
  • To assess the modified algorithm's convergence time, accuracy, and scalability compared to standard EM.

Main Methods:

  • A modified EM algorithm employing a two-stage structure with partial-step updating over data subsets.
  • Simulation studies with varying subset sizes, item counts, and a large-scale testing scenario (1 million respondents, 100 items).
  • Evaluation of parameter recovery, standard error estimation, and robustness under unidimensionality departures.

Main Results:

  • The modified EM algorithm demonstrated significant time reductions, especially with larger item pools (e.g., 60% reduction for 40-item forms from 100 items).
  • Comparable accuracy and precision in parameter estimation were maintained across simulations.
  • The algorithm proved scalable and efficient for large-scale testing scenarios.

Conclusions:

  • The modified EM algorithm offers a computationally efficient alternative for parameter estimation in large-scale IRT applications.
  • It provides substantial runtime advantages while preserving estimation quality.
  • Potential for integration into existing EM routines and extension to multidimensional IRT models.