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A stochastic approximation expectation maximization algorithm for estimating Ramsay-curve three-parameter normal

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|December 12, 2022
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Summary

This study introduces a new method for item response models when latent traits are not normally distributed. The proposed algorithm improves accuracy for item parameters in real-world testing scenarios.

Keywords:
3PNO modelRamsay curvedensity estimationitem response theorymarginal maximum likelihood estimationstochastic approximation EM algorithm (SAEM)

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Area of Science:

  • Psychometrics
  • Statistical modeling
  • Educational measurement

Background:

  • Item response models commonly assume normal latent traits, which may not hold true in practice.
  • The conventional three-parameter normal ogive (3PNO) model is limited by this normality assumption.
  • Flexible latent trait distributions are needed for more realistic item response modeling.

Purpose of the Study:

  • To propose a novel stochastic approximation expectation maximization (SAEM) algorithm for estimating a Ramsay-curve item response theory (RC-IRT) based 3PNO model (RC-3PNO).
  • To address the limitations of traditional models by allowing for non-normal latent trait distributions.
  • To evaluate the accuracy of the proposed SAEM algorithm for item parameter estimation.

Main Methods:

  • Development of a SAEM algorithm tailored for the RC-3PNO model.
  • Simulation studies comparing the SAEM algorithm with the conventional 3PNO model under various latent trait distributions (normal, skewed, bimodal).
  • Application of three model selection criteria to determine optimal B-spline parameters (knots and degree) for the RC-3PNO model.
  • Validation using a real dataset from the PISA 2018 test.

Main Results:

  • The SAEM algorithm demonstrates superior accuracy in estimating item parameters for the RC-3PNO model compared to the standard 3PNO model, particularly when latent trait distributions deviate from normality.
  • The proposed method effectively handles skewed and bimodal latent trait distributions.
  • Model selection criteria successfully identified optimal B-spline configurations for the RC-3PNO model.

Conclusions:

  • The SAEM algorithm provides a robust and accurate approach for estimating item response models with flexible latent trait distributions.
  • The RC-3PNO model, estimated via SAEM, offers a more realistic alternative to traditional models in educational and psychological assessments.
  • The findings have significant implications for improving the precision of measurement in large-scale testing environments.