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Latent variable sdelection in multidimensional item response theory models using the expectation model selection

Ping-Feng Xu1,2, Laixu Shang2, Qian-Zhen Zheng2

  • 1Academy for Advanced Interdisciplinary Studies, Northeast Normal University, Changchun, China.

The British Journal of Mathematical and Statistical Psychology
|December 17, 2021
PubMed
Summary
This summary is machine-generated.

The expectation model selection (EMS) algorithm effectively identifies latent traits in multidimensional item response theory (MIRT) models. This method, applied to the Eysenck Personality Questionnaire, proves more accurate and efficient than other regularization techniques.

Keywords:
Bayesian information criterionexpectation model selection algorithmlatent variable selectionmultidimensional item response theory model

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Area of Science:

  • Psychometrics
  • Statistical Modeling

Background:

  • Multidimensional item response theory (MIRT) models are crucial for understanding complex cognitive abilities.
  • Latent variable selection is essential for accurately interpreting MIRT results.
  • Existing methods for latent variable selection can be computationally intensive and less accurate.

Purpose of the Study:

  • To apply and verify the expectation model selection (EMS) algorithm for latent variable selection in MIRT.
  • To assess the performance of the EMS algorithm in identifying latent traits using the Bayesian information criterion (BIC).
  • To demonstrate the practical application of the EMS algorithm using real-world personality data.

Main Methods:

  • Utilizing the expectation model selection (EMS) algorithm to minimize the Bayesian information criterion (BIC).
  • Proving the numerical convergence of the EMS algorithm under mild assumptions, including handling missing data.
  • Implementing and verifying the EMS algorithm for the multidimensional two-parameter logistic (M2PL) model under specific identifiability assumptions.

Main Results:

  • The EMS algorithm demonstrates numerical convergence for latent variable selection in MIRT models, even with missing data.
  • The EMS algorithm shows superior performance compared to EM-based L1 regularization in correctly selecting latent variables and reducing computation time.
  • Successful application of the EMS algorithm to the Eysenck Personality Questionnaire data.

Conclusions:

  • The EMS algorithm is a reliable and efficient tool for latent variable selection in MIRT models.
  • The EMS algorithm offers a significant improvement over existing methods for identifying latent traits.
  • The study validates the utility of the EMS algorithm in both simulated and real-world psychometric analyses.