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Regularized Joint Maximum Likelihood Estimation of Latent Space Item Response Models.

Dylan Molenaar1, Minjeong Jeon2

  • 1Department of Psychology, University of Amsterdam, The Netherlands.

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We introduce faster estimation methods for latent space item response models (LSIRMs) using regularized joint maximum likelihood (JML). These methods enable efficient analysis of complex item response data, including ordinal outcomes.

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Area of Science:

  • Psychometrics
  • Statistical Modeling

Background:

  • Latent space item response models (LSIRMs) embed subjects and items in a low-dimensional Euclidean space, revealing interactions beyond conventional item response theory.
  • Current Markov Chain Monte Carlo (MCMC) Bayesian estimation for LSIRMs is computationally intensive, limiting their practical application.

Purpose of the Study:

  • To propose and evaluate regularized joint maximum likelihood (JML) estimation methods for LSIRMs.
  • To address computational challenges and extend LSIRM applicability to ordinal data and dimensionality selection.

Main Methods:

  • Developed two variants of regularized JML estimation: penalized JML and constrained JML.
  • Derived JML approaches for LSIRM estimation, addressing maximum likelihood specific issues.
  • Utilized cross-validation for latent space dimensionality selection.

Main Results:

  • Simulation studies demonstrated acceptable parameter recovery and effective cross-validation performance.
  • Applied binary and ordinal LSIRMs to real datasets on deductive reasoning and personality.
  • Implemented JML methods in the R package 'LSMjml'.

Conclusions:

  • Regularized JML estimation offers a computationally efficient alternative to MCMC for LSIRMs.
  • The proposed methods facilitate broader application of LSIRMs, including for ordinal data and with automated dimensionality selection.