Regularized Joint Maximum Likelihood Estimation of Latent Space Item Response Models

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.