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Random effects and extended generalized partial credit models.

David J Hessen1

  • 1Department of Methodology and Statistics, Utrecht University, Utrecht, The Netherlands.

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Summary
This summary is machine-generated.

This study introduces a new random effects generalized partial credit model for latent variable measurement. It enables parameter estimation without assuming latent variable distribution or using numerical integration, improving accuracy and efficiency.

Keywords:
expected a posteriori estimatesextended generalized partial credit modelmarginal maximum likelihood estimationrandom effects generalized partial credit model

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Educational Measurement

Background:

  • Traditional latent variable models often assume specific distributions for the latent variable.
  • Estimating parameters in polytomously scored item models can be computationally intensive.
  • Existing models may lack flexibility in capturing complex response patterns.

Purpose of the Study:

  • To present a random effects generalized partial credit model with a closed-form marginal probability distribution.
  • To develop estimation methods that do not require distributional assumptions or numerical integration.
  • To introduce an extended generalized partial credit model for enhanced flexibility.

Main Methods:

  • Derivation of a closed-form expression for the joint marginal probability distribution of item scores.
  • Application of marginal maximum likelihood estimation for parameter estimation.
  • Development and application of generalized likelihood ratio tests for model fit assessment.
  • Computation of expected a posteriori estimates for person parameters.

Main Results:

  • The proposed model allows for parameter estimation without assuming a specific latent variable distribution.
  • Marginal maximum likelihood estimation is feasible without numerical integration.
  • New special cases and a more general extended model are identified.
  • Expected a posteriori estimates are obtainable for all score patterns.

Conclusions:

  • The developed models offer a more flexible and computationally efficient approach to latent variable measurement.
  • The proposed methods provide accurate parameter and person estimation.
  • Simulation studies and empirical examples demonstrate the practical utility of the new models.