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Generalized Fiducial Inference for Logistic Graded Response Models.

Yang Liu1, Jan Hannig2

  • 1Psychological Sciences, School of Social Sciences, Humanities, and Arts, University of California, Merced, 5200 North Lake Road, Merced, CA, 95343 , USA. yliu85@ucmerced.edu.

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|February 23, 2017
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Summary

Generalized fiducial inference (GFI) provides reliable parameter estimates for multidimensional graded response models, even with small sample sizes. This novel method outperforms traditional approaches in psychological and educational assessments.

Keywords:
Bernstein–von Mises theoremMarkov chain Monte Carlobifactor modelconfidence intervalgeneralized fiducial inferencegraded response modelitem response theory

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Educational Measurement

Background:

  • The graded response model (GRM) is widely used for analyzing ordinal data in psychology, education, and health.
  • Accurate point and interval estimates for GRM parameters are crucial for robust assessment.
  • Existing methods may face challenges with small sample sizes or extreme parameter values.

Purpose of the Study:

  • To derive and implement generalized fiducial inference (GFI) for multidimensional graded response models.
  • To evaluate the finite-sample performance of GFI compared to likelihood-based and Bayesian methods.
  • To demonstrate the utility of GFI in quantifying sampling variability with real-world data.

Main Methods:

  • Derivation of generalized fiducial inference (GFI) for multidimensional graded response models.
  • Implementation of a Gibbs sampler for fiducial estimation.
  • Comparison via simulation studies with likelihood-based and Bayesian estimation approaches.

Main Results:

  • The proposed GFI method yields reliable parameter estimates, outperforming common methods.
  • GFI demonstrates robust performance even with small sample sizes and extreme parameter values.
  • Empirical analysis showcases GFI's effectiveness in quantifying sampling variability.

Conclusions:

  • Generalized fiducial inference offers a powerful and reliable alternative for estimating parameters in multidimensional graded response models.
  • GFI is particularly advantageous in scenarios with limited data or challenging parameter distributions.
  • The method provides a valuable tool for psychometricians and researchers in various assessment fields.