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Generalized Fiducial Inference for Binary Logistic Item Response Models.

Yang Liu1, Jan Hannig2

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

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Summary
This summary is machine-generated.

Generalized fiducial inference (GFI) offers a novel statistical approach without requiring prior distributions. This study applies GFI to item response theory models, demonstrating its utility in complex analyses.

Keywords:
Markov chain Monte Carloconfidence intervalexploratory item factor analysisgeneralized fiducial inferenceitem response theorytwo-parameter logistic model

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Area of Science:

  • Statistics
  • Psychometrics
  • Item Response Theory

Background:

  • Generalized fiducial inference (GFI) is an emerging statistical framework.
  • It provides an alternative to traditional likelihood-based and Bayesian methods.
  • GFI constructs confidence intervals (CIs) without needing prior distributions, ideal for data-scarce scenarios.

Purpose of the Study:

  • To apply Generalized Fiducial Inference (GFI) to binary logistic item response theory (IRT) models.
  • To investigate the performance of GFI-derived confidence intervals (CIs) compared to existing methods.
  • To demonstrate the application of GFI in high-dimensional exploratory item factor analysis.

Main Methods:

  • Application of GFI to a family of binary logistic IRT models.
  • Development of a Markov chain Monte Carlo (MCMC) algorithm for sampling from the fiducial distribution.
  • Monte Carlo simulation to compare fiducial percentile CIs with maximum likelihood (ML) based Wald-type CIs.
  • Analysis of Eysenck Personality Questionnaire data using GFI in exploratory item factor analysis.

Main Results:

  • The study successfully applied GFI to various IRT models, including 2PL, bifactor, and exploratory item factor models.
  • Asymptotic properties of the fiducial distribution were theoretically discussed.
  • The proposed MCMC algorithm effectively generated random draws from the fiducial distribution.
  • Fiducial percentile CIs showed comparable or superior performance to Wald-type CIs in finite-sample simulations.

Conclusions:

  • Generalized Fiducial Inference (GFI) is a viable and effective method for parameter estimation and confidence interval construction in item response theory models.
  • GFI provides a robust alternative when prior information is unavailable.
  • The method is particularly useful for complex, high-dimensional psychometric analyses, as demonstrated with real-world personality data.