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Generalized Fiducial Inference for Binary Logistic Item Response Models

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  • Yang Liu

    (University of California, Merced)

  • Jan Hannig

    (The University of North Carolina at Chapel Hill)

Abstract

Generalized fiducial inference (GFI) has been proposed as an alternative to likelihood-based and Bayesian inference in mainstream statistics. Confidence intervals (CIs) can be constructed from a fiducial distribution on the parameter space in a fashion similar to those used with a Bayesian posterior distribution. However, no prior distribution needs to be specified, which renders GFI more suitable when no a priori information about model parameters is available. In the current paper, we apply GFI to a family of binary logistic item response theory models, which includes the two-parameter logistic (2PL), bifactor and exploratory item factor models as special cases. Asymptotic properties of the resulting fiducial distribution are discussed. Random draws from the fiducial distribution can be obtained by the proposed Markov chain Monte Carlo sampling algorithm. We investigate the finite-sample performance of our fiducial percentile CI and two commonly used Wald-type CIs associated with maximum likelihood (ML) estimation via Monte Carlo simulation. The use of GFI in high-dimensional exploratory item factor analysis was illustrated by the analysis of a set of the Eysenck Personality Questionnaire data.

Suggested Citation

  • Yang Liu & Jan Hannig, 2016. "Generalized Fiducial Inference for Binary Logistic Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 81(2), pages 290-324, June.
    • Handle: RePEc:spr:psycho:v:81:y:2016:i:2:d:10.1007_s11336-015-9492-7
    DOI: 10.1007/s11336-015-9492-7
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    References listed on IDEAS

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    Cited by:

    1. Yang Liu & Ji Seung Yang, 2018. "Bootstrap-Calibrated Interval Estimates for Latent Variable Scores in Item Response Theory," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 333-354, June.
    2. Ionut Bebu & George Luta & Thomas Mathew & Brian K. Agan, 2016. "Generalized Confidence Intervals and Fiducial Intervals for Some Epidemiological Measures," IJERPH, MDPI, vol. 13(6), pages 1-13, June.
    3. Yang Liu & Jan Hannig, 2017. "Generalized Fiducial Inference for Logistic Graded Response Models," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1097-1125, December.
    4. Yang Liu & Ji Seung Yang, 2018. "Interval Estimation of Latent Variable Scores in Item Response Theory," Journal of Educational and Behavioral Statistics, , vol. 43(3), pages 259-285, June.
    5. Piero Veronese & Eugenio Melilli, 2021. "Confidence Distribution for the Ability Parameter of the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 131-166, March.

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