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Generalized Fiducial Inference for Logistic Graded Response Models

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  • Yang Liu

    (University of California, Merced)

  • Jan Hannig

    (The University of North Carolina, Chapel Hill)

Abstract

Samejima’s graded response model (GRM) has gained popularity in the analyses of ordinal response data in psychological, educational, and health-related assessment. Obtaining high-quality point and interval estimates for GRM parameters attracts a great deal of attention in the literature. In the current work, we derive generalized fiducial inference (GFI) for a family of multidimensional graded response model, implement a Gibbs sampler to perform fiducial estimation, and compare its finite-sample performance with several commonly used likelihood-based and Bayesian approaches via three simulation studies. It is found that the proposed method is able to yield reliable inference even in the presence of small sample size and extreme generating parameter values, outperforming the other candidate methods under investigation. The use of GFI as a convenient tool to quantify sampling variability in various inferential procedures is illustrated by an empirical data analysis using the patient-reported emotional distress data.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:4:d:10.1007_s11336-017-9554-0
    DOI: 10.1007/s11336-017-9554-0
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    References listed on IDEAS

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    2. 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.

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