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Generalized Fiducial Inference for Logistic Graded Response Models

Published online by Cambridge University Press:  01 January 2025

Yang Liu  and
Jan Hannig
Yang Liu*
Affiliation:
University of California, Merced
Jan Hannig
Affiliation:
The University of North Carolina, Chapel Hill
*
Correspondence should be made to Yang Liu, Psychological Sciences, School of Social Sciences, Humanities, and Arts, University of California, Merced, 5200 North Lake Road, Merced, CA 95343, USA. Email: yliu85@ucmerced.edu
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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.

Keywords

generalized fiducial inferenceconfidence intervalMarkov chain Monte CarloBernstein–von Mises theoremitem response theorygraded response modelbifactor model

Information

Type
Original Paper
Information
Psychometrika , Volume 82 , Issue 4 , December 2017 , pp. 1097 - 1125
Copyright
Copyright © 2017 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (doi:10.1007/s11336-017-9554-0) contains supplementary material, which is available to authorized users.

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