title: Generalized Fiducial Inference for Logistic Graded Response Models.
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.
authors.affiliation: Psychological Sciences, School of Social Sciences, Humanities, and Arts, University of California, Merced, 5200 North Lake Road, Merced, CA, 95343 , USA. yliu85@ucmerced.edu.
authors.forename: Yang
authors.initials: Y
authors.lastname: Liu
authors.affiliation: Department of Statistics and Operations Research, The University of North Carolina, Chapel Hill, Chapel Hill, NC, USA.
authors.forename: Jan
authors.initials: J
authors.lastname: Hannig
mesh_terms: D001499:Bayes Theorem; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D016015:Logistic Models; D008390:Markov Chains; D009010:Monte Carlo Method; D000071066:Patient Reported Outcome Measures
keywords: Bernstein–von Mises theorem; Markov chain Monte Carlo; bifactor model; confidence interval; generalized fiducial inference; graded response model; item response theory