Order-Constrained Bayes Inference for Dichotomous Models of Unidimensional Nonparametric IRT

2004/03/01 by George Karabatsos, Ching‐Fan Sheu · 34 citations
Computer Science · Decision Sciences · Mathematics · #Advanced Statistical Modeling Techniques #Artificial intelligence #Bayes factor #Bayes' theorem #Bayesian probability #Computer science #Conditional independence #Econometrics #Gibbs sampling #Inference #Item response theory #Mathematics #Monotonic function #Nonparametric statistics #Psychometric Methodologies and Testing #Psychometrics #Statistical Methods and Bayesian Inference #Statistical inference #Statistics

paper · doi:10.1177/0146621603260678

published in Applied Psychological Measurement 28(2), 110-125 (SAGE Publishing)

openalex publication_date 2004/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/04

Abstract

This study introduces an order-constrained Bayes inference framework useful for analyzing data containing dichotomous-scored item responses, under the assumptions of either the monotone homogeneity model or the double monotonicity model of nonparametric item response theory (NIRT). The framework involves the implementation of Gibbs sampling to estimate order-constrained parameters, followed by inference with the posterior-predictive distribution to test the monotonicity, invariant item ordering, and local independence assumptions of NIRT. The Bayes framework is demonstrated through the analysis of real test data, and possible extensions of it are discussed.

Citations

• Additive Conjoint Isotonic Probabilistic Models (ADISOP)
• Two-Group Classification in Latent Trait Theory: Scores with Monotone Likelihood Ratio
• Enumerating and testing conjoint measurement models
• Estimation of Latent Ability Using a Response Pattern of Graded Scores

Cited by

• The Rasch Model from the Perspective of the Representational Theory of Measurement
• Theory of conjoint measurement [wikipedia]