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A General Diagnostic Model Applied to Language Testing Data IRT MCMC GDM GPCM 2PL TOEFL iBT

von Davier, Matthias
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Cognitive Diagnosis, Item Response Theory (IRT), Latent Class Models, EM Algorithm, Skill Profile, Markov Chain Monte Carlo (MCMC), General Diagnostic Model (GDM), Generalized Partial-Credit Model (GPCM), 2-Parameter Logistic (2PL) Model, Test of English as a Foreign Language (TOEFL), Internet Based Testing (iBT)


This report uses one member of this class of diagnostic models, a compensatory diagnostic model that is parameterized similar to the generalized partial credit model (GPCM). Many well-known models, such as uni- and multivariate versions of the Rasch model and the two parameter logistic item response theory (2PL-IRT) model, the GPCM, and the FACETS model, as well as a variety of skill profile models, are special cases of this member of the class of GDMs. This paper describes an algorithm that capitalizes on using tools from item response theory for scale linking, item fit, and parameter estimation. In addition to an introduction to the class of GDMs and to the partial credit instance of this class for dichotomous and polytomous skill profiles, this paper presents a parameter recovery study using simulated data and an application to real data from the field test for TOEFL® Internet-based testing (iBT).

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