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Bayesian Multidimensional IRT Models With a Hierarchical Structure

Southern Illinois University Carbondale, ysheng{at}siu.edu

Christopher K. Wikle

University of Missouri-Columbia

As item response models gain increased popularity in large-scale educational and measurement testing situations, many studies have been conducted on the development and applications of unidimensional and multidimensional models. Recently, attention has been paid to IRT-based models with an overall ability dimension underlying several ability dimensions specific for individual test items, where the focus is mainly on models with dichotomous latent traits. The purpose of this study is to propose such models with continuous latent traits under the Bayesian framework. The proposed models are further compared with the conventional IRT models using Bayesian model choice techniques. The results from simulation studies as well as actual data suggest that (a) such models can be developed; (b) compared with the unidimensional IRT model, the proposed models better describe the actual data; and (c) the use of the proposed IRT models and the multiunidimensional model should be based on different beliefs about the underlying dimensional structure of a test.

Key Words: item response theory • hierarchical MIRT model • general and specific abilities • unidimensional model • multiunidimensional model • MCMC • Gibbs sampling • Bayesian model choice

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