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In recent years, multidimensional Item
Response Theory (MIRT) has been proposed as a basis for solving a number of
applied testing problems, including problems in the areas of adaptive
testing, item-pool construction, and differential item functioning. However,
the estimation of item-parameters for multidimensional item-response models
has proven to be a major impediment to the application of MIRT. This paper
presents a methodology for multidimensional item-parameter estimation based
on Markov chain Monte Carlo (MCMC) techniques, where the pattern of free and
fixed item-factor loadings is specified a priori. By using MCMC methodology,
the problem of parameter estimation can be decomposed into a series of
relatively simple estimation steps. One particular application of the
proposed methodology is demonstrated: Online calibration in computerized
adaptive testing (CAT).
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