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Abstract:
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Evaluating person-fit in Bayesian Item Response Theory (IRT) models has traditionally been done using the posterior-predictive (PP) method. In recent years, methods which are more powerful and less conservative than the person-fit PP method have been introduced. We propose a new Bayesian person-fit method based on pivotal discrepancy measures (PDMs), which has already been used for general Bayesian model checking applications. This method can be employed using standard MCMC output. We apply this new PDM method to person-fit checking in Bayesian IRT models using the popular Lz and Lz* person-fit measures. Simulation studies are done to compare the PDM method with the existing methods under a three-parameter logisitc model (3PL). Type I error rates and detection rates of some specific model violations are investigated. The main results show that our PDM method is less conservative and more powerful than the PP method, and comparable in performance to the newer methods under all simulation conditions.
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