ABSTRACT
A statistical model that is appropriate for a data set should be able to explain the key features in the data set adequately. According to the Standard 3.9 of the Standards for Educational and Psychological Testing, evidence of model fit should be provided when an item response theory model is used to make inferences from a test data set. There has been a recent surge in the use of Bayesian estimation in Item Response Theory. Some popular Bayesian model-fit methods are as follows: Bayesian residual analysis; prior predictive checks; and posterior predictive checks. Naturally, research on Bayesian model-fit and model-comparison methods has also flourished in an attempt to keep pace with this advancement in Bayesian Item Response Theory modeling. To avoid making an incorrect choice of an Item Response Theory model and to ensure the best possible model-data fit, it is essential to apply model-fit and model-comparison methods.
