A connection between item/subtest regression and the Rasch model

The purpose of this paper is to link empirical Bayes methods with two specific topics in item response theory--item/subtest regression, and testing the goodness of fit of the Rasch model--under the assumptions of local independence and sufficiency. It is shown that item/subtest regression results in empirical Bayes estimates only if the Rasch model holds. Additionally, it is shown that a newly-derived exploratory goodness-of-fit test for the Rasch model, which does not need item and person parameter estimates, can be seen as an empirical Bayes test. This test compares the observed proportions of correct answers to one specific item, given any pattern that leads to a number-right score.