Bayesian Modeling for a Uniform Differential Item Functioning Analysis Procedure in Item Response Theory: Probability That Item Difficulty Parameters and Correct Answer Probabilities Differ Between Groups

Item response theory (IRT) is a theory that aims to separate and analyze characteristics of examinees and characteristics related to item difficulty. In item response theory, if 2 examinees have the same characteristic value, all probabilities of correct response to an item that has the same item characteristic are equal, regardless of whether or not the examinees belong to the same subgroup. If the mutual probabilities are different between the subgroups to which the examinees belong, the item has differential item functioning (DIF). Differential item functioning analysis in item response theory traditionally relies on null hypothesis tests. That method may identify a non-differential item functioning item as a differential item functioning item. Also, the magnitude of differential item functioning cannot be interpreted directly from the results of null hypothesis significance tests. The present paper proposes a differential item functioning analysis procedure based on Bayesian modeling for uniform differential item functioning. When the proposed method is used, it is possible to combine the traditional procedure of estimating the item parameters separately for each subgroup and, from that, estimating the equating coefficient.