Effects of anchor item methods on the detection of differential item functioning within the family of Rasch models

Scale indeterminacy in analysis of differential item functioning (DIF) within the framework of item response theory can be resolved by imposing 3 anchor item methods: the equal-mean-difficulty method, the all-other anchor item method, and the constant anchor item method. In this article, applicability and limitations of these 3 methods are discussed and their performances of DIF detection are compared using Monte Carlo simulations within the family of Rasch models (Rasch, 1960). The results show that when the test contained multiple DIF items, only when the difference in the mean item difficulties between the reference and focal groups approached zero did the equal-mean-difficulty method and the all-other method function appropriately. In contrast, the constant method yielded unbiased parameter estimates, well-controlled Type I error, and high power of DIF detection, regardless of large differences in the mean item difficulties between groups and high percentages of DIF items in the tests. In addition, the more anchor items in the constant method, the higher the power of detecting DIF. Therefore, the constant anchor item method is recommended when conducting DIF analysis. Methods of locating anchor items for implementing the constant method are also discussed.