Title: Measurement Invariance Tests for IRT Models Estimated by Bayesian MAP Authors: Rudolf Debelak, Samuel Pawel Affiliation: University of Zürich Abstract: A variety of recent studies have proposed the use of score-based tests for detecting differential item functioning (DIF) in item response theory (IRT) models. This method has been found to be readily applicable for many widely applied IRT models, like Rasch models and other logistic IRT models, like the two-parametric logistic (2PL) model. However, for some widely used models, like the three-parametric logistic (3PL) model, these tests were found to lead to an increased Type I error rate. This makes their application problematic under specific conditions. In this talk, we will first briefly discuss possible reasons for this increased Type I error rate. We will then present an alternative method based on Bayesian Maximum-a-Posteriori (MAP) estimates as an alternative. The alternative method is evaluated for various IRT models (2PL and 3PL), different conditions of DIF effects, test length and sample size and also different test statistics and prior distributions and compared against the score-based tests. The new method is found to have comparable power against uniform and non-uniform DIF while having a lower rate of false-positive results. However, in contrast to the frequentist score-based tests, the new method requires the selection of a suitable prior distribution for all item parameters.