Debelak R Strobl C 2019 M-fluctuation tests are a recently proposed method for detecting differential item functioning in Rasch models. This article discusses a generalization of this method to two additional item response theory models: the two-parametric logistic model and the three-parametric logistic model with a common guessing parameter. The Type I error rate and the power of this method were evaluated by a variety of simulation studies. The results suggest that the new method allows the detection of various forms of differential item functioning in these models, which also includes differential discrimination and differential guessing effects. It is also robust against moderate violations of several assumptions made in the item parameter estimation. application/pdf https://sonar.ch/global/documents/253940 eng info:eu-repo/semantics/altIdentifier/doi/10.1177/0013164418777784 info:eu-repo/semantics/altIdentifier/pmid/30911198 info:eu-repo/semantics/openAccess Educational and psychological measurement. - 2019 Monte Carlo simulation differential item functioning item response theory measurement invariance Investigating Measurement Invariance by Means of Parameter Instability Tests for 2PL and 3PL Models. http://purl.org/coar/resource_type/c_6501