A fixed effect item response theory (IRT) model is developed for modeling group specific item parameters. Two applications are presented. The first application is that the proposed model can be used to detect whether a response mechanism is ignorable using the splitter item technique. The second application is the detection of differential item functioning. In the latter application, the fixed effect item parameters can model item parameter differences between groups. Simulation studies are presented to show the feasibility and performance of the method on both applications.