Using Deterministic, Gated Item Response Theory Model to detect test cheating due to item compromise

The Deterministic, Gated Item Response Theory Model (DGM, Shu, Unpublished Dissertation. The University of North Carolina at Greensboro, 2010) is proposed to identify cheaters who obtain significant score gain on tests due to item exposure/compromise by conditioning on the item status (exposed or unexposed items). A "gated" function is introduced to decompose the observed examinees' performance into two distributions (the true ability distribution determined by examinees' true ability and the cheating distribution determined by examinees' cheating ability). Test cheaters who have score gain due to item exposure are identified through the comparison of the two distributions. Hierarchical Markov Chain Monte Carlo is used as the model's estimation framework. Finally, the model is applied in a real data set to illustrate how the model can be used to identify examinees having pre-knowledge on the exposed items.