Abstract: We consider two generalizations of the area under the receiver operating characteristic curve (“AUC”), a popular measure of discrimination, to accommodate clustered data. We describe situations in which the two cluster AUCs diverge and other situations in which they coincide. Differences are described using concrete models and visualizations, while quantitative results are used to relate the two generalizations. Procedures for joint estimation and inference are also presented, along with a simulation study. We apply the results to data collected on urban policing behavior.

Key words and phrases: AUC, clustered data, confounding, Simpson’s paradox.