Procedures for collective inference make simultaneous statistical judgments about the same variables for a set of related data instances. For example, collective inference could be used to simultaneously classify a set of hyperlinked documents or infer the legitimacy of a set of related financial transactions. Several recent studies indicate that collective inference can significantly reduce classification error when compared with traditional inference techniques. We investigate the underlying mechanisms for this error reduction by reviewing past work on collective inference and characterizing different types of statistical models used for making inference in relational data. We show important differences among these models, and we characterize the necessary and sufficient conditions for reduced classification error based on experiments with real and simulated data. Categories and Subject Descriptors I.2.6 [Artificial Intelligence]: Learning; I.5.1 [Pattern Recognition]: Models. Gener...