A simple hierarchical Bayesian model for simultaneous inference of tournament graphs and informant error

Abstract: The paper presents a hierarchical Bayesian model for simultaneous inference of tournament graphs and informant error. From multiple informant reports or measurement instrument outputs, the model estimates the structure of a criterion (i.e., true) tournament graph with possibly tied outcomes. Tournament graphs with possibly tied outcomes are graphs in which there are three possible states for each unordered pair of graph nodes: node i wins and node j loses; node j wins and node i loses; neither node wins (i.e., tied outcome). The model also estimates the rates at which individual informants (or instruments) mistake the winning and losing dyad members, falsely report a tied outcome, and falsely report a decisive outcome. The model was developed to infer social dominance structure from multiple informants' reports, but is potentially useful for inferring any structure that can be characterized by a tournament graph, and which is measured from multiple reports.