Systemic testing on Bradley-Terry model against nonlinear ranking hierarchy.

• Main Authors: Aaron Shev, Kevin Fujii, Fushing Hsieh, Brenda McCowan
• Format: Article
• Language: English
• Published: Public Library of Science (PLoS) 2014-01-01
• Series: PLoS ONE
• Online Access: http://europepmc.org/articles/PMC4274013?pdf=render

We take a system point of view toward constructing any power or ranking hierarchy onto a society of human or animal players. The most common hierarchy is the linear ranking, which is habitually used in nearly all real-world problems. A stronger version of linear ranking via increasing and unvarying winning potentials, known as Bradley-Terry model, is particularly popular. Only recently non-linear ranking hierarchy is discussed and developed through recognition of dominance information contents beyond direct dyadic win-and-loss. We take this development further by rigorously arguing for the necessity of accommodating system's global pattern information contents, and then introducing a systemic testing on Bradley-Terry model. Our test statistic with an ensemble based empirical distribution favorably compares with the Deviance test equipped with a Chi-squared asymptotic approximation. Several simulated and real data sets are analyzed throughout our development.