title: Systemic testing on Bradley-Terry model against nonlinear ranking hierarchy.
abstract: 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.
authors.affiliation: Department of Statistics, University of California Davis, Davis, California, United States of America.
authors.forename: Aaron
authors.initials: A
authors.lastname: Shev
authors.affiliation: Department of Statistics, University of California Davis, Davis, California, United States of America.
authors.forename: Kevin
authors.initials: K
authors.lastname: Fujii
authors.affiliation: Department of Statistics, University of California Davis, Davis, California, United States of America.
authors.forename: Fushing
authors.initials: F
authors.lastname: Hsieh
authors.affiliation: Department of Population Health & Reproduction, University of California Davis, Davis, California, United States of America.
authors.forename: Brenda
authors.initials: B
authors.lastname: McCowan
mesh_terms: D000818:Animals; D006801:Humans; D008962:Models, Theoretical; D018709:Statistics, Nonparametric