Modeling Intransitivity in Pairwise Comparisons with Application to Baseball Data
提出一种半参数模型，通过将球员对分配到随机数量的非传递性水平，灵活捕捉不同策略导致的非传递性，同时将球员分配到随机数量的技能水平以提高效率，在棒球数据中优于传统模型。
The seminal Bradley-Terry model exhibits transitivity, that is, the property that the probabilities of player A beating B and B beating C give the probability of A beating C, with these probabilities determined by a skill parameter for each player. Such transitive models do not account for different strategies of play between each pair of players, which gives rise to intransitivity. Various intransitive parametric models have been proposed but they lack the flexibility to cover the different strategies across n players, with the O(n2) values of intransitivity modeled using O(n) parameters, while they are not parsimonious when the intransitivity is simple. We overcome their lack of adaptability by allocating each pair of players to one of a random number of K intransitivity levels, each level representing a different strategy. Our novel approach for the skill parameters involves having the n players allocated to a random number of A<n distinct skill levels, to improve efficiency and avoid false rankings. Although we may have to estimate up to O(n2) unknown parameters for (A,K) we anticipate that in many practical contexts A+K<n. Our semiparametric model, which gives the Bradley-Terry model when (A=n−1,K=0), is shown to have an improved fit relative to the Bradley-Terry, and the existing intransitivity models, in out-of-sample testing when applied to simulated and American League baseball data. Supplementary materials for the article areavailable online.