Bradley-Terry 1
2
3
paired comparison 4
paired comparison 1860 Landau 5
6
A B B C A C 7
n 0.5n(n-1) n 2 0.5n(n-1) 3 8
9
A B B C A C 10
0.5n(n-1) (n-1) 11
Kendall coefficient of consistence ζ (1940) null 0.5 12
null 0.5 2^3= ABC ACB BAC BCA CAB CBA 75% 13
null 75% 37.5% 11.7% 2.2% 0.2% 5% 14
15
0.62 0.34 5,8,11,14 1 10000 16
0.0 0.2 0.4 0.6 0.8 1.0 rank correlation exact estimation of ranks 20% 10% 0.00 0.05 0.10 0.15 0.20 17
Bradley-Terry model A B A A B A B A A A B paired comparison linear models 18
Bradley-Terry model A B A A A B A A B A B 19
Bradley-Terry model or 20
Bradley-Terry model rank correlation exact estimation of ranks 0.0 0.2 0.4 0.6 0.8 1.0 BT 20% 10% 0.00 0.05 0.10 0.15 0.20 BT 21
Bradley-Terry model RBradleyTerry2 LearnBayes Psychotree eba prefmod 22
Bradley-Terry model 23
(NPO) 2010 24 4 0.5 24
(NPO) 24 4 25
RBradleyTerry2 BTm 0.30 0.40 0.50 0.60 0.0 0.1 0.2 0.3 0.4 1 2 3 4 5 6 nullbt deviance 5.01 P=0.41 AICnull 26
0.30 0.40 0.50 0.60 0.0 0.2 0.4 0.6 0.8 1.0 1 2 3 4 5 6 nullbt deviance 19.36 P=0.0016 AICBT 27
0.30 0.40 0.50 0.60 0.0 0.2 0.4 0.6 0.8 1.0 1.2 2 4 6 8 10 12 nullbt P=0.0019 deviance 29.43 AICBT 28
0.30 0.40 0.50 0.60 0.0 0.2 0.4 0.6 0.8 1.0 1.2 2 4 6 8 10 12 29
Bradley-Terry model object-specific player-specific contest-specific order effect 1-0 30
Bradley-Terry model. order effect A,AgrestiCategorical Data Analysis +7.5% 31
0.01861±0.0127 0.46% z=1.63 p>0.05 AIC 0.01442±0.009 0.36% z=1.53 p>0.05 AIC 32
Bradley-Terry 33