58 (W15) 2011 03 09 kubo@ees.hokudai.ac.jp http://goo.gl/edzle 2011 03 09 (2011 03 09 19 :32 )
: Bradley-Terry Burczyk
? ( )
1999 2010 9 R : 7 (1) 8 7??! 15 http://www.atmarkit.co.jp/fcoding/articles/stat/07/stat07a.html
? 2011 03 09 (2011 03 09 19 :32 )
0.5
fixed effects:? random effects:!
: 1000 5 as.numeric(table(factor(w, levels = 0:size))) 0 50 100 150 200 0 5 10 15 15
0.5? 15 y? 0.0 0.2 0.4 0.6 0.8 1.0 as.numeric(table(factor(w, levels = 0:size))) 0 50 100 150 200 0 5 10 15 15
(GLMM) 2011 03 09 (2011 03 09 19 :32 ) 0.0 0.2 0.4 0.6 0.8 1.0 as.numeric(table(factor(w, levels = 0:size))) 0 50 100 150 200 0 5 10 15 15
4. σ 2011 03 09 (2011 03 09 19 :32 ) BUGS code for (i in 1:N) { Win[i] ~ dbinom(q[i], 15) # 15 logit(q[i]) <- re[i] re[i] ~ dnorm(0, tau) # } tau <- 1 / (sigma * sigma) sigma ~ dunif(0, 1000) # 1. (q i, 15 ) 2. q i 1 1+exp( r i ) 3. r i (, σ)
BUGS code for (i in 1:N) { Win[i] ~ dbinom(q[i], 15) # 15 logit(q[i]) <- beta1 + beta2 * Size[i] + re[i] re[i] ~ dnorm(0, tau) # } # beta1, beta2: beta1 ~ dnorm(0, 1.0E-4) # beta2 ~ dnorm(0, 1.0E-4) # ( ) logit(q i ) ( ) + ( ) ( ) + r i 2011 03 09 (2011 03 09 19 :32 )
Bradley-Terry
??
: -3-2 -1 0 1 2 3??
Bradley-Terry model: fixed effects random effects -3-2 -1 0 1 2 3 (A ) = exp( A ) exp( A ) + exp( B )
Bradley-Terry A 0.0 0.2 0.4 0.6 0.8 1.0-3 -2-1 0 1 2 3-4 -2 0 2 4 A B ( ) = ( ) + ( fixed effects ) + ( random effects ) 2011 03 09 (2011 03 09 19 :32 )
Random effects? Bradley-Terry (factor ) ( ) : : (or GLMM)? ( )? 2011 03 09 (2011 03 09 19 :32 )
?
-3-2 -1 0 1 2 3 2011 03 09 (2011 03 09 19 :32 )
( ) ( ) -3-2 -1 0 1 2 3
-3-2 -1 0 1 2 3 0.0 0.2 0.4 0.6 0.8 1.0???
? ( )?
??
-2.0-1.5-1.0-0.5 0.0 0 1 2 3 4 5 6 2011 03 09 (2011 03 09 19 :32 )
? -2.0-1.5-1.0-0.5 0.0 0 1 2 3 4 5 6
0.0 0.1 0.2 0.3 0.4 0.5 0.6 N = 50 0 1 2 3 4 5 6
! 0.0 0.1 0.2 0.3 0.4 0.5 0.6 N = 50 0 1 2 3 4 5 6?
2
BUGS code for (j in 1:N.loser) { B1 ~ dbern(win1[j]) # 1 ( ) B2[j] ~ dbern(win2[j]) # 2 ( ) # B-T model logit(win1[j]) <- x[t.b1, Loser[j]] - x[t.b1, Winner1[j]] logit(win2[j]) <- x[t.b2[j], Loser[j]] - x[t.b2[j], Winner2[j]] for (t in 1:T.max) { x[t, Loser[j]] ~ dnorm(meanl[t], 20) # x[t, Winner1[j]] ~ dnorm(0.0, 20) } } ( ) logit( ) ( ) 2011 03 09 (2011 03 09 19 :32 )
BUGS code # meanl[t.b1] <- 0.0 meanl[t.b1 + 1] <- ab for (t in 3:T.max) { meanl[t] <- meanl[t - 1] * a # } ( ) 2011 03 09 (2011 03 09 19 :32 )
2011 03 09 (2011 03 09 19 :32 ) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0 1 2 3 4 5 6
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0 1 2 3 4 5 6?
feeder 2011 03 09 (2011 03 09 19 :32 ) Kawamori, A. and Matsushima, T. (2010) feeder
B-T : Burczyk
N B-T 3 (A ) = exp( A ) exp( A ) + exp( B ) + exp( C ) N exp( A ) (A ) = N i exp( i ) : : : random effects 花 2011 03 09 (2011 03 09 19 :32 ) 花
(1) Bradley-Terry Burczyk ( ) 2011 03 09 (2011 03 09 19 :32 )
(2) random effects ( )? + 2011 03 09 (2011 03 09 19 :32 )
http://goo.gl/edzle ( )
http://goo.gl/edzle ( )?!