R? http://hosho.ees.hokudai.ac.jp/ kubo/ce/2004/ : kubo@ees.hokudai.ac.jp
(2/24) : 1. R 2. 3. R R
(3/24)? 1. ( ) 2. ( I ) : (p ) : cf. (power) p?
(4/24) p ( ) I p ( ) I? ( )
(5/24)? 0 2 4 6 8 A B A B (control) B I ( p )? (p )
(6/24)? 1. ( ) 2. ( ) 3. 4. 5. ( ) : ( ) AIC Akaike s Information Criteria ( ) AIC = 2( ) +2 ( ) ( ) ( )
(7/24) : R http://www.r-project.org/ OS free software S The R Book (2004) Modern Applied Statistics With S Venables & Ripley (2002) Introductory Statistics with R P. Dalgaard (2002) ( )
[ ] 1. 2. R 3.
(9/24) : B A 0 2 4 6 8 A A (A) 20 2.5 B (B) 10 3.5 (C) 20 3.5 B, : :
(10/24) 0 2 4 6 8 A B (A+B+C)? (A+B)(C)? (A+C)(B)? (A)(B+C)? ( ) (A)(B)(C)?? ( ) A ((A)) B ((B)) ((C))? (? )
(11/24)! 1.? : {, }, : {0.56, 1.33, 12.4, 9.84, } 2.? {0, 1,, N}, {0, 1,, }, [y min, y max ], [, ], 3. ( )?,,, n,
(12/24) (Poisson distribution) y i {0, 1, 2,, } (paramter: λ) R : dpois(y, λ) 0.4 λ y exp( λ) y! λ λ : 0.0 0 2 4 6 8 10 y 0.3 0.2 0.1?
(13/24) [ ] [ (GLM)] + [ ] +
(14/24) (generalized linear model, glm()) ( ) link : ( ) link(µ(x)) = β 0 1 + β 1 x 1 + β 2 x 2 + = i β i x i R glm() stepaic() AIC
(15/24) R (glm()) ( ) rbinom() rbinom() rpois() rnbinom() ( ) rgamma() rnorm() glm(family = binom) glm(family = binom) glm(family = poisson) glm.nb() glm(family = gamma) glm(family = gaussian) glm() glm.nb() MASS library rnegbin()
(16/24) 1. ( ) level n.flower A 3 A 0 A 1 B 4 B 1 B 2 C 5 C 4 C 2 0 2 4 6 8 A B level: A A B B C n.flower: n.flower {0, 1, 2, }
(17/24) 2. (A - B - C) 0 2 4 6 8 A B (A+B+C) 1 (A+B)(C) 2 (A+C)(B) 2 (A)(B+C) 2 (A)(B)(C) 3 : (A)(B+C) A (A) B (B+C) C (B+C) level n.flower level.mapped A 3 (A) B 4 (B+C) C 5 (B+C)
(18/24) 3. R glm() 0 2 4 6 8 A B (A+B)(C), (A+C)(B), (A)(B+C), (A)(B)(C) glm() : glm(n.flower level.mapped - 1, family = poisson(link = log)) (A+B+C) glm() : glm(n.flower 1, family = poisson(link = log))
(19/24) 4. AIC = 2( ) +2 ( ) ( ) ( ) > result <- glm(n.flower level.mapped - 1, family = poisson(link... > result # Call: glm(formula = n.flower level.mapped - 1, family = poisson(... Coefficients: level.mapped(a) level.mapped(b+c) 0.875 1.243 Degrees of Freedom: 50 Total (i.e. Null); Null Deviance: 189 Residual Deviance: 50.2 AIC: 193 > result$aic # AIC [1] 192.91 48 Residual
(20/24) 5. AIC > results <- estimate.poisson(samples) > cat(sapply(results, function(r) sprintf("model %-12s, AIC = %.1f", r$tag, r$glm$aic)), sep = "\n") Model (A+B+C), AIC = 195.5 Model (A+B)(C), AIC = 194.7 Model (A+C)(B), AIC = 197.3 Model (A)(B+C), AIC = 192.9 Model (A)(B)(C), AIC = 194.8 0 2 4 6 8 A B AIC ( ) estimate.poisson() ( glm() AIC ) R
(21/24) :? : familywise : A = B B = C A C ; : -
R R
(23/24)? R generate.groups() (4 ) > sapply(generate.groups(c("a", "B", "C", "D")), function(g) g$tag) [1] "(A+B+C+D)" "(A+B+C)(D)" "(A+B+D)(C)" "(A+C+D)(B)" "(A)(B+C+D)" [6] "(A+B)(C+D)" "(A+C)(B+D)" "(A+D)(B+C)" "(A+B)(C)(D)" "(A+C)(B)(D)" [11] "(A+D)(B)(C)" "(A)(B+C)(D)" "(A)(B+D)(C)" "(A)(B)(C+D)" "(A)(B)(C)(D)" (?) partition.int(): generate.groups(): estimate.poisson(): generate.groups()
(24/24) 1. I?? 2. AIC 3. R ( ) R (multcomp library )