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1 R? kubo/ce/2004/ : kubo@ees.hokudai.ac.jp

2 (2/24) : 1. R R R

3 (3/24)? 1. ( ) 2. ( I ) : (p ) : cf. (power) p?

4 (4/24) p ( ) I p ( ) I? ( )

5 (5/24)? A B A B (control) B I ( p )? (p )

6 (6/24)? 1. ( ) 2. ( ) ( ) : ( ) AIC Akaike s Information Criteria ( ) AIC = 2( ) +2 ( ) ( ) ( )

7 (7/24) : R OS free software S The R Book (2004) Modern Applied Statistics With S Venables & Ripley (2002) Introductory Statistics with R P. Dalgaard (2002) ( )

8 [ ] R 3.

9 (9/24) : B A A A (A) B (B) (C) B, : :

10 (10/24) A B (A+B+C)? (A+B)(C)? (A+C)(B)? (A)(B+C)? ( ) (A)(B)(C)?? ( ) A ((A)) B ((B)) ((C))? (? )

11 (11/24)! 1.? : {, }, : {0.56, 1.33, 12.4, 9.84, } 2.? {0, 1,, N}, {0, 1,, }, [y min, y max ], [, ], 3. ( )?,,, n,

12 (12/24) (Poisson distribution) y i {0, 1, 2,, } (paramter: λ) R : dpois(y, λ) 0.4 λ y exp( λ) y! λ λ : y ?

13 (13/24) [ ] [ (GLM)] + [ ] +

14 (14/24) (generalized linear model, glm()) ( ) link : ( ) link(µ(x)) = β β 1 x 1 + β 2 x 2 + = i β i x i R glm() stepaic() AIC

15 (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 (16/24) 1. ( ) level n.flower A 3 A 0 A 1 B 4 B 1 B 2 C 5 C 4 C A B level: A A B B C n.flower: n.flower {0, 1, 2, }

17 (17/24) 2. (A - B - C) 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 (18/24) 3. R glm() 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 (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) Degrees of Freedom: 50 Total (i.e. Null); Null Deviance: 189 Residual Deviance: 50.2 AIC: 193 > result$aic # AIC [1] Residual

20 (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 = Model (A+B)(C), AIC = Model (A+C)(B), AIC = Model (A)(B+C), AIC = Model (A)(B)(C), AIC = A B AIC ( ) estimate.poisson() ( glm() AIC ) R

21 (21/24) :? : familywise : A = B B = C A C ; : -

22 R R

23 (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 (24/24) 1. I?? 2. AIC 3. R ( ) R (multcomp library )

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