日本疫学会 第19回疫学セミナー 「統計解析ソフトRの活用」内で講演した「Rで線形モデル」のスライドです

1. R
,
19 ( 22 )
2012/1/26

2. R : lm() ,R
: , ,
, ,
: glm()

3. R
R
R lm
lm

4. : Edgar Anderson’s Iris Data
R
help(package=”datasets”)
iris 150
( 50 : Species
(Sepal.Length , Sepal.Width )
(Petal.Length , Petal.Width )

5. > m1 <- lm(Sepal.Length ~ Petal.Length, data=iris)
> m1
Call:
lm(formula = Sepal.Length ~ Petal.Length, data = iris)
Coefficients:
(Intercept) Petal.Length
4.3066 0.4089
• iris Sepal.Length Petal.Length
m1
• m1

6. > summary(m1)
Call:
lm(formula = Sepal.Length ~ Petal.Length, data = iris)
Residuals:
Min 1Q Median 3Q Max
-1.24675 -0.29657 -0.01515 0.27676 1.00269
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.30660 0.07839 54.94 <2e-16 ***
Petal.Length 0.40892 0.01889 21.65 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
( )
• summary
summary coef fitted ,
residuals

7. ( )
Residual standard error: 0.4071 on 148 degrees of freedom
Multiple R-squared: 0.76, Adjusted R-squared: 0.7583
F-statistic: 468.6 on 1 and 148 DF, p-value: < 2.2e-16
• summary , ,
=0 t ( ), ,
R2, R2, F
• coef fitted
residuals

8. > m2 <- lm(Sepal.Length ~ Petal.Length + Petal.Width, data=iris)
> m2
Call:
lm(formula = Sepal.Length ~ Petal.Length + Petal.Width, data = iris)
Coefficients:
(Intercept) Petal.Length Petal.Width
4.1906 0.5418 -0.3196
• Petal.Width
• iris Sepal.Length Petal.Length Petal.Width
m2
• m2

9. > summary(m2)
( )
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.19058 0.09705 43.181 < 2e-16 ***
Petal.Length 0.54178 0.06928 7.820 9.41e-13 ***
Petal.Width -0.31955 0.16045 -1.992 0.0483 *
( )
Residual standard error: 0.4031 on 147 degrees of freedom
Multiple R-squared: 0.7663, Adjusted R-squared: 0.7631
F-statistic: 241 on 2 and 147 DF, p-value: < 2.2e-16
• summary

10. > m2 <- lm(Sepal.Length ~ Petal.Length + Petal.Width, data=iris)
”~”
”+”
data

11. > m3 <- lm(Sepal.Length ~ Petal.Length + Petal.Width +
Petal.Length:Petal.Width , data=iris)
”:”
2
“*”
> m3d <- lm(Sepal.Length ~ Petal.Length * Petal.Width ,data=iris)
m3 m3d

12. > m4 <- lm(Sepal.Length ~ Petal.Length^2 , data=iris)
> m4 <- lm(Sepal.Length ~ I(Petal.Length^2) , data=iris)
“^” “+” “-” ”*” “:”
I( i)

13. > m5 <- lm(Sepal.Length ~ Petal.Length + Species, data=iris)
> summary(m5)
( )
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.68353 0.10610 34.719 < 2e-16 ***
Petal.Length 0.90456 0.06479 13.962 < 2e-16 ***
Speciesversicolor -1.60097 0.19347 -8.275 7.37e-14 ***
Speciesvirginica -2.11767 0.27346 -7.744 1.48e-12 ***
( )
Species factor (“setosa”, “versicolor”, “virginica” )
factor -1
(Speciesversicolor, Speciesvirginica)

14. > m2
Call:
lm(formula = Sepal.Length ~ Petal.Length + Petal.Width, data = iris)
Coefficients:
(Intercept) Petal.Length Petal.Width
4.1906 0.5418 -0.3196
> coef(m2)
(Intercept) Petal.Length Petal.Width
4.1905824 0.5417772 -0.3195506
> sd(iris$Petal.Length) / sd(iris$Sepal.Length)
[1] 2.131832
> sd(iris$Petal.Width) / sd(iris$Sepal.Length)
[1] 0.9205034
> 0.5417772 * 2.131832
[1] 1.154978
> -0.3195506 * 0.9205034
[1] -0.2941474
> coef(m2)[-1] * apply(m2$model[-1],2,sd) / sd(m2$model[,1])
Petal.Length Petal.Width
1.1549781 -0.2941474

15. > cor(iris[,1:4])
Sepal.Length Sepal.Width Petal.Length Petal.Width
Sepal.Length 1.0000000 -0.1175698 0.8717538 0.8179411
Sepal.Width -0.1175698 1.0000000 -0.4284401 -0.3661259
Petal.Length 0.8717538 -0.4284401 1.0000000 0.9628654
Petal.Width 0.8179411 -0.3661259 0.9628654 1.0000000
(factor) 5 (Species )
iris[,1:4] cor

16. > m6 <- lm(Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width
+ Species, data = iris)
> step(m6)
Start: AIC=-348.57
Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width + Species
Df Sum of Sq RSS AIC
<none> 13.556 -348.57
- Petal.Width 1 0.4090 13.966 -346.11
- Species 2 0.8889 14.445 -343.04
- Sepal.Width 1 3.1250 16.681 -319.45
- Petal.Length 1 13.7853 27.342 -245.33
step AIC( )
AIC

17. (Residual-Fitted plot)
> m1 <- lm(Sepal.Length ~ Petal.Length, data=iris)
> m6 <- lm(Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width
+ Species, data = iris)
> plot(m1, which=1)
> plot(m6, which=1)
Residuals vs Fitted Residuals vs Fitted
1.0
15 132 15 136
0.5
0.5
Residuals
Residuals
0.0
0.0
-0.5
-0.5
-1.0
107 85
-1.5
5.0 5.5 6.0 6.5 7.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Fitted values Fitted values
lm(Sepal.Length ~ Petal.Length) lm(Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width + Species)

18. ( q-q plot)
> m1 <- lm(Sepal.Length ~ Petal.Length, data=iris)
> m6 <- lm(Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width
+ Species, data = iris)
> plot(m1, which=2)
> plot(m6, which=2)
Normal Q-Q Normal Q-Q
3
3
132 15 15 136
2
2
Standardized residuals
Standardized residuals
1
1
0
0
-1
-1
-2
-2
-3
107 85
-2 -1 0 1 2 -2 -1 0 1 2
Theoretical Quantiles Theoretical Quantiles
lm(Sepal.Length ~ Petal.Length) lm(Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width + Species)

19. glm
glm lm

20. : data from a case-control study of
esophagaeal cancer in Ile-et-Vilaine, France
R esoph
agegp(Age group, 6 ), alcgp(Alcohol consumption, 4 ),
tobgp(Tobacco consumption, 4 ), ncases (number of
cases), ncontrols(number of controls) 5
agegp, alcgp, tobgp case control

21. > m7 <- glm(cbind(ncases, ncontrols) ~ agegp+tobgp+alcgp,
data=esoph, family=binomial,contrasts=list(agegp="contr.treatment",
tobgp="contr.treatment", alcgp="contr.treatment"))
• esoph agegp tobgp alcgp
m7
• 1 1 0 or 1
iris ” ”
• “family=binomial”
• contrasts
( )
factor

22. > summary(m7)
( )
Deviance Residuals:
Min 1Q Median 3Q Max
-1.6891 -0.5618 -0.2168 0.2314 2.0642
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -5.9108 1.0302 -5.737 9.61e-09 ***
agegp35-44 1.6095 1.0676 1.508 0.131652
agegp45-54 2.9752 1.0242 2.905 0.003675 **
agegp55-64 3.3584 1.0198 3.293 0.000991 ***
agegp65-74 3.7270 1.0253 3.635 0.000278 ***
agegp75+ 3.6818 1.0645 3.459 0.000543 ***
tobgp10-19 0.3407 0.2054 1.659 0.097159 .
tobgp20-29 0.3962 0.2456 1.613 0.106708
tobgp30+ 0.8677 0.2765 3.138 0.001701 **
alcgp40-79 1.1216 0.2384 4.704 2.55e-06 ***
alcgp80-119 1.4471 0.2628 5.506 3.68e-08 ***
alcgp120+ 2.1154 0.2876 7.356 1.90e-13 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 227.241 on 87 degrees of freedom
Residual deviance: 53.973 on 76 degrees of freedom
AIC: 225.45
Number of Fisher Scoring iterations: 6

23. summary
lm Residual Deviance( )
Wald z =0
AIC

24. > exp(cbind(coef(m7),confint(m7)))
Waiting for profiling to be done...
2.5 % 97.5 %
(Intercept) 0.002710046 0.0001500676 0.01309911
agegp35-44 5.000426461 0.9048631872 93.44857822
agegp45-54 19.592860766 4.1082301889 351.60508496
agegp55-64 28.741838956 6.1156513661 513.64343522
agegp65-74 41.554820823 8.6954216578 746.54178414
agegp75+ 39.716132031 7.3282690051 740.73696224
tobgp10-19 1.405982889 0.9376683713 2.10030180
tobgp20-29 1.486221090 0.9107730044 2.39108827
tobgp30+ 2.381435327 1.3753149494 4.07656452
alcgp40-79 3.069638047 1.9438541677 4.96418587
alcgp80-119 4.250811157 2.5569142185 7.18622034
alcgp120+ 8.292938857 4.7505293148 14.70778864
95% confint
95% exp
95%

25. Web

26. R 3500 R
Epi, epicalc, epitools,epiR, epibasix
2x2 APC
, Mantel-Haenszel

27. Web ,
RjpWiki :
Q and A
R-bloggers : R
inside-R : R Revolution R
Twitter: #rstats, #rstatsj

28. “R ”
slideshare.net Twitter R
Ustream
R

29. R