library(Rcmdr)
## Loading required package: splines
## Loading required package: RcmdrMisc
## Loading required package: car
## Loading required package: carData
## Loading required package: sandwich
## Loading required package: effects
## lattice theme set by effectsTheme()
## See ?effectsTheme for details.
## コマンダーの GUI はインタラクティブなセッションでしか起動しません.
## 
## Attaching package: 'Rcmdr'
## The following object is masked from 'package:car':
## 
##     Confint
#irisデータ読み込み
data(iris)

#三次元散布図描画
library(rgl, pos=17)
library(nlme, pos=18)
library(mgcv, pos=18)
## This is mgcv 1.8-24. For overview type 'help("mgcv-package")'.
scatter3d(Sepal.Length~Petal.Length+Petal.Width|Species, data=iris, 
          surface=FALSE, residuals=TRUE, parallel=FALSE, 
          bg="white", axis.scales=TRUE, grid=TRUE, ellipsoid=FALSE)

#【1】クラスター分析
#Iris setosa (1) の4変量データ
iris[1, 1:4]
##   Sepal.Length Sepal.Width Petal.Length Petal.Width
## 1          5.1         3.5          1.4         0.2
#Iris versicolor (51) の4変量データ
iris[51, 1:4]
##    Sepal.Length Sepal.Width Petal.Length Petal.Width
## 51            7         3.2          4.7         1.4
#偏差ベクトル
iris[1, 1:4]-iris[51, 1:4]
##   Sepal.Length Sepal.Width Petal.Length Petal.Width
## 1         -1.9         0.3         -3.3        -1.2
#マンハッタン距離(偏差絶対値和)
sum(abs(iris[1, 1:4]-iris[51, 1:4]))
## [1] 6.7
#平方ユークリッド距離(偏差平方和)
sum((iris[1, 1:4]-iris[51, 1:4])^2)
## [1] 16.03
#ユークリッド距離(偏差平方和平方根)
sqrt(sum((iris[1, 1:4]-iris[51, 1:4])^2))
## [1] 4.003748
#階層的クラスター分析によるデンドログラム描画
#[ユークリッド距離に基づく群平均法=UPGMA]
HClust.2 <- hclust(dist(model.matrix(~-1 + 
    Petal.Length+Petal.Width+Sepal.Length+Sepal.Width, iris)) , 
    method= "average")
plot(HClust.2, main= "Cluster Dendrogram for Solution HClust.2", 
    xlab= "Observation Number in Data Set iris", 
    sub="Method=average; Distance=euclidian")

#【2】主成分分析
#相関係数行列に基づく主成分計算
local({.PC <- princomp(~Petal.Length+Petal.Width+Sepal.Length+Sepal.Width,
    cor=TRUE, data=iris)
    cat("\nComponent loadings:\n")
    print(unclass(loadings(.PC)))
    cat("\nComponent variances:\n")
    print(.PC$sd^2)
    cat("\n")
    print(summary(.PC))
    screeplot(.PC)
    iris <<- within(iris, 
      {
      PC4 <- .PC$scores[,4]
      PC3 <- .PC$scores[,3]
      PC2 <- .PC$scores[,2]
      PC1 <- .PC$scores[,1]
      })
    })
## 
## Component loadings:
##                  Comp.1     Comp.2     Comp.3     Comp.4
## Petal.Length  0.5804131 0.02449161  0.1421264  0.8014492
## Petal.Width   0.5648565 0.06694199  0.6342727 -0.5235971
## Sepal.Length  0.5210659 0.37741762 -0.7195664 -0.2612863
## Sepal.Width  -0.2693474 0.92329566  0.2443818  0.1235096
## 
## Component variances:
##     Comp.1     Comp.2     Comp.3     Comp.4 
## 2.91849782 0.91403047 0.14675688 0.02071484 
## 
## Importance of components:
##                           Comp.1    Comp.2     Comp.3      Comp.4
## Standard deviation     1.7083611 0.9560494 0.38308860 0.143926497
## Proportion of Variance 0.7296245 0.2285076 0.03668922 0.005178709
## Cumulative Proportion  0.7296245 0.9581321 0.99482129 1.000000000

#元データの散布図行列
scatterplotMatrix(~Petal.Length+Petal.Width+Sepal.Length+Sepal.Width | 
      Species, regLine=FALSE, smooth=FALSE, 
      diagonal=list(method="density"), by.groups=TRUE, data=iris)