Principal component analysis biplots - Understanding Biplots - page 135

0.20

0.15

0.10

0.05

S50 S20 S250

0.00

X1 (0.47)

33.5 33 32.5 32

X2 (0.03)

6600 6500 6400

X3 (0.82)

500 450 400 350 300 250

X4 (0.82)

− 5.5 − 5.4 − 5.3 − 5.2 − 5.1 − 5

X5 (0.93)

20 15 10 5

X6 (0.94)

− 16 − 14 − 12 − 10 − 8 − 6 − 4

X7 (0.82)

5000 10000 15000 20000 25000 30000 35000

X8 (0.11)

0.96 0.98 1 1.02 1.04 1.06 1.08

Figure 3.38 One-dimensional PCA biplot of the copper froth data with density esti-

mate added.

The full function call resulting in Figure 3.38 is

PCAbipl(X = CopperFroth.data[,1:8], scaled.mat = TRUE,
dim.biplot = 1, density.plot = TRUE, colours = "green",
constant = -0.6, label = FALSE, means.plot = FALSE,
n.int = c(5,15,8,5,5,5,5,25), offset = c(0, 2.4, 0, 0.2),
ort.lty = 2, predictivity.print = TRUE,
predictions.sample = c(20,50,250))

The biplot representation of the sample points, together with their density estimate in
Figure 3.38, has also a specific statistical interpretation: it is a graphical display of the
principal component scores with respect to the first principal component. Similar plots can
be made for the other principal components by specifying them in the argument e.vects
argument of PCAbipl . This is shown for principal components 2 to 5 in Figure 3.39.

3.8.5 Three-dimensional PCA biplots

Three-dimensional PCA biplots are obtained by specifying dim.biplot = 3 in calls to
PCAbipl . Package rgl is required and on calling PCAbipl with dim.biplot = 3 the