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In-Depth Information
Sites
Low N:
High N:
Cra.L
Cra.H
Beg.L
Beg.H
Fow.L
Fow.H
Tru.L
Tru.H
Box.L
Box.H
Ear.L
Ear.H
Edn.L
Edn.H
Varieties
Conventional
Semi-dwarf
Fun
Dur
Hob
Spo
T95
T64
T68
Cap
Ran
Hun
Tem
Kin
Figure 6.1
Legend to accompany biplots related to the wheat data set.
but serves as an introduction to the usage of biadbipl . The legend given in Figure 6.1
is obtained by adding the specifications
legend.show = TRUE, legend.columns = c(7,1)
in our call to biadbipl , given below. This legend applies not only to Figure 6.2 but to
all the figures in this section and will therefore not be repeated for later figures.
In our first example of a biadditive biplot we examine a biplot of Table 6.1 after
eliminating the overall mean, obtained by specifying biad.variant = "Xminus-
MeanMat" . Thus the biplot will approximate both the main effects and interaction part
of the model. This biplot is obtained in the usual way, from the SVD X adj = U V ,
and is shown in Figure 6.3, where the first two dimensions of U = X adj V are plotted
for the sites and of V for the varieties in the top panel, as well as in the bottom left
panel. In the bottom right panel the roles of the sites and varieties have been switched
by specifying X = t(wheat.data) . The full function call to produce the biplot in the
top left panel of Figure 6.2 is
biadbipl(wheat.data, lambda = F, ax = 1:12, biad.variant =
"XminMeanMat", show.origin = F, SigmaHalf = FALSE,
predictivity.print = TRUE, pch.row.points = 17,
row.points.col = rep(c("green","red"),2),
row.points.size = 1.25, ax.name.col =
c(rep("blue",5),rep("orange",7)), pch.col.points = 15,
column.points.col = c(rep("blue",5),rep("orange",7)),
column.points.size = 1.25, pos = "Orthog",
axis.col = c(rep("blue",5),rep("orange",7)),
column.points.text = TRUE, offset = c(2.5, 2.8, 0.1, 0.1),
offset.m = rep(-0.1, 14))))
The quality of the display has the high value of 95.3%, and Table 6.4 shows that the
two-dimensional row and column predictivities are equally impressive.
Nevertheless, this does not guarantee a satisfactory biplot: the biplot in the top left
panel of Figure 6.2 is evidently unsatisfactory in many ways. In particular, the points for
the varieties very nearly coincide. We can adjust for this by using lambda-scaling as in
the top right panel. The result is far more satisfactory. A striking feature of the figure
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