Canonical variate analysis biplots - Understanding Biplots - page 151

VesD

180

300

160

140

350

1000 120

1200

1400

1600

1800

400

FibL

100

Obul; n = 20
Oken; n

80

450

= 7. (C hull)

Opor; n = 10

VesL

Figure 4.3 CVA biplot of the Ocotea data set using only variables FibL , Ve s L and
Ve sD . Group means are indicated by the solid symbols in the key. 0.95-bags are shown.

Comparison of Figure 4.3 with Figure 4.2 shows that the distribution of the samples
and the orientation of the three biplot axes for FibL , Ve s L and Ve sD remain very much
the same as when using all six variables. Referring to the distribution of the sample
points around their respective class means shows that the indigenous Oken are well
separated from the other two species, while the indigenous Obul and the exotic Opor
are closer to each other. Note, however, that the two indigenous species Obul and Oken
overlap on each of the individual axes (variables) and that separation of the species is
only obtained by the simultaneous analysis of all three variables. Furthermore, there is
overlap between Oken and Opor with respect to Ve s L and Ve sD when each variable is
considered individually. The two species are, however, well separated when orthogonally
projected onto the FibL -axis. On the other hand, there is much more overlap between
the projections of Obul and Opor on the FibL -axis, than with respect to the remaining
two variables.
Comparing the class mean values in Table 4.1 with the predicted values obtained by
orthogonal projection onto the biplot axes confirms that the mean values can be accurately
read off from the graphical display. It will be shown in Section 4.2 that these CVA biplots
are in fact exact representations of the class means in two dimensions.