Introduction - Understanding Biplots - page 4

140

Amea

Egran

90

170

Emac

130

150

160

Edun

− 2 − 1 0 1 2 3 4

Figure 1.2 Biplot for a two-way table representing Species × Temperature.

We shall see that this distinction between symmetric and asymmetric biplots affects
what is permissible in the construction of a biplot. Within this broad classification, other
major considerations are:

• the types of variable (quantitative, qualitative, ordinal, etc.);

• the method used for displaying samples (multidimensional scaling and related

methods);

• what the biplot display is to be used for (especially for prediction or for

interpolation).

The following can be represented in an asymmetric biplot:

• distances between samples;

• relationships between variables;

•

inner products between samples and variables.

However, only two of these characteristics can be optimally represented in a single biplot.
In the simple biplot in Figure 1.1 all the calibration scales are linear with evenly spaced
calibration points. Other types of scale are possible and we shall meet them later in other
types of biplots. Figure 1.3 shows the main possibilities.
Figure 1.3(a) is the familiar equally spaced calibration of a linear axis that we have
already met in Figure 1.1. Figure 1.3(b) shows logarithmic calibration of a linear axis;