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Gower and Hand (1996) discuss a detailed algorithm for computing the boundaries
of the prediction regions. If the dimension of L is r = 2 they provide a simpler, but
less efficient, method for obtaining the prediction regions:
× m grid of pixels in L ,say E : m 2
Construct a two-dimensional m
× 2.
For each pixel of E , calculate which CLP is nearest.
Label (i.e. colour) the pixel in L accordingly.
Grid points can be labelled with colours corresponding to the different category levels.
In all the previous biplots, the biplot trajectories of all the variables were displayed in
one representation. The coloured prediction region diagram described above, however,
pertains to one categorical variable and is the equivalent of one continuous biplot trajec-
tory. Usually, to avoid confusing overlap, different prediction region diagrams will be
needed for each categorical variable.
In Figure 9.8 the pixels are coloured to show the prediction regions for blue , green
and brown eyes. The prediction biplot axis for the continuous variable height is obtained
Figure 9.8
Prediction regions for the generalized biplot of the Table 9.1 data.
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