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to be discovered. Computing advances that allow density plotting enable large samples
to be exhibited. Calibrated axes simplify use and classification regions, supplemented
by uncertainty regions, readily allow the investigation of separation and discriminatory
properties. We have emphasized, perhaps too much, the various measures of fit that
are now available. These are best used in an interactive environment and one would
not normally require these measures for all dimensionalities, especially when we know
they must attain their optimal 100% values. Variables with low predictivity might be
recognized and dropped interactively. However, we think that axis predictivities ought
to be shown on most biplot maps to highlight any remaining ineffective variables. We
have already shown (see Section 3.3) that usually adequacy is not a useful measure
of the effectiveness of a variable. The scale invariance properties of canonical variate
space extend to measures of fit in that space. However, one should be aware that fit
measures concerning the original variables should be used with care and most safely by
first normalizing as in PCA; this normalization has no effect on the CVA analysis itself.
A happy exception to this warning is that axis predictivity for the original variables relies
on ratios, so is invariant to scale. Finally, we have discussed three ways of centring the
points representing the canonical means. These variants have had marginal effects on the
examples discussed above, but could have major effects when group sizes are disparate.
Only in the disparate case would one consider using more than one method.
