Bias in Multiple Discriminant Analysis

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Abstract
Sample estimates of predictive power in N-way discriminant analysis are likely to be subject to a strong upward bias. This bias occurs because the discriminant technique tends to fit the sample data in ways that are systematically better than would be expected by chance, even if the underlying populations are identical (i.e., no predictive power truly exists). Sample tests of predictive power against chance models are often invalid, and no simple methods of adjusting for the bias are available, as in the analogous case of multiple regression. The nature and causes of sample bias are discussed, and two validation procedures are presented and illustrated that can be used to obtain realistic estimates of predictive power in discriminant analysis.

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