Quadratic logistic discrimination

SUMMARY Previous papers on logistic discrimination have only considered linear discriminant functions, although there are situations where quadratic discriminators are important and useful. The full quadratic logistic discriminant approach has too many parameters to be estimated if the dimensionality, p, is not small, say p > 4. An approximation is suggested here which gives a quadratic term in the discriminant function but with a greatly reduced number of parameters. The method is applied to the data published by Smith (1947) and compared with his results obtained using normal distribution theory. Other approximations are suggested in some special cases.