A comparison of linear and mixture models for discriminant analysis under nonnormality.

Methods for discriminant analysis were compared with respect to classification accuracy under nonnormality through Monte Carlo simulation. The methods compared were linear discriminant analyses based both on raw scores and on ranks; linear logistic discrimination; and mixture discriminant analysis. Linear discriminant analysis and linear logistic discrimination were suboptimal in a number of scenarios with skewed predictors. Linear discriminant analysis based on ranks yielded the highest rates of classification accuracy in only a limited number of situations and did not produce a practically important advantage over competing methods. Mixture discriminant analysis, with a relatively small number of components in each group, attained relatively high rates of classification accuracy and was most useful for conditions in which skewed predictors had relatively small values of kurtosis.