Assessment of fisher and logistic linear and quadratic discrimination models

Abstract

This paper summarizes the results from a study comparing the performance of the Fisher and logistic linear and quadratic discriminant functions. Three types of bivariate distributions are studied. Each classification rule is compared to the optimal maximum likelihood procedure for the different data types. The theoretical misclassification probabilities of the sample discriminant functions are calculated directly and used for the comparison of the different procedures both in terms of bias and variation. Generalizations and recommendations are made to assist the applied statistician in making the correct choice of a discrimination procedure and the results of this study are compared with earlier investigations. This study shows that specification of the form of the discriminant function may be one of the most important parts of a discriminant analysis.