Computational Statistics & Data Analysis 1 (1983) 257-273 North-Holland 257 Assessment of Fisher and logistic linear and quadratic discrimination models * C.K. BAYNE, J.J. BEAUCHAMP, V.E. KANE ** Union Carbide Corporation, Nuclear Division, Oak Ridge, TN 37830, USA G.P. McCABE Department of Statistics, Purdue University, West Lafayette, 1N 47907, USA Received July 1983 Revised September 1983 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. Keywords: Linear and quadratic discrimination models, Logistic discrimination, Misclassification probabihty estimation. I. Introduction The purpose of this paper is to compare the performance of Fisher's linear (LDF) and quadratic (QDF) discriminant functions and the linear logistic (LLF) and quadratic logistic (QLF) discriminant functions for classifying observations from three types of bivariate distributions. The three distributional types are the bivariate normal distribution with equal and unequal covariance" matrices, a * Research sponsored by the Applied Mathematical Sciences Research Program, Office of Energy Research, US Department of Energy under contract W-7405-eng-26 with the Union Carbide Corporation. Free of fights for all U.S. Government purposes. ** Presently employed by Ford Motor Company, Detroit, Michigan. 0167-9473/83/$3.00 © 1983, Elsevier Science Publishers B.V. (North-Holland)