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)