The relative merits of the Fisher linear discriminant function
(Efron, 1975) and logistic regression procedure (Press and Wilson,
1978; McLachlan and Byth, 1979), applied to the two group
discrimination problem under conditions of multivariate normality and
common covariance, have been debated. In related research, DiPillo
(1976, 1977, 1979) has argued that a biased Fisher linear
discriminant function is preferable when one or more collinearities
exist among the classifying variables.
This paper proposes a generalized ridge logistic regression
(GRL) estimator as a logistic analog to DiPillo's biased alternative
estimator. Ridge and Principal Component logistic estimators
proposed by Schaefer et al. (1984) for conventional logistic
regression are shown to be special cases of this generalized ridge
logistic estimator.
Two Fisher estimators (Linear Discriminant Function (LDF) and
Biased Linear Discriminant Function (BLDF)) and three logistic
estimators (Linear Logistic Regression (LLR), Ridge Logistic
Regression (RLR) and Principal Component Logistic Regression (PCLR))
are compared in a Monte Carlo simulation under varying conditions of
distance between populations, training set s1ze and degree of
collinearity. A new approach to the selection of the ridge parameter
in the BLDF method is proposed and evaluated.
The results of the simulation indicate that two of the biased
estimators (BLDF, RLR) produce smaller MSE values and are more stable
estimators (smaller standard deviations) than their unbiased
counterparts. But the improved performance for MSE does not
translate into equivalent improvement in error rates. The expected
actual error rates are only marginally smaller for the biased
estimators. The results suggest that small training set size, rather
than strong collinearity, may produce the greatest classification
advantage for the biased estimators.
The unbiased estimators (LDF, LLR) produce smaller average apparent
error rates. The relative advantage of the Fisher
estimators over the logistic estimators is maintained. But, given
that the comparison is made under conditions most favorable to the
Fisher estimators, the absolute advantage of the Fisher estimators is
small. The new ridge parameter selection method for the BLDF
estimator performs as well as, but no better than, the method used by
DiPillo.
The PCLR estimator shows performance comparable to the other
estimators when there is a high level of collinearity. However, the
estimator gives up a significant degree of performance in conditions
where collinearity is not a problem. / Graduation date: 1991
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/37471 |
| Date | 27 September 1990 |
| Creators | O'Donnell, Robert P. (Robert Paul) |
| Contributors | Thomas, David R. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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