The Effect of Prior Probability on Skill in Two-Group Discriminant Analysis

The Effect of Prior Probability on Skill in Two-Group Discriminant Analysis Although the weights in a discriminant function (both linear and quadratic) are independent of group prior probabilities, the performance of the classifier (on the training and validation data) is sensitively dependent on these often unknown probabilities. After reviewing some defects of a popular measure of performance in the situation where the group sizes are naturally disproportionate, three alternative measures of performance (or association) are considered and it is shown that the behavior of the measures as a function of group prior probability is different between measures. Consequently, the optimum choice of the group prior probability depends on the specific measure of performance. Among the measures considered, only two measures - the index of mean square contingency and the Heidke Skill Statistic - are found to be well defined in the disparate-group size situation, and are, therefore, recommended. An empirical data set, dealing with delinquency among high school students is employed to illustrate all of the findings. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality & Quantity Springer Journals

The Effect of Prior Probability on Skill in Two-Group Discriminant Analysis

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 1998 by Kluwer Academic Publishers
Subject
Social Sciences; Methodology of the Social Sciences; Social Sciences, general
ISSN
0033-5177
eISSN
1573-7845
D.O.I.
10.1023/A:1004359127048
Publisher site
See Article on Publisher Site

Abstract

Although the weights in a discriminant function (both linear and quadratic) are independent of group prior probabilities, the performance of the classifier (on the training and validation data) is sensitively dependent on these often unknown probabilities. After reviewing some defects of a popular measure of performance in the situation where the group sizes are naturally disproportionate, three alternative measures of performance (or association) are considered and it is shown that the behavior of the measures as a function of group prior probability is different between measures. Consequently, the optimum choice of the group prior probability depends on the specific measure of performance. Among the measures considered, only two measures - the index of mean square contingency and the Heidke Skill Statistic - are found to be well defined in the disparate-group size situation, and are, therefore, recommended. An empirical data set, dealing with delinquency among high school students is employed to illustrate all of the findings.

Journal

Quality & QuantitySpringer Journals

Published: Oct 6, 2004

References

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