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.
Quality & Quantity – Springer Journals
Published: Oct 6, 2004
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