Maximizing proportions of correct classifications in binary logistic regression

In this paper, we give simple mathematical results that allow us to get all cut-off points that maximize the overall proportion of correct classifications in any binary classification method (and, in particular, in binary logistic regression). In addition, we give results that allow us to get all cut-off points that maximize a weighted combination of specificity and sensitivity. In addition, we discuss measures of association between predicted probabilities and observed responses, and, in particular, we discuss the calculation of the overall percentages of concordant, discordant, and tied pairs of input observations with different responses. We mention that the calculation of these quantities by SAS and Minitab is sometimes incorrect. The concepts and methods of the paper are illustrated by a hypothetical example of school retention data.