Coefficients of Determination in Logistic Regression Models—A New Proposal: The Coefficient of Discrimination

Abstract

Many analogues to the coefficient of determination R2 in ordinary regression models have been proposed in the context of logistic regression. Our starting point is a study of three definitions related to quadratic measures of variation. We discuss the properties of these statistics, and show that the family can be extended in a natural way by a fourth statistic with an even simpler interpretation, namely the difference between the averages of fitted values for successes and failures, respectively. We propose the name “the coefficient of discrimination” for this statistic, and recommend its use as a standard measure of explanatory power. In its intuitive interpretation, this quantity has no immediate relation to the classical versions of R2, but it turns out to be related to these by two exact relations, which imply that all these statistics are asymptotically equivalent.