Journal Article

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

Tjur, Tue

2009

Overview

Many analogues to the coefficient of determination R 2 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 R 2 , but it turns out to be related to these by two exact relations, which imply that all these statistics are asymptotically equivalent.

• Publisher: Taylor & Francis,American Statistical Association
• Subject: Asymptotic methods / Averages / Coefficient of determination / Datasets / Definitions / Discrimination / Exact sciences and technology / Explanatory power / General topics / Histograms / Linear inference, regression / Linear models / Logistic regression / Mathematical independent variables / Mathematics / Modeling / Multivariate analysis / Probability and statistics / Property / R-square / Regression analysis / Regression coefficients / Sciences and techniques of general use / Standard deviation / Statistical variance / Statistics / Variables