Bounds on Concordance-Based Validation Statistics in Regression Models for Binary Responses

Abstract

Association measures based on concordance, such as Kendall’s tau, Somers’ delta or Goodman and Kruskal’s gamma are often used to measure explained variations in regression models for binary outcomes. As responses only assume values in {0, 1}, these association measures are constrained, which makes their interpretation more difficult as a relatively small value may in fact strongly support the fitted model. In this paper, we derive the set of attainable values for concordance-based association measures in this setting so that the closeness to the best-possible fit can be properly assessed.