Researchers and practitioners have long held that the probit and logit link functions generally yield the same performance in binary classification. Despite this widespread recognition of the strong similarities between these two link functions, very few (if any) researchers have dedicated time to carry out a formal study aimed at establishing and characterizing firmly all the aspects of the similarities and differences. This paper proposes a definition of both structural and predictive equivalence link functions-based binary regression models, and provides both a theoretical and computational justification of the long held claim that probit and logit are indeed very similar. From a predictive analytics perspective, it turns out that not only are probit and logit perfectly predictively equivalent, but the other link functions like cauchit and complementary log log enjoy very high percentage of predictive equivalence. Throughout this paper, simulated and real life examples demonstrate clearly all the equivalence results that we prove theoretically

Publication Date



Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type

Technical Report

Department, Program, or Center

The John D. Hromi Center for Quality and Applied Statistics (KGCOE)


RIT – Main Campus