ON THE PREDICTIVE PROPERTIES OF BINARY LINK FUNCTIONS

Abstract

This paper provides a theoretical and computational justi...cationof the long held claim of the similarity of the probit and logit link functions often used in binary classi...cation. Despite this widespread recognitionof 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 ...rmly all the aspects of the similarities and diğerences.This paper proposes a de...nition of both structural and predictive equivalenceof link functions-based binary regression models, and explores the various waysin which they are either similar or dissimilar. From a predictive analytics perspective, it turns out that not only are probit and logit perfectly predictivelyconcordant, but the other link functions like cauchit and complementary loglog enjoy very high percentage of predictive equivalence. Throughout this paper, simulated and real life examples demonstrate all the equivalence resultsthat we prove theoretically.