On the predictive properties of binary link functions

Abstract

ON THE PREDICTIVE PROPERTIES OF BINARY LINK FUNCTIONS NECLA GÜNDÜZ AND ERNEST FOKOUÉAbstract. This paper provides a theoretical and computational justi…cation of the long held claim of the similarity of the probit and logit link functions often used in binary classi…cation. 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 …rmly all the aspects of the similarities and di¤erences. This paper proposes a de…nition of both structural and predictive equivalence of link functions-based binary regression models, and explores the various ways in which they are either similar or dissimilar. From a predictive analytics perspective, it turns out that not only are probit and logit perfectly predictively concordant, 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 all the equivalence results that we prove theoretically.

Bayesian transition models for ordinal longitudinal outcomes

“…The logit link function given by $$$ f(x)=\log \left(x/\left(1-x\right)\right) $$$ is the most widely used, but other common choices are the probit and complementary log‐log link functions. These link functions usually have a negligiable effect on model performance 23 . We focus on the logit link in this paper because it is the standard link function used for binary and ordinal regression in biostatistics, and because the model parameters can be interpreted as log‐odds ratios, while a similar interpretation is not available for other link functions such as probit.…”

“…These link functions usually have a negligiable effect on model performance. 23 We focus on the logit link in this paper because it is the standard link function used for binary and ordinal regression in biostatistics, and because the model parameters can be interpreted as log-odds ratios, while a similar interpretation is not available for other link functions such as probit. When the logit link function is used, the model is commonly referred to as the proportional odds model.…”