Regression models for binary data with scale mixtures of centered skew-normal link functions

TL;DR

This paper introduces centered skew-normal based link functions for binary regression, addressing identifiability issues and asymmetry in success probabilities, with Bayesian inference and real data application.

Contribution

It proposes a novel centered parameterization for skew-normal link functions and fixes skewness sign to improve model identifiability in binary regression.

Findings

Model performs well in simulation studies.

Method effectively captures asymmetry in data.

Application to heart disease data demonstrates practical utility.

Abstract

For the binary regression, the use of symmetrical link functions are not appropriate when we have evidence that the probability of success increases at a different rate than decreases. In these cases, the use of link functions based on the cumulative distribution function of a skewed and heavy tailed distribution can be useful. The most popular choice is some scale mixtures of skew-normal distribution. This family of distributions can have some identifiability problems, caused by the so-called direct parameterization. Also, in the binary modeling with skewed link functions, we can have another identifiability problem caused by the presence of the intercept and the skewness parameter. To circumvent these issues, in this work we proposed link functions based on the scale mixtures of skew-normal distributions under the centered parameterization. Furthermore, we proposed to fix the sign of the skewness parameter, which is a new perspective in the literature to deal with the identifiability problem in skewed link functions. Bayesian inference using MCMC algorithms and residual analysis are developed. Simulation studies are performed to evaluate the performance of the model. Also, the methodology is applied in a heart disease data.