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.

翻译：对于二元回归，当有证据表明成功概率的增加速率与减少速率不同时，使用对称连接函数并不合适。在这些情况下，基于偏态厚尾分布累积分布函数的连接函数可能更为适用。最常用的选择是偏态正态分布的某些尺度混合形式。该分布族可能存在由所谓直接参数化引起的可识别性问题。此外，在使用偏态连接函数的二元建模中，截距项与偏度参数的同时存在可能导致另一种可识别性问题。为解决这些问题，本研究提出基于中心化参数化下偏态正态分布尺度混合的连接函数。进一步地，我们提出固定偏度参数的符号，这是处理偏态连接函数可识别性问题文献中的新视角。研究发展了基于MCMC算法的贝叶斯推断与残差分析方法，并通过模拟研究评估模型性能。该方法还被应用于心脏病数据集进行分析。