  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.
