Penalized complexity priors for the skewness parameter of power links

The choice of a prior distribution is a key aspect of the Bayesian method. However, in many cases, such as the family of power links, this is not trivial. In this article, we introduce a penalized complexity prior (PC prior) of the skewness parameter for this family, which is useful for dealing with imbalanced data. We derive a general expression for this density and show its usefulness for some particular cases such as the power logit and the power probit links. A simulation study and a real data application are used to assess the efficiency of the introduced densities in comparison with the Gaussian and uniform priors. Results show improvement in point and credible interval estimation for the considered models when using the PC prior in comparison to other well-known standard priors.