An iteratively reweighted least squares algorithm for skew-probit binary regression with Firth’s penalization

A skew-probit link offers a useful alternative for modeling binary outcomes when symmetric link functions are inadequate due to response asymmetry.This study develops an iteratively reweighted least squares (IRLS) type algorithm tailored for the skew-probit link model, addressing both the naive maximum likelihood estimator (MLE) and Firth's penalized MLE.Through comprehensive numerical studies, the properties of IRLS estimates are investigated and compared with estimates obtained using a numerical optimization approach for both naive and Firth's penalized MLE.Strategies for initial value selection are also suggested to improve algorithmic convergence.We further analyze two real datasets to illustrate the usage of the skew-probit link with the proposed algorithm.