In 1993 a version of penalized logistic regression was introduced by Firth in order to reduce the bias due to outliers and/or (quasi-)perfect prediction in logistic regression: Bias Reduction of Maximum Likelihood Estimates.
In 2002 Heinze and Schemper claimed that Firth's method is the optimal one in such cases: A solution to the problem of separation in logistic regression
Just a year after that, Andreas Christmann and Peter J. Rousseeuw introduced The Hidden Logistic Regression Model, yet another version of logistic regression which is claimed to be robust against perfect prediction and outliers. For some reason, Christmann and Rousseeuw do not cite Firth.
Another version of logistic regression is due to Shen and Gao (2008): A Solution to Separation and Multicollinearity in Multiple Logistic Regression.
Question: Which of these methods is most used/considered best today? Are there any conceptual reasons for which one may prefer one over the others in some cases?
A paper by Godinez-Jaimes et al. seems to indicate that Shen and Gao's estimator is the more robust/less biased of the three. However, the paper dates back to 2012 and was only cited twice. See LA COLINEALIDAD Y LA SEPARACIÓN EN LOS DATOS EN EL MODELO DE REGRESIÓN LOGÍSTICA (translation into English included in the paper).
