Bayesian Adaptive Lasso binary regression with ridge parameter

Abstract

The variable selection (VS) characteristic was considered very important in the data analysis. Regularization technique is one gorgeous way that has proven effective for dealing with high dimensional data. In previous years, statistical researchers have made great efforts in developing procedures of regularization to solved problems of VS. In this paper, we have proposed a new technique for model selection in Binary regression. This technique is Bayesian adaptive Lasso Binary regression (BALBR). It has many features that give optimum estimation and VS property. Specifically, we introduced a new hierarchal model. Then, a new Gibbs sampler method is introduced. We also extend the new approach by adding the ridge parameter inside the variance-covariance matrix to avoid the singularity in case of multicollinearity or in case the number of observations less than the number of predictors. A comparison was made with other previous techniques applying the simulation examples and real data. It is worth mentioning, that the obtained results were promising and encouraging, giving better results compared to the previous methods.