Optimizing Variable Selection with Bayesian t-Lasso Regression: A Comparison of Normal-mixture and Uniform-mixture Representations for Outlier Data Analysis

Abstract

One of the discussed parts of the regression model is choosing the optimal model. The choice of the optimal model in regression models is to determine the important explanatory variables and the negligible variables and to express the relationship between the response variable and the explanatory variables in a simpler way. With the limitations of classical variable selection processes such as step-by-step selection, compensated regression methods can be used. One of the compensated regression models is Lasso regression. For data collection and statistical analysis in the presence of remote observations, instead of normal distribution, T-Student distribution can be used for the error of these data. In this article, we propose a variable selection method called T-Lasso Bayesian regression model for data analysis in the presence of outlying observations. Bayesian t-lasso regression model with two different representations of Laplace's prior density function for the coefficients of the regression model is investigated, so that first the Laplace density function is discussed in the form of mixed distribution-normal scale and then in the form of mixed distribution-uniform scale. Then, by using simulation methods and real data analysis, the superiority of the Bayesian T-lasso regression method is shown by showing the Laplace density function in mixed-uniform scale over normal mixed-scale display.