Variable Selection with Convex and Non-Convex Penalized Likelihood Models Using Rainfall Data

Abstract

Accurate estimate of rainfall is very important for effective use of water resources and optimal planning of water structure in a day-to-day activity of life. Variable selection is an important aspect in penalization for the estimation of accurate outcome. Traditional variable selection such as stepwise and subset selections are usually used which can be computationally expensive and ignore stochastic errors in the variable selection process. Penalized likelihood methods are applied to select the important variables which can be used for accurate predictions. In this study, penalized likelihood approach is applied to select variables and estimate coefficients simultaneously. Some of penalized penalty functions were used to produce sparse solutions. From the results obtained the penalty functions produce the important variables that influence the total rainfall. Lasso model produces Four (4) important variables, Elastic net produces Two (2) important variables while SCAD produces only One (1) variable as important. This indicates that Lasso model is more complex than SCAD model. The results also show that SCAD penalty function out performed Ridge, Lasso and Elastic net. Based on the RMSE criteria, Ridge regression performed less compared to the other models.