A study on group lasso for grouped variable selection in regression model

Abstract

Estimation of regression parameters using the Least Squares (LS) method could not be performed when the number of explanatory variables exceeds the number of observations. An approach that can solve the problem is the LASSO (Least Absolute Shrinkage and Selection Operator) method. This method produces a stable model but with slight bias as the trade-off. Yuan and Lin [6] introduced the Group LASSO method which can be used when there are grouped structure in the variables. This current paper provided a study of the performance of the Group LASSO method through a simulation with several different scenarios. Furthermore, the Group LASSO method was applied to the Human Development Index (HDI) data of Bengkulu Province in 2019. The simulation yieled that the Group LASSO analysis was better than LASSO in term of its Mean Squared Error of Prediction (MSEP), False Negative Rate (FNR) and R-Squared. In the application of the approach to the HDI data, our result was in line with the simulation results that the analysis of Group LASSO was better than LASSO with MSEP Group LASSO of 0.25 and R-Squared of 98%.