The ISLasso Estimator for Multicollinearity and High-Dimensional Problems in Linear Regression with Continuous and Categorical Outcomes

Abstract

This paper compares the efficiency of seven penalized regression estimators-Ridge, LASSO, Elastic Net (ENET), Adaptive LASSO (ALASSO), Adaptive Elastic Net (AENET), ISLasso, and MAENet-designed to improve predictive performance under conditions of multicollinearity and high dimensionality. By incorporating penalty terms into the ordinary least squares (OLS) framework, these methods reduce variance at the cost of introducing some bias, thereby shrinking coefficient estimates toward zero. The study evaluates estimator performance for both continuous and binary dependent variables using Mean Squared Error (MSE) and Mean Absolute Error (MAE). Analysis is based on simulated datasets with varying sample sizes, numbers of predictors, and correlation levels (ρ = 0.0 to 0.80), with 500 replications per simulation condition.