Assessing Robustness of Regularized Regression Models with Applications

Abstract

In this Big-data and computational innovation era, advanced level analysis and modelling strategies are essential in data science to understanding the individual activities which occur within very complex behavioral, socio-economic and ecological systems. However, the scales at which models can be developed, and the subsequent problems they can inform, are often limited by our inability or challenges to effectively understand data that mimic interactions at the finest spatial, temporal, or organizational resolutions. Linear regression analysis is the one of the widely used methods for investigating such relationship between variables. Multicollinearity is one of the major problem in regression analysis. Multicollinearity can be reduced by using the appropriate regularized regression methods. This study aims to measure the robustness of regularized regression models such as ridge and Lasso type models designed for the high dimensional data having the multicollinearity problems. Empirical results show that Lasso and Ridge models have less residual sum of squares values. Findings also demonstrate an improved accuracy of estimated parameters on the best model.