Novel Data-Driven Shrinkage Ridge Parameters for Handling Multicollinearity in Regression Models with Environmental and Chemical Data Applications

Multicollinearity among predictor variables is a common challenge in modeling chemical and environmental datasets in physical sciences, often leading to collinearity issues and unreliable parameter estimates when fitting regression models. Ridge regression method emerges as an effective solution to this problem by introducing a penalty term (k) that shrinks parameters to mitigate multicollinearity and balances bias and variance. In this study, we propose three novel shrinkage parameters for ridge regression and use them to develop three ridge-type estimators, referred to as SPS1, SPS2, and SPS3, which are designed to enhance parameter estimation based on sample size (n), number of predictors (p), and standard error (σ). These shrinkage estimators aim to improve the accuracy of regression models in the presence of multicollinearity. To evaluate the performance of the SPS estimators, we conduct comprehensive Monte Carlo simulations comparing them to ordinary least squares (OLS) and other existing estimators based on the mean squared error (MSE) criteria. The simulation results demonstrate that the SPS estimators outperform OLS and other methods. Additionally, we apply these three shrinkage estimators to two real-world environmental and chemical datasets, showing their ability to address multicollinearity as compared to OLS and other estimators. The proposed SPS estimators offer more stable and accurate regression results, contributing to improved decision-making in environmental modeling, pollution analysis, and other scientific research involving correlated variables.