Pengaruh Parameter Regularisasi (λ) terhadap Stabilitas Estimasi pada Regresi Ridge

Abstract

Multicollinearity is one of the common issues in multiple linear regression that can lead to instability in the estimation of regression coefficients. This study aims to examine the impact of multicollinearity on regression models and to evaluate the use of Ridge Regression as an alternative estimation method. The study employs simulated data consisting of 1,000 observations, including one dependent variable and four independent variables designed to exhibit high correlation. The analysis begins with model estimation using the Ordinary Least Squares (OLS) method, followed by multicollinearity testing using the Variance Inflation Factor (VIF). The OLS results indicate that most independent variables significantly influence the dependent variable, with a coefficient of determination (R²) of 0.9863. However, the high VIF values reveal the presence of strong multicollinearity in the model. To address this issue, Ridge Regression is applied, with the optimal penalty parameter determined through cross-validation, yielding a lambda value of 4.201589. The results show that the regression coefficients in the Ridge model undergo shrinkage, resulting in greater stability compared to the OLS estimates. Model evaluation indicates that the Mean Squared Error (MSE) for the OLS model is 24.77, whereas the Ridge model produces an MSE of 29.72. Although the Ridge model exhibits a slightly higher MSE, it effectively mitigates the impact of multicollinearity and provides more stable parameter estimates.