Evaluating Shrinkage Regression Techniques: a Comparative Analysis of Lasso, Ridge, Elastic Net and Best Subset Models in Forecasting Macroeconomic Variables
Student: Khadijat Idowu Adebeshin (Project, 2025)
Department of Mathematics and Statistics
Federal Polytechnic, Ilaro, Ogun State
Abstract
This study compares the performance of four regression models; Lasso, Ridge, Elastic Net, and Best Subset Model in forecasting macroeconomic variables, focusing on predictive accuracy, model stability, and generalizability. The evaluation metrics adopted include Mean Squared Error (MSE), R-Squared, Adjusted R-Squared, and Leave-One-Out Cross-
Validation (LOOCV) MSE. Lasso, known for feature selection, showed moderate accuracy with an MSE of 0.0347 and LOOCV MSE of 0.0039, but had low R-Squared due to excessive shrinkage. Ridge regression effectively managed multi-collinearity, achieving an MSE of
0.0034 and LOOCV MSE of 0.0037, showing consistent performance. Elastic Net balanced feature selection and multi-collinearity with an MSE of 0.0153 and LOOCV MSE of 0.0032.
The Best Subset Model excelled with the lowest MSE (0.0009888) and LOOCV MSE (0.0016), offering superior accuracy and stability. Therefore, the Best Subset Model emerged as the most reliable for forecasting, providing an optimal balance between model complexity and interpretability.
Keywords
For the full publication, please contact the author directly at: idowukhad@gmail.com
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Institutions
- Covenant Polytechnic, Aba, Abia State 1
- Covenant University, Canaan Land, Ota, Ogun State 4
- Crawford University of Apostolic Faith Mission Faith City, Igbesa, Ogun State 2
- Crescent University, Abeokuta, Ogun State 1
- Cross Rivers University of Technology, Calabar, Cross Rivers State 142
- Delta State Polytechnic, Ogwashi-Uku, Delta State 11
- Delta State Polytechnic, Otefe, Delta State 12
- Delta State University, Abraka, Delta State 138
- Ebonyi State University, Abakaliki, Ebonyi State 17
- Edo University, Iyamho, Edo State 10