Comparative Analysis of Ordinary Least Squares, Ridge, and a Proposed Modified Ridge Regression Method for Modelling Nigeria’s Economic Development - Onu, Obineke Henry; Nelson, Maxwell (Faculty of Natural and Applied Sciences Journal of Mathematical and Statistical Computing, 2025)
This study investigated the performance of Ordinary Least Squares (OLS), Ridge Regression, and three newly proposed biased estimators such as, Sub-Ridge, Multi-Ridge, and Inverse-Ridge regressions in the presence of multicollinearity among predictor variables. Unlike Ridge Regression, which adds a biasing constant KI to the variance–covariance matrix (X′X), the Sub-Ridge, Multi-Ridge, and Inverse-Ridge estimators respectively subtract, multiply, and divide (X′X) by KI. The Gross Domestic Product (GDP) of Nigeria served as the response variable, while exchange rate, unemployment rate, inflation rate, and foreign direct investment were used as predictors. Multicollinearity diagnostics were conducted using the Variance Inflation Factor (VIF), correlation analysis, determinant of X′X, condition number, and condition index. Results showed moderate multicollinearity, primarily between exchange rate and unemployment rate (r = 0.838). Simulated datasets with varying sample sizes (50, 75, and 100) were analyzed, and model performances were compared across different shrinkage parameter values. Findings revealed that the proposed Multi-Ridge and Inverse-Ridge estimators provided more stable and efficient estimates under moderate multicollinearity compared to OLS and standard Ridge estimators. The study concludes that these new estimators offer promising alternatives for handling multicollinearity in econometric modeling.