Comparative Analysis of Ordinary Least Squares, Ridge, and a Proposed Modified Ridge Regression Method for Modelling Nigeria’s Economic Development
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Abstract
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.
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References
Akinwande, M. O., Dikko, H. G., & Samson, A. (2015). Variance inflation factor: As a condition for the inclusion of suppressor variable(s) in regression analysis. Open Journal of Statistics, 5(7), 754–767.
Draper, N. R., & Smith, H. (1998). Applied regression analysis (3rd ed.). Wiley.
Gujarati, D. N., & Porter, D. C. (2009). Basic econometrics (5th ed.). McGraw-Hill.
Hocking, R. R. (1976). The analysis and selection of variables in linear regression. Biometrics, 32(1), 1–49.
Hoerl, A. E., & Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55–67.
Iwundu, M. P., & Onu, O. H. (2017). Preferences of equiradial designs with changing axial distances, design sizes and increase center points and their relationship to the N-point central composite design. International Journal of Advanced Statistics and Probability, 5(2), 77-82.
Khalaf, G., & Shukur, G. (2021). Some new ridge-type estimators and their applications. Communications in Statistics – Simulation and Computation, 50(3), 652–667.
Kutner, M. H., Nschtsheim, C. J., Neter, J. and Li, W. (2005).
Applied linear statistical model, fifth edition, McGraw-
Hilit:a Irwin.
Marquardt, D. W. (1980). You should standardize the predictor variables in your regression models. Journal of the American Statistical Association, 75(369), 87–91.
Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to linear regression analysis (5th ed.). Wiley.
Nelson, M., Biu, O. E., & Onu, O. H. (2024). Comparing the proposed Sub-Ridge Regression with Ridge and OLS for a shrinkage factor; Data with or without Multicollinarity. International Journal of Computer Science and Mathematical Theory, 10(2), 22-34.
Nelson, M., Onu, O. H., & Ijomah, M. A. (2024). Mult-Ridge, and Inverse-Ridge Regressions for data with or without multicollinearity for certain shrinkage factors. International Journal of Applied Science and Mathematical Theory, 10(2), 29-41.
Nwakoby, I. C., & Chukwuma, E. (2020). Macroeconomic variables and economic growth in Nigeria. Journal of Economics and Sustainable Development, 11(12), 45–57.
Onu, O. H., George, D. S., Uzoamaka, E. C., & Okerengwu, B. (2021). The statistical bias in genetic model analysis with varying model parameters. International Journal of Research, 8(6), 178-185.
Onwumere, J. U. J., Ibe, I. G., & Ozoh, F. O. (2019). Exchange rate, inflation, and GDP growth in Nigeria: An econometric approach. International Journal of Economics and Finance Studies, 11(1), 89–102.