Ridge Estimates of Regression Coefficients for SoilMoisture Retention of IraqiSoils

Khasraw A. Rashid1 & Hanaw A. Amin2

1 Faculty of Agricultural Science, University of Sulaimani

2 Faculty of Science and Science Education, University of Sulaimani.

DOI: https://doi.org/10.17656/jzs.10537

Abstract

Statistical literature has several methods for coping with multicollinearity problem.Ridge regression “RR” is compared with multiple linear regression for studying “Suction Characteristics of Subgrade Soils from North Iraq- SCSSNI”. Multiple linear regression “MLR” of “SCSSNI” data usually encounters a collinearly problem, which adversely affects long term prediction performance. The collinearly problem can be eliminated or greatly improved by using ridge regression, which is a biased estimation method with potentially smaller mean square error “MSE” as an alternative to ordinary least square “OLS”. In this study, ridge regression (a biased estimation method has been evaluated with a constant bias ) and the prediction performance was compared with that of ordinary least square“OLS” based multiple linear regression “MLR”. The bias constant of was selected bu examining the ridge trace. At this point, the estimated coefficients are stable and their variance inflation factors “VIFs” become smaller. To evaluate the robustness of each model the standard error of prediction” SEPs” has been compared, the prediction of original values using MLR model shows slightly better results comparing to that of ridge regression model, which is due to an intentional bias is associated in the ridge model. To compare RR and MLR, the coefficient of determination, “VIFs”, and standard error “SE” of parameters has been studied. If the variance of the ridge estimator could be tremendously reduced, the mean square error tends to be smaller than the OLS. The prediction results of a ridge model showed more stable prediction performance as compared to that of MLR, by removing or decreasing the collinearly problem.

Key Words:  Multiple Regression Model, Ridge Regression Model, Collinearly, SCSSNI.

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