Ridge Estimates of Regression Coefficients for SoilMoisture Retention of IraqiSoils


  • Khasraw A. Rashid Faculty of Agricultural Science, University of Sulaimani, Kurdistan Region, Iraq. Author
  • Hanaw A. Amin Faculty of Science and Science Education, University of Sulaimani, Kurdistan Region, Iraq. Author




Multiple Regression Model, Ridge Regression Model, Collinearly, SCSSNI


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.


Baver, L. D. Gardner W. H and Gardner W. R. “Soil Physics” 4th edition, New York, Wiley and Sons,(1972).

Kilmer, V. J. and L. T. Alexander. “Methods of Making Mechanical Analysis of Soil”. Soil Sci. Vol.68, pp 15 – 24. DOI: https://doi.org/10.1097/00010694-194907000-00003

Russell, M. B. “Soil Moisture Sorption Curves for Four Iowa Soils”. Soil Sci. Amer Proc. Vol.4, pp 51-54, (1940). DOI: https://doi.org/10.2136/sssaj1940.036159950004000C0009x

Child, E. C., “The Use of Soil Moisture Characteristics in Soil Studies”, soil science Vol. 50, pp 239 –252, (1940). DOI: https://doi.org/10.1097/00010694-194010000-00001

Richards, L. A. A. “Pressure Membrane Extraction Apparatus for Soil Solution. Vol. 15 p. 377 – 389,(1940). DOI: https://doi.org/10.1097/00010694-194105000-00005

Rashid, Khasraw Abdulla. “Suction Characteristics of Subgrade Soil from North Iraq”.Dep. Of Civil Engineering, University of Salahaddin, Arbil- Iraq. Engineering and Technology Vol. 12 No. 9, (1993).

James, Gareth, Witten Daniela, Hastie Trevor, and Tibshirani Robert. “An Introduction to Statistical Learning with Applications in R”.Springer New York Heidelberg Dordrecht London, (2013).

Tibshirani, Robert, James Gareth, Witten Daniela, Hastie Trevor. “An Introduction to Statistical Learning with Applications in R”.Springer New York Heidelberg Dordrecht London, (2013).

Chung, Hoeil, and Jun, Chi- Hyuck. “Determination of Research Octane Number Using NIR Spectral Data and Ridge Regression”.Department of Industrial Engineering Pohang University of Science and Technology, Korea, (2000).

Richards, L. A., “Physical Condition of Water in Soil, A me. Soc. Agron, Inc Madison, Wis. P. 128-151, (1965). DOI: https://doi.org/10.2134/agronmonogr9.1.c8

Richards, L. A..“Diagnosis and Improvement of Saline and Alkaline Soils”.Agr.Hanbook No. 60, USDA. US. Government Printing Office Washington DC., (1954).

Wakley, A. and Black, 1934 cited in L. E. Allison, Organic Carbon, P. 1367 – 1378in black C. A. et al., (Ed.) 1965, Methods of Soil Analysis part 2, Agron. No. 9.

Chapman, H. D. and Partt, P. E. “Method of Analysis for Soils, Plant and Water”. Univ. California Press.California (1961).

Cule, Erika, Vineis Paolo and De Iorio Maria. “Significance Testing in Ridge Regression for Genetic Data”.Cule et al. BMC Bioinformatics,(2011). DOI: https://doi.org/10.1186/1471-2105-12-372

Batah, Feras Sh. M. and Damodar, Sharad Gore. “Ridge regression estimator: Combining Unbiased and Ordinary Ridge Regression Methods for Estimations”. Surveys in Mathematics and its Applications.ISSN 1842-6298 (electronic), P. 99 – 109, Vol. 4, (2009).

Ehsanes, A.K.Md. Saleh.“Ridge Regression Estimation Approach to Measurement Error Model”. Carleton University, Ottawa (CANADA), Department of Mathematics & Statistics, Indian Institute of Technology, Kanpur - 208 016, (INDIA).

https:// STAT 897D - Applied Data Mining and Statistical Learning. "Lesson 5: Regrassion Shrinkage Methods", The Pennsylvania State University Privacy and Legal Statements Department of Statistics online Programs.Copyright 2015. Last revised 26 / 8 / 2015.

Shedden, Kerby. “Prediction”.Department of Statistics, University of Michigan. November 3, 2014.

https://onlinecourses.science.psu.edu/stat512/node/217.“Applied Linear Models Topic 5a.Ridge Regression (Section 11.2)”. Last revised 31 / 8 / 2015.

Marquardt, Donald W. and Ronald D. SneeSource. “Ridge Regression in Practice”. The American Statistician, Vol. 29, Pa. 3-20.No. 1, (Feb., 1975). DOI: https://doi.org/10.1080/00031305.1975.10479105



How to Cite

Ridge Estimates of Regression Coefficients for SoilMoisture Retention of IraqiSoils. (2016). Journal of Zankoy Sulaimani - Part A, 18(3), 85-98. https://doi.org/10.17656/jzs.10537