Mishra, SK (2004): Estimation under Multicollinearity: Application of Restricted Liu and Maximum Entropy Estimators to the Portland Cement Dataset.
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A high degree of multicollinearity among the explanatory variables severely impairs estimation of regression coefficients by the Ordinary Least Squares. Several methods have been suggested to ameliorate the deleterious effects of multicollinearity.
In this paper we aim at comparing the Restricted Liu estimates of regression coefficients with those obtained by applying the Maximum Entropy Leuven (MEL) family of estimators on the widely analyzed dataset on Portland cement. This dataset has been obtained from an experimental investigation of the heat evolved during the setting and hardening of Portland cements of varied composition and the dependence of this heat on the percentage of four compounds in the clinkers from which the cement was produced. The relevance of the relationship between the heat evolved and the chemical processes undergone while setting takes place is best stated in the words of Woods et al.: "This property is of interest in the construction of massive works as dams, in which the great thickness severely hinder the outflow of the heat. The consequent rise in temperature while the cement is hardening may result in contractions and cracking when the eventual cooling to the surrounding temperature takes place."
Two alternative models have been formulated, the one with an intercept term (non-homogenous) that exhibits a very high degree of multicollinearity and the other with no intercept term (extended homogenous) that characterizes perfect multicollinearity.
Our findings suggest that several members of the MEL family of estimators outperform the OLS and the Restricted Liu estimators. The MEL estimators perform well even when perfect multicollinearity is there. A few of them may outperform the Minimum Norm LS (OLS+) estimator. Since the MEL estimators do not seek extra information from the analyst, they are easy to apply. Therefore, one may rely on the MEL estimators for obtaining the coefficients of a linear regression model under the conditions of severe (including perfect) multicollinearity among the explanatory variables.
|Item Type:||MPRA Paper|
|Institution:||North-Eastern Hill University, Shillong (India)|
|Original Title:||Estimation under Multicollinearity: Application of Restricted Liu and Maximum Entropy Estimators to the Portland Cement Dataset|
|Keywords:||Multicollinearity; Estimator; Restricted Liu; Maximum Entropy Leuven estimator; MEL family; Modular Maximum Entropy Leuven estimator; Least Absolute Deviation; Minimum Norm Least Squares; Moore-Penrose inverse; Portland cement dataset|
|Subjects:||C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis
C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C31 - Cross-Sectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions ; Social Interaction Models
C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C30 - General
C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs
|Depositing User:||Sudhanshu Kumar Mishra|
|Date Deposited:||16. Feb 2007|
|Last Modified:||23. Apr 2015 07:01|
· Belsley, DA, E Kuh & RE Welsch (1980). Regression Diagnostics, Identifying Influential Data and Sources of Collinearity, Wiley, New York. · Dasgupta, M & SK Mishra (2004) “Least Absolute Deviation Estimation of Linear Econometric Models: A Literature Review”, http://ssrn.com/abstract=552502 (Full paper is available). · Daniel, C & FS Wood (1980) Fitting Equations to Data : Computer Analysis of Multifactor Data, 2nd Ed. (with the assistance of JW Gorman), Wiley, New York. · Golan, A, G George & D Miller (1996). Maximum Entropy Econometrics, Wiley, London. · Gorman, JW & RJ Toman (1966). “Selection of Variables for Fitting Equations to Data”, Technometrics, 8, pp. 27-51. · Hald, A (1952). Statistical Theory with Engineering Applications. Wiley, New York. · Hoerl, AE & RW Kennard (1970). “Ridge Regression: Biased Estimation for Non- Orthogonal Problems”, Technometrics, pp. 55-68. · Kaçiranlar, S, S Sakallioglu, F Akdeniz, GPH Styan & HJ Werner (1999)”A New Biased Estimator in Linear Regression and a Detailed Analysis of the Widely-Analysed Dataset on Portland Cement”, Sankhya : The Indian J. of Stat. , 61.B.3, pp. 443-459. · Liu, K (1993).”A New Class of Biased Estimate in Linear Regression”, Communications in Statistics – Theory and Methods, 22, pp. 393-402. · Mishra, SK (2004). “Multicollinearity and Modular Maximum Entropy Leuven Estimator”, http://ssrn.com/abstract=557662 (Full paper is available). · Paris, Q (2001-a). “Multicollinearity and Maximum Entropy Estimators”, Economics Bulletin, 3(11), pp. 1-9. · Paris, Q (2001-b). “MELE: Maximum Entropy Leuven Estimators.” UC Davis Dept. of Agricultural & Resource Economics Working Paper No. 01-003, http://ssrn.com/abstract=280304 (Full paper is available). · Sarkar, N (1992).”A New Estimator Combining the Ridge Regression and the Restricted Least Squares Methods of Estimation”, Communications in Statistics – Theory and Methods, 21, pp. 1987-2000. · Theil, H (1971). Principles of Econometrics, Wiley, New York. · Woods, H, HH Steinour & HR Starke (1932) “Effect of Composition of Portland Cement on Heat Evolved During Hardening”, Industrial and Engineering Chemistry, 24, pp. 1207-1214.