Treating Multicollinearity Problem Using Gool Programming Technique | ||||
| The Egyptian Statistical Journal | ||||
| Article 1, Volume 55, Issue 2, December 2011, Page 67-92 | ||||
| DOI: 10.21608/esju.2011.314312 | ||||
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| Abstract | ||||
| Multiple regression analysis is usually efficient for prediction, but often produces poor results because of the multicollinearity among the independent variables. Multicollinearity causes a reduction in statistical power and leads to wider confidence intervals for the regression parameters, so they could be incorrectly identified as being insignificant. Generalized ridge regression estimator has been introduced us an alternative to the ordinary least squares estimator (OLS) in the presence of multicollinearity. Several studies concerning the generalized ridge regression have been dealt with the choice of the ridge parameters. In this paper, a suggested goal programming model is introduced to find the optimal values of the ridge parameters for generalized ridge regression estimates. These optimal values achieve three objectives which are: 1) generalized ridge regression estimates have smaller variances than the ordinary least squares estimator (OLS), 2) generalized ridge regression estimates have the minimum sum of squared residuals, and 3) generalized ridge regression estimates have the maximum correlation coefficient each independent variable and the fitted values of the dependent variable, with different priorities. A procedure of the successive steps for solving the suggested goal programming model is introduced. The results of applying the suggested goal programming model are compared with the results of applying some existing estimators (ridge regression [4,13,14], Stien [15], multi-objective programming model (191) using an example [12]. The results show that the suggested model is superior to the other estimators in terms of a reduction in the variances of the generalized ridge regression estimates and also reduction in the Mean Squared Errors of Responses (MSER) and the Mean Absolute Errors of Responses (MAER) | ||||
| Keywords | ||||
| Generalized Ridge Regression - Goal Programming; Multicollinearity - Multiple Linear Regression; Multi objective Programming - Stein Estimates - Ridge Regression - Optimization | ||||
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