Abstract
Problem statement: The Least Squares (LS) method has been the most popular technique for estimating the parameters of a model due to its optimal properties and ease of computation. LS estimated regression may be seriously disturbed by multicollinearity which is a near linear dependency between two or more explanatory variables in the regression models. Even though LS estimates are unbiased in the presence of multicollinearity, they will be imprecise with inflated standard errors of the estimated regression coefficients. It is now evident that the multiple high leverage points which are the outliers in the X-direction may be the prime source of collinearity-influential observations. Approach: In this study, we had proposed robust procedures for the estimation of regression parameters in the presence of multiple high leverage points which cause multicollinearity problems. This procedure utilized mainly a one step reweighted least square where the initial weight functions were determined by the Diagnostic-Robust Generalized Potentials (DRGP). Here, we had incorporated the DRGP with different types of robust methods to down weight the multiple high leverage points which lead to reducing the effects of multicollinearity. The new proposed methods were called GM-DRGP-L1, GM-DRGP-LTS, M-DRGP, MM-DRGP, DRGP-MM. Some indicators had been defined to obtain the best performance of robust method among the existing and new introduced methods. Results: The empirical study indicated that the DRGP-MM emerge to be more efficient and more reliable than other methods, followed by the GM-DRGP-LTS as they were able to reduce the most effect of multicollinearity. The results seemed to suggest that the DRGP-MM and the GM-DRGP-LTS offers a substantial improvement over other methods for correcting the problems of high leverage points enhancing multicollinearity. Conclusion/Recommendations: In order to solve the multicollinearity problems which are mainly due to the multiple high leverage points, two proposed robust methods, DRGP-MM and the GM-DRGP-LTS, were recommended.
Highlights
Least squares estimation is one of the predominant regression analysis techniques due to the universal acceptance, elegant statistical properties and computational simplicity
It is important to note here that the multiple high leverage points will be the prime source of multicollinearity when they are detected as high leverage points with the large magnitude in at least two explanatory variables
The development of robust methods that deal with the multicollinearity problems which are mainly due to multiple high leverage points has not been published extensively in the literature
Summary
Least squares estimation is one of the predominant regression analysis techniques due to the universal acceptance, elegant statistical properties and computational simplicity. Two of the assumptions that make least squares so attractive in terms of general model hypothesis and parameter significance testing, are normality of error distribution and independency of explanatory variables. The normality assumption can be violated in the presence of one or more sufficiently outlying observations in the data set resulting in less reliable estimates of the model parameters[1]. The second condition that potentially impacts the reliability of least squares estimation is multicollinearity, which is a near-linear dependency among the explanatory variables (X-direction). Sometimes it causes the parameters estimation to be different from the true values by orders of magnitude or incorrect sign. It may inflate the variance of the estimations. The points far from the rest of the data in the X-direction, have high potential for influencing most of the regression results such as eigenstructure and condition index of X[10]
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