Abstract
Problem statement: Least Squares (LS) method has been the most popular method for estimating the parameters of a model due to its optimal properties and ease of computation. LS estimated regression may be seriously affected by multicollinearity which is a near linear dependency between two or more explanatory variables in the regression models. Although LS estimates are unbiased in the presence of multicollinearity, they will be imprecise with inflated standard errors of the estimated regression coefficients. Approach: In this study, we will study some alternative regression methods for estimating the regression parameters in the presence of multiple high leverage points which cause multicollinearity problem. These methods are mainly depend on a one step reweighted least square, where the initial weight functions were determined by the Diagnostic-Robust Generalized Potentials (DRGP). The proposed alternative methods in this study are called GM-DRGP-L1, GMDRGP- LTS, M-DRGP, MM-DRGP and DRGP-MM. Results: The empirical results of this study indicated 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: The study had established that the DRGP-MM and the GM-DRGP-LTS methods were recommended to solve the multicollinearity problem with high leverage data points.
Highlights
Least squares estimation is one of the most important regression techniques used for estimating the parameters of a model
Diagnosing the multiple high leverage points and recognizing estimations, methods which are resistant to these points may improve regression estimations
The classical diagnostics measures of the original data clearly indicate that the data set does not have collinear explanatory variables
Summary
Least squares estimation is one of the most important regression techniques used for estimating the parameters of a model. Sometimes it causes the parameters estimation to be different from the true values by orders of magnitude or incorrect sign. Diagnosing the multiple high leverage points and recognizing estimations, methods which are resistant to these points may improve regression estimations. In this respect, alternative robust regression methods are designed to be less sensitive than least squares to outliers mostly in Ydirection, resulting in improved fits to the non-outlying observations. The main objective of this study is to propose some alternative estimators that are able to perform well where multiple high leverage points cause multicollinearity problem in regression analysis.
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