Indian Journal of Science and Technology

Abstract

Objectives: To examine the performance of several regression methods comprising of Ordinary Least Square (OLS), and certain robust methods including; M-regression, Least Median of Squared (LMS), Least Trimmed Square (LTS), MMestimation and S-estimation, under fluctuating levels of collinearity, using the criterion, Total Absolute Deviation (TAB) and Total Mean Square Error (TMSE) with some graphical tools. Methods/Statistical Analysis: Robust Regression methods insure good performance even in case the fundamental assumption of normality is not satisfied. The presence of multicollinearity affects the results of robust regression methods and marks them unsatisfactory. A quantitative evaluation of these techniques is provided by using the criterion, TAB and TMSE. Results are summarised by using box plot of absolute bias, along with the graphs of TAB, and TMSE. Findings: The results show that for minor levels of collinearity the effect is low and similar, but at greater levels of collinearity the effect is high and performance wise all the methods give quite incompatible results. It is also illustrated that greater magnitude of collinearity along with higher percentages of outliers ranks the underlying methods quite differently, resulting in MM-estimation method to be the most unpleasant. Conclusion: While applying any statistical method it is necessary to consider all the assumption underlying that method as well as every aspect of our data to avoid misleading results. It is illustrated that MM-estimation method although a best candidate for higher percentages of outliers alone, become the most unpleasant, by a simultaneous interruption of high level of collinearity, hence robust ridge techniques need to be adopted.

Keywords: Multicollinearity, Ordinary Least Squares, Outliers, Robust Regression Methods