Research Information System
5. Uluslararası Araştırmacılar, İstatistikçiler ve Genç İstatistikçiler, Aydın, Turkey, 18 - 20 October 2019, pp.1-2
Abstract: Multicollinearity
is the existence of linear relationships among two or more independent
(explanatory) variables. The presence of multicollinearity poses a serious
problem for regression analysis studies. This problem leads to unstable estimates
of the regression coefficients and causes some serious problem in validation
and interpretation of the regression model. In this study, the effect of multicollinearity
on the regression coefficient estimators is examined with a simulation study. In
the simulation study, in case of multicollinearity, the least squares
estimation method and a robust method (using MATLAB Robustfit command which
uses the Tukey M-estimators as default) are compared and the answer to the
question of whether there is a difference in the variances of the regression
coefficients between the estimations based on the least squares method and the
estimations using robust methods is investigated. In other words, we are
investigating that whether robust methods can be a remedy against
multicollinearity. The simulation results show that the robust methods are also
badly affected by multicollinearity because multicollinearity does not influence
the residuals and the robust methods mostly produce solutions for the outliers
in the residuals. At the end of the study, a real-life application is given. We
also discuss the causes of multicollinearity and its detection methods and the
possible remedies.
Key
words:
Regression analysis, Multicollinearity, Least squares method, Robust methods.