Some data reduction methods to analyze the dependence with highly collinear variables: a simulation study

The dependence relationship between two sets of variables is a subject of interest in statistical field. A frequent obstacle is that several of the explanatory variables will vary in rather similar ways. As a result, their collective power of explanation is considerably less than the sum of their individual powers. This phenomenon, called multicollinearity, is a common problem in regression analysis. The major problem with multicollinearity is that the ordinary least squares coefficients estimators involved in the linear dependencies have large variances. All additional adverse effects are a consequence of them. In statistical literature several methods have been proposed to counter with multicollinearity problem. By a simulation study and considering different case of collinearity among the regressors, in this paper we have compared, using RV coefficient, five statistical methods, alternative to the ordinary least square regression.