CRI: A Collinearity Resistant Implement for analysis of regression problems

摘要

Collinearity among predictors in a regression model can make interpretation of the model difficult. We suggest a useful multivariate technique that keeps the signs of regression coefficients the same as those of the pairwise correlations. This method could be seen as a new technique related to the family of such multivariate methods as redundancy analysis, partial least squares, and robust canonical correlation analysis. Using a multiobjective approach, we show how to obtain a regression that has desirable interpretative properties while retaining a level of explanatory power similar to that of the usual linear regression model.