A revision on Multicollinearity and Augmentation Methods

This book presents a new augmentation method to eliminate the multicollinearity in datasets that contain several correlated predictor variables. The objective in mind is to reduce the estimation error of the regression coefficients. The main contribution of this work consists in offering a new alternative to eliminate multicollinearity in datasets by using small runs which are added in a sequential manner. The algorithm proposed will indicate the point in which the augmentations have sufficiently contributed to find the true regression model. The procedure is based on addition of new observations to the point in which an appropriate regression model can be constructed. The new information is obtained through designed experiments using the R3 algorithm as a guideline to perform the augmentations and the Ridge Trace and VIF statistic as verification tools that help to determine the point in which the correlations have been significantly reduced. The final result is a linear regression model that accurately represents the process under study.