A sequential augmentation method to eliminate multicollinearity

ABSTRACT

This article presents a new augmentation method to eliminate multicollinearity in observational datasets that contain several correlated variables. The purpose is to eliminate the correlations to facilitate the application of the least squares regression method. The procedure is based on the addition of new observations to the point in which an appropriate linear regression model can be constructed. Original data can be observational but the new information is obtained through designed experiments. The proposed method uses the R3 algorithm to perform the augmentations and the VIF statistic to determine the point in which the correlations have been significantly reduced.

KEYWORDS:

• augmentation
• correlation matrix
• R3 algorithm
• regression
• VIF

Additional information

Notes on contributors

Armando J. Ríos

Armando J. Ríos is a full time professor and researcher in the department of Industrial Engineering at Instituto Tecnologico de Celaya. Dr. Ríos received his BS from ITC and obtained his MS and PhD from Florida State University. His concentration areas include design of experiments, regression analysis and simulation.

James R. Simpson

James R. Simpson is Chief Operations Analyst for the Air Force's 53rd Test Management Group at Eglin Air Force Base, FL. He formerly served as an Associate Professor of Industrial Engineering at Florida State University and Associate Professor of Operations Research at the United States Air Force Academy. He is the past Editor-in-Chief for Quality Engineering and an associate editor for Quality and Reliability Engineering International. He earned a BS in Operations Research from the United States Air Force Academy, an MS in Operations Research from the Air Force Institute of Technology, and a PhD in Industrial Engineering from Arizona State University. He is a senior member of ASQ and IIE, a member of ASA and AIAA. His research interests include design and analysis of experiments, simulation, response surface methods, applied optimization, regression analysis, and quality control.