Dr.  Catalina  García
Granada University,  Spain

Title: An overview of multicollinearity: contributions and alternative to ridge regression

Abstract:

Multicollinearity exists in a linear regression model when there is a strong relationship between at least two exogenous variables. In this case, the ordinary least squares estimation can present instability, leading to erroneous conclusions that could even call into question the validity of the analysis. For this reason, alternative estimation methodologies are traditionally applied, such us ridge regression which is systematically applied in many different fields where multicollinearity appears. Despite its consequences, multicollinearity is not always adequately treated in some studies and it is even completely ignored in others. In this same way, the ridge regression is not always adequately applied. This presentation aims to clarify some aspects of the diagnosis and treatment of multicollinearity. First, we share some contributions in relation to the measures traditionally apply to diagnose multicollinearity. Second, we provide an alternative measure to diagnose multicollinearity after the application of the ridge regression and propose the mitigation of multicollinearity as criteria to select the ridge factor. We also review some limitations of ridge regression and propose the application of the raise regression that allows the mitigation of the multicollinearity maintaining the global characteristics of the original model and modifying the information matrix (X’X) from a geometrical point of view of multicollinearity. Finally, some future research lines are presented with the goal of generating potential synergies with the audience.

Biography:

Catalina B. García is professor of Quantitative Methods in Business and Economics in the Department of Quantitative Methods for Economics and Business at the University of Granada (Spain). She has a Bachelor in Financial and Actuarial Sciences from the Autonomous University of Madrid (Spain) and another in Business Administration from the Complutense University in Madrid (Spain). Her Phd was presented in 2007 with the titled “The generalization of biparabolic distrinbution: application to financial and valuation fields” within the field of theory distribution. From August 2008 to November 2008, she was invited by Professor J.R. van Dorp for a research stay-out. In the Department of Engineering Management and Systems Engineering of the George Washington University. As a result of this stay, the work "Modeling heavy-tailed, skewed and peaked uncertainty phenomena with bounded support" was presented, which presents the family of Elevated Two Sided Power (ETSP) distributions by using as generating distributions mixtures of the uniform distribution and the family of power distributions. She was also invited by Professor J. Bazan for Research stay-out during November 2010 in the Mathematic Department of the Pontificia Universidad Catolica del Peru (UPCM), Lima, Peru, publishing a joint contribution in relation to a regression model for proportions based on the rectangular beta distribution proposed by Hahn (2008). With the purpose of bringing closer the teaching and research activities, nowadays her main research line is within econometric and more specifically the treatment and diagnose of multicollinearity. Among other contributions, it was proposed an alternative expression for the variance inflation factor to be applied after application of ridge regression and, also, an alternative estimator to ridge regression. She is the responsible of the research group “Quantitative Techniques for Economics and Business Administration” of the University of Granada and the co-responsible of the research project “Disruption in the multicollinearity problem: a new vision for its diagnosis and treatment” (A-SEJ-496-UGR20) of the Andalusian Government's Counseling of Economic Transformation, Industry,Knowledge and Universities (Spain). Her main fields of interest are development of models and quantitative methods in economics and business, estimation of econometric models and detection of lineal dependence in regression models. She also parcipates regularly in different international conferences and as reviewer for journal such as European Journal of Operations Research, Physica A and Mathematics.