A Family of Enhanced Ridge Regressions in Comparison with Adjusted Shapley Model

• Activity Number: 683
• Type: Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and Marketing
• Author(s): Stan Lipovetsky*+
• Companies: GfK Custom Research North America
• Keywords: least squares objective ; modified ridge regressions ; adjusted Shapley regression ; stable solutions ; multicollinearity

Abstract

A modified least squares objective is used to produce a family of new ridge regressions with enhanced properties. The models are additionally adjusted to attain the best possible fit. They outperform the regular ridge model, in contrast to which the enhanced and adjusted ridge solutions have a stabilized profile behaviour and a better quality of fit. The coefficients of these regressions do not shrink to zero when the ridge parameter increases, the coefficient of multiple determination stays high, bias and generalized cross-validation are low. Comparison with adjusted coefficients of Shapley regression based on cooperative game theory shows that results of both approaches are very similar and support each other. Both models are stable, meaningful, easily interpretable, and especially helpful for analysis of individual predictors role in regressions with multicollinear variables.