Visualization Approaches for Evaluating Ridge Regression Estimators in Mixture and Mixture-Process Experiments

When the component proportions in mixture experiments are restricted by lower and upper bounds, the input space of a designed experiment space can become an irregular region that can induce multicollinearity problems when estimating the component proportion parameters. Thus, ridge regression provides a beneficial means of stabilizing the coefficient estimates in the fitted model. Previous research has focused on using prediction variance as a metric for determining an appropriate value of the ridge constant, k. We use visualization techniques to illustrate and evaluate ridge regression estimators and the robustness of estimation with respect to the variance and the bias. The addition of bias allows better balancing between the stability of the estimators and minimally changing the estimates. We illustrate the graphical methods with mixture and mixture-process examples from the literature. Copyright (C) 2014 John Wiley & Sons, Ltd.