Fraction of design space plots for evaluating ridge estimators in mixture experiments

Abstract

When the component proportions in mixture experiments are restricted by lower and upper bounds, the design space can become an irregular region that can induce multicollinearity among the component proportions. Thus, we suggest the use of ridge regression as a means of stabilizing the estimates of the coefficients in the fitted model. We use fraction of design space plots and violin plots to illustrate and evaluate the effect of ridge regression estimators with respect to the prediction variance and to guide the decision about the value of ridge constant k. We illustrate the methods with three examples from the literature. Copyright © 2010 John Wiley & Sons, Ltd.