Experiments with Mixtures, Ill-Conditioning, and Ridge Regression

Experiments with mixtures require a special form of polynomial model called the canonical polynomial model. Moreover, many mixtures problems are also subject to additional constraints that often cause ill-conditioning, or collinearity. Using the eigenvalues and Variance Inflation Factors (VIF's) as measures of conditioning, we have looked at a variety of mixtures data sets. We have considered the effect on conditioning of such remedial measures as standardizing the variables, transforming to pseudocomponents, and ridge regression. In particular, ridge regression is used as a method for displaying the effects of collinearity on the regression coefficients. We conclude that since ill-conditioning is a problem in so many mixtures experiments, the mixtures practitioner should always use VIF's or eigenvalues to look for it.