Additive Heredity Model for the Analysis of Mixture-of-Mixtures Experiments

Abstract

The mixture-of-mixtures (MoM) experiment is different from the classical mixture experiment in that the mixture component in MoM experiments, known as the major component, is made up of subcomponents, known as the minor components. In this article, we propose an additive heredity model (AHM) for analyzing MoM experiments. The proposed model considers an additive structure to inherently connect the major components with the minor components. To enable a meaningful interpretation for the estimated model, the hierarchical and heredity principles are applied by using the nonnegative garrote technique for model selection. The performance of the AHM was compared to several conventional methods in both unconstrained and constrained MoM experiments. The AHM was then successfully applied in two real-world problems studied previously in the literature. Supplementary materials for this article are available online.

Keywords:

• Mixture experiments
• Model selection
• Nonnegative garrote method

Supplementary Materials

The online supplementary materials include the lemma for the relationship between the major–minor model and the additive model, the algorithm of generating maximin distance designs for major components, and simulation results for the type (b) MoM experiments in Section 4 of the main article.

Acknowledgments

The authors acknowledge the editor, associate editor, and reviewers for their insightful comments to revise this article.

Additional information

Funding

This work was supported by the National Science Foundation CMMI-1435996.