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

The mixture-of-mixtures experiment is different from the classical mixture experiment in that the mixture component in mixture-of-mixtures experiments, known as the major component, is made up of sub-components, known as the minor components. In this paper, we propose an additive heredity model for analyzing mixture-of-mixtures 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 additive heredity model was compared to several conventional methods in both unconstrained and constrained mixture-of-mixtures experiments. The additive heredity model was then successfully applied in two real-world problems studied previously in the literature.