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

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.

混混（mixture-of-mixtures，MoM）实验与经典混料实验存在本质差异：MoM实验中的混料组分被定义为主组分，该主组分由若干子组分（即次组分）构成。本文针对MoM实验提出了一种加性遗传模型（additive heredity model，AHM），该模型通过构建加性结构，从本质上实现主组分与次组分之间的关联建模。为确保估计模型具备可解释性，本文引入层次化与遗传原则，并采用非负Garrote（nonnegative garrote）技术开展模型选择。本文在无约束与有约束两类MoM实验场景中，将所提AHM的性能与多种经典方法进行了对比。随后，本文将所提AHM成功应用于文献中已被前人研究过的两类实际应用问题。本文配套补充材料可在线获取。