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.混混试验（mixture-of-mixtures, MoM）与经典混料试验存在本质差异：混混试验中的混料组分（即主组分）由多个子组分（即次组分）构成。本文针对混混试验提出了一种加性遗传模型（additive heredity model, AHM），该模型通过加性结构实现主组分与次组分的内在关联。为确保估计得到的模型具备合理的解释性，本文结合层次化与遗传原则，采用非负绞子技术开展模型选择。随后，将所提AHM与多种常规方法在无约束与有约束混混试验场景下进行性能对比，并将该模型成功应用于已有文献中已研究的两类实际问题。本文的补充材料可在线获取。