Orthogonalized moment aberration for mixed-level multi-stratum factorial designs with partially-relaxed orthogonal block structures
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部分放宽正交区组结构下混合水平多层析因设计的正交化矩偏差
- 研究问题
- 当实验单位存在多个误差来源及异质层级结构时，如何统一评价混合水平析因设计中处理因素组合的安排？
- 方法与思路
- 作者提出正交化矩偏差，用核函数比较设计矩阵的行，并通过线性混合效应模型与高斯过程模型解释该无模型准则。
- 材料陈述的贡献
- 摘要称该准则覆盖多类规则及非规则设计，特定核可恢复已有最小偏差准则，并可在贝叶斯框架下生成高 D 效率设计。
- 阅读关注点
- 核对部分放宽正交区组结构的定义、核选择与既有准则的对应关系，以及贝叶斯 D 效率的理论和数值评价条件。
- 阅读边界
- 仅据所给 Crossref 摘要；未提供核函数、设计构造算法或效率数值，不能将所述高效率解释为对所有设计准则的普遍优越性。
原文摘要
Abstract Multi-stratum factorial designs, such as block designs and row–column designs, are widely used for screening treatment factors in experiments involving complex structures of experimental units due to multiple sources of error. In this study, we propose a unified model-free approach, termed orthogonalized moment aberration, to compare the similarities between level combinations of treatment factors assigned to heterogeneous experimental units. The proposed approach, which uses kernel functions to evaluate the rows of design matrices rather than the columns, can assess a wide variety of mixed-level regular/nonregular factorial designs with an extensive class of heterogeneous experimental unit structures called partially-relaxed orthogonal block structures. This approach is flexible in that it can be adapted to various scenarios by choosing different kernel functions, with certain choices yielding well-known minimum aberration criteria proposed in the literature. Although model-free, the proposed method is justified by using linear mixed-effect models and Gaussian process models. Theoretical results and numerical examples presented in this article collectively demonstrate that the proposed approach can generate multi-stratum factorial designs with high D-efficiencies within a Bayesian framework.