Abstract

Weighted optimality criteria allow an experimenter to express hierarchical interest across estimable functions through a concise weighting system. We show how such criteria can be implicitly influenced by the estimable functions’ minimum variances, leading to nonintuitive variance properties of the optimal designs. To address this, we propose a new optimality and evaluation approach that incorporates these minimum variances. A modified c-optimality criterion is introduced to calculate an estimable function’s minimum variance while requiring estimability of all other functions of interest. These minimum variances are then incorporated into a standardized weighted A-criterion that has an intuitive weighting system. We argue that optimal designs under this criterion tend to satisfy the conditions of a new design property we call weight adherence that sets appropriate expectations for how a given weighting system will influence variance properties. A practical, exploratory approach is then described for weighted optimal design generation and evaluation. Examples of the exploratory approach and weight adherence are provided for two types of factorial experiments.

摘要

加权最优性标准允许实验者通过简明的加权系统表达跨可估计函数的层次兴趣。我们展示了这些标准如何受到可估计函数的最小方差的隐含影响，从而导致最优设计的非直观方差特性。为了解决这个问题，我们提出了一种新的最优性和评估方法，该方法结合了这些最小方差。引入了修改的c最优性标准来计算可估计函数的最小方差，同时要求所有其他感兴趣的函数的可估计性。然后将这些最小方差合并到标准化加权A-具有直观加权系统的标准。我们认为，该标准下的最优设计倾向于满足我们称之为权重依从性的新设计属性的条件，该属性为给定的加权系统将如何影响方差属性设定适当的期望。然后描述了一种实用的探索性方法，用于加权优化设计的生成和评估。为两种类型的因子实验提供了探索性方法和权重依从性的示例。