Forward selection and post-selection inference in factorial designs
析因设计中的前向选择与选择后推断AI 解读 ↓
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析因设计中的前向选择与选择后推断
- 研究问题
- 析因实验的处理组合随因素数指数增长时，前向因素选择何时具有一致性，选择结果又如何影响析因效应推断？
- 方法与思路
- 作者在潜在结果框架下，以实验的实际随机化为基础建立理论，结合稀疏性、层级与遗传原则研究前向选择。
- 材料陈述的贡献
- 摘要称证明了选择一致性，量化一致选择下的渐近效率增益，并提出两种策略处理高阶交互项选择不一致的情况。
- 阅读关注点
- 应核对选择一致性的条件、效应与交互项的定义、效率增益的比较基准，以及两种策略如何影响选择后推断。
- 阅读边界
- 仅据版本未注明的 OpenAlex 摘要；具体条件与两种策略未展开，不依赖正确结果模型并不意味着无需其他假设。
原文摘要
Ever since the seminal work of R. A. Fisher and F. Yates, factorial designs have been an important experimental tool to simultaneously estimate the effects of multiple treatment factors. In factorial designs, the number of treatment combinations grows exponentially with the number of treatment factors, which motivates the forward selection strategy based on the sparsity, hierarchy and heredity principles for factorial effects. Although this strategy is intuitive and has been widely used in practice, its rigorous statistical theory has not been formally established. To fill this gap, we establish design-based theory for forward factor selection in factorial designs based on the potential outcome framework. We not only prove a consistency property for the factor selection procedure but also discuss statistical inference after factor selection. In particular, with selection consistency, we quantify the advantages of forward selection based on asymptotic efficiency gain in estimating factorial effects. With inconsistent selection in higher-order interactions, we propose two strategies and investigate their impact on subsequent inference. Our formulation differs from the existing literature on variable selection and post-selection inference because our theory is based solely on the physical randomization of the factorial design and does not rely on a correctly specified outcome model.