On the Impossibility of Specification Testing of Interference Models Based on Exposure Mappings
基于暴露映射的干扰模型设定检验之不可能性AI 解读 ↓
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基于暴露映射的干扰模型设定检验之不可能性
- 研究问题
- 在存在个体间干扰的随机实验中，能否通过设定检验可靠识别暴露映射模型的错误，还是存在不可避免的检验功效边界？
- 方法与思路
- 作者分析任意设定检验的最坏第一、二类错误，并通过限制备择模型，构造区分无干扰与网络线性均值模型的检验。
- 材料陈述的贡献
- 摘要称最坏两类错误率之和为一，排除一致有效的统一检验；即使结果有界、备择最大分离，该困难仍然存在。
- 阅读关注点
- 应核对原假设与备择空间、最坏错误率的量词及随机化机制，并理解附加备择限制如何使示例检验获得一致性。
- 阅读边界
- 这是 arXiv 预印本，不能据此声称已同行评审或期刊接收。摘要结论针对最坏情形，并不意味着所有具体模型偏离都无法检出。
原文摘要
Researchers use interference models based on exposure mappings to facilitate estimation of causal effects in randomized experiments with interference. To test the veracity of such models, researchers can use specification tests that aim to detect departures from the stipulated model. However, existing tests suffer from poor power and are often unable to detect important model violations. The main result in this paper is to show that the specification testing problem for exposure mapping models is inherently difficult, and the poor power of existing tests is inescapable. In particular, the worst-case Type I and Type II error rates must sum to one for any specification test of such models, ruling out the existence of a uniformly consistent test. This is the worst-case overall error rate achieved by a naive test that discards all data and arbitrarily rejects the null at random; the testing problem is in this sense impossible. This negative result holds true for all exposure mappings, all sample sizes, for uniformly bounded outcomes, and for alternatives that are maximally separated from the null. While some tests can detect some type of departures from the null model, there will always be relevant departures from the null that are undetectable. Informative specification tests must therefore restrict the alternative model against which they seek to attain power for, beyond the restrictions imposed by the exposure mappings alone. We illustrate this by providing a uniformly consistent test for differentiating no-interference from a network-linear-in-means model.