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.

翻译：研究人员利用基于暴露映射的干扰模型来促进对存在干扰的随机实验中因果效应的估计。为了检验此类模型的真实性，研究者可采用旨在检测与规定模型偏离程度的设定检验。然而，现有检验存在统计功效不足的缺陷，且往往无法识别重要的模型违背。本文的主要结论表明，暴露映射模型的设定检验问题本质上是困难的，现有检验的低功效不可避免。具体而言，对此类模型的任何设定检验，其最坏情形下的第一类与第二类错误概率之和必须等于1，从而排除了存在一致检验的可能性。这恰好等同于随机丢弃所有数据并任意拒绝原假设的朴素检验所达到的最坏情形整体错误率；从这个意义上说，该检验问题是不可能的。该否定结论对所有暴露映射、所有样本量、一致有界的结果变量以及与零假设最大分离的备择假设均成立。尽管某些检验能检测出对原假设模型的特定偏离，但始终存在无法被检测的相关偏离。因此，有意义的设定检验必须对目标备择模型施加超越暴露映射本身限制的额外约束。我们通过为区分无干扰与网络线性均值模型提供一致检验来阐明这一观点。