Causal inference necessarily relies upon untestable assumptions; hence, it is crucial to assess the robustness of obtained results to violations of identification assumptions. However, such sensitivity analysis is only occasionally undertaken in practice, as many existing methods only apply to relatively simple models and their results are often difficult to interpret. We take a more flexible approach to sensitivity analysis and view it as a constrained stochastic optimization problem. We focus on linear models with an unmeasured confounder and a potential instrument. We show how the $R^2$-calculus - a set of algebraic rules that relates different (partial) $R^2$-values and correlations - can be applied to identify the bias of the $k$-class estimators and construct sensitivity models flexibly. We further show that the heuristic "plug-in" sensitivity interval may not have any confidence guarantees; instead, we propose a boostrap approach to construct sensitivity intervals which perform well in numerical simulations. We illustrate the proposed methods with a real study on the causal effect of education on earnings and provide user-friendly visualization tools.
翻译:因果关系推断必然取决于无法检验的假设;因此,评估在违反身份认定假设的情况下所取得的结果是否可靠至关重要;然而,这种敏感性分析只是偶尔在实践中进行,因为许多现有方法只适用于相对简单的模型,其结果往往难以解释;我们对敏感性分析采取更灵活的方法,并将它视为一个有限的随机优化问题;我们注重线性模型,而没有测算的混淆者和潜在的工具;我们展示的是,如何能够应用2美元计算法——一套与不同(部分)2美元价值和相关性有关的代数规则——来查明美元类估计值和相关性的偏向性,并灵活地构建敏感度模型;我们进一步表明,超常性“插入”敏感性间隔可能没有任何信心保证;相反,我们提议一种加速法,以构建敏感度间隔,在数字模拟中表现良好。我们用真实研究教育对收入的因果关系和提供方便用户的可视化工具来说明拟议的方法。