Researchers want to know whether the change in an explanatory variable X affects the change in a response variable Y (i.e., X causes Y). In practice, there can be two causal paths from X to Y, the path through a mediating variable M (indirect effect) and the path not through M (direct effect). The parameter estimation and hypothesis testing can be performed by a regression-based mediation model. It is already known that randomization of X is not enough for unbiased estimation, and the bias due to an unobserved variable has been discussed in literature but often overlooked. In this article, we first review the challenge under a simple mediation model, then we provide a formula for the exact bias due to an unobserved precursor variable W, the variable which potentially causes the changes in X, M, and/or Y. We present simulation studies to demonstrate the impact of an unobserved precursor variable on hypothesis testing for indirect effect and direct effect. The simulation results show that the inflation of type I error is serious particularly in a large sample study. To numerically demonstrate the formula of the exact bias, a popular data set published in a journal of statistics education is revisited, and we quantify why the conclusion of data analysis can be different before and after accounting for the precursor variable. The result shall remind the importance of a precursor variable in mediation analysis.

研究人员想知道解释变量X的变化是否影响响应变量Y的变化（即X导致Y）。实际上，可能存在从X到Y的两个因果路径，即通过中介变量M的路径（间接影响）和不通过M的路径（直接影响）。可以通过基于回归的中介模型执行参数估计和假设检验。已经知道X的随机化不足以进行无偏估计，并且由于文献中已讨论了由于未观察到的变量而引起的偏见，但常常被忽略。在本文中，我们首先在简单的调解模型下回顾了挑战，然后提供了一个因未观察到的前体变量W而引起的确切偏差的公式，该变量可能导致X，M和/或Y的变化。我们目前的仿真研究，以证明间接作用和直接作用的假设检验中未观察到的前体变量的影响。仿真结果表明，特别是在大样本研究中，I型错误的膨胀是严重的。为了以数字方式显示精确偏差的公式，我们重新研究了在统计教育杂志上发布的流行数据集，并且我们量化了为什么在分析前体变量之前和之后数据分析的结论可能会有所不同。结果应提醒调解分析中前体变量的重要性。