统计与数据科学学院知识库

揭示变量间的关系是定量研究的一个重要目标。在这个过程中，中介效应扮演着重要的角色，近年来此技术在很多领域发挥着重要作用。在经济研究中，为了确保研究结果的准确性，研究人员通常会采用统计控制的手段来减少其他变量的干扰。

选择错误的控制变量可能导致中介效应结果的不准确。在选择控制变量时，应该考虑与中介变量和因变量相关的潜在干扰因素，并努力排除这些因素的影响，以确保对中介效应的准确评估和解释。但目前很多研究者并没有充分理解控制变量的关键作用以及应该如何有效地运用控制变量，其影响程度及路径也没有被确切地说明。

当前关于控制变量的研究还相当零散，因此有必要对已有的文献进行全面地整理。目前关于控制变量选择问题的研究主要是围绕已发表的文献中对于控制变量的使用规范问题进行讨论，但关于不同情况下的控制变量对中介效应稳健性的影响及其大小并未有深入研究。

基于以上问题，本文以中介效应为研究对象，从其控制变量的选择问题出发，首先给出了控制变量选择及中介效应的综述总结，其次介绍了控制变量与中介模型的基本理论及研究现状，接着以中介效应稳健性影响问题为切入点，通过蒙特卡洛随机模拟的方法设置了各种参数，分别针对模型中不同控制变量数量、不同中介变量与控制变量相关性、不同控制变量间相关性、不同控制变量与随机扰动项相关性的情况，模拟了不同中介效应大小和不同样本量下控制变量对中介效应稳健性的具体影响，进一步总结控制变量选择对中介效应分析稳健性影响的一般化结论。

研究结果表明：（1）随着模型中控制变量的数量增加，中介效应的稳健性增强。且中介效应的显著的概率与控制变量数量的关系受到中介效应大小的影响。中介效应越大，控制变量的加入更容易使得中介效应稳健。（2）自变量对中介变量的影响系数随着控制变量和中介变量的相关性增大而偏离真实值，中介变量对因变量的影响系数随着控制变量和中介变量的相关性增大而接近真实值。且样本量越大，相关性增强使得中介效应更不容易稳健。（3）自变量对中介变量的影响系数随着控制变量间相关性增大而接近真实值，中介变量对因变量的影响系数，随着控制变量间相关性增大而偏离真实值。且样本量越大，相关性增强使得中介效应更不容易稳健。（4）中介变量对因变量的影响系数随着控制变量与随机扰动项相关性增强而偏离真实值。但是在较弱的内生性（0.1）和较少的样本量（200）下无偏概率可以达到90%以上。

Discovering the relationship between variables is an important goal of quantitative research. In this process, mediating effects play an important role, and this technique has played an important role in many fields in recent years. In economic research, in order to ensure the reliability of research conclusions, researchers usually use statistical control methods to eliminate the influence of other variables.

Choosing the wrong control variable can lead to inaccurate results of the mediating effect. When selecting a control variable, potential interfering factors related to the mediating variable and the dependent variable should be considered, and efforts should be made to exclude the influence of these factors to ensure an accurate assessment and interpretation of the mediating effect. However, many researchers do not have a deep understanding of the importance of the control variable and how to use the control variable rationally, and the degree and path of its influence have not been precisely explained.

At present, the research on control variables is relatively fragmented, and it is necessary to systematically review the existing literature. It can be found that the research on the selection of control variables mainly focuses on the discussion of the use of control variables in the published literature, but there is no in-depth study on the influence of control variables on the robustness of the mediating effect under different circumstances.

Based on the above problems, this paper takes the mediating effect as the research object, starting from the selection of its control variables, firstly gives a summary of the selection of control variables and the mediating effect, and secondly introduces the basic theory and research status of the control variables and the mediating model. Then, taking the problem of the influence of the robustness of the mediating effect as the starting point, various parameters are set through the Monte Carlo stochastic simulation method. According to the number of different control variables in the model, the correlation between different mediating variables and control variables, the correlation between different control variables, and the correlation between different control variables and random perturbations, the influence of control variables on the robustness of the mediating effect under different mediating effect sizes and different sample sizes is simulated, and the general conclusion of the influence of control variable selection on the robustness of the mediating effect analysis.

The research results show that: (1)With the increase of the number of control variables in the model, the robustness of the mediating effect increases. And the relationship between the significant probability of the mediating effect and the number of control variables is affected by the size of the mediating effect. The larger the mediating effect, the easier it is to add the control variable to make the mediating effect robust. (2) The influence coefficient of the independent variable on the mediating variable deviates from the true value as the correlation between the control variable and the mediating variable increases, and the influence coefficient of the mediating variable on the dependent variable approaches the true value as the correlation between the control variable and the mediating variable increases. And the larger the sample size, the stronger the correlation makes the mediating effect less robust. (3) The influence coefficient of the independent variable on the mediator variable approaches the true value as the correlation between the control variables increases, and the influence coefficient of the mediator variable on the dependent variable deviates from the true value as the correlation between the control variables increases. And the larger the sample size, the stronger the correlation makes the mediator effect less likely to be robust.  (4) The influence coefficient of the mediator variable on the dependent variable deviates from the true value as the correlation between the control variable and the random perturbation term increases. However, the unbiased probability can reach more than 90% under weak endogenicity (0.1) and small sample size (200).