Causal inference in psychological research is typically hampered by unobserved confounding. A copula-based method can be used to statistically control for this problem without the need for instruments or covariates, given relatively lenient distributional assumptions on independent variables and error terms. The current study aims to: (a) provide a user-friendly introduction to the copula method for psychology researchers, and (b) examine the degree of non-normality in the independent variables required for satisfactory performance. A Monte Carlo simulation study was used to assess the behavior of the copula method under various combinations of conditions (sample size, skewness of independent variables, effect size, and magnitude of confounding). In addition, an applied example from research on the effects of parental rearing on adult personality and life satisfaction was used to illustrate the method. Simulations revealed that the copula method performed better at higher levels of skewness in the independent variables, and that the impacts of lower skewness can be offset to some extent by larger sample size. When skewness and/or sample size is too small, the copula method is biased toward the uncorrected model. In the applied example, parental rejection/punishment predicted less adaptive personality and life satisfaction, with no evidence of confounding. For parental control/overprotection, there was evidence that confounding attenuated the estimated relationship with personality/life satisfaction. Copula adjustment is a promising method for handling unobserved confounding. The discussion focuses on how to proceed when assumptions are not quite met, and outlines potential avenues for future research. (PsycInfo Database Record (c) 2021 APA, all rights reserved)

中文翻译：

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使用 copula 从非实验数据中进行因果推理：教程和模拟研究。

心理学研究中的因果推理通常会受到未观察到的混杂因素的阻碍。鉴于对自变量和误差项的相对宽松的分布假设，基于 copula 的方法可用于统计控制此问题，而无需工具或协变量。当前的研究旨在：(a) 为心理学研究人员提供一个用户友好的 copula 方法介绍，以及 (b) 检查令人满意的表现所需的自变量的非正态程度。蒙特卡罗模拟研究用于评估 copula 方法在各种条件组合（样本大小、自变量偏度、效应大小和混杂程度）下的行为。此外，以父母教养对成人人格和生活满意度影响研究中的应用实例进行说明。模拟表明，copula 方法在自变量偏度较高的情况下表现更好，并且较大的样本量可以在一定程度上抵消较低偏度的影响。当偏度和/或样本量太小时，copula 方法会偏向于未校正的模型。在应用的例子中，父母的拒绝/惩罚预测适应性较差的人格和生活满意度，没有混淆的证据。对于父母控制/过度保护，有证据表明混杂削弱了与人格/生活满意度的估计关系。Copula 调整是一种很有前途的处理未观察到混杂的方法。讨论的重点是假设未完全满足时如何进行，并概述了未来研究的潜在途径。（PsycInfo 数据库记录 (c) 2021 APA，保留所有权利）