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Using Copulas to Enable Causal Inference From Nonexperimental Data: Tutorial and Simulation Studies
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DOI：10.1037/met0000414.png)
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Abstract
En 中文
Translational Abstract Psychology researchers are accustomed to the statement correlation does not imply causation, given the possibility of spurious relationships due to unobserved causes. To mitigate this problem, researchers typically try and measure a wide variety of additional covariates or control variables that are related to both the focal independent and dependent variables, and/or employ instrumental variables that are assumed to be uncorrelated with all unmeasured causal influences. This article describes an alternative method for protecting against spurious relationships that does not require any external variables: the use of a copula function to directly capture the dependency between the modeled independent variables and unobserved causes. After providing an introduction to the copula method, we use Monte Carlo simulations to assess its behavior under various combinations of conditions (i.e., sample size, skewness of independent variables, effect size, and magnitude of confounding). In addition, we apply the approach in an illustrative example from research on the effects of parental rearing on adult personality and life satisfaction. The 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 results of the copula correction are biased in the direction of the uncorrected results. 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 tackling the ubiquitous problem of unobserved confounding in observational and quasi-experimental research. The discussion focuses on how to proceed when assumptions of this method are not quite met, and outlines avenues for future research. 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.
Keywords:
confounding
omitted variable bias
instrumental variables
causal inference
copula
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