Using Copulas to Enable Causal Inference from Non-Experimental Data: Tutorial and Simulation Studies

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: (1) provide a user-friendly introduction to the copula method for psychology researchers; and (2) 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 towards 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.