Using copulas to enable causal inference from nonexperimental data: Tutorial and simulation studies

Area of Science:

• Psychological Research
• Statistical Methods
• Causal Inference

Background:

• Unobserved confounding frequently limits causal inference in psychological studies.
• Traditional methods often require instruments or covariates, which may not be available.
• Copula-based methods offer a potential solution with fewer restrictive assumptions.

Purpose of the Study:

• To introduce the copula method for psychological researchers.
• To evaluate the performance of the copula method under varying degrees of non-normality in independent variables.
• To assess the impact of sample size, skewness, effect size, and confounding on copula method performance.

Main Methods:

• Monte Carlo simulation study examining copula method behavior under diverse conditions.
• Application of the copula method to real-world data on parental rearing, personality, and life satisfaction.
• Statistical analysis of simulated data including sample size, variable skewness, effect size, and confounding magnitude.

Main Results:

• The copula method demonstrated improved performance with higher skewness in independent variables.
• Larger sample sizes could compensate for lower levels of skewness.
• Insufficient skewness or sample size led to bias towards uncorrected models.
• Applied example showed copula adjustment mitigating confounding effects for parental control/overprotection.

Conclusions:

• Copula adjustment is a valuable and promising method for handling unobserved confounding in psychological research.
• The method's performance is influenced by the skewness of independent variables and sample size.
• Further research is needed to explore performance when assumptions are not fully met.