A copula-based portrayal of the collider bias

This article proposes to use copulas to characterize the collider bias that concerns the non-substantive change in the causal dependence between variables before and after conditioning on their common effect (collider). This copula-based portrayal allows scholars (1) to capture the sophisticated (e.g., asymmetric or heavy-tail) causal dependence structure that is usually not evidenced by a summative causal effect estimate, such as the regression coefficient based on a well-matched sample; (2) to focus on the causal dependence structure that is insensitive to the influences from the marginal distributions; and (3) to directly and formally test the significance of change in the causal dependence structure using the Cramer-von Mises statistic. Both simulation and real data examples are presented, which suggest that copulas can be a handy tool for practical researchers to describe the collider bias.