Multi Co-Moment Structural Equation Models: Discovering Direction of Causality in the Presence of Confounding

We present the Multi Co-moment Structural Equation Model (MCM-SEM), a novel approach to estimating the direction and magnitude of causal effects in the presence of confounding. In MCM-SEM, not only covariance structures but also co-skewness and co-kurtosis structures are leveraged. Co-skewness and co-kurtosis provide information on the joint non-normality. In large scale non-normally distributed data, we can use these higher-order co-moments to identify and estimate both bidirectional causal effects and latent confounding effects, which would not have been identified in regular SEM. We performed an extensive simulation study which showed that MCM-SEM correctly reveals the direction of causality in the presence of confounding. Subsequently, we applied the model empirically to data of (1) height and weight and to (2) education and income, and compared the results to those obtained through instrumental variable regression. In the empirical application, MCM-SEM yielded expected results for (1), but also highlighted some caveats when applied to (2). We provide an MCM-SEM R-package and recommendations for future use.