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

Abstract

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.

Three methods that advance tests of complex psychological theory using structural equation models.

“…The present aim was to demonstrate that lasso selection of instrumental variables (Windmeijer et al, 2019), heteroscedasticity (Hogan & Rigobon, 2002;Rigobon, 2003), and higher order moments (Boudt et al, 2020;Tamimy et al, 2022) can be incorporated in the general SEM framework to advance causal modeling in correlational designs. While the methods outlined here come with annotated scripts R, their successful application is more challenging than standard SEM (say, cross-lagged panel modeling; Hamaker et al, 2015;Mulder & Hamaker, 2021).…”

“…SEMs can be extended to accommodate higher (co)moments like (co)skewness and (co)kurtosis (Boudt et al, 2020). As outlined in Tamimy et al (2022), in the SEM, these moments can be leveraged to identify causal paths in the presence of confounding. The work is grounded in a tradition of causal inferences based on higher moments (Shimizu & Bollen, 2014;Shimizu & Kano, 2008;Wiedermann & von Eye, 2016).…”

“…Provided the exogenous variance, attributable to external influences differ systematically between groups, these differences can be used to identify directional and mutualistic SEM network models. The third method is an extension of multi-co-moment structural equation models (MCM-SEM), as presented by Tamimy et al (2022). This method jointly models the covariance, co-skewness, and co-kurtosis between variables.…”