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Welcome to the wiki for the multi co-moment structural equation modelling (MCMSEM) R-package.
MCMSEM 0.27.0 supports both the existing Contemporaneous Structural MCMSEM
kernel and the new Stationary Dynamic MCMSEM kernel. Read
Choosing between contemporaneous and dynamic kernels
before selecting kernel = "contemporaneous" or kernel = "dynamic".
To impose distribution-based relationships among second through fourth moments, see Specifying constrained moments from parametric distributions. It explains free, fixed, and derived parameters, the different moment conventions of both kernels, complete signed-gamma examples, standard errors, and diagnostic checks.
For more information on the methodology behind this R-package please refer to the original publication. Also, don't forget to cite the original paper if you use it for your own work.
Tamimy, Z., van Bergen, E., van der Zee, M. D., Dolan, C. V., & Nivard, M. G. (2022, June 30). Multi Co-Moment Structural Equation Models: Discovering Direction of Causality in the Presence of Confounding. https://doi.org/10.31235/osf.io/ynam2
For the Stationary Dynamic MCMSEM kernel, also cite:
Recke, C. O., Lumpp, S., Kushnerchuk, N., Oldekop, J., Li, J., Coons, J. I., & Robeva, E. (2026). Identifiability in Graphical Discrete Lyapunov Models. arXiv preprint arXiv:2601.21818. https://arxiv.org/abs/2601.21818
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.