  Pairwise network models such as the Gaussian Graphical Model (GGM) are a
powerful and intuitive way to analyze dependencies in multivariate data. A key
assumption of the GGM is that each pairwise interaction is independent of the
values of all other variables. However, in psychological research this is often
implausible. In this paper, we extend the GGM by allowing each pairwise
interaction between two variables to be moderated by (a subset of) all other
variables in the model, and thereby introduce a Moderated Network Model (MNM).
We show how to construct the MNM and propose an L1-regularized nodewise
regression approach to estimate it. We provide performance results in a
simulation study and show that MNMs outperform the split-sample based methods
Network Comparison Test (NCT) and Fused Graphical Lasso (FGL) in detecting
moderation effects. Finally, we provide a fully reproducible tutorial on how to
estimate MNMs with the R-package mgm and discuss possible issues with model
misspecification.
