Moderated Network Models

TL;DR

This paper introduces Moderated Network Models (MNMs), extending Gaussian Graphical Models to include moderation effects, with a new estimation method and demonstrated superior performance in simulations.

Contribution

The paper develops a novel Moderated Network Model framework that incorporates moderation effects into pairwise interactions and proposes an L1-regularized estimation approach.

Findings

MNMs outperform NCT and FGL in simulation studies

Proposed method effectively detects moderation effects

Provides a reproducible R-package implementation

Abstract

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.