An information-theoretic approach to hypergraph psychometrics

Abstract

Psychological network approaches propose to see symptoms or questionnaire items as interconnected nodes, with links between them reflecting pairwise statistical dependencies evaluated on cross-sectional, time-series, or panel data. These networks constitute an established methodology to assess the interactions and relative importance of nodes/indicators, providing an important complement to other approaches such as factor analysis. However, focusing the modelling solely on pairwise relationships can neglect potentially critical information shared by groups of three or more variables in the form of higher-order interdependencies. To overcome this important limitation, here we propose an information-theoretic framework based on hypergraphs as psychometric models. As edges in hypergraphs are capable of encompassing several nodes together, this extension can thus provide a richer representation of the interactions that may exist among sets of psychological variables. Our results show how psychometric hypergraphs can highlight meaningful redundant and synergistic interactions on either simulated or state-of-art, re-analyzed psychometric datasets. Overall, our framework extends current network approaches while leading to new ways of assessing the data that differ at their core from other methods, extending the psychometric toolbox and opening promising avenues for future investigation.

Emergence of High-Order Functional Hubs in the Human Brain

“…While considering the high-order structure of complex systems brings with it a host of combinatorial challenges, it is nonetheless essential for a more realistic modeling and enhanced understanding of complex systems. In this vein, there has been a significant effort recently in quantifying high-order interactions in multiple complex systems [1][2][3][4], from ecology [5] to social contagion [6,7], across different time and spatial scales [8][9][10], and for areas such as the synchronization of coupled oscillators [11], gene expression [12] and psychometrics [13] -just to name a few. While some of these approaches focus on the topological analysis of high-order networks [2], others use information theory for inferring high-order statistical interdependence in complex systems, including the brain [8,[14][15][16][17][18].…”

Reconstructing networks via discrete state dynamical data: A mini-review

“…For example, a hypergraph can contain hyperedges with different sizes, a hyperedge with large size may contain some hyperedges with small size, or hypergraphs do not meet the constraint condition as simplicial complexes (i.e., higherorder interactions should include lower-order interactions). Therefore, how to reconstruct hypergraphs from the discrete state data is a meaningful and challenging research area [72,73].…”

Understanding the complexity of individual developmental pathways: A primer on metaphors, models, and methods to study resilience in development

“…In a hypergraph, edges can connect to more than one node, so a node can belong to different subsets that represent different types of associations or states. Recently, hypergraphs have been applied to model psychological data (Marinazzo et al, 2022). In a multihypergraph, the different edge types are placed on separate layers.…”