An information-theoretic approach to build hypergraphs in psychometrics

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 visualise and conceptualise the interactions and relative importance of nodes/indicators, providing an important complement to other approaches such as factor analysis. However, limiting the representation to pairwise relationships can neglect potentially critical information shared by groups of three or more variables (higher-order statistical interdependencies). To overcome this important limitation, here we propose an information-theoretic framework to assess these interdependencies and consequently to use hypergraphs as representations in psychometrics. As edges in hypergraphs are capable of encompassing several nodes together, this extension can thus provide a richer account on 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-the-art, re-analysed 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, enriching the psychometrics toolbox, and opening promising avenues for future investigation.