Same Score, Different Network: Configuration-Level Heterogeneity in Composite Risk Measures

Composite risk instruments compress multiple indicators into a single severity score. This is operationally efficient, but it obscures how risk factors are organised and how equifinal pathways generate the same total score. We propose a network-based framework to examine configuration-level heterogeneity among score-equivalent cases. Using 17,272 administrative assessments from a criminological risk instrument, we analyse item co-occurrence within narrow, overlapping score windows to hold overall severity constant. Items are recoded into present/absent indicators to focus on relational structure rather than withinitem severity gradations. Recurrent configurations are detected via clustering based on Jaccard similarity, their stability is evaluated across windows, and their internal structures are estimated using Ising network models. Identical scores map onto distinct and recurring network architectures, showing that relational structure contains substantively relevant information beyond additive scoring. More broadly, the framework illustrates how network psychometrics can uncover latent structural heterogeneity in applied measurement instruments and in other administrative score-based systems.