Competitive salience–reconstruction: Separating intensity and shape in psychological measurement

Psychological measurement traditionally summarizes multi-item responses using scalar scores that discard information about how individuals distribute emphasis across indicators. This paper introduces Competitive Salience–Reconstruction (CSR), a latent measurement framework that decomposes responses into volume, a scalar capturing overall intensity, and salience, a vector capturing relative allocation across indicators. The within-person decomposition is geometric and applies to any nonnegative response profile, whereas between-person patterns contain two layers: a baseline layer induced by bounded response support and a directional layer reflecting systematic differences in salience allocation across individuals. CSR explicitly separates these layers. Salience is defined as an estimand through self-consistent reconstruction, while classical sum scores emerge as a special case retaining only volume. Simulations characterize the baseline layer and confirm that CSR recovers directional structure with appropriate sensitivity and specificity. An empirical illustration using a self-selected online extraversion dataset identifies directional-layer structure beyond the bounded-support baseline: individuals with similar trait levels differed systematically in the behavioral facets they emphasized. The CSR measurement model provides a principled framework for separating support-induced baseline structure from substantively meaningful directional heterogeneity.