Profile Allocation Analysis: A Measurement Framework with Individual-Specific Allocation

Classical measurement models represent indicator–construct relations through shared loading and threshold parameters. Profile Allocation Analysis (PAA) addresses a different object: a declared, profile-consistent, simplex-valued representation of how relative response emphasis is organized across indicators. One shared shallow allocation network maps each within-person standardized profile to an allocation vector; individual allocations are realizations of that common mapping, not independently identified person-specific loadings. Within-person standardization yields affine profile invariance, distinct from classical measurement invariance, while allocation homogeneity provides the internal null condition. Simulations show that PAA recovers profile-visible allocation under heterogeneous and nonlinear conditions, returns near-homogeneous allocation under homogeneous generating structure, remains stable across noise, response-style, ordinal, architectural, and regularization variations, and spans fixed, discrete, smoothly varying, and moderated structures. A visibility experiment further establishes the operating boundary: recovery of a designated generating allocation declines as its information is removed from the profile even when the fitted mapping still realizes its profile-implied target, distinguishing realization and reproducibility from validity. The allocation-coherent composite is not level-optimal and should not replace conventional scoring when only construct level is of interest. In a PHQ-9 application, PAA identifies reproducible, severity-organized allocation heterogeneity; null calibration shows that the somatic–cognitive severity shift is not separable from between-band differences in item prevalence.