The Aggregated Latent Profile Index: Measuring Person Profile Differentiation Within a Bootstrap-Validated Latent Profile Space.

Abstract

Multivariate assessment profiles contain two conceptually distinct sources of variation: overall level and profile shape. Existing approaches recover some aspects of this structure, but none jointly establishes the replicability of latent pattern dimensions and provides a principled, population-referenced summary of person profile differentiation independent of overall level. We introduce the Aggregated Latent Profile Index (ALPI), a variance-weighted Euclidean distance that quantifies the degree to which an individual's profile departs from a flat population reference within a bootstrap-validated latent profile space. ALPI is derived from the Aggregated Latent Profile Space (ALPS), a framework that combines parallel analysis with bootstrap stability diagnostics - principal angles between subspaces and Tucker's congruence coefficients - to identify replicable latent pattern dimensions, then assembles the retained dimensions into a K-dimensional latent space through singular value decomposition, into which individuals and variables are jointly projected. In a simulation benchmark, ALPS recovered the known four-factor population structure as three replicable ipsatized pattern dimensions, confirming that the pipeline performs as intended when the true structure is known. In an application to normative WAIS-IV data (n = 900), ALPS identified a stable three-dimensional pattern space, and ALPI distinguished individuals with identical Full-Scale IQ - ranging from the 7th to the 85th percentile - on the basis of their ipsatized subtest configurations. ALPI provides assessment researchers and clinicians with a single, measurement-principled index of person profile differentiation that is grounded in replicable latent structure and independent of overall score level.