Abstract
<p>Person-centered psychology has primarily used exploratory discovery algorithms, such as latentprofile analysis and cluster analysis, to identify population subgroups (e.g., “Resilient”). Thesemethods face several well-documented limitations: identified profiles vary across datasets(sample dependence), the number of profiles relies on ambiguous stopping rules, and forcingcontinuous personality configurations into discrete categories can conflate the measurementgranularity of Likert lattices with genuine structure. In response, we introduce fixed-framearchetypal analysis (FFAA), which represents each individual as a continuous compositionalmixture relative to fixed theoretical extrema (the absolute corners of the Big Five hypercube)using closed-form multilinear interpolation. The method contributes at two levels. For theindividual respondent, FFAA is a lossless reparameterization of trait scores into a fixed, sample-independent coordinate system, providing (1) fixed profile definitions, (2) high-resolutionmeasurement of configural differences, and (3) computational scalability. Across respondents,because compositions are nonlinear functions of the traits, averaging them encodes thecovariation among traits that marginal averages do not retain. We illustrate the individual-levelproperties through simulation studies and establish a normative baseline from over 10 millionrespondents; at the aggregate level, these data characterize the maturity principle across the adultlifespan not as discrete stages but as a continuous geometric migration that is broadly similaracross regions. We propose that moving from “profile discovery” to “compositionalmeasurement” offers a mathematically grounded approach to person-centered psychology,though establishing predictive validity and extending FFAA to other personality measures remainimportant next steps.</p>