Segmented profile analysis (SEPA): Plane-wise decomposition of within-person variation via ipsatized singular value decomposition

Abstract Traditional profile analyses summarize multivariate person data with overall mean levels and relative patterns, but existing methods often blur these sources of variation or reduce each individual to a single best-fitting profile. Segmented Profile Analysis (SEPA) offers a unified, ipsatized singular-value decomposition (SVD) framework that decomposes individual profiles into orthogonal level (LE) and pattern (PE) effects and, crucially, introduces plane-wise segment profiles (summaries of each person's response pattern within each variable-contrast dimension) as primary person-oriented objects. Within each low-dimensional plane, SEPA defines a projected response pattern (segment profile), domain–person cosines that index variable-by-variable alignment, and plane-fit correlations that summarize how closely an individual’s pattern follows the plane’s domain structure. Across planes, SEPA aggregates information via singular-value weighting to yield an overall segment profile while preserving contrast-specific signal. A practical workflow combines ipsatized SVD, parallel analysis for PE dimensionality, marker-domain rules, bootstrap confidence intervals, and subspace-stability diagnostics. Using multivariate cognitive data from the Woodcock–Johnson IV, SEPA identifies interpretable marker domains, reveals distinct pattern facets across planes, and provides person-oriented indices that can be carried into standard regression models. Simulation studies examine the stability of segment profiles and cosines under varying sample sizes and variance structures. SEPA thus supplies a reproducible, geometry-based foundation for person-centered measurement that connects Q-type factor analysis, biplot methods, and contemporary within-person profiling in multidomain assessments.