Topologization in Psychological Modeling: From Two-Dimensional Analysis to the Third Dimension in Psychometrics

• DOI: 10.31234/osf.io/fd4sb_v2
• Publication Date: 2025-03-27T21:19:00Z
• Authors: Agnieszka Szymańska
• Keywords: Multidimensional analysis

This article contributes to the ongoing debate on topological explanations by developing concept of topologization in psychological modeling. Referring mathematical topology—particularly notions dimensionality and projection—it proposes a new interpretation constructs that goes beyond classical two-dimensional representations. The addresses issue modeling, indicating many existing models—traditionally analyzed spaces—may fact possess hidden three-dimensional structure. Based conceptual, methodological, psychometric analyses, author shows transition modeling allows for more complete representation studied constructs. example Antonina Gurycka’s model upbringing errors serves as an illustration situation which emergence additional dimension results from interpretative inconsistencies center circular model. discusses limitations statistical methods, such factor analysis, alternative analytical approaches—including support vector machines with RBF kernel (from field artificial intelligence) data analysis (TDA). These methods enable detection depth structural complexity models, thereby challenging assumptions psychometrics diagnosis. conclusion indicates how may influence future theory, measurement therapeutic interpretation.