Psychometric Models in Higher Dimensions: How Artificial Intelligence Can Expand the Space of Measurement

Some psychological models—especially complex, typological ones or those with a three-dimensional structure—cannot be properly verified within the classical 2D measurement space. Their projection onto a plane geometrically distorts the actual relationships between variables or persons, leading to false simplifications and erroneous interpretations. In response to this limitation, the article proposes an expansion of the measurement space using tools from artificial intelligence—specifically, Support Vector Machines (SVM) with a Radial Basis Function (RBF) kernel—which enable the transformation of data into higher-dimensional spaces.The article shifts the focus of measurement from relationships between variables to relationships between individuals, treated as vectors of psychological traits. It demonstrates that the kernel RBF not only classifies data but transforms the very space in which the data operate—creating a new geometric framework in which the verification of complex and deep models becomes possible. In this new logic, individuals become carriers of the model rather than mere data observations. The concept culminates in a proposal for a psychometric scale based on independent response vectors, compatible with the structure of kernel space. Altogether, this constitutes a breakthrough shift: from variable space to person space, from geometric projections to the structural depth of psychological models.