A geometrical perspective on parametric psychometric models

TL;DR

This paper explores how non-Euclidean geometric concepts can be applied to psychometric models, potentially offering new insights into psychological measurement.

Contribution

It introduces a geometric perspective to psychometric models, highlighting the relevance of non-Euclidean geometry in psychological measurement.

Findings

Illustrates the connection between geometry and measurement.

Proposes potential applications of non-Euclidean geometry in psychometrics.

Suggests new directions for research in psychological measurement.

Abstract

Psychometrics and quantitative psychology rely strongly on statistical models to measure psychological processes. As a branch of mathematics, geometry is inherently connected to measurement and focuses on properties such as distance and volume. However, despite the common root of measurement, geometry is currently not used a lot in psychological measurement. In this paper, my aim is to illustrate how ideas from non-Euclidean geometry may be relevant for psychometrics.