A Vector Model for Describing and Comparing Profiles

Abstract

This paper develops and tests an algorithm for computing indices for scoring and comparing multidimensional psychometric profiles. A Euclidean distance, d, derived from the Pythagorean theorem, is generally preferred over other indices of profile similarity. However, d assumes orthogonal profile dimensions. A model, which relaxes the orthogonality assumption, is offered. The model calculates a distance vector that comprises elevation, scatter and shape to describe a profile. It also operationalizes a new concept, the angular orientation of a profile. In addition, it calculates two indices of profile similarity: a distance vector and a measure of angular alignment. A brief example follows the model.