Triadic distance models for the analysis of asymmetric three-way proximity data

Triadic distance models can be used to analyse proximity data defined on triples of objects. Three‐way symmetry is a common assumption for triadic distance models. In the present study three‐way symmetry is not assumed. Triadic distance models are presented for the analysis of asymmetric three‐way proximity data that result in a simultaneous representation of symmetry and asymmetry in a low‐dimensional configuration. An iterative majorization algorithm is developed for obtaining the coordinates and the representation of the asymmetry. The models are illustrated by an example using longitudinal categorical data.