Algebra and geometry of tensors for modeling rater agreement data

TL;DR

This paper explores the algebraic and geometric structures of tensor models used to analyze rater agreement data, providing insights into their invariants and differences between pairwise and multi-rater scenarios.

Contribution

It introduces a geometric framework for understanding quasi-symmetry and mixture tensor models in rater agreement analysis, highlighting invariants and differences for various tensor sizes.

Findings

Geometric description of tensor model varieties

Invariants distinguishing n=2 from n>2 cases

Results on pairwise Cohen's kappa coefficients

Abstract

We study three different quasi-symmetry models and three different mixture models of $n\times n\times n$ tensors for modeling rater agreement data. For these models we give a geometric description of the associated varieties and we study their invariants distinguishing between the case $n=2$ and the case $n>2$. Finally, for the two models for pairwise agreement we state some results about the pairwise Cohen's $\kappa$ coefficients.