Geometry of diagonal-effect models for contingency tables

TL;DR

This paper investigates the geometric and algebraic properties of diagonal-effect models in contingency tables, using toric and mixture models to understand their invariants and structure.

Contribution

It introduces a detailed algebraic and geometric analysis of diagonal-effect models, including invariants and structural insights, within the framework of Algebraic Statistics.

Findings

Computed invariants of diagonal-effect models

Explored geometric structure of these models

Compared toric and mixture model approaches

Abstract

In this work we study several types of diagonal-effect models for two-way contingency tables in the framework of Algebraic Statistics. We use both toric models and mixture models to encode the different behavior of the diagonal cells. We compute the invariants of these models and we explore their geometrical structure.