A class of statistical models to weaken independence in two-way contingency tables

TL;DR

This paper introduces a new class of statistical models for contingency tables that relax the independence assumption, utilizing algebraic methods to compute estimates and perform exact inference, with broad practical applications.

Contribution

It defines a novel class of models based on binomial equations, proves their log-linear nature, and provides methods for maximum likelihood estimation and exact inference.

Findings

Models are log-linear and flexible for various applications.

Maximum likelihood estimates can be computed explicitly.

Exact inference is feasible using the Diaconis-Sturmfels algorithm.

Abstract

In this paper we study a new class of statistical models for contingency tables. We define this class of models through a subset of the binomial equations of the classical independence model. We use some notions from Algebraic Statistics to compute their sufficient statistic, and to prove that they are log-linear. Moreover, we show how to compute maximum likelihood estimates and to perform exact inference through the Diaconis-Sturmfels algorithm. Examples show that these models can be useful in a wide range of applications.