Graphical Log-linear Models: Fundamental Concepts and Applications

TL;DR

This paper provides a comprehensive overview of graphical log-linear models for analyzing high-dimensional contingency tables, emphasizing their use in understanding interactions and conditional independences among categorical variables.

Contribution

It introduces the fundamental concepts of graphical log-linear models, explores their connection to conditional independence, and discusses estimation and model selection techniques.

Findings

Graphical models effectively interpret conditional independences.

Decomposable models facilitate estimation and model selection.

Applications span biology, surveys, and census data.

Abstract

We present a comprehensive study of graphical log-linear models for contingency tables. High dimensional contingency tables arise in many areas such as computational biology, collection of survey and census data and others. Analysis of contingency tables involving several factors or categorical variables is very hard. To determine interactions among various factors, graphical and decomposable log-linear models are preferred. First, we explore connections between the conditional independence in probability and graphs; thereafter we provide a few illustrations to describe how graphical log-linear model are useful to interpret the conditional independences between factors. We also discuss the problem of estimation and model selection in decomposable models.