A comprehensive study of graphical log-linear models for contingency tables is presented. High-dimensional contingency tables arise in many areas. 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. Connections between the conditional independence in probability and graphs are explored, followed with illustrations to describe how graphical log-linear model are useful to interpret the conditional independences between factors. The problem of estimation and model selection in decomposable models is discussed.
Gauraha, N. (2017). Graphical log-linear models: fundamental concepts and applications. Journal of Modern Applied Statistical Methods, 16(1), 545-577. doi: 10.22237/jmasm/1493598000