Graphical Methods for Hierarchical Log-Linear Models

Quasi-Symmetric Graphical Log-Linear Models

We propose an extension of graphical log-linear models to allow for symmetry constraints on some interaction parameters that represent homologous factors. The conditional independence structure of such quasi-symmetric (QS) graphical models is described by an undirected graph with coloured edges, in which a particular colour corresponds to a set of equality constraints on a set of parameters. Un...

Markov Chain Monte Carlo Model Determination for Hierarchical and Graphical Log-linear Models

SUMMARY The Bayesian approach to comparing models involves calculating the posterior probability of each plausible model. For high-dimensional contingency tables, the set of plausible models is very large. We focus attention on reversible jump Markov chain Monte Carlo (Green, 1995) and develop strategies for calculating posterior probabilities of hierarchical, graphical or decomposable log-line...

The conjugate prior for discrete hierarchical log-linear models

In the Bayesian analysis of contingency table data, the selection of a prior distribution for either the log-linear parameters or the cell probabilities parameter is a major challenge. Though the conjugate prior on cell probabilities has been defined by Dawid and Lauritzen (1993) for decomposable graphical models, it has not been identified for the larger class of graphical models Markov with r...

Graphical Log-Linear Models: Fundamental Concepts and Applications

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 l...

Building Measurement Models from Scratch: Graphical Models, Exchangeability Models, and Log-linear Models