The Annals of Statistics

Markov Fields and Log-Linear Interaction Models for Contingency Tables

J. N. Darroch, S. L. Lauritzen, and T. P. Speed

Full-text: Open access

Abstract

We use a close connection between the theory of Markov fields and that of log-linear interaction models for contingency tables to define and investigate a new class of models for such tables, graphical models. These models are hierarchical models that can be represented by a simple, undirected graph on as many vertices as the dimension of the corresponding table. Further all these models can be given an interpretation in terms of conditional independence and the interpretation can be read directly off the graph in the form of a Markov property. The class of graphical models contains that of decomposable models and we give a simple criterion for decomposability of a given graphical model. To some extent we discuss estimation problems and give suggestions for further work.

Article information

Source
Ann. Statist., Volume 8, Number 3 (1980), 522-539.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345006

Digital Object Identifier
doi:10.1214/aos/1176345006

Mathematical Reviews number (MathSciNet)
MR568718

Zentralblatt MATH identifier
0444.62064

JSTOR
links.jstor.org

Subjects
Primary: 62F99: None of the above, but in this section
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Contingency tables decomposability Gibbs states graphical models triangulated graphs

Citation

Darroch, J. N.; Lauritzen, S. L.; Speed, T. P. Markov Fields and Log-Linear Interaction Models for Contingency Tables. Ann. Statist. 8 (1980), no. 3, 522--539. doi:10.1214/aos/1176345006. https://projecteuclid.org/euclid.aos/1176345006


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