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Markov Fields and Log-Linear Interaction Models for Contingency Tables
J. N. Darroch, S. L. Lauritzen and T. P. Speed
The Annals of Statistics
Vol. 8, No. 3 (May, 1980), pp. 522-539
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2240590
Page Count: 18
You can always find the topics here!Topics: Markov models, Vertices, Multilevel models, Maximum likelihood estimators, Statism, Statistical models, Mathematics, Finite model property, Coordinate systems, Conditional probabilities
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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.
The Annals of Statistics © 1980 Institute of Mathematical Statistics