Quasi-Symmetric Graphical Log-Linear Models

Quasi-Symmetric Graphical Log-Linear Models

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Article ID: iaor201112566
Volume: 38
Issue: 3
Start Page Number: 447
End Page Number: 465
Publication Date: Sep 2011
Journal: Scandinavian Journal of Statistics
Authors: , ,
Keywords: statistics: general, statistics: inference, biology
Abstract:

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. Unlike standard QS models, the proposed models apply with contingency tables for which only some variables or sets of the variables have the same categories. We study the graphical properties of such models, including conditions for decomposition of model parameters and of maximum likelihood estimates.

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