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Quasi‐Symmetric Graphical Log‐Linear Models
Author(s) -
GOTTARD ANNA,
MARCHETTI GIOVANNI MARIA,
AGRESTI ALAN
Publication year - 2011
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2010.00713.x
Subject(s) - mathematics , graphical model , contingency table , conditional independence , graph , independence (probability theory) , set (abstract data type) , extension (predicate logic) , undirected graph , log linear model , mixed graph , combinatorics , linear model , discrete mathematics , statistics , computer science , voltage graph , line graph , programming language
. 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.