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Parameterizations and Fitting of Bi‐directed Graph Models to Categorical Data
Author(s) -
LUPPARELLI MONIA,
MARCHETTI GIOVANNI M.,
BERGSMA WICHER P.
Publication year - 2009
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.1467-9469.2008.00638.x
Subject(s) - mathematics , categorical variable , graphical model , multivariate statistics , graph , markov chain , property (philosophy) , extension (predicate logic) , transformation (genetics) , statistics , discrete mathematics , computer science , philosophy , biochemistry , chemistry , epistemology , gene , programming language
. We discuss two parameterizations of models for marginal independencies for discrete distributions which are representable by bi‐directed graph models, under the global Markov property. Such models are useful data analytic tools especially if used in combination with other graphical models. The first parameterization, in the saturated case, is also known as thenation multivariate logistic transformation, the second is a variant that allows, in some (but not all) cases, variation‐independent parameters. An algorithm for maximum likelihood fitting is proposed, based on an extension of the Aitchison and Silvey method.