Parameterizations and Fitting of Bi-directed Graph Models to Categorical Data

Authors: LUPPARELLI, MONIA¹; MARCHETTI, GIOVANNI M.²; BERGSMA, WICHER P.³

Source: Scandinavian Journal of Statistics, Volume 36, Number 3, September 2009 , pp. 559-576(18)

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Abstract:

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.

Keywords: complete hierarchical parameterizations; connected set Markov property; constrained maximum likelihood; covariance graphs; marginal independence; marginal log-linear models; multivariate logistic transformation; variation independence

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9469.2008.00638.x

Affiliations: 1: Dipartimento di Scienze Statistiche `P. Fortunati', University of Bologna 2: Dipartimento di Statistica `G. Parenti', University of Florence 3: London School of Economics and Political Science

Publication date: 2009-09-01